Document [original]

Formation, atomic structure,

and electronic properties of

GaSb quantum dots in GaAs

vorgelegt von

Diplom-Physiker

Rainer Timm

aus Kiel

Von der Fakult¨at II – Mathematik und Naturwissenschaften

der Technischen Universit¨at Berlin

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften

– Dr. rer. nat. –

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Erwin Sedlmayr

Berichter: Prof. Dr. Mario D¨ahne

Berichter: Prof. Dr. Dieter Bimberg

Tag der wissenschaftlichen Aussprache: 14. Dezember 2007

Berlin 2007

D 83

Abstract

GaSb quantum dots (QDs) in a GaAs matrix exhibit a type-II band alignment with a strong

hole localization and only weakly Coulomb-bound electrons, making these structures very

promising for application in optoelectronic and especially charge storage devices. However,

comparatively little has been known yet about the atomic structure of capped GaSb/GaAs

QDs, as it results from the initial growth of GaSb nanostructures and structural changes

upon subsequent GaAs overgrowth.

In this work, cross-sectional scanning tunneling microscopy and spectroscopy are used for

the first time to study the shape, size, strain, chemical composition, and electronic properties

of capped GaSb/GaAs QDs at the atomic scale. By evaluating such structural results on a

variety of nanostructures built using different epitaxy methods and growth conditions, details

on the underlying QD formation processes can be revealed.

A cross-over from flat quantum wells (QWs) to optically active QDs can be observed in

samples grown by metalorganic chemical vapor deposition (MOCVD) with increasing amount

of GaSb, including self-assembled Sb accumulations within a still two-dimensional layer and

tiny three-dimensional GaSb islands probably acting as precursor structures. The QWs

consist of significantly intermixed material with stoichiometries of maximally 50% GaSb,

additionally exhibiting small gaps filled with GaAs. A higher GaSb content up to nearly pure

material is found in the QDs, being characterized by small sizes of up to 8 nm baselength

and about 2 nm height. In spite of the intermixing, all nanostructures have rather abrupt

interfaces, and no significant Sb segregation in growth direction is observed.

This changes completely when molecular beam epitaxy (MBE) is used as growth method,

in which case individual Sb atoms are found to be distributed over several nm above the

nanostructures. Massive group-V atomic exchange processes are causing this strong inter-

mixing and Sb segregation during GaAs overgrowth. In combination with the large strain

inherent to GaSb/GaAs QDs, this segregation upon overgrowth is assumed to be the reason

for a unique structural phenomenon: All MBE-grown QDs, independent of the amount of

deposited GaSb, exhibit a ring structure, consisting of a ring body of high GaSb content

and a more or less extended central gap filled with GaAs. These rings have formed in a

self-assembled way even when the initial GaSb layer was overgrown considerably fast and

continuously by GaAs, without any growth interruption or annealing step after partial cap-

ping. Depending on the exact growth conditions, some rings are found to be rather flat, while

others exhibit an outer shape of a truncated pyramid with {111}side facets, in both cases

showing lateral extensions typically ranging between 10 nm and 20 nm, inner diameters of in

average around 40% of the outer ones, and densities of 5 to 9 ×1010 cm−2. Hole localization

energies of ∼0.3 eV for the flat and ∼0.4 eV for the somewhat higher ring-shaped QDs are

obtained, with a type-II conduction band offset amounting to about 0.1 eV.

The observed results, which are extensively discussed in the context of literature data,

reveal many new aspects of the atomic structure and allow a detailed and consistent under-

standing of the formation of GaSb/GaAs QDs.

iii

Zusammenfassung

GaSb Quantenpunkte (QP) in GaAs zeichnen sich durch eine Typ-II-Bandkantenanpas-

sung mit einer hohen Lokalisierungsenergie der L¨ocher aus, was sie vielversprechend f¨ur

die Verwendung in optoelektronischen Bauelementen und insbesondere Halbleiter-Speichern

macht. Trotzdem ist bisher vergleichsweise wenig ¨uber die atomare Struktur von vergrabenen

GaSb/GaAs QP bekannt, die sich beim ¨

Uberwachsen von freistehenden QP ergibt.

Diese Arbeit beinhaltet die erstmalige Untersuchung vergrabener GaSb/GaAs QP mittels

Rastertunnelmikroskopie und -spektroskopie an Querschnittsfl¨achen, wobei die Form, Gr¨oße,

Verspannung, chemische Zusammensetzung und elektronischen Eigenschaften der QP auf

atomarer Ebene bestimmt werden. Durch die Auswertung entsprechender Ergebnisse f¨ur eine

Vielzahl unterschiedlich hergestellter Nanostrukturen lassen sich zahlreiche R¨uckschl¨usse auf

die zu Grunde liegenden QP-Wachstumsprozesse ziehen.

Anhand von Proben, die mit metallorganischer Gasphasenepitaxie (MOCVD) gewach-

sen wurden und unterschiedliche Mengen an GaSb enthalten, l¨asst sich der ¨

Ubergang von

flachen Quantengr¨aben zu optisch aktiven QP nachvollziehen, der ¨uber selbstorganisierte Sb-

Ansammlungen innerhalb von flachen Schichten und winzige drei-dimensionale GaSb-Inseln

als Vorstufen der QP verl¨auft. W¨ahrend die Quantengr¨aben deutlich durchmischt sind und

außerdem kleine L¨ucken aufweisen, ist der GaSb-Anteil der QP h¨oher, teilweise bis fast 100%.

Mit Basisl¨angen von bis zu 8 nm und H¨ohen von etwa 2 nm sind die QP allerdings noch sehr

klein. Alle Nanostrukturen weisen relativ abrupte Grenzfl¨achen und keine nennenswerte Sb-

Segregation in Wachstumsrichtung auf.

Dies ¨andert sich allerdings v¨ollig, wenn Molekularstrahlepitaxie (MBE) als Wachstums-

methode verwendet wird: Umfangreiche Austauschprozesse zwischen Gruppe-V-Atomen sind

die Ursache f¨ur eine hier beobachtete starke Durchmischung und Sb-Segregation beim ¨

Uber-

wachsen, die zusammen mit der hohen Verspannung von GaSb/GaAs QP als Ursache f¨ur

einen weiteren, besonderen Effekt angenommen wird: Alle mit MBE hergestellten QP – unab-

h¨angig von der GaSb-Materialmenge – weisen die Form eines Ringes auf, der aus Material mit

einem hohen GaSb-Anteil besteht und eine mehr oder weniger ausgedehnte, durchgehende

L¨ucke aus reinem GaAs umschließt. Diese Ringe bilden sich selbstorganisiert w¨ahrend des

Wachstumsprozesses, auch wenn hier die GaSb-Schichten schnell und ohne Unterbrechung

mit GaAs ¨uberwachsen wurden. Je nach genauen Wachstumsbedingungen werden sowohl

flache Ringe gefunden als auch solche, deren ¨außere Form in etwa einem Pyramidenstumpf

mit {111}-Seitenfl¨achen entspricht. In beiden F¨allen variiert die laterale Ausdehnung etwa

zwischen 10 nm und 20 nm bei inneren Ringdurchmessern von im Durchschnitt etwa 40% der

¨außeren, und es werden Dichten von 5 bis 9×1010 cm−2beobachtet. Die Lokalisierungsener-

gien der L¨ocher betragen ∼0.3 eV in den flachen und ∼0.4 eV in den h¨oheren Strukturen,

wobei ein Typ-II-Leitungsbandkantenversatz von etwa 0.1 eV ermittelt wird.

Die beobachteten Ergebnisse, deren Konsistenz mit Literaturdaten ausf¨uhrlich diskutiert

wird, offenbaren viele bisher unbekannte Aspekte der atomaren Struktur und erm¨oglichen ein

detailliertes Verst¨andnis der Entstehung von GaSb/GaAs QP.

Contents

1 Introduction 1

I Theoretical and experimental background 5

2 Quantum dots 7

2.1 Low-dimensional semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Epitaxyofquantumdots ............................. 8

2.2.1 Stranski-Krastanow growth . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.2 Molecular beam epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.3 Metalorganic chemical vapor deposition . . . . . . . . . . . . . . . . . 11

2.3 Structural and electronic properties of quantum dots . . . . . . . . . . . . . . 12

2.3.1 Shape of free-standing quantum dots . . . . . . . . . . . . . . . . . . . 13

2.3.2 Changes of the quantum dot shape upon overgrowth . . . . . . . . . . 15

2.3.3 Energy states and wavefunctions in quantum dots . . . . . . . . . . . 16

2.4 GaSb/GaAs nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4.1 Type-II band alignment . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.2 Literature data on GaSb quantum dot structure . . . . . . . . . . . . 19

2.5 Applications of GaSb quantum dots . . . . . . . . . . . . . . . . . . . . . . . 22

2.5.1 Storagedevices............................... 22

2.5.2 Optoelectronics............................... 23

3 Scanning tunneling microscopy (STM) 25

3.1 TheoryofSTM................................... 26

3.1.1 One-dimensional tunneling . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1.2 Bardeen and Tersoff-Hamann approaches . . . . . . . . . . . . . . . . 27

3.2 OperationmodesofSTM ............................. 28

3.2.1 Constant current mode of STM . . . . . . . . . . . . . . . . . . . . . . 28

3.2.2 Tip-induced band bending . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.3 Voltage-dependent imaging . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.4 Scanning tunneling spectroscopy (STS) images . . . . . . . . . . . . . 32

3.2.5 STSpointspectra ............................. 33

3.3 Cross-sectionalSTM................................ 35

3.3.1 Structuralcontrast............................. 36

3.3.2 Electroniccontrast............................. 37

3.4 The zincblende (110) surface . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

vii

viii CONTENTS

4 Experimental setup 41

4.1 TheSTMchambers ................................ 41

4.1.1 UHVconditions .............................. 41

4.1.2 The universal STM chamber . . . . . . . . . . . . . . . . . . . . . . . 42

4.1.3 The XSTM/XSTS chamber . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 TheXSTMexperiment............................... 45

4.2.1 Tippreparation............................... 45

4.2.2 Outlook: Improved tip preparation and characterization . . . . . . . . 46

4.2.3 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2.4 Sample cleavage and finding the nanostructures . . . . . . . . . . . . . 47

II Results and discussion 49

5 XSTM results on MOCVD-grown samples 51

5.1 Samplestructures.................................. 51

5.2 OverviewofXSTMresults............................. 53

5.2.1 Layer 1: 21 s GaSb deposition . . . . . . . . . . . . . . . . . . . . . . 55

5.2.2 Layer 2: 22 s GaSb deposition . . . . . . . . . . . . . . . . . . . . . . 56

5.2.3 Layer 3: 25 s GaSb deposition . . . . . . . . . . . . . . . . . . . . . . 56

5.3 Results from other characterization methods . . . . . . . . . . . . . . . . . . . 58

5.3.1 Photoluminescence spectroscopy . . . . . . . . . . . . . . . . . . . . . 59

5.3.2 Transmission electron microscopy . . . . . . . . . . . . . . . . . . . . . 60

6 Analysis of the chemical composition 63

6.1 Evaluation of the local lattice constant . . . . . . . . . . . . . . . . . . . . . . 63

6.2 Comparison with strain simulations . . . . . . . . . . . . . . . . . . . . . . . . 65

6.3 Local bending of the cleavage surface . . . . . . . . . . . . . . . . . . . . . . . 67

6.4 Stoichiometry of MOCVD-grown GaSb QDs . . . . . . . . . . . . . . . . . . . 70

7 The onset and pathway of quantum dot formation 71

7.1 Gaps within the Sb layers: GaSb growth . . . . . . . . . . . . . . . . . . . . . 71

7.2 GaSb content of the quantum wells . . . . . . . . . . . . . . . . . . . . . . . . 73

7.3 Structures from quantum wells to quantum dots . . . . . . . . . . . . . . . . 76

8 XSTM results on MBE-grown samples 79

8.1 Samplestructures.................................. 79

8.2 Overviewimages .................................. 81

8.3 QuantumdotsinsampleC ............................ 83

8.3.1 Quantum dot shapes in XSTM images . . . . . . . . . . . . . . . . . . 83

8.3.2 Statistical and simulated data on quantum dot cleavage . . . . . . . . 85

8.3.3 Dependence on the amount of deposited GaSb material . . . . . . . . 87

8.3.4 Shape anisotropy of the QDs . . . . . . . . . . . . . . . . . . . . . . . 90

8.4 QuantumdotsinsampleD ............................ 90

8.5 Wettinglayers ................................... 92

8.6 Opticalresults ................................... 94

8.6.1 Optically active QDs in sample D . . . . . . . . . . . . . . . . . . . . 94

8.6.2 Optically inactive small islands in sample D . . . . . . . . . . . . . . . 96

8.6.3 Optical results on QDs in sample C . . . . . . . . . . . . . . . . . . . 97

8.7 Dislocations..................................... 97

CONTENTS ix

9 Sb segregation and atomic exchange processes 99

9.1 XSTM imaging of Sb atoms in GaAs . . . . . . . . . . . . . . . . . . . . . . . 99

9.2 Soaking and group-V-exchange . . . . . . . . . . . . . . . . . . . . . . . . . . 102

9.2.1 Soaking of growth surfaces . . . . . . . . . . . . . . . . . . . . . . . . 102

9.2.2 Soaking-induced GaSb quantum well . . . . . . . . . . . . . . . . . . . 103

9.3 From2Dto3Dgrowth............................... 104

9.3.1 Smallest MBE-grown quantum dots . . . . . . . . . . . . . . . . . . . 104

9.3.2 Critical thickness of dot formation . . . . . . . . . . . . . . . . . . . . 105

9.3.3 Amount of incorporated GaSb . . . . . . . . . . . . . . . . . . . . . . 107

9.4 Sb segregation during overgrowth . . . . . . . . . . . . . . . . . . . . . . . . . 109

9.4.1 Analysis of Sb segregation . . . . . . . . . . . . . . . . . . . . . . . . . 109

9.4.2 Origin of Sb segregation and intermixing . . . . . . . . . . . . . . . . . 112

10 Formation and structure of quantum rings 117

10.1 Atomic structure of quantum dots . . . . . . . . . . . . . . . . . . . . . . . . 117

10.1.1 Outer shape of the quantum dots . . . . . . . . . . . . . . . . . . . . . 117

10.1.2 Local stoichiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

10.2 Literature data on quantum rings . . . . . . . . . . . . . . . . . . . . . . . . . 124

10.2.1 Quantum ring structures in other material systems . . . . . . . . . . . 124

10.2.2 Proposed formation of quantum rings . . . . . . . . . . . . . . . . . . 127

10.2.3 Persistent currents and Aharonov-Bohm effect . . . . . . . . . . . . . 128

10.3Ringformation ................................... 131

10.3.1 Origin of ring formation in the GaSb/GaAs material system . . . . . . 131

10.3.2 Growth model for ring-shaped GaSb quantum dots . . . . . . . . . . . 132

11 Electronic properties and type-II band alignment 137

11.1Specificimagecontrast............................... 138

11.1.1 Bias-dependent appearance of GaSb/GaAs quantum wells . . . . . . . 138

11.1.2 Calculation of tip-induced band bending and tunneling current . . . . 140

11.2 CITS imaging of GaSb nanostructures . . . . . . . . . . . . . . . . . . . . . . 143

11.3 Type-II induced electronic states in XSTS spectra . . . . . . . . . . . . . . . 147

11.3.1 Physical significance and normalization of point spectra . . . . . . . . 148

11.3.2 STS point spectra of GaSb nanostructures . . . . . . . . . . . . . . . . 152

12 Conclusion 159

Appendix 165

A Outlook: Tip sputtering and characterization 167

B Simulated distribution of ring cleavage 175

List of abbreviations 181

Bibliography 183

Publications and presentations 205

Acknowledgments 209

xCONTENTS

HERR, mein Gott,

wie sind deine Werke so groß und viel!

Du hast sie alle weise geordnet,

und die Erde ist voll deiner G¨uter.

Psalm 104, 24

Chapter 1

Introduction

The development of semiconductor devices [1] has fundamentally changed the scientific and

technological world over the last decades, which therefore are also called the “semiconduc-

tor age” or “information age”. Besides Si crystals, which are predominantly used in the

broad field of information technology, semiconductor heterostructures [2] like GaAs and

other III-V material systems have become important for high-speed applications and opto-

electronics [3], including the large area of semiconductor lasers [4–7].

A general and very impressive trend in the progress of semiconductor devices is the

miniaturization of the structures to generally achieve a better performance and to decrease

the power consumption and the production costs, often illustrated by Moore’s Law, saying

that the number of components per integrated circuit doubles every two years [8].

Semiconductor nanostructures and especially quantum dots (QDs) [2, 9] can be regarded

as the end of miniaturization, or as the perfection of miniaturized structures, as they use

single charge carriers for device performance [3, 10–13]. Even more, as typical QD sizes

are in the regime of the de Broglie wavelength of their charge carriers, these nanostructures

reveal fundamentally new physics as compared with bulk semiconductors, being dominated

by quantum effects [2, 3, 14–17]. In addition to these electronic effects inherent to QDs, also

their structures and possible formation exhibit unique possibilites in device fabrication as

they can be grown in a self-assembled way [2, 9, 18–25].

Obviously, this self-assembled growth of nanostructures and especially QDs is not that

straightforward as in Fig. 1.1, but is an interplay of different complex processes, many of

which are still not completely understood [2, 9, 26–36]. Thereby the atomic structure of the

QDs – i.e. their size, shape, and chemical composition, which result from the growth and

overgrowth processes – is crucial for their electronic properties [37–43].

Figure 1.1: The author of this

work during his first experiments

on three-dimensional growth, still

on a macroscopic scale.

2CHAPTER 1. INTRODUCTION

Most research and application development on III-V semiconductor QDs have been con-

centrated on the InAs/GaAs material system. Comparatively few studies on GaSb QDs in

GaAs can be found [44–62], although these structures are very promising both for fundamen-

tal physical effects and for special devices. GaSb/GaAs nanostructures exhibit a staggered

type-II band alignment, meaning that only for holes a strong confinement exists at the GaSb,

with localization energies of up to 450 meV [63, 64], while electrons are only weakly localized

by Coulomb binding in the surrounding GaAs [44, 65–77]. Thus, rather low electron-hole re-

combination energies result, which have led to the realization of room temperature GaSb QW

lasing [78, 79] and QD photoluminescence emission [55, 56] at the technologically important

wavelength of 1.3 µm. Probably even more important will be the application of GaSb/GaAs

QDs for charge storage devices [63, 80–83], as the strong hole confinement and the long

exciton lifetime resulting from the type-II band alignment principally enable charge storage

times in the QDs of up to years. Regarding the growth mechanisms of GaSb nanostructures in

GaAs including intermixing and segregation effects, the interface with the different group-V

elements Sb and As is an additional challenge for epitaxy, as under typical growth conditions

it is much easier to change the group-III element, while abrupt interfaces are difficult to

achieve between GaSb and GaAs [55, 69, 84]. Thus the rather poor supply of high-quality

structural data on GaSb/GaAs QDs in literature may probably not be due to lacking interest

in this system, but can rather more be explained by the difficulties inherent to the stable

growth of GaSb nanostructures in GaAs.

Scanning tunneling microscopy (STM) [85–90] is a well-suited tool for the investigation

of semiconductor nanostructures, as it is able to resolve the size, shape, inherent strain, and

chemical composition of QDs with atomic resolution [3, 24, 25, 32, 91–103]. Especially in

combination with scanning tunneling spectroscopy (STS), also electronic properties of the

sample like the surface local density of states can be analyzed [104–110]. Thus, a detailed

structural and electronic knowledge can be achieved, which is essential for understanding the

underlying physical effects of QD growth.

Quantum dots need to be capped for nearly all applications in order to protect the nano-

structures against ambient conditions and to even establish device performance like lumi-

nescence. As such an overgrowth process significantly changes the atomic structure of the

QDs [29, 35, 36, 111–118], an atomically resolved structural characterization after the cap-

ping process is crucial for modeling and improving the QD properties and therewith the final

device performance. This requirement can be fulfilled by employing cross-sectional STM

(XSTM), as in this case the capped sample is cleaved and the cleavage surface of the QDs is

investigated by STM [36, 119–133].

Although STM can generally be considered as a non-destructive characterization method,

the scanning tip nevertheless interacts with the sample surface by its electric field [107, 134–

138]. Therefore a detailed understanding of this interaction and the involved STM contrast

mechanisms is crucial for quantitatively evaluating electronic sample properties from XSTM

and especially XSTS data.

This work focuses on XSTM data on GaSb/GaAs QDs, presenting results on nano-

structures grown under various growth conditions using both metalorganic chemical vapor

deposition (MOCVD) and molecular beam epitaxy (MBE), and discussing details on the

formation, atomic structure, and electronic properties of the QDs.

In the first part, a short overview is given on QDs in general, including their growth and

structural properties as well as electronic states, and especially on GaSb/GaAs QDs with

their band alignment, reported structural data, and possible applications (chapter 2). This

is followed by an introduction into (X)STM and STS, covering several operation modes that

have been applied in this work and also the contrast mechanisms which are relevant for the

(110) cleavage surface (chapter 3). The experimental STM setups used here are sketched in

chapter 4, as are the main preparation steps of the XSTM experiment itself.

The main part of the work covers the XSTM results and their discussion, separated into

structural data on MOCVD-grown (chapters 5-7) and MBE-grown samples (chapters 8-10)

as well as results on electronic properties mainly derived from STS data (chapter 11). The

structural variety in MOCVD-grown samples covers the range from a flat GaSb quantum

well (QW) over a QW near the critical thickness of dot formation and possible QD pre-

cursor structures up to small, but optically active GaSb/GaAs QDs (chapter 5). Thus –

after introducing and discussing a method used to evaluate the chemical composition of the

nanostructures from the variation of the local lattice constant (chapter 6) – the onset and a

possible pathway of QD formation is analyzed in chapter 7.

Larger GaSb/GaAs QDs could be observed in the MBE-grown samples, but – very aston-

ishingly – all these QDs, formed within a rather broad range of growth conditions, exhibit a

ring-like structure (chapter 8). Extensive exchange processes of the group-V atoms As and

Sb are found to be typical for the MBE-grown samples, resulting in strong Sb segregation, as

shown in chapter 9. This segregation, together with the large strain of the nanostructures, is

obtained to be the main driving force for the formation of rings. A model of the transforma-

tion of initially compact free-standing GaSb QDs into ring structures upon GaAs overgrowth

is presented in chapter 10, together with the analysis of the atomic shape of the ring-like QDs

and an outlook on new quantum mechanical effects that can be assumed at such nm-sized

rings.

Having understood many details on QD growth in the GaSb/GaAs material system, and

after the discovery and explanation of the unique ring-formation, chapter 11 will focus on the

special electronic properties of GaSb/GaAs structures, i.e. the type-II band alignment: A spe-

cific contrast observed in the XSTM images of the nanostructures as well as the appearance

of current and conductance images can be explained in the context of this band alignment.

With this knowledge, the type-II conduction band offset and also the hole localization energy

can even quantitatively be evaluated from STS spectra for the GaSb/GaAs nanostructures.

Finally, both structural and electronic results will be summarized in chapter 12, thereby

comparing MOCVD- and MBE-grown structures and distinguishing between general trends

and details that rely on specific growth conditions. Thus, important effects and challenges

for the growth as well as promising perspectives for the application of GaSb/GaAs QDs will

be concluded.

4CHAPTER 1. INTRODUCTION

Part I

Theoretical and experimental

background

Chapter 2

Quantum dots

Semiconductor nanostructures, meaning structures with sizes in the nanometer regime, are of

large importance, not only for the industrial purpose of miniaturizing and modifying electronic

devices to increase their performance and decrease their costs and consumption of resources,

but also because of their inherent change of physical properties due to nanoscale quantum

effects [3, 9]. Although being solid crystals and of the same material as conventional bulk

structures, semiconductor nanostructures like the so-called “quantum dots” (QDs) behave

more like single atoms and differ significantly from the macroscopic crystal [2, 14].

Some main consequences of the reduced dimensionality of nanostructures are described

in the first part of this chapter, followed by preparation processes and main properties of

the zero-dimensional QDs. Finally, GaSb QDs in GaAs, the material system chosen for this

work, will be highlighted.

2.1 Low-dimensional semiconductors

Crystal semiconductors are usually described as a periodic system consisting of a broad

amount of interacting atoms, being characterized by an electronic bandstructure with an en-

ergy gap between the filled valence band and the empty conduction band [139, 140]. However,

if the size of the structure is decreased at least in one dimension down to the range of the

de Broglie wavelength of the charge carriers, the free motion of the carriers within the crystal

(according to the bandstructure) is disturbed and the carriers get confined in this dimension.

The de Broglie wavelength is

λ=h

p=h

p2meff kBT(2.1)

and depends on the effective mass of the charge carrier meff and the temperature T[141].

At room temperature the de Broglie wavelength is in the range of 30 nm for electrons in

GaAs [9]. Thus, GaAs-based nanostructures have typical sizes of some tens of nm or below.

The simplest model structure of a quantum mechanically confined system is a particle

in a box or so-called “quantum well” (QW) with infinitely high barriers in one dimension.

In actual quantum wells built using semiconductor heterostructures, the finite barrier height

leads to confined states only for carrier energies smaller than the barrier potential, for larger

energies the carriers can propagate [1, 14].

A further reduction of dimensionality leads to the creation of so-called “quantum wires”

(confinement within two directions) [1] and finally quantum dots with a confinement in all

three dimensions [9].

8CHAPTER 2. QUANTUM DOTS

bulkmaterial quantumwire quantumdotquantumwell

µE1/2 µE0µE-1/2

d-shape

E E E

Z(E) Z(E) Z(E) Z(E)

Figure 2.1: Spatial confinement of semiconductor structures and corresponding electronic density

of states.

Among many material properties which are altered by the spatial and electronic con-

finement, the electronic density of states (DOS) has a strong significance for many possible

applications. The change of the DOS as a function of energy with reduced dimensionality is

shown in Fig. 2.1. In bulk semiconductors the DOS increases with increasing energy separa-

tion from the band edges according to E1/2. In QWs the possible energies are quantized in

one direction, therefore the DOS behaves like a step function (E0dependence). The quanti-

zation in two directions for quantum wires leads to a DOS variation according to E−1/2, and

ultimately for quantum dots the possible energies are completely quantized, corresponding

to a δ-like DOS at discrete energies [142]. Due to these quantized energy states QDs are also

denoted as “artificial atoms” [143], and especially this energy quantization has made QDs

a fascinating system for studying fundamental physics and an outstanding system for new

electronic and optoelectronic devices [17, 144, 145].

2.2 Epitaxy of quantum dots

The method of choice to create semiconductor nanostructures with high crystal quality and

very few structural defects is epitaxial growth [9, 146], depositing individual atoms in crys-

talline layers on a given substrate. Some elementary processes taking place during epitaxy

are sketched in Fig. 2.2, including adsorption or chemisorption of precursor molecules with

subsequent dissociation, diffusion of the atoms on the substrate, partial desorption off the

substrate, and finally incorporation at energetically preferable places like steps and terraces

or as a new nucleus. The exact underlying physics of epitaxial growth are much more com-

plex, already for homoepitaxy with substrate and epitaxial layers being of the same material

(see for example [147] and references therein), and even more for heteroepitaxy using different

materials, which is necessary for QD growth [2, 9, 26]. Depending on the chosen experimental

conditions, the growth can be governed more by thermodynamics or more by surface kinetics.

The growth of semiconductor heterostructures and QWs using epitaxy has been known

for more than 30 years by now [149–154] and is meanwhile well established. The formation

of QDs within the semiconductor crystal, however, is even more complex and demanding

2.2. EPITAXY OF QUANTUM DOTS 9

dissociation

adsorption/chemisorption

ofmolecules

nucleation

diffusion

terrace/

steps

Figure 2.2: Elementary processes at the growth surface during epitaxial growth, taken from [148].

than heterostructure growth. One possibility to create QDs is post-growth structuring by

lithography and chemical etching (see for example [155, 156]), the more direct way is the

self-assembled formation of QDs via the Stranski-Krastanow growth mode [9, 23, 157]. A

combination of both methods is the deposition of the QD material onto substrates which

were previously patterned by lithography [158] or additional growth steps [159, 160].

2.2.1 Stranski-Krastanow growth

For heteroepitaxy near the thermodynamical equilibrium, there are three possible growth

modes: If a complete wetting of the substrate by the deposited material is energetically

favorable, i.e., if the energy of the substrate surface σsubstrate is larger than the sum of the

energies of the epilayer surface plus the interface σepilayer +σinterface, the film-like Frank-

van der Merve growth occurs, labelled after F. C. Frank and J. H. van der Merwe [161],

Fig. 2.3(a). This is mainly the case for materials with no or only a very small lattice mismatch.

However, it is also possible that such film formation is energetically unfavourable, σepilayer +

σinterface > σsubstrate, leading to the formation of islands according to the Volmer-Weber

growth (Fig. 2.3(b), after M. Volmer and A. Weber [162]).

In combination of both modes, islands can evolve on top of a thin wetting layer (WL),

called Stranski-Krastanow (SK) growth (Fig. 2.3(b), after I. N. Stranski (working at TU

Berlin from 1945–1953) and L. Krastanow [163]). This SK growth can occur especially in

material systems with a considerable lattice mismatch – like 4.2% for Ge on Si, 7.2% for

InAs on GaAs, or 7.8% for GaSb on GaAs [164] – when the increasing strain in the growing

epilayer can induce an inversion of the energetic situation.

The critical thickness of the deposited material, after which the transition from two-

Frank-vanderMerve Vollmer-Weber Stranski-Krastanow

(c)(b)(a)

Figure 2.3: Schematic diagram of the three growth modes for heteroepitaxy on an atomic scale.

The sizes and distances of the different atoms are not drawn to scale.

10 CHAPTER 2. QUANTUM DOTS

dimensional (2D) to three-dimensional (3D) growth occurs, depends on the growth conditions,

but is mainly determined by the lattice mismatch and the elastic constants of the material

system [19, 27, 28, 165, 166]. Thereby the island formation is characterized by pseudomorphic

growth, meaning that the lateral positions of the atoms within the islands can be slightly

shifted in respect to those of the WL and the bulk crystal, but the crystal lattice and symmetry

are continued, each island atom is located at a lattice site defined by the underlying crystal.

With proceeding deposition, the size of the islands increases, until the strain gets too large

for continuing this pseudomorphic growth even in the islands. At this stage dislocations

may form to reduce the strain energy [20], disturbing the crystal lattice and therewith the

electronic and optical properties of the nanostructures.

Within the large and complex parameter range of epitaxial growth, only small windows

exist and have to be explored for each material system for the self-assembled SK growth

of QDs. Moreover, the QD density, shape, stoichiometry and size critically depend on the

chosen growth parameters [18, 167–169].

2.2.2 Molecular beam epitaxy

The first self-assembled QDs have been grown using molecular beam epitaxy (MBE) [18].

This growth method is schematically shown in Fig. 2.4: The whole setup is situated within

an ultrahigh vacuum (UHV) chamber serving as growth reactor. Within this reactor, the

mounted sample substrate can be heated to the desired growth temperature. All growth

components are evaporated from individually heatable effusion cells which are placed adjacent

to the sample surface. Thus, the partial pressures of the different materials, which determine

the chemical nature of the epitaxial film and the growth rate, are given by the geometry and

the temperature of the effusion cells. For exact conditions and for enabling a fast change of

the deposited material in heteroepitaxy, the effusion cells are equipped with shutters.

In many MBE reactors, the partial pressures can directly be measured by a mass spec-

trometer or an ion gauge in the beam, in others the growth rate can be controlled by a

quartz-crystal oscillator. The surface structure of the evolving epitaxial layer can in situ be

monitored by reflection high energy electron diffraction (RHEED), which shows the geometry

Figure 2.4: Schematic diagram of an MBE setup, adapted from [170].

2.2. EPITAXY OF QUANTUM DOTS 11

of the surface reconstruction in reciprocal space, characterized by specific spots [26, 171, 172].

The layer by layer growth of a semiconductor film results in an oscillating surface roughness

and therewith an oscillating RHEED signal e.g. of the specular reflex, allowing to count the

deposited atomic layers directly. When QD growth sets in, the pattern changes from a spotty

appearance to a streaky one due to the reduced periodicity [172].

The growth of III-V semiconductors can be controlled by the flux of the group-III atoms:

Because the group-V atoms cannot stick on the substrate surface without the presence of

group-III atoms, they are typically offered abundantly in the reactor, while the group-III flux

governs the growth rate [9]. The ratio of group-V to group-III atoms (often called “V/III-

ratio” which should be much larger than one) and the substrate temperature determine

which kind of possible surface reconstructions appears [173–176]. Therefore it is much easier

to change the group-III element during growth, like switching from GaAs to InAs, than the

group-V element, like changing between GaAs and GaSb. In the latter case, As and Sb atoms

form a permanent background within the reactor which needs some time to decline [177] and

which can influence the stability and stoichiometry of the growth surface [55, 69].

Additionally important for the growth of As compounds is the possible existence of As as

As4or As2molecules within the beam: Direct evaporating of metallic As usually produces As4

tetramers, while a special cracker unit can be used to split the As4into As2molecules, which

can be easier and faster dissociated and incorporated at the growth surface [26, 171, 176].

Typical growth rates of MBE are in the range of 0.01 to 1 monolayers per second (ML/sec),

implicating an often time-consuming but very precise growth method. The necessary use of

UHV conditions enables various characterization methods to study the grown structures ei-

ther simultaneously during growth (like RHEED) or as an additional analysis step but with-

out breaking the vacuum and contaminating the sample [like scanning tunneling microscopy

(STM)]. One challenge in MBE chamber design is to avoid too much material being deposited

somewhere in the chamber apart from the sample while securing identical growth conditions

on the whole substrate.

Introdutions and technical details of MBE can be found in many textbooks (like e.g.

[9, 26, 140, 170, 171]), theoretic approaches especially to island nucleation in GaAs growth

are for example given by Kratzer et al. [30, 178, 179].

2.2.3 Metalorganic chemical vapor deposition

The other broadly used method for the self-assembled growth of QDs is metalorganic chemical

vapor deposition (MOCVD) [43, 167, 168, 180, 181], shown schematically in Fig. 2.5: In this

case, all or most of the growth components are extracted from metalorganic precursors by

the use of a carrier gas which also transports the gaseous material to the heated sample

substrate where it decomposes and gets incorporated [9, 26]. Gaseous precursors can easily

be mixed with the carrier gas, but in the case of liquid or solid precursors special so-called

“bubblers” are used in which the carrier gas flows through the precursor and dissolves the

desired material. Group-III and group-V elements are transported separately and get mixed

directly in the reactor to prevent pre-reactions. A homogeneous distribution of the growth

components within the carrier gas and a laminar gas flux above the sample substrate are

crucial for a uniform sample growth.

Due to the requirement of the carrier gas, which is usually nitrogen or hydrogen, the

MOCVD reactor typically operates at pressures between 20 and 500 mbar (1 mbar = 100 Pa),

where lower pressures are chosen if abrupt heterointerfaces are desired [183]. Nevertheless, the

carrier gas has to be very clean in order to prevent contamination of the grown layers. These

conditions inhibit the use of several in situ characterization methods which are known from

MBE growth taking place in UHV, decreasing the possibility to directly control the growth.

12 CHAPTER 2. QUANTUM DOTS

runhydrid/groupVMO

vent

AsH3

TESb

rungroupIIIMO

heating

TMIn TMGa TMAl

pump

b c d

Figure 2.5: Schematic diagram of the MOCVD setup used for growing samples described in this

work, from [182]. (a) Gas inlet, (b) susceptor, (c) substrate, (d) thermocouple.

On the other hand, growth can proceed significantly faster than in MBE, with typical growth

rates in the range of 0.1 to 10 ML/sec.

The growth rate and composition of the sample is determined by the substrate temper-

ature and the partial pressures of the individual growth components, which can be directly

controlled by gas valves for each precursor line. Similar to the MBE-growth mentioned above,

for the group-V elements significantly more material is supplied than can be incorporated, so

that the group-III flux limits the growth process. The dependance of the growth rate on the

temperature, however, is more complex in MOCVD, showing a different behavior in different

temperature regimes [182, 183], which is beyond this short introduction.

For most components of III-V semiconductors like e.g. In, Ga, Al, As, or Sb, several

metalorganic precursors are available, respectively, and the best choice of precursors for QD

growth is a field of wide discussion [184–191]. For the samples studied in this work, trimethyl-

gallium [TMGa, Ga(CH3)3] or triethylgallium [TEGa, Ga(C2H5)3] and trimethylaluminium

[TMAl, Al(CH3)3] were used for the group-III elements, triethylantimony [TESb, Sb(C2H5)3]

as Sb precursor, and the gaseous arsine (AsH3) for As [51, 182, 192, 193]. Although the latter

gets more and more displaced by the less toxic tertiarbutylarsine (C4H9AsH2) as standard

As precursor [182, 193], it was found that arsine is still superior for GaSb/GaAs growth.

2.3 Structural and electronic properties of quantum dots

Quantized tunable electronic states are the unique characteristics of semiconductor QDs.

These electronic properties crucially depend on the QD size, shape and stoichiometry. There-

fore, the exact knowledge and controllability of structural properties of QDs is essential both

for understanding the underlying physics and for enabling and improving (new) QD applica-

tions [2, 3, 37, 194].

The structure of QDs is often analyzed for free-standing ones by local probes like STM or

atomic force microscopy (AFM), yielding information on typical shapes, density, size distribu-

2.3. STRUCTURAL AND ELECTRONIC PROPERTIES OF QUANTUM DOTS 13

tion, and evolution of QDs and on the structure of the surrounding WL [24, 31–33, 91, 96, 195–

201]. However, for nearly all applications QDs have to be overgrown by a cap layer in order to

protect them and especially to establish the spatial and electronic confinement. This capping

process essentially alters the nanostructures, changing their stoichiometry, strain distribution,

shape, and size [35, 111–116, 202, 203]. Thus, it is not sufficient to analyze QDs on the growth

surface, but the structural details of overgrown QDs need to be known for understanding the

overgrowth process and for modeling the electronic properties of capped QDs.

2.3.1 Shape of free-standing quantum dots

Free-standing QDs usually have a pyramidal shape with a symmetry resembling the surface

symmetry of the host material [24, 31, 33, 36, 197, 204, 205]. On typical (001) growth

surfaces, QDs thus exhibit the shape of a pyramid with a polygonal base, a (110) and a (¯

110)

symmetry plane, and a clear apex. However, the simple and often used model comprising

a four-sided pyramidal shape is strictly speaking only observed for small (Si)Ge islands on

Si(001) [99, 206] and for InAs QDs on GaAs(001) in a very small, initial stage [33].

Actual QD shapes are more complex, as can be seen in Fig. 2.6, showing an example

of the first atomically resolved STM data on InAs/GaAs QDs, obtained by Jacobi et al.

[24, 25, 31, 176]. The authors were able to unambiguously identify the dominating side facets

of the QD with the high-indexed {137}facets using their specific surface structure [33]. These

facets form an angle against the (001) surface of only 24◦, resulting in a relatively flat QD

shape with a low aspect ratio, defined as the ratio between height and base diameter. The

anisotropy of the shape is underlined by height profiles along the two symmetry axes of the

QD, shown in Fig. 2.6(b).

With encreasing QD size, this flat structure becomes unfavorable due to strongly in-

creasing strain of the lattice-mismatched material, and a shape evolution towards steeper

structures occurs, described in detail by Jacobi et al. in Refs. [31, 33, 36]. Two examples of

this evolution are displayed in Fig. 2.7: The QD shown in the STM image (a), together with

50Å

[110]

[ 10]1

[121]

(a)

[110]

200100

[1 0]1

200100

(b)

(c)

( 7)31 (137)

( 7)13 (317)

( 11)1

(1 1)1

[110]

[ 10]1

Figure 2.6: Structure of a free-standing InAs/GaAs QD, from [24], [36], and [207]. (a) STM image,

taken at VT= -2.75 V and IT= 0.15 nA. (b) Profiles of the [1¯

10]-and [110]-direction, respectively,

with corresponding STM images. (c) Structural model of the QD shown in (a) with Miller indices of

the side facets.

14 CHAPTER 2. QUANTUM DOTS

(a) (c)(b) (d) [1 0]1

[110]

Figure 2.7: Structure of larger InAs/GaAs QDs, from [33]. (a) STM image of a “hut”-shaped

QD with (b) corresponding structural model. (c) STM image of a “dome”-shaped QD with (d)

corresponding structural model.

a sketch of its structure (b), is still dominated by {137}facets, but several steeper facets have

additionally emerged at two sides. In the STM image (c), a steeper and more compact QD

can be seen, with its structure sketched in (d): Now, the structure is dominated by {101}

facets, forming an angle of 45◦against the (001) surface, and only the small top area of the

QD is still characterized by the flatter {137}facets.

Costantini et al. have first shown that this transition from a flat to a steep shape with

increasing QD volume seems to be universal, as it occurs not only in the InAs/GaAs material

system, but also for Ge/Si, exhibiting much larger QDs, but with a comparable shape evolu-

tion [32, 101, 198, 208]. In both material systems the QD structures are sometimes also called

”hut” for the flat one and ”dome” for the steep one. Such a shape transition had already

theoretically been predicted by Daruka et al. [209], and Kratzer et al. have succeeded in the-

oretically modeling the transition between atomic shapes observed experimentally [34, 210].

The main driving force for the formation of QDs according to the SK growth mode, for

the shape evolution of free-standing QDs, and also for structural changes upon overgrowth

is the strain due to the lattice-mismatch between QD and host material. During WL growth

the material has to adopt the lateral lattice constant of the host matrix and can only partly

compensate this by an increased lattice constant in growth direction, leading to cumulative

strain with increasing WL thickness. This situation changes in the QD, where only the

bottom interface is defined by the material underneath, while towards the top also the lateral

lattice constant can increase for strain relaxation [2, 3, 9].

A quantitative analysis of the strain field in QDs is difficult to obtain. A possible exper-

imental method is x-ray diffraction under grazing incidence, combining the reciprocal space

mapping of x-ray diffraction with surface sensitivity, as has been demonstrated by Kegel et

al. [195, 196]. Alternatively, the strain distribution can be theoretically simulated, which is

also essential for precise calculations of electronic QD properties [3, 41, 92, 211–214], and

which has also been performed for uncapped QDs [215].

Examples of both calculated results and x-ray measurements are presented in Fig. 2.8,

displaying (a) the calculated trace of the strain tensor as a direct measure of the strain in a

single InAs QD and the GaAs(001) matrix underneath [215], and (b) the measured lateral

lattice parameter in free-standing InAs QDs also on GaAs(001) [195]. It should be noted

that a pyramidal QD shape with a sharp peak was assumed for the calculation [Fig. 2.8(a)],

while the summit of the experimentally observed QD is slightly rounded (b). Comparing

both data, it can nicely be seen that the increasing lattice parameter towards the apex of the

QD, as shown in Fig. 2.8(b), leads to a decrease of the strain, as indicated in (a). The strain

is maximum, however, at the bottom edges of the QD, and also the GaAs matrix underneath

is influenced.

2.3. STRUCTURAL AND ELECTRONIC PROPERTIES OF QUANTUM DOTS 15

InAsisland

(101)

(a) (b)

Figure 2.8: Strain within an uncapped InAs/GaAs QD: (a) Calculated trace of the strain tensor for

the (010) cross section through an idealized QD, from [16, 215]. (b) Deviation of the lateral lattice

parameter from that of GaAs, experimentally obtained from grazing-incidence x-ray diffraction on

free-standing QDs, adapted from [196].

2.3.2 Changes of the quantum dot shape upon overgrowth

During overgrowth of the formerly free-standing QDs with the host material, the strain

distribution changes drastically, as the QD is forced to fit into the surrounding host matrix.

As a consequence, the region of the sharp summit of the pyramid, which possessed hardly any

strain in free-standing QDs due to the increased lattice constant, gets strongly compressed

and becomes a very unfavorable place for the QD material. The result is a truncation of

the QD pyramid upon overgrowth [35], coming along with steeper side facets like {101}

or {111}[36, 118].

Obviously, no direct three-dimensional imaging of capped QDs is possible, but two-

dimensional projections and cross sections of the QD shape can be obtained, e.g. by cross-

sectional STM (XSTM). A cross section through a typical, large InAs/GaAs QD grown in the

same MBE reactor under similar conditions as the free-standing QDs shown in Figs. 2.6 and

2.7 is presented in Fig. 2.9(a). The flat (001) top face of the truncated pyramid is evident,

and also the side facets are significantly steeper than the {137}facets discussed above.

Several authors have studied the initial capping of QDs and report drastical shape changes

and material redistribution already during the first few MLs of overgrowth [29, 111, 114, 115,

117, 202, 203]. Just recently, the shape transition from free-standing to capped QDs was

studied step-by-step using AFM and in-situ STM. The complex process of shape transition

was divided into two successive regimes, namely an initial, fast strain-driven material trans-

fer, leading to QD shapes near thermodynamical equilibrium, which upon further capping

was followed by kinetically limited surface diffusion [35]. Not only the shape, but also the sto-

ichiometry of the QDs can get rearranged upon overgrowth, especially for larger structures:

reversed

truncated

In-rich

cone

border

5nm

(a) (b)

growth

direction

[001]

Figure 2.9: Cross sections

through different capped

QDs, obtained by XSTM.

(a) InAs/GaAs QD grown

by MBE. (b) InGaAs/GaAs

QD, grown by MOCVD:

The shape of the QD (yel-

low) and an In-rich central

region (red) are indicated.

16 CHAPTER 2. QUANTUM DOTS

Liu et al. first reported a nonuniform chemical composition of In0.5Ga0.5As/GaAs QDs, ob-

taining an In-rich core characterized by an inverted-cone shape [95]. Similar results have

been observed by several groups [100, 216–218], and also theoretical considerations support

this inverted pyramid-like In composition [219]. An example of a nonuniform In distribution,

here having the shape of a reversed truncated cone [100], is shown in Fig. 2.9(b).

Beyond such material redistributions within the QDs, additional effects can happen under

special growth conditions: Firstly, when QDs are only thinly or partially overgrown prior

to a long growth interruption or annealing step, a complete dissolution of the QDs can

occur, often accompanied by the formation of a second WL. Such a dissolution has been

experimentally observed [125, 220, 221] and theoretically predicted [222]. Also a partial

dissolution of formerly sane QDs was found, leading to the existence of nanoholes within or

beside the QDs [36, 118, 127, 132].

Secondly, a growth interruption after only partial overgrowth of existing QDs can also

lead to a redistribution of material from the top center of the QD towards the surrounding

growth surface, resulting in ring-like structures. Such quantum rings were first described by

Garc´ıa, Lorke et al. [202, 223–227] and were obtained also by other groups in the InAs/GaAs

system [228–231] as well as in other material systems of III-V [60, 232, 233], II-VI [234], and

Si-Ge [235–237] semiconductors. Recently these quantum ring structures found considerable

interest because of the possibility of persistent currents and quantized magnetic fluxes under

external magnetic fields [77, 224, 238–242].

2.3.3 Energy states and wavefunctions in quantum dots

The electronic confinement of a QD is schematically sketched in Fig. 2.10(a): The QD material

(InAs) has a smaller bandgap than the host material (GaAs), leading to an electronic band

offset for both valence band (VB) and conduction band (CB) at the interface between the

two materials. The bandgaps of the bulk materials at room temperature are Eg= 1.42 eV

for GaAs and Eg= 0.35 eV for InAs [164]. However, it is too simplified to regard the QD

material as bulk InAs, actually the situation at the QD is an interplay between the properties

of the GaAs host material and quantized states, leading to confined ground and excited states

for electrons and holes within the GaAs bandgap and to resonant electron and hole states in

the GaAs CB and VB, respectively.

According to the structure of the QD, different wavefunctions exist for both electrons

and holes at distinctive energies, respectively, ranging from the ground state up to excited

states of higher order with different symmetries, as illustrated in Fig. 2.10 (b,c). Overviews

on calculated QD states regarding their energies and the shapes of their probability density

can, for example, be found in Refs. [37, 39, 41, 42, 211]. Stier et al. have also shown that the

electron ground state is mainly of s-like symmetry, while the hole ground state is strongly

p-like [37, 211]. Additionally, due to the larger effective masses of the holes compared to the

electrons, the confinement energy and the energetic distance between excited states are larger

for electrons than for holes, too, as can be seen in Fig. 2.10(b).

Both the distribution of electron and hole states and their absolute energies strongly

depend on the structure of the QDs, which is also displayed in Fig. 2.10(b). This dependence

is evident from simulations [37, 39, 42, 240] and is as well confirmed by experimental results

[13, 244–246]. Thereby not only the pure size and shape of the quantum box influences

the electronic states, but also the strain distribution [16, 41, 211] and the stoichiometry

[38, 40, 247, 248] of the QDs. Thus, an exact knowledge of these structural parameters

is essential for simulating the electronic details of QDs [43], and, even more, the ability of

reproducibly adjusting size, shape and stoichiometry of QDs enables one to tune the energetic

properties of the grown nanostructures and possible devices.

2.4. GASB/GAAS NANOSTRUCTURES 17

pyramids(45°)ofdifferentbaselength

electronenergy[meV]

holeenergy[meV]

InAsCBedge

InAsVBedge

GaAsCBedge

GaAsVBedge

electron

ground

state

holeg.st.

holee.sts.

electron

excited

states

(a) (b) (c)

Figure 2.10: (a) Schematic energy diagram of an InAs/GaAs QD. (b,c) Calculated energies and

wavefunctions of confined states for pyramidal InAs/GaAs QDs of different size. Adapted from [211]

and [243].

The spatial and electronic confinement of single charge carriers in QDs embedded in a

semiconductor crystal enable a large variety of new applications. Of special importance is the

formation of a confined electron-hole pair, a so-called exciton, and its recombination under

emission of a photon of the corresponding energy, as this process opens the wide area of nano-

optoelectronics [3]. The emission wavelength of an optical device based on QDs is determined

by their quantized energies, resulting in very sharp luminescence peaks [15, 17, 21, 142, 143,

249]. This narrow linewidth, possible photoluminescence and lasing wavelengths covering the

whole visible spectrum and the technologically important near infrared, very low threshold

current densities, and very fast electronic processes are some of the advantages of applying

QDs for light emitting diodes (LEDs) and in particular for lasers [6, 7, 17, 250–252].

2.4 GaSb/GaAs nanostructures

Compared to InAs/GaAs QDs, which are most common for III-V semiconductor nanostruc-

tures, GaSb QDs in GaAs are much less intensively studied. The structural parameters are

similar, with a GaSb bulk lattice constant of 0.610 nm compared to 0.606 nm of InAs, result-

ing in a GaSb/GaAs lattice misfit of 7.8% at similar elastic moduli [164]. A comparison of

these lattice constants of the GaAsSb system with those of other III-V heterostructures can

be found in Fig. 2.11. However, the electronic properties are completely different, because

not only the absolute bandgap of bulk GaSb, 0.75 eV at room temperature, is significantly

18 CHAPTER 2. QUANTUM DOTS

wavelength [mm]l

bandgapenergyE [eV]

GaAs

GaSb

InAs

latticeconstanta [Å]

Figure 2.11: Bulk lattice con-

stants, bandgap energies, and corre-

sponding luminescence wavelengths

of various binary and ternary III-

V semiconductors, adopted from

[253].

larger than the InAs value [164], but the band alignment of GaSb/GaAs nanostructures has

a specific, staggered appearance, leading to distinctive physical effects and a new class of

promising applications.

2.4.1 Type-II band alignment

Many material systems like the common InAs/GaAs quantum dots build a so-called “type-I”

band alignment, meaning that both electrons and holes are confined within the nanostructure,

as sketched in Fig. 2.12(a). However, there are also systems forming a staggered or so-called

“type-II” band alignment with only one sort of charge carriers being confined [2]. GaSb/GaAs

represents such a type-II alignment, exhibiting a strong confinement for holes but a repulsive

potential for electrons [44], as shown schematically in Fig. 2.12(b). Just when a hole is

confined within the QD but no corresponding electron is present due to the energetically

unfavorable GaSb CB offset, the system gets charged, leading to a local band bending and a

weak Coulomb attraction for electrons in the GaAs surrounding the QD [44, 66, 69, 71, 72, 75].

This situation is sketched in Fig. 2.12(c).

The exact band alignment and especially the CB offset of GaSb/GaAs QDs and QWs are

still under discussion [44, 67, 68, 75–77] and depend strongly on the strain [44, 75, 77] and the

chemical composition of the often alloyed GaSb or GaAs1−xSbxnanostructures in GaAs [47,

57]. A strong hole confinement, however, is evident for GaSb/GaAs QDs: Using capacitance-

voltage (CV) and deep level transient spectrocsopy (DLTS), Geller et al. obtained hole local-

ization energies around 450 meV and charged QDs containing up to 15 holes each [63, 64, 80].

CB CB

VB VB

type-I type-IIuncharged type-IIcharged

GaAs GaAs

GaAs

GaSb

InAs GaAs GaAs

GaAs

(a) (b) (c)

Figure 2.12: Schematic band alignment of type-I and type-II nanostructures.

2.4. GASB/GAAS NANOSTRUCTURES 19

In a classical model considering the staggered type-II band alignment, holes confined

within the QD GaSb material and electrons in the surrounding GaAs matrix are spatially

separated, leading to only weak Coulomb interaction. Quantum mechanically, however, there

is a partial spatial overlap between the hole and electron wavefunctions as they decline ex-

ponentially in the classically forbidden regions. Thus, a recombination of electrons and holes

is possible, but with a strongly reduced probability compared to type-I QDs. This combina-

tion of the staggered band alignment, a strong hole confinement, and the low electron-hole

recombination probability leads to two important consequences for the physics and appli-

cations of GaSb/GaAs nanostructures: Firstly, extraordinary long exciton lifetimes can be

achieved [47, 66, 254, 255]. Secondly, the recombination energy of holes confined in the QD

and electrons in the CB of the surrounding matrix is considerably low, in principle it can be

even smaller than the bandgap of bulk GaSb [see Fig. 2.12(c) for illustration] [55, 56].

2.4.2 Literature data on GaSb quantum dot structure

First data on GaSb/GaAs quantum dots, grown by MBE, were published in 1995 by Hatami

et al. in a cooperation of the Technische Universit¨at Berlin, the Max-Planck-Institut f¨ur

Mikrostrukturphysik in Halle, Germany, and the Ioffe Physical-Technial Institute in St. Pe-

tersburg, Russia [44]. They concluded a nearly square-based pyramidal QD shape, finding

an average lateral size of 22 nm and a density of about 4 ×1010 cm−2. Extended optical

studies explored the carrier dynamics of these QDs using photoluminescence (PL), photolu-

minescence excitation (PLE) and cathodoluminescence spectroscopy, confirming the type-II

band alignment by an observed blueshift of the QD luminescence with increasing excitation

energy [47]: This blueshift can be explained by the spatial separation between holes and elec-

trons, leading to the formation of an increasing dipole layer and an increased band bending

at the QD interfaces with increasing carrier density and thus to a larger energy separation

between confined hole states in the QD and Coulomb-bound electron states in the neighbor-

ing GaAs [65]. The optical results were shortly later confirmed by results from Sun, Kroemer,

and coworkers at the University of California at Santa Barbara, USA [66]. In the same group,

details of the band alignment were studied by Rubin et al. using ballistic electron emission

microscopy [67].

A large step towards the understanding of GaSb growth and QD formation was done by

the group around Bennett, Shanabrook, and Whitman at the Naval Research Laboratory

in Washington D.C., USA, intensively studying the growth of III-Antimonides on GaAs by

MBE. Using transmission electron microscopy (TEM), atomic force microscopy (AFM) and

in-situ STM, they observed several stages of the QD formation process, ranging from flat

2D GaSb layers over small QDs of 15 nm lateral size, larger QDs with in average 28 nm

diameter and 3.2 nm height up to large, relaxed GaSb islands containing dislocations [45,

46, 256, 257]. For an enhanced understanding of the growth surface they also studied the

atomic reconstructions of GaSb(001) by STM [258]. The type-II nature of their QDs was

confirmed by PL measurements [65], and DLTS studies revealed the strong hole confinement

with activation energies of 400 meV and more [70].

Some more specific QD structures were grown by Suzuki, Arakawa, and coworkers at

the University of Tokyo, Japan: After studying general optical and structural properties of

GaSb/GaAs QDs and especially the influence of the amount of deposited material, obtaining

QD sizes from about 26 nm diamter with 6.2 nm height to 32 nm diameter with 9.5 nm height

[48, 69, 255], they grew the first stacked GaSb QD layers [49]. By suppressing the effect of

intermixing of As and Sb during the overgrowth process, they were able to produce GaSb

QDs with a PL peak at the technologically important wavelength of 1.3 µm [56]. Studies

on Sb/As exchange reactions during GaSb QD growth and overgrowth are also published by

20 CHAPTER 2. QUANTUM DOTS

Silveira, Garcia and Briones from the Instituto de Microelectr´onica de Madrid, Spain [50].

All GaSb QD structures discussed above were grown by MBE, today still being the dom-

inant growth method for GaSb/GaAs nanostructures. The first publication on intentionally

obtained 3D GaSb structures grown on GaAs by MOCVD was given by Bozek et al. from

Warsaw University, Poland. However, they deposited 20 ML or more of GaSb and obtained

large islands which most probably contained many crystal defects, showing no photolumi-

nescence or carrier confinement [259]. Even earlier, Graham et al. from the University of

Oxford, UK, had observed the unwanted formation of islands of several 100 nm size when

they intended to grow thick flat GaSb films on GaAs [185, 186]. Large, relaxed GaSb/GaAs

islands were also grown by Kinder, Subekti and Goldys at Macquarie University in Sydney,

Australia [260, 261].

Some years later the latter group produced the first real GaSb QDs using MOCVD,

published by Motlan et al. [52]. They obtained QDs of about 40 nm average width and

5 nm height at a density of 1.6 ×1010 cm−2, investigated with AFM, TEM, and scanning

electron microscopy (SEM), but also large islands of more than 100 nm size. Also stacked

multilayer structures were studied optically and structurally, showing a vertical ordering of

the QDs [61, 262]. Using PL spectroscopy, Motlan and Goldys found a seperation between

their QD and WL PL peaks of 0.3 eV, which is about twice as large as the corresponding value

reported for MBE-grown GaSb QDs. They suggested a systematically different intermixing at

the WL for MOCVD and MBE growth to be the reason [74, 263]. A blueshift of the PL peak

with increasing excitation energy, as already known from MBE-grown samples, confirmed the

type-II band alignment also for the MOCVD-grown GaSb QDs.

MOCVD was also used at the Technische Universit¨at Berlin by M¨uller-Kirsch and cowork-

ers in the group of Bimberg to grow GaSb/GaAs QD structures with typical sizes of 26 nm

width and 3.5 nm height [51, 264]. At smaller amounts of GaSb deposition, prior to the forma-

tion of distinctive QD structures, stoichiometric fluctuations of a strongly intermixed GaAsSb

QW have been observed by high-resolution transmission electron microscopy (HRTEM).

Antimony-rich regions within this layer of about 10 nm lateral extension have been found to

exhibit QD confinement [71, 73, 265]. The QD evolution with increasing GaSb deposition

and the influence of growth interruptions prior to overgrowth were intensively studied using

AFM and TEM [51, 182, 264, 265], finding that a correct length of the growth interruption

is crucial for QD formation. A combination of GaSb and InAs QDs in GaAs was also suc-

cessfully demonstrated: Taking InAs QDs as stressors, GaSb QDs could be grown on top

with a very high QD density of 1 ×1011 cm−2[53], which could not yet be achieved in the

pure GaSb/GaAs system. From PL spectroscopy measurements the type-II band alignment

could be confirmed and many-particle effects and state filling in GaSb/GaAs QDs were ex-

plored [71–73]. Also the DLTS and capacitance-voltage measurements mentioned above were

performed in this group [63, 80], demonstrating the feasibility of GaSb QDs as storage me-

dia, as will be shown in more detail in the next chapter. Calculations of the band structure

motivated by the optoelectronic results complete the GaSb QD research of this group [75].

During the last three years, several other groups have published individual results on

GaSb/GaAs QDs: The effect of a growth interruption prior to QD overgrowth was studied

by Luo et al. at the Chinese Academy of Sciences in Beijing, China [54]. Yamamoto et al. at

the Communications Research Laboratory in Tokyo, Japan, introduced a new growth method

when they irradiated the GaAs growth surface by Si atoms prior to GaSb deposition in order

to increase the QD density [58]. Promising are the works of Nakai et al. at the University of

Electro-Communications in Tokyo, Japan, obtaining QDs with a very narrow PL linewidth

of 67 meV [59] and of Kobayashi et al. at the University of Tokyo, Japan, demonstrating the

self-assembled formation of either GaSb QD or quantum ring structures on GaAs, depending

2.4. GASB/GAAS NANOSTRUCTURES 21

on the growth parameters [60]. Balakrishnan, Huffaker, and coworkers at the Center of

High Technology Materials in Albuquerque, New Mexico, USA, have compared SK growth

of coherently strained GaSb QDs with the formation of GaSb islands upon a growth mode

characterized by laterally propagating interfacial misfit dislocations [62, 266]. Finally, detailed

studies on the initial deposition of GaSb on GaAs and the onset of QD formation have been

performed by Farrer, Ritchie, and coworkers at the University of Cambridge, UK, for MBE

growth [55] and by Pitts, Watkins, and coworkers at the Simon Fraser University in Burnaby,

Canada, for MOCVD growth [57].

Although the investigation of GaSb/GaAs nanostructures has increased during the last

years, the number of institutions being involved with GaSb QD growth and structural char-

acterization is still concise, as the map shown in Fig. 2.13(a) illustrates, without necessarily

being exhaustive. The main structural and some optical results on GaSb QDs of the publi-

cations mentioned above are summarized in Table 2.1.

In conclusion, GaSb/GaAs QDs have been grown over the last ten years using both MBE

year growth depo- GaSb QDs charac- PL energy refe-

method sited width height density terized QD WL rence

GaSb ×1010 with

[ML] [nm] [nm] [cm−2] [eV] [eV]

1995 MBE 4 22 ±4 4 TEM 1.09 1.23 [44, 47]

x-ray

1995 MOCVD 20 200 100 0.04 SEM, STM [259]

1996 MBE 1.4 80 ±7 10 0.4 AFM 1.32 [66]

1996 MBE 2.5 ∼15 TEM [46]

3.0 28 ±4 3.2±0.9 1 AFM 1.13 1.27 [45, 256]

3 33 ±4 5 ±1.3 1–2 AFM 1.14 [70]

1997 MBE 50 5 STM [67]

1998 MBE 2.5 32 ±5 9.5 0.26 AFM [48, 69]

2.8 28 ±6 6.7 0.75

3.1 26 ±6 6.2 1.2 1.1 1.3

1998 MOCVD 2 ∼100 15 AFM [260]

1999 MBE 1.1 30 9.5 SEM [267]

45 3.0

55 0.38

2001 MOCVD 38 ±2 5 ±0.3 1.55 AFM 1.08 1.40 [52, 263]

2001 MOCVD ∼2 10 HRTEM 1.10 ∼1.4 [71, 73]

4.5 26 3.5 3 TEM 1.06 1.40 [51, 264]

2003 MBE 5 31 ±5 7.2±0.8 2.2 AFM 1.01 1.38 [55]

2004 MBE 3.0 30–45 6–8 1 AFM 0.9 1.28 [56]

2004 MBE 2.0 80 14 0.2 AFM 1.12 1.41 [58]

2004 MBE 3.5 50–70 2 0.5 AFM 1.2 1.28 [60]

2004 MBE 3–4 30 12 1 STEM 1.09 1.41 [59]

2005 MOCVD 3.8 44 5 1.5 AFM 1.11 1.32 [61]

2006 MBE 3 10 5 3 AFM, TEM 1.2 [62]

Table 2.1: Overview on reported structural data on GaSb/GaAs QDs and corresponding PL energies,

arranged by publication time and workgroups of the authors.

22 CHAPTER 2. QUANTUM DOTS

(a)

(b)

Figure 2.13: (a) Places of GaSb/GaAs QD growth and structural characterization worldwide (world

map from [268]). (b) Structure of a GaSb/GaAs QD, imaged with cross-sectional STEM, from [59].

or MOCVD. Typical published QD sizes are in the range of 25 to 40 nm width and 3 to 7 nm

height, with a roughly pyramidal shape and densities of typically 1 ×109to 4 ×1010 cm−2.

However, to my knowledge the best structural image of a GaSb QD obtained yet is the one

shown in Fig. 2.13(b), aquired by Nakai et al. using cross-sectional scanning transmission

electron microscopy (STEM) in a high-angle annular dark field mode, and no structural

data with atomic resolution has been available yet — with the exception of the XSTM data

presented in this work.

2.5 Applications of GaSb quantum dots

Due to the all in all comparatively low interest in GaSb QDs during the last decades and to

the still existing difficulties in growing high quality GaSb structures, no commercial devices

based on GaSb/GaAs QDs are available yet. Nevertheless, several very promising approaches

have been published, mainly in the fields of long-wavelength luminescence and in particular

charge storage.

2.5.1 Storage devices

Due to the large hole confinement and large exciton lifetimes, GaSb QDs are very promising

for charge storage devices on a nanometer scale. The charging and charge emission of GaSb

QDs has been studied in detail by CV spectroscopy and DLTS [63, 70, 80], and a hole

retention time at room temperature of about 1 µs for a single hole with a ground state

energy of 450 meV has been obtained, which is five orders of magnitude larger than for

InAs/GaAs QDs [63].

The principal idea how to use GaSb QDs as single charge storage device is illustrated in

Fig. 2.14, based on a concept of Geller, Marent, and Bimberg [82, 83, 269]. The device struc-

ture consists of a semiinsulating GaAs substrate, followed by a highly p-doped GaAs contact

layer and another p-doped GaAs layer. Onto this, the GaSb QDs are grown, sandwiched be-

tween thin undoped GaAs layers. After deposition of another p-doped GaAs layer, a highly

n-doped GaAs cap layer completes the structure, which can be lithographically etched and

contacted by metal evaporation [63, 81]. As a result, the GaSb QD is situated within the

depletion zone of a p-n diode, as depicted for the VB in Fig. 2.14(a).

All necessary processes of charging and discharging the QDs can now be controlled by

adjusting the voltage at the p-n junction: At sufficiently high reversed voltages, the band

bending is so strong that the holes can tunnel out of the QD in a reasonably short time, as

sketched in Fig. 2.14(b). For charging the QDs, on the other hand, a forward bias enables

the charge carriers to reach the QD where the holes get trapped, shown in Fig. 2.14(c).

2.5. APPLICATIONS OF GASB QUANTUM DOTS 23

EFEF

GaAs

p-doped

GaAs

p-doped

GaAs n-

GaAs

p pp

n+n+

GaSb

tunneling

AlGaAs

barrier

GaAs n-

GaAs

depleting

oftheQD charging

oftheQD

(a) (b) (c) (d)

Figure 2.14: Schematic diagram of the VB of a GaSb QD embedded in a p-n-junction, used for

charge storage. (a) Storage: The hole is confined. The red pointed arrow indicates the energy needed

to overcome the emission barrier. (b) Discharging: Increasing the electrical field, the hole can tunnel

out of the QD. (c) Charging: Decreasing the electrical field, holes can relax into the QD. (d) By using

an additional AlGaAs layer, the emission barrier for confined holes gets enlarged.

These processes are already established from the DLTS measurements, thus the relevant time

constants are well-known: Adjusting the diode voltage is extremely fast, and the relaxation

process of the holes occurs within picoseconds. Thus, writing in such a QD-based charge

storage device is even faster than in conventional dynamic random access memory (DRAM)

devices [82]. Reading the stored information could be implemented in the same way as in

conventional Flash storage devices by depositing a thin QW containing a 2D electron gas

near the QD layer and measuring the current in this layer, getting influenced by the charge

of the QDs.

Crucial for an application as storage device is the storage time of the QDs at room

temperature. For InAs/GaAs QDs with an hole localization energy of 210 meV this storage

time amounts to about 0.5 ns [270], and for Ge/Si QDs with 350 meV hole localization it is

∼0.1 µs [271], in comparison to ∼1µs for GaSb/GaAs QDs. Recently, the emission barrier

for holes in InAs/GaAs QDs was significantly increased by growing an Al0.6Ga0.4As barrier

closely underneath the QD layer: In this way, the hole localization energy could be extended

to 560 meV and a storage time of about 5 ms was obtained [81]. By increasing the Al content

in the AlGaAs buffer to 90%, corresponding to a hole localization of ∼700 meV, even storage

times in the range of seconds could be obtained in the latest experiments [82].

These results can be extrapolated for an intended structure using an AlGaAs barrier un-

derneath a GaSb QD layer, as sketched in Fig. 2.14(d): For this structure, a hole localization

energy of more than 1 eV is expected, corresponding to storage times of months up to years.

Yielding such timescales, the proposed GaSb QD device could combine the storage times of

nonvolatile Flash memories with the fast access and the durability of DRAM devices and ex-

ceed both conventional memories by very low electrical currents and extremely high storage

densities.

2.5.2 Optoelectronics

For optoelectronic applications within the technologically important telecommunication area,

lasing wavelengths of 1.3 µm or 1.55 µm are required as these are the values of least absorption

and optical dispersion in fiber optics. In the InAs/GaAs system, QD emission or even lasing

at these wavelengths has been achieved mainly by using additional complex strain reducing

layers, often containing small amounts of antimony [272–277]. For GaSb/GaAs QDs, room

temperature emission wavelengths of 1.3 µm have been obtained without the necessity of

additional layers [55, 56], due to the low electron-hole recombination energy. However, special

care had to be taken to prevent strong Sb-As exchange processes, for this reason the correct

sequence of Ga, As, and Sb flux and intermitting growth interruptions is essential.

24 CHAPTER 2. QUANTUM DOTS

While lasing at 1.3 µm has already been established some years ago for GaAsSb/GaAs

QW heterostructures in edge emitting lasers [78] as well as in vertical cavity surface emitting

lasers [79], the device formation using GaSb/GaAs QDs is still on the way. One challenge is

the luminescence intensity, which – due to the only partial overlap of electron and hole wave

functions – is comparably low for GaSb QDs. Possible strategies to overcome this limitation

and to increase the intensity could be using stacked QD layers [49, 61, 262] or the use of InAs

QD stressors for an increased GaSb QD density [53]. If, in the latter case, the GaSb QDs

are grown in close proximity or directly on an InAs layer, a combined band alignment can

be expected with electrons confined in the InAs layer and holes confined in the GaSb QDs,

leading to an even smaller recombination energy [182]. However, such a structure has not

been realized yet.

Chapter 3

Scanning tunneling microscopy

Since its invention in 1982 by Binnig, Rohrer, Gerber, and Weibel [85, 86, 88], scanning tun-

neling microscopy (STM, also used for “scanning tunneling microscope”) has revolutionized

the characterization and description of crystal surfaces, enabling one to analyze topografic

and electronic properties of surfaces with atomic resolution [89, 90, 278, 279].

The principle of STM is shown schematically in Fig. 3.1: A sharp metal probe tip is

scanned over a conductive sample surface in close proximity but without physically touching

it. When a bias voltage is applied, a tunneling current results which depends exponentially on

the distance between the tip and the sample and also on the electronic potential of the surface.

Thus, the topography of the sample can be imaged as well as local variations of electronic

properties of the surface, induced for example by variations of the chemical composition. It

should always be kept in mind that STM results represent an interaction between tip and

sample properties. This is exemplarily sketched in Fig. 3.1 as sharp edges and interfaces of

the sample surface appear rounded in the STM data due to the geometry of the probe tip.

Figure 3.1: Operation principle of the STM, from [85]: A metal probe tip is scanned over a conductive

sample in a distance sby a piezo tripod Px,Py,Pz. The tunneling voltage VTis generated by a control

unit CU, which also keeps the tunneling current ITconstant by adjusting the voltage of the z-Piezo

VZ. This regulation of the tip height ∆srepresents the STM signal (dashed line), which depends on

the topography of the sample surface (A) as well as on local variations of the electronic or chemical

composition (B, C). It is additionally influenced by the geometry of the probe tip, leading for example

to an apparent broadening δof actually sharp surface steps.

26 CHAPTER 3. SCANNING TUNNELING MICROSCOPY (STM)

Although the theory and some possible applications of electron tunneling were quite well

understood (see [89, 90] and references therein) and even vacuum tunneling of electrons from

metal to metal was established already in 1971 [280], two large challenges had to be overcome

by the realization of the first STM showing atomic resolution: The obtained tunneling cur-

rents are very small, typically in the 100 pA range, and are extremely sensitive to variations

of the tip-sample distance, so that sensitive amplifiers and fast feedback electronics have to

be used. To establish a stable tip-sample distance and to control the lateral tip position with

atomic precision, a very precise positioning of the tip is crucial. This task can be coped with by

piezo-ceramic actuators. Additionally, for atom-resolved surface studies very clean ultrahigh

vacuum conditions and an enhanced vibration isolation are necessary. Once this precondi-

tions were fulfilled [85, 281], STM soon proved its ability to resolve surface atomic structures

[88, 279, 282–284] and also to analyze local electronic properties [104, 105, 107, 285, 286].

In this section, first some aspects on STM theory will briefly be introduced, followed

by a presentation of the operational modes of STM used for this work. Then the special

issues of cross-sectional STM (XSTM) are presented, enabling the characterization of capped

nanostructures. As most III-V semiconductor heterostructures crystallize in the Zincblende

structure, revealing a (110) cleavage surface in XSTM studies, finally the appearance of this

surface and the mechanisms relevant to the generation of corresponding STM images are

discussed.

3.1 Theory of STM

The underlying physical effect of STM is the quantum mechanical effect of tunneling. Its

basic consequences for STM imaging can qualitatively be understood even in a simple one-

dimensional model. The actual STM situation, however, the three-dimensional interaction

between a probe tip and a sample surface, is much more complex; and its theoretical de-

scription goes far beyond the scope of this thesis. So only some implications of STM theory,

which are directly relevant for the STM data of this work, will be mentioned here. For an

extensive introduction textbooks like Refs. [89, 287, 288] are suggested.

3.1.1 One-dimensional tunneling

Tunneling from a metal tip through a vacuum barrier into a conductive sample (or vice versa)

can, in a most simple case, be described by a one-dimensional model with a potential barrier

of finite height, sketched in Fig. 3.2. An electron of energy Ecan classically not penetrate

a barrier of the potential V0> E. In quantum mechanics, however, the electron can be

described by the time-independent Schr¨odinger equation

Ã−¯h2

∂2

∂x2+V(x)!ψ(x) = E ψ(x) (3.1)

with the potential V(x) = V0in the barrier between x= 0 and x=sand V(x) = 0 elsewhere.

This equation can be solved by electron wave functions

ψ(x) = ψ(0) exp (−κ x),with κ=p2m(V−E)

¯h.(3.2)

This solution implies a sinusoidal oscillation of the wave function in regions with V(x) = 0,

where κis imaginary, but an exponential decay of the probability density |ψ(x)|2within the

barrier, where κis real. Correspondingly, the electron can tunnel from the tip (or the sample)

into the vacuum, where its probability density decays exponentially.

3.1. THEORY OF STM 27

Re(y)

V(x)

Figure 3.2: One-dimensional tunnel-

ing through a potential barrier.

Regarding a current density in front of and behind the potential barrier, the transmission

coefficient through the barrier can be calculated straightforwardly (as it is carried out in

typical textbooks like [141]). The current density behind the barrier results approximately

j∝e−2κ s,(3.3)

meaning that the tunneling current depends exponentially on the tip-sample distance, and

also on the applied tunneling voltage VT, as κcontains the electron energy E=eVT.

3.1.2 Bardeen and Tersoff-Hamann approaches

Although the simple one-dimensional model can already explain the exponential behavior

of the tunneling current, the actual tunneling situation at STM experiments is much more

complex. A three-dimensional configuration has to be considered, with potentials of probe

tip and sample surface which in general vary both spatially and temporally. The tunneling

itself is not a straight-forward and unidirectional process, but is a transition of electrons and

holes between tip and surface states, as the wavefunctions of tip and surface atoms partially

overlap.

This situation can theoretically be described by quantum mechanical perturbation theory:

The tip and the sample are first modeled as independent systems, and the tunneling process

then corresponds to a transition of a charge carrier from a certain state of one system into

a state of the other system [87, 89]. Considering tip states ψt

µwith energy Et

µand sample

states ψs

νwith energy Es

νto solve the time-dependent Schr¨odinger equation, respectively, and

regarding a tunneling voltage VTbeing applied to the surface, the tunneling current results

I=2πe

¯hX

µ,ν

f(Et

µ) [1 −f(Es

ν+eVT)] |Mµν|2δ(Et

µ−Es

ν),(3.4)

with the Fermi-distribution f(E) and the transition matrix element Mµν. Thereby the sum

extends over all possible tip and sample states, while the delta-distribution restricts the

current to elastic tunneling processes and the Fermi-distributions imply that tunneling can

only occur from occupied into empty states. At room temperature and typical energy ranges

of interest covering some eV, the Fermi-distribution comes close to a step function. When

additionally the sum over discrete energies is replaced by an integral over all states in the tip

and the sample, the tunneling current can approximately be written as

I=4πe

¯hZeVT

%s(EF−eVT+²)%t(EF+²)|M|2d² . (3.5)

Thereby %sand %tare the electronic density of states (DOS) of the sample surface and the

tip, respectively. The transition matrix element Mhas to be evaluated for all tip and sample

28 CHAPTER 3. SCANNING TUNNELING MICROSCOPY (STM)

states. For this, an approach based on Bardeen can be used, who parameterized it as an

integral over an arbitrary plane ~

Sbetween the two subsystems [289]:

Mµν =−¯h2

2mZ³ψt∗

µ∇ψs

ν−ψs

ν∇ψt∗

µ´·d~

S(3.6)

Therefore, the value of the matrix element is determined by the specific wave functions of

both tip and sample and especially by the interaction between these wave functions.

A widely used approximation of the matrix element and the tunneling current goes back

on the model of Tersoff and Hamann, developed shortly after the invention of STM [87, 278,

290]. In this model the tip is considered as a locally spherical potential well, including the

assumptions that the tip is geometrically and electronically isotropic and that its contribution

to the tunneling matrix element is dominated by wave functions with s-orbital shape. Under

these restrictions, which resemble the ideal STM tip, equation 3.5 transforms into

I∝%tZeVT

%s, loc ³~

R, EF+²´d² . (3.7)

The term %s, loc (~

R, E) means the local density of states (LDOS) of the sample surface for

a certain energy Eat the position ~

Rof the topmost atom of the probe tip, whereas the

tip DOS %tis considered as constant. An exponential dependence of the current on the

tip-sample distance is not directly evident in formula 3.7 any more, but it is still valid, at

least approximately, as the sample LDOS typically decays exponentially in the vacuum. The

tunneling voltage influences the current as upper limit of the energy integral.

It should be noticed that hardly any STM tip satisfies the assumption of an isotropic,

locally and temporally invariant DOS, being necessary to obtain the expression 3.7. Instead,

real STM images are very often affected by the tip geometry and changes of the geometric and

electronic structure of the tip. The influence of different tip wave functions on the tunneling

current and the STM images was studied by Chen [89, 291], including sand different pand d

wave functions. He showed theoretically that for some surfaces the experimentally observed

resolution and atomic corrugation amplitude can only be reached by STM tips with specific

wave functions of higher angular momentum l.

Nevertheless, Eq. 3.7, called the Tersoff-Hamann approximation, is the most general and

simple expression of the tunneling current, interpreting it as an energy integral over the

sample LDOS at the position of the tip.

3.2 Operation modes of STM

STM can be performed in different ways, leading to real-space images of the sample surface

containing different kind of information. Scanning tunneling spectroscopy can contribute

additional electronic details, either for specific points or also in combination with a whole

STM image. Those of the possible operation modes which have been used for this work will

shortly be introduced in the following.

3.2.1 Constant current mode of STM

The most common way to obtain STM images is the constant current mode: When the tip

is scanned over the sample surface, the resulting tunneling current is permanently measured

by a control electronic, which compares it with a given reference value. A feedback loop

adjusts the tip-sample distance by controlling the voltage of the z-piezo actuator so that the

tunneling current is kept constant. This method has already been sketched in Fig. 3.1. A

3.2. OPERATION MODES OF STM 29

stable, fast, and sensitive performance of this feedback loop is crucial for obtaining STM

images in a reasonable time without damaging the tip or the sample surface.

Typical STM currents are about 50 pA to 100 pA for semiconductor samples and up

to several nA for metals. The tip-sample distance depends on the chosen combination of

tunneling voltage and reference current and is typically in the range of 1 nm. As a role of

thumb, decreasing the tip-sample distance about 1 ˚

A (1 ˚

Angstrøm = 0.1 nm) increases the

tunneling current by a factor of ten.

As the current is intended to be kept constant, the actual STM signal in this opera-

tion mode is the height adjustment of the tip above the surface. This signal could easily

be understood as the direct topography of the sample surface, but that would be strongly

simplified. Regarding the STM theory and the Tersoff-Hamann approximation (Eq. 3.7), the

contour lines of the STM measurement or the areas of the same color in a grayscale or color

picture represent areas of the same integrated LDOS of the sample at the position of the tip,

evaluated for the energy integral from E=EFto E=EF+eVT.

Thereby electronic states with larger energies contribute stronger to the integral than

states with smaller energies, as depicted in Fig. 3.3 for both polarities of the tunneling voltage:

The decay of the sample LDOS into the vacuum barrier can in first order be approximated

as exponentially with an energy dependence given by Eqs. 3.3 and 3.2. Accordingly, states

with energies near the vacuum potential decay comparatively slow and contribute stronger

to the tunneling current than states with small energies [287].

3.2.2 Tip-induced band bending

Although STM is a non-destructive method, meaning that ideally the sample surface is exactly

the same before and after being scanned by the tip, it is important to notice that nevertheless

the tip can significantly influence the STM images by the effect of tip-induced band bending

(TIBB) [107, 134–137, 292, 293].

The tunneling regime of a metal tip in close proximity to the semiconductor sample sur-

face, separated by the vacuum barrier, can be described as a metal–insulator–semiconductor

junction, which – in the planar case – is well understood and described in appropriate text-

books (see [294, 295] for example). The exact band alignment of this junction is determined

tip tip tipsample sample sample

EFEF

E +eV

F T

E -eV

F T

Evac

(a) (b) (c)

Figure 3.3: Tunneling between the tip (with work function φt) and the sample (with work function

φs) through the vacuum barrier. An arbitrary sample LDOS is sketched with empty (yellow) and

filled (green) states. The tunneling probabilities are indicated by black arrows (a) without applied

voltage, where no tunneling current results, (b) for a positive sample voltage, and (c) for a negative

sample voltage. Adapted from [287].

30 CHAPTER 3. SCANNING TUNNELING MICROSCOPY (STM)

by the Fermi energies of tip and sample, the metal work function, the electron affinity and

the doping of the semiconductor, and by the gap width [see Fig. 3.4(a)].

When a tunneling voltage is applied to the sample, the resulting electric field between the

sample and the tip will induce a bending of the bands [Fig. 3.4(b-d)]. Such a bending can

also occur without an applied voltage [Fig. 3.4(a)], when a strong doping or surface states of

the sample cause additional charges at the surface, which will also induce an electric field, or

just because of the band alignment due to the electron affinity [134, 296]. The electric fields

are shielded both in the tip and the sample by space charges. In the metal, the high density

of free electrons leads to a shielding of the fields within about 1 ˚

A, so that the effect of band

bending is negligable within the tip. In the semiconductor, however, the lateral extension of

the space charge region depends on the available number of free charge carriers [296]: Strongly

doped samples have a very small space charge region, while for intrinsic and very pure regions

of semiconductors TIBB can even extend over several hundred nm. The band bending can

easily amount to several eV for GaAs already at moderate tunneling voltages [107, 297],

and especially in very pure samples a dominant influence of TIBB has been observed [298].

Additionally, the amount of TIBB depends on the width of the vacuum barrier, being the

tip

tip tip

tip

sample

sample sample

sample

EFEF

ECB

ECB ECB

ECB

EVB

EVB EVB

EVB

E +eV

F T

E +eV

F T

E +eV

F T

E +eV

F T

Evac

(a)

(b)

(d) (e)

depletion

nobias

accumulation accumulation

inversion

V >0V

V <0V

(c)

Figure 3.4: Schematic overview on typical regimes of tip-induced band bending at an n-type semi-

conductor: (a) No voltage applied, the band bending is determined by the tip work function φt, the

sample electron affinity χs, the doping concentration, and the width of the vacuum barrier. No tunnel-

ing current is obtained. (b) Moderate positive sample voltage, the sample CB is depleted of electrons

and tunneling into this CB occurs. (c) Large positive sample voltage, in spite of the n-type doping of

the sample there are empty states in the VB at the surface (inversion), leading to additional tunneling.

(d,e) Negative sample voltage, the CB is accumulated with electrons near the sample surface, leading

to tunneling into the tip. (e) For larger negative sample voltages, also tunneling from the sample VB

into the tip occurs.

3.2. OPERATION MODES OF STM 31

tip-sample distance [134, 135].

As a consequence of TIBB, a tip-induced accumulation of electrons has been observed at

the sample surface directly underneath the tip, leading to the formation of a two-dimensional

electron gas [299] or even of so-called tip-induced QDs with zero-dimensional confinement

of the accumulated electrons [136]. As the band bending is induced by the STM tip, the

geometry of the tip strongly influences the lateral and spatial extension of the space charge

zone in the sample [135, 299].

Depending on the polarity and amount of the applied tunneling voltage, different typical

regimes of TIBB are occuring, which are labeled in literature with respect to the used type

of doping, defining the majority charge carriers in the sample [107, 297]. Figure 3.4 sketches

these regimes for a moderately n-doped sample, with electrons being the majority charge

carriers: With no applied voltage, or for small positive and very small negative sample

voltages, both the conduction band (CB) edge and valence band (VB) edge of the sample are

bend upwards, so at the surface the CB is depleted of electrons. As additionally the Fermi

energies of tip and sample are equal while no external bias is applied and are lying within

the band gap of the sample, no tunneling current occurs (a).

The term depletion is also used to describe the situation at moderate positive sample

bias, where the sample CB edge is below the Fermi energy of the tip and electrons can tunnel

from the tip into the empty states of the sample (b). At large positive voltages also inversion

may take place, meaning that the sample VB edge is shifted above EF, and holes as minority

charge carriers contribute to the tunneling current from the sample into the tip (c). However,

it is still under discussion whether inversion actually occurs at GaAs or not [297].

A downward band bending is yielded with negative sample voltages (d): At moderate

negative voltages the CB edge is shifted below EF, resulting in an accumulation of electrons

in the CB at the surface which can tunnel into the tip. For larger negative voltages (e) the

Fermi energy of the tip is below the sample VB edge, and additional tunneling from filled

VB states of the sample into empty states of the tip can occur. Such a tunneling from the

sample VB for strong accumulation can also occur if the Fermi energy of the tip is still slightly

above the VB edge, as in this case the electrons can additionally tunnel through the thin

space charge region, leading to a correspondingly decreased current. The same argument is

valid, too, for electron tunneling from the tip through the vacuum and through the thin space

charge region into the CB at strong depletion.

3.2.3 Voltage-dependent imaging

As STM images represent the integrated LDOS of the sample at the tip, the applied tunneling

voltage determines the energy range over which the integration is performed. This can have

significant influence on the information stored in the images. As a general consequence,

the energy range of the integral gets larger with increasing tunneling voltage, so that the

reference current is reached for larger tip-sample distances. At such large distances, the

sample LDOS will be less distinctive and corrugated, as early calculations of Tersoff et al.

have shown [87, 290], displayed in Fig. 3.5(a). Thus, good atomic resolution can easier be

achieved at lower voltages, although then the stability of the tunneling current often reduces

as electronic effects gain in importance. Especially at STM studies on semiconductors care

has to be taken when applying very low voltages, as obviously no or only very weak tunneling

can occur within the bandgap, easily leading to a tip crash.

Beside the amount of the tunneling voltage, its polarity is of even larger significance,

especially at semiconductors with a pronounced band structure. Depending on the tunneling

polarity, either the filled or the empty states of the sample LDOS get imaged, as is sketched in

Fig. 3.3(b,c). Feenstra et al. have impressively shown that for III-V semiconductors like GaAs

32 CHAPTER 3. SCANNING TUNNELING MICROSCOPY (STM)

distance[Å]

3Å

[001]

[1 0]1

(a) (b)

(d)

(c)

Figure 3.5: (a) Calculated LDOS of an Au(110) surface with (2x1) reconstruction, shown in the (1¯

10)

plane, from [87]. Positions of the Au nuclei are indicated by solid circles (in plane) and squares (out

of plane). Contour lines of constant LDOS are plotted and labeled in units of a.u.−3eV−1. (b,c) STM

images of a GaAs (110) surface, aquired at sample voltages of (b) VT= + 1.9 V, representing the

Ga atoms, and (c) VT= - 1.9 V, representing the As atoms. (d) A sketch of the GaAs (110) surface,

containing both Ga (closed circles) and As atoms (open circles). The corresponding surface unit cell

is also indicated in (b) and (c). Taken from [106].

the empty states are attributed to the group-III atoms and the filled states to the group-V

atoms, so that either the Ga or the As atoms are seen in the STM images, depending on the

bias polarity [106, 300]. The corresponding images are shown in Fig. 3.5(b-d), together with

a sketch of the GaAs(110) surface and its unit cell.

In accordance with these and most other STM publications, in the following tunneling

voltages will be designated regarding the sample, so a negative VTmeans that the sample is

negatively biased in respect to the tip, and vice versa.

3.2.4 Scanning tunneling spectroscopy images

While by decreasing the tunneling voltage the energy range of the LDOS integration can

be limited, it is yet not possible to study the sample surface at one specific energy. A very

elegant way to enable this is by using scanning tunneling spectroscopy (STS), meaning a

continuous variation of the tunneling voltage.

Starting from STM theory and the Tersoff-Hamann approximation of the tunneling cur-

rent (Eq. 3.7)

I∝%tZeVT

%s, loc ³~

R, EF+²´d² ,

the integration of the LDOS over a certain energy range can be avoided if the tunneling

current is differentiated in respect to the voltage:

dV ∝%t·%s, loc ³~

R, EF+²´.(3.8)

Thus the differential conductance dI/dV has to be obtained to directly study the LDOS

of the sample at the position of the tip for a certain energy EF+eVT, so the variation of the

tunneling current with varying bias voltage needs to be measured. This can experimentally

be realized by using a lock-in amplifier: The given tunneling voltage is slightly modulated

and the variation of the tunneling current per voltage modulation can then be measured.

3.2. OPERATION MODES OF STM 33

Thereby the modulation amplitude and frequency have to be chosen in such a way that they

do not interfere with the feedback loop of the STM. Then the conventional constant current

STM image can be taken at the average tunneling voltage, and additionally the dI/dV -signal

is obtained for every image pixel. As a result, two images are aquired simultaneously, namely

the constant current STM image, often called topographic image, and an additional dI/dV -

image, in the following called STS image. The first one represents the sample LDOS for

energies integrated up to the tunneling voltage, while the latter shows the sample LDOS

directly at the energy corresponding to the tunneling voltage.

In a further step, the tunneling voltage can not only be slightly modulated but strongly

varied at each pixel of the image: Using this method, called current imaging tunneling spec-

troscopy (CITS), a common STM image is aquired in the constant current mode at a certain

voltage, but at each pixel the feedback loop is opened, the voltage is ramped from the initial

stabilization value over a large voltage range, and at various specific voltages during this

ramp the corresponding current is measured. Thus, a data cube containing several images

of tunneling currents at specific voltages is obtained within one scan. Due to the applied

voltage ramp special care has to be taken to perform the measurement slowly enough to

avoid decaying capacitive currents during data aquisition and fast enough to keep the time

per image within reasonable limits.

The CITS method has first been developed to investigate different surface states of a

Si(111) sample [285, 286]. But it is even more useful to study confined states of QDs, as it

is possible to stabilize the tunneling feedback at sufficiently large voltages and at the same

time studying the QDs at energies which lie within the band gap of the host material. In

this way Grandidier et al. were able to distinguish between s- and p-like states of cleaved

InAs/GaAs QDs from CITS images at different voltages [108]. Maltezopoulos et al. used

the CITS method in combination with lock-in technique and obtained not only current but

also dI/dV -images at various voltages, mapping the wave functions of single electrons in

free-standing InAs QDs [110].

3.2.5 STS point spectra

Besides the possibility to aquire different kinds of images of two-dimensional sample surfaces

at certain voltages, STS also enables one to obtain continuous tunneling spectra over the

complete voltage range at specific positions on the surface, preferentially at points of special

interest.

By varying the tunneling voltage and at the same time measuring the resulting current,

local I–V-spectra can be taken, showing directly the dependence of the tunneling current on

the applied voltage. By using the lock-in technique described above, also dI/dV –V-spectra

can simultaneously be obtained.

Typical I–V- and dI/dV –V-spectra of GaAs are shown in Fig. 3.6, obtained by Feenstra

et al. [107, 301, 302]. The intrinsic GaAs band gap can clearly be recognized as voltage

region for which no tunneling current results, provided that no additional states, induced

for example by dopant atoms, are present at the surface [Fig. 3.6(a)]. The more voltage is

applied to the sample of either positive or negative polarity, the larger the tunneling current

gets, as more states contribute to the energy integral of the current. Although the onsets of

the valence band and conduction band are evident, the energy distance between them does

not agree with the literature value of 1.4 eV. Generally, in I–V- and dI/dV –V-spectra the

absolute energies especially of the band edges are often shifted due to TIBB, while the slope

and characteristic peaks of individual bands of the sample’s LDOS and also the energetic

distances between distinct features within one band are well resembled [107, 134, 135].

If the local area of the GaAs sample contains dopant atoms, the Fermi energy is shifted

34 CHAPTER 3. SCANNING TUNNELING MICROSCOPY (STM)

towards the VB or CB edge and the apparent band gap in the spectra is decreased, as an

additional small conductivity is implied. Figure 3.6(b,c) shows this additional contribution of

dopant-induced states for (b) p-type and (c) n-type doping, respectively, which can only be

understood considering the effect of TIBB [107, 297, 301]: In the case of p-type doping, the

Fermi energy is near or within the VB of the sample, and the holes are the majority charge

carriers. At negative sample voltages electron tunneling out of the VB occurs (which can

equally be described as hole tunneling into the depleted VB), but the corresponding curve

in the spectra (b) is shifted towards positive voltages with respect to the intrinsic case (a)

due to the shifted Fermi energy. For larger positive voltages electrons can tunnel into the

CB, resulting in a strong current, but already at low positive voltages an additional small

current can be observed, which is a doping-induced contribution: In this voltage regime TIBB

leads to an accumulation of holes in the VB at the sample surface, leading to small electron

tunneling into the VB (or hole tunneling out of the accumulated VB).

In the case of n-type doping, the Fermi energy is near or within the CB, and electrons are

the majority charge carriers [Fig. 3.6(c)]. Correspondingly, the I–V-curves corresponding to

electron tunneling out of the VB and into the CB are shifted towards negative voltages, and a

doping-induced contribution of the tunneling current occurs for small negative voltages. This

dopand component can be explained as tunneling of accumulated electrons from the CB of

the sample due to TIBB (see also Fig. 3.4 for illustration). In the insets of Fig. 3.6(b,c) the

samplevoltage[V]

samplevoltage[V]=E-E [eV]

(dI/dV)/( )I/V

samplevoltage[V]=E-E [eV]

(dI/dV)/( )I/V

logI [1decade/div]

norm

samplevoltage[V]

current[nA]

iii

(a) (b) (c) (d)

(e) (f)

Figure 3.6: STS point spectra on GaAs(110): (a-c) I–V-spectra of GaAs pn-diode structures,

plotted using a logarithmic I scale, aquired at (a) the depleted interface region, (b) a p-doped layer,

and (c) an n-doped layer; from [301]. The insets of (b,c) sketch the tunneling from and into CB,

VB, and dopant-induced states, respectively. (d) I–V-spectra of one p-doped GaAs layer, while the

tip-sample distance is decreased by (ii) 1.2 ˚

A, (iii) 3.2 ˚

A, and (iv) 4.8 ˚

A; from [107]. (e,f) Spectra of

the normalized differential conductance over the tunneling voltage for (e) p-doped and (f) n-doped

GaAs; from [302].

3.3. CROSS-SECTIONAL STM 35

respective electron tunneling into CB and acceptor states and out of VB and donator states

is depicted for p- and n-doped GaAs.

As the tunneling current is determined not only by the tunneling voltage, but varying also

exponentially by the tip-sample distance, the slope of the I–V-spectra strongly depends on

this distance, too. In Fig. 3.6(d) several I–V-spectra of the same GaAs layer are shown, taken

at different tip-sample distances. This time the current is plotted on a linear scale. Besides

the obvious increase of the current with decreasing distance, it should also be mentioned that

a doping-induced contribution to the tunneling current can only be seen for small tip-sample

distances, as in this case the effect of TIBB is stronger.

The measurement of the current is technically limited to a few orders of magnitude, be-

cause too large currents would destroy the tip or sample and too small currents cannot be

resolved. Thus, only a small range of the actual I–V-characteristic can be obtained experi-

mentally with one spectrum, especially for semiconductors with a considerable band gap.

This limitation can be overcome by performing STS point spectra using the variable gap

mode, first introduced by Feenstra et al. [278, 303, 304]: In this mode, the tip-sample distance

is changed as a function of the applied tunneling voltage. During the voltage ramp of the

spectrum, the distance is decreased while the absolute value of the voltage is decreased, and

increased again when the absolute value of the voltage is increased at the other polarity.

Afterwards, the measured current has to be normalized by a function which includes the

dependence on the distance. By this method, the dynamic range of the spectra can be

increased by several orders of magnitude [302].

As described above, the dI/dV -signal is better suited to describe the sample LDOS

than the tunneling current itself, therefore in many studies using STS point spectra also

dI/dV –V-spectra are obtained, either by numerically differentiating the measured tunneling

current, or by directly measuring the differential conductance by lock-in technique. These

data, too, are influenced by the tip-sample distance, especially in the variable gap mode. A

very elegant way to normalize the measured differential conductance is by dividing it through

the absolute conductance, which eliminates the dependence on the distance. Additionally,

this (dI/dV )/(I/V )-signal has been shown to directly represent a normalized sample LDOS,

independent of the distance of the tip [105, 305, 306]. One modification has to be added

for spectroscopic studies on semiconductors with a considerable band gap like GaAs: For

such systems, the normalized conductivity diverges at the band edges for a division by (I/V )

because the current approaches zero faster than the conductivity. To avoid this divergence, a

broadened conductivity can be used for normalizing the differential conductance, resulting in

a signal (dI/dV )/(I/V) [302]. Several methods for such a broadening are proposed and used

in literature [278, 303, 307, 308]. Figures 3.6(e,f) show examples of (dI/dV )/(I/V)–V-spectra

of p- and n-doped GaAs, respectively [302]. In this spectra it can well be distinguished be-

tween intrinsic and dopant-induced tunneling, and the VB edge and CB edge can clearly be

labeled.

3.3 Cross-sectional STM

STM imaging of semiconductor nanostructures is in most cases performed in a top view

configuration, meaning that QDs are typically imaged at the (001) growth surface (see for

example Refs. [19, 24, 29, 31, 32, 35, 91, 96, 109, 198, 309, 310]). Thereby only free-standing

QDs or the initial stages of overgrowth can be investigated, but the structure of capped QDs,

which are of much higher relevance for almost all kinds of applications, remains hidden.

This important information can be obtained when STM is performed in a cross-sectional

configuration instead: In cross-sectional STM (XSTM) the sample is cleaved, and the cleavage

36 CHAPTER 3. SCANNING TUNNELING MICROSCOPY (STM)

cap

layer

~1-3µm

substrate

layersofinterest

STMtip

~200µm

[001]

[ 10]1

[110]

topview

STM XSTM

growth

surface

cleavage

surface

STMtip

Figure 3.7: Comparison of STM in the conventional top-view configuration with cross-sectional

STM, imaging a QD on the growth surface (top-view STM) or an overgrown QD (XSTM).

surface is scanned with the STM tip. In the case of QD investigations, the nanostructures

can be completely capped during the initial growth, as it is done for optoelectronic or other

applications, and the overgrown QDs are studied in cross section. This STM situation,

compared with a conventional top view configuration, is shown schematically in Fig. 3.7. An

additional benefit of XSTM is that the sample is typically cleaved in ultrahigh vacuum (UHV),

yielding a clean and fresh investigated surface, indepedent of the history of the sample.

XSTM was first used to study semiconductor QDs, to my knowledge, by W. Wu and

J. R. Tucker at the University of Illinois in Urbana, USA, in 1997 [119]. Within the following

ten years, only a few scientific groups worldwide joined in this experimentally complex XSTM

investigation on QDs. Among these are (in chronological order of the earliest publications)

the groups of D. Sti´evenard at the Institut d’Electronique et de Micro´electronique du Nord

in Lille C´edex, France [108, 120, 311], of R. S. Goldman at the University of Michigan in

Ann Arbor, USA [94, 121, 312, 313], and the group of M. D¨ahne at the Berlin University of

Technology, Germany [92, 93, 100, 103, 122, 125, 127, 131], in which this work was realized;

further the groups of C. K. Shih at the University of Texas in Austin, USA [95, 123, 314],

of P. M. Koenraad at the University of Technology Eindhoven, The Netherlands [97, 126,

128, 130, 133, 277, 315–318], and just recently the groups of E. Lundgren at Lund University,

Sweden [129], A. Nakamura at Nagoya University, Japan [319], and W. W. Pai at the National

Taiwan University [320].

Like all STM data also XSTM images contain structural and electronic information on

the investigated sample. Remembering the tunneling current representing the integrated

sample LDOS at the position of the tip, the topography of the sample will most directly

influence the tip-sample distance and therewith the current, while the electronic properties

of the sample surface and their local variations are contained within the LDOS. Beside these

general considerations, there are also a structural and an electronic contrast mechanism

specific for XSTM studies on cleaved QDs.

3.3.1 Structural contrast

Surface steps, adatoms, and other structural features within the cleavage surface can directly

be observed in the XSTM images due to their structural image contrast. But even atomically

3.3. CROSS-SECTIONAL STM 37

flat cleavage surfaces will significantly contribute to the structural contrast if they contain a

cross section through a strained QD: Self-assembled QDs achieved by the SK growth mode

contain a lot of strain which is even increased upon capping (see also chapter 2.3). When

such a QD is cleaved during the XSTM experiment, it can release a part of the strain energy

by a structural relaxation at the cleavage surface, leading to a protrusion at the position of

the QD and its surrounding. Such a protrusion typically amounts to a few ˚

A in height at the

QD, declining laterally within several nm [92, 93, 124].

3.3.2 Electronic contrast

The structural contrast of cleaved QDs in XSTM images is often increased by an electronic

contrast, given by different band gaps and tunneling probabilities of chemically different

materials and by the electronic confinement in nanostructures. This is illustrated in Fig. 3.8

for bulk GaAs (a), bulk GaSb (b), and for a GaSb/GaAs QD (c): At a negative sample

voltage, which is considered in Fig. 3.8, the electronic states within the energy interval from

EFto EF+ eVT, which contribute to the tunnling current, stem from the VB for the bulk

material (a,b). The LDOS of the VB of bulk GaAs and GaSb increases in first approximation

with E1/2. Due to the smaller absolute band gap and the staggered type-II band alignment

of GaSb, the resulting tunneling probability is larger for GaSb than for GaAs, leading to a

retraction of the tip in constant current mode and to a brighter appearance. By this image

contrast not only pure GaAs and GaSb can clearly be distinguished in XSTM images, but

also intermixed GaAsSb material has its specific image contrast depending on the grade of

alloying.

In the case of nanostructures, the existence of confined states plays a special role also

for the image contrast: For GaSb QDs in GaAs, the GaSb electronic states have to satisfy

the boundary conditions of the spatial confinement and the band gap of the host material.

The resulting confined states, energetically placed above the position of the GaAs VB edge,

are characterized by a δ-like LDOS [Fig. 3.8(c)]. In constant current STM imaging, the

integrated LDOS of GaSb/GaAs nanostructures is similar to that of bulk GaSb, resulting in

a similar electronic contrast. Using STS, however, individual confined states can in principle

be distinguished in STS images or spectra [108, 110], provided that the energy separation

between the states is larger than the thermal broadening, which at room temperature is about

25 meV.

tip tip tip

GaAs GaSb GaSb

EFEFEF

ECB

ECB ECB

EVB EVB

EVB

(a) (b) (c)

E +eV

F T E +eV

F T

EEE

DOS DOS DOS

Figure 3.8: Electronic image contrast for (a) bulk GaAs, (b) bulk GaSb, and (c) a GaSb/GaAs QD.

Contributions to the tunneling current for small negative sample voltages are indicated by arrows.

38 CHAPTER 3. SCANNING TUNNELING MICROSCOPY (STM)

The differences regarding the band alignment, confined states, and the resulting LDOS

are dominant at energies near the Fermi energy, corresponding to small tunneling voltages.

Thus the electronic image contrast is of special significance at small tunneling voltages, as

in this case a large fraction of the energy integral contributing to the tunneling current is

affected. The structural image contrast, however, is given by the topography of the cleavage

surface and is therefore comparatively independent of the tunneling voltage. So by varying

the applied voltage in XSTM measurements it is possible to distinguish whether observed

features are of structural or electronic nature, making XSTM an additionally powerful tool

for studying capped nanostructures.

3.4 The zincblende (110) surface

Most III-V semiconductors, including GaAs, GaSb, and also InAs, crystallize in the zincblende

structure. It consists of two fcc sublattices of group-III and group-V atoms, being separated

from each other by a quarter of the diagonal of the cubic unit cell. The resulting structure

is sketched in Fig. 3.9(a), the cubic lattice is plotted with respect to the group-V atoms.

Zincblende crystals can nicely be cleaved in one of the {110}planes [see Fig. 3.9(b)],

because these planes are non-polar and contain the least density of unsaturated bonds, being

the energetically most favorable among all possible crystal planes. As a consequence, the

(110) surface has no reconstructions, meaning a rearrangement of atomic bonds, but shows

a relaxation, a shifting of the atomic positions. Additionally, no surface states consist within

the band gap of the bulk material for zincblende (110) surfaces, making them very suitable

for an electronic characterization of the underlying material by STS.

Relaxation leads to a so-called buckling of the GaAs(110) surface, affecting mainly the

atoms of the first surface layer and slightly those of the second layer, too [321–323]. It is

displayed for GaAs in Fig. 3.9(c): In the surface layer, the Ga atoms are shifted into and the

As atoms out of the crystal, resulting in a vertical height difference of about 0.7 ˚

A. The lateral

positions are also adjusted to maintain the Ga–As bond lengths. The complete relaxation

results in a projected angle of the surface layer Ga–As bond of 27◦to 30◦(see [324] and

references therein). Beside this geometric relaxation, the formation of double As dangling

bonds at the relaxed GaAs(110) surface instead of an equal distribution of single unsaturated

bonds at both the Ga and As atoms leads to a further energy reduction.

Looking at the GaAs(110) surface in top-view [Fig. 3.9(d)], atomic zig-zag-chains along

[1¯

10]-direction are the dominant feature, consisting of alternating Ga and As atoms. However,

in STM images only either the Ga or the As atoms can be seen, depending on the polarity,

as mentioned above [106, 300]. This effect is independent of the surface buckling, and it was

explained by the empty states being attributed to the Ga atoms and the filled states to the

As atoms. The exact distribution of electronic states to Ga and As atoms is very complex

(see for example Refs. [325, 326]). At least at sufficiently small voltages, however, the main

contribution to the tunneling current are – for the respective polarities – the empty dangling

bonds of the Ga atoms and the filled dangling bonds of the As atoms.

It is also important to note that in STM data on zincblende {110}surfaces only every

second atomic ML in the typical epitaxial growth direction is imaged: Regarding the [001]-

direction, the topmost Ga and As atoms are alternately situated either in the (110) surface

layer or in the second atomic layer, and at common STM conditions the imaging process

is restricted to the surface atoms. (For exceptions at extreme conditions like very small

tip-sample distances see for example [292, 327]).

A nearly perfect example image of a GaAs(110) surface can be seen in Fig. 3.9(e). It has

been imaged by XSTM with a negative sample voltage, so the LDOS corresponding to the

3.4. THE ZINCBLENDE (110) SURFACE 39

(110)

[001]

[010]

[100]

[1 0]1

[001]

[110]

5.653Å

3.998Å

[1 0]1

[001]

surface

unitcell

[110]

[001]

[ 10]1

(a) (b)

(c)

(d)

(e)

Gaatoms

Asatoms

Figure 3.9: Atomic model of the zincblende structure, showing (a) a cubic unit cell, (b) the

(110) cross section through this cell, and the (110) cleavage surface in (c) side-view and (d) top-view.

The radius of the circles displays the position of the corresponding atoms regarding the respective

line of sight. Buckling of the surface, with tilt angle ω, and the angles of the filled dangling bonds are

considered in (c), according to Refs. [324, 326]. (e) XSTM filled state image of GaAs, representing

the As atoms.

filled dangling bonds of the As atoms can be seen. The surface unit cell and the distances

between neighboring surface As atoms are indicated, amounting in [001]-direction to the

GaAs lattice constant a= 5.65 ˚

A and in [1¯

10]-direction to a/√2 = 4.00 ˚

A. These atomic

constants are perfectly suited to calibrate the XSTM images. Such a calibration is principally

necessary for each XSTM image, as perturbing effects like thermal drift, piezo non-linearity,

and others may vary with time or depending on the image parameters. Unfortunately atomic

40 CHAPTER 3. SCANNING TUNNELING MICROSCOPY (STM)

resolution is often given only within the [001]-direction, enabling one to determine the size

of the investigated structures in one direction, but leaving an uncertainty of typically 10%

to 20% regarding the exact shape. However, when atomic resolution is present in both

directions, the aquired images can be corrected by lengthening or shearing them according

to the measured angles and distances of the surface unit cell.

As mentioned above, the image contrast in STM images generally consists of a structural

and an electronic part. This can well be understood at the atomistic level, too: Obviously, a

surface step and also a protrusion of the surface at the position of a cleaved QD, producing

a structural contrast, will influence the position of each individual atom; and different bulk

electronic band structures of, for example, GaAs and GaSb correspond to different atomic

bond characteristics and electronic states. But also the smallest possible variation of the

sample, an exchange of a surface As atom by an Sb atom, varies the structural and electronic

image contrast: Due to the larger bond length of GaSb compared with GaAs, the Sb atom will

structurally slightly protrude out of the GaAs(110) surface, and also the dangling bond of a

single Sb atom is very different to those of the neighboring As atoms, leading to a distinctive

change of the sample LDOS. Imaging of single Sb atoms within the GaAs matrix will be

analyzed in more detail in chapter 9.1. Extensive studies on XSTM imaging of GaAs(110)

surfaces can be found for example in Refs. [327–330] for intrinsic GaAs and in [331–335] for

GaAs surfaces with single dopant atoms.

Chapter 4

Experimental setup

Two different home-built STM systems have been used for the XSTM studies of this work.

The principal setup of these chambers, including the use of ultrahigh vacuum (UHV), sample

preparation stages, data aquisition and processing, and the STM design, are shortly presented

in the following, while details on the mechanical and electronic setup of the STM chambers

can be found elsewhere [124, 336–339]. The procedures used until now for tip and sample

preparation will be introduced as well as an extensive future tip preparation stage. Finally

the process of sample cleaving and positioning the STM tip at the nanostructures will be

highlighted, together with some typical structural aspects of the cleavage surface.

4.1 The STM chambers

The MOCVD-grown GaSb/GaAs samples studied within this work were examined in a more

universal kind of STM system, being used for XSTM studies [92, 100, 124, 127, 221] as well as

for growth and top-view STM characterization [340, 341]. For the MBE-grown samples an-

other STM was used, which was directly designed for XSTM measurements on semiconductor

samples [103, 124, 131, 132, 338, 342]. Both STM setups equally consist of two coupled UHV

chambers, respectively, one of which contains the STM itself, while the other one can be used

for tip or additional sample preparation and storage. All chambers contain several pump

stages and pressure gauges and have especially be designed for the intended STM work.

4.1.1 UHV conditions

In order to keep and preserve atomically clean sample surfaces, excellent UHV conditions

are crucial: At a pressure of about 1 ×10−6mbar (1 mbar = 100 Pa), each atom of the

surface is on the average hit by one residual gas atom per second [295], so even at very good

UHV conditions of less than 1 ×10−10 mbar adsorbates could have reached the complete

surface within less than three hours. Fortunately the sticking probability of such residual gas

adsorbates on III-V semiconductor (110) surfaces is very low: The experiments described here

are typically carried out at pressures p <5×10−11 mbar, enabling good XSTM conditions

for about one to two weeks until the cleavage surface is significantly contaminated.

Such pressures are routinely reached by a combination of diaphragm, turbomolecular,

titanium sublimation, and ion getter pumps. The absence of water molecules is of special

importance, therefore the whole system has to be baked out at at least 100◦C for several

days after venting. In order to avoid mechanical vibrations as well as Ti contamination of the

sample, only ion getter pumps are used to maintain the UHV during STM measurements.

42 CHAPTER 4. EXPERIMENTAL SETUP

4.1.2 The universal STM chamber

The more universal STM system was developed in 1995 by T. Kalka [337] and further en-

hanced in several steps later on by C. Preinesberger [336], H. Eisele [124], and S. Becker [343].

The STM unit itself is suspended by soft springs in the STM chamber, mechanically isolat-

ing it from the surrounding, whereupon vibrations are additionally reduced by eddy current

damping. Twelve backup tips can be stored within the STM chamber, as it is necessary to

exchange damaged or insufficient tips from time to time during the experiment. A prepa-

ration stage for heating the tips by electron bombardment under an applied electrical field

(as described in section 4.2.1) is included. Five samples can be stored in the preparation

chamber, attached by a UHV valve, where they are cleaved and transferred into the STM

using a magnetic transfer.

A challenge of STM instrumentation is to exactly position and move the tip in close

proximity to the sample surface, combined with a desired large range of motion. These

requirements of a coarse movement including the tip-sample approach as well as the scan

movement of the tip are here fulfilled by a walker unit carrying the scanning tip, shown in

Fig. 4.1(a) together with the sample. This walker unit consists of a copper block, mounted

on three crossed pairs of shear piezos with sapphire balls underneath. It stands on a polished

steel plate and moves as a slick-and-slide motor when a saw tooth voltage is applied to the

shear piezos. Inside the copper block a sectorized tube piezo is mounted, carrying a magnet

which holds the STM tip, isolated by a thin glass and contacted by a gold platelet. The

xy scan movement of the tip can be accomplished by applying a high voltage to specific

sectors of the tube piezo, bending it into the respective direction, while the zpositioning of

the tip is obtained by compressing or extending the piezo tube.

The bias voltage is applied to the sample, while the tunneling current is measured at

the tip. An in-situ preamplifier, which converts the tunneling current into a voltage by

a factor 108VA−1, is situated directly above the STM unit, minimizing electronic pickup.

The completely home-built control unit of the STM consists of three parts, including the

main control electronics, a high-voltage amplifier supplying the scan piezo, and another high-

voltage unit which controls the approach of the walker. All three parts are addressed by

STMtip

sample

holder

shear

piezos

copper

walker

containing

tubepiezo

(a) (b)

Figure 4.1: (a) The STM unit: A copper walker, standing on pairs of shear piezos on top of a steel

ball, contains a tube piezo which holds the tip at its end by a magnet, opposite to the sample screwed

on the sample holder. (b) The STM tip near the cleavage surface (gleaming brightly orange) of the

sample (with the growth surface appearing dark), photographed through the optical microscope.

4.1. THE STM CHAMBERS 43

a personal computer. A non-commercial software, written by M. D¨ahne and T. Kalka, is

used [344], controlling STM operation and enabling STS images and point spectra. Image

processing was performed employing another home-built software, written by S. Becker [345].

Before the STM imaging can be performed and governed by the feedback electronic and

the software using the constant current mode, the tunneling contact has to be established by

bringing the tip and the sample together very closely without touching each other. The last

few µm of this approach can be performed automatically by repeatedly moving the whole

walker and stretching the scan tube piezo until a tunneling current is measured. As this

procedure is rather slow, for a fast initial positioning of the tip opposite the sample cleavage

surface, including the lateral adjustment, the slick-and-slide motor of the walker is controlled

manually. This is enabled by an ex-situ optical microscope with long working distance (Leica

M 420 with apozoom 1:6 lens), allowing an optical access to the cleavage surface and the

walking STM tip. A view through the optical microscope is shown in Fig. 4.1(b), where

(from right to left) a sample with the cleavage surface and the tip mounted to a tip holder

can be seen.

4.1.3 The XSTM/XSTS chamber

To improve and facilitate the experimental conditions for XSTM studies, a new system was

built in 2001 by H. Eisele [124], with additional contributions from M. Ternes [338], Ch. Hen-

nig [346], A. Lenz [347], L. Ivanova [348], J. Grabowski [349], F. Streicher [350], and in the

frame of this work. While the principal setup of the STM system is similar to that of the

universal STM chamber described above, many details are optimized for specific needs of

XSTM and XSTS experiments.

An overview image of the XSTM system can be seen in Fig. 4.2. The STM unit itself is

ion

pressure

gauge wobblestickfor

tipandsample

coarsepositioning

load-lock

forfasttip

andsample

exchange

tippreparationand

storagechamber

optical

microscope

(open)flange

forSTMunit

valvebetween

bothchambers

UHVpumps

control

electronics

Figure 4.2: Look from above on the XSTM chamber (the STM unit itself is temporarily taken out)

and the attached preparation chamber.

44 CHAPTER 4. EXPERIMENTAL SETUP

located centrally within the larger STM chamber, enabling a more direct and ample access,

both optically by the external microscope (also a Leica M 420 with apozoom 1:6 lens) and

mechanically by a wobble stick used for tip and sample exchange. Five backup tips can be

stored within the STM chamber, while an additional storage for 32 tips and the tip heating

stage are located within the preparation chamber, enabling the preparation of fresh tips

without polluting the vacuum in the STM chamber. Four samples can also be stored in the

preparation chamber. Additionally, tips and samples can be exchanged via a loadlock coupled

to the preparation chamber without destroying the vacuum.

The STM unit, shown in Fig. 4.3, is suspended at the STM flange of the chamber by

springs. It is designed as a very stiff and compact unit, which in combination with rather

soft springs results in a high stability against external vibrations, assisted by eddie current

damping. In this setup, three crossed piezo pairs with steel balls glued on top are mounted

firmly to the STM unit. The sample holder made of copper lies on top of these balls,

completing the inertial walker, which enables the coarse positioning and tip-sample approach

by a slick-and-slide motor. A sectorized tube piezo carrying the tip and performing the scan

movement is mounted directly on the STM unit. The tunneling current is measured at the

tip and converted into a voltage by an in-situ amplifier mounted to the STM unit with a

factor of 108VA−1, while the bias voltage is applied to the sample via contacts at the steel

balls of the walker.

A commercial SPM 1000 Control System from RHK Technology was used, consisting of an

SPM 100 Rev. 8 control electronic and the associated SPM 32 software, which was recently

exchanged by the Windows-based XPMProTM software, running on a personal computer.

All STM imaging and STS spectroscopy were performed by this control system, whereas

an additional home-built high-voltage amplifier was used to actuate the walker for coarse

positioning and approach of the sample. For an improved control of this approach by hand

using the optical microscope, two mirrors have been attached to the STM unit, enabling

an optical access of the tip-sample system from different perspectives. Besides the RHK

software, also the WSXM freeware tool [351] was used for image processing.

mirrorsfor

opticalapproach goldplateletontubepiezo

STMtip

sample

sampleholder

(a)

(b)

Figure 4.3: Pho-

tographs of (a) the

compact and stiff

XSTM unit, which

contains, magnified

in (b), the sample

holder standing on

shear piezos and the

tip held on a tube

piezo by magnets.

4.2. THE XSTM EXPERIMENT 45

4.2 The XSTM experiment

Although the XSTM measurements themselves are rather challenging, implying high re-

quirements on the accuracy of electronic and mechanical components as well as the UHV

conditions, and also time consuming, the preparation steps necessary for setting up new tips

and samples are comparatively straightforward.

A short overview of the preparation steps for tips and samples used here is presented

in the following, while more detailed descriptions of this procedure [339] or of STM tip

preparation in general [352–354] can be found elsewhere. The aim of sample preparation

(besides contacting it) is to receive a good cleavage surface. The cleavage process, forming

the basis of any XSTM experiment, and the remaining steps until finally the nanostructures

can be imaged with STM are outlined in the last part of this section.

4.2.1 Tip preparation

The quality of the probe tip is crucial for all STM experiments, therefore care has to be

taken in the preparation of the tips. At flat surfaces also rather blunt or irregularly shaped

tips can lead to good atomic resolution due to the strong exponential dependence of the

tunneling current on the tip-sample distance. But as the partly relaxed QDs protrude out of

the cleavage surface and strongly influence the local electronic properties, well defined tips

with a sufficiently small radius of curvature are necessary to resolve the nanostructures and

to avoid multiple tip effects. Additionally, STM tips generally need to be mechanically stable,

though easy to prepare, chemically inert at the experimental conditions, conductive with a

possibly uniform DOS around the Fermi energy, and made of material of an affordable price.

Forming a good compromise between these requirements, electrochemically etched W tips

are used here, prepared as follows: Starting with a 0.25 mm thick polycrystalline tungsten

filament, this wire is firstly annealed under nitrogen atmosphere to heal possible defects and

cleaned with isopropanol before it gets etched. Using sodium hydroxide at a concentration of

10% as electrolyte, a voltage is applied between the tungsten wire and a steel cathode, so that

the tungsten gets oxidized [355]. The porous tungsten oxide (WO4) drops down, shielding

the lower part of the wire and enhancing the etching process close to the interface between

electrolyte and air, which forms a meniscus around the wire. Finally, the bottom part of the

intersected wire falls down, leaving a sharp, tapered end at the opposite part of the wire.

Now the etching current has to be stopped immediately by a fast electronic, as otherwise this

sharp end would get blunt again [352, 356]. Evenly tapered W tips with a radius of curvature

of much less than a µm can routinely be obtained by this procedure. A typical tip can be

seen in the scanning electron microscopy (SEM) images of Fig. 4.4, obtained using a JEOL

JSM-5410 SEM.

(a) (b) (c)

50µm 10µm 200nm

Figure 4.4: Scanning electron micrographs of an etched W tip for STM: (a) The initial tungsten

wire and the tapered tip, (b) the sharp end of the tip, and (c) at large magnification the oxide layer

and some contamination around the sharp tip can be seen.

46 CHAPTER 4. EXPERIMENTAL SETUP

As a result of the etching process, a several nm thick oxide layer is covering the sharp

tip [Fig. 4.4(c)], which would severely obstruct a stable tunneling current. Therefore the

tips are heated in-situ prior to the STM experiment by electron bombardment, removing the

predominant part of the oxide [89, 357]. This is achieved by placing the tip opposite to a

W filament within UHV (in the STM or the preparation chamber), applying a high voltage

of about 350 V between the negatively biased filament and the tip, and increasing a heating

current through the filament until an emission current to the tip in the range of 1 mA is

established, which then lasts for some minutes.

4.2.2 Outlook: Improved tip preparation and characterization

Within STM imaging, sudden changes in the appearance of the surface or the nanostructures

or in the resolution occur from time to time. Such phenomena are rather common for STM

experiments [358] and also occured in the measurements described here. They can be ex-

plained by small structural changes of the tip geometry [359] which can significantly influence

the electronic states of the tip like localized surface states [291].

Although the used STM tips have a macroscopically sharply tapered shape, at their very

end they usually consist of several microtips, being separated by several nm [358]. Usually

the strong dependence of the tunneling current on the tip-sample distance selects only one of

these microtips, but small local structural or electronic changes of one of the microtips can

alter this choice, leading to a strongly different appearance of the STM image, as shown in

Fig. 4.5. Changes of the electronic properties of the tip are hardly to avoid upon tunneling

spectroscopy, when the voltage applied to the tip is repeatedly changed over a large range,

sometimes also at high frequency.

To overcome these obstructions and increase the structural and electronic tip quality and

reliability, an additional UHV chamber containing a strongly improved tip preparation stage

was designed for the XSTM chamber and is currently under construction. It combines the

preparative step of ion sputtering with characterization possibilities by measuring the field

[1 0]1

[001]

tipchanges GaSblayer

10nm

Figure 4.5: STM filled state image

of a GaSb layer in GaAs. Due to

several changes of the tip, the layer

seems to jump and change its appear-

ance. Repeating the image, it was

proven that those apparent structural

changes are not real.

emission current or taking field ion microscopy images. A

short introduction into these methods and a description

of the new chamber are given in appendix A. By using

this enhanced preparation stage very sharp and defined

tips will be created which can then be transferred into

the STM without breaking the UHV.

4.2.3 Sample preparation

The samples studied in this work have been grown on

industrial GaAs(001) 2 inch wafers, or on fragments of

those, with a typical thickness of 400 to 550 µm. Sam-

ples of such rather large thicknesses are difficult to cleave,

often resulting in many large steps on the cleavage sur-

face or completely irregular cleaves. Therefore they are

thinned mechanically to about 150 to 200 µm, which

has turned out to be sufficiently thin for good cleavage,

though still thick enough to prevent too frequent dam-

ages during preparation and handling.

The thinned samples are cut to pieces of about 4 mm

×5 mm with edges along the [110]- and [1¯

10]-directions

and are provided with a notch of 1 to 2 mm length

4.2. THE XSTM EXPERIMENT 47

along [1¯

10] for (110) cleavage planes or along [110] for (¯

110) cleavage planes: Starting from

the position of this notch, the cleavage of the sample will take place later on. After cutting,

the samples are glued on small copper plates and contacted with indium, enabling an Ohmic

back contact of the sample. The copper plates can then be screwed into the sample holder

in such a way that a part of the sample including the notch is protruding.

As the surface investigated by STM will be created upon cleaving within UHV, no elab-

orate cleaning of the samples is necessary. Nevertheless, when the samples are transferred

into the UHV chamber through a loadlock, they should get outgased by heating the loadlock

for several hours, as otherwise the fresh cleavage surface will get contaminated by mobile

adsorbates from the sample surface or the sample holder.

4.2.4 Sample cleavage and finding the nanostructures

When the designated sample and enough tips are readily prepared and the base pressure of

the STM chamber is below about 5 ×10−11 mbar, the XSTM experiment can be started by

cleaving the sample. For this purpose the protruding part of the sample must be cleaved off

the mounted and back-contacted part, so that the small notch prepared ex-situ will proceed

throughout the whole sample, yielding a (110) cleavage surface. In the universal STM setup

this has to be realized by pressing the sample against a fixed rod of the preparation chamber,

while in the XSTM setup the protruding part of the sample can directly be hit by a wobble

stick.

After a successful cleave, the sample is positioned within the STM unit and the tip is

approached. While the distance between tip and sample (zdirection) and the horizontal

position of the tip relative to the cleavage surface (xdirection) can precisely be changed by

the walker, the height of the tip (ydirection) can only coarsely be adjusted by manually

pushing or pulling the tip on the gold platelet at which it is held by a magnet. Depending

on the quality of the cleavage surface, more or less large areas are suitable for the XSTM

measurement. A macroscopically good cleavage surface can be seen in Fig. 4.1(b), imaged

through the optical microscope which is used for controlling the coarse approach: The top

end of the cleavage surface (A) is rough as it was notched externally. At the very bottom the

cleavage surface also contains many irregular steps (C), but the large region between appears

macroscopically flat and is well suited for XSTM investigation. The bright feature protruding

behind the cleavage surface (B) is a small piece of the glue with which the sample is mounted

to the copper plate beneath.

Once the tip has approached the sample at an appropriate position and tunneling is

established, it is still a long way to the desired nanostructures. While the cleavage surface

has a thickness of 150 to 200 µm (which is already challenging for tip positioning), only the

outmost 1 to 3 µm consist of epitaxially grown layers containing the QDs of typically 10 to

30 nm size. These relations can be compared, for illustration, to an object with the size of

a cherry pit (the QD) within a football pitch (the cleavage surface). The scan range of the

STM is about 1 ×1µm2(one step of a football player). It can be extended by adding an

offset voltage to the piezos, reaching about 5 µm, which can cover the width of the epitaxial

layers, but only a very small fraction of the cleavage surface.

Therefore a special strategy was developed to find the epitaxial layers [124, 338, 339]

(based on ideas from Refs. [360, 361]), without losing too much time by scanning large areas

of the cleaved wafer, and without damaging the tip by running into a large surface step

or scanning across the edge of the cleavage surface: Starting at the position of the initial

approach, the tip is retracted, moved several walker steps along [001] growth direction, and

extended again until tunneling. This procedure is repeated until a tunneling current fails to

appear, indicating that the tip was moved across the edge of the sample. From this position,

48 CHAPTER 4. EXPERIMENTAL SETUP

only a few steps have to be moved backward to be within the area of interest, where the

nanostructures can then be searched for by large STM overview images.

Along the way from somewhere on the wafer over the epitaxially grown buffer layers to

the nanostructures, the appearance of the GaAs surface often changes in an astonishingly

systematic manner, displayed in Fig. 4.6: The GaAs (110) cleavage surface typically consists

of large terraces intersected by surface steps of 1 or 2 ML height running along [1¯

10]- or

[2¯

21]-direction, as can be seen in Fig. 4.6(b), taken at the original GaAs wafer but close

to the epitaxially grown area. At the wafer further away from the strained layers, and

under the influence of dopants and crystal impurities, the surface steps are sometimes less

regular, shown in Fig. 4.6(a). But very often, the regularity and density of the surface steps

strongly increases when the tip reaches the area of the strained heterostructures, until closely

underneath the first wetting layer the structure suddenly changes. This change can – in good

cases – lead to a very flat surface, but – in bad cases – also to large and steep hills, or it can

reveal only few, but merged and correspondingly high steps or a change of the slope of the

steps. The latter two cases can be seen in Fig. 4.6(c), which is taken at an epitaxially grown

GaAs buffer, 200 nm underneath the first GaSb WL of the sample.

This changing character of the cleavage surface is due to the strain induced by the het-

erostructures, leading to locally inhomogeneous conditions during the cleave. On the one

hand it can help as an assisting sign to find the nanostructures, but on the other hand it

often hides the QDs in a strongly stepped surface dominating the image contrast. As the

strain is largest at the heterostructures, large surface steps often form directly along a WL,

making it impossible to analyze the embedded structures.

Such microscopic surface conditions of the epitaxially grown area cannot be seen macro-

scopically, so several approaches can be necessary, each at another position of the cleavage

surface, until a suitable region for XSTM studies on the nanostructures is obtained. Once

such a region is found and the used tip has proven to be of good quality, the measurement

should not be unnecessarily interrupted. Therefore and due to the limited durability of an

adsorbate-free surface the XSTM experiments are performed around the clock.

(a) (b)

2nm 5nm 50nm

(c)

[1 0]1

[001]

Figure 4.6: Appearance of the GaAs (110) cleavage surface with predominantly mono-atomic surface

steps (a) at the n-doped wafer, (b) still at the wafer but near the epitaxially grown layers, and (c) at

a buffer layer grown by MOCVD, 200 nm underneath a GaSb WL. The large step on the right side

of image (c) has a height of 2.2 nm or 11 ML.

Part II

Results and discussion

Chapter 5

XSTM results on MOCVD-grown

samples

A variety of samples containing GaSb nanostructures in GaAs has been examined within the

context of this work. Not all attempts were effective, sometimes due to unexpected challenges

during growth or during preparation of the samples, sometimes because some detail of the

experimental setup did not work properly. However, several samples could successfully be

studied, and thus a pool of nearly 2,500 XSTM images could be generated, aquired during

more than 1,500 hours.

The data chosen for this thesis can be devided into those obtained from samples prepared

by MOCVD and those from MBE-grown samples. Firstly, this is an easy classification to

structure the large amount of data, which also is a chronological one because the MOCVD-

grown samples have been grown and studied first and the MBE samples later. Secondly, the

designs of the samples have changed with time, too, in such a way that the studied MBE-

grown QDs generally contain more GaSb material than the MOCVD ones. Finally, as some

of the obtained results can directly be related to the growth conditons or to effects which are

typical for only one of both growth methods, this classification can also be helpful to discuss

and understand the underlying physics.

According to this classification, firstly an overview over XSTM results on two MOCVD-

grown samples containing three different GaSb/GaAs layers is given in this chapter, followed

by a detailed analysis of the chemical composition and a discussion of the QD formation in

chapters 6 and 7. Data on two MBE-grown samples containing another seven GaSb/GaAs

layers with varying growth conditions and the resulting different QD structures are presented

in chapters 8 to 10. Finally, in chapter 11 results on the electronic properties of both MOCVD-

and MBE-grown GaSb nanostructures will be shown.

5.1 Sample structures

Both MOCVD-grown samples reported here were fabricated by Lutz M¨uller-Kirsch in the

group of D. Bimberg at Berlin University of Technology [51, 71, 73, 264, 362]. They were

grown in the same machine, which is an AIXTRON AIX-200 reactor with rotating susceptor,

using hydrogen as carrier gas at a flow of about 5 l per minute and at a total pressure of

20 mbar [182, 265]. Epiready n-type GaAs(001) wafers were taken as substrates, with a

nominal Si dopant concentration of 1.5−3.6×1018 cm−3.

Onto these substrates, heterostructures consisting of several undoped GaAs and AlGaAs

buffer layers and the GaSb layers were grown using AsH3and TESb as precursors for the

group-V elements and TEGa, TMGa, and TMAl as group-III precursors. For growth at

52 CHAPTER 5. XSTM RESULTS ON MOCVD-GROWN SAMPLES

600◦C or below, TEGa is used instead of the more common TMGa because of the limited

dissociation of TMGa at lower temperatures [186].

The sample structures are finished by an n-doped cap layer of about 1.3 µm thickness

with Si dopant concentrations of 1×1017 cm−3for sample A and 2×1016 cm−3for sample B,

respectively. While the active layers are not intentionally doped in order to study preferably

pure GaSb/GaAs nanostructures, an increased conductivity of the substrate by dopant atoms

is crucial for stable tunneling conditions. Recently we observed that also the doping of the

cap layer can be helpful to prevent too strong effects of tip-induced band bending [298]. The

thickness of more than 1 µm of the cap layer has been chosen to prevent the STM tip at the

cleavage surface beside the GaSb layers from reaching the edge of the sample.

Figure 5.1: Comparison of detailed sample structures of the MOCVD-grown samples.

5.2. OVERVIEW OF XSTM RESULTS 53

Detailed sample structures are shown in Fig. 5.1: In both samples, the epitaxial growth

was started by thick buffer layers of GaAs and AlGaAs (about 300 nm GaAs and 300 nm

Al0.67Ga0.33As in sample A and 300 nm GaAs and 100 nm Al0.8Ga0.2As in sample B, respec-

tively), grown at 720◦C, in order to heal possible crystal defects or impurities of the substrate

and the interface and to obtain a flat growth surface. In XSTM experiments, AlGaAs layers

are additionally helpful for finding the tiny nanostructures within the cleavage surface, as

they act as marker layers.

After growth of these thick buffer layers, the temperature was decreased to 600◦C in

both samples and another 100 nm GaAs were deposited, followed by the first GaSb layer

at 470◦C. In sample A, this GaSb layer was overgrown with a sequence of 30 nm GaAs,

20 nm Al0.33Ga0.67As and 30 nm GaAs, before another GaSb layer was grown, again followed

by 30 nm GaAs, a 20 nm thick Al0.33Ga0.67As marker, 15 nm GaAs, and finally the thick

GaAs cap layer. The spatial separation between both GaSb layers is so large that they can

be regarded as completely independent. Sample B contains only one GaSb layer, which is

covered by 40 nm GaAs, a 30 nm thick Al0.8Ga0.2As marker, and the thick GaAs cap layer.

Thus three GaSb/GaAs layers with different amounts of deposited GaSb material are

existing within the two samples. The top layer of sample A is the one with least GaSb

material, labeled “layer 1” in the following. “Layer 2” with a medium GaSb content is that

of sample B, while the bottom layer of sample A is that containing most GaSb, labeled

“layer 3”. Prior to the growth of all three GaSb layers was a long growth interruption (GI)

under AsH3pressure, lasting 10 min for layer 1 and 21

2min for layer 2 and 3, respectively,

in order to flatten the surface. After this, AsH3was switched off and another GI of 4 s took

place, during which the arsine background in the reactor should decline [177, 182], before the

TESb flux was switched on and GaSb was deposited.

After GaSb growth, layer 1 was immediately covered by 3 ML GaAs before a 1 min GI

took place, while the deposition of layer 2 and layer 3 was followed by a GI of 2 s under TESb

pressure for QD formation, before the next GaAs layer was grown. It has been found that

such a GI is essential for the formation and increase of size of GaSb QDs, but that a longer

GI time can already lead to a dissolution of formerly existing QDs or to a contamination of

the QDs with rest gas molecules from the reactor [51, 182]. For all three GaSb layers, grown

at 470◦C, the first few nm of covering GaAs had the same growth temperature, respectively,

and only after deposition of 3 to 5 nm GaAs, the temperature was raised again to 600◦C.

The deposition times of the GaSb layers were 21 s for layer 1, 22 s for layer 2, and 25 s

for layer 3. A nominal growth rate of ∼0.1 ML/s was chosen with a V/III ratio of 6, but

it is not possible to derive the actual amount of deposited material from these parameters,

because the initial MOCVD growth of GaSb on GaAs is strongly non-linear in time: It was

observed that under similar growth conditions after 10 s deposition time no GaSb layer could

be found at all and that generally the growth rate of the first ML GaSb on GaAs is much

smaller than that of the following monolayers [182]. Thus the nominally small variations in

deposition time of 21 s, 22 s, and 25 s result in a considerable difference of the amount of

deposited GaSb material.

5.2 Overview of XSTM results

Overview images of the (110) cleavage surfaces of both samples are shown in Fig. 5.2. The

three GaSb layers can clearly be seen in the images as thin stripes with a brighter image

contrast, parallel to the atomic zig-zag chains in [1¯

10]-direction. It should be noted that

atomic resolution is only given in Fig. 5.2(b). The different appearance of layers 1 and 3

in sample A compared with layer 2 in sample B is due to the different tunneling polarities

54 CHAPTER 5. XSTM RESULTS ON MOCVD-GROWN SAMPLES

of both XSTM images, this effect will be discussed in detail in section 11.1. All images of

sample A were taken with a tunneling current of IT= 80 pA, while the current used for

imaging sample B was always IT= 100 pA.

Common for all three GaSb layers are an inhomogeneous contrast, appearing a little

brighter in some parts and less bright in others, and even discontinuities, i.e. small gaps

within the stripes which look the same as the surrounding GaAs matrix.

The functionality of the AlGaAs layers as markers is obvious from the images: Firstly,

these layers generally look darker than the surrounding GaAs due to a larger bandgap of

AlGaAs and the resulting electronic image contrast (as mentioned in section 3.3.2). Secondly,

they have an inhomogeneous appearance of darker and brighter areas given by an alloying and

formation of Ga-rich and Al-rich regions [131, 363, 364]. Finally, the AlGaAs layers contain

many white and black spots arising from adsorbates, as the AlGaAs(110) surface has a much

higher sticking coefficient for rest gas atoms than the surrounding GaAs(110) surface [131].

GaSb

layer

GaSb

layer

AlGaAs

layer

GaAs

matrix

deficient

scanlines change

ofthetip

conditions

gap

AlGaAs

layer

GaAs

matrix

defectsinthe

cleavagesurface

adsorbate 10nm

10nm

(a)

(b)

[1 0]1

[001]

[1 0]1

[001]

layer2

layer3 layer1

Figure 5.2: XSTM overview images of (a) sample A, containing GaSb layers 1 (on the right) and 3 (on

the left), and (b) sample B, containing GaSb layer 2. Growth direction is from the left to the right.

Sample voltages were chosen as (a) VT= -3.5 V and (b) VT= +2.4 V.

5.2. OVERVIEW OF XSTM RESULTS 55

Significantly less adsorbates can be found on the GaAs surface.

In Fig. 5.2(a) also a typical artifact of XSTM images can be recognised: The image shows

several deficient scanlines caused by an unstable tip. After a rather severe instability in the

center of the image, in particular the AlGaAs layer looks different than before, with the

former white spots of adsorbates becoming dark, which is a strong sign for a change of the

electronic properties of the STM tip during the instability. Another STM artifact in this

image is the fact that the left and right edges appear much darker than the central part,

which can be explained by the non-linear scan movement of the tip over the considerably

large overview image area: The tip on top of a tube piezo moves along a spherical surface

instead of a plane, thus it is slightly closer to the sample in the center of the image than in

the outer parts.

5.2.1 Layer 1: 21 s GaSb deposition

A more detailed view of layer 1 is shown in Fig. 5.3, which is an overlay of two XSTM images

of partly overlapping areas of the cleavage surface. In this way, an extended region of the

sample can be studied image by image.

GaSb layer 1 is characterized by a very thin extension in growth direction, the increased

image contrast of the layer is mainly concentrated to one atomic chain. Within this thin layer,

the contrast is strongly inhomogeneous, ranging from small gaps in the layer, which obviously

[1 0]1

[001]

growth

direction

10nm

ML steps

withinthe

GaSblayer

Figure 5.3: Overlapping XSTM

filled state images of layer 1, aquired

at VT= -3.0 V.

consist of pure GaAs, over parts of the layer with an

only weakly increased contrast up to parts with a much

brighter appearance, which are often dominated by small

bright spots with a lateral extension of only about one

to three atoms. Thus, the layer is found to be strongly

intermixed, consisting of GaAsSb with a strongly varying

ratio between As and Sb atoms. Nevertheless, the term

“GaSb layer” will be maintained in the following, keeping

in mind that an uncertain amount of As is contained

within this layer.

It should be noted that the large white spot directly

on the GaSb layer in the bottom part of the image in

Fig. 5.3 is an adsorbate and not part of the layer it-

self. Additionally, the atomic zig-zag chains are clearly

resolved in the image along the [1¯

10]-direction, while the

somewhat whinding lines perpendicular to these do not

represent any real structures but are due to some elec-

tronic or mechanical oscillations.

Nevertheless, Fig. 5.3 is a typical image of layer 1,

as this GaSb layer looks almost the same all over the

investigated parts of the sample: There are no three-

dimensional (3D) structures at all, thus this GaSb layer

is a clear quantum well, and also its thin vertical exten-

sion of only one atomic chain with the inhomogeneous

contrast and smaller or larger gaps, ranging up to 7 nm

lateral extension, is everywhere the same.

One special feature can be observed in the bottom

part of Fig. 5.3: Just at the bottom of the image, the

QW is clearly situated at one atomic chain, then further

up the contrast gets weaker but extends over a second

56 CHAPTER 5. XSTM RESULTS ON MOCVD-GROWN SAMPLES

chain, and finally it is completely concentrated at the second chain. As the chains of the

(110) surface represent only each second atomic ML (see section 3.4), this appearance can

be explained by two ML steps of the QW due to steps on the (001) growth surface of the

underlying GaAs layer.

5.2.2 Layer 2: 22 s GaSb deposition

GaSb layer 2, as shown in Fig. 5.4(a), presents an appearance which in many aspects is

very similar to that of layer 1: Again, the thin layer exhibits several gaps of different lateral

extensions, consisting of pure GaAs, and it has an inhomogeneous contrast with brighter and

darker parts, standing again for an intermixed GaAsSb stoichiometry. However, the vertical

extension of the layer appears to be a bit larger, covering about two atomic chains. It should

be noted that Fig. 5.4(a) shows an excellent cleavage surface of the surrounding GaAs matrix,

containing no adsorbates and also no segregated Sb atoms, dopant atoms or crystal defects.

Also this layer shows no 3D structures at all and is therefore considered a quantum well.

However, within the intermixed QW, there are many structures like those shown in Fig. 5.4(b),

which are completely flat, two-dimensional (2D) islands with a very bright contrast. Thus

these islands have to consist of material with a significantly higher GaSb content than the

residual QW. The lateral extension of these 2D islands varies strongly, the maximum of the

size distribution is at about 4 nm, but also islands with up to 20 nm lateral size were observed,

which is comparable with typical base lengths of QDs. The density of these 2D islands of

∼6 x 1011 cm−2is very high.

5.2.3 Layer 3: 25 s GaSb deposition

In layer 3, finally, GaSb quantum dots can be observed, as shown in Fig. 5.5. The structure

of the wetting layer is similar to that of the QWs of layers 1 and 2: Its vertical extension

is concentrated to one or two atomic chains, but within this layer there are small gaps and

the image contrast of the WL varies inhomogeneously, standing for an intermixed GaAsSb

stoichiometry [Fig. 5.5(a)].

The flat WL, however, is interrupted by small QDs. These QDs have a significantly larger

image contrast than the WL, as can be seen in Fig. 5.5(b), which cannot be explained by a

Figure 5.4: XSTM

filled state images

of layer 2, taken

at VT= -1.8 V.

(a) A typical im-

age of the GaSb

QW, (b) flat two-

dimensional GaSb-

rich islands within

the QW.

5.2. OVERVIEW OF XSTM RESULTS 57

[1 0]1

[001]

GaSb

quantum

dot

GaSb

wetting

layer

gaps

within

theWL

5nm 10nm

(a) (b)

Figure 5.5: XSTM filled state images of layer 3, aquired at VT= -2.3 V. (a) A typical image of the

GaSb wetting layer, (b) overview image of a GaSb quantum dot.

purer GaSb stoichiometry of the QD alone. In fact, two additional effects are responsible for

the bright appearance of the QD in the XSTM image: Firstly, the electronic image contrast

(see also section 3.3.2) is increased by a higher tunneling probability from the electronic states

of the QD [92]. Secondly, also the structural image contrast (see section 3.3.1) is affected by

strain relaxation of the QD upon cleavage, leading to a local outward bending of the cleavage

surface at the intersected QD [93, 97, 124] and underlining the significant amount of strain

within the QD. It is notable that in the direct neighborhood of the QDs the WL seems to

contain less GaSb material, being indicated by a decreased general contrast and larger gaps

than in the residual WL.

A closer view of the QD shown in Fig. 5.5(b) is given in Fig. 5.6(a). In [001] growth

direction, the bright contrast extends over four atomic chains, indicating that the height of

the QD amounts to about 2 nm. The base length is around 8 nm, and the shape of the QD is

rather flat with the largest lateral extension just at the base, similar to truncated pyramids.

However, no exact structure can be identified due to the small extension and the contrast,

which again is slightly inhomogeneous at the QD and especially at its borders, indicating an

island

5nm 5nm 5nm

(a) (b) (c)

[001]

Figure 5.6: XSTM filled state close-view images of (a,b) GaSb quantum dots and (c) a tiny 3D

GaSb island in layer 3, taken at (a,b) VT= -1.6 V and (c) VT= -3.3 V.

58 CHAPTER 5. XSTM RESULTS ON MOCVD-GROWN SAMPLES

(001)samplesurface

(110)cleavageface

0% 50% 100% 120%

Figure 5.7: Sketch of differ-

ently cleaved QDs. The cleav-

age positions are indicated in

regard to the QD extension in

[110]-direction.

intermixed stoichiometry also for the QD. An even smaller QD is shown in Fig. 5.6(b), with

a base length of about 4 nm and a height of two to three atomic chains, corresponding to

∼1.5 nm. It should be noted that the smaller size of the structure shown in Fig. 5.6(b) can

be due to a cleavage outside the center of the formerly larger QD (see also Fig. 5.7).

From the observed size of the QDs and the frequency of their occurence when scanning a

larger area of GaSb layer 3, the QD density can be estimated as follows: QDs can randomly be

cleaved upon sample cleavage at any position, as sketched schematically in Fig. 5.7, resulting

in different cross sections in the XSTM image. If the cleavage position of the QD, indicated as

percentage of its lateral extension, is somewhere between 0% (completely cleaved away) and

120% (20% of its diameter underneath the cleavage surface), it can be detected in the XSTM

image due to the increased image contrast, which is influenced also by the strain of completely

buried QDs [124]. Thus, the range of sight of the XSTM for QDs in [110]-direction is around

120% of the mean QD diameter, at least at good tunneling conditions and flat cleavage

surfaces as it is the case here. In an area of ∆x≈1µm extension in [1¯

10]-direction, studied

image by image using small images with atomic resolution, three QDs were detected with a

mean diameter of about 8 nm. Dividing this number of observed QDs through the lateral

extension times the range of sight of ∆y≈120% ×8 nm, the QD density results here to

∼3×1010 cm−2.

Besides such small, but distinctive quantum dots, tiny 3D island structures were observed

in the WL. These islands are not only even smaller than the QDs, but they exhibit a qual-

itatively different nature, as can be seen in Fig. 5.6(c): The bottom atomic chain of the

structure has exactly the same appearance as the surrounding WL, and the image contrast

of the whole island does not significantly exceed that of the WL. This indicates that there

is no electronic confinement and only little strain within this island, even the stoichiometry

does not seem to differ from that of the intermixed WL. What remains outstanding for these

islands is their three-dimensional shape, extending vertically over two to three atomic chains

or 1.5 nm, with a lateral extension of only about 2.5 nm. The density of these islands can be

estimated in the way described above to ∼5×1010 cm−2.

The GaAs matrix, likewise for layer 2, shows a nearly perfect cleavage surface with hardly

any defects, dopant atoms, or segregated Sb atoms, as can be seen in Fig. 5.5(a).

5.3 Results from other characterization methods

Although XSTM is a very elaborate investigation tool for semiconductor nanostructures,

comparing the obtained XSTM data with other structural or optical characterization methods

is of course helpful.

5.3. RESULTS FROM OTHER CHARACTERIZATION METHODS 59

5.3.1 Photoluminescence spectroscopy

Sample A, containing GaSb layers 1 and 3, has been studied by photoluminescence (PL)

spectroscopy. These measurements were performed by Lutz M¨uller-Kirsch, using the 514 nm

line of an Ar+laser as excitation source, a cooled Ge pin-diode for detection, a double-grating

monochromator and a He cryostat [182]. A PL spectrum taken at a temperature of 10 K and

with a moderate excitation density of 50 W cm−2is shown in Fig. 5.8.

Three peaks can clearly be distinguished within the spectrum: The most intensive peak

arises from the GaAs matrix and has an energy of hν = 1.52 eV, corresponding to a wavelength

of λ= 820 nm, in nice agreement with the GaAs band gap. The second peak with an energy

of 1.37 eV or a wavelength of 906 nm can be identified with that of a two-dimensional layer,

thus this peak can be associated both with the QW of layer 1 and the WL of layer 3, what

also explains the asymmetric broadening of the peak. Finally, a third peak is obtained at an

energy of 1.20 eV, corresponding to a wavelength of 1036 nm. This peak, which is evident

but much less pronounced than the other two and strongly broadened, is assigned to the

QDs of layer 3. Its broadness stands for a rather broad size distribution of the QDs, and

its rather smooth transition to the WL peak corresponds to the small size of the QDs, the

additionally found tiny 3D islands and to the inhomogeneity of the WL, because all these

structural details impede a clearer separation between QD and WL photoluminescence. On

the other hand, the existence of a QD PL peak confirms that the observed structures shown

above are indeed QDs with an electronic confinement, in spite of their rather small size.

Comparing these results with other PL data on MOCVD-grown GaSb QDs found in

literature [51, 71, 74], two trends are evident: Firstly, the QDs studied here have a larger PL

energy, amounting to 1.20 eV compared with 1.13 eV [71], 1.12 eV [51], and 1.09 eV [74] for

equal or similar temperature and excitation energy. Secondly, the separation between QD

and WL peak of 0.17 eV here is smaller than the reported values of 0.23 eV [71], 0.24 eV [51],

or 0.30 eV [74]. Both trends point out that the QDs studied here are smaller than those

reported, leading to a weaker confinement within the QDs relative to the WL.

1.0 1.1 1.2 1.3 1.4 1.5

10000

100000

T=10K

50W/cm2

GaAs

GaSbQD

GaSbQW

energy[eV]

Figure 5.8: Photoluminescence spectrum of sample A, containing GaSb layers 1 and 3, taken at low

temperatures and a moderate excitation density. Intensity peaks arising from the GaAs matrix, from

the GaSb QW and WL, and from the GaSb QDs can be distinguished.

60 CHAPTER 5. XSTM RESULTS ON MOCVD-GROWN SAMPLES

5.3.2 Transmission electron microscopy

For a sample that has been grown much earlier, but in the same MOCVD reactor and with

similar growth parameters as GaSb layer 3, also transmission electron microscopy (TEM) was

used for structural characterization. These measurements were done by Holm Kirmse and Ines

H¨ausler at the Humbold University of Berlin, Institute of Physics, Chair of Crystallography,

using a Hitachi H-8110 microscope [51, 365, 366].

Using dark-field TEM imaging in top-view geometry, QDs capped with 20 nm GaAs could

be studied, as shown in Fig. 5.9(a). The (220) reflection was used for imaging, which is mainly

sensitive to strain. Randomly distributed QDs with an isotropic shape and different sizes can

be seen. A size distribution with a maximum at a QD diameter of 21 nm is obtained from

the data, as shown in Fig. 5.9(b). This value is much larger than the XSTM data showing

QDs with diameters between 4 and 8 nm. Though it has to be considered that the extensions

obtained by top-view TEM represent rather the strain distribution in the QD layer than the

actual QD size. However, the broadness of the size distribution over more than one order of

magnitude is of larger significance, as this is at least partially maintained during overgrowth.

The total QD density of about 3×1010 cm−2agrees nicely with the value obtained for capped

QDs by XSTM.

A more direct comparison is possible for cross-sectional TEM results on capped QDs.

Figure 5.10(a) displays a composition-sensitive image using the (002) reflection, showing

only weak variations of the GaSb layer contrast. From the coarse resolution of the TEM

image, it cannot be concluded whether these variations stem from fluctuations within a QW

or from flat QDs, but the absence of large QD structures observed in the equally grown

XSTM sample is confirmed. When the same GaSb layer is imaged using the strain-sensitive

(004) reflection, as shown in Fig. 5.10(b), a very different appearance is found: A flat WL

contains structures comprising very different amounts of strain, partly reaching several nm

into the surrounding GaAs matrix. While the bright feature in the center of Fig. 5.10(b)

can only be assigned to a quantum dot, the weaker and smaller bright spots may arise from

fluctuations within the WL or also from the tiny 3D islands observed by XSTM.

Beyond the potential of such conventional dark-field TEM images, the lateral resolution

can be increased by using energy filtered high resolutional TEM, considering element-specific

0 10 20 30

d [nm]

number [109cm -2]

(a) (b)

Figure 5.9: (a) Top-view dark-field TEM image of GaSb QDs on GaAs, using the strain-sensitive

(220) reflection. (b) Size distribution of the QDs shown in (a).

5.3. RESULTS FROM OTHER CHARACTERIZATION METHODS 61

(a) (b)

Figure 5.10: Cross-sectional TEM images of a GaSb/GaAs QD layer, using (a) the composition-

sensitive (002) reflection and (b) the strain-sensitive (004) reflection.

electron energy losses: In Fig. 5.11(a), only the signal energetically corresponding to Sb is

mapped, leading to a rather noisy image with an increased contrast at the GaSb layer.

For a quantitative analysis of the stoichiometry this method is strongly limited by lattice

distortions and the thickness of the TEM specimen in the order of 10 nm [3, 366]. However,

keeping in mind the statistical averaging over many atomic layers which is immanent to all

TEM techniques, the extension of an increased Sb content can be obtained from signal profiles

across the GaSb layer, as shown in Fig. 5.11(b,c) for a QD and the WL, respectively. A QD

height of about 2.1 nm can be estimated, which agrees well with the XSTM result of 2 nm

shown above. Also the observed WL thickness of about 0.9 nm confirms the XSTM data,

showing an extension over one to two atomic chains.

Wettinglayer 0.9nm

2.1nm

0.9nm

22nm

(a) (b)

(c)

Figure 5.11: (a) Sb-sensitive energy-filtered TEM image of a GaSb/GaAs QD layer. The indicated

areas are evaluated regarding their Sb content for (b) a QD (red) and (c) the WL (blue).

62 CHAPTER 5. XSTM RESULTS ON MOCVD-GROWN SAMPLES

Chapter 6

Analysis of the chemical

composition

As mentioned before, the XSTM image contrast is a first qualitative indication of the chemical

composition of nanostructures. However, a more precise and quantitative knowledge of the

local stoichiometry of quantum dots and wells is essential for understanding the growth and

modeling the electronic and optical properties of the structures (see chapter 2.3).

For this purpose, a method has been developed (basically by H. Eisele [92, 124] and

further by M. D¨ahne, A. Lenz [100], E. Lenz [367], and in the framework of this work) to

evaluate the local lattice constant in XSTM images and compare the results with simulations

of strain relaxation. By this method the chemical composition of cleaved nanostructures can

be analyzed with typical errors of less than 5% for QWs and 10% for QDs.

6.1 Evaluation of the local lattice constant

During epitaxial growth of strained heterostructures, the lateral positions of the single atoms

are predefined and the only direction into which the strain induced by lattice misfit can

partly relax is the growth direction (see sections 2.2.1 and 2.3.1). Thus the local lattice

constant in growth direction is a measure for the inherent strain and therewith for the chemical

composition.

The method to evaluate this lattice constant is illustrated step by step in Fig. 6.1: First,

a height profile has to be taken in [001] growth direction across the QD which is to be

analyzed, performed here for the QD already shown in Figs. 5.5(b) and 5.6(a). In order to be

independent of atomic positions or short-range fluctuations in [1¯

10]-direction and for noise

reduction, the height profile needs to be averaged in [1¯

10] over a few nm, typically over about

100 data points of the XSTM image. For this purpose, a homebuilt software tool written by

S. K. Becker [345] has been used for this work. The area of the averaged height profile is

indicated within the XSTM image in Fig. 6.1(a).

Within the height profile, shown as black line in Fig. 6.1(b), the atomic corrugation in

[001]-direction can clearly be seen, but its amplitude is strongly exceeded by the steeply

increased apparent height at the position of the QD, arising from the actual structural pro-

trusion of the QD material and the increased electronic contrast. Additionally, the adsorbate

that can be seen slightly above the QD in Fig. 6.1(a) also leads to a small peak in the height

profile. In a next step, the pure atomic corrugation has to be isolated from these other in-

fluences. For this purpose, a background is evaluated from the measured height profile by

averaging it over about one wavelength of the atomic corrugation. The resulting background,

shown as blue line in Fig. 6.1(b), can then be subtracted from the height profile, obtaining

64 CHAPTER 6. ANALYSIS OF THE CHEMICAL COMPOSITION

Figure 6.1: Procedure for evaluating the local lattice constant: (a) XSTM image with indicated

averaging area of the height profile, (b) height profile across the QD, (c) atomic corrugation of the

height profile, (d) atomic chain distances, (e) normalized atomic chain distances, (f) local lattice

constant averaged from various XSTM images.

the atomic corrugation, as shown in 6.1(c). Each peak of this (green) corrugation curve cor-

responds to one atomic chain and is formed only by a few data points which are subject to

electronic noise – it should be noted that the amplitude of the corrugation is only of the order

of 0.1 ˚

A = 10 pm. Therefore, every single peak has to be fitted with a Gaussian shape, so

that the maxima of these Gaussian peaks represent the exact positions of the atomic chains

along [1¯

10].

The therewith obtained distances between neighboring atomic chains, which resemble

the distribution of the local lattice constant, are displayed in Fig. 6.1(d) as orange points:

A maximum can clearly be seen at the position of the QD, but the plotted chain distance

at the GaAs matrix is not constant but seems to increase homogeneously in average. This

artifact of XSTM imaging is created by the nonlinear movement of the STM tip, resulting

in a non-perfectly planar course as mentioned above (section 5.2), and by a nonlinearity of

6.2. COMPARISON WITH STRAIN SIMULATIONS 65

the piezo properties themselves. It has to be corrected by normalizing the data: The plotted

chain distances at the GaAs matrix several nm away from the QD are fitted linearily or

quadratically, and this line of best fit [indicated in Fig. 6.1(d) as red curve] is normalized to

0.5653 nm, the literature value of the GaAs lattice constant at room temperature. By this

way, also a calibration of the XSTM data is done.

Finally, the normalized atomic chain distance is obtained, as shown in Fig. 6.1(e). A

sharp increase of the chain distance can clearly be seen at the position of the QD, extending

over three to four atomic chains, agreeing nicely with a dot height of about 2 nm as already

obtained from the visual inspection of the XSTM images.

In analogy to the enlarged lattice constant of the QD directly shown by the increased

chain distance, the decreased chain distance observable directly underneath the QD – and

to a less extent also above it – has to refer to a locally reduced lattice constant. It can be

explained by a compression of the neighboring GaAs material by the highly strained QD.

It should be noted that it can be difficult to fit the maxima of the atomic corrugation

correctly, especially at the steep flanks of the height profile at the bottom and top edges of

the QD. This leads to rather large errors of the chain distance for the lowest and topmost

chain of the QD. However, these errors compensate each other regarding the integral under

the curve for the area of increased chain distance, corresponding to the total strain within

the QD. For reducing the influence of these errors at the flanks of the QD region and for

general noise reduction, the complete procedure of evaluating the local lattice constant can

be repeated for different XSTM images of the same position, averaging the obtained data.

Figure 6.1(f), for example, is achieved by averaging the results from five images of the same

QD, and especially for the GaAs matrix the reduced statistical noise is evident.

The whole procedure of evaluating the lattice constant is time consuming already for one

XSTM image. Therefore, a part of the chain distance results shown in this work is obtained

using a software routine written by E. Lenz [367] for half-automatically performing the fitting

and normalizing of the chain maxima. However, if the XSTM conditions are not ideal (i.e.

only weak atomic resolution, electronic noise, or adsorbates, defects, or steps on the cleavage

surface), the whole procedure remains challenging.

6.2 Comparison with strain simulations

Up to here, the local lattice constant was evaluated, which is an essential, but not sufficient

step towards a determination of the local stoichiometry of the QD material: The relation

between measured lattice constants and chemical composition is still missing. Such a relation

can only be attained by simulating the strain corresponding to given stoichiometries.

A model for the strain relaxation for QDs and QWs upon cleavage has been developed by

H. Eisele especially for the simulation of XSTM data [92, 93, 124]: The model is based on the

continuum-mechanical theory of elasticity, which was modified to discrete atomic positions.

The stress tensor is applied in a linear approximation, considering only next-neighbor atoms.

The bulk lattice parameters and the linear elastic moduli of GaAs and GaSb are taken from

Ref. [368]. For the simulation, a cuboid with the extensions of 48 nm in [001]- and [1¯

10]-

directions, respectively, and 24 nm in [110]-direction, resulting in 2.65×106atoms, resembles

the sample cleaved in [110]-direction. As a starting configuration, this model cuboid contains a

GaSb or GaAsSb QW of defined thickness and stoichiometry within a GaAs matrix, arranged

at the atomic positions of the GaAs zincblende structure. During the iterative simulation,

only the five side facets are held fixed, while all atoms of the cleavage surface and inside

the cuboid can relax according to strain energy minimization. Additionally, an offset of the

atomic distances in growth direction is allowed to form at the GaSb layer. After several

66 CHAPTER 6. ANALYSIS OF THE CHEMICAL COMPOSITION

thousand iteration steps, the variation of the atomic positions becomes negligible compared

with the resolution of the XSTM.

As results of the simulation, both the structural relaxation of the GaSb material out of

the (110) cleavage surface and the local lattice constant in [001] direction can directly be

obtained from the calculated atom positions.

Alternatively to the method described here, also valence-force field theory can be applied

to calculate strain in nanostructures [41, 213]. This atomistic approach, based on atomic

potentials and the deformation of atomic bands, is superior concerning the material interfaces

and strongly intermixed material, whereas continuum mechanics should be used to describe

the interior of compositionally pure QDs [124, 211, 369].

For the simulation of XSTM data, also simpler analytical models are used to describe

the strain and local lattice constant within cleaved nanostructures [97, 98, 217, 315, 317].

Although these models are much less precise, they can resemble the experimental findings at

least qualitatively [98] and to some extent, especially with more complex enhancements to

the model, also quantitatively [102]. However, all simple approaches lack atomic resolution in

the zincblende configuration and are therewith principally limited regarding their preciseness.

Using the described model based on continuum elasticity, the experimentally obtained

atomic chain distances could be compared with simulations of the local lattice constant:

In Fig. 6.2(b) both the experimental data obtained from the QD shown in Fig. 6.2(a) and

calculated values for a GaAsSb/GaAs QW with a thickness of one atomic chain (2 ML)

and chemical compositions of GaAs0.75Sb0.25 and GaAs0.5Sb0.5, respectively, are displayed,

together with the line corresponding to pure bulk GaAs. Now it can be seen directly that the

GaSb content of the QD is mainly in the range of 50%, in nice agreement with the observed

inhomogeneity in the image contrast.

While a simulation of a QD would need its exact three-dimensional shape and size as

prerequisite which differs from dot to dot and mostly is not evident from two-dimensional

XSTM images, simulating QWs leads to much more general results like the calculated lat-

tice constants indicated in Fig. 6.2(b). Though, the difference of the local lattice constants

regarding QDs and QWs need to be discussed: The compressive strain in the QD is sig-

nificantly higher than in the QW, also influencing the surrounding host material, what can

be seen by the strong undershoot of the measured chain distance at the two atomic chains

just below the QD in Fig. 6.2(b), representing a compression of the two GaAs atomic chains

underneath the QD. Above the QD a slightly smaller undershoot is expected, too, regarding

the typical QD shape of a truncated pyramid with a smaller lateral extension at the top than

at the bottom. However, the observed compression is much less pronounced above the dot

5nm

[001]

positionin[001]-direction(nm)

atomicchaindistance(nm)

25%GaSb

50%GaSb

0.64

0.60

0.56

0.52

-8 -6 -4 -2 0246 8

(a)

(b)

Figure 6.2: (a) XSTM image, the area for analyzing the chain distances is indicated, and (b) analyzed

local lattice constant within the area shown in (a), compared with calculated values for GaAs0.75Sb0.25

and GaAs0.5Sb0.5QWs.

6.3. LOCAL BENDING OF THE CLEAVAGE SURFACE 67

material, indicating that the bottom interface of the QD is more abrupt than the top face.

These undershoots within the chain distance profile and the larger strain in a QD compared

to QWs lead to a small underestimation of the QD GaSb content when comparing it with

the calculated QW values. However, this is partly compensated by another effect explained

in the following section.

6.3 Local bending of the cleavage surface

Besides the atomic corrugation, the height profiles across a QD in XSTM images also show a

considerable outward protrusion of QD material due to partial strain relaxation upon cleavage.

Especially at tunneling voltages with a higher absolute value the contribution of the electronic

contrast to the apparent height in XSTM images decreases, so that the structural contrast is

dominating, showing the actual morpholgy of the cleavage surface (see section 3.3).

This structural relaxation gets evident in Fig. 6.3(a), displaying a height profile (green

curve) across the GaSb QD of Fig. 6.2(a) and the corresponding outward protrusion (blue

curve) without the atomic corrugation, obtained by averaging the green curve. The profile

is taken from an XSTM image acquired at a relative high absolute voltage of VT= -2.7 V.

An outward relaxation of the QD material of about 1.5 ˚

A can be obtained, implying a

strong convex bending of the cleavage surface at the QD and a strong concave bending just

underneath and above.

Now one has to consider that not the position of the atomic core is measured by STM,

but the charge density which is mainly concentrated at the dangling bonds. More precisely,

the “equipotential” surface of the integrated LDOS of the sample at the position of the tip is

imaged, which is determined by different contributions of the surface atoms and dominated

by the occupied and empty dangling bonds of the group-V and group-III atoms, respectively

(for a more detailed view see for example Refs. [325, 326, 370]). When the sample surface

is bended, the surface atoms and also the directions of their dangling bonds follow, at least

partly, this bending. This situation is shown schematically in Fig. 6.3(b): All sketched

atoms have equal distances in [001]-direction, but the surface is exaggeratedly bended in

[110]-direction, assuming for illustration an outward protrusion which is ten times larger

than the measured one shown in Fig. 6.3(a). For simplicity, the atomic dangling bonds are

plotted perpendicular to the local surface, and due to the surface bending the dangling bonds

increase their distance to each other at the center of the QD but move together below and

above it. When the tip is scanned across the QD, the tunneling probability is largest at

the positions directly above the dangling bonds, marked by red lines. Thus, the distance

between neighboring atomic chains appears larger than it really is at the QD center and

smaller underneath and above.

This effect gets additionally enlarged when the background is subtracted from the height

profile in order to locate the maxima positions of the atomic corrugation, as described above,

because in this case the peaks of the dangling bonds are regarded, as indicated by green lines

in Fig. 6.3(b), and not their largest protrusion in [110]-direction (red lines). The background

subtraction is nevertheless necessary for the chain distance analysis, as in most cases it is not

possible to locate the positions of the atomic chains directly in the height profile at the steep

flanks of the QD region.

It should be noted that only a large curvature of the surface bending significantly con-

tributes to the derivation of the apparent chain distance, while at areas with a small curvature

this effect is negligible and the local lattice constant is evaluated correctly. The latter case

is given, for instance, at the flanks of the QD shown here and also at the center of larger

QDs [92, 100, 118]. Additionally, the surface bending leads to enlarged apparent chain dis-

68 CHAPTER 6. ANALYSIS OF THE CHEMICAL COMPOSITION

positionin[001]-direction(nm)

apparentheight(Å)

-2 -1 0 1 2 3 4

[110]

[001]

Asatomwith

filleddanglingbond

Gaatomwith

emptydanglingbond

70.2° 28.2°

-2 -1 0 1 2 3 4

0.0

0.5

1.0

1.5

2.0

apparentheight(Å)

positionin[001]-direction(nm)

(a)

(e)

(c)

(d)

(b)

0.1

"peak"position

Figure 6.3: (a) Height profile (green curve) in growth direction across the GaSb QD shown in

Fig. 6.2(a), and averaged over one wavelength of the atomic corrugation (blue curve). (b) Schematic

drawing of the effect of surface bending on the apparent distances between neighboring atoms within

the cleavage surface. The amount of the surface bending is strongly exaggerated for illustration,

and the outlined atoms (blue) and their dangling bonds (orange) are only for illustration and not

drawn to scale. The red lines indicate the apparent positions of the atoms looked from above, while

the green lines indicate the peak positions of the dangling bonds. (c) Sketch of the GaAs(110)

cleavage surface including buckling and the actual angles of the dangling bonds, according to Ref. [326].

(d,e) Calculated charge density distributions at occupied (d) and empty (e) dangling bonds at the

(110) cleavage surface of a III-V zincblende semicondutor, taken from Ref. [326]. Equiprobability lines

for different values of the probability density |Ψ|2are indicated.

tances directly at the QD but to reduced ones below and above the QD, so that both errors

compensate each other when the chain distance is integrated over the complete QD region.

As mentioned above, the sketch of Fig. 6.3(b) is strongly exaggerated and not drawn to

scale. Actual dangling bonds are not perpendicular to the local sample surface, but have

an angle of 70◦for empty states and 28◦for filled states [326], as displayed in Fig. 6.3(c).

Detailed calculations of the different contributions to the local charge density at the (110)

cleavage surface of III-V zincblende semiconductors were performed by Ebert et al. [325] and

Engels et al. [326]. Charge density distributions for occupied and empty dangling bonds are

shown in Fig. 6.3(d,e), respectively, taken from Ref. [326]: For both kinds of dangling bonds

6.3. LOCAL BENDING OF THE CLEAVAGE SURFACE 69

the equiprobability lines of the corresponding wavefunctions are plotted, showing that the

idea of strongly localized dangling bonds is only valid for areas of high probability density

|Ψ|2. At the tunneling conditions of rather high absolute voltages and moderate currents

used here, however, the STM tip does not get so close to the sample surface but images the

equiprobability surfaces of rather low |Ψ|2, which are much more delocalized, as can be seen

by the dashed lines in (d) and (e). The surface bending can be expected to strongly modify

the direction of the dangling bonds regarding the strongly localized part, while it should be of

less influence on the comparably smoothly varying charge density distribution corresponding

to low probability densities.

Although it is far beyond the scope of this work to exactly calculate the amount of

the surface bending effects, at least a quantitative estimation can be performed as follows:

From the experimental height profile a measured outward relaxation of the QD ∆yof about

1.5 ˚

A and an extension of the surface bending in [001] direction 4∆xof about 4 nm can

be obtained. According to the geometric considerations sketched in Fig. 6.4, the radius of

curvature of a homogeneous surface bending can be obtained from r2−(r−∆y)2= ∆x2,

resulting here in

r=(∆x)2+ (∆y)2

2∆y= 3.4 nm .(6.1)

The relevant length lof the filled As or Sb dangling bond is estimated to about 1.3 ˚

A, which

is in the range of the As and Sb atomic radii of 1.25 ˚

A and 1.45 ˚

A, respectively [371], and

about half the GaAs covalent bond length of 2.45 ˚

A [322]. Considering Fig. 6.3(d,e) and

the discussion above, l≈1.3 ˚

A also corresponds to the extension of the strongly localized

charge density of the dangling bond, thus being a good upper limit of this error estimation.

As a last parameter, the distance between neighboring atoms is needed, which is estimated

to about d0= 0.6 nm being a rough average value for both GaAs matrix and GaSb QD

material, also considering the variation of the distance due to the surface bending. Then

the maximum effect of the surface bending on the apparent chain distance, according to the

situation sketched in Fig. 6.4, results to

∆d=d0

rl= 0.02 nm .(6.2)

In conclusion, the effect of the surface bending on the measured chain distances can

roughly be estimated to about 0.02 nm or 10% of the typical chain distance variations [see

for example Fig. 6.2(b)]. Thus, the chain distances at the compressed GaAs matrix are

actually about 0.02 nm larger than evaluated from the XSTM images, while at the QD itself

they are up to 0.02 nm smaller. Remembering the underestimation of the GaSb content in

the QDs resulting from the strain simulations – which may be of the same size or slightly

larger depending on the exact QD structure –, both effects mainly compensate each other

directly at the QD, where only a small underestimation remains. Directly below and above the

cleavage

surface

[110]

[001]

2nm

Figure 6.4: Schematic draw-

ing of the geometrical situation

at the bended cleavage surface,

showing four surface atoms and

their dangling bonds. The ra-

dius of curvature of the bended

surface is indicated.

70 CHAPTER 6. ANALYSIS OF THE CHEMICAL COMPOSITION

QD, however, both effects have the same direction, leading here to a significantly decreased

apparent chain distance.

6.4 Stoichiometry of MOCVD-grown GaSb QDs

Coming back to the evaluation of the lattice constant with its corresponding Sb stoichiometry

and considering the discussed corrections for the simulations and the surface bending, the

chemical composition of the discussed QD can now be specified. Figure 6.5(a) displays the

atomic chain distance across the center (orange line) and across the outer parts (green line)

of the QD, as indicated in the XSTM image in the inset. For comparison, also the analyzed

chain distances for the WL far away from any QD are shown (blue line).

Within the QD the chain distance varies between 0.63 nm and 0.67 nm, which is about

0.1 nm above the value of bulk GaAs. Considering the corrections discussed above, this value

firstly has to be corrected by -0.02 nm due to the surface bending. On the other hand, for

the same local lattice constant the actual GaSb content in a QD is about 20% higher than in

a QW, which was considered in the simulations. With both effects partly compensating, the

maximum GaSb content within the QD can be concluded to be 60% to 70%, with an error

of about 10%. At the quantum dot center, the high GaSb content extends over three atomic

chains and drops significantly at the topmost fourth chain. It should be noted that the slight

reduction of the GaSb content at the second chain corresponds to a locally darker part of the

QD in the XSTM image, indicating fluctuations of the chemical composition within the QD.

At the outer parts of the quantum dot, the high GaSb content is kept only at one central

chain, with two additional chains of moderate composition, again in good agreement with

the XSTM image contrast.

Beside this intensively discussed QD, also purer GaSb material was observed in another

QD, as already shown in Fig. 5.6(b). The stoichiometry analysis of this QD is displayed in

Fig. 6.5(b), reaching a GaSb content of nearly 100%. Corresponding to the nearly pure GaSb

material, also an increased local strain within this QD can be concluded from the increased

compression of the GaAs matrix underneath, as compared with Fig. 6.5(a).

The analysis of the wetting layer yields that both its vertical extension and composition

do not reach the values of the QDs: The stoichiometry shows a maximum GaSb content of

nearly 50% for one atomic chain, with a second chain of only about 10%, corresponding to the

XSTM images showing a strongly intermixed layer extending over one to two atomic chains.

positioningrowthdirection[nm] position[nm]

atomicchaindistance[nm]

25%GaSb

50%GaSb

QDcenter

QDedge

50%GaSb

100%GaSb

25%GaSb

WL WL

0.64 0.64

0.68

0.60 0.60

0.56 0.56

0.52 0.52

-4 -4

-2 -2

[001]

5nm

(a) (b)

5nm

Figure 6.5: Analysis of the chemical composition of GaAsSb quantum dots.

Chapter 7

The onset and pathway of quantum

dot formation

Comparing the XSTM data on different MOCVD-grown GaSb layers and knowing the tool

to analyze their local stoichiometry, it is now possible to discuss the growth of GaSb nanos-

tructures and especially the initial development of self-assembled quantum dots. In the first

section of this chapter, the general growth mechanism of GaSb layers on GaAs will be high-

lighted in the context of earlier publications. Secondly, the GaSb content of the QWs and

the WL will be evaluated, allowing conclusions on the cross-over from 2D to 3D growth

and a comparison with the strongly varying literature data for the critical thickness of QD

formation. The onset of this QD formation will finally be examined, introducing a possible

pathway from quantum wells to quantum dots.

7.1 Gaps within the Sb layers: GaSb growth

All three MOCVD-grown GaSb layers studied here are not continuous, but are interrupted

by smaller or larger gaps consisting of pure GaAs, as has been demonstrated in section 5.2

and the XSTM images shown there. These gaps are most pronounced in layer 1 with lateral

extensions of up to 7 nm, but also in layer 2 many gaps are found with a maximum extension

of 5 nm, and even the WL of layer 3 is interrupted. Typical examples of gaps are indicated

in Fig. 7.1(a), imaged at layer 2. The gaps are randomly distributed over the layer, with

typical distances between neighboring gaps of 2 to 15 nm and an average lateral extension of

the gaps of 1.4 nm.

In order to ensure that a gap shows the same contrast in an XSTM image as the surround-

ing GaAs, at least the two topmost atomic layers have to consist of pure GaAs [372, 373].

This means that for a typical gap extension of 2 nm within a 1 nm thick WL, within an area

of 10 surface unit cells and a volume of at least 20 group-V atoms no Sb but only As atoms

may be found. Such a decomposition is too unlikely for a statistical fluctuation within an

inhomogeneous GaAsSb layer, but has to be a systematic feature of GaSb growth. It should

be noted, too, that such gaps are not common for intermixed InGaAs QWs or other III-V

material systems.

However, this effect is consistent with results published by Bennett, Thibado et al.

[45, 46, 257], who studied GaSb growth on GaAs(001): After depositing 1 ML GaSb on

a c(4x4)-reconstructed GaAs(001) surface, they observed a network of 2D GaSb islands of

10 to 20 nm size and thin, 1 ML deep trenches, as shown in Fig. 7.1(b). Even when a second

ML GaSb is deposited, this material grows predominantly on top of the existing islands,

increasing their height but maintaining their diameter and preserving the trenches [46]. At

72 CHAPTER 7. THE ONSET AND PATHWAY OF QUANTUM DOT FORMATION

10nm

[ 10]1

[110]

[1 0]1

[001]

10nm

Figure 7.1: (a) XSTM

image of GaSb layer 2,

acquired at VT=

-2.0 V. Sb-free gaps

within the layer are

indicated. (b) Top-view

STM image of a 1 ML

thick GaSb layer on

GaAs, taken from [46].

this point the growth is still of two-dimensional kind. Just upon depositing a third ML GaSb,

three-dimensional growth sets in and quantum dots evolve in a self-assembled way.

Comparing these results obtained by top-view STM and the XSTM samples studied here,

one can see that the initial structure of larger 2D GaSb islands and thin trenches in between

remains conserved during dot growth: The observed gaps are the cross section of the initial

trenches, getting filled with pure GaAs when the GaSb layers are overgrown.

It should be mentioned that in a later publication from the same group, Bennett et al. [257]

report a transformation of the rather isotropic 2D island structure shown in Fig. 7.1(b) into

a strongly anisotropic surface upon further GaSb deposition: The surface of the WL studied

after deposition of 3.5 ML GaSb and accompanying QD growth is found to consist of thin

2D islands strongly elongated along the [¯

110]-direction. Corresponding structures could not

be found in the present XSTM images. However, due to the complete lack or the small size of

the observed QDs, respectively, probably significantly less than 3.5 ML GaSb were deposited

in all three layers studied by XSTM.

The discussed publications of Bennett, Thibado et al. are, to my knowledge, the only

studies of GaSb/GaAs QD growth using top-view STM. Although the authors used MBE,

their observed GaSb growth mode characterized by 2D GaSb islands interrupted by thin

trenches seems to agree also with the MOCVD-grown samples studied here.

In the PL spectroscopy results on the QD sample, shown in section 5.3.1, a clear intensity

peak which was related to a WL was obtained, indicating that the existence of gaps within

the layer does not prevent the 2D electronic confinement inherent in QWs and WLs. This

behavior agrees with an observation of Thibado et al., stating that the 2D islands form

an interconnected network [46], which could explain the lateral mobility of charge carriers

confined within the layer. Additionally, even if the 2D islands of the GaSb WL were actually

separated by the thin trenches filled with GaAs, electron tunneling across these trenches

could take place.

The gaps observed in the XSTM images show that the structure of the GaSb WL is

significantly less homogeneous and continuous than that of WLs in the InAs/GaAs [3, 92, 100]

or other material systems. Neverthelss, the Stranski-Krastanow growth mode, leading to the

formation of QDs embedded in a WL as described in section 2.2.1, is confirmed – at least in

a slightly modified case – also for the GaSb growth on GaAs studied here.

7.2. GASB CONTENT OF THE QUANTUM WELLS 73

7.2 GaSb content of the quantum wells

The structures of the GaSb QWs of layers 1 and 2 and of the GaSb WL of layer 3, which have

been presented in section 5.2, are compared in Fig. 7.2. Although they show the same general

appearance, smaller differences between the three layers can be identified, with layer 1 being

the thinnest and most inhomogeneous and layer 2 having the largest vertical extension.

For a more quantitative analysis of the GaSb content of these layers, their local lattice

constants have been evaluated by the method described in chapter 6, resulting in the data

shown in Fig. 7.3. Thereby typical areas of the XSTM images, containing parts of the

layers with different GaSb composition and small gaps, too, were chosen for averaging and

evaluating the chain distances, as can be seen in the insets of Fig. 7.3. Layer 1 exhibits the

sharpest peak of increased chain distance, with the GaSb material being mainly concentrated

to one atomic chain and a maximum GaSb content of 50%. In layer 2, in contrast, the

maximum GaSb content reaches only about 27%, but in [001] direction the QW extends over

slightly more than two atomic chains, with a smoother decay of the lattice constant at the

top side of the layer. The chain distances of layer 3, finally, resemble more those of layer 1,

showing an abrupt decrease at the top side. Layer 3 extends over two atomic chains, with

chain distances corresponding here to 16% and 36% GaSb content, respectively.

In spite of the different extensions and maximum stoichiometries of the three layers, their

total GaSb content, which can be evaluated from the chain distance analysis by integrating

the curves over the area of increased GaSb content, amounts to 1 ML of pure GaSb for each

of the three layers. Thus, the higher maximum content in one layer is balanced by the larger

vertical extension of another. This result is important for understanding GaSb growth on

GaAs: Layers 1 and 2 have been grown with nearly the same GaSb deposition time of 21 s

for layer 1 and 22 s for layer 2, while at layer 3 GaSb was deposited at the same rate for

25 s. The fact that only layer 3 exhibits quantum dots agrees well with the observed identical

GaSb content within the 2D layers, showing that the additional GaSb material of layer 3

was completely incorporated into the 3D structures. Therefore, layer 2 has been grown very

close to the critical thickness of QD formation. The observed existence of Sb-rich 2D islands

in layer 2 supports this result, as will be discussed in the next section. The intermixed

stoichiometry of all three layers not exceeding 50% antimony, which leads to the relatively

large vertical extension of 2 to 4 ML compared with only 1 ML total GaSb content, shows a

10nm 10nm

[1 0]1

[001]

(a) (b) (c) 10nm

Figure 7.2: XSTM

filled state images of

the QWs of (a) layer 1,

(b) layer 2, and

(a,b) VT= -3.0 V and

two bright spots at the

QW in the bottom part

of (c) are adsorbates.

74 CHAPTER 7. THE ONSET AND PATHWAY OF QUANTUM DOT FORMATION

layer1

layer3

layer2

Figure 7.3: Evaluation of the local lattice constant of the MOCVD-grown GaSb layers, far away

from any Sb-rich islands or QDs. Calculated values for GaAs0.75Sb0.25 and GaAs0.5Sb0.5QWs are

indicated. The areas for analyzing the chain distances in the XSTM images are shown as insets.

strong intermixing between Sb and As atoms.

Coming back to the exact characteristics of the analyzed chain distances, more details

about the GaSb growth mechanisms can be revealed: The QW of layer 1 and the WL of layer 3

have the same total GaSb content and nearly the same variation of the lattice constant,

except that in layer 1 the antimony is more concentrated in only one atomic chain. The

growth parameters of these two layers differ regarding the GaSb deposition time, which has

lead to the QD formation at longer deposition in layer 3, and regarding a growth interruption

subsequent to GaSb deposition which only took place at layer 3. This 2 s growth interruption

under TESb flux was chosen to give the deposited material enough time for QD formation

[51, 182], and it also seems to have the effect of an additional intermixing of the deposited

Sb atoms with the As atoms of the underlying GaAs matrix. Even stronger intermixing may

have occured during overgrowth of the GaSb layers, but such intermixing should influence

layers 1 and 3 to the same extent.

Layer 2 was grown with 22 s GaSb deposition time, slightly longer than layer 1, also

followed by a 2 s growth interruption, equal to layer 3. However, the variation of the local

lattice constant is considerably different to that of layers 1 and 3, although the remaining

growth parameters were nominally the same. The sample containing layer 2 was grown in

the same MOCVD chamber, but several months earlier than the sample with layers 1 and 3.

Therefore, slightly different conditions of the reactor, such as an unintended As background

pressure during GaSb growth, are supposed to cause the observed larger intermixing of layer 2.

All three chain distance curves shown in Fig. 7.3 show a significant undershoot just before

they increase, standing for compressive strain within the GaAs matrix directly underneath

the GaSb layers. However, a homogeneous quantum well does not compress the underlying

material, because the strain in growth direction can completely relax by increasing the chain

distance, in contrast to quantum dots with a locally enlarged strain [3, 124]. An apparently

decreased chain distance can also be given by a concave surface curvature directly underneath

the GaSb layer, as discussed in section 6.3. However, this effect cannot sufficiently explain

the observed undershoot, as a QW undergoes only very small cleavage-induced relaxation as

7.2. GASB CONTENT OF THE QUANTUM WELLS 75

compared with a QD [124], and because for homogeneous WLs studied in the InAs/GaAs

material system, hardly any undershoot of the chain distances is present [100]. Thus the

existence of locally compressed strain underneath all three GaSb layers studied here is a clear

evidence for a laterally inhomogeneous composition of the layers, with fluctuations of the

stoichiometry in [1¯

10] direction leading to fluctuations of the local strain.

Values of the critical thickness of deposited material upon which epitaxial growth changes

from 2D to 3D (often called “critical thickness of dot formation”), which depend weakly on

the growth parameters and essentially on the material system, vary strongly in literature for

the GaSb/GaAs system [44, 46, 49–51, 55, 57, 59, 69, 182, 256, 260, 264, 267]. Almost all

publications about MOCVD growth of GaSb QDs can, to my knowledge, be distributed to

either M¨uller-Kirsch in the group of Bimberg at Berlin University of Technology in Germany

[51, 53, 71, 73, 264, 265] or Motlan in the group of Goldys at Macquarie University in

Sydney, Australia [52, 61, 74, 260, 262, 263]. Recently, also GaSb QDs grown by organo-

metallic vapour phase epitaxy were published by Pitts from the group of Watkins at Simon

Fraser University in Burnaby, Canada [57].

M¨uller-Kirsch reports a large critical thickness of dot formation of about 4 ML GaSb

deposition [51, 264], obtained by growing several samples with varying GaSb deposition

times and observing by AFM in which samples QDs have formed. For this evaluation, the

GaSb growth rate has to be known which is a non-trivial issue as this growth rate can change

dramatically with deposition time (see section 5.1 and Ref. [182]). In an early publication

from Kinder and Goldys [260], the critical thickness of GaSb dot formation is quoted to

be less than 2 ML, also obtained by comparing different samples by AFM. For this value,

however, a constant growth rate was assumed which was extrapolated from growing thick

GaSb layers, which could be a critical premise. Later on Motlan et al. from the same group

specify only deposition times and no definite values of a critical thickness [52, 74, 263]. An

astonishingly smaller value of the critical thickness between 0.3 and 0.5 ML is given by Pitts

et al. [57], also after studying the GaSb growth surface by AFM. On the other hand, when

the investigated sample was not cooled down after GaSb deposition for examination by AFM

but was immediately overgrown by GaAs, flat GaSb films were maintained up to a deposition

of 1 ML. Both values, however, might be somewhat arguable, because the growth rate again

was assumed to be constant and, even more, it was extrapolated from certain volumes of

observed QDs after certain deposition times as evaluated from AFM measurements under

ambient conditions.

The majority of results on GaSb QD growth has been obtained using MBE. Amongst

these, most authors specify the critical thickness of dot formation to amount between 2 and

3 ML, as for examples in Ref. [46, 49, 55, 59, 69, 256]. Even larger values of about 4 ML can be

found, too [44, 267], but also a critical thickness of only about 1 ML was reported [50]. These

data will be discussed in detail in section 9.3.2. Summarizing this variety of literature results,

controversial values ranging from 0.4 ML to 4 ML are reported for the critical thickness of dot

formation, which at least for the MOCVD-grown samples are obtained under assumptions

which are not necessarily fully appropriate.

In XSTM studies, the total GaSb content of capped layers can be analyzed, amounting

here to 1 ML for the QW near the onset of QD formation and equally to 1 ML for the WL.

This value is not necessarily the critical thickness of dot formation, as a part of the originally

deposited GaSb material can have been transferred into QDs or have segregated from the

GaSb layer upon capping. Due to the observed GaSb content, however, the critical thickness

of dot formation must at least amount to 1 ML. The XSTM images of the GaSb layers shown

in section 5.2 are characterized by a nearly perfect cleavage surface of the GaAs matrix

several nm below or above the layers, containing no incorporated Sb atoms. Therefore, in

76 CHAPTER 7. THE ONSET AND PATHWAY OF QUANTUM DOT FORMATION

spite of the strong intermixing directly at the GaSb layers, no significant segregation during

overgrowth can be detected. It cannot be excluded that a part of the initially deposited GaSb

has stayed at the growth surface as surfactant during overgrowth, but the observed lack of

significant Sb segregation and reincorporation increases the probability that the observed

GaSb content of 1 ML is also the critical thickness of dot formation.

Two publications confirm the observed results: Besides studying growth surfaces, M¨uller-

Kirsch has also evaluated the GaSb content of capped GaSb layers with and without QDs

from high-resolution TEM images and by simulating PL data [182]. He derived an intermixed

GaAs0.6Sb0.4layer of 2 ML height at the cross-over from 2D to 3D growth, resulting in a

total GaSb amount of about 0.8 ML, which agrees well with the value of 1 ML found here by

XSTM. Using x-ray diffraction and a rather complex epitaxial growth sequence, Pitts et al.

studied the maximum incorporation of Sb into GaSb QWs before QD growth sets in, also

resulting in approximately 1 ML [57], again in good agreement with the XSTM data.

7.3 Structures from quantum wells to quantum dots

Knowing that the formation of QDs starts after depositing 1 ML or slightly more GaSb,

the question remains how the transition from 2D to 3D growth occurs. The initial GaSb

film on GaAs consists of flat islands and small trenches, as it was discussed in section 7.1,

revealing a 2D island growth. The QWs of layer 1 and 2, shown in Fig. 7.2(a,b), are results

of such a GaSb layer growth, with the difference that the 2 s growth interruption under

TESb flux following GaSb deposition at layer 2 has lead to a slightly more homogeneous

well structure. Additionally, Sb-rich 2D islands of only a few nm size and a high density of

∼6 x 1011 cm−2have been observed in layer 2 (see section 5.2.2 for details). Two typical

examples of these Sb-rich flat structures are shown again in Fig. 7.4(a), clearly recognizable

by their strongly increased image contrast. No such Sb-rich islands have been found in layer 1,

thus the slightly longer GaSb deposition at layer 2 has supplied the necessary material and

the growth interruption enabled the material to agglomerate in these self-assembled Sb-rich

islands. The observance that layer 1 and the QW of layer 2 beside the islands contain the same

amount of GaSb confirms that the additional material of layer 2 has moved into these areas

of increased Sb concentration. Thus, the observed small 2D islands are first self-assembled

Sb accumulations and possibly act as QD precursors.

The cross-over from 2D to 3D growth occurs during the additional 3 s GaSb deposition

5nm5nm

islands

island

(a) (b)

[001]

quan-

tum

dot

5nm

(c)

Figure 7.4: Comparison of XSTM filled state images of (a) 2D-islands in layer 2, (b) a tiny 3D-island

in layer 3, and (c) a quantum dot in layer 3. For details see sections 5.2.2 and 5.2.3.

7.3. STRUCTURES FROM QUANTUM WELLS TO QUANTUM DOTS 77

time making up the difference between layers 2 and 3. The smallest known 3D GaSb structures

are the tiny islands observed in layer 3 like that shown again in Fig. 7.4(b). No comparable

structures have been mentioned in literature yet, what is not very surprising, because most

earlier work on GaSb QDs has used characterization methods like AFM [48, 49, 51, 55–

58, 256, 260, 263, 374], SEM [56, 267] or TEM [44, 51, 53, 262, 263, 374], which are not able

to resolve structures of only 2 or 3 nm size. The density of these tiny 3D islands is with

∼5×1010 cm−2about one order of magnitude smaller than that of the 2D islands of layer 2,

but it is similar to that of the QDs also found in layer 3, amounting to ∼3×1010 cm−2. It

cannot securely be said whether the tiny 3D islands have emerged from the 2D GaSb-rich

islands, the latter ones not being observed in layer 3 any more. The total GaSb content of

a tiny 3D island is approximately the same as that of a 2D GaSb-rich island, as estimated

from the volumes of typical examples of the structures. Another possibility is that the longer

GaSb deposition lead directly to the formation of 3D GaSb structures during the subsequent

growth interruption.

As both the tiny 3D islands and small, but distinctive QDs as the one shown again in

Fig. 7.4(c) are observed within layer 3, GaSb QDs most probably develop from such tiny 3D

islands which act as precursors. The qualitative difference between both kinds of structures

is that the XSTM images reveal significant strain and electronic confinement only for QDs,

as has been discussed in section 5.2.3. The coexistence of the islands with only about 2 nm

size and the QDs with typically 4 to 8 nm lateral extension and about 2 nm height in the

same GaSb layer is comparable to the large size fluctuation found for larger GaSb QDs by

top-view TEM (see section 5.3.2 for details).

From XSTM images like Fig. 7.4(c) it can be seen that the WL in the direct neighborhood

of the QD contains very few Sb atoms. This indicates a growth and ripening of the QDs not

only by direct incorporation of deposited material, but also by mass transfer along the growth

surface from the surrounding WL. It should be noted that for the InAs/GaAs system a general

mass transfer from the WL to ripening QDs has been reported, together with a coexistence

of QDs and small 3D clusters [375].

The electronic confinement within the GaSb QDs has also been confirmed by the PL

data shown in section 5.3.1, exhibiting a PL emission energy of the QDs of 1.2 eV. This

energy corresponds to the small size of the QDs. The energy separation between confined

states within a QD depends critically on its size [3, 37, 211], implying a minimum QD size

for the existence of a first confined state. In the InAs/GaAs material system, this minimum

size is between 3 nm and 5 nm of lateral extension [2]. For GaSb/GaAs QDs, however, the

confinement condition must be fulfilled only for VB hole states. Because the energy separation

between confined hole states is generally much smaller than between electron states (see

Fig. 2.10 and Refs. [3, 37]) due to the about one order of magnitude larger effective masses of

the holes also for GaSb [164], and because of the large VB offset for GaSb/GaAs QWs and

small QDs of 0.5 eV [75], the minimum size for electronic confinement is thus significantly

smaller in the GaSb/GaAs system. Therefore, the observed small size of typically 4 to 8 nm

base diameter does not inhibit the QDs to be optically active.

Comparing the shape and size of the QDs studied here with literature data, it is found that

they are not only smaller than typical InAs/GaAs QDs [24, 33, 38, 95, 100, 119, 120, 122],

but also smaller than most GaSb/GaAs QDs. Although results obtained by ex-situ top-view

characterization methods on uncapped, oxidized GaSb QDs [49, 52, 56, 69, 267] cannot be

compared with XSTM data, also in-situ STM measurements on uncapped QDs during growth

[46, 257] and studies on overgrown QDs [51, 59, 263] obtained GaSb QD sizes of more than

10 nm. Smaller QD sizes are not published, but M¨uller-Kirsch et al. reported stoichiometry

fluctuations of a strongly intermixed GaAsSb WL [71, 73, 265], which can be compared with

78 CHAPTER 7. THE ONSET AND PATHWAY OF QUANTUM DOT FORMATION

the structures observed here: Possibly those reported fluctuations, which exhibited a PL

peak at an energy about 0.1 to 0.2 eV below the WL peak, actually were structures similar to

the QDs studied here, but could not be resolved as 3D structures due to the limited atomic

resolution of HRTEM used in that work.

The flat QD shape with a small aspect ratio observed for the QDs studied here agrees

well with published results on larger capped QDs grown by MOCVD [51, 263]. From the

observed coexistence of precursor structures and QDs in the same layer and from the small

size of the QDs in comparison with published data, it can be assumed that the QDs studied

here represent an early stage of MOCVD QD growth.

In conclusion, the following pathway of GaSb QD formation can be proposed: The initial

GaSb deposition on GaAs(001) produces a thin film consisting of 2D islands of 10 to 20 nm

size, separated by small trenches. Continuing GaSb growth up to the critical thickness of

dot formation, which amounts to about 1 ML or more, the formation of several nm large

flat 2D islands of increased Sb concentration can occur during a short growth interruption.

With further continued GaSb deposition, three-dimensional growth sets in by forming tiny

3D islands, which then ripen to optically active QDs which can further increase in size. This

process includes a GaSb depletion in the WL close to the growing dot. During overgrowth,

the initial trenches of the WL get filled with GaAs. Significant intermixing occurs, probably

already during GaSb deposition, during the growth interruption thereafter, and during the

capping process, leading to a QD stoichiometry of about 60% - 100% GaSb concentration

and strongly intermixed QWs and WLs with less than 50% GaSb content.

Chapter 8

XSTM results on MBE-grown

samples

While the data on MOCVD-grown samples concentrated on the onset of QD formation, a

broader range of GaSb/GaAs QD structures could be studied on samples grown by MBE. As

the MBE method allows a more direct control of the GaSb deposition and the growth process

than MOCVD (see chapter 2.2), it was possible to study several GaSb layers with system-

atically varied amounts of deposited material within one MBE-grown sample. Additionally,

samples grown in two different places by different cooperation partners could be compared.

8.1 Sample structures

The results on MBE-grown structures can be devided in data derived from two samples:

Sample C has been grown by Ganesh Balakrishnan in the group of D. L. Huffaker at the

Center of High Technology Materials in Albuquerque at the University of New Mexico, USA

[376], and sample D by Ian Farrer in the group of D. A. Ritchie at the Cavendish Laboratory

at the University of Cambridge, UK [377].

Both samples were fabricated in a VG-V80H MBE system, respectively, using conventional

solid sources for gallium, antimony, and aluminum as well as a cracker source for arsenic.

Sample C was grown with As2, received from the cracker unit operated at high temperatures,

while for sample D the cracker source was operated at 600◦C, resulting in an arsenic beam

consisting of As4. Antimony was provided as Sb4in both samples. Detailed sample structures

can be seen in Fig. 8.1: On GaAs(001) substrates, highly n-doped with silicon, first a thick

GaAs layer was grown (300 nm in sample C, 200 nm in sample D), followed by an AlGaAs

buffer layer of 100 nm thickness. Thereafter, the heterostructures consisting of several GaSb

QD layers and GaAs spacers were deposited, followed by 200 nm AlGaAs, respectively. An

additional 5 nm AlGaAs / 5 nm GaAs / 5 nm AlGaAs marker was grown above the second

GaSb layer of each sample, helping to rapidly identify the individual layers during the XSTM

measurements. The complete structures were finished by a GaAs cap layer, which is about

800 nm thick and undoped in sample C and 1000 nm thick and p-doped with a Be dopant

concentration of 5 ×1016 cm−3in sample D.

The actual heterostructure of sample C consists of four GaSb layers with increasing

amount of deposited material, separated by 90 to 100 nm thick GaAs spacer layers and

the AlGaAs marker mentioned above, and is embedded within two additional 100 nm thick

GaAs layers. Sample D contains three GaSb layers, with GaAs spacers of 120 nm thickness

between the first and second and 215 nm including the AlGaAs marker between the second

and third, also embedded within additional GaAs layers of 150 nm thickness each.

80 CHAPTER 8. XSTM RESULTS ON MBE-GROWN SAMPLES

substrate

-doped

GaAs:Si

~300nm

GaAs

100nm

AlGaAs

50nmGaAs

90nmGaAs

200nm

AlGaAs

5nm AlGaAs

5nmAlGaAs

5nmGaAs

~800nmcap

GaAs

1ML GaSb

5sSbsoaking

2ML GaSb

5sSbsoaking

2.7ML GaSb

5sSbsoaking

3.1ML GaSb

5sSbsoaking

10sgr.i.

without As flux

beloweachGaSb

layer(cooling)

nogr.i.above

theGaSblayers

100nmGaAs

AlGaAs

markerlayer

growthtemperature

550°C 490°C

sampleC

substrate

-doped

GaAs:Si

200nmGaAs

100nm

Al Ga As

0.33 0.67

150nmGaAs

110nmGaAs

10nmGaAs

90nmGaAs

100nmGaAs

140nmGaAs

200nm

Al Ga As

0.33 0.67

5nm AlGaAs

5nmAlGaAs

5nmGaAs

1000nmcap

-doped

GaAs:Be

1minSbsoaking

1ML GaSb

1minSbsoaking

2ML GaSb

1minSbsoaking

AlGaAs

markerlayer

10nmGaAs

growthtemperature

600°C 515°C

7mingr.i.under

As fluxbelow

eachGaSblayer

(cooling)

30secgr.i.above

eachGaSblayer:

first15sSb flux,

second15s As flux

sampleD

Figure 8.1: Comparison of the detailed sample structures of the MBE-grown samples.

While the layer sequence of both samples is very similar, the growth rates, temperatures

and the detailed parameters for depositing GaSb layers differ quite strongly for both sam-

ples, representing different approaches and special experiences with GaSb growth in the two

involved epitaxy groups. For sample C, a growth rate of 0.3 ML/s was chosen for all layers,

while the growth temperature was changed between 550◦C for all GaAs and AlGaAs layers

and 490◦C for the GaSb layers and the following 5 to 10 nm of GaAs, respectively. Sample D

was grown with a higher growth rate of 0.7 ML/s for all layers. The temperatures here were

8.2. OVERVIEW IMAGES 81

600◦C for the GaAs and AlGaAs layers and 515◦C for the GaSb layers and the subsequent

10 nm of GaAs, respectively, as measured during growth by an infra-red pyrometer.

One main challenge of GaSb/GaAs QD growth by MBE is the precisely controlled change

of the group-V atoms during epitaxy and the resulting abruptness of the interfaces (see section

2.2.2 and Refs. [55, 57, 59, 177]). Usually epitaxial growth is controlled by the group-III flux,

while the group-V atoms are offered abundantly as a permanent background, also during

growth interruptions (see chapter 2.2). When Sb atoms are offered to a GaAs surface during

epitaxy, considerable As-Sb exchange reactions occur, leading to an Sb-rich growth surface

[50, 55, 57, 59]. Thus it has been found to be helpful for GaSb QD growth to expose the

underlying GaAs surface to an antimony flux during a growth interruption (GI) prior to GaSb

deposition, a process called “Sb soaking” [55, 59, 69].

Such an Sb soaking was used in both samples, but with special emphasis in sample D:

Here, the first GaSb layer was formed only by this Sb-for-As exchange process during a 1 min

long Sb soaking, with the gallium source being closed during the whole antimony supply. For

the second layer, the same 1 min long Sb soaking was followed by a direct deposition of 1 ML

GaSb, and in the third layer 2 ML GaSb were grown subsequently to 1 min of Sb soaking.

GaSb growth was followed for all three layers by a GI of 15 s under antimony background for

annealing the deposited material and subsequently 15 s during which the valve of the arsenic

cracker cell was opened again, before GaAs growth was continued. This exit valve of the As4

cracker unit, needing several seconds to be operated, is used additionally to the conventional

shutters of the effusion cells. The latter can be closed and opened much faster, but can reduce

the arsenic flux only by about 80%, while the cracker valve enables the growth of much purer

GaSb material [55]. The growth temperature was reduced during a 7 min GI prior to each

Sb soaking and held at this value until the GaSb layer was covered with 10 nm GaAs, then

during another 7 min GI it was raised again.

At sample C, the four GaSb layers were grown with increasing amounts of deposited

material of 1 ML, 2 ML, 2.7 ML, and 3.1 ML. Each layer was preceded by 5 s of Sb soaking,

expectedly corresponding to sufficient Sb to replace nearly one ML As at the surface. Even

prior to this, growth interruptions of 10 s took place without supply of either antimony or

arsenic, so that the reconstruction of the underlying GaAs surface became metal rich. This

sequence of GI, Sb soaking, and GaSb growth was chosen to increase the QD uniformity and

density. During the 10 s GI also the growth temperature was reduced for GaSb growth for

all four layers. It was increased again during GaAs deposition when the GaSb layers had

already been overgrown by about 5 to 10 nm.

While the GaSb growth sequence of sample D was ascertained by calibrated growth rates

and experience from reference samples, RHEED measurements enabled a direct control of

the deposited material at sample C. For the latter sample, in spite of the small amount of

only 1 ML of deposited GaSb at the first layer, a clear QD signal was monitored by RHEED

for all four GaSb layers during growth.

8.2 Overview images

In XSTM images of the overgrown samples GaSb QDs could be observed in all four layers

of sample C and also in those two layers of sample D for which GaSb material was directly

deposited. Overview images of the first three GaSb layers of sample C and of the third GaSb

layer of sample D can be found in Figs. 8.2 and 8.3, respectively. All STM images of samples

C and D were taken with tunneling currents ITbetween 50 pA and 100 pA.

Figure 8.2 is dominated by cleavage-induced surface steps running mainly along the [1¯

11]

and [1¯

12] directions, but the three GaSb layers are also clearly visible by their bright contrast.

82 CHAPTER 8. XSTM RESULTS ON MBE-GROWN SAMPLES

2.7ML GaSb

2ML GaSb

1ML GaSb

markerlayer

AlGaAs

100nm

[001]

growth

direction

surface

steps

adsorbates

Figure 8.2: Overlapping XSTM overview images of sample C, taken at VT= -2.7 V, together with

the sketched sample structure. GaSb layers 1 to 3 and the AlGaAs marker can be identified, together

with many cleavage-induced surface steps. Small spots are adsorbates on the cleavage surface.

The helpful role of the thin AlGaAs double layer as marker is obvious. Additionally, many

adsorbates, arising from residual gas contamination of the cleavage surface, can be seen

as small bright or dark spots. At this low magnification, individual QDs are only weakly

observable within the GaSb layers. Especially the presence of the surface steps makes it

difficult to identify the QDs and to observe their structure: Firstly, the image contrast of

these one or several atomic ML high steps exceeds that of the QDs. Secondly, as the course of

the surface steps is partly random but finally governed by strain, these steps often run parallel

to the wetting layers (WLs) or end directly within a QD. Therefore, multiple attempts to

position the XSTM tip on macroscopically different positions of the cleavage surfaces were

necessary to obtain data on all seven GaSb layers at areas with a sufficiently low step density.

In XSTM images of sample D, the GaSb layers generally exhibit a somewhat weaker

image contrast, corresponding to less strain or a lower Sb content of the nanostructures,

although their nominal GaSb content is comparable to that of the thinner layers of sample C.

Figure 8.3 shows overview images of the third GaSb layer of sample D, displayed with an

about two times larger magnification compared to Fig. 8.2. At this image size, individual,

very flat QDs can be recognized by their increased contrast. Similar QDs, embedded in a

distinctive WL, could be obtained in GaSb layers 2 and 3. Layer 1, however, which contains

no directly deposited GaSb but has formed only due to Sb soaking, is rather a thin region

of individual GaSb atoms than a continuous layer. This first layer will be discussed in more

detail in chapter 9.2.

Those results and a comparison of this soaking-induced layer with the other two layers of

sample D will reveal new insight into group-V exchange processes, their influence on QDs and

the onset of GaSb QD formation; while the data on sample C, containing more and larger

[001]

growthdirection

GaSbQDs

50nm

Figure 8.3: Overlapping XSTM images of sample D, taken at VT= -2.7 V, showing the third GaSb

layer containing flat QDs.

8.3. QUANTUM DOTS IN SAMPLE C 83

QDs in GaSb layers with a broader range of deposited material, are more suited to study the

atomic structure and further development of GaSb QDs.

The appearance of the QDs in XSTM images of both samples C and D can generally

be grouped into two kinds of structures: Besides QDs with trapezoidal cross sections, cor-

responding to the well-known QD shape of a truncated pyramid, also cross-setions showing

small paired features, symmetrically to each other, with a more or less pronounced gap be-

tween them are found regularly, which can be attributed to ring-like QD structures. Typical

examples of both types of QD cross sections in samples C and D are presented in the next

two sections, including a statistical analysis of the apparent QD structure, respectively. By

comparing these statistical data with numerical simulations on random cleavage processes

the origin of the different appearance of QD cross sections will be revealed. The exact atomic

structure of the QDs and the evolution of their shape will be discussed in chapter 10.

8.3 Quantum dots in sample C

A total number of 140 GaSb QDs in sample C has been investigated, distributed over four

layers with increasing amount of deposited GaSb material and QD densities increasing corre-

spondingly from 4×1010 cm−2in the first layer to 9×1010 cm−2in the fourth layer, evaluated

from the XSTM data as described in section 5.2.3.

8.3.1 Quantum dot shapes in XSTM images

Nearly half of the QDs, 69 of 140, have a rather compact appearance like those two shown in

Fig. 8.4(a,b), imaged in layer 2 (a) and layer 3 (b). Their shape generally resembles that of

common capped QD structures, which are well-studied for example in the In(Ga)As/GaAs

system [92, 95, 97, 100, 119]. In detail, the cross sections through the QDs reveal a trapezoidal

Figure 8.4: XSTM filled state images of sample C: Close-view images of (a) a QD in layer 2, taken

at VT= -1.7 V, and (b) a QD in layer 3, taken at VT= -2.6 V, (c) overlapping images of the QD

shown in (b) together with another, ring-shaped, QD structure, acquired at VT= -2.5 V, and (d) a

close-view image of another QD in layer 2 with a depression at the top center, acquired at VT= -1.9 V.

84 CHAPTER 8. XSTM RESULTS ON MBE-GROWN SAMPLES

shape, which can clearly be seen in Fig. 8.4 by the strong contrast, with a rather flat (001)

top facet and comparatively steep side facets. Typical base lengths are between 10 and 20 nm

with heights roughly about 2 nm. The interfaces between the GaSb QD and the surrounding

GaAs are not perfectly abrupt, but in some places smeared over about one atomic chain.

In addition, the varying image contrast within the QDs indicates an alloyed GaAsxSb1−x

material with inhomogeneous chemical composition. Within the GaAs matrix grown on top

of the GaSb layers, several bright spots are visible both above the QDs and above the WL.

These spots can be attributed to single Sb atoms, indicating antimony segregation into the

overgrowth layer.

However, in Fig. 8.4(c) together with the nice, compact QD shown in (b) also a different

QD structure can be seen in the upper part of the image: This structure appears as a pair of

bright, nearly axially symmetric features, each with a lateral extension of about 6 nm and a

height of four to five atomic chains or about 2.5 nm, distanced to each other by about 10 nm.

Therewith this structure is of the same height and slightly larger in lateral extension than the

neighboring compact QD, and it is a typical example for the other half of the QD structures

in the sample: Indeed, 71 of 140 QD structures observed in sample C consist of two paired

features with a more or less distinct gap in between.

A close-view image of the paired QD structure shown above is presented in Fig. 8.5(a),

together with an even more pronounced example of such a structure observed in layer 4

[Fig. 8.5(b)]. These structures represent a cross section through a quantum ring, as the

sketch of Fig. 8.5(c) illustrates: The paired features of bright appearance occur when the

ring of high GaSb content is cut, while the dark gap in between is a region containing only a

few or no Sb atoms at all. Actually, many ring-shaped QD structures are not that well defined

as those in Fig. 8.5(a,b), but are asymmetric or with much smaller central gaps containing

some residual Sb atoms, as the structure of Fig. 8.5(d) shows.

To confirm the assumption of the observed paired features representing ring-shaped struc-

tures and to exclude the possibility that they are only a random distribution of individual

small islands, the free distance between neighboring GaSb structures in the XSTM images was

evaluated statistically for layers 2 and 3, as shown in Fig. 8.6(a). For this analysis a paired

feature was first considered as two independent islands, resulting in a broad, irregular distri-

bution of QD distances along [1¯

10]-direction with a strong increase for very small distances

5nm

(a)

[1 0]1

[001]

5nm

(b) 5nm

(d)

10nm

[1 0]1

[110] [001]

(c)

height

width inner

radius

outer

radius

ring

body

Figure 8.5: Ring-shaped QDs in sample C: (a,b) close-view XSTM images of (a) layer 3, taken at

VT= -2.3 V, and (b) layer 4, taken at VT= -1.8 V; (c) sketch of a cross section through a ring, the

notation of the geometric parameters used in the text is indicated; (d) XSTM image of an asymmetric

ring structure in layer 3, acquired at VT= -1.7 V.

8.3. QUANTUM DOTS IN SAMPLE C 85

( 1)11

(111)

(1 1)1 ( 11)1

[ 10]1

(001)

different

(110)

cleavage

planes [110]

(b)

(a)

frequency

distancebetweenneighboringQDs[nm]

0 20 40 60 80 100 120 140 160

pairedfeatures

with

without

Figure 8.6: (a) Histogram of the free distances between neighboring QDs along [1¯

10]-direction in

layers 2 and 3, interpreting the paired features either as two separate QDs (blue columns) or as

one ring-shaped structure (red columns), obtained from XSTM images. (b) Model of different cross

sections through a ring-shaped QD.

(blue columns). Alternatively, each paired feature was considered as one ring-shaped QD

(red columns). In the latter case, a nice distribution of next-neighbor QD distances results,

ranging from 8 nm to 148 nm in the observed area with a maximum peak at about 40 nm

and an expected exponential decay for longer distances. The statistic average of 60 ±33 nm

corresponds to a QD density of about 8 ×1010 cm−2. In contrast to this rather broad and

smooth distribution, the free distance between the paired features – i.e. the inner ring di-

ameter – only ranges from 1 to 14 nm with an average of 5.4±2.9 nm. This very narrow

distribution shows no correlation to that of the QD distances, verifying that it can well be

distinguished between the paired features of a cleaved ring structure and two independent,

neighbored QDs.

The fact that the extension of the central gap (the inner diameter) varies between the

images of different ring-shaped QDs needs not necessarily be due to actual differences of

the ring structures: Because the position at which a QD is cleaved in an XSTM experiment

is random, different QDs with nearly the same structure will result in very different cross

sections in XSTM images, as sketched schematically in Fig. 8.6(b). Central cross sections

along line 1 and 2 will exhibit a central gap of decreasing extension, as in the images of Fig. 8.5,

but a cut through the edge of a ring structure along line 4 will result in a rather compact,

continuous cross-sectional image. Therefore, also the two nice QDs of Fig. 8.4(a,b) could

actually have a ring-shaped structure, which is cut at the edge. Indeed, in both images the

brightest contrast, standing for high GaSb content and large strain, can be found in the outer

parts of the QDs, while the center is a bit darker and more inhomogeneous, indicating less

strain and GaSb content. Especially when a ring is cut at its edge in that way that the larger

part of the ring is still in the sample underneath the cleavage surface, a strain distribution

which is larger at the outer parts and smaller in the center will result. Additionally, some of

the compact QDs observed in sample C exhibit a depression in the center of the top face, as

it can weakly be seen already in Fig. 8.4(b) and very clearly in Fig. 8.4(d), showing another

QD in layer 2. Such a depression agrees well with the expected cross section along line 3 of

the sketch in Fig. 8.6(b).

8.3.2 Statistical and simulated data on quantum dot cleavage

Considering that the paired features observed in sample C as well as the QDs with a rather

compact appearance can both represent cross sections through ring-shaped QD structures, the

86 CHAPTER 8. XSTM RESULTS ON MBE-GROWN SAMPLES

question arises whether all observed structures are actually rings, or whether ring-shaped and

conventional, continuous QDs coexist as two different structures. To answer this question, a

detailed statistical analysis of all QDs observed in sample C will be compared with simulated

data on random cross sections through ring structures.

In all four layers of sample C, QD images with and without central gap (i.e. paired features

and compact looking QDs) were obtained to about the same amount in the XSTM data. As

the absolute sizes of the structures vary due to the size distribution of the QDs within one

layer and due to an increasing average QD size from layer to layer, a parameter is needed

which can describe the characteristics of the central gap independent of the total size of the

structure. Therefore the ratio of apparent inner to outer ring diameter ˜r=din, cut / dout, cut

was studied, which is zero for a QD image with compact appearance and nonzero but smaller

than one for a paired feature. This ratio was evaluated for all 140 QDs observed in sample C,

as shown by the red columns of the histogram in Fig. 8.7. As expected, the value ˜r= 0 was

obtained 69 times, corresponding to XSTM images showing a rather compact QD. For those

QDs revealing a ring shape in the images, the measured inner and outer diameters result

in a ratio varying from nearly zero up to 0.7, with a statistical average of ˜r= 0.35 ±0.14.

The irregular jump in the histogram between ratios of 0.3 and 0.4 is probably only due to

statistical noise.

In order to either confirm or disprove the assumption that the statistical XSTM data

represent a random distribution of cross sections exclusively through ring-shaped QDs, such

a distribution was simulated as follows: Firstly, for a given ring structure with a certain

ratio of actual inner and outer diameter r=din / dout the apparent ratio ˜rwas calculated

in dependence of the position were the QD is cleaved [see Fig. 8.6(b)], obtaining a frequency

distribution of different ratios (obviously, the diameter din, cut appearing in an XSTM image is

nearly always smaller than the actual diameter din and only equal if the ring is cut centrally).

In a second step, the calculation was repeated many times while the actual ratio of diameters

was varied in small steps from r= 0.1 to 0.9. Probably the inner diameter is not the

same for all rings but varies, as the total size of the structures also does. Therefore a

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100

experimentalhistogram[numberofQDs]

simulateddistribution[a.u.]

apparentratior=d /d

in, cut out, cut

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

experimentalhistogram

simulateddistribution

apparentratior

r =0.42

=0.13

Figure 8.7: Distribution of the ratio ˜rof apparent inner to outer ring diameter, obtained from

the XSTM images of the QDs in sample C (red column) and by simulation (blue column) using the

indicated parameters r0and σ. The inset shows a magnification, leaving out the large peak at ˜r= 0.

8.3. QUANTUM DOTS IN SAMPLE C 87

Gaussian distribution of the actual ratio ris assumed with an average value r0and a standard

deviation σ. Consequently, the calculated distributions of ˜rfor various actual ratios rhave

to be weighted by this Gaussian distribution. Finally, the parameters r0and σare optimized

to receive a best fit of the calculated, weighted distribution with the experimental histogram.

The details of this procedure, the used algorithms, and the distributions corresponding to the

single steps are presented in App. B, while the final result is represented by the blue columns

in Fig. 8.7. It should be noted that the ring-shaped QD structures were assumed to have

a square outer base with a circular central gap, as shown in Fig. 8.6(b). This assumption

is partly based on the observed atomic structure of the QDs, which will be discussed in

section 10.1.1. Additionally, it is shown in App. B that the choice of either a square or a

circular outer shape of the QDs has only marginal influence on the calculated distribution.

In Fig. 8.7 the experimental histogram and the result of the simulated cleavage distribution

are compared. For fitting the simulated distribution of the apparent ratio ˜r=din, cut / dout, cut

to the experimental histogram only the values between ˜r= 0.05 and ˜r= 0.9 were taken into

account, corresponding to those structures which show a central gap in the cross section.

Indeed, a very good agreement between both distributions can be found here, keeping in

mind the small statistical database. But importantly, the peak for ˜r= 0, corresponding to

the structures with the appearance of a compact QD, has not been considered for fitting

but results from the calculated distribution. If the sample contained both compact and ring-

shaped QDs, the red peak for ˜r= 0 should be significantly higher than the blue one, which

is not the case, meaning that all QDs actually have a ring-shaped structure.

The fact that the experimental peak for ˜r= 0 misses about 30% of the calculated value

may be explained – additionally to the rather large statistical error – by different visibilities

of differently cleaved QDs in the XSTM images: In images of lower quality a paired feature,

corresponding to a centrally cut QD, is much more distinct and thus much easier to detect

than a QD cut at the edge, which results in a more diffuse contrast. Especially when almost

the entire QD is cleaved away, the low strain-induced contrast may prevent a detection of

this QD. In the other case, when the major part of the QD remains within the sample upon

cleavage, its strain distribution increases the XSTM image contrast at both outer parts of

the QD image, as shown above, leading to the possible appearance of a paired feature even

if the ring-shaped QD is cleaved at the edge.

Beside the fact that all QDs have a ring shape, also the statistical average of the actual

inner to outer diameter of this ring can be derived from the simulations, amounting to

r0= 0.42 with a standard deviation of σ= 0.13.

8.3.3 Dependence on the amount of deposited GaSb material

While the (apparent) ratios of inner to outer diameter of the ring-shaped QDs are nearly the

same for all four layers of sample C, the outer shape of the QDs varies between the layers.

While the exact atomic structure including the specialities associated with the ring shape

will be discussed in more detail in chapter 10, the dependence of the outer QD shape on the

amount of deposited material will be investigated in the following.

QD shapes like those displayed in Fig. 8.8(b,c) are typical for layers 2 and 3 and for the

majority of the QDs in layer 4, with base lengths varying between about 10 and 20 nm and

heights of about 3 to 4 atomic chains or 1.5 to 2.5 nm. For these layers, the QD density

increases with the amount of deposited material, but no significant changes of the QD size

can be found. The situation is different in the first layer, where smaller and especially very

flat QDs were observed, as the one shown in Fig. 8.8(a): The base length of this QD is

15 nm, slightly smaller than for the QDs shown in Fig. 8.8(b,c). But the GaSb material is

mainly concentrated in one atomic chain and only in some places extends over a second chain,

88 CHAPTER 8. XSTM RESULTS ON MBE-GROWN SAMPLES

3 layer

rd 4 layer

5nm

STMtip

artefact

(a)

1 layer

5nm

[1 0]1

[001]

(d)

5nm

(c)

5nm

(b)

2 layer

Figure 8.8: XSTM filled state images of QDs in layers 1 - 4 of sample C, respectively; acquired at

tunneling voltages of (a) VT= -2.2 V, (b) VT= -1.7 V, (c) VT= -2.6 V, and (d) VT= -2.0 V.

corresponding to a QD height of ∼1 nm. Again, several segregated Sb atoms can be seen

above the QD, while the spotty bright line parallel to one atomic chain is just an artifact,

resulting from an adsorbed molecule shifted along one atomic chain by the scanning tip.

In the fourth layer, the observed QDs generally have a similar size to those of layers 2

and 3. However, in some QD structures like the one shown in Fig. 8.8(d), dramatic changes

of the image contrast occur over a very small range within the QD. Especially the dark

“holes” with a size of two or three atoms cannot be explained by electronic effects but rather

represent defects in the crystal lattice. Such defects may have emerged during the cleavage

at positions of strongly varying local strain due to a locally strongly varying chemical com-

position. However, they might also represent actual nanovoids, though being much smaller

than those reported recently for the InAs/GaAs material system [127, 132], or they could

possibly indicate dislocations within the QD. In the latter case, the large amount of GaSb in

the considerably large QD and the corresponding strain would have let to a partial relaxation

of the QD. The possibility of dislocations will be further discussed in section 8.7.

For a detailed comparison of the size of the studied QDs in dependence on the layer in

which they were observed, and therefore in dependence on the amount of nominally deposited

GaSb material, the structural parameters of all observed QDs were statistically analyzed. Al-

though the total number of 140 observed QDs is, as mentioned above, a large value for XSTM

experiments, it is still a rather poor statistical database, leading to relatively large errors.

In Table 8.1 the following parameters are given: In layers 1 to 4, corresponding to increas-

ing amounts of nominally deposited GaSb, differently large ranges of the four layers could be

investigated, resulting in different numbers of observed QDs. Both for the QD base length

and their height, the mean values are given as arithmetic average together with the standard

deviation and as median, respectively. While the arithmetic average is the more common

statistical parameter, some extraordinary small or large QDs which might be untypical for

the corresponding layer have less influence on the median value. Knowing the mean QD

size, the QD density was calculated for each layer as described in section 5.2.3. Thereby the

range of sight of the XSTM was assumed to be only about the mean QD size, as the possible

8.3. QUANTUM DOTS IN SAMPLE C 89

GaSb scanned QDs QD base length QD height density GaSb

layer deposited range found average median average median [1010 in QDs

[ML] [µm] [nm] [nm] [nm] [nm] cm−2] [ML]

1 1.0 5.1 27 12.7±4.1 13.0 1.6±0.3 1.8 4.3±0.8 0.17

2 2.0 4.7 55 16.3±4.9 17.0 2.0±0.3 1.8 7.3±1.0 0.59

3 2.7 3.1 37 15.4±4.3 14.5 2.1±0.4 2.1 8.1±1.3 0.63

4 3.1 1.5 21 15.2±4.0 14.5 2.1±0.3 2.1 9.3±2.0 0.71

Table 8.1: Statistical data on structural parameters of QDs observed in layers 1 to 4 of sample C.

detection of completely buried QDs is probably compensated by the number of those QDs

cleaved at the edge which were overlooked, as indicated by the results of the simulations

discussed above. For each layer, a statistical error of the QD density could be evaluated

from the number of observed QDs. Finally, from the QD base length, their height, and their

density the total amount of material incorporated within the QDs was calculated, assuming

a square QD base, a truncated pyramidal shape with a ratio of top extension to base length

of 0.8, and a central circular gap with a diameter of 0.4 times the base length, corresponding

to the ring shape analyzed above. Additionally, a chemical composition of the QDs of only

60% GaSb was considered, which will be discussed in chapter 10.1.2. Accordingly not the

total QD material but the incorporated GaSb is given in the right column of Table 8.1.

Some key results of the statistical data are visualized in Fig. 8.9, supporting the trends

described above: The mean size of the QDs is nearly constant for layers 2 to 4, while sig-

nificantly smaller QDs are observed in layer 1. Although the QD density increases with the

amount of deposited material, only a small fraction of the nominally deposited additional

GaSb material gets incorporated into the QDs, especially in layers 3 and 4.

In several XSTM publications it is stated that only the largest values of measured lateral

QD extensions may be considered as the actual QD base length, as all smaller values corre-

spond to QDs which are not centrally cut at the cleavage [124, 217]. This is true for QDs

with {101},{102}, or similar side facets, as in this case the rectangular QD bases are cut

diagonally. However, if the QDs are characterized by {111}side facets, as it is most probably

the case in this sample (see section 10.1.1), the measured lateral extensions could directly be

regarded as base length of the corresponding QDs.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

100

150

200

250

300

350

400

averageQDvolume[nm3]

nominallydepositedGaSb[ML]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

GaSbincorporatedinQDs[ML]

QDdensity[1010 cm-2]

Figure 8.9: De-

pendence of the av-

erage QD volume,

the QD density, and

the amount of GaSb

incorporated in the

QDs on the nomi-

nally deposited mate-

rial, as obtained from

the XSTM images of

sample C by statisti-

cal analysis.

90 CHAPTER 8. XSTM RESULTS ON MBE-GROWN SAMPLES

8.3.4 Shape anisotropy of the QDs

Using XSTM, cross sections through the QDs either along the [1¯

10]- or along the [110]-

direction can be studied at one time. From literature, the question whether a shape anisotropy

of the QD base should be expected or not remains ambigious: There are only a few studies

published, characterizing GaSb QDs in top-view geometry, which have sufficient lateral res-

olution. Among these, the majority of the authors report on an anisotropy, with a ratio of

the lengts of side A to side B ranging from 1.2 [44] up to 2.0 [52] and a larger extension in

[110]- than in [¯

110]-direction [46, 59]. However, also symmetric QD base shapes have been

reported for both MOCVD- [51] and MBE-grown [67] GaSb QDs.

To evaluate the symmetry of the base shape, different specimens of sample C have been

cleaved in the (110) and in the (¯

110) cleavage surface, respectively. All QD images shown yet

stem from the (110) cleavage surface, only because the database on this surface is larger and

the STM tips used at this specimen achieved a better lateral resolution, which is a random

effect.

Comparing the data obtained from both cleavage surfaces, no systematic differences are

evident. The mean values of the measured QD base lengths differ slightly, but these differences

are much smaller than the statistical error and have opposite trends for the single layers of

the sample. The statistical base of these measurements is too small to observe very small

anisotropies, but an asymmetry of more than 20% to 30% between both sides of the QD base

can be excluded.

8.4 Quantum dots in sample D

As mentioned above, QDs have also been observed in the second and third layer of sam-

ple D; again obtaining images with a rather continuous QD appearance, like those shown in

Fig. 8.10(a-c), as well as cross sections of QDs revealing a more or less pronounced central

gap, shown in Fig. 8.10(d-g). The database of these QDs is too small to repeat the statisti-

cal analysis und simulations performed for sample C. Nevertheless, the amount of QD cross

sections with and without central gap is nearly the same also in both layers of sample D,

respectively, so it can be concluded that probably all QDs of sample D are ring-shaped, too.

The ratio of apparent inner to outer diameter varies rather strongly for the ring structures

in sample D, ranging from rings that are nearly filled but have a significantly lower contrast

and thus a lower GaSb stoichiometry in the central region [Fig. 8.10(d,e)] up to structures

with a very large central gap, like the one shown in Fig. 8.10(g).

Especially the QDs in layer 2 appear to be rather small, with an inhomogeneous and weak

image contrast. Two representative QDs of this layer are shown in Fig. 8.10(a,d), extending

laterally over only 10 nm and 12 nm, respectively. Only at some regions of the QDs their

height exceeds one atomic chain, extending here over a second chain or about 1.2 nm in

total. The image contrast varies strongly within these QDs, indicating a low average GaSb

composition with only some regions of higher GaSb content.

For QDs in layer 3 lateral extensions of about 20 nm are typical [Fig. 8.10(b,e,f)], but

also large structures with up to 30 nm like the one shown in Fig. 8.10(g) have been observed.

Nevertheless, also in most of these QDs the GaSb is mainly concentrated at one atomic chain,

and only some regions of the QDs reach a height of two or three chains. The image contrast of

most QDs in layer 3 is stronger and more homogeneous than in layer 2, standing for a higher

average GaSb content, as it can be seen in Fig. 8.10(b,e-g). Additionally to such flat, but

rather continuous ring-shaped QDs, also GaSb structures like the one shown in Fig. 8.10(c)

were observed, having a different appearance: No well-defined three-dimensional structure

8.4. QUANTUM DOTS IN SAMPLE D 91

[1 0]1

[001]

5nm 5nm5nm

(a) (b) (c)

WL WL WL

5nm 10nm

(g)

layer3

5nm

(f)

ring

body

ring

body

(e)(d)

[1 0]1

[001]

ring

body

ring

body

4nm

layer2

Figure 8.10: XSTM images of ring-shaped QDs in sample D, cleaved through (a-c) the ring body

and (d-g) through the central gap: (a,d) Small GaSb QDs in layer 2, (b,c,e-g) GaSb QDs in layer 3.

The images were acquired at (a,b,d) VT= -2.4 V, (c,e,f) VT= -2.1 V, and (g) VT= -3.0 V.

can be determined here, but an agglomeration of individual Sb atoms is found over about

11 nm within the WL, leading to a locally increased image contrast, which – with decreasing

Sb content – also extends to the first and second atomic chain above. It cannot exactly

be said whether this structure is a diluted QD or a density fluctuation of the WL strongly

segregating in growth direction. Generally, strong Sb segregation is evident for all QDs in

sample D, as all images show many individual Sb atoms incorporated in the GaAs matrix

above the QDs.

The structural results obtained from the XSTM images of representative QDs are also

confirmed by statistical data of all QDs observed in sample D, although it should be kept

in mind that the database is relatively small especially for layer 2. The QD density was

evaluated to 3.8±1.9×1010 cm−2in layer 2 and 5.1±1.2×1010 cm−2in layer 3, with

average base lengths of 14.6±6.7 nm and 18.8±6.4 nm as well as heights of 1.2±0.2 nm

and 1.3±0.4 nm for QDs in layers 2 and 3, respectively.

Comparing the QD structures of sample D with those of layers 1 and 2 in sample C, which

have nominally the same amount of deposited GaSb, the QD densities and base lengths

92 CHAPTER 8. XSTM RESULTS ON MBE-GROWN SAMPLES

are found to be similar, while the very small heights of the QDs in sample D have to be

emphasized. In most QD structures the height does not exceed two atomic chains, with the

GaSb content being concentrated to the bottom chain. Additionally, the QDs in layer 2 of

sample D are characterized by a varying and in average rather low GaSb content.

8.5 Wetting layers

In both samples the GaSb QDs are embedded within wetting layers. On a nm scale these WLs

generally exhibit a rather inhomogeneous and even discontinuous structure, as can be seen

in Figs. 8.11 and 8.13. At atomic resolution the WLs have a spotty appearance, representing

individual Sb atoms within a more As-dominated intermixed GaSbAs material, and strong

Sb segregation is evident above all WLs. Sb-free gaps within the WLs of several nm lateral

extension can be recognized, consisting of pure GaAs. Beside this general behavior, also

structural differences between the individual layers of both samples are obtained.

Figure 8.11 shows XSTM images of the four WLs of sample C, with nominal amounts of

deposited GaSb of 1.0 ML, 2.0 ML, 2.7 ML, and 3.1 ML, respectively. The resolution and

image quality of Fig. 8.11(b) falls behind those of the other three images, but this is attributed

to the varying tip condition. Regarding the structure of the WLs, however, layer 1, shown in

Fig. 8.11(a), is outstanding: Here the total amount of incorporated Sb is significantly smaller

than in the other three layers. The WL itself is strictly limited to one atomic chain, containing

large gaps. An image contrast hardly exceeding that of single segregated Sb atoms underlines

the low Sb stoichiometry of the WL. Although the image contrast is not significantly larger

in the other three WLs, too, those layers have a larger vertical extension, as can be seen in

Fig. 8.11(b-d). Intermixed WLs of about two, sometimes three atomic chains height show

a smooth transition into a region of strong segregation, extending over about 10 nm with a

declining amount of incorporated Sb atoms.

In order to study the chemical composition quantitatively, the local lattice constants for

all four WLs of sample C were evaluated, as described in detail in chapter 6. The results are

[1 0]1

[001]

5nm5nm5nm5nm

layer1 layer3 layer4layer2

(a) (b) (c) (d)

Figure 8.11: XSTM filled state images of the GaSb WLs in layers 1 to 4, respectively, of sample C,

acquired at (a) VT= -2.5 V, (b) VT= -2.0 V, (c) VT= -1.9 V, and (d) VT= -2.0 V. The small dark

holes visible in (a) are atomic vacancies within the cleavage surface, while the larger dark depressions

present in (b-d) represent charged atoms like dopands, contaminants or antisite lattice defects. The

diagonal dark line in image (b) is a deficient STM scanline.

8.5. WETTING LAYERS 93

-3 -2 -1 0 1 2 3 4 5

0.55

0.56

0.57

0.58

0.59

0.60

10%GaSb

20%GaSb

atomicchaindistance[nm]

layer1

layer4

layer3

layer2

Figure 8.12: Analysis of

the chemical composition

of the WLs in sample C.

plotted in Fig. 8.12: In accordance with the weak image contrast, typical GaSb contents of

the WLs of only 10% to 20% are derived for the rather continuous, gap-free regions. The WL

of layer 1 is indeed restricted to one atomic chain, while at the other three WLs the lattice

constant is increased over several chains. Although the data are averaged over the results of

several XSTM images, respectively, a noise in the range of 0.01 to 0.02 nm, corresponding

to ±10% GaSb, could not be avoided for layers 2 to 4. Therefore the exact course of the

curves and especially a comparison of individual data points for WLs 2, 3, and 4 is not

that significant. However, a WL height of about two to four atomic chains or 1 to 2 nm, a

WL GaSb composition decaying in growth direction with a maximum of about 20%, and a

measurable amount of segregated and incorporated Sb atoms above the actual WLs can be

derived from the chain distance analysis as common trends for layers 2, 3, and 4. From this,

the total amount of incorporated antimony can be estimated to about 0.3 ML in layer 1 and

0.9 ML in layers 2 to 4, respectively. Thereby differences of less than 0.06 ML are found

between layers 2 to 4, which is below the resolution of the chain distance analysis of about

0.1 ML, although Fig. 8.11(b-d) gives the impression of a slight increase.

While the principal appearance of the WLs in sample C is similar to those in sample D, the

latter contain even less GaSb. Figure 8.13(a) shows layer 2 of sample D, nominally containing

1 ML GaSb. Again a thin WL and segregated Sb atoms above can be seen, but this WL

consists more of totally Sb-free gaps than of the actual GaSbAs layer itself. Thus, this layer

does hardly fulfill the definition of a wetting layer any more. In layer 3 of sample D, shown

in Fig. 8.13(b), the gaps are much smaller than in layer 2, and more segregated Sb can be

found above the WL, too. However, although 2.0 ML GaSb were nominally deposited at this

layer, the WL itself is mainly concentrated to only one atomic chain, and the total amount

of incorporated Sb is significantly smaller than in the corresponding layer of sample C. The

chain distances cannot be evaluated quantitatively for the WLs of sample D due to the low

GaSb content, the strong Sb segregation, and the weak image quality, but the total amount

of GaSb within the WL of layer 3 can be estimated to be less than 0.5 ML.

Comparing the WLs of both MBE-grown samples with the MOCVD structures, clear

trends are evident: The MOCVD-grown WLs and QWs are more sharply defined, with a

GaSb content of up to 50% but a vertical extension of only one to two atomic chains, as

discussed in chapter 7.2. Hardly any segregated Sb atoms can be found above the MOCVD-

grown layers. The broadened and more intermixed WLs and the strong segregation above

the layers within the MBE-grown samples indicate a higher mobility of the antimony during

the MBE process.

94 CHAPTER 8. XSTM RESULTS ON MBE-GROWN SAMPLES

5nm

(a) 5nm

(b)

[1 0]1

[001]

layer2 layer3

Figure 8.13: XSTM filled state images

of the GaSb WLs of sample D: (a) Layer 2,

acquired at VT= -2.4 V, (b) layer 3, ac-

quired at VT= -2.1 V. The streaky spots

in the lower left part of image (a), marked

by green dashed ellipses, are STM tip arti-

facts.

Gaps within the WLs, while varying in size and density for the different layers, are

observed in all GaSb samples. For MOCVD growth, as explained in section 7.1, these gaps

indicate a 2D island growth mode of GaSb. In MBE, the strategy of a soaking layer leads to

a more complex situation, as will be discussed in detail in sections 9.2 and 10.3. Nevertheless,

the observed gaps, which are unique and typical for the GaSb/GaAs material system, seem

to indicate a similar kind of 2D island growth also for MBE.

8.6 Optical results

In order to be able to supplement the structural data with optical results, two reference

samples have additionally been grown of layer 2 and 3 in sample D, using identical growth

parameters in the same MBE machine but optimizing the sample structure for optical mea-

surements. Thus undoped GaAs substrates have been used, no AlGaAs barriers and a thinner

GaAs cap layer without doping have been grown, and each reference sample contains only

one GaSb layer, in contrast to the XSTM sample structure shown in Fig. 8.1. Both reference

samples were studied using optical spectroscopy by Till Warming in the group of D. Bimberg.

8.6.1 Optically active QDs in sample D

Figure 8.14(a,b) shows photoluminescence (PL) and photoluminescence excitation (PLE)

spectra, taken at a temperature of 7 K with moderate excitation densities, for the sample

corresponding to layer 3 of sample D: In the PL spectrum, three peaks are evident and can be

related to luminescence from the GaAs bulk, the GaSb WL, and from GaSb QDs. The GaAs

peak is located at 1.49 eV, close to the literature value of the GaAs band gap of 1.52 eV

(the small discrepancy can be explained by the GaAs electron-hole recombination energy

being slightly reduced by the exciton binding energy or by defects located slightly within the

bandgap). Nearly the double PL intensity is arising from the GaSb WL, exhibiting a rather

narrow peak with a full width of half maximum (FWHM) of about 35 meV and a maximum

at 1.38 eV. This WL peak shape indicates a relatively high electron-hole recombination

probability and agrees well with the rather compact structure of the corresponding WL

observed by XSTM in sample D, appearing as a thin layer with only small gaps, as shown

in Fig. 8.13(b). The QD peak is significantly lower and broader, showing a FWHM of about

130 meV and a maximum at 1.11 eV (or 1119 nm). The broadness confirms the large size

distribution of the QDs in layer 3 of sample D discussed above, which is characterized by an

8.6. OPTICAL RESULTS 95

Figure 8.14: Low-temperature optical characterization of the 2 ML reference sample, corresponding

to layer 3 of sample D: (a) PL spectrum, (b) PL spectrum (black, left axis) together with different PLE

spectra (colors, right axis) with the respective detection energies indicated. The corresponding band

alignment of the GaSb/GaAs QDs is sketched schematically for (c) PL and for (d) PLE spectroscopy.

average base length of 18.8±6.4 nm. Additionally, the rather small intensity of the QD peak

compared with other material systems is also expected because of the type-II band alignment

of the QDs.

While the WL PL peak position of 1.38 eV at this MBE-grown sample is similar to that

of the MOCVD-grown sample amounting to 1.37 eV, as discussed in section 5.3.1, the QD

peaks of 1.20 eV for the MOCVD QDs and 1.11 eV at the MBE sample differ considerably,

resulting in an increased energetical distance of 0.27 eV between the WL and the QD peak

at the MBE structures. Thus, the MBE QDs studied here have a clearly larger electronic

confinement than the MOCVD QDs shown above, in agreement with their larger base lengths,

independent of the ring-shaped structure. Comparing these PL data with published values

on other MBE-grown GaSb QDs [44, 45, 47, 48, 55, 56, 58–60, 69, 256], the WL peak energy

observed here is relatively large, as the literature values vary between 1.23 eV and 1.41 eV.

This indicates a comparatively small electronic confinement in the WL studied here, agreeing

well with the small amount of incorporated GaSb. However, the QD PL peak measured

at 1.11 eV lies well within the very small range of 1.09 to 1.14 eV which includes most

published values [44, 45, 47, 48, 58, 59, 69, 256]. This result is astonishing, as the reported

QD structures corresponding to those PL energies are much larger than the QDs observed

96 CHAPTER 8. XSTM RESULTS ON MBE-GROWN SAMPLES

here. A possible explanation might be that most of the authors have measured the sizes of

their QDs ex-situ in top-view geometry on free-standing QDs [48, 58, 69, 256], so that any

shape transitions upon overgrowth are not considered, though all PL results are taken at

capped QDs, as also the XSTM data.

Following the PL measurements, also PLE spectra were taken from the reference sample

of 2 ML, shown in Fig. 8.14(b). Using PLE, electron-hole pairs are excited resonantly with

a varying excitation energy, while the detection energy is held fixed. Here, five different

detection energies were chosen which all lie within the PL peak of the GaSb QDs, obtaining

a strong GaAs bulk signal and a weaker signal corresponding to excited WL states (please

note the logarithmic scale of the PLE intensity axis). The energy difference of 0.05 to 0.1 eV

between the PL peak and the PLE shoulder of the WL is partly due to the excited states

contributing to the PLE signal and additionally given by the Stokes-shift between emission

and absorption states [378].

Astonishingly, no excited QD states could be observed, only a very small and broad

increase of the PLE signal for energies smaller than 1.3 eV can be seen. This means that

electron-hole pairs can relax from the GaAs matrix or from excited WL states to the GaSb QD

ground state and recombine there, but that it seems to be hardly possible to directly create

excited QD electron-hole pairs. In other QD material systems like InAs/GaAs clear peaks

of excited QD states would be expected, and the actual existence of QDs in this reference

sample was proven before by PL, therefore the lack of excited QD states in the PLE spectra

is not completely understood yet. In literature, many PL data on GaSb/GaAs QDs can be

found [44, 45, 49, 51, 54–56, 59, 64–66, 69, 71, 73–76, 263–265], but only two PLE studies

are known to me [47, 255], also revealing only a very weak QD PLE signal.

One idea to partly explain the lack of a clear QD signal in PLE spectroscopy is sketched in

Fig. 8.14(c,d): As mentioned in section 2.4.1, the staggered type-II band alignment provides

a strong confinement of holes in the GaSb nanostructures, but the weak electron confinement

in the surrounding GaAs matrix is only created by the Coulomb attraction of previously

captured holes. The situation of PL spectroscopy with excitation energies larger than the

matrix bandgap comprises partly filled QDs and thus the existence of confined states for both

electrons and holes, as displayed in Fig. 8.14(c). Using PLE spectroscopy at low temperature,

however, excited electron-hole pairs are generated resonantly, so in the initial state the GaSb

QD is uncharged, as sketched in Fig. 8.14(d), and confined electron states do not exist. As a

consequence, the resulting PLE response at energies slightly above the QD PL peak is broad

and unstructured due to the lack of electron confinement, and the small overlap of electron

and hole wavefunction results in the weak signal. Both observations then could be regarded

as an indication of a type-II band alignment.

In order to conclude the optical measurements on the 2 ML reference sample, correspond-

ing to layer 3 of sample D, two main results need to be emphasized: Firstly, in spite of their

small size and especially small height, the QDs exhibit a relatively large hole confinement.

Secondly, although these QDs are strongly intermixed, the PLE signal differs significantly

from that of type-I QDs and gives evidence of a type-II band alignment.

8.6.2 Optically inactive small islands in sample D

The other reference sample, corresponding to the second layer of sample D with nominally

1 ML deposited GaSb, was likewise studied by PL spectroscopy. However, although the GaAs

peak and a WL signal were observed, no photoluminescence could be obtained from QDs at

all, even at increased laser excitation densities. From this lack of QD signal, it has to be

concluded that the small 3D structures obtained in layer 2 of sample D, which have also been

called QDs above in a structural point of view, do actually not exhibit any zero-dimensionally

8.7. DISLOCATIONS 97

confined QD states.

Comparatively little statistical data exist for these structures, but they have base lengths

of about 15 nm and a height of about 1.2 nm, accompanied by a very Sb-poor stoichiometry.

Considering that the QDs in layer 3 of the same sample show a rather strong electronic

confinement in spite of their very flat shape, and that the optically active MOCVD-grown

QDs in sample A (see chapter 5) are also very small with base lengths of less than 10 nm

and heights of up to 2 nm, the low GaSb content of the small islands in layer 2 of sample D

seems to be the reason for the lack of electronic QD confinement rather than their size.

8.6.3 Optical results on QDs in sample C

For the MBE-grown QD layers in sample C no reference samples exist. Nevertheless, opti-

cal measurements were performed using the XSTM sample with its complex structure (see

Fig. 8.1). Thus, a rather weak PL intensity was expected due to the thick cap layer, several

AlGaAs layers and the use of a doped wafer, as well as a possibly blurred superposition of the

different WL and QD signals. However, hardly any PL signal related to GaSb was obtained:

Even with very high laser excitation densities, beside a strong GaAs bulk luminescence only

a very small GaSb WL signal (about 1000 times smaller than in the reference samples of

sample D) and no GaSb QD signal at all could be measured.

The reason for this behavior is not yet clear. Of course a large fraction of the exciting laser

power gets absorbed within the more than 1 µm thick GaAs and AlGaAs layers above the

GaSb nanostructures, nevertheless a sufficient amount of light should still reach the embedded

GaSb layers. Another explanation would be the dominance of non-radiative recombination.

Dislocations within QDs are such centers of non-radiative recombination, so a significantly

high percentage of spatially relaxed QDs or a strong occurence of other kinds of dislocations

within the GaSb layers would explain why nearly no luminescence from these layers can be

obtained.

8.7 Dislocations

Dislocations are line defects within the crystal. They can reduce strain, influence the charge

carrier transport, and act as centers of non-radiative electron-hole recombination [2, 3, 9,

26]. Usually, the growth of coherently strained QDs is limited by plastic relaxation building

dislocations (see also section 2.2.1), which inhibits any optical activity of the QD.

Figure 8.15(a) shows a dislocation line which emerges at the edge of a QD of the third

layer of sample C, having a relatively large base length of about 30 nm. The dislocation

proceeds most probably along the [112]-direction (with a measured angle towards the WL of

about 50◦), disrupting the GaAs atomic chains, and ends after about 17 nm. However, this

dislocation line is the only one found within the whole investigated scan range of more than

14 µm. Therefore, this kind of crystal defect is quite rare within the sample and seems to

be related to the exceptionally large size of the QD beside which it is located. No similar

structure has been observed in sample D.

While a considerable number of dislocations running through the GaAs matrix around the

GaSb nanostructures can thus be excluded, the existence or absence of dislocations restricted

within the QDs is more difficult to verify. Cross-sectional transmission electron microscopy

images of free-standing GaSb/GaAs QDs grown under similar conditions and in the same

MBE chamber as sample C show a large number of misfit dislocations within the QDs,

arising at their bottom interface to the GaAs matrix. An example of these images, acquired

by Ganesh Balakrishnan in Albuquerque, New Mexico, USA, is shown in Fig. 8.15(b): From

98 CHAPTER 8. XSTM RESULTS ON MBE-GROWN SAMPLES

20nm

[001]

(b)

[110]

[001]

dislocation

line

[112]

[1 0]1

[001]

(a) (d)

10nm (c)

Figure 8.15: (a) XSTM image of a dislocation line near a QD in the layer 3 of sample C, acquired

at VT= -2.1 V. (b) TEM image of free-standing GaSb QDs on GaAs, showing misfit dislocations.

(c,d) Evaluation of Burgers vectors in XSTM images of QDs in the layer 2 of sample C, acquired at

left to right, the GaAs matrix, the GaSb WL and two QDs, a thin oxide layer, and a bright

image background can be seen. However, the two QDs are rather large with base lengths of

45 and 25 nm, respectively, and cannot directly be compared with the capped QDs studied

in this work: Although they have been initially grown under similar conditions, the QDs

for the TEM sample had to be cooled down without being capped, and during this cooling

the monitoring RHEED signal changed dramatically, indicating drastic changes of the QD

morphology. This behavior is a nice example that care has to be taken when comparing

results from different characterization methods.

So the question remains, whether the existence of dislocations within the QDs can be

decided using the XSTM images. If a misfit dislocation arised within the QD due to the lattice

mismatch between GaAs and GaSb, it would modify the atomic positions in such a way that

two paths of the same nominal length along atomic chains underneath and above the QD

would contain different numbers of atoms. This is a simplified description of characterizing

the dislocation by its Burgers vector [26, 379]. The Burgers vector can be analyzed from

an XSTM image with atomic resolution in xand yby considering a loop around the QD

consisting of lines along the [1¯

10]- and the [001]-direction and counting the atoms of this

loop at each side of the QD. This procedure has been exercised for five QDs of sample C

which could have been imaged with sufficient atomic resolution, and in all cases the number

of atoms underneath and above the QD is the same, meaning that no Burgers vector exists

and no dislocation is contained within the QD. Two examples of this procedure are displayed

in Fig. 8.15, for a QD with a rather homogeneous (c) and even with a rather inhomogeneous

image contrast (d).

Due to the limited resolution of the XSTM images this procedure could not be repeated

for other QDs, especially not for any one in layer 4 of sample C, in which some larger QDs

with a locally strongly varying image contrast were observed (see section 8.3.3). Therefore,

the existence of dislocations cannot completely be excluded, especially not for this layer 4.

However, at least the large majority of QDs is definitely free of dislocations and is coherently

strained.

Chapter 9

Sb segregation and atomic

exchange processes

Having studied the GaSb nanostructures in the MBE-grown samples C and D and knowing

many structural results about WLs and ring-shaped QDs, the self-assembled formation of

these structures remains as key question. Before the details of the atomic QD shapes and

possible growth mechanisms of the ring structures can be discussed (see chapter 10), some un-

derlying physical effects taking place upon growth and especially overgrowth of GaSb/GaAs

nanostructures will be focused on in this chapter. It will be shown that segregation, diffu-

sion, and atomic exchange processes, which occur in nearly all III-V heterostructures, are of

strongly increased importance for the GaSb/GaAs material system, especially at the atomic

interfaces. In order to analyse such exchange and segregation processes from the XSTM data,

first the involved XSTM imaging mechanisms, taking place on the atomic scale, need to be

understood.

9.1 XSTM imaging of Sb atoms in GaAs

A good example of the relevance of the tunneling polarity on the information available in

XSTM images is given in Fig. 9.1: All six images show the same GaSb QD or a part of it,

but the three images on the left hand side were taken with negative sample voltages, while

the images on the right hand side were acquired at positive polarity. At negative sample

bias the image is sensitive for group-V atoms, thus Sb and As can be distinguished at the

atomic level, whereas at positive sample bias the Ga atoms are imaged. As a consequence,

individual Sb atoms can be seen within the chains of As atoms and in the intermixed QD in

Fig. 9.1(a), while in Fig. 9.1(b) the QD appears rather homogeneous: Here, with a positive

bias, the structural contrast dominates which is mainly given by outward relaxation of the

QD and therewidth by its strain. The different appearance is even more pronounced at the

WL, which appears as a broadened, diffuse stripe at positive sample voltage, whereas at

negative voltage the inhomogeneous atomic structure of the intermixed layer can be seen. It

should be noted that both images show atomic resolution in [001]- and [1¯

10]-direction [which

gets more apparent in Fig. 9.1(c-f)], so the less pronounced appearance of the nanostructures

in Fig. 9.1(b) is not due to image quality.

As a final consequence of polarity dependence, the segregated Sb atoms which can clearly

be seen above the WL and the QD in Fig. 9.1(a) cannot be found at all in (b). To further

study this effect, a small part of the images is shown with larger magnification in (c) and

(e). Here, the image contrast has been adjusted to the individual Sb atoms within the GaAs

matrix, thus the strained QD containing much GaSb material is outshined and appears

100 CHAPTER 9. SB SEGREGATION AND ATOMIC EXCHANGE PROCESSES

tip

artefacts

surface

step

10nm

[001][1 0]1

5nm

(a)

(b)

Figure 9.1: XSTM images of the same GaSb QD, observed in layer 2 of sample C: (a,c,d) filled state

images, acquired at VT= -1.7 V, (b,e,f) empty state images, acquired at (b) VT= +1.8 V and (e,f)

VT= +1.7 V. In (d) and (f) the image background is subtracted to highlight individual Sb atoms.

Some Sb atoms are marked in (f) by circles.

completely white. Additionally, the slowly varying image background has been subtracted in

Fig. 9.1(d,f) to further pronounce short-range differences in the image contrast, highlighting

individual atoms. As a result, several single Sb atoms within the GaAs matrix can clearly be

seen in (c) and (d), corresponding to negative sample voltage. However, in (e) and (f) with

positive bias, only a few Sb atoms can be found above the QD, marked by small circles in (f),

giving a very small image contrast. The bright spots in the upper right corner are too large

to represent single atoms and are probably adsorbates on the cleavage surface. Additionally,

the positions of the Sb atoms in (e) and (f) are not correlated to those in (c) and (d), so that

different atoms have been imaged.

In order to understand this appearance, the atomic structure of the zinkblende crystal

at the (110) cleavage surface, consisting of GaAs and single Sb atoms, has to be considered,

as sketched in Fig. 9.2. The relaxed and buckled (110) surface is characterized by GaAs

atomic zigzag chains of alternating height. Using STM at common tunneling conditions,

either the Ga or the As atoms of the upper rows are imaged, depending on the polarity, so

only each second ML in [001]-direction is visible [106]. For an Sb atom (1) directly within

the topmost (110) plane, the buckling is slightly larger than for an As atom, because its

atomic radius and the bond lengths to the neighboring Ga atoms are larger. The Sb atom

protrudes geometrically about 6 pm further out of the cleavage surface than the As atoms,

according to Kim et al. [380]. Thus, its filled dangling bond is closer to the STM tip, leading

to an increased tunneling current at negative sample voltage. The tunneling probability is

additionally locally enhanced for this polarity at low absolute voltages due to the electronic

properties of antimony compared with arsenic. However, the Ga atoms and especially their

empty dangling bonds are hardly influenced by the adjacent Sb atoms in the topmost plane.

Furthermore, the small CB offset leads to negligible electronic differences. Thus, at positive

tunneling voltage, no sign of these Sb atoms can be found in the STM images.

9.1. XSTM IMAGING OF SB ATOMS IN GAAS 101

Gainfront

Asinfront

Gabehind

Asbehind

[110]

[001]

[ 10]1

(1)

(2)

(3)

(4)

(5)

Figure 9.2: Side-view of the buckled GaAs(110) surface, containing single Sb atoms in the first,

second, and third atomic layer. The position in [110]-direction of the undisturbed As surface atoms

is indicated. The shifts of the atomic positions due to the Sb atoms are not drawn to scale.

A different situation occurs for an Sb atom (2) in the subsurface (110) plane. This atom

cannot directly be imaged, but its larger size and bond length shifts the neighboring Ga

atoms, which in turn slightly shift the As atoms beside. As a result, at the position of the

subsurface Sb atom, one surface Ga atom (3) and also four surface As atoms are protruding

slightly further out of the cleavage surface than without Sb. Consequently, in filled state

images the tunneling current should be slightly increased over a region of four As atoms

(which can hardly be seen in the images due to the dominant contrast of the individual

surface Sb atoms), while in empty-state images the current is increased at one Ga atom (3)

bonded to the subsurface Sb atom. Thus, the existence of this second layer Sb atom can

also be observed in STM images taken with positive voltage, originally sensitive to group-III

atoms. This effect is responsible for the appearance of Fig. 9.1(e,f) described above: The

structural contrast due to some second layer Sb atoms can weakly be seen in the images, but

this contrast is significantly lower than the combination of structural and electronic contrast

associated with the top layer Sb atoms in Fig. 9.1(c,d). As atoms of different planes are

imaged, the absence of any correlation between the Sb positions in (c,d) and (e,f) can now

well be understood.

According to the crystal structure, even Sb atoms within the third (110) plane can weakly

influence the geometry of the cleavage surface: As can be seen in Fig. 9.2, the size and bond

length of such an Sb atom (4) slightly raises the surface As atom (5) directly above. Thus,

third layer Sb atoms could principally be seen in STM images with negative sample voltage.

The inverse case of a third layer As atom within a GaSb matrix has been observed as a slight

depression by Steinshnider et al. [381], but in that case an extremely good image quality and

surface flatness supported the observability of this weak contrast difference. Nitrogen atoms,

another group-V element, in a GaAs matrix generate a clearly larger dark image contrast, so

that even third layer N atoms can clearly be seen in XSTM images [298, 382]. This is due to

stronger variations within the atomic structure: While the As and Sb atomic radii amount

to 124.5 pm and 145 pm, respectively, N atoms have a radius of only 71 pm [371].

For analysing the amount of segregated Sb atoms, it is important to know whether all

Sb atoms observed in a filled state XSTM image are located within the first (110) plane, or

102 CHAPTER 9. SB SEGREGATION AND ATOMIC EXCHANGE PROCESSES

whether also the second and third layer have to be considered. The Sb atoms in Fig. 9.1(c,d)

exhibit strong variations of their image contrast, which could indicate an origin from different

layers. However, the images have been acquired at negative sample voltages and the increased

contrast is concentrated to single atoms instead of groups of four, so that Sb atoms from

the second layer can be excluded. Additionally, the geometric contrast due to second layer

Sb atoms is already very small, as can be seen at the empty state images (e,f), and therefore

the contrast of third layer Sb atoms should be expected to be even smaller and not resolvable

in the images shown here. Several XSTM studies are reported which clearly observed first

layer Sb atoms in GaAs [380, 381, 383, 384], partly with excellent image quality over large

areas [385–387], but to my knowledge no clear evidence of third layer Sb is given.

The situation is similar for the InAs/GaAs system: With 260 pm the InAs bond length

comes very close to the GaSb bond length of 262 pm, with the GaAs bond length amounting to

242 pm [380]. The appearance of first and second layer In in GaAs was studied in detail [372],

but it is assumed by several authors that all In atoms observed in group-III sensitive XSTM

images belong to the cleavage surface, and the third layer is not considered [97, 217, 373, 388].

In conclusion, from comparison with literature data and especially from considering the

very small geometrical effects of subsurface antimony, in the following all Sb atoms observed

in a GaAs matrix in filled state XSTM images will be assumed to belong directly to the (110)

cleavage surface.

9.2 Soaking and group-V-exchange

9.2.1 Soaking of growth surfaces

Self-assembled III-V semiconductor heterostructures are usually grown using group-V surplus,

meaning that during epitaxy more group-V atoms are offered than can be incorporated, so

that growth is controlled by the parameters regarding the group-III elements. Thus, an

abrupt change between group-III atoms like In and Ga is much more easy to realize than

between group-V atoms like As and Sb (see section 2.2.2). Additionally to the interface

quality, also the stoichiometry of nanostructures formed upon deposition of nominally pure

GaSb can strongly be influenced by an arsenic background during GaSb epitaxy, which to

some extend was already observed for the MOCVD-grown structures (see section 7.2).

Besides these more technical aspects related to the growth of III-V heterostructures,

interfaces between GaSb and GaAs are also different from those between InAs and GaAs

for more fundamental physical reasons: Interfaces with a common group-V atom, like InAs

and GaAs, are influenced by group-III surface segregation, while interfaces with a common

group-III atom, as it is the case for GaSb and GaAs, are dominated by group-V exchange

reactions [50, 84, 389], leading to strong As-Sb intermixing [69].

These different effects have intensively been studied on InAs-GaSb superlattices, also by

using XSTM [308, 384, 385, 390]. In this system, also the effect of Sb soaking was investigated,

meaning the exposure of an InAs layer to an Sb flux: Already in 1993, Wang et al. observed

an Sb-for-As exchange at the InAs growth surface upon soaking, saturating at an amount of

about 1 ML, as measured with x-ray photoelectron spectroscopy [391, 392].

This concept of Sb soaking has been adopted to the growth of GaSb nanostructures on

GaAs, too, in order to produce a sharp GaSb/GaAs interface and to decrease the arsenic

background in the MBE reactor prior to GaSb deposition, leading to stoichiometrically purer

nanostructures [44, 55, 59, 69, 267, 393]. Already Hatami et al. used an Sb soaking step prior

to GaSb deposition when growing the first GaSb/GaAs QDs. They reported on 1 ML or

2 ML thick GaSb layers formed by anion exchange upon Sb soaking, depending on soaking

9.2. SOAKING AND GROUP-V-EXCHANGE 103

time [44, 393]. Suzuki et al. [69] and later on Nakai et al. [59] observed using RHEED

a change of the growth surface from a c(4 ×4) reconstruction of GaAs(001) to a (1 ×3)

reconstruction typical for GaSb during soaking with Sb4, indicating that at least 1 ML of

GaAs was exchanged by GaSb. A smaller amount of only 0.2 ML GaSb was estimated by

Silveira et al. to form upon very short Sb soaking times [50]. On the other hand, Ledentsov et

al. [393] and Farrer et al. [55] reported that up to 2 ML of GaSb can be formed via exchange

of As by Sb atoms, obtaining a first ML GaSb after 10 s soaking, and a second ML GaSb

after additional 20 s, with a saturation thereafter. It should be noted that the concept of Sb

soaking is typical for, but not restricted to MBE growth, as it has successfully been used for

MOCVD growth of GaSb/GaAs heterostructures, too, by Pitts et al. [394].

9.2.2 Soaking-induced GaSb quantum well

Also for both MBE-grown samples studied here, the GaAs growth surface was soaked with Sb

for all GaSb layers, following a growth interruption under As flux prior to GaSb deposition.

In sample C, this Sb soaking endured only 5 s, while in sample D a soaking time of 75 s was

chosen. The result of such a soaking step can particularly be studied for sample D, as here

layer 1 was caused only by soaking, without any direct deposition of GaSb.

A typical XSTM image of this first layer, capped with GaAs, is shown in Fig. 9.3. Many

individual Sb atoms within the GaAs matrix are evident as small, bright spots. For clarifica-

tion, the incorporated Sb atoms are marked in Fig. 9.3(b) by small blue circles. In addition,

some bright vertical stripes parallel to the GaAs atomic chains, which are XSTM tip arti-

facts, and three large, bright spots, given by adsorbates from the residual gas on the cleavage

surface, are observed.

10nm

tipartifacts

[1 0]1

[001]

restgas

adsorbates

positionoforiginal

soakinglayer

(a) (b)

Figure 9.3: XSTM filled state image of layer 1 of sample D, taken at VT= -2.7 V. The vertical bright

stripes are due to tip artifacts. Both figures show the same image, but the positions of incorporated

Sb atoms are marked in (b) by small blue circles.

104 CHAPTER 9. SB SEGREGATION AND ATOMIC EXCHANGE PROCESSES

It is evident in Fig. 9.3 that the material induced by Sb-for-As exchange during Sb soaking

has not remained within an atomically flat layer, but became intermixed and segregated dur-

ing GaAs capping. The area of increased Sb content extends in growth direction over about

15 atomic chains or 8 nm, with a sharp beginning, where the amount of Sb atoms per atomic

chain jumps from zero to its maximum value from one chain to the other, and an Sb content

continually decreasing in [001] growth direction. The total Sb content within this broadened

layer can be evaluated by counting the Sb atoms within a distinct area and comparing this

number with the corresponding number of group-V atomic positions in [1¯

10]-direction. The

area imaged in Fig. 9.3 has an extension in [1¯

10]-direction of 35 nm, including 87 lattice

sites for group-V atoms. In comparison, the number of Sb atoms marked in Fig. 9.3(b)

amounts to 47. Considering that only every second (001) ML can be imaged and assuming

that all marked Sb atoms are located within the cleavage surface, as discussed above, the

total amount of incorporated Sb results to 1.1 ML.

Considering earlier results of GaSb growth obtained by I. Farrer [55], about 1 ML of

antimony or slightly more was expected from the chosen growth conditions to be incorporated

at the growth surface [395], agreeing very well with the experimentally obtained value. Thus,

the model of an Sb-for-As exchange upon soaking is nicely confirmed. Additionally, the

distribution of incorporated Sb atoms over several nm in [001]-direction, as shown in Fig. 9.3,

gives information about the overgrowth process: It is generally assumed that the Sb-for-As

exchange results in a GaSb composition mainly concentrated at the growth surface, no or only

very short-range Sb diffusion into the underlying GaAs matrix is expected [55, 59, 84, 387,

392, 396]. Thus, the spreaded distribution imaged here develops upon overgrowth of the GaSb

layer, as antimony segregates into the deposited GaAs material. The observed concentration

profile of a maximum GaSb content at a first, distinct atomic chain, followed by a decrease

in growth direction over several nm, fits well to the idea of Sb segregation during capping.

As the total amount of GaSb found in this layer agrees with the expected value, it can be

supposed that almost all Sb atoms get re-incorporated into the overgrowth layer, although a

larger amount of initially incorporated Sb atoms that was only partly re-incorporated upon

overgrowth cannot be excluded. It should be noted that according to Wang et al. [391], the

effect of Sb soaking could have even been enhanced if an Sb2cracker source was used for

epitaxy instead of Sb4as it was the case here. The exact profiles and possible consequences

of Sb segregation will be further analyzed and discussed in the next sections.

9.3 From 2D to 3D growth

9.3.1 Smallest MBE-grown quantum dots

While the soaking-induced GaSb layer does not contain any three-dimensional structures,

GaSb quantum dots have been observed for both MBE-grown samples C and D in the layers

grown by directly depositing GaSb following the soaking step. Regarding sample D, the

smallest 3D structures, observed in layer 2 corresponding to 1 ML GaSb deposition, are not

optically active, while the QDs of layer 3, which have been formed by depositing 2 ML GaSb,

show a clear PL signal (see section 8.6). For sample C, no luminescence data are available, but

the statistical analysis of layer 1, also consisting of nominally 1 ML deposited GaSb, revealed

a mean QD base length of about 13 nm with an average height of 1.6 nm (section 8.3.3).

Compared with sample D, this size and the rather high GaSb stoichiometry come closer to

the optically active QDs in layer 3 than to the small 3D structures in layer 2 (see section 8.4).

For illustration, typical structures of the discussed three layers are shown in Fig. 9.4. A

very flat shape is obvious for all structures. However, while at sample D the shape remains

9.3. FROM 2D TO 3D GROWTH 105

(a) (b)

[1 0]1

[001]

5nm5nm5nm5nm

sampleC,layer1

sampleD,layer2

sampleD,layer3

Figure 9.4: XSTM filled

state images of GaSb layers

of both MBE-grown samples:

(a,b) Layer 1 of sample C,

corresponding to 1 ML GaSb

deposition, acquired at (a) VT=

-2.2 V and (b) VT= -2.5 V.

of sample D, corresponding

to 1 ML and 2 ML deposited

GaSb, respectively, taken at

VT= -2.4 V.

flat even for the QDs formed after deposition of 2 ML GaSb, the corresponding layer 2 of

sample C contains much larger and higher QDs.

Remembering that in sample C GaSb deposition was preceded by only 5 s Sb soaking, but

in sample D the soaking time was 75 s, one would have expected a more enhanced Sb-for-As

exchange and therewith a higher amount of GaSb at sample D, which should still remain after

directly depositing equal amounts of GaSb at both samples. However, the opposite behavior

has been observed by the fact that the QDs in sample C contain more GaSb material. Thus,

the idea of the Sb soaking time directly influencing the QD size is too simplified, especially

as other growth parameters seem to have stronger influence on the final QD structure.

Among these, three parameters have to be taken into account: The first is the growth

temperature, which has generally been higher at sample D with 600◦C for GaAs and 515◦C

for GaSb, compared to 550◦C and 490◦C at sample C, respectively. A higher growth temper-

ature increases the mobility of the atoms and would be of special significance if the relevant

processes were kinetically limited. On the other hand, the growth rate was chosen to 0.3 ML/s

for sample C but 0.7 ML/s for sample D, so the higher mobility given by the increased tem-

perature is compensated by a faster growth.

The third and probably most important difference when comparing the growth of both

samples lies within the overgrowth sequence of the GaSb layers: At sample C, after GaSb

deposition the formed layers were immediately overgrown by GaAs, while at sample D a 30 s

long growth interruption took place, the first 15 s under Sb flux, and the second 15 s under

increasing As flux. Therewith, the material was given time to redistribute after deposition.

The observed QD structures indicate that this redistribution did not lead to higher QDs

with an increased GaSb content, on the contrary, a partial leveling and dilution of initially

existing QD structures is likely. From the InAs/GaAs material system it is known generally

that fast overgrowth leads to stoichiometrically pure QDs and WLs [92], while segregation

and dilution effects have been observed during growth interruptions [118, 125, 221]. For

GaSb/GaAs QDs, probably group-V exchange processes not only lead to Sb-for-As exchange

at the GaAs growth surface upon Sb soaking, but also induce an As-for-Sb exchange at the

GaSb layer during the GI. As the strain within the GaSb layer is highest at the QDs, the

tendency for an Sb atom to move laterally on the growth surface or to be replaced by an As

atom is highest here.

9.3.2 Critical thickness of dot formation

Before the processes involved during overgrowth of the GaSb layers will be further discussed

in the next section, now the focus is switched to the astonishing fact that QDs have been

formed even upon deposition of only 1 ML GaSb, which is contradictory to most published

106 CHAPTER 9. SB SEGREGATION AND ATOMIC EXCHANGE PROCESSES

values of the critical thickness of dot formation in the GaSb/GaAs system [44, 46, 49, 51, 55,

59, 69, 256, 260, 264, 267]. For MOCVD growth, the difficulties to exactly specify the amount

of deposited GaSb material upon which QD growth sets in have already been discussed in

section 7.2. But also for MBE growth, typical published values of the critical thickness lie

between 2 and 3 ML [46, 49, 55, 59, 69, 256] or even above [44, 267].

However, a detailed look on the exact growth conditions and the meaning of the given

values is necessary: While Bennett, Thibado et al. reported on a 2D to 3D growth transition

to occur between 2 ML and 3 ML GaSb growth without using an Sb soaking step [46, 256]

and Wang et al. observed an onset of islanding after depositing 1.1 nm GaSb corresponding

to nearly 4 ML [267], most other authors include both the directly deposited GaSb and

additionally the amount of GaSb formed upon Sb soaking when defining a critical thickness

of dot formation [49, 50, 55, 59, 69]. Hatami et al. estimated the thickness of the GaSb

layer formed upon soaking to 2 ML and needed additional 2 ML deposited GaSb until they

observed QD formation by TEM and x-ray diffractometry [44]. Suzuki et al. used RHEED

to observe a change from 2D to 3D growth after the deposition of 1.5 ML GaSb following

an Sb soaking associated with further 1 ML GaSb, resulting in a total GaSb amount of

2.5 ML [49, 69]. The same values are also given by Nakai et al. [59]. Silveira et al. measured

the inherent stress in very thin GaSb/GaAs samples upon GaSb growth by evaluating the

bending of the flexible samples and stated the onset of QD formation to occur already after

0.8 ML direct GaSb deposition plus another 0.2 ML GaSb formed by Sb-for-As exchange,

although accompanying RHEED measurements indicated an amount of 1.6 ML deposited

GaSb to be necessary for QD formation [50]. Farrer et al. again estimated the thickness of

the GaSb layer formed upon soaking to 2 ML and observed QD formation, using AFM, after

additional deposition of 0.75 ML GaSb [55].

Care has to be taken regarding the accuracy of all these values as the thickness of the

soaking-induced GaSb layer can only roughly be estimated from RHEED [59, 69] or other

diffraction measurements [44]. Additionally, although these layers have to be antimony-rich,

they need not necessarily consist of pure GaSb but can be slightly intermixed, which would

reduce the total amount of incorporated Sb. The amount of directly deposited material can

more precisely be verified by intensity oscillations of the RHEED signal or by a carefully

calibrated flux, although these values, too, are difficult to obtain for GaSb growth.

For the samples of this work, the amount of antimony that originally was exchanged

for arsenic during Sb soaking, prior to GaSb deposition and prior to capping, could not

be determined. But the direct deposition of GaSb was gauged by RHEED for sample C,

confirming the rather exact deposition of 1.0 ML in layer 1. The existence of small QDs in this

layer shows that the critical thickness of dot formation, regarding only the directly deposited

GaSb independent of the material gained by anion exchange, has to be slightly below 1 ML

here. This value is at the lower edge of the range of literature data. Remembering that the

QDs of layer 1 have a very flat structure, the question arises whether these QDs could be seen

at all when using TEM or AFM, or whether some of the published values describe rather the

formation of larger GaSb QDs than the actual onset of QD formation.

Regarding the results of sample D, another uncertainty about the critical thickness of dot

formation becomes apparent: Similar to sample C, the deposition of 1 ML GaSb, in addition

to the material induced by soaking, has lead to the formation of 3D islands. Though, in layer 2

of sample D these islands are too flat and too intermixed to be optically active, and only for

the QDs in layer 3 formed by depositing 2 ML GaSb an electronic confinement was obtained.

Thus, the change from 2D to 3D growth can be different from the onset of QD formation,

at least if the term quantum dot is used in a strict, electronic meaning. Additionally, the

comparison of samples C and D shows that the onset coverage for QD formation is not a

9.3. FROM 2D TO 3D GROWTH 107

constant value but depends, within some extent, on the exact growth conditions.

Nevertheless, it can be concluded that the change from 2D to 3D growth can occur already

slightly before the direct deposition of a full ML GaSb, following an Sb soaking step.

9.3.3 Amount of incorporated GaSb

Using XSTM, the epitaxial processes taking place at the growth surface cannot directly be

studied, but the structure of the capped samples can be analyzed. Thus, the structure of the

soaking-induced QW of sample D, already presented in section 9.2.2, yields a total amount

of incorporated antimony of 1.1 ML. Unfortunately, the image quality and the rather poor

statistics limit the quantitative evaluation of layers 2 and 3 of sample D, but the four GaSb

layers of sample C could nicely be analyzed.

The WL and a typical QD of layer 1 are shown in Fig. 9.4(a,b), the ring-shaped QD being

cleaved through the ring body. From the average size and density of the QDs, the assumed

ring shape, and the average chemical composition, the total GaSb content within all QDs of

layer 1 could be calculated to 0.17 ML, as it was discussed in section 8.3.3 (see Table 8.1).

According to the analysis of the local lattice constant, the WL contains about 0.3 ML GaSb

(see section 8.5). Finally, the Sb atoms have to be considered which segregated from the

GaSb WL and got re-incorporated in the GaAs overlayer. These atoms can be counted

within the XSTM images in the same way as it was done in Fig. 9.3 for the soaking-induced

QW, resulting in a total Sb content of about 0.5 ML. Thus, layer 1 contains a total of about

1.0 ML GaSb.

In the same way as for the first layer, also the GaSb content of the other three layers

of sample C was analyzed. The results for all four layers are summarized in Table 9.1 and

visualized in Fig. 9.5. A large difference between the first and the other three layers is evident:

As the size and density of the QDs is especially small in layer 1, the material contained within

all QDs is consequently much less for this layer compared to the others, which show quite

similar values. Also the WL is very thin for layer 1 and nearly equally antimony-rich for

layers 2 to 4. As a consequence, the total GaSb material incorporated within the layers

amounts to about 1.0 ML in layer 1 and varies only slightly around 2.0 ML in the other

layers.

For the four layers of sample C GaSb has been deposited following a 5 s Sb soaking

step. Thus, a small amount of antimony being incorporated by anion exchange during the

soaking should be expected. This explains the total GaSb content in layer 1 and especially

layer 2, which is slightly larger than the nominal amount of deposited material. On the other

hand, layer 1 of sample C still contains slightly less GaSb material than layer 1 of sample D,

which was formed only by Sb soaking, thus the extent of Sb-for-As exchange in sample C

has to be significantly smaller. In the XSTM images of capped GaSb layers it is not possible

nominally total GaSb material segregated Sb atoms total

layer deposited GaSb within QDs within WL in GaAs overlayer GaSb content

[ML] [ML] [ML] [ML] [ML]

1 1.0 0.2 0.3 0.5 1.0

2 2.0 0.6 0.9 0.6 2.1

3 2.7 0.6 0.9 0.4 1.9

4 3.1 0.7 0.9 0.5 2.1

Table 9.1: GaSb material incorporated within the different layers of sample C (approximate values).

108 CHAPTER 9. SB SEGREGATION AND ATOMIC EXCHANGE PROCESSES

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.2

0.4

0.6

0.8

1.0

GaSbmaterialwithinWL[ML]

nominallydepositedGaSb[ML]

0.0

0.5

1.0

1.5

2.0

totalGaSbcontent[ML]

0.2

0.4

0.6

0.8

segregatedSbatoms[ML]

Figure 9.5: Com-

parison of the four

layers in sample C

regarding the GaSb

content within the

WL, the amount of

segregated Sb atoms

incorporated within

the GaAs overlayer,

and the total GaSb

content including

QDs, WL, and

segregated Sb.

to distinguish between directly deposited GaSb and antimony that was incorporated during

soaking, but apparently the material within the GaSb layers is not simply the sum of a

constant amount of GaSb given by anion exchange plus the directly deposited material.

Even more, for layers 2 to 4 the increase of material deposition seems to have no explicit in-

fluence on the amount of actually incorporated GaSb. Instead, the amount of material seems

to saturate after about 2 ML GaSb deposition. As the epitaxy was observed by RHEED,

indicating that the additionally deposited GaSb was actually incorporated in the GaSb layer

during growth, the excess material has to be taken away again during overgrowth. Accord-

ingly, there seems to be a maximum strain energy which can be permanently accumulated in

the GaSb layers, corresponding to about 2.1 ML GaSb. When this level is exceeded during

growth, the additional antimony may get incorporated at the GaSb growth surface, where the

strain is partly relaxed, but upon overgrowth this excess antimony does not remain within

the GaSb layer but gets removed, either as surfactant, i.e. as floating layer at the growth

surface (see next section), or by re-evaporation.

Another interesting detail of GaSb QD growth is revealed by the GaSb content of the

WLs: While the WL of layer 1 contains only 0.3 ML GaSb, about 0.9 ML were obtained in

the WLs of the other layers, respectively. Nevertheless, all four layers exhibit QDs. Thus, the

beginning of 3D growth seems not to instantly replace the 2D growth, as the WL increases

in thickness parallel to QD growth. This would not only be a different behavior to e.g. the

InAs/GaAs material system, where QD growth consumes all additionally deposited material

or even a part of the WL [2, 20, 22, 375], but would also be different from classical Stranski-

Krastanow growth. However, this idea cannot be verified, as the observation of less GaSb

material within the first WL could possibly also be explained by the layer sequence itself:

Assuming that a part of the initially deposited antimony remains at the growth surface as

surfactant, this material will additionally contribute to the GaSb content of layers 2 to 4,

while such a contribution does not exist for layer 1.

The amount of about 1 ML GaSb incorporated within the WLs of layers 2 to 4 is equal

to the GaSb material observed in the MOCVD-grown WL and the QW near the onset of

QD formation (see chapter 7.2). Therefore, this value can be assumed universal for capped

GaSb WLs – indicating that layer 1 of sample C represents some kind of incomplete WL –

independent of the growth method.

9.4. SB SEGREGATION DURING OVERGROWTH 109

9.4 Sb segregation during overgrowth

9.4.1 Analysis of Sb segregation

GaSb material which got dissolved and completely removed from the heterostructures can of

course not directly be detected by XSTM. Those Sb atoms, however, that segregated from

the GaSb layers but got incorporated within the GaAs overlayer, are visible in the XSTM

images. They can, for example, be seen as small bright spots above the WLs and QDs of

both samples C (Figs. 8.4 and 8.11) and D (Figs. 8.10 and 8.13), respectively. From such

images, segregation profiles can be generated by counting the Sb atoms seperately for each

atomic chain above the GaSb layer. While the density and lateral extension of the QDs and

the number of sufficiently resolved XSTM images are too small to quantitatively analyze

segregation above the QDs, it was possible to successfully evaluate the segregation above

the WLs. Corresponding profiles are shown in Fig. 9.6(a-d) for all four layers of sample C:

Directly at the WL the GaSb stoichiometry is so high that individual Sb atoms cannot

be resolved, but within the next 50 atomic monolayers directly above the WL in growth

direction the Sb atoms can be counted. By dividing the number of Sb atoms per ML through

the corresponding number of atomic lattice sites, a GaSb stoichiometry can be specified for

each chain separately, plotted as an individual bar in the histogram. Thereby only each

second ML can be analyzed due to the structure of the cleavage surface (see section 3.4).

Comparing the four histograms, different starting values of the GaSb content are apparent,

ranging from about 16% in layer 2 down to less than 8% in layer 3. However, this discrepancy

does not necessarily indicate a different total amount of incorporated Sb atoms in the four

GaAs overlayers, as the first columns plotted in the histograms may correspond to different

GaAs MLs in respect to the WL position: Firstly, an uncertainty of ±1 ML is generally

inherent to the data obtained from the XSTM images. Additionally, in the images of layers 1

and 2 already the first atomic chain above the WL base could be analyzed, while in the

images of layers 3 and 4 evaluating the segregated Sb atoms could only be started at the

second chain above due to the image contrast of the WL.

Nevertheless, all four segregation profiles show a very similar decay with a decreasing

slope, therefore exponential decay curves are fitted to the data. While principally the expo-

nential decay fits the data quite well, a rather large noise is obvious due to the small database

of only a few Sb atoms per atomic chain. The fitted decay lengths l0of the exponential curves

amount to 6.5±0.7 ML, 6.8±0.9 ML, 7.2±1.1 ML, and 7.5±0.5 ML for layers 1, 2, 3,

and 4, respectively. This means that the ratio of decreasing GaSb stoichiometry between

successive atomic MLs is similar in all four layers, showing that the segregation processes

during overgrowth of the four different layers are rather uniform.

Because the slope is comparable for all layers, the data can be averaged in order to increase

the database and reduce statistical noise. The resulting segregation profile of sample C

is shown in Fig. 9.6(f) by blue columns. A closer view at a section of the histogram is

also given in (e), here additionally showing the statistical errors of the data. Besides the

segregated Sb atoms located within several nm above the GaSb layers, a small nearly constant

concentration of Sb atoms can be observed as a background in XSTM images of the complete

heterostructure of sample C. Such Sb atoms are already observed several nm underneath the

first GaSb layer, therefore they cannot stem from intentionally grown GaSb, but are most

probably due to a permanent small antimony flux in the MBE reactor. As the Sb source of

the MBE is closed only by a conventional shutter and no additionally valved cracker unit is

used, such an antimony background is easily explainable. From the XSTM images, the Sb

background incorporated in the sample was evaluated to 0.25%, resulting in the asymptotic

level in Fig. 9.6.

110 CHAPTER 9. SB SEGREGATION AND ATOMIC EXCHANGE PROCESSES

10 20 30 40

atomicML abovetheWL base

0 10 20 30 40 50

%GaSbcontent

0 10 20 30 40 50

%GaSbcontent

0 10 20 30 40 50

%GaSbcontent

0 10 20 30 40 50

%GaSbcontent

ML abovetheWL base

GaSbbackground:0.25%

x :94%

R :0.84

i,1

x :126%

R :0.91

i,2

crossover:~5nmaboveWL

0 10 20 30 40 50

%GaSbcontent

layer1

layer2

layer3

layer4

(a)

(f)

(e)

(b)

(d)

(c)

Figure 9.6: Segregation profiles for layers 1 to 4 of sample C, showing (a-d) individual histograms

of the GaSb stoichiometry in each second atomic ML above the respective WL and (e,f) histograms

which are averaged over all four layers. The blue curves are exponential decay fits to the data. At

a closer view at a cutout of the histogram including the statistical errors of the data (e), fitting the

complete data by one exponential curve (blue) proves to be not ideal. Instead, two regions have to

be distinguished, characterized by a fast decay (red curve, region 1) and a somewhat slower decay

(green curve, region 2), with a crossover at about 20 ML. The corresponding segregation seeds and

coefficients (see text) are indicated for both regions in (f).

At a careful analysis of the segregation profile, an anomaly of the exponential decay gets

evident at around 20 ML above the WL base [indicated by orange arrows in (f)]. At this

position, the GaSb concentration increases slightly over about 8 ML, before it decreases again

exponentially, but at a somewhat slower decay. Consequently, it is not wise to fit the complete

data by only one exponential decay curve, but the region directly above the WL up to about

20 ML and the region further above should be distinguished and fitted separately, resulting

in a much better fit, as shown in (e). Before the physical meaning and the origin of these

separate regions can be discussed, first an improved understanding of the segregation profiles

is necessary.

To describe the effect of segregation upon overgrowth quantitatively, Steinshnider et al.

[385] have developed a model, based on a notation given by Muraki et al. [397], which is

used here, too, in a slightly modified form: When capping of the GaSb layer begins, obvi-

ously a certain amount of more or less mobile Sb is available, forming a segregation seed xi.

Upon capping, a fraction Rof this seed is expelled and floats at the growth surface, while

the reminding part 1 −Rgets incorporated into the next monolayer. Thereby Rdefines a

9.4. SB SEGREGATION DURING OVERGROWTH 111

phenomenological segregation coefficient. Thus, for a given monolayer indexed n, there is a

certain Sb stoichiometry x(n) that gets incorporated, and another fraction xfloating(n) that

remains floating at the growth surface. As the amount of Sb in the monolayer n+ 1 depends

on that in layer nand on the segregation coefficient, the segregation can be described by the

two recursive relations

xfloating(n+ 1) = R xfloating(n) (9.1)

x(n) = (1 −R)xfloating(n−1) ,(9.2)

with the segregation seed xi=xfloating(0). Also the constant Sb background can be consid-

ered, giving the term x0:

xfloating(n+ 1) = R[xfloating(n) + x0] (9.3)

x(n) = (1 −R) [xfloating(n−1) + x0].(9.4)

These independent recursion relations can be solved and combined to the following one-

dimensional segregation profile:

x(n) = xiRn−1(1 −R) + x0(1 −Rn).(9.5)

In a continuous model, this discrete formula would actually transform into an exponen-

tial decay function characterized by a decay length l0plus a constant offset. Thus, from

the fitted parameters obtained from the experimental segregation profiles the coefficients of

Eq. 9.5 can be calculated for both regions 1 and 2 indicated in Fig. 9.6(f), respectively. The

fitted exponential curves have the form y=Aexp (−x/l0) + x0, and the discrete segregation

parameters result to

x0= 0.0025 ;

xi=A+x0

exp 1 ML

l0−1=⇒xi,1= 0.94 , xi,2= 1.26 ;

R= exp −1 ML

=⇒R1= 0.84 , R2= 0.91 .

Concentrating firstly on region 1, the obtained parameter xi,1= 0.94 stands for an initial

segregation seed of nearly 1 ML, which gets incorporated during overgrowth. This value seems

to disagree with the data of Table 9.1, indicating the amount of Sb observed in the QDs, in

the WL, and in the overgrowth layer of the GaSb layers 1 to 4, respectively. However, for

that table all Sb atoms observed within about three atomic chains above the base of the WL

were attributed to the WL itself, and only all Sb atoms further above were counted for the

overlayer, while here the segregation analysis was extrapolated from the overlayer to the WL.

Correspondingly, a substantial part of the obtained segregation seed, forming at the WL base,

is incorporated again within the first one to three MLs above. The more significant value

is the obtained segregation coefficient of R1= 0.84, implying that during overgrowth of the

GaSb layers the probability of a floating Sb atom to get incorporated in the next GaAs ML is

only about 16%, while the probability to remain at the growth front amounts to about 84%.

In region 2, the segregation coefficient is even increased to R2= 0.91, meaning that only

about 9% of the floating Sb atoms get incorporated per ML, in good agreement with the

decreased slope of the corresponding exponential decay curve in Fig. 9.6(f). The obtained

segregation seed – extrapolated to the base of the WL – amounts here to xi,2= 1.26, exceeding

by far the value of xi,1, again in good agreement with the slight increase of the measured

112 CHAPTER 9. SB SEGREGATION AND ATOMIC EXCHANGE PROCESSES

GaSb content between MLs 18 and 24 in the histogram of Fig. 9.6(f). At the first view, this

increase of the GaSb content per ML combined with an increased segregation coefficient at

about 20 ML above the WL base is unexpected and even seems to be impossible, as this

would imply that the remaining amount of Sb atoms in the floating layer gets somehow

increased at this position. However, remembering the growth structure of sample C (see

section 8.1), the crossover between both segregation regimes, which can be located at about

18 to 24 ML or 5 to 7 nm above the WL base, occurs just at that area of the overgrowth layer

where the growth temperature was increased from 490◦C (GaSb growth) to 550◦C (GaAs

growth). Consequently, a change of the segregation behavior can well be expected here: The

increase of the segregation coefficient Rbetween regions 1 and 2 thus stands for a decreased

incorporation probability of the remaining Sb at higher temperatures.

Considering the raised growth temperature, also two explanations for the increased

amount of Sb atoms available for incorporation into the overgrowth layer further above are

possible: Firstly, an increase of the growth temperature is combined with an also increased

temperature at various mechanical parts of the MBE chamber around the sample itself,

including the sample holder, leading to a re-evaporation of antimony which was formerly

deposited at the surfaces and is now available for incorporation into the sample.

Secondly, it has been assumed above and will be explained in the next section that during

overgrowth some antimony remains at the growth surface as surfactant layer, meaning that

the Sb atoms influence the growth kinetics and surface energy, but do not get incorporated at

all [103], in contrast to the Sb floating layer. Accordingly, the originally deposited Sb atoms

are divided into three parts upon GaAs overgrowth, namely a first part which directly remains

within the QDs or WL, a second part which forms the floating layer and gets incorporated

within several MLs above the GaSb layer, and finally the surfactant atoms. The ratio between

these three parts is probably determined by the initial amount of Sb atoms, the strain within

the GaSb layer including the QDs, the surface energy, and the growth kinetics. Therefore

it can well be imagined that an increase of the overgrowth temperature varies the distribu-

tion of Sb atoms in the floating and the surfactant layer, supplying additional antimony for

incorporation, explaining the observed changes between the two segregation profiles.

9.4.2 Origin of Sb segregation and intermixing

After the strong Sb segregation present in both investigated MBE-grown samples could em-

pirically be described by a one-dimensional model, and having in mind the strong intermixing

of antimony and arsenic in the observed GaSb nanostructures, the basic questions remain:

Which are the reasons for the strong segregation and intermixing, and why are these effects

so extraordinarily pronounced in the GaSb/GaAs system?

For a possible answer, first the macroscopic level with the crystal parameters is considered.

The main driving force of QD formation and changes during overgrowth is the strain inherent

to the heterostructure, given by the lattice mismatch and the stiffness of the materials. The

latter can be described by the elastic moduli c11,c12, and c44 of the crystals, which are listed

for GaSb, InAs, and, in comparison, for GaAs in Table 9.2. Accordingly, the elasticity of

c11 c12 c44 lattice

material elastic moduli constant

[×1010 N m−2] [nm]

GaSb 8.8 4.0 4.3 0.6096

InAs 8.3 4.5 4.0 0.6058

GaAs 11.9 5.4 6.0 0.5653

Table 9.2: Room-temperature

lattice properties of GaSb, InAs,

and GaAs, from [164].

9.4. SB SEGREGATION DURING OVERGROWTH 113

GaSb is very similar to that of InAs, while the stiffness of GaAs is slightly larger. Thus, for

comparing the strain only the lattice mismatch has to be considered, which amounts to 7.84%

for GaSb/GaAs and 7.16% for InAs/GaAs. Therewith, the strain in GaSb/GaAs layers is

about 9% larger than in InAs/GaAs layers with the same amount of material, resulting in

18% more strain energy, so that a partial removal of antimony from the GaSb layer releases

slightly more energy than a corresponding process at InAs layers.

However, this difference is too small to fully explain the strong Sb segregation and inter-

mixing, and processes taking place at the atomic level have to be regarded as the main con-

tribution. Three features will be discussed in the following, namely anion exchange processes,

the surfactant nature of antimony, and the surface reconstructions of GaSb(001) layers.

While the Sb-for-As exchange process is intentionelly used during Sb soaking of the GaAs

growth surface prior to GaSb deposition, the unwanted opposite exchange reaction also occurs

during overgrowth of the GaSb layers with GaAs: Strong As-for-Sb exchange has been clearly

verified by mass spectrometry [389, 392, 398], RHEED [392], x-ray photoelectron spectroscopy

[391, 392], x-ray diffraction [386], and XSTM experiments [386, 392]. Thereby, As-for-Sb

exchange at the GaSb surface has been found to occur more efficiently and with more material

redistribution than the opposite Sb-for-As exchange, because GaAs has a much larger bond

strength than GaSb [392]. The values for the amount of exchangable GaSb material vary in

literature between 0.85 ML observed by Xie et al. [398] and up to 3 ML reported by Nosho

et al. [386]. Anyway, the exact literature values, in most cases obtained for the surfaces of

strain-free thick GaAs or GaSb layers, respectively, are not directly transferable to the case

of a strained GaSb WL on GaAs. Nevertheless, the principle mechanism of strong Sb-for-

As exchange occurs here as well. Additionally, Wang et al. [392] observed that As-for-Sb

exchange is not limited to the growth surface, but can extend into the bulk: As mentioned

above, upon Sb soaking of a GaAs surface the amount of exchanged material saturates when

1 or 2 ML GaSb are formed [44, 55, 69]. However, the increase of Sb exchanged by As during

As soaking of a GaSb surface gets slower after a certain time, indicating the termination of

surface exchange, but remains to continue linearily for several minutes [392]. Thus, not only

the chemical composition at the material interface changes, but strong intermixing also of

the GaSb layer underneath results.

The extent of As-for-Sb exchange depends on the molecular species used as arsenic source:

In the case of As4, the necessary dissolution of the molecular bonds prior to incorporation is

more complex than for As2, thus the latter is more reactive to a GaSb surface when used as

soaking material. According to Nosho et al. [386], no anion exchange at all occurs upon soak-

ing with As4, whereas Wang et al. [391] as well as Brown et al. [84, 396] report that also

under the use of As4an As-for-Sb exchange occurs, but to a smaller extent as in case of As2.

With this premise, on the first sight it seems astonishing that sample C, grown with As2,

contains larger QDs with purer GaSb material than sample D, grown with As4. However, also

the other growth parameters have to be taken into account: Firstly, in sample C the GaSb

layers were immediately overgrown with GaAs, leaving less time to surface exchange reactions

as in sample D, where a growth interruption under increasing arsenic pressure took place prior

to GaAs overgrowth. This GI was necessary, as for the growth of sample D a valved As cracker

source was used, which can effectively reduce the As background during GaSb growth, but

needs several seconds to be opened again [55]. Secondly, the growth temperature chosen

for the GaSb layers was 490◦C in sample C but 515◦C in sample D. In this temperature

regime, the As-for-Sb exchange increases with increasing substrate temperature [389, 398],

as does the amount of Sb atoms in the floating layer [see Fig. 9.6(f) and the change of the

segregation profiles discussed above]. Thus, the smaller reactivity of the arsenic species used

for sample D was probably more than compensated by a longer As soaking time and an

114 CHAPTER 9. SB SEGREGATION AND ATOMIC EXCHANGE PROCESSES

increased temperature, as compared with sample C, resulting in a stronger intermixing of the

GaSb layers. Additionally, for the use of As4instead of As2, a reduced As-for-Sb exchange

efficieny, but an enhanced incorporation of segregated Sb material into the overgrowth layer

was reported [391].

Once some antimony of the GaSb layers has been exchanged by arsenic, this Sb material

has to remain somewhere. Besides the possibility of direct re-evaporation, the excess Sb

can remain at the growth front, from which it can also be re-evaporated later on, or get

incorporated into the overgrowth layers. The latter case of antimony floating on the growth

surface for some time and getting reincorporated has been extensively described for InAs

layers grown on GaSb [385, 387, 389, 392] and to some extend also for the GaSb/GaAs system

[57, 84, 394]. Indeed, this process has lead here to the segregation profiles described above.

Although the re-incorporation of floating Sb atoms is energetically unfavorable because of the

larger bond length and weaker bond strength of GaSb compared with GaAs, it nevertheless

happens due to the large Sb supply from the floating layer and for entropy reasons [392].

As the material observed by XSTM in the capped GaSb layers – including the respective

GaAs overlayers – is, at least for the upper layers, less than the amount of originally deposited

material (see section 9.3.3), some antimony must have been removed from the sample during

overgrowth, in addition to the floating Sb atoms. The role of antimony as surfactant, riding

up on the growth surface, decreasing the surface energy [399, 400], and limiting the surface

diffusion rates of other atoms [103], but not getting incorporated, is a well-known effect in

several material systems: An Sb supply during the deposition of Ge on Si, for example,

drastically changes the formation of the corresponding Ge/Si nanostructures, although no

Sb gets integrated in the heterostructure (see, for example, [401] or [402] and the references

therein). During the last years, the Sb surfactant effect has also been used in the InAs/GaAs

system for increasing the InAs content of the nanostructures and thereby redshifting their

photoluminescence to the technologically important lasing wavelength of 1.3 µm, both for

QW [403, 404] and for QD structures [103, 400, 405]. Therefore it is assumed that also in the

case of the GaSb/GaAs nanostructures studied here a considerable amount of the originally

deposited Sb atoms acts as surfactant upon GaAs overgrowth, explaining the apparent loss

of GaSb material in the capped structures.

The effects of As-for-Sb exchange, Sb as surfactant, and a floating Sb layer have in common

that Sb atoms comparatively easily can get exchanged or removed from the GaSb layer,

leading to intermixing and segregation processes upon overgrowth that are much stronger than

in the case of InAs/GaAs QDs or other material systems. To understand this special behavior

of Sb at the growth surface in the GaSb/GaAs system, the (001) surface reconstructions of

GaSb and especially GaSb films on GaAs have to be regarded and compared with typical

surface reconstructions of other materials.

At typical growth conditions, the (001) growth surfaces of III-V semiconductors are ter-

minated by group-V atoms like As or Sb [171, 294]. Thus, the group-III atoms like In or Ga

are completely bonded by group-V atoms, while the surface Sb atoms exhibit dangling bonds,

or form some dimer structures for energy reduction. Correspondingly, Sb atoms should eas-

ier be repelled from the GaSb surface than In atoms from InAs, and the group-V exchange

processes at interfaces with a common cation are expected to be stronger than group-III

exchange processes at common anion interfaces. This effect can partly explain the observed

strong As-for-Sb exchange, but it is strongly enhanced by a uniqueness of the GaSb(001)

surface reconstructions.

For homoepitaxial GaSb(001) [258, 406, 407] and also for unstrained thin films [389, 392]

often a (1 ×3) or a c(2 ×6) reconstruction was suggested. According to calculations from

Righi et al. [408], a (4 ×3) reconstruction would be energetically favourable to (1 ×3) or

9.4. SB SEGREGATION DURING OVERGROWTH 115

(2 ×3) structures for GaSb(001), but would lead to similar patterns in RHEED experiments,

so probably in some earlier works an actual (4 ×3) may have been misinterpreted as (1 ×3)

reconstruction. Indeed, GaSb(001) surfaces in three stoichiometrically different (4 ×3) re-

constructions were observed by Barvosa-Carter using STM [409].

For substrate temperatures below about 380◦C - 420◦C, the (n×3) can change to a

(1 ×5) reconstruction, which contains more excess Sb at the topmost layers [389, 392]. This

excess Sb has been found to be an additional source of strong Sb segregation [389, 392],

although significant Sb segregation has been observed for different (4 ×3)-reconstructed

surfaces, too [385]. At low temperatures and Sb-rich growth conditions, also (2×8), (2×10),

or c(2×10) reconcstructions have been observed, exhibiting an even more Sb-enriched surface

[258, 407, 410].

Even more unique than the observance of these Sb-rich surfaces is the fact that GaSb(001)

never reconstructs in a c(4 ×4) geometry, although stable c(4 ×4) reconstructions ex-

ist for most other III-V semiconductor surfaces, including GaAs and InAs [258]. Instead,

GaSb favours surface reconstructions containing many Sb dimers, because the Sb-Sb bond is

stronger than the Ga-Sb bond, in contrast to As-As bonds, which are weaker than Ga-As or

In-As bonds [408].

In order to fully understand the influence of surface reconstructions on the segregation

observed above the GaSb layers of samples C and D, also the strain within these layers

has to be considered, as strain can generally influence the energetics of surfaces. InAs thin

films on GaAs, for example, exhibit surface reconstructions which are different to those of

homoepitaxial InAs or GaAs at the same growth conditions. The sub-ML deposition of InAs

on a (2 ×4)- or c(4 ×4)-reconstructed GaAs(001) surface typically leads to a (1 ×3) or

(2 ×3) reconstruction [179, 411, 412], which, by the way, indicates InGaAs alloying. With

further InAs deposition, at about 1 ML, the reconstruction of the growth surface changes

into a (2 ×4) [411–413]. For the WLs of InAs/GaAs QD layers, it is more difficult to resolve

the surface reconstructions than for flat films, but in recent years some results have been

obtained using STM: Krzyzewski et al. found a (4 ×2) reconstruction for low As2fluxes

and a (1 ×3) one for more conservative growth conditions [309], while Costantini et al. [198]

report a coexistence of both structures. Jacobi and M´arquez, finally, only observed a (2 ×4)

reconstruction [31, 176].

To my knowledge, no surface reconstructions for the WL of a GaSb/GaAs QD layer has

been published yet. However, the change of GaAs(001) reconstructions upon Sb soaking

have been studied: Laukkanen et al. [414] have grown GaAs at 580◦C and As-rich conditions,

leading to the formation of the (2 ×4) reconstruction. This surface was soaked by Sb4while

the substrate temperature was reduced to 450◦C. With decreasing temperature, the RHEED

pattern corresponding to the (2 ×4) reconstruction first became broader and then, below

500◦C, disappeared while a (2 ×8) diffraction pattern arose. The suggested structural model

for the (2 ×8) reconstruction has an Sb coverage of 1.25 ML. A (2 ×8) reconstruction had

already earlier been reported by Whitman et al. [415], consistently observed with RHEED,

x-ray photoemission spectroscopy, and STM, after soaking a GaAs(001) surface with Sb4at

490◦C. Possible structures of the (2×8) and the (2×4) reconstructions are shown in Fig. 9.7.

While Laukkanen et al. proposed a δ2 configuration for the (2×4) reconstrucion, Esser et al.

[416] have reported on α(2 ×4) and β2(2 ×4) surface reconstructions of thin GaSb films on

GaAs(001).

The exact surface reconstructions of the GaSb WLs in sample C and D prior to overgrowth

are not clear. A measurement during epitaxy was not possible, as the RHEED signal was

dominated by the QD geometry. Also a direct comparison with the cited publications cannot

be performed as those include only Sb soaking, but no direct GaSb deposition. However,

116 CHAPTER 9. SB SEGREGATION AND ATOMIC EXCHANGE PROCESSES

1 layerSb

1 layer As

st 2 layerGa

nd 3 layerSb

additionaltoplayerSb

SbinGasite

surface

unitcells

(a)

(b)

Figure 9.7: Atomic models of Sb-on-GaAs(001) surfaces, displaying a (a,b) (2 ×8), (c) α(2 ×4), (d)

β2(2 ×4), and (e) δ2(2 ×4) reconstruction, according to (a) [415], (b,e) [414], and (c,d) [416].

because in sample D the soaking-induced layer exhibited similar segregation as the other two

GaSb layers, and because also the results for sample C are comparable, it can be assumed

that the GaSb layers of both samples had either a (2 ×4) or a (2 ×8) reconstruction, too.

Thereby, at least for the GaSb layers of sample C, grown at 490◦C, a (2×8) structure is more

probable than a (2 ×4) one. In both cases, a large amount of excess Sb has been available

at the growth surface, becoming a floating or surfactant Sb layer upon overgrowth.

These unique GaSb/GaAs surface reconstructions thus can explain the observed strong Sb

segregation which is not known in that amount from other QD systems. For the well-studied

InAs/GaAs system, the situation is very different, as not only the (2 ×8) reconstruction is

not common, but even more because both the As-rich (1 ×3) and (2 ×4) reconstructions

observed in WLs restrict In segregation. Also for other QD systems with a common group-III

atom, the surface reconstructions do not contain that much excess group-V material as do

the GaSb surfaces on GaAs(001).

It should be noted that additionally to segregation in growth direction, also the lateral

atomic diffusion on the growth surface is strongly influenced by its surface reconstruction

[179]. This can explain why a strong anisotropy, which has been observed for some InAs/GaAs

QDs [31, 35], does not exist for the GaSb/GaAs QDs studied here.

In conclusion, the strong Sb segregation upon GaAs overgrowth, which could be modeled

by a temperature-dependent exponential decay corresponding to an Sb floating layer and

additional Sb surfactants, is induced by a very Sb-rich reconstruction of the GaSb(001)

growth surface, providing many excess Sb atoms, in combination with a comparably weak

Ga-Sb bond.

Chapter 10

Formation and atomic structure of

ring-shaped quantum dots

Having understood some of the antimony-related effects taking place during growth, now the

formation of ring-shaped quantum dots can be studied in more detail. Therefore, firstly the

atomic structures of the QDs will be analyzed from the XSTM data. Then, by comparing

these results with published ring structures in other material systems, a model of the growth

of GaSb/GaAs nanostructures observed here will be discussed.

10.1 Atomic structure of quantum dots

All QD layers of both MBE-grown samples C and D contain ring-shaped QD structures, also

called quantum rings (QRs), as have been analyzed in sections 8.3 and 8.4. For sample C,

a distribution of the ratio of inner to outer ring diameter was obtained with a maximum at

r0= 0.42 and a standard deviation of 0.13. Both from this statistical result and from an

optical inspection of the XSTM images it is obvious that the extension of the central gap of

the ring varies from QD to QD, partially also leading to asymmetric or irregular ring shapes.

Keeping these results on this sort of inner QD shape in mind, now the typical outer

contour as well as the chemical composition of the QDs shall be analyzed. Figure 10.1,

showing XSTM images of typical QD structures of sample C, underlines the ability of XSTM

to study the atomic structure and to elaborate local variations of the stoichiometry and Sb

distribution. Considering the strong segregation effects taking place during overgrowth, as

shown above, the possibility to study capped nanostructures, which is inherent to the XSTM

method, is additionally important.

Structures like those shown in Fig. 10.1 are common for the QDs in layers 2 and 3 and

for most QDs in layer 4 of sample C. Layer 1 is characterized by rather flat nanostructures,

which have a smaller height and also a slightly smaller base length than those in the other

layers (for details see section 8.3.3). Nevertheless, the shape of a truncated pyramid with flat

bottom and top facets and rather steep side facets is found in all layers. A strongly varying

stoichiometry within the QDs has been observed for all layers, too.

10.1.1 Outer shape of the quantum dots

Due to the varying contrast and the slightly diffuse and intermixed interfaces, it is difficult

to specify the exact shape of the QDs. For the QD shown in Fig. 10.1(a), the contour can

approximately be determined, as visualized in Fig. 10.2(a) by a thin dashed line. Accordingly,

this QD has a lateral extension of 15.5 nm at the base and 11.5 nm at the top with a height of

117

118 CHAPTER 10. FORMATION AND STRUCTURE OF QUANTUM RINGS

5nm

[1 0]1

[001]

(a) (b)

5nm

(c)

5nm

Figure 10.1:

XSTM filled state

images of typi-

cal GaSb QDs of

(a) layer 3 and

(b,c) layer 2 of

sample C, acquired

at (a) VT= -2.6 V,

(b) VT= -1.7 V,

and (c) VT=

-2.4 V.

four atomic chains, corresponding to 2.4 nm. At the sides, the QD seems to be characterized

by plain facets. The angle between contour lines from these side facets and the QD base can

be measured in the XSTM images, amounting to 51◦and 46◦for the upper and lower side of

the QD shown here, respectively. For the QD shown in Fig. 10.1(b), angles of 52◦and 41◦

can be evaluated, while the side facets of the QD of Fig. 10.1(c) have an angle of 49◦and 57◦,

respectively. The large variance of these measured angles displays the large error inherent to

these data, consisting of three parts: The first is the imperfect abruptness of the interfaces

mentioned above, in combination with often missing atomic resolution in [1¯

10]-direction in

the XSTM images, making it difficult to determine exactly where the border between the

QD and the surrounding matrix is. This difficulty is further increased by the small height of

the QDs, extending only about four atomic chains. Finally, the calibration of the XSTM has

an error of about 10% due to piezo effects and thermal drift. This error can be eliminated in

images with atomic resolution, as it is nearly always done for the [001]-direction, but only a

few images like the one shown in Fig. 10.1(b) offer atomic resolution in both directions and

are corrected correspondingly; the QDs in most other images may appear slightly compressed

or sheared in [1¯

10]-direction (for details see section 3.4).

Assuming a simple QD shape of a four-sided truncated pyramid with low-indexed side

facets, there are two possible structures, as sketched in Fig. 10.2: For QD models with {101}

and {111}side facets, the top view from [001]-direction (b,e), the (110) cross section (c,f) and

the corresponding planes in the cube of the Zincblende unit cell (d,g) are plotted, respectively.

For the top view, a square QD base is sketched – a rectangular base with differently long

sides, which is not generally excluded, would lead to a somewhat more complex structure.

The angle between the side facet and the base in a (110) cross section for a QD with {101}

side facets is α= arcsin 1

√3= 35.3◦, and for {111}side facets β= arctan √2 = 54.7◦. Thus,

the measured angles varying between 41◦and 57◦mostly lie between these calculated values,

with a tendency towards the {111}oriented side facets.

From Figs. 10.2(b) and (e) another difference between the {111}and {101}bounded QD

shape regarding XSTM data is evident: For the {111}shape, the sample cleavage cuts the

QDs parallel to a side of their base, while QDs with {101}facets are cut parallel to a diagonal

of their base. In the latter case, the observed lateral extension of a QD measured by XSTM

actually is the length of a diagonal cut of its base, which depends on the position of the cross

section within the QD. In the case of {111}side facets, however, the measured extension

equals the length of one side of the rectangular base, independent of the cleavage position.

10.1. ATOMIC STRUCTURE OF QUANTUM DOTS 119

5nm

(110)

cleavage

plane

[ 0]11

(001) (001)

(110)

(101) (1 1)1

[ 0]11

( 1)11

(111)

(1 1)1 ( 11)1

[110][110]

[1 0]1 [ 10]1

[ 00]1 [0 0]1

[100][100]

[0 0]1

(0 1)1

(101) (011)

( 01)1

[ 00]1

[010] [010]

(001) (001)

(001)

(110)

(0 1)1

(1 1)1

[001]

[010]

[100]

(a)

(b)

(f)

(d) (g)

(e)

(c)

Figure 10.2: (a) XSTM image of the QD shown in Fig. 10.1(a). The contour of the QD is highlighted

by a dashed line. Possible QD structures assuming (b-d) {101}and (e-g) {111}side facets are displayed

in (b,e) top view, in (c,f) (110) cross section and (d,g) regarding the intersection of the relevant planes

in the Zincblende cube.

It should be noted that the higher-indexed (1¯

12) side facet shows the same angle in the

cross section as the (101) facet, accordingly a (201) facet would lead to the same angle as a

(1¯

11) facet. However, at least the (201) facet has not been observed for QDs yet. Additionally,

calculations of the strain relaxation in cleaved QDs, performed by H. Eisele [124], have shown

that a cut through a QD bounded by {101}or {201}facets produces a laterally strongly

varying strain profile of the QD because of the strongly varying amount of QD material lying

underneath the cleavage plane. This would lead to a strongly increased image contrast at the

QD center and a significantly weaker contrast at the outher parts of the QD in XSTM images,

which is not the case for the data shown here. Considering these arguments and the tendency

of the measured angles, the QDs studied here most probably seem to be characterized by

{111}side facets.

Remembering the ring structure of the QDs, the question still needs to be answered why

the QD base is assumed to be square and not circular. Firstly, any cut through a circular

QD would result in a cross section showing a rather small angle between the base and the

side of the structure, comparable to a cross section through a square QD characterized by

{101}facets, while the XSTM images reveal considerably larger angles. Secondly, assuming

a circular base, from the XSTM images with a compact QD appearance (like those shown

in Fig. 10.1), resembling cross sections through the edge of the ring, a considerably smaller

lateral extension of the QD should be obtained in average than from images with paired

features (see Fig. 10.3), representing ring structures cut in the center. A ratio of about

0.7 between the average QD extensions in both types of XSTM images would be expected.

120 CHAPTER 10. FORMATION AND STRUCTURE OF QUANTUM RINGS

5nm

(a) (b) (c) (d)

[1 0]1

[001]

5nm

Figure 10.3: XSTM images of centrally cleaved ring-shaped QDs in layer 3 of sample C, acquired at

(a,b) VT= -2.3 V and (c,d) VT= -1.8 V. The outer contours of the QDs shown in (a,c) are marked

in (b,d) by black lines, while the inner face of the ring body is marked green. In (d) the area of

additional diluted GaSb material within the gap of the ring is indicated by blue lines.

Analyzing the experimental XSTM data, however, the average QD extensions of centrally

and marginally cleaved ring structures differ only about 6% to 7%, excluding a circular

QD base. The small discrepancy observable in the data, with the larger average length for

the centrally cut structures, may indicate that the QD base is also not exactly square but

sometimes slightly extended in the center. But it could as well be due to an increased GaSb

stoichiometry in the center of the square base compared with its edges, leading to a sharper

interface between the QD and the surrounding matrix for the centrally cut structures and a

slight underestimation of the actual length for structures cleaved at the edge.

The inner face of the ring body, i.e. the interface between the GaSb QD and the central gap

filled with GaAs, is much less regular than the outer QD shape, as it can be seen in Fig. 10.3.

It seems to be approximately circular, and generally the diameter of the gap increases from

the bottom to the top of the QD. Thus, a cross section through the ring body ideally has a

double-trapezoidal shape, with the outer sides slightly steeper than the inner ones, although

this shape is often asymmetric or imperfect. Additionally, instead of an abrupt interface

between GaSb at the ring body and GaAs in the central gap, often a cross-over characterized

by strongly diluted GaSb material can be found, as it is indicated in Fig. 10.3(d).

10.1.2 Local stoichiometry

Knowing the shape of the QDs, the missing information to completely resolve the atomic

structure is the local stoichiometry. Therefore, the distance between neighboring atomic

chains in growth direction has been analyzed as a measure for the local lattice constant and

thus for the chemical composition, as described in detail in chapter 6. The results for two

typical QDs of sample C are shown in Fig. 10.4, obtained as averaged data from several XSTM

images. The chemical composition has been evaluated separately for the central region and

for the outer parts of the QD images, underlining the varying local stoichiometry within one

structure.

Focusing at first on the QD shown in Fig. 10.4(a), several details need to be discussed.

The GaSb composition is inhomogeneous, varying between the edges and the center of the

10.1. ATOMIC STRUCTURE OF QUANTUM DOTS 121

(b) -2 0 2 4 6

0.45

0.50

0.55

0.60

0.65

0.70

25%GaSb

50%GaSb

100%GaSb

(a) -2 0 2 4 6

0.50

0.55

0.60

0.65

center

edge

25%GaSb

50%GaSb

}

ofQD

image

center

edge

}

ofQD

image

Figure 10.4: Analysis of the chemical composition of QDs in sample C: The variation of the local

lattice constant for different regions of the QDs shown in the insets is plotted together with calculated

values for a GaSbxAs1−xQW.

structure as well as from bottom to top, with a maximum of about 60% being reached just at

some parts of the QD top, while its bottom consists of only 20% to 40% GaSb. The increased

lattice constant extends over five atomic chains at the outer parts of the structure, marked

in green and orange, but only over four chains at the center of the QD image, marked in

purple, which can well be understood remembering the ring shape of the QD: Obviously,

this ring structure has been cleaved just at the edge of its central gap, which is widest at

the top of the QD, so that the topmost atomic chain of the cross section in Fig. 10.4(a) is

already affected by the gap, while the other four chains still resemble the ring body. This

idea is further supported by a comparison of an optical inspection of the XSTM image with

the chain distance analysis: Although the image contrast is weakest in the QD image center,

which usually indicates a lower stoichiometry, the analysis of the local lattice constant yields

about the same GaSb composition within the QD also in this area. Thus, the idea mentioned

above (section 8.3.1) that the image contrast is significantly affected by the ring structure is

nicely confirmed: When a GaSb ring is cleaved slightly in front of the central gap, resulting

in a cross section as the one shown in Fig. 10.4(a), the strain related to the GaSb content is

lower at the center of the cross section, where the gap consisting of GaAs is behind, than at

the edges of the QD image having the GaSb-rich ring body in the back.

The QD shown in Fig. 10.4(b) has a similar shape and size as the one discussed above, but

a significantly higher GaSb content, reaching up to a GaSb composition of about 90%, at least

at the outer parts of the QD image. For the center of the QD cross section, a slightly weaker

GaSb content is obtained, which could indicate that the material near the central gap of the

ring is partly diluted. The strain corresponding to the large amount of GaSb incorporated

within the ring body is underlined by a very strong undershoot-like reduction of the measured

chain distances underneath the QD, extending over about four atomic chains into the GaAs

matrix. To a minor part this undershoot stems from a systematic error of the evaluation

method due to the local bending of the cleavage surface (see section 6.3), but the major

part is actually due to the GaSb-related strain which significantly compresses the underlying

GaAs. If the GaSb-GaAs interfaces were equally abrupt at the QD bottom and top, a similar

reduction of the chain distances would also be expected at the GaAs above the QD. The fact

that no such reduction is present is a strong indication for Sb segregation in growth direction

out of the QD. Indeed, in the XSTM image many individual Sb atoms can be seen as small

bright spots above the QD. Nevertheless, the GaSb composition is not decreased at the top

122 CHAPTER 10. FORMATION AND STRUCTURE OF QUANTUM RINGS

of the QD, thus the idea of these indiviual Sb atoms just having segregated from the top

layer of a readily formed QD structure is much too simplified, also because a large amount

of segregated Sb atoms can be found above the WL, too.

A different approach to further study the chemical composition and the strain distribution

in and around the QD analyzed in Fig. 10.4(b) is chosen in Fig. 10.5, showing a regular

XSTM image (b), a contour plot (a), and a highpass-filtered image (c) of the same QD. In

the contour plot, the complete z range of 1.0 nm is divided into eight intervals separated by

black lines, representing lines of the same apparent height. For better contrast, a full color

map is used here. Interestingly, the height is not only strongly increased at the QD itself, but

also weakly at the regions underneath and above. Underneath the QD, where no Sb atoms

are incorporated, the increased height is due to a strain-relaxing outward bending of the

cleavage surface. Accordingly, the apparent height is largest at that region underneath the

QD edge which corresponds to the strong undershoot of the chain distance analysis shown

in Fig. 10.4(b) by the orange curve. Above the QD and the WL, both a structural image

contrast induced by strain relaxation and an electronic image contrast from the segregated

Sb atoms contribute. The corresponding area of increased apparent height has an extension

in growth direction two or three times larger than the QD itself.

In order to differentiate between the long-range structural contrast and the short-range

electronic or chemical contrast and therewith between strain effects and the distribution of

Sb atoms, firstly the regular STM image of Fig. 10.5(b) was smoothened by averaging every

image pixel with its neighbors weighted by a Gaussian distribution. Then 90% of this image

background were subtracted from the original image, resulting in the high-pass filtered image

shown in Fig. 10.5(c). The WL and especially the QD now appear as an accumulation of

many individual bright Sb atoms. In addition, Sb segregation directly above the WL and even

more above the QD is evident. The blurred bright stripes visible underneath the QD always

in the same distance to the GaSb layer are scan artifacts from the XSTM measurements.

Only two or three spots which could be attributed to Sb atoms are present underneath the

layer.

Strong Sb segregation can have even more drastic consequences on the QD structure,

Figure 10.5: Filtered XSTM images of the same GaSb QD in sample C, displaying (a) an equal-

height contour plot, (b) the regular image, acquired at VT= -1.7 V, and (c) a high-pass filtered image.

10.1. ATOMIC STRUCTURE OF QUANTUM DOTS 123

Figure 10.6: A diluted GaSb QD in layer 2 of sample C: (a) Filled state and (b) high-pass filtered

XSTM image, taken at VT= -2.4 V, and (c) analysis of the chemical composition.

as demonstrated by the strongly diluted QD shown in Fig. 10.6(a): While the shape of a

truncated pyramid with a base length of 15 nm and three atomic chains or 1.8 nm height

can still be recognized, within the QD areas of comparatively low image contrast on the one

hand and individual bright Sb atoms on the other hand are noticeable. By evaluating the

local lattice constant within a broad stripe across nearly the complete QD, a maximum GaSb

content of this QD of only about 40% was analyzed [see Fig. 10.6(c)]. While the bottom

interface of the QD is relatively sharp, the GaSb composition decreases smoothly from about

20% to zero over five to six atomic chains or 3 nm at the top of the QD and above it. Thus,

for this structure the interface between the QD itself and the GaAs overlayer containing

segregated Sb atoms is not well-defined any more, in contrast to the QDs shown in Fig. 10.4.

Many individual Sb atoms can well be seen in Fig. 10.6(b), showing an XSTM image filtered

by background subtraction analogously to the method described above.

Due to the good image quality and the comparatively low GaSb content it is possible to

count the individual Sb atoms in the XSTM image of this QD, resulting in a GaSb composition

between 30% and 40% in the bottom two atomic chains, about 25% in the third chain, and

between 10% and 20% in the fourth and fifth chain. For the next ten atomic chains the

GaSb content changes only between 10% and zero. It should be kept in mind that only each

second atomic ML can be seen in the XSTM images, and that the strain analysis evaluates

the distance between neighboring chains, thus always obtaining the average stoichiometry of

two neighboring chains. The good agreement with the counted Sb atoms once more indicates

the validity of the stoichiometry determination from chain distance data.

In contrast to this diluted structure, a QD with a chemical distribution considerably

different to those discussed yet is shown in Fig. 10.7: Here, a GaSb composition of about

80% in one part and rather pure GaSb in the other part of the ring structure is observed.

However, this high GaSb content is concentrated to only two atomic chains, neighbored by

one to three chains with a low GaSb concentration of 10% to 20%. This rather compact GaSb

distribution within the ring body is accompanied by a QD structure characterized by a large

central gap with a ratio of apparent inner to outer ring diameter of ˜r= 0.5. As a consequence

of this nearly perfect ring structure with its high GaSb content a strongly varying local strain

at this structure leads to a considerable bending of the atomic chains directly at the bottom

and below the ring body, as shown in Fig. 10.7(b,c).

From a comparison of the chemical compositions of the different QD structures in sample C

124 CHAPTER 10. FORMATION AND STRUCTURE OF QUANTUM RINGS

Figure 10.7: A GaSb QD in layer 3 of sample C with a compact ring structure: (a) Analysis of the

chemical composition, (b) magnification and (c) high-pass filtering of the upper part of the XSTM

image shown in the inset of (a), acquired at VT= -2.3 V. A part of the atomic lattice is indicated by

black and blue lines: The atomic chains are bended by the large strain inherent in the ring body.

it seems that the broad distribution of the inner ring radius characterized by a distribution

of ring ratios of r= 0.42 ±0.13 comes along with a distribution of the GaSb content within

the ring-shaped QDs, too, ranging from strongly diluted QDs over those with a varying GaSb

composition of about 30% to 60% up to structures consisiting of nearly pure GaSb.

For the QDs of sample D, an analysis of the local lattice constant results in an even

stronger variation of the GaSb composition both between different QDs and within single QD

structures. Considerably high GaSb concentrations are only reached within the bottom two

chains of the generally very flat structures, but nevertheless GaSb contents locally reaching

about 50% in QDs of layer 2 and up to 80% in QDs of layer 3 are evaluated. In addition,

also diluted QD structures with a GaSb composition of only 30% and less were observed.

10.2 Literature data on quantum rings

10.2.1 Quantum ring structures in other material systems

Self-assembled ring-shaped semiconductor QDs, mostly being called QRs, have first been ob-

served in the InAs/GaAs system in 1997 by J. M. Garc´ıa et al. in the group of P. M. Petroff

at the University of California in Santa Barbara, USA [202, 223, 224]. Intending to study

the initial overgrowth process, they capped InAs QDs with differently thick GaAs layers and

studied the growth surface with AFM at ambient conditions. Thereby, after growing InAs

QDs at 530◦C, capping them with 2 nm GaAs at the same temperature, annealing them also

under the same temperature for 30 s to 60 s, and finally cooling them down to room tempera-

ture under arsenic flux, islands with crater-like depressions in the center were observed [202].

Later on, the growth conditions were optimized [225, 226] and the QRs were studied sys-

tematically using photoluminescence and capacitance-voltage spectroscopy [223, 226] as well

as resonant tunneling I-V-spectroscopy [417] and optical spectroscopy for varying external

magnetic fields [224, 225]. These electronic results could theoretically be modeled by Barker

et al., showing strong dependence on the ring geometry and stoichiometry profile [240].

Usually, the structure of InAs/GaAs QRs was determined using AFM in top-view arrange-

ment [202, 224–227, 418]. An example of such AFM images is given in Fig. 10.8(a), taken

from Ref. [227]. These ring-shaped islands, capped with 2 nm GaAs, have a density of

10.2. LITERATURE DATA ON QUANTUM RINGS 125

(b)(a)

Figure 10.8: InAs/GaAs QR structures, from [227]: (a) AFM top-view image of InAs QDs capped

with 2 nm GaAs, (b) XSTM images of 2 InAs/GaAs layers containing QRs, cleaved in the (1¯

10)

(upper image) and (110) plane (lower image), acquired at VT= -3.0 V. The inset shows a model of

the QR structure.

∼1×1010 cm−2and are slightly anisotropic, with a larger elongation along the [1¯

10]-direction.

The outer sizes are about 100 by 70 nm2with an average height of about 1 nm. The holes are

also asymmetric with a size of 30 by 20 nm2and a depth of about 0.5 to 1.5 nm. It should be

noted, though, that all these values were acquired from structures capped with 2 nm GaAs

using AFM under ambient conditions. From spectroscopic measurements and a modeling of

the experimental data, an electronic diameter of the QRs of 28 nm was evaluated [224]. This

value is far below the QR sizes obtained by AFM.

This discrepancy could be explained when the structure of completely overgrown

InAs/GaAs QRs was studied with XSTM by P. Offermans et al. in the group of P. M. Koen-

raad at Eindhoven University of Technology, the Netherlands [227, 418]. The samples studied

in that work consisted of InAs QDs which were grown by MBE at 540◦C, partially capped

with 2 nm GaAs, annealed at 500◦C for 1 min under As2flux, and further overgrown with

GaAs. This sequence was repeated several times to form an InAs/GaAs QR superlattice.

Two XSTM images of that work are shown in Fig. 10.8(b), comparing cross sections through

InAs QR structures in the (1¯

10) (upper image) and in the (110) (lower image) cleavage plane.

According to the XSTM results, the corresponding InAs structures are no real rings, as

Offerman et al. have stated [227, 418]: “The nanostructures have a crater-like shape which can

be attributed to the remainder of the quantum dots after the QR formation process. It can be

clearly seen that these quantum craters do not have an opening at the center.” The diameters

of the InAs structures along [110] and [1¯

10] are evaluated to 23 nm and 20 nm, respectively,

with a total height of 3.6 nm and an InAs thickness of 1.6 nm at the center of the structure.

From comparing the different ring shapes obtained by AFM and XSTM, the authors conclude

that only the XSTM images reveal the actual shape of the InAs nanostructures, while the

AFM data are dominated by the material additionally deposited during capping. Thus, the

apparent rings of the AFM images, having a comparatively large diameter, consist of GaAs

rather than InAs.

Meanwhile, the growth of ring-like structures by partially capping and annealing

InAs/GaAs QDs has been realized by several other groups, too, using MBE [213, 230, 231]

126 CHAPTER 10. FORMATION AND STRUCTURE OF QUANTUM RINGS

or MOVPE [228]. Thereby, the ring-like shapes within the growth surface, which had been

resolved by AFM, were confirmed with synchrotron x-ray scattering in small angle grazing

incidence geometry by M. Sztucki et al. [230]: They used comparatively low temperatures

of 490◦C during InAs QD growth and 450◦C during partial capping of the QDs with 3 nm

GaAs and obtained rings with an average outer diameter of 51 nm. These rings had compar-

atively large craters with 1.7 nm depth and a diameter of 0.8 times the outer ring diameter.

Although the shape of the rings has circular symmetry, the InAs concentration, as evaluated

by simulating the x-ray intensity maps, varies strongly and amounts to more than 80% along

[1¯

10]-, but less than 20% along [110]-direction.

Costantini et al. have studied the initial overgrowth of InAs QDs with GaAs for a broader

range of growth conditions using STM [35]. They found that the question whether ring-like

structures evolve upon partial capping of QDs or not does not only depend on the growth

temperature and the thickness of the capping layer, but also on the capping rate: When the

InAs QDs were overgrown very slowly (0.08 ML/s), strongly elongated structures without any

craters or depressions resulted, but for a faster overgrowth (0.6 ML/s), ring-like structures

were observed. The importance of the exact position and duration of the growth interruption

taking place after partial capping has been studied in detail in the group of this work, using

XSTM [125, 127, 132, 221]: After Eisele et al. verified a total dissolution of formerly existing

QDs during an extended GI [221], Lenz et al. even observed the coexistence of conventional

InGaAs QDs together with ring-like structures and QDs containing nanovoids within the

same WL, all three structures resulting from an interplay of different QD sizes and segregation

effects during the GI [127].

InAs/GaAs is not the only material system, apart from the GaSb/GaAs QRs studied

here, in which ring-like structures were observed instead of more compact QDs; and a careful

comparison of the structural and growth details of different systems will help to understand

the formation of QRs. It should be noted, however, that all studies mentioned below have

been performed in top-view geometry on free-standing QRs, lacking the information that can

possibly be obtained by comparing top-view and cross-sectional investigation, and missing

all effects that take place during capping of the QRs. InAs/InP was the second material

system for which the formation of ring-like structures was succeeded, obtained by Raz et al.

at the Technion–Israel Institute of Technology in Haifa, Israel [232]: Similar to the structures

shown above, InAs QDs were grown on InP(001) and partially capped with 1 nm InP prior

to a GI of varying duration, all steps were done at 495◦C using MOCVD. In AFM studies

performed after cooling the sample, large asymmetric rings with outer diameters of about

220 nm along [110] and 110 nm along [1¯

10] were found. However, for PL studies identical

samples were further overgrown with InP after the initial GI, and for GI times up to 1 min

these samples showed the same PL spectrum as a reference QD sample. Only for GIs lasting

4 min or longer, the PL signal changed significantly, which can be attributed to the formation

of QRs. Thus, the transformation of partially capped QDs into these much larger QRs upon

annealing takes several minutes here and is therewith drastically slower as in the InAs/GaAs

system, where growth interruptions of several seconds are sufficient for QR formation.

Additional insight in the QR formation was obtained by Sormunen et al. at the Helsinki

University of Technology, Finland, who also formed InAs/InP QRs using MOCVD [233, 419]:

They grew very large InAs QDs on InP at 560◦C and annealed them for 10 s or more under

either tertiarbutylphosphine (tBP) or tertiarbutylarsine (tBAs), without an additional partial

capping. The resulting structures kept a compact QD shape for tBAs flux, but became

clearly ring-like upon annealing under tBP at growth temperature. This shows that instead

of a directly deposited partial capping layer, also the soaking of the QD layer with resulting

group-V P-for-As exchange may trigger QR formation.

10.2. LITERATURE DATA ON QUANTUM RINGS 127

Similar results as for the mentioned III-V nanostructures were also obtained in the

Ge/Si material system, using both MBE growth [235] and UHV chemical vapor deposi-

tion (CVD) [236]: Ge QDs were grown on Si(001) and partially capped with Si. In the case of

CVD growth, a 3 min GI followed the partial capping, while at MBE growth, the overgrowth

was very slow so that no additional GI had to be performed. With increasing thickness of the

cap layer, a QD shape was restored or only slightly changed, ring-like structures evolved, or

a smooth growth surface was obtained. In contrast, Mashanov et al. observed a co-existence

of QD and ring-like structures after partial capping, using MBE growth [237]. Thereby, the

QRs had a larger diameter and height than the partially capped QDs.

In contrast to all ring-like structures mentioned above, GaSb/GaAs is the only material

system in which QRs can evolve without any partial capping or soaking step, even without

intentional annealing. Kobayashi et al. at the University of Tokyo, Japan, first observed such

GaSb/GaAs ring structures [60]: Using MBE, they grew GaSb QDs on GaAs at 490◦C and a

growth rate of 0.1 ML/s. Omitting the common Sb soaking step, they directly deposited 3.5

ML GaSb on GaAs(001), yielding a spotty RHEED pattern indicating 3D growth. After this,

and without any intentional annealing step they cooled down the sample (which probably

may have been accompanied by As-for-Sb exchange reactions due to some As background

in the chamber) and analyzed the growth surface with AFM. As a result, clear ring-like

structures at a density of about 5 ×109cm−2were observed, with typical outer diameters of

50 – 70 nm, heights of about 1 nm, inner diameters of 15 – 20 nm and depths of the central

hole of about 2 nm. When slightly more GaSb material was deposited, GaSb QDs were

observed additionally to the QRs, until for 5 ML or more deposited GaSb large, elongated,

and relaxed GaSb islands dominated the growth surface. It should be noted, though, that

the structural data stem from AFM measurements at ambient conditions, which can partly

mislead the size analysis, as discussed above.

10.2.2 Proposed formation of quantum rings

It is generally assumed that InAs/GaAs and similar ring-like structures evolve by a substantial

material redistribution during the GI or annealing step following the partial cap. At this

growth step, the InAs WL is completely covered by GaAs, while the summits of the QDs

probably protrude out of the partial cap layer. This is especially confirmed by the XSTM

data on corresponding InAs/GaAs structures: A few nm above the initial InAs WL, at the

position where the partial cap layer was finished and an extended GI took place, a second

thin InAs layer was observed, which shows that during the GI at this stage In atoms from

the partially capped QDs have been spread out over the whole growth surface [127, 227, 418].

In order to explain this material redistribution, basically two different models have been

proposed, based either on kinetic or on thermodynamic considerations. The kinetic model

describes a diffusion-driven transformation from QDs to QRs [225, 420]: Regarding the lateral

diffusion on the growth surface, under typical growth conditions the mobility is much higher

for In atoms than for Ga [420], resulting in a strong out-diffusion of In out of the QD center.

No compensating in-diffusion can take place as in the direct neighborhood of the QD the

growth surface consists of GaAs. Thus, the observed rim around the crater-like depression

mainly consists of material that was formerly within the QD center.

Such a diffusion-driven material transport could also explain the often observed anisotropy

of the QRs, as In diffusion is preferred along the [1¯

10]-direction as compared with the [110]-

direction [35, 225, 227, 230], which can be explained by surface reconstructions of the [001]

growth surface [179]. However, also the opposite behavior of QRs elongated along [110] was

reported for MOVPE-grown structures, being explained in this case by an anisotropy in the

migration length of Ga precursors in MOVPE growth [228].

128 CHAPTER 10. FORMATION AND STRUCTURE OF QUANTUM RINGS

The thermodynamic model focuses on the changes in surface free energy induced by the

partial capping of QDs. An equilibrium balance of surface forces, which is given for free-

standing QDs, is no longer valid in the changed geometry of partially capped QDs, assuming

a pyramidal QD shape. Thus, a net force remains which points radially outward from the QD,

inducing a material redistribution from the former QD center into a new-built rim [225, 421].

However, this model implies that the InAs material is considered as liquid, in spite of the InAs

bulk melting point at 942◦C [164], including a de-wetting process at the QD and a floating

In or InAs layer at the growth surface, regarding InAs QDs as wetting droplets [226, 421].

Both models have intensely been discussed in literature regarding different QR systems

[60, 225, 226, 230–233, 235]. For InAs/GaAs QRs, some authors favor the diffusion model,

as it can explain a significant material transport as well as an inhomogeneous stoichiometry

[230]. Others prefer the wetting droplet model and consider the elastic energy as the driving

force of QR formation, in combination with a simultaneous Ga-In alloying process, which

again is more kinetically driven [226]. Costantini et al. finally proposed that the overgrowth

of InAs QDs generally consists of two regimes, the initial one being governed by fast dynamics,

which result in island shapes close to thermodynamic equilibrium, while the second regime

is controlled by kinetically limited surface diffusion [35].

Considering the formation of QRs in the InAs/InP system, the kinetic model based on

different diffusion rates of different group-III atoms can be excluded [232, 233]. Instead,

group-V exchange reactions and especially elastic strain relaxation were proposed to be the

driving force for QR formation here [233]: At the top summit of free-standing QDs, the

local lattice constant is closest to the bulk value of the QD material, therefore this place is

very unfavorable for the incorporation of cap material. When InAs QDs are annealed in a

P-rich atmosphere, P-for-As exchange occurs at the growth surface and can release some As

atoms at the QD summits. These released As atoms will, as a consequence of strain, migrate

outward and get incorporated at the side of the QDs, forming a ring around the initial QD.

Also for the Ge/Si material system, strain relaxation is proposed to be the driving force

for QR formation [235, 236], while both the diffusion and the wetting droplet model are

assumed to be of low significance [235]. Therefore, again the summit of free-standing Ge

QDs is the most unfavorable place for Si incorporation, which will drive Si adatoms from the

QD center to its side. The more Si gets accumulated at the side of the QD, the more Ge

which was previously located at the QD center will also migrate to the side by short-range

surface diffusion to alloy with Si. This process leads to a height decrease at the QD center

and the formation of a ring structure around.

In conclusion, different processes have been proposed to cause the evolution of QDs into

QRs. While In diffusion and the wetting droplet model are most discussed for the InAs/GaAs

QRs, from other material systems the relaxation of strain has been favored as main driving

force. All models have in common that the ring-like structures that can be seen in top-view

geometry on the growth surface have just formed upon partial capping during a subsequent

GI or annealing step around the initial QD. These rings thus consist of the cap material,

possibly alloyed with the former QD material.

10.2.3 Persistent currents and Aharonov-Bohm effect

Ring-like semiconductor nanostructures can be grown in stacked layers in a similar way as QDs

[422], and first attempts have successfully been undergone to use stacked QR layers in classical

QD applications like laser devices, yielding shorter lasing wavelengths [423]. However, beside

such applications, another aspect of nano-scale QRs regarding fundamental quantum physics

is much more exciting, namely the existence of persistent currents and so-called Aharonov-

Bohm–type oscillations.

10.2. LITERATURE DATA ON QUANTUM RINGS 129

Y. Aharonov and D. Bohm predicted theoretically, already in 1959, that in the quantum

regime, charged particles can be influenced by electromagnetic potentials even if they are

not affected by any fields and do not feel any forces [424]. An exemplary setup for this

effect, proposed by Aharonov and Bohm, is sketched in Fig. 10.9(a): An electron beam is

split in two paths and combined again. In the middle of both paths, there is a cylindrical

solenoid, meaning a long coil which is formed to a ring, of (nearly) infinite height, so that an

magnetic field is only present within the closely packed loops of the solenoid and not outside.

Nevertheless, it can be shown theoretically that the passing electrons are influenced by the

vector potential in that way that the solutions to their wavefunctions obtain an additional

phase term depending on the magnetic flux in the solenoid. So, when the split electron

beams are brought together again, interference effects will take place, being solely a quantum

mechanical phenomenon. A continuous increase of the magnetic flux will then lead to periodic

oscillations of the interference pattern.

Later on, quantum mechanical interference effects based on magnetic fluxes were generally

called Aharonov-Bohm effects (AB effects) or Aharonov-Bohm oscillations (AB oscillations),

being realized in several different areas of physics [425, 426]. A basic requirement for the AB

effect is a strict phase coherence, therefore any phase loss from scattering of the electrons

destroys the AB effect. Thus, the electron confinement within a true QR structure is an ideal

prerequisite to observe AB oscillations.

An additional, but related quantum mechanical effect in nano-scale rings is the appear-

ance of persistent currents: In a strictly one-dimensional conducting ring, with no electron

scattering, a magnetic flux through the ring is expected to produce a persisting equilibrium

current, similar as a superconducting ring with a Josephson junction. This was first predicted

by Buettiker et al. in 1983 [427], showing that the potential of the ring under the influence of

the external vector potential leads to the formation of a (one-dimensional) band structure, in

which the kwavenumber of the electron within the band is determined by the magnetic flux

through the ring. Evidence for weak persistent currents was, for example, found in copper

rings of 0.55 µm size, as the magnetization of these rings oscillated in dependence on an

oscillating magnetic flux through the rings [428]. However, temperatures far below 1 K were

necessary to avoid substantial electron scattering within these rings of mesoscopic scale.

Considering a charge carrier being confined within a QR (an electron or a hole in an

InAs/GaAs QR, a hole in a GaSb/GaAs QR, or a charged exciton), its state probability

is mainly restricted to the ring body, but within this the particle can move freely. Thus,

the orbiting particle gets influenced by the magnetic flux through the interior of the ring,

and the phase of its wavefunction becomes changed. As the wavefunction itself and the exact

position and movement of the particle is principally indeterminable according to fundamental

inter-

ference

region

electron

beam

solenoid

metal

foil

(a)

E[ /2m*R ]h2 2

(b)

magneticflux

Figure 10.9: (a) Experimental setup suggested by Aharonov and Bohm: A coherent electron beam

is split into two paths, surrounding a solenoid with a certain magnetic flux, and interferes again;

from [424]. (b) Calculated energy levels of an ideal one-dimensional ring for increasing magnetic flux;

from [224].

130 CHAPTER 10. FORMATION AND STRUCTURE OF QUANTUM RINGS

quantum physics, the probability density of a single particle state can be considered as an

overlay of contributions from both circular directions, including interference effects. Thus,

the corresponding eigenenergies of a single charge carrier within the QR will oscillate with

the magnetic flux through the ring. For the occurence of such a AB–type oscillation, it does

not matter whether the ring body itself is also exposed to the magnetic field or not, as any

direct interaction of confined charge carriers with this field would lead to forces which change

continuously with increasing magnetic field, but not to oscillations.

For an idealized one-dimensional QR of radius Rin a magnetic field, the energy levels are

determined by the periodic boundary conditions to

Em=¯h2

2meff

m,with km=m1

whereby mis the magnetic quantum number and meff the effective mass of the charge carrier.

When the QR is penetrated by the magnetic flux φ=πR2Bresulting from a magnetic field B

perpendicular to the ring plane, the AB effect leads to an additional phase contribution, and

the resulting energies are

Em=¯h2

2meff R2µm+φ

φ0¶2

, m = 0,±1,±2, . . . ,

according to [224], with the magnetic flux quantum φ0. Thus, with increasing magnetic field,

the minimum of the ground state energy changes from m= 0 over m=−1 to m=−2, and

so on, whenever the magnetic flux through the QR is a multiple of the flux quantum. These

oscillating energy levels are displayed in Fig. 10.9(b).

The main challenge now is to observe experimental evidence on such AB oscillations in

actual ring-like nanostructures. This was first realized indirectly by Lorke et al. for InAs

QR-like structures grown by Garc´ıa and Petroff in 1999, using capacitance and far-infrared

transmission spectroscopy in dependence on the magnetic field [224]. For this purpose, the

QRs were situated within a field-effect transistor, so that the gate voltage could be tuned and

thus the number of electrons per ring could be controlled. From the transmission spectra,

electronic excitations could be observed at characteristic energies, which shift slightly with

varying magnetic field, showing a weak AB–type oscillation. This energy shift with increasing

B field, together with corresponding calculated energy levels, is shown in Fig. 10.10(a). These

experimental data were an incentive for further theoretical work, which could explain and

reproduce the observed capacitance and state-filling results [241] and could model the exact

ring geometries and stoichiometry profiles [240]. Just recently, also an astonishingly strong

single electron persistent current could be demonstrated for the same nanostructures using a

very sensitive torque magnetometer [429].

A more direct detection of the AB effect in QR-like structures was succeeded by Bayer

et al., using artificial InGaAs/GaAs QRs of 90 nm and 30 nm outer and inner diameter,

respectively, fabricated by lithography techniques: They studied the emission energy of such

single QRs and observed clear oscillations of the energy of charged excitons with increasing

magnetic field [430].

While the original AB effect is found only for charged particles, also for the electrically

neutral exciton AB oscillations in the energy of optically active states have been proposed

theoretically [77, 238] and were also observed in experiment [239]. This can be explained by

a small spatial displacement between the electron and the hole, leading to a polarization of

the exiton, being induced by locally different electron and hole state densities [77, 238, 240]

or by a type-II band alignment [77, 239]. The calculated electron density for a GaSb/GaAs

QR is shown in Fig. 10.10(b).

10.3. RING FORMATION 131

magneticfield[T]

calculatedenergy[meV]

measuredvoltageshift[mV]

GaSb/GaAsQR

y [nm]

x [nm]

(b)(a)

Figure 10.10: (a) Calculated energy levels of a wire with a parabolic cross section bent into a ring

(see inset) for an increasing external magnetic field. The dotted blue curve represents experimental

data (right-hand scale), showing the gate voltage shift of the lowest capacitance maximum of an

InAs/GaAs QR embedded in a FET; adapted from [224]. (b) Calculated electron density (without

magnetic field) of a GaSb/GaAs QR with an outer and inner diameter of 16 nm and 8 nm, respectively;

from [77]. The angular position of the center of the electron density within the ring is arbitrary.

Up to now, AB oscillations have been observed experimentally for type-I QRs [224, 430]

and for type-II QDs [239], but not for type-II QRs. However, according to extensive cal-

culations the latter structures are best suited to observe large persistent currents and pro-

nounced AB oscillations [77]. Combining this prediction and the fact that the commonly used

InAs/GaAs QRs are no real rings but still contain some intact InAs layers at the bottom

center (see above and [217]), the GaSb/GaAs QRs observed in this work are very promising

structures to show a strong AB effect.

10.3 Ring formation

Concluding the structural results of this work on MBE-grown GaSb/GaAs QDs, comparing

them with literature, and keeping in mind the strong Sb segregation and Sb-As–exchange

reactions analyzed in chapter 9, a pathway for the formation of ring-shaped QD structures

can be deduced.

10.3.1 Origin of ring formation in the GaSb/GaAs material system

For the comparatively well-known InAs/GaAs QRs, typically the diffusion model and the wet-

ting droplet model (see section 10.2.2) are discussed. Obviously, different diffusion lengths of

group-III elements cannot be responsible in the GaSb/GaAs system with a common group-III

atom. As the shape anisotropy observed for InAs/GaAs QRs is explained by In diffusion on

the growth surface being differently preferred in different directions [35, 225, 227, 230], the

lack of a corresponding anisotropy in the GaSb QRs can well be understood.

The wetting droplet model, on the other hand, is based on thermodynamic considerations

valid for a sufficiently long growth interruption, taking place after a partial capping of former

QDs with a compact shape. No partial capping step was used here, on the contrary, as the

GaSb layers were overgrown with at least 10 nm GaAs at fast growth rates of 0.3 ML/s or

even 0.7 ML/s. For sample C, this overgrowth took place immediately after GaSb deposition,

without any intentional growth interruption. Additionally, an assumption for the wetting

droplet model is a perfectly flat base interface of the QDs and QRs, as the liquid droplet

does not modify the underlying atomic chains [421]. However, the XSTM data of this work

132 CHAPTER 10. FORMATION AND STRUCTURE OF QUANTUM RINGS

show unambigiously that the GaAs matrix underneath a GaSb QR is compressed and the

atomic positions are shifted (see section 10.1.2), at least for an overgrown sample at room

temperature.

Instead, strain relaxation has to be the driving force of QR formation here, as it has

already been proposed for the InAs/InP [233] and the Ge/Si system [235, 236]. Also for the

InAs/GaAs system, strain has been considered to result – at respective growth conditions – in

a dissolution of formerly existing QDs [125, 221] or in the formation of crater-like structures

or even nanovoids within QDs [118, 127, 132]. Indeed, between these material systems, the

lattice mismatch and strain is highest for GaSb on GaAs, even larger than for InAs/GaAs

nanostructures. Strain relaxation is assumed to be the main reason for the truncation of

QDs [35, 36, 118] and for the formation of composition profiles within QDs [95, 100] upon

overgrowth — here, in the case of QRs, the effects of strain relaxation go even beyond.

The reason why strain relaxation has such drastic consequences in the GaSb/GaAs system

lies within the weak Ga-Sb bond and the amount of excess Sb on the GaSb growth surface

reconstructions, which by strong group-V exchange reactions lead to the formation of an

Sb floating layer and therewith to strong segregation and even to Sb acting as surfactant

(see section 9.4.2). These processes cause a partial dissolution of former compact GaSb QD

structures upon overgrowth with GaAs.

10.3.2 Growth model for ring-shaped GaSb quantum dots

Considering the effects discussed above and the observed structural results, the following

growth mechanism for ring-shaped GaSb QDs is proposed, being sketched in Fig. 10.11:

The growth starts on a GaAs(001) buffer layer (a). During Sb soaking, Sb-for-As exchange

occurs at the growth surface, so that about 1 ML GaAs gets exchanged by GaSb (b). At

the following direct GaSb deposition, the thickness of the GaSb layer increases until the

critical thickness of dot formation is reached and QD growth sets in (c). With further GaSb

deposition, the QD density and size increase, including a certain size fluctuation. Until now,

the QDs have a pyramidal shape with a more or less sharp summit, which is typical for

free-standing QDs, e.g. with rather flat site facets like {137}. The GaSb WL is terminated

by a very antimony-rich surface reconstruction of (2x4) or, more probably, (2x8) geometry,

and it is probably not completely continuous but interrupted by thin trenches.

When GaSb deposition is finished and the Sb flux is switched back to As flux, the crucial

step for the shape evolution of the nanostructures is reached. Within a few seconds of growth

interruption or initial GaAs overgrowth, the excess antimony gets released from the GaSb

surface and forms a floating layer, and substantial As-for-Sb exchange takes place (d). The

shoulders of the QDs possibly undergo less As-for-Sb exchange than the WL as they have

another surface reconstruction. Even more important, the strain distribution in the QDs

differs from that of the WL, including that upon overgrowth the strain within the sharp

summits of the QDs increases drastically as they are forced to fit into the GaAs atomic

lattice. As a consequence, the Sb atoms with their rather weak Ga-Sb bonds are repelled

from the QD centers and become part of the floating layer. This effect does not only lead to

a truncation of the pyramidal shape, as it is also the case in other material systems, but goes

further by repelling even more antimony down to the bottom of the QD centers, where it is

replaced by arsenic, stabilizing the structure and lowering the strain. When the structures

are completely capped, the repulsion and exchange of Sb have lead to an evolution of the

formerly compact QDs into QRs (e). Additional to the truncation and the formation of a

central gap, the outer contour of the QDs became steeper, as the ring-shaped QDs are now

bordered by {111}site facets.

As a consequence of the As-for-Sb exchange, the WL has become strongly intermixed.

10.3. RING FORMATION 133

Sbsoaking

GaAsbuffer

GaSbdeposition

growthinterruptionunder Asflux

GaAsovergrowth

finalstructure

(a)

(b)

(c)

(d)

(e)

(f)

(g)

[001]

10nm

Figure 10.11: (a-f) Proposed mechanism

of MBE GaSb growth and subsequent GaAs

overgrowth, leading to the formation of ring-

shaped GaSb QDs: A GaAs buffer layer (a) is

initially soaked by Sb (b), resulting in a GaSb

layer due to Sb-for-As exchange. Upon direct

GaSb deposition (c) the growth of QDs with

a sharp summit sets in, which increase in size

and density with further deposition, together

with an increase of the WL thickness. During

a growth interruption under As pressure or

when GaAs overgrowth starts strong As-for-

Sb exchange occurs (d), leading to a trunca-

tion or partial dilution of the QDs and to the

formation of an Sb floating layer. The strain-

driven shape transition of the QDs into ring-

shaped structures is completed upon further

GaAs overgrowth (e), together with strong Sb

segregation, until finally a diluted WL con-

taining QRs can be observed (f), which is ex-

emplary shown in the XSTM data of (g).

From a floating Sb layer at the growth surface, a lot of antimony gets incorporated upon

further overgrowth, forming an Sb segregation profile above the initial GaSb layer (not shown

in the model). Finally, when the overgrowth of the sample is completed, the residual antimony

which has not become incorporated but acted as surfactant gets completely removed from

the nanostructure region (f). The result of this process is a capped GaSb layer containing

ring-shaped QDs, as observed in this work (g).

Some details of the proposed growth mechanism deserve to get further discussed:

The exact amount of GaSb which gets incorporated by Sb-for-As exchange during Sb

soaking prior to GaSb deposition is unknown for sample C, while it could be determined to

about 1.1 ML for sample D. It might well be that random fluctuations of the thickness of

this soaking-induced GaSb layer act as some kind of precursors for QD growth: This idea is

supported by the observation that the bottom interface of the WL is typically very flat, while

for several QDs small protrusions of GaSb material underneath the bottom atomic chain of

the WL are observed, as for example in Fig. 10.1(a,b).

A significant difference exists for the growth processes of samples C and D, as in sample D

the GaSb deposition was followed by 15 s GI under Sb flux and additional 15 s under increasing

As flux, while in sample C no intentional GI took place. Additionally, the growth temperature

of 515◦C in sample D was 25◦C higher than in sample C, further enhancing the surface

exchange reactions. As a consequence, the QDs in sample D have a smaller height than in

sample C, showing that an increased As-for-Sb exchange process leads to a further flattening

of the nanostructures. Probably this flattening is additionally supported by the increased

lateral mobility of the surface atoms due to the increased temperature. The importance of

134 CHAPTER 10. FORMATION AND STRUCTURE OF QUANTUM RINGS

atomic group-V exchange processes was confirmed recently for another material system, also

by an XSTM study: C¸ elebi et al. found that the height of InAs QDs capped with InP was

about 2 ML smaller than the height of equally grown QDs capped with InGaAs, which they

attributed to a P-for-As exchange process upon overgrowth [130].

Beside the flattening of the QDs, the As-for-Sb exchange also leads to a dilution of the

WL, combined with strong Sb segregation into the GaAs overlayer. The QDs are also more

or less affected by this dilution process, varying in their chemical composition from less than

20% GaSb content up to nearly pure GaSb. From the XSTM measurements it cannot be

concluded if the observed stoichiometry of the nanostructures is completely due to group-V-

exchange and segregation processes during the capping or if the initial GaSb growth layer

was already intermixed. At least for sample D a rather pure GaSb layer should have been

expected, as in the corresponding growth setup the arsenic restgas pressure was specially

decreased by using a valved cracker cell. Nevertheless, also this technique could not prevent

the resulting QDs from exhibiting an even stronger variation of chemical composition than

the structures of sample C, probably due to the longer GI after GaSb deposition and the

increased temperature.

Despite the differences in the growth process, all QDs in both samples C and D were

found to have a ring-shaped structure instead of a compact one. Even the duration of the GI

prior to GaAs overgrowth only influences the exact shape but not the general occurence of

the QRs. Thus, the strain-induced formation of QRs probably starts during the more or less

extended As-for-Sb exchange process but can also occur within seconds upon a comparatively

fast overgrowth. This striking result shows that the self-assembled and spontaneous evolution

of compact QDs into QRs upon capping is a general aspect of GaSb/GaAs QD growth using

MBE and not only restricted to a small growth window.

It should be reminded that most structural data on GaSb/GaAs QDs in literature have

been obtained for free-standing QDs by using AFM [45, 48, 49, 55, 56, 58, 59, 62, 69, 70,

255–257], SEM [267], TEM [62], or STM without atomic resolution [46]. All these studies,

confirming a more or less sharp summit of the free-standing QDs, have been performed prior

to a possible transition of the compact QDs into ring-shaped structures. Only a few structural

results on capped QDs have been published: A part of these were obtained by cross-sectional

TEM [45, 59], averaging the strain information over the complete thickness of the sample

specimen and thus being unable to detect ring-structures. In other studies the GaSb QDs

were capped using exceptionally low temperatures [45], after a special Ga irradiation step [56],

or using an additional Au layer [67]. Also strain-sensitive TEM images of GaSb QDs capped

by a 50 nm thick GaAs/AlGaAs heterostructure can only show the existence of the QDs but

not their exact structure [44, 47]. To my knowledge, there are no structural studies with

sufficient resolution to confirm that any GaSb QDs capped under typical growth conditions

do actually have a compact structure. Instead, the results of this work strongly suggest

that – also for most literature data – the ring-shape is the typcial structure of MBE-grown

capped GaSb QDs. This assumption gets further confirmed by the photoluminescence results

of sample D shown in section 8.6: Although generally the QD shape determines the energy

levels of the confined states and therewith the PL energy [13, 37, 246], the PL peak at 1.11 eV

of the ring-shaped QDs in layer 3 of sample D agrees perfectly well with typical GaSb QD

PL energies in literature [44, 45, 47, 58, 59, 65, 69].

Besides the formation of the central gap resulting in a ring structure, the shape transition

of the GaSb QDs upon capping also includes a steepening of the side facets. Such a steepening

is a general aspect of QD overgrowth, which is already known from the InAs/GaAs system,

where typically {101}side facets are found [35, 97, 100, 118, 122]. Here, even steeper {111}

side facets are obtained for the QDs in sample C. From simple geometric considerations it can

10.3. RING FORMATION 135

be concluded that the compressive strain at the top of a GaSb ring structure is significantly

lower than it would be for a respective compact QD with a truncated pyramidal shape.

Therefore it is energetically favorable to increase the material content in the upper part of

the ring body and thus to form steeper side facets.

The comparison of the structural results of layers 1 to 4 of sample C still keeps some

challenging questions. All four layers contain ring-shaped QDs at a density increasing from

layer to layer, while the average QD size is significantly smaller for layer 1 but similar for

layers 2 to 4. Astonishingly, the WL of layer 1 contains less than half the amount of GaSb

than those of the other three layers, although QD formation had set in and therefore this

WL should have reached the same critical thickness of dot formation as the other three. This

effect may partly be explained by different Sb extraction from the WLs upon overgrowth

due to the formation of an Sb floating layer: Prior to layer 1, no such floating layer exists,

but once some GaSb has been overgrown, the surfactant nature of antimony probably leads

to a permanent Sb floating layer at the growth front until the whole sample is completed.

Thereby the initial floating layer has to be built of Sb atoms originating from layer 1 by strong

As-for-Sb exchange, while at layers 2 to 4 the surfactant Sb layer already exists. However, it

is hardly imaginable that this effect alone can lead to the observed GaSb content in the WL,

being three times larger in layers 2 to 4 than in layer 1.

Instead, it seems as if the formation of GaSb QDs cannot sufficiently be described by

Stranski-Krastanow (SK) growth, but is a combination of the SK and Volmer-Weber island

growth mode, meaning that after the initial formation of three-dimensional structures further

GaSb deposition leads to an increase of the size and density of these QDs as well as to an

increase of the WL thickness. The gaps which are observed in the XSTM images of all GaSb

WLs further support this idea of an combined SK and island growth mode: Although the

formation of trenches between interconnected 2D GaSb islands upon GaSb layer growth has

directly been observed only for growth conditions without an Sb soaking step yet [45, 46, 257],

the gaps in the WLs of samples C and D indicate a similar GaSb island growth process even

upon a combination of Sb soaking and direct GaSb deposition using MBE.

While from layer 1 to layer 2 of sample C an increase of both the average QD size and

the thickness of the WL is observed, surprisingly layers 2 to 4 contain about the same total

amount of GaSb, namely 2 ML, in spite of the additional GaSb deposition. Therefore, the

strain within the GaSb layers may play a double role: While the strain is the driving force

for the formation of QDs and also for the transition of such compact QDs into ring-shaped

structures upon overgrowth, there also seems to exist an upper limit of total strain in the

complete layer: When this limit is reached, any additional antimony seems to get repelled

from the GaSb layer upon overgrowth.

Obviously some of the ideas and specific growth aspects discussed in this section cannot

be taken as secure conclusions but need further investigation in forthcoming experiments.

However, the main mechanism of spontaneous QR formation, which is observed uniquely at

the GaSb/GaAs system, could unambigiously be resolved, being the combination of large

strain and the possibility to easily repell or exchange Sb atoms from the strained structures

upon overgrowth.

136 CHAPTER 10. FORMATION AND STRUCTURE OF QUANTUM RINGS

Chapter 11

Electronic properties and type-II

band alignment

Most existing or intended applications of GaSb/GaAs QDs rely on the large hole confinement

energy and the type-II band alignment (see sections 2.4.1 and 2.5). Also the QRs are very

promising structures for a superior realization of phenomena like the Aharonov-Bohm effect

due to the assumed type-II alignment (see section 10.2.3).

On the other hand, the structural and compositional analysis of the observed nanostruc-

tures by XSTM has shown that many of the structures are strongly intermixed with GaAs,

raising the question whether these structures still show a type-II alignment or are instead of

type-I.

In literature the exact band structure of intermixed GaAs1−xSbx/GaAs QDs in depen-

dence on the Sb content can, to my knowledge, not be found yet. However, several studies

have investigated the electronic properties of GaAs1−xSbx/GaAs QWs for different xvalues:

A type-II band alignment has unambigiously been evaluated for a stoichiometriy of x= 0.3

[76], and also for Sb contents down to x= 0.17 [275] or x= 0.16 [431] type-II behavior

was observed, while QWs with x= 0.12 were found to be of type-I [432]. Liu et al. finally

evaluated the transition from type-I to type-II to occur at x= 0.14 [169, 276].

Accordingly, the band alignment of the intermixed GaSb layers studied here can strongly

be expected to be a type-II one. Nevertheless, an experimental confirmation of this assump-

tion especially for the intermixed QDs and QRs, which have not been dwelled on in literature,

is essential. Besides the knowledge about the existence of a type-II or type-I alignment, also

the determination of the exact band structure would be desirable, including the often dis-

cussed amount of the VB offset [44, 67, 68, 75–77]. It should be reminded here that in most

cases the published band alignment has not been measured directly, but the type-II align-

ment is derived from an observed blueshift of the luminescence with increasing excitation

energy [47, 65, 66].

A more direct way to locally study the electronic properties including the band alignment

is to analyze their influence on STM images or to directly measure the LDOS using STS

imaging or STS point spectra, which is the focus of this chapter: GaSb/GaAs nanostructures

exhibit a unique image contrast mechanism which is related to the strong CB offset, the

type-II band alignment, and effects due to tip-induced band bending. Understanding this

contrast mechanism, STS or CITS images of GaSb QDs can be interpreted; and finally from

STS point spectra, acquired at different positions at and around GaSb QDs and QRs, the

local band alignment can be derived.

137

138 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

11.1 Specific image contrast

In STM images on cleaved semiconductor nanostructures, the image contrast is generally

given by a structural contribution, displaying the outward protrusion of the partly relaxed

nanostructure, and by an electronic contribution (for details see section 3.3). Therefore,

from the appearance of GaSb/GaAs nanostructures in XSTM images, conclusions on their

electronic properties can be drawn.

11.1.1 Bias-dependent appearance of GaSb/GaAs quantum wells

It has been explained in section 3.2.3 and shown in section 9.1 that the polarity of the tun-

neling bias determines which sort of atoms is imaged. As a consequence, the local chemical

composition and atom distribution of the GaSb/GaAs nanostructures is better resolved at

a negative polarity, imaging the different group-V atoms; while at a positive polarity, show-

ing the common Ga atoms, the strain-driven structural protrusion of the cleaved material

dominates. A corresponding behavior is also well known from other material systems like

InAs/GaAs nanostructures, in the latter case with different group-III elements being distin-

guished at positive sample bias [100, 127].

Unique for these measurements on GaSb/GaAs nanostructures, however, is the image

contrast behavior shown in Fig. 11.1: At positive sample voltages all nanostructures ap-

pear smoothly broadened with an image contrast changing from GaSb to GaAs over sev-

eral nm (a,d,f), while at negative sample voltages the QDs (b,c) and especially the QWs (e)

Figure 11.1: Specific STM image contrast of GaSb/GaAs nanostructures, shown at (a-d) an MBE-

grown QD of layer 2 in sample C and (e-g) the MOCVD-grown QW of layer 2 in sample B. In empty

state images the neighborhood of the QDs appears brighter than the GaAs matrix far away (a,d),

while in filled state images the apparent change from QD to GaAs contrast is very abrupt (b,c),

independent of the amount of the voltage. Especially a QW appears very thin and sharply defined in

filled state images like (e), while the same QW looks smoothly broadened in empty state images like

(f), as indicated by arrows. Apparent height profiles across the QW, smoothened in growth direction

to exclude the atomic corrugation, are shown in (g).

11.1. SPECIFIC IMAGE CONTRAST 139

are sharply defined. It should be noted that the interfaces of the MBE-grown QDs actually

are somewhat blurred, in contrast to the MOCVD-grown QWs. Although the filled states

images, showing the As and Sb atoms, are expected to look rougher due to the short-range

chemical fluctuations of the intermixed nanostructures, this effect is by far not sufficient to

explain the strong discrepancy observed in the images.

The different tunneling behavior at both polarities can more quantitatively be seen in

height profiles, which were taken across the QW shown in Fig. 11.1(e,f). After smoothening

the profiles to exclude the atomic corrugation, these height profiles underline the different

appearance of the same QW at different polarity (g). A nearly step-like increase of the tip

height at the interface of the QW imaged with negative sample bias is evident, while the

apparent height increases smoothly over an area of about 10 nm when imaged with positive

sample bias. If the broaded appearance of the nanostructures in empty state images was due

to strain, the same strain should occur also in filled state imaging, which is unambigiously

not the case.

In order to explain this specific GaSb/GaAs image contrast, the staggered type-II band

alignment has to be considered, in combination with the effect of tip-induced band bend-

ing (TIBB, see section 3.2.2). The proposed contrast mechanism is schematically shown in

Fig. 11.2: TIBB occurs in the sample at the position of the tip, locally bending the bands near

the sample surface. At positive sample voltages the bands are bend upwards, so that the VB

tip

sample

sample GaAs

GaAs

GaSb

GaAs

EFEF

ECB

EVB

E +eV

F T

E +eV

F T

emptystates

images

tip-induced

bandbending bandalignment

filledstates

images

[110] [001]

(c)

(d) (f)

(e)

10nm

(a)

(b)

Figure 11.2: XSTM image contrast mechanism of GaSb/GaAs nanostructures, leading to (a,b)

the strongly different appearance at different bias polarity: The effect of tip-induced band bending

is shown for (c) empty state and (d) filled state imaging. As a consequence, the band structure is

locally shifted at the nanostructures with respect to the Fermi energy (e,f), which in the case of

positive sample voltages can lead to a charging of the nanostructure and an additional band bending.

The direction of the band bending is indicated at the bottom. Band offsets and the amounts of

band bending are not drawn to scale, and the depicted wavefunctions (e,f) are only for illustration,

corresponding to filled VB states (magenta), empty VB states (pink), and empty CB states (yellow).

140 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

shifts close to the Fermi energy, which remains fixed, as shown in Fig. 11.2(c). Analogically

at negative sample voltages the bended CB gets near the Fermi energy (d). In the latter

case, all electronic states in the GaAs and GaSb CB are empty and the VB states are filled,

so when the filled states are imaged a clear increase of the tunneling current results directly

at the position of the GaSb due to the VB offset and the high LDOS of localized states, as

sketched in (f). At positive sample voltages, in contrast, the GaAs bulk VB maximum comes

so close to the Fermi energy that the energetically highest localized GaSb VB states shift

above the Fermi level. As a consequence these states get depleted of electrons or – in other

words – filled by holes, resulting in a net charge of the structure. Such a charge will in turn

lead to a band bending parallel to the sample surface, inducing weakly localized CB states

in the GaAs surrounding the GaSb (e). These empty GaAs CB states, which are localized

within a few nm around the GaSb nanostructure, lead to an increased current in empty state

imaging, strongest close to the nanostructures but smoothly declining over a few nm.

Accordingly the sharply defined, thin QW appearance upon filled state imaging actually

corresponds to the electronic VB states of the GaSb QW [magenta states in Fig. 11.2(f)].

At empty state imaging, in contrast, the increased tunneling probability from CB states of

the GaAs directly surrounding the QW [yellow states in Fig. 11.2(e)] causes the broadened

appearance. At both polarities, also the different tunneling probabilities into the GaAs and

GaSb states contribute to the XSTM signal, which is further influenced by the strain-induced

structural contrast of the nanostructures.

11.1.2 Calculation of tip-induced band bending and tunneling current

In order to verify the model described above, calculations on the amount of TIBB and simu-

lations of the resulting tunneling current were performed by R. M. Feenstra at the Carnegie

Mellon University in Pittsburgh, Pennsylvania, USA. For these simulations, he assumed an

STM tip with 10 nm radius of curvature and an opening angle of the apex of 90◦, a GaSb layer

width of 2 nm, and a band alignment for an undoped GaAs/GaSb/GaAs QW heterostructure

with a VB offset of 0.6 eV and a type-II CB offset of 0.1 eV. With these values, Poisson’s

equation was numerically solved using a finite element method as described in Ref. [433].

Thereby the tip-vacuum-semiconductor configuration including the specific shape of an STM

tip was parameterized by a specific coordinate system using so-called “prolate spheroidal

coordinates” [433], generalized here for three dimensions.

The resulting calculated band bending is given in Fig. 11.3(a): The electrostatic potential

energy variations at the cleavage surface directly opposite the tip apex are plotted as a

function of the tip position relative to the center of the GaSb QW. Thus, the variation of

the TIBB across the QW in [001] direction can be tracked in that curve. Surface potential

energies are shown for four different sample voltages of VT= +2.5 V, +2.0 V, -2.0 V, and

-2.5 V, corresponding to different moderate bias voltages at both polarities.

For positive sample voltages, the band bending at the sample surface opposite the tip

strongly varies as the tip moves from the GaAs matrix to the GaSb QW and further on. The

effect is qualitatively the same for both exemplary values of VT= +2.5 V and +2.0 V, but

increases in size with increasing voltage. In order to understand the potential variation, again

the model of the contrast mechanism shown in Fig. 11.2 needs to be considered: At sufficiently

large positve sample voltages, the GaSb is partly depleted of electrons [Fig. 11.2(e)], so that

the resulting charge density pins the Fermi energy and prevents a stronger band bending. As

the tip moves away from the QW and the GaSb states increasingly get out of the influence

of its electric field, a stronger band bending is necessary to compensate the charge of the tip.

In contrast, for negative sample voltages the potential energy profiles shown in Fig. 11.3(a)

are relatively flat, with the amount of TIBB being comparatively large over the complete

11.1. SPECIFIC IMAGE CONTRAST 141

relativeheightvariation[nm]

surfacebandbending[eV]

tippositionalong[001]directionwithrespecttotheQWcenter[nm]

0.351.1

0.30

0.9

0.25

0.7

0.20

0.5

0.15

0.3

0.10

-0.8

0.05

-0.9

0.00

-1.0

-20-20 -10-10 00 1010 2020

(a) (b)

Figure 11.3: (a)

Calculated electrosta-

tic potential variation

at positions on the

sample surface directly

opposite the STM tip

apex, plotted in [001]

direction relative to the

center of a GaSb QW

for different sample

voltages. (b) Simulated

tip height variations

obtained from (a), with

arbitrary zero levels.

heterostructure. Significant differences between the GaSb and GaAs area only occur for

larger amounts of sample voltage, where also the amount of band bending is increased, but

these differences still have a much weaker extension than for positive voltages. This strong

band bending both at the GaAs and GaSb corresponds to a Fermi energy being close to the

CB minimum, which for GaSb lies even slightly above the GaAs value [Fig. 11.2(f)]. At larger

negative voltages like VT= -2.5 V the TIBB seems to be large enough to pull the CB close

to or under the Fermi energy, as in that case the small GaAs/GaSb CB offset leads to the

observed specific behavior at the GaAs/GaSb interface [Fig. 11.3(a)].

Accordingly, the assumed band alignment shown schematically in Fig. 11.2(e,f) is well

confirmed by the calculations, especially for smaller bias voltages of both polarities.

Taking the band bending results, tunneling currents were simulated in a semi-classical

approximation using effective-mass bands, following a method described in Refs. [107] and

[302] for a one-dimensional potential and extending it for the three-dimensional case. Effective

masses for the CB and VB of 0.063 and 0.53 for GaAs, respectively, and 0.041 and 0.82 for

GaSb were used, taken from Ref. [164]. With the GaAs electron affinity χ= 4.07 eV and an

assumed tip work function of φ= 4.74 eV, which is well in the range of possible tungsten

work functions for different crystal geometries [434], flat-band conditions occur for zero sample

voltage. The tip-sample distance at the GaAs matrix was assumed to be 0.8 nm.

The resulting tip height variations are shown in Fig. 11.3(b), plotted in yellow for positive

sample voltages of VT= +2.5 V and +2.0 V and in magenta for negative voltages of VT=

-2.5 V and -2.0 V. The curves are shifted in height for better visibility, so the given values

are only relative and do not indicate absolute heights.

For negative voltages, the simulated current profiles display a narrow maximum at the

QW, sharply defined at the GaSb/GaAs interfaces, which resembles well the contrast observed

in STM images like the one shown in Fig. 11.2(b). It should be noted that the calculations are

based on electronic properties like band offsets and TIBB and do not take into account the

strain-induced structural protrusion of cleaved nanostructures. Additionally, the calculations

assume that the material interfaces are abrupt and that the tunneling current is confined to

the position at the cleavage surface directly opposite the tip apex. Due to these restrictions

142 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

the rectangular profiles of the simulated tip height do not exactly match the slightly broad-

ened actual profiles at negative bias, like the measured one displayed in Fig. 11.1(e,g). The

apparent heights of the GaSb QW of 0.1 nm at the calculated profile for VT= -2.0 V and

slightly more than 0.1 nm at the measured profile for VT= -1.8 V agree nicely.

The tip height profiles calculated for positive voltages exhibit a strongly different shape:

They are quite broad, independent of the amount of voltage, with the tunneling probability

increasing over a range of 20 nm as the tip is approaching the GaSb QW. This broad increase

resembles well the smoothly broadened appearance of the GaSb QWs in actual STM images,

like the one shown in Fig. 11.1(f,g).

A discrepancy between simulated [Fig. 11.3(b)] and measured [Fig. 11.1(g)] profiles exists

directly at the position of the QW for positive sample voltages: Here a slight depression of

the tip height is calculated, as the number of states available for tunneling is decreased at the

GaSb due to the type-II CB offset. However, as this depression is not present in the measured

GaSb QW profile, it can be expected that quantum effects reduce or completely eliminate

this decrease of tunneling probability, which is not considered in the present semi-classical

calculation. Regarding the situation at the CB near the GaSb QW for positive voltages, the

states concentrated at the GaAs near the QW will show a considerable tailing into the GaSb

band gap, as already depicted by the yellow area in Fig. 11.2(e).

The amount by which the empty GaAs CB states penetrate into the GaSb band gap region

can roughly be estimated using the model of a one-dimensional finite potential barrier [141]:

Regarding a barrier of width ∆xand height V0, the quantum mechanical tunneling probability

T(E) for states with energy Eis given by

T(E) = 4²

4²+ (1 + ²)2sinh2³1

¯hq2meff (V0−E)∆x´,with ²=V0−E

Using the GaAs CB effective mass meff of 0.063, a CB offset V0= 0.1 eV, a barrier width of

half the WL height ∆x= 1 nm, and a room temperature energy E=kBT= 0.025 eV, the

tunneling probability for a GaAs state results to T(E) = 0.85. Therefore the GaAs CB states

extend throughout the complete GaSb QW without significant decrease of their amplitude.

Correspondingly also no measurable decrease of the tunneling probability directly at the QW

should be expected, which is exactly the case in the STM images [Fig. 11.1(f,g)].

While this consideration is valid for thin QWs, the situation may change when QDs with

a larger height and much more initial strain are imaged, the latter resulting in an increased

CB offset (see section 2.4.1). As a consequence, a decrease of the tunneling current in the

center of QDs imaged at positive sample bias can be expected. Indeed, a thin region of darker

appearance can be seen in the QD images of Figs. 11.1(a,d), acquired at VT= +2.4 V and

+2.0 V, respectively. This dark region is not present in the images of the same QD taken at

negative sample bias, shown in Figs. 11.1(b,c).

Although all these observations and simulation results support the model of a type-II

related XSTM image contrast as introduced above, one assumption of the model needs to be

further discussed: For positive sample voltages, the model implies that the GaSb QD states

within the VB are partly depleted of electrons, which induces a charging of the system.

Though the GaSb layers and the surrounding GaAs are undoped, the wafer and the cap layer

of both MOCVD-grown samples are n-doped, so that the whole sample can be regarded as

slightly n-type. In this case, an electron depletion in the GaSb corresponds to the situation of

inversion (see section 3.2.2), as the electrons being the majority charge carriers are replaced

by holes.

The question whether inversion occurs at all upon STM imaging of semiconductors is

currently discussed by several authors like R. M. Feenstra, N. D. J¨ager, and Ph. Ebert

11.2. CITS IMAGING OF GASB NANOSTRUCTURES 143

[138, 330, 435]. Based on experimental findings and theoretical considerations inversion was

excluded for bulk GaAs with a band gap of 1.4 eV [330, 436], while it was observed for

Ge samples, for which a surface band gap (considering a reduction of the bulk band gap

by surface states) of 0.5 eV was obtained [138, 435]. The reason is that for the occurence

of inversion charge carriers necessarily have to tunnel across the band gap of the sample,

which in principle is possible if the bands are sufficiently bent at the space charge region by

strong TIBB, and this tunneling current decreases exponentially with increasing band gap

energy [138, 330]. At the GaSb/GaAs nanostructures, the band gap between the GaSb VB

maximum and the GaAs CB minimum accounts approximately to about 0.8 eV – or slightly

more due to the localized nature of the GaSb states. Nevertheless, for this value an occurence

of inversion can be expected [138, 436]. Even more, the observed image contrast gives strong

experimental evidence for the existence of inversion at GaSb/GaAs QWs.

For the MBE-grown samples the situation is less critical, as the cap layers are undoped

(sample C) or even p-doped (sample D) and thus the structures are not n-type. Accordingly,

the occurence of electron depletion at the GaSb layers can more easily be realized for the

MBE-grown samples, especially for sample D.

In conclusion, a specific contrast mechanism is observed in XSTM imaging of GaSb/GaAs

nanostructures, consisting of an interplay between the type-II band alignment and tip-induced

band bending. At negative sample voltages, the effect of TIBB is nearly the same both at

the GaAs and the GaSb, and the nanostructures appear sharply defined as the filled VB

states and the additional confined states of the GaSb are imaged. For positive voltages, the

amount of TIBB is stronger at the GaAs as the GaSb is partly depleted of electrons, which

in the case of n-type doping corresponds to inversion. As a consequence weakly localized

electronic states exist in the GaAs neighboring the nanostructure. These states contribute

to the tunneling current upon empty state imaging, together with the VB states and, to a

small extent, with the depleted GaSb states, resulting in a smoothly broadened appearance

of the GaSb structures.

11.2 Probing the confined states: CITS imaging of GaSb

nanostructures

Conventional STM imaging of GaSb/GaAs nanostructures is limited regarding the analysis

of electronic properties by two restrictions: Firstly, STM in the constant current mode does

not probe electronic states at discrete energies, but a weighted average of states between the

Fermi energy EFand the energy corresponding to the tunneling bias EF+eVT. Secondly, it

is obviously not possible to acquire STM images at bias voltages corresponding to band gap

energies of the host material, therefore the imaged localized states of the nanostructures are

always superposed by resonances and bulk states.

Both restrictions can generally be overcome by use of lock-in technology to image the

differential conductance dI/dV and by performing current imaging tunneling spectroscopy

(CITS), as described in section 3.2.4. Using these techniques to study III-V semiconductor

nanostructures is challenging due to the relatively large bandgap of the materials, the required

mechanical and electronic stability of the STM system, and especially regarding the stability

and electronic uniformity of the probe tip. Only a few, though impressive studies on localized

QD states using CITS technique have been published, based on current images [108, 109] and

dI/dV data [110].

A first series of CITS images at GaSb samples is shown in Fig. 11.4(a-e), taken at the

WL of layer 1 in the MBE-grown sample C: While a regular STM image (a) was taken in

constant current mode at a stabilization voltage of VT= -2.3 V, at a grid of 64 times 64

144 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

points the image aquisition was stopped, the feedback loop was opened, and the bias voltage

was stepwise varied up to -1.0 V. After such a voltage ramp, during which the corresponding

current was measured at specific voltages, the feedback was enabled again, the tunneling

current was stabilized, and image aquisition was continued until the next point of the grid

was reached. From the currents at every grid point a current image can be computed for each

of the specific voltages (c-e), in addition to the STM image. Regarding the voltages applied

here for CITS, the images are expected to correspond to energies within the GaAs VB and

even slightly above.

The GaSb WL is clearly visible in the constant current topography image of Fig. 11.4(a)

by its inhomogeneously increased contrast, consisting of Sb-richer and Sb-poorer areas. The

oscillation of the contrast appearing in the image under an angle of about 50◦towards the

WL is due to the time delay produced by the voltage ramp which causes thermal drift at each

grid point. In the current image (b), acquired simultaneously with the filled state image (a)

at the stabilization voltage, no structures at all can be seen, just as it is expected for constant

current imaging. However, at smaller absolute values of the voltage, realized by the CITS

technique, the WL is apparent in the current images, too, as shown in (c-e). The position of

the tip was controlled by the feedback loop in such a way that constant current conditions

were fulfilled at VT= -2.3 V, meaning that the tip-sample distance was already increased at

the GaSb WL. The fact that nevertheless the WL has a brighter image contrast in the CITS

images shows that for decreasing absolute values of the voltage the current decreases faster at

the GaAs than at the GaSb. This effect gets even more pronounced when the contrast range

-2.3V

topography

z=0.25nmD

-1.9V

current

10pADI=

-1.5V

current

10pADI=

-1.0V

current

4pADI=

-1.0V

current

4pADI=

-0.7V

current

0.5pADI=

-2.3V

topography

0.25nmDz=

-2.3V

current

20pADI=

(a)

(b) (f)

10nm

Figure 11.4: CITS imaging of the WL of layer 1 in sample C: (a,f) constant current filled state

images, acquired at the stabilization voltage of VT= -2.3 V, (b) the current image corresponding to

(a), (c-e) CITS images taken upon the aquisition of image (a) at a grid of 64 ×64 points, and (g,h)

CITS images corresponding to (f). The contrast range (color) of each image is indicated.

11.2. CITS IMAGING OF GASB NANOSTRUCTURES 145

of the CITS images is considered: At -1.9 V and -1.5 V still considerable tunneling occurs

from the GaAs into the tip, while the tunneling probability is increased at the GaSb (c,d).

At a voltage of -1.0 V, corresponding to (e), hardly any tunneling probability is left at the

GaAs, while at the GaSb WL the current is decreased, too, but is still significantly larger

than at the surrounding material.

In another CITS series taken at the same position of the WL, shown in Fig. 11.4(f-h),

the CITS voltage was even further reduced to -0.7 V (h). At this condition no tunneling at

all takes place at the GaAs matrix, while a weak but still significant current is imaged at the

GaSb WL. Accordingly, at this image the tip Fermi energy lies within the GaAs bandgap, and

only the confined GaSb WL states are imaged. With decreasing absolute voltage of the CITS

images the appearance of the WL gets more and more inhomogeneous (c-e,g-h), exhibiting

regions of increased and others of decreased tunneling probability, correlating with structural

details of the layer (a,f). This behavior shows impressively that local variations of the GaSb

content within the WL strongly influence the energy of the localized states.

Also at the GaAs surrounding the GaSb some fluctuations of the current, although weaker

than within the WL, are present especially at smaller absolute values of the voltage (d,e,g).

Thereby most areas of decreased current are localized around defects of the sample surface,

which can be seen in the topography images (a,f). This is probably due to small potential

variations induced by Fermi-level pinning at the defects and shows how such defects can

inhibit the diffusion of charge carriers. It should be noted that the voltages of the CITS

images showing localized states or an absence of bulk GaAs tunneling cannot directly be

associated with absolute band energies due to the occurence of tip-induced band bending.

A more detailed CITS series, obtained for positive sample voltages at a QD within layer 2

of the MBE-grown sample C, is shown in Fig. 11.5, containing CITS current and dI/dV

images. The QD which has been studied is displayed in detail in (a), taken from a reference

image acquired without any spectroscopy modes. The weaker image quality and the contrast

oscillations of the constant current topography image of the CITS series (b) are due to the

reduced point resolution and to drift during the time delay related to the spectroscopy.

Regarding the current images, several regimes can be recognized: The image acquired

simultaneously with the topography shows only noise, as expected (c). For CITS voltages

higher than the stabilization voltage of VT= 1.8 V the GaSb structures appear darker

in the current images (e,f), while for smaller voltages they look rather bright (g-n). Both

features have the same reason already observed for the QW discussed above: With decreasing

voltage the electronic image contrast increases, as the relative difference between the tunneling

currents at the GaAs and at the GaSb increases, too. Due to the constant current mode

applied for VT= 1.8 V, the tip-sample distance is enlarged at the QD to compensate the

increased tunneling probability given by an increased integrated LDOS. At larger voltages

less additional states are added to the integrated LDOS of the GaSb QD than it is the case

for the GaAs, so that the QD appears darker. At smaller voltages, however, the integrated

LDOS decreases faster at the GaAs than at the GaSb, giving the QD a brighter appearance.

For voltages of 1.7 V and 1.6 V, besides the bright GaSb contrast considerable tunneling

also occurs from the GaAs, both near the QD and also some nm away (g,h). This changes

as the voltage decreases to 1.3 - 1.5 V (i-k): Now the current from the GaAs is significantly

lower and increases only when the tip comes closer to the GaSb nanostructures. Therefore

this situation exactly resembles the observed image contrast analyzed above, implying a

smoothly broadened appearance of the GaSb structures at positive voltages (compare also

Fig. 11.1). At this moderately low voltage regime tunneling into the empty states of the

GaAs CB locally bent near the charged GaSb nanostructures is very effective. As the voltage

is further decreased to 1.2 V (l), this tunneling channel gets closed, and finally at 1.1 V or

146 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

Figure 11.5: CITS imaging of a QD of layer 2 in sample C: (a) reference image without CITS,

(b) empty state image with simultaneously acquired (c) current and (d) dI/dV images. (e-n) CITS

current images taken upon the aquisition of (b) at a grid of 64 ×64 points, and (o-x) corresponding

CITS dI/dV images. The sample voltage and contrast range (color) of each image are indicated,

extending in the dI/dV images over several pA/V.

11.3. TYPE-II INDUCED ELECTRONIC STATES IN XSTS SPECTRA 147

1.0 V no tunneling at all occurs at the GaAs but only at the GaSb (m,n). At these conditions

all CB states are out of reach and the electrons coming from the tip can only tunnel into the

depleted GaSb states.

Thereby three local maxima of the current can be discovered within the QD, while the

complete area of increased current resembles well the shape of the QD as exhibited in the

topography images (a,b). At closer inspection of these images, some structural defects of

the WL surface directly below the QD and a little further in the lower right corner of the

images can be recognized. The very bright spot in the CITS current images and also the

inhomogeneous spots of irregular shape in the lower right corner of Figs. (j-n) probably can be

correlated to these surface defects of the WL. The remaining spots of the current observable

at low voltages are those of the QD, while the WL states at the upper left corner of the

images only appear at slightly higher voltages. This behavior is in good agreement with the

expected electronic properties of the nanostructures, where the QD states also should have

larger confinement energies than those of the WL.

While up to here only CITS current images were regarded, additional information can

be received from the CITS dI/dV images obtained using lock-in technique (o-x). In most

of these images and also in the STS image (d) acquired simultaneously with the topography

the GaSb layer appears dark, while it gets bright for the lowest voltages. Astonishingly, the

cross-over of the contrast does not occur at the stabilization voltage, as for the current images,

but at the much lower voltage of 1.3 V (u). Again one has to consider that due to constant

current imaging at the stabilization voltage the tip is closer to the sample at the GaAs than

at the GaSb. dI/dV images show the sample LDOS for the energy corresponding to the

tunneling voltage at the position of the tip. The local variation of the tip-sample distance

inhibits a direct comparison of the LDOS for GaSb and GaAs, but for voltages larger than

1.3 V the GaSb LDOS does at least not exceed the GaAs LDOS far enough to compensate

the increased distance. Especially for voltages between 2.0 V and 1.6 V [please note the

increased contrast range in (p-r)] the dI/dV signal is much weaker at the GaSb than at the

GaAs. The contrast turns around for small voltages below 1.3 V: At these energies the GaAs

LDOS falls to zero as the band gap is reached, but the confined GaSb states holding a large

LDOS can be seen with a bright contrast in the dI/dV images.

Although the noise level is too high and the spatial and energetical resolution of the CITS

images too low to map probability densities of individual GaSb QD wavefunctions, the local

observance of QD states in XSTM images is an experimental success. The nature of these

confined GaSb states and especially of the type-II induced localized GaAs states near the

nanostructures will be further analyzed in the next section by evaluating STS point spectra.

11.3 Type-II induced electronic states in XSTS spectra

While STS and CITS imaging can – with experimental challenges and limitations of the reso-

lution – probe the spatial distribution of the LDOS at some discrete energies, the continuous

variation of the LDOS over the energy at distinctive points can be investigated by STS I–V-

and dI/dV –V-spectra, as generally described in section 3.2.5.

STS spectra have been taken at both MBE-grown samples C and D. By comparing spectra

acquired at different positions directly at, near, and far away from the GaSb nanostructures,

their electronic properties can be studied. Before such spectra will be shown and discussed,

it is necessary to understand the physical meaning of the measured data, and how they have

to be processed.

148 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

11.3.1 Physical significance and normalization of point spectra

In order to increase the dynamic range of the measurements and thus being able to resolve

electronic effects near the band gap, all spectra have been acquired using the variable gap

mode: During the voltage ramp of a single spectrum the tip-sample distance was automat-

ically varied in such a way that it decreased for decreasing absolute values of the voltage.

Accordingly any spectral features occuring at small absolute voltages appear enlarged in the

measured curves. For knowing the actual dependence of the tunneling current on the voltage

the spectra have to be normalized.

The dependence of the tunneling current Ion the tip-sample distance sis approximately

exponential, given by

I∼I0exp (−2κs).(11.1)

Thereby κis the half inverse decay length of the tunneling current [278], and only weakly

dependent on the tip-sample distance sand on the tunneling voltage VTat typical STS

conditions. Thus a constant value can be approximated, amounting to κ≈q2m¯

φ/¯hwith

the electron mass mand an average barrier height ¯

φ[106]. Using the variable gap mode, the

tip-sample distance is usually varied linearly with the absolute voltage: ∆s=−cvg (|V0|−|V|),

with the stabilization voltage V0. The constant of gap variation cvg is typically within the

range of 1 ˚

A/V.

In order to exclude the influence of the distance variation from the spectra, each value of

the measured current Iex has to be normalized by

Inorm =Iex ·exp [−2κ cvg (|V0|−|V|)] .(11.2)

While the variable gap constant cvg is freely chosen at the experiment, the correct value of the

inverse decay length κis not trivial. In a first and rough approximation it can be assumed to

be κ≈1˚

A−1[106]. A more accurate way is to evaluate the best fit of κexperimentally: The

decay length of the current can directly be evaluated by measuring the tunneling current as

a function of the tip-sample distance in an I–s-spectrum. Unfortunately, such a measurement

was technically not possible in this work, so another approach is chosen here.

The measured current of an I–V-spectrum with variable gap mode is compared to a

reference spectrum taken with the same tip and comparable tunneling conditions, but without

varying the tip-sample distance. With decreasing absolute voltage, the current Iref of the

reference spectrum decreases much faster than the current Ivg of the spectrum with variable

gap mode, and the ratio Ivg/Iref increases exponentially with decreasing voltage. When this

ratio is plotted logarithmically over the voltage, a linear curve is obtained. The relevant decay

length κcan then directly be derived from the slope of this line, amounting to m= 2 κ cvg.

An example for the normalization of I–V-spectra is given in Fig. 11.6: Two spectra

acquired at different sample positions are shown (a). While the blue curve comes close to

the shape of typical bulk GaAs spectra, the green one appears strongly different. With

decreasing amount of negative voltage the absolute current first decreases, before at smaller

negative voltages it seems to be shifted in voltage with respect to the blue curve, and finally

a small additional current is found at small positive voltages. When the current is plotted at

a logarithmic scale [dashed curves in (b)], the latter feature gets even more pronounced.

However, the appearance of the green curve is strongly influenced by the use of the variable

gap mode: For both spectra, also the normalized currents are plotted in (b), with the red

curve corresponding to the blue one and the orange curve to the green one, respectively. The

increased range of the normalized current is apparent by the different axis scales. Several

aspects are noticeable after normalization of the green curve into the orange one: Firstly, the

11.3. TYPE-II INDUCED ELECTRONIC STATES IN XSTS SPECTRA 149

Figure 11.6: Normalization of I–V-spectra: (a) I–V-spectra acquired using the variable gap mode

at two different sample positions, plotted on a linear scale. (b) Logarithmic plot of the spectra shown

in (a) (dashed curves), and of the same spectra after normalizing the current (straight curves). The

red curve corresponds to the blue one and the orange curve to the green one, respectively. In the

inset, the ratio of measured current through the current of a reference sample taken at fix tip-sample

distance is plotted at a logarithmic scale. The slope of this curve gives the exponential normalization

factor for the measured current.

hump of the current at large negative voltages was only given by the variation of the tip-

sample distance and is not related to an actual physical property. Instead, both normalized

spectra exhibit a quite similar current and shape at higher negative voltages. With decreasing

negative voltage the distance between both curves slightly increases, but not to such a large

amount that could be expected from the shift of the blue and green curves. Finally, the

additional current contribution at small positive voltages is pronounced in the orange curve,

too, but the actual slope of this distribution is significantly different from the one of the green

curve.

The experimental evaluation of the correct normalization factor is shown in the inset of

Fig. 11.6(b): The ratio of measured current of the blue spectrum and the current of a ref-

erence spectrum, acquired at a fix tip-sample distance, is plotted at a logarithmic scale over

the corresponding voltage for a suited range, which is limited by the noise of the current

ratio increasing dramatically when the current of the reference sample approaches zero. For

the lowest absolute voltages shown in the plot the beginning of that noise can be seen. The

slope of the plotted data was used to normalize both spectra of Fig. 11.6, resulting in an

experimental value of the decay length of κ= 0.5 ˚

A−1.

In analogy to the I–V-spectra, also the dI/dV –V-spectra obtained by simultaneously

using the lock-in technique are influenced by the variable gap mode. A very elegant way to

normalize the differential conductance dI/dV is to divide it by the absolute conductance I/V ,

which eliminates the dependence on the varied distance. Even more, the value (dI/dV )/(I/V )

represents a normalized sample LDOS, independent of the distance of the tip [105, 305, 306].

However, because GaAs and also GaSb have a large band gap with zero conductivity due

to the absence of surface states, (dI/dV )/(I/V ) diverges with decreasing voltage when the

150 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

band gap is reached, as the current Iapproaches zero faster than the voltage Vor the

differential conductance dI/dV . This is demonstrated in Fig. 11.7(a) for the I–V-spectrum

shown above (blue curve), the corresponding dI/dV –V-spectrum (green curve), and their

calculated quotient (dI/dV )/(I/V ) (grey curve).

Several solutions to overcome this problem are suggested in literature [278, 302, 303,

307, 308], having in common that the diverging signal is broadened in different ways. Three

approaches have been tried to normalize the conductance spectra of this work, which will be

introduced and compared in the following.

A first and rather straightforward method to overcome the zero conductivity for small

voltages is to add a constant offset, as suggested by Prietsch et al. [307]. Thereby the

conductivity I/V is replaced by the term

I/V =q(I/V )2+c2,(11.3)

with cbeing a suitable constant, which should be chosen very small in order not do dominate

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

8c=1x10A/V

-12

c=1x10 A/V

-11

c=5x10A/V

-11

c=5x10A/V

-10

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-2

8DV=0.5V

DV=1.0V

DV=2.0V

voltage[V]

(dI/dV/(I/V)[a.u.](dI/dV/(I/V)[a.u.]

(dI/dV/(I/V)[a.u.]

dI/dV[a.u.]

measuredcurrent[pA]

(a) (b)

(d)(c) -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

8DV=0.5V

DV=1.0V

DV=1.5V

Figure 11.7: Normalization of dI/dV –V-spectra: (a) dI/dV –V- (green curve) and I–V-spectrum

(blue curve), together with the calculated value (dI/dV )/(I/V ) (grey curve), which strongly diverges.

(b-d) (dI/dV )/(I/V )–V-spectra, obtained by normalizing the spectra shown in (a) by (b) broadening

with different offsets cor by convolution with (c) an exponential function or (d) a Gaussian function

of different voltage widths ∆V. The values of the used constants and voltage widths are indicated.

11.3. TYPE-II INDUCED ELECTRONIC STATES IN XSTS SPECTRA 151

the conductivity, but large enough to inhibit the divergence and reduce the noise in the band

gap region. The best choice of cdepends on the local electronic properties of the sample and

the quality of the spectra, so for each set of spectra the offset has to be adapted empirically.

Several tries of certain offsets and their influence on the normalized spectra can be seen in

Fig. 11.7(b): Using an offset of only c= 1 ×10−12 A/V already stops the divergence, but

leads to strong noise and to deficiently large values at the CB onset (small positive voltages).

With c= 1 ×10−11 A/V the shape of the curve is better reproduced, but still relatively

high noise is left. The value c= 5 ×10−11 A/V seems to be the best choice here, resulting

in a smooth curve, while at larger values like c= 5 ×10−10 A/V the complete spectrum

gets unnecessarily flattened. Although this method using an unweighted, constant offset is

insensitive especially to weak features and small differences within the spectrum, it though

produces an effective normalization of the differential conductance. Additionally, it is by far

the fastest and easiest one of the used methods.

Instead of adding an offset and thereby artificially shifting the conductance, a more so-

phisticated way to broaden the conductance for avoiding zero values is to convolute it with a

suitable function. Feenstra and Stroscio have suggested the convolution with an exponential

function [278, 302, 303], according to:

I/V =1

2∆VZ∞

−∞

I(V0)

V0exp µ−|V0−V|

∆V¶dV 0.(11.4)

Thus for any certain voltage, the broadened conductance is convoluted by an infinite voltage

integral, weighted around the respective voltage by an exponential function of given width

∆V. To evaluate real spectra, the integral can be transferred into the sum over all voltage

points of the spectrum. As the integral is infinite, the sum over measured voltages has to

be artificially continued beyond the largest values of positive and negative applied voltage.

Therefore the current corresponding to these lowest and highest voltage can be estimated to

occur for all other voltages below and above, respectively. Due to the exponential weighting

these artificially extended values can maximally contribute over about an energy width ∆V

outside the experimentally obtained values.

Similarly to the first method, also here a parameter has to be chosen by hand, which is

the voltage width ∆V. This parameter again should be kept as small as possible, but on the

other hand it should at least cover the half width of the semiconductor energy gap to prevent

divergence of the normalized conductance. For spectra on doped GaAs, typically widths of

∆V= 0.5 V can be used [302]. However, as no dopant-induced components reduce the GaAs

band gap at the samples investigated here, this value is too small to avoid significant noise,

as Fig. 11.7(c) shows. At a larger value of ∆V= 1.5 V the resulting curve is very smooth,

but for both polarities the curves of the normalized conductance are slightly shifted towards

higher absolute voltages. The parameter ∆V= 1.0 V has been proven to be the best choice

for the spectra studied here.

Although the latter method of normalization has become widely known and accepted, the

question remains why the measured conductance at a specific voltage should be convoluted

by an exponential function containing the absolute value of this voltage. Instead, the use of a

Gaussian distribution containing the square of the voltage seems to be at least more intuitive

for weighting a specific value. In this case, the broadened conductance would amount to:

I/V =1

2∆VZ∞

−∞

I(V0)

V0exp Ã−(V0−V)2

∆V2!dV 0.(11.5)

Curves obtained by normalizing the dI/dV –V-spectrum with this method are shown in

Fig. 11.7(d). As the weighting of the Gaussian function is more narrow than that of the

152 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

exponential function used above, the voltage width ∆Vhas to be chosen slightly larger here:

While at a value of ∆V= 0.5 V dramatic noise of the normalized conductance results, best

results were obtained for values ∆Vbetween 1 and 2 V. Due to this narrower weighting of

the Gaussian function, this method of normalization should be best suited to resolve small

features within the dI/dV –V-spectra. Accordingly, the dI/dV –V-spectra shown below have

been normalized by this method, being convoluted with a Gaussian function of the width

∆V= 1.4 V or 1.5 V.

11.3.2 STS point spectra of GaSb nanostructures

Several GaSb nanostructures of both MBE-grown samples could be investigated by means of

STS point spectra. While for sample C only I–V-spectra were obtained, for sample D also

dI/dV –V-spectra could successfully be acquired.

A typical set of I–V-spectra acquired at and around a QD of the third GaSb layer in sam-

ple C is presented in Fig. 11.8, with individual spectra being colored according to their local

position. The area at which the spectra, presented in (a), were taken is shown in (b): During

aquisition of a constant current STM image taken at a stabilization voltage of VT= -2.3 V

(not shown here), the scanning process was interrupted at ten distinct points. At each of these

points, the feedback loop was disabled and the voltage was varied from -2.0 V to +2.0 V in

small steps of 30 mV. For each voltage point the corresponding current was measured during

a time of 40 ms after an initial delay time of 20 ms, which is necessary to avoid capacitance

effects. As the absolute voltage was decreased, the tip-sample distance was simultaneously

reduced by 1.2 ˚

A/V.

At every position, ten spectra were taken with alternating direction of the voltage ramp,

with the feedback being shortly enabled after every second spectrum to stabilize the tip-

sample distance. As the current signal of a single spectrum is strongly affected by electronic

noise, these ten spectra are averaged for each position. After yielding the experimental

data, the measured currents were normalized with regard to the used variable gap mode as

described above. No reference spectrum with fixed tip-sample distance was available here,

so the spectra could only be normalized assuming a common value of the decay constant of

κ= 1 ˚

A−1.

Comparing the ten spectra corresponding to the positions indicated in (b), a clear corre-

lation between the spatial position and the shape of the spectrum gets apparent: Five spectra

have been taken directly at the QD, showing a very similar shape (red curves). Significantly

different from these, but similar to each other, are the three blue curves corresponding to po-

sitions at the GaAs several nm away from the GaSb layer. The remaining two curves belong

to the positions indicated in green in (b), being located at a diluted region of the WL and

at the GaAs near the WL, respectively. For positive voltages, both corresponding spectra

look similar and lie between the blue curves (GaAs matrix) and the red ones (GaSb QD). For

negative voltages, however, the green curve corresponding to the diluted WL behaves like the

GaSb QD curves, while the spectrum taken underneath the WL comes closer to the GaAs

spectra, although slightly shifted for small negative bias.

As the spectra corresponding to comparable spatial positions exhibit a nearly identical

shape, they were averaged for further noise reduction and for clearer illustration, the resulting

curves being shown in (c). From a comparison of the three curves several conclusions can

be drawn: Firstly, the voltage interval of zero current, displaying the semiconductor band

gap, is much larger for the GaAs matrix than for the GaSb QD. At negative sample voltages,

corresponding to filled state tunneling from the VB, the blue and red curves of GaAs and

GaSb have a similar and homogeneous shape, but are shifted to each other by ∼0.4 V.

Such a behavior is expected due to the large VB offset between GaAs and GaSb, slightly

11.3. TYPE-II INDUCED ELECTRONIC STATES IN XSTS SPECTRA 153

[001]

5nm (c)

(a)

(b)

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

100

voltage[V]

GaAsmatrix

GaSbQD

GaAsnearGaSb

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

100

voltage[V]

Figure 11.8: I–V-spectra taken at layer 3 of sample C: (a) Ten spectra of normalized current over

voltage are plotted, taken at the positions indicated in the STM filled state image (b), acquired at

VT= -2.3 V. A few nm beside the GaSb layer a large surface step dominates the image contrast.

several nm away (blue curve) and at the GaAs near the GaSb layer (green curve) are averaged.

reduced by quantum effects. For positive bias, imaging the empty states of the CB, all three

curves lie closely together at larger voltages. With decreasing voltage, however, the blue

curve of the GaAs spectra continues homogeneously, while the GaSb-related spectra exhibit

an increased current at voltages below about +1.4 V as compared to GaAs, which on a

first hand is unexpected regarding the type-II CB offset. On the other hand, the observed

feature looks very similar to spectra containing a dopant-induced component of the current

[107, 301]. However, as all epitaxially grown layers are undoped, another mechanism has to

be responsible for this contribution of additional small currents at small positive voltages.

Obviously, this mechanism should be due to the type-II band alignment, and to the specific

tunneling conditions resulting from this band structure in combination with tip-induced band

bending, described in section 11.1.

Before such effects are discussed and the spectra are analyzed in more detail, additional

data derived by dI/dV –Vspectroscopy should be taken into account. Such spectra, prevent-

ing the energy integration of the tunneling current, have the advantage of directly representing

the sample LDOS at the corresponding energy.

154 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

5nm

(a) (b)

(c)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

0.1

GaSbQR

GaAsnearGaSb

GaAsmatrix

voltage[V]

normalizedcurrent[pA]

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

GaSbQR

GaAsnearGaSb

GaAsmatrix

voltage[V]

(dI/dV)/(I/V)[a.u.]

Figure 11.9: STS point spectra taken at layer 3 of sample D: (a) Filled state STM image, acquired

at VT= -2.1 V, showing a ring-shaped GaSb QD and the positions of nine spectra. The corresponding

(b) I–V-spectra and (c) dI/dV –V-spectra are averaged for the different positions as shown in (a).

In (c), the voltage values of the GaAs and GaSb VB maxima and CB minima, respectively, are ex-

trapolated from the spectra and indicated. The red arrows depict the region of GaSb hole occupation.

Figure 11.9 shows a QR in layer 3 of sample D together with I–V- and dI/dV –V-spectra

taken at different positions at and around this GaSb nanostructure. At each position indicated

in the STM image (a), ten spectra were acquired and averaged, similarly as described above,

applying a variation of the tip-sample distance of cvg = 3.5 ˚

A/V. By comparing the I–V-

spectra with reference spectra taken at a fixed distance, the inverse decay length could be

evaluated to κ= 0.50 ˚

A−1, which was then used to normalize the spectra. The measured

differential conductivity dI/dV was normalized by the absolute conductivity I/V , broadened

by a convolution with a Gaussian function of width ∆V = 1.5 V. Simultaneously to the

data of Fig. 11.8, the spectra shown in Fig. 11.9 were averaged according to their position:

The spectra taken at the positions marked in blue in (a) are combined in the blue curves

of (b) and (c), representing GaAs several nm away from the nanostructures, green curves

correspond to positions at the GaAs, but only 1 to 2 nm away from the GaSb QR, and the

red curves show the spectra taken directly at the QR.

11.3. TYPE-II INDUCED ELECTRONIC STATES IN XSTS SPECTRA 155

The I–V-spectra are qualitatively very similar to those taken at the QD of sample C,

shown in Fig. 11.8(c): At the VB side, the GaSb curve is shifted by ∼0.3 eV to smaller

negative voltages with respect to the GaAs curve, with the green curve (GaAs near the GaSb)

in between. For larger positive voltages all three curves are close together, while for small

positive values an additional current contribution can be seen in the red curve corresponding

to the GaSb QD. By comparing these spectra with those taken at sample C, qualitatively the

same behavior can be found for both ring-shaped GaSb QDs, while the smaller height of the

very flat QD structures in sample D results in slightly smaller confinement energies.

More information on the properties of GaSb nanostructures can be derived from the

dI/dV –V-spectra [Fig. 11.9(c)]. From the slope of the curves corresponding to the GaSb QD

(red), the GaAs matrix (blue), and the GaAs near the GaSb layer (green), three different

regimes can be distinguished: For sufficiently large absolute voltages of both polarities, the

conductivity increases monotonously with increasing absolute voltage at all positions, as

expected for the increasing LDOS of the VB and CB, respectively. Between these VB and

CB states the conductivity is zero, clearly indicating the bandgap. Only in the GaSb spectra,

however, a small but definite additional contribution is observed between +0.5 and +1.0 V

(marked by a red arrow).

The VB maxima and CB minima should easily be determinable from the curves by the

values at which the LDOS falls to zero. In the actual spectra, however, these expected distinct

onsets of the dI/dV -values are smeared out over about 0.2 V, due to the necessary averaging

of individual spectra and to a broadening given by the oscillator amplitude of the lock-

in technique and the thermal broadening. In order to nevertheless evaluate the respective

values from the spectra, the fast decay of the GaAs and GaSb spectra was extrapolated

linearly until zero, as shown in Fig. 11.9(c). For GaAs a VB maximum of -0.6 eV and a

CB minimum of +1.1 eV were obtained, corresponding to the Fermi energy being slightly

above midgap. The fact that the apparent band gap of 1.7 eV is about 0.3 eV above the

literature value was already expected, as tip-induced band bending would enlarge this value.

For the GaSb QD, a CB minimum of +1.2 eV could be evaluated, while the energy of -0.3 eV

corresponds to the confined hole ground state. Although the absolute values of these energies

and the obtained band gap underlie the effect of TIBB, the relative values are much more

significant: Accordingly, a hole localization energy of 0.2 to 0.3 eV was found, in agreement

with the value derived from the I–V-spectra. Even more, a type-II alignment with a CB

offset of 0.1 eV could directly be obtained for the investigated GaSb QD.

While the blue GaAs spectra and most parts of the GaSb spectra of Fig. 11.9 could be

understood, the additional GaSb LDOS at small positive voltages and the green curve of the

spectra acquired at GaAs near the nanostructures still need to be explained. Therefore the

exact tunneling conditions for the positions at the QD, just beside the QD and far away at

the GaAs matrix have to be taken into account. These conditions are sketched schematically

in Fig. 11.10, both for negative (a-c) and for small positive sample voltages (d-f).

At negative bias, the TIBB causes the Fermi energy to be close to the CB, so that all VB

states and also the confined GaSb hole states are filled [for additional visualization see also

Fig. 11.2(f)]. At the GaAs tunneling can occur from the VB states into the tip, as depicted

in Fig. 11.10(a). At the GaSb QD, confined states contribute to the LDOS, together with

a continuous spectrum from GaSb resonances (c). Consequently, the GaSb LDOS is larger

than the GaAs one at lower voltages, as seen in the spectra.

Although the confined GaSb states are strongly localized, they penetrate into the GaAs

band gap, characterized by an exponential decay over a few nm. A similar behavior is valid

for the GaSb resonances, too. So when the STM tip is at GaAs regions directly neighboring

a GaSb nanostructure, additional to the GaAs states also tunneling from the decaying GaSb

156 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

tip

GaAs

GaSbQD

GaAs

nearGaSb

ECB

EVB

E +eV

F T

E +eV

F T

E +eV

F T

(a)

(c)

(b)

tip

GaAs

GaSbQD

GaAs

nearGaSb

ECB

EVB

E +eV

F T

E +eV

F T

E +eV

F T

(d)

(f)

(e)

filledstateimaging:

negativesamplevoltage

emptystateimaging:

smallpositivesamplevoltage

Figure 11.10: Different tun-

neling conditions at GaSb/GaAs

nanostructures due to TIBB,

sketched for (a-c) negative and

(d-f) small positive sample volt-

ages. The displayed configura-

tions correspond to GaAs sev-

eral nm away from GaSb (blue

curves in Figs. 11.8, 11.9, and

11.11), to GaAs near the GaSb

structures (green curves), and

to a GaSb nanostructure (red

curves). TIBB and confinement

energies are not drawn to scale.

states can occur to a small amount, as depicted in (b). This effect causes the slightly increased

LDOS at GaAs positions directly below or above the GaSb layer as compared to the GaAs

matrix, observed in the spectra for negative voltages (green curves). The amount of this

additional contribution depends strongly on the distance to the GaSb structures and on the

decay length of the confined states.

Different mechanisms occur for positive sample voltages, leading to an upward band

bending. This band bending shifts the onset of tunneling into empty GaAs CB states to

higher voltages, as shown in (d). Accordingly, at small positive voltages no tunneling occurs

at GaAs positions, and the apparent GaAs band gap is larger than the literature value.

At the GaSb, the TIBB causes a partial electron depletion or hole occupation, as explained

above (see section 11.1), due to the large offset between GaAs VB and hole quantum-state

energy. These depleted GaSb states are the reason for the additional contribution in GaSb

I–V- and dI/dV –V-spectra at small positive voltages, as electrons can easily tunnel from the

tip into such depleted states, as shown in (f). The requirement is a sufficient TIBB, which

obviously is given already at +0.5 V. With increasing bias voltage, also tunneling from the

tip into GaSb CB states occurs and dominates over the small contributions from the localized

states. However, due to the type-II GaSb/GaAs CB offset, larger voltages are necessary for

GaSb CB tunneling as for GaAs, leading to the small shift of the GaSb spectra in relation to

GaAs at larger positive voltages.

11.3. TYPE-II INDUCED ELECTRONIC STATES IN XSTS SPECTRA 157

Because of the hole occupation of the GaSb and the resulting charge, the TIBB is weaker

at the GaSb than at the GaAs matrix. At the GaAs close to the nanostructures it increases

with increasing distance over a range of several nm, as shown in section 11.1. As a result,

weakly confined electron states arise at the GaAs neighboring the GaSb at energies below the

GaAs CB, contibuting to the LDOS, as depicted in (e). Electrons can thus tunnel from the

tip into these additional empty GaAs states (shown in yellow) at tunneling voltages which

are not sufficient to enable tunneling at the GaAs matrix (black).

These weakly confined electron states can also slightly penetrate into the GaSb, as in-

dicated by the dashed yellow line in (f) and already discussed in section 11.1, additionally

contributing to the small conductivity at GaSb for energies slightly below the CB.

The influence of the different effects contributing to these complex tunneling conditions

depends on the properties of the investigated GaSb nanostructures and on the specific tip

conditions. As a consequence, some effects may occur stronger in one set of spectra and

other effects in a second set, although the tunneling mechanism as such is always the same.

This gets underlined by a comparison of the spectra of Fig. 11.9 discussed above and those

of Fig. 11.11, also taken at a GaSb QD in layer 3 of sample D.

(a) (b)

(c)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

GaSbQR

GaAsinsideQR

GaAsnearGaSb

GaAsmatrix

voltage[V]

(dI/dV)/(I/V)[a.u.]

voltage[V]

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

100

GaSbQR

GaAsinsideQR

GaAsnearGaSb

GaAsmatrix

normalizedcurrent[pA]

Figure 11.11: STS point spectra taken at a different QD in layer 3 of sample D: During the aquisition

of the filled state STM image shown in (a), taken at VT= -2.1 V, twelve I–V- (b) and dI/dV –V-

spectra (c) were taken at the positions indicated in (a) and averaged accordingly. The arrow in (c)

depicts the region of weakly localized empty states.

158 CHAPTER 11. ELECTRONIC PROPERTIES AND TYPE-II BAND ALIGNMENT

Both I–V- and dI/dV –V-spectra of Fig. 11.11 were acquired similarly as described above,

using the variable gap mode with a distance variation of cvg = 2 ˚

A/V. I–V-spectra were

normalized using a reference spectrum, yielding an inverse decay length of κ= 0.5 ˚

A−1.

The general appearance of the spectra is very close to that of the spectra shown above,

nevertheless some differences can be obtained. Firstly, the voltage shift between the GaSb and

GaAs dI/dV –V-spectra is slightly larger here for negative voltages, corresponding to a hole

localization energy of about 0.35 eV. Secondly, at the GaSb spectrum for positive voltages

the contribution due to hole occupation smoothly passes over into the LDOS increase at the

GaSb CB, making it impossible to distinguish between both effects. On the other hand, the

effect of additional tunneling into localized GaAs electronic states near the GaSb structures

is very pronounced in this set of spectra, shown by the green curve and indicated by the

arrow. Thus by comparing different sets of spectra, the contributions of both kinds of charge

carriers in GaSb/GaAs quantum structures to the LDOS could well be observed.

Finally, an important conclusion about the electronic nature of the ring-shaped GaSb

QDs can be drawn from the data: In Fig. 11.11 it is distinguished between spectra acquired

at GaAs positions slightly above or below the GaSb layer, displayed by green curves, and

spectra taken at the GaSb-free interior of the ring, shown in orange. No substantial difference

between both positions can be derived, neither from the I–V- nor from the dI/dV –V-spectra.

Correspondingly, the observed QDs also electronically behave as an actual ring, with the GaAs

interior of the ring behaving just the same as the GaAs around the ring.

In conclusion, different sets of point spectra taken at QDs and QRs of both MBE-grown

samples confirm the GaSb/GaAs specific tunneling mechansim derived earlier from observed

STM image contrasts. Thereby the type-II character of the nanostructures could quantita-

tively be studied, giving clear evidence on GaSb hole occupation and a resulting weak electron

confinement in the surrounding GaAs. Additionally, the hole localization energy could be

obtained to about 0.3 eV for the flat QDs in sample D and to about 0.4 eV for the slightly

higher QD structures in sample C.

Chapter 12

Conclusion

After presenting a rich variety of GaSb nanostructures in GaAs within the main part of this

work, and having discussed many details on the formation and evolution of GaSb quantum

dots (QDs) as well as their electronic properties, this chapter has the task to summarize

these results and draw conclusions for future growth, characterization, and application of

GaSb/GaAs QDs. For this purpose, both the MOCVD- and MBE-grown structures will

be highlighted and compared to distinguish between general aspects of GaSb/GaAs QD

formation and the complex interplay of specific growth conditions, thereby evaluating the

different physical effects determining the resulting atomic structure of the QDs.

Within the MOCVD-grown samples studied here only small QDs of up to 8 nm base

length and 2 nm height could be observed, revealing a rather broad size distribution with a

QD density of ∼3×1010 cm−2. The local stoichiometry of the QDs varies, too, from about

60% maximum GaSb content up to nearly pure material. Due to the small size and the

varying chemical composition the QD shape is not well pronounced, but comes close to that

of a truncated pyramid. The small size together with the obtained size and stoichiometry

distribution coincide with a rather broad QD photoluminescence (PL) signal, showing a

maximum at 1.2 eV, measured at low temperature.

The QDs are surrounded by an intermixed wetting layer (WL) with a GaSb content

of up to 40% and a vertical extension of about 3 monolayers (ML) or 1 nm. In spite of

the significant intermixing of GaSb and GaAs material in the QDs and the diluted WL,

hardly any Sb atoms were observed within the GaAs matrix underneath and above the

nanostructures, demonstrating the absence of long-range segregation or diffusion processes

in growth direction.

By comparing this QD layer with two QWs grown under similar conditions, several steps

during the initial formation and further ripening of QDs could be revealed. As the exact

amounts of deposited GaSb material remained unknown due to strong uncertainties in the

MOCVD growth rate of monolayer thin GaSb films on GaAs, the different layers can only

be characterized by the GaSb deposition time. After 21 s GaSb deposition, directly followed

by GaAs overgrowth, a QW of about 2 ML vertical extension and a composition of about

50% GaSb was observed, resulting in a total GaSb content of 1 ML. The average chemical

composition varies significantly on a scale of a few nm, and even gaps consisting of pure GaAs

were found, distributed inhomogeneously over the QW, with lateral extensions of typically

1 to 3 nm, in some cases up to 7 nm. These gaps remain also under further GaSb deposition,

though slightly decreasing in size, as similar structures were observed in all GaSb QWs and

WLs. They stand for a kind of 2D island growth of the GaSb layer, consisting of broad GaSb

islands interrupted by thin trenches, which get filled with GaAs upon overgrowth [46]. Strictly

speaking, this corresponds to a slight deviation from classical Stranski-Krastanow growth. A

159

160 CHAPTER 12. CONCLUSION

significant inhomogeneity of all GaSb layers is further confirmed by the fact that the GaAs

material directly below the Sb-rich parts of the GaSb layer is compressively strained, which

is not the case for a homogeneous QW.

When the GaSb deposition time is increased, the critical thickness of QD formation

is reached: A GaSb layer formed upon 22 s GaSb deposition, followed by a 2 s growth

interruption (GI) and GaAs overgrowth, was observed to contain the same total GaSb amount

of 1 ML, again distributed in an inhomogeneously intermixed layer containing small gaps.

Within this generally intermixed QW, flat Sb-rich islands were found at a high density of

∼6×1011 cm−2, showing lateral extensions of typically about 4 nm, which can reach up to

20 nm. These 2D islands do not exceed the vertical extension of the QW, but are characterized

by a significantly increased GaSb composition, representing first self-assembled local GaSb

accumulations. The necessary GaSb material has been provided by the 1 s longer GaSb

deposition, while the following 2 s long GI enabled the GaSb accumulation in the 2D islands by

lateral Sb segregation prior to overgrowth. Accordingly, the GaSb layer is intermixed already

in this growth stage, meaning that the intermixing cannot just occur upon the overgrowth

of a formerly pure GaSb layer, but that already the initial layer has to consist of GaAsSb

material. This can be due either to a direct intermixing of the deposited GaSb with the

underlying GaAs growth surface, or possibly to an unintended, but hardly preventable As

background in the MOCVD reactor during GaSb growth. In any case, the amount of GaSb

material and the corresponding strain energy of this layer is still not sufficient to allow the

formation of 3D structures.

This changes when the GaSb deposition time is further increased to 25 s, as in this case

a WL with again 1 ML total GaSb content and small, but optically active QDs were formed.

Besides those QDs, which have already been described above, also tiny 3D GaSb islands were

observed in the same layer, exhibiting no electronic confinement and only little strain. These

smallest self-assembled 3D GaSb structures ever observed, with lateral extensions of about

2.5 nm and heights of 1.5 nm at a density of ∼5×1010 cm−2, are assumed to act as QD

precursors. While these precursor structures appear as small protrusions within a locally

continuous WL, the direct neighborhood of the somewhat larger QDs is partly depleted of

GaSb, indicating a ripening of the QDs on cost of the surrounding WL by lateral mass

transfer. The co-existence of tiny 3D islands and optically active QDs in the same layer is in

good agreement with the broad QD peak and the rather smooth transition from the QD to

the WL signal in the PL spectra.

Comparing these results with literature PL data on MOCVD-grown QDs [51, 71, 74], an

about 0.1 eV larger QD energy and also about 0.1 eV smaller energy separation between

QD and WL peak, corresponding to a smaller hole localization, are apparent for the QDs of

this work, which can be explained by the small QD size leading to rather small localization

energies. Indeed, for all published results on (optically active) QDs grown by MOCVD [51,

52, 61, 71, 263, 264] sizes between 10 nm and 44 nm are reported, by far exceeding the QD

sizes obtained here. It should be noted that the applied characterization methods would even

not have been able to detect 3D GaSb structures as small as the tiny 3D islands. Anyway,

also the coexistence of precursor structures and small QDs in the same layer observed here

indicates that these QDs represent a very early stage of GaSb QD growth.

As it was not possible to obtain MOCVD-grown GaSb samples containing larger QDs for

structural characterization within this work, which was mainly due to the generally consid-

erable challenges connected with MOCVD growth of GaSb nanostructures, this task has to

remain for future studies. The step by step pathway up to the formation of GaSb QDs using

MOCVD, however, could be revealed here in detail.

This pathway is considerably different when MBE is used as growth method. Again,

161

the occurence of more or less pronounced gaps is common for all MBE-grown GaSb layers

studied here, indicating a similar 2D island growth mode of thin GaSb films on GaAs. The

general appearance of the QWs and WLs, on the other hand, differs significantly from the

MOCVD-grown structures, and neither 2D Sb-rich islands nor tiny, compact 3D GaSb islands

could be observed. Instead, flat and significantly intermixed QDs of already more than 10 nm

baselength are observed even for small amounts of deposited material, which increase in size

and GaSb composition with increasing GaSb supply. Additionally and most astonishingly,

all GaSb QDs observed in MBE-grown samples exhibit a ring shape, in contrast to the small,

compact MOCVD-grown QDs described above.

The outer contour of these ring-shaped QDs depends on the exact growth conditions,

ranging from very flat structures to truncated pyramidal shapes with rather steep {111}side

facets. However, all these QD structures are not massive, but exhibit a central gap, with

an average diameter of about 40% of the outer baselength. The inner contour of the rings

is not regularly defined, and in several cases a rather smooth transition from the GaSb ring

body over strongly diluted material to the ring center consisting of pure GaAs was observed.

In contrast to reported ring-like structures in the InAs/GaAs [224, 226, 230, 231] or other

material systems [213, 232, 235, 236], these ring-shaped GaSb QDs have been formed upon

considerably fast, nonstop overgrowth, without any partial capping or annealing step. Even

more, these GaSb QDs are actual rings, whereas the reported In(Ga)As structures were shown

to have a central depression, filled with GaAs and surrounded by an InAs rim only at the

top, while the bottom part is still continuous In(Ga)As [227].

Ring-shaped GaSb QDs are obtained already when 1 ML GaSb is deposited, subsequent to

Sb soaking and followed by GaAs overgrowth. With increasing GaSb supply, first the observed

outer extensions of the QDs increase, too, until a final size is reached with baselengths of

about 15 nm to 20 nm and heights varying between 1.3 nm and 2.1 nm for different growth

conditions. Further GaSb deposition then only leads to a slight increase of the QD density

up to ∼9×1010 cm−2. Parallel to the QD size, also the height of the intermixed WL is

found to increase until a final GaSb content is reached, indicating a significant deviation from

classical SK growth.

All MBE-grown GaSb layers are characterized by significant intermixing, reaching a max-

imum GaSb content of the WLs of less than 30%, and strong Sb segregation in growth

direction, as many individual Sb atoms can be seen above the QDs and WLs, being incorpo-

rated in the GaAs overlayer. Both effects are correlated, as a lower GaSb content of the WL

comes along with even stronger Sb segregation. Correspondingly, the total amount of GaSb,

consisting of the material within the QDs and the WL as well as the Sb atoms incorporated

in the overlayer, was found to have an upper limit of 2 ML. The material distribution between

QDs, WL, and antimony within the overlayer has to fulfill this condition, which is given by

the maximum strain that can be included in the GaSb layer.

This large strain inherent to GaSb/GaAs QDs in combination with the strong segrega-

tion upon overgrowth is assumed to be the driving force for ring formation. Thus, initially

compact, free-standing GaSb QDs are supposed to be transformed into rings upon GaAs

overgrowth by strain-driven material redistribution, occuring predominantly at the highly

strained center of the QD. Correspondingly, the shape of free-standing GaSb QDs is still

characterized by a more or less sharp summit, which agrees well with literature data ob-

tained on such structures [44, 55, 69, 256, 267], while the ring shape is observed here for all

capped QDs. Also the PL peak energy of about 1.1 eV obtained here for the flat, ring-shaped

QDs agrees perfectly well with published PL data on capped GaSb QDs [47, 58, 59, 65, 69].

Since the electronic properties of ring-shaped QDs should be expected to differ strongly from

compact ones, it can be assumed that capped GaSb QDs grown under typical MBE growth

162 CHAPTER 12. CONCLUSION

conditions generally exhibit a ring structure.

The reason for the strong Sb segregation as well as for the significant intermixing is given

by extraordinary strong group-V atomic exchange processes at the GaSb-GaAs interfaces.

The process of Sb-for-As exchange at a GaAs growth surface exposed to an Sb4flux is well-

known and intentionally used as Sb soaking. Indeed, more than 1 ML GaSb is evaluated here

to have been incorporated only by such an Sb soaking step. The contrary case of As-for-Sb

exchange at a GaSb growth surface under As2or As4flux, however, is usually unwanted as

it causes the Sb segregation observed here: When Sb soaking is succeeded by direct GaSb

deposition and subsequent GaAs overgrowth, a strongly inhomogeneous and intermixed, but

distinguishable GaSb layer of typically about 2 to 5 ML thickness is obtained in addition to

individual, broadly distributed Sb atoms. From the fact that these individual Sb atoms are

only found above the GaSb QW, it can be confirmed that the exchange processes related

to Sb soaking occur over a very short range of only a few ML, while the extended range of

distributed Sb atoms is due to exchange and segregation effects during GaAs overgrowth. This

different growth behavior at GaSb-on-GaAs and GaAs-on-GaSb interfaces can be explained

by differences of the respective growth surfaces: Especially Sb-rich surface reconstructions

of GaSb thin films on GaAs(001) [414–416] were analyzed to be a prerequisite for strong Sb

segregation, as the resulting excess Sb in combination with a rather weak Ga-Sb bond enables

massive As-for-Sb exchange.

Considering the material supplied by Sb soaking and GaSb deposition as well as the

amount of GaSb observed in the capped QDs, WLs, and GaAs overlayers, three different

destinations of the deposited antimony that got initially incorporated into free-standing QDs

and WLs can be distinguished: A first fraction just remains where it is deposited or moves

only over a short distance contributing to intermixing of the WL or shape transitions of the

QDs. A second fraction of the Sb atoms is removed from the GaSb layer upon As exposure

by As-for-Sb exchange and forms a floating layer at the growth surface, from which it gets

re-incorporated during GaAs overgrowth, resulting in individual Sb atoms being distributed

within the GaAs overlayer. As-for-Sb exchange additionally results in a third fraction of the

Sb atoms, being removed from the GaSb surface but not re-incorporated again, remaining

at the growth front as surfactant or being re-evaporated. The ratios between these three

fractions depend on the amount of initially supplied GaSb, corresponding to the total amount

of strain, on the growth sequence including GIs and fluxes, and on thermodynamic conditions

as growth rate and temperature.

This model is confirmed by the analysis of exponential segregation profiles obtained from

the XSTM data, corresponding to the re-incorporation of Sb atoms from the Sb floating layer

during GaAs overgrowth. Indeed, the amount of material being available for re-incorporation

was found to increase with increasing growth temperature, while the evaluated segregation

coefficient, meaning the ratio of Sb atoms in the floating layer that are re-incorporated per

ML upon GaAs overgrowth, changes simultaneously from 16% to only 9%.

In addition to the growth temperature, the growth sequence itself even more determines

the extent of group-V exchange processes and thus the atomic structure of the QDs and WLs.

The strongest Sb segregation is observed in samples which are grown including a 15 s long GI

under As4flux, resulting in very flat QDs and rather low GaSb compositions of both the QDs

and the WLs. For example, GaSb islands formed upon deposition of 1 ML GaSb prior to such

a GI and subsequent capping exhibit lateral extensions of about 15 nm, which is twice as large

as the baselength of the MOCVD-grown QDs, but are found still not to be optically active

due to the low GaSb content. However, when the GaSb layers are immediately overgrown

with GaAs (although always some time is needed for switching the fluxes), still significant Sb

segregation occurs, but the resulting QDs have a larger height and especially a higher GaSb

163

content of the ring body, with chemical compositions ranging from 40% up to pure GaSb.

Comparing the MBE- and MOCVD-grown QDs of this work, apart from the small size of

those formed using MOCVD, the ring shape only occuring in MBE-grown structures is the

most striking difference. It cannot completely be excluded that some kind of ring structure

might also occur upon further GaSb deposition in MOCVD growth. However, the fact that

the GaSb ring structures observed yet have all been grown by MBE can well be explained by

the lack of significant intermixing or Sb segregation during GaAs overgrowth using MOCVD,

as these processes are essential for ring formation. Accordingly, the role of group-V exchange

processes is much less dominant in MOCVD growth. The surface reconstructions could

be a possible reason for this, as the mentioned extraordinary Sb-rich reconstructions have

only been reported from MBE studies yet and do not necessarily have to occur in MOCVD

growth, too. Additionally, the growth methods themselves, including the generally faster

growth rates of MOCVD and the different source substances, are probably the main reason

for the completely different influence of Sb segregation effects in MOCVD- and MBE-grown

GaSb/GaAs nanostructures [74, 263].

For the MOCVD-grown QDs and QWs as well as for the MBE-grown ring-shaped QDs a

type-II band alignment could be confirmed. Confined hole states of the GaSb nanostructures

and Coulomb-bound electron states in the surrounding GaAs were analyzed to induce a

specific contrast in XSTM images. This contrast mechanism could be explained in detail,

considering tip-induced band bending interacting with the confined states. In XSTS spectra a

type-II CB offset could directly be measured, amounting to about 0.1 eV. Despite of the ring

structure of the MBE-grown QDs and the underlying strong intermixing and segregation, a

hole localization of ∼0.3 eV already in rather flat QDs and ∼0.4 eV in somewhat larger

ones was obtained.

Combining these type-II related electronic properties with the actual ring geometry, the

MBE-grown QDs are exciting structures for fundamental physical effects like Aharonov-Bohm

oscillations, according to theoretical predictions [77]. First respective experiments using

magneto-PL and other methods studying the behavior of the ring-shaped GaSb QDs under

external magnetic fields are planned for the near future [437].

Considering the electronic properties derived from PL and especially XSTS data in com-

parison with the structural details obtained by XSTM, an impressively large and yet hardly

utilized potential of GaSb QDs for device applications gets apparent: Strong confinement and

particularly large hole localization energies were observed at structures which – in respect of

device suitability – are still far from perfect, exhibiting rather small sizes and being charac-

terized by strong intermixing and segregation. The growth of large QDs consisting of rather

pure GaSb with abrupt GaSb/GaAs interfaces, which is still a challenging task for epitaxy,

would result in unique QD properties which were highly promising for optoelectronic and

especially charge storage devices.

Regarding the MBE-grown QDs observed in this work, a considerable baselength could

be achieved together with a rather pure GaSb stoichiometry at least in a part of the QDs. A

GI subsequent to GaSb deposition was shown to result in strong intermixing and a flattening

of already existing QDs and thus should be kept as short as possible. In order to further

increase the GaSb content of the QDs and to achieve more abrupt interfaces, the strong Sb

segregation upon GaAs overgrowth has to be strongly decreased, and therefore the massive

As-for-Sb exchange needs to be avoided.

Hardly any Sb segregation was found at the MOCVD-grown nanostructures, which also

exhibit a chemical composition with a considerably high GaSb percentage. The observed very

small QDs were shown to represent an early stage of QD formation, thus from an extended

GaSb deposition during MOCVD growth the formation of significantly larger QDs with rather

164 CHAPTER 12. CONCLUSION

abrupt interfaces and a high GaSb content can be expected.

The realization of such QDs and the use of their potential in device applications will

require extensive future research in many places. Hopefully the results of this work will

contribute to that task, as this first XSTM investigation enhances the detailed and compre-

hensive understanding of the formation, atomic structure, and electronic properties of GaSb

quantum dots in GaAs.

Appendix

165

Appendix A

Outlook: Tip sputtering and

characterization by field ion

microscopy

To further improve the structural and electronic quality of the STM tips, a special tip prepa-

ration and characterization chamber was designed as an extension of the XSTM chamber,

as mentioned in chapter 4.2.2. This setup, which is currently under construction, combines

an ion sputtering stage for tip preparation with possibilities for fast and easy field emis-

sion current measurements or field ion microscopy as a more sophisticated characterization

method.

In this appendix a brief introduction into the techniques of ion sputtering, field emission

measurements, and field ion microscopy will be given, followed by the main aspects of the

new tip preparation and characterization chamber.

Tip sharpening by Ar+sputtering

Amongst the different proposed strategies to remove the oxide layer of etched W tips, sput-

tering of the tips by ions or electrons is a comparatively extensive method, but it can clean

the tip very thoroughly and additionally lead to a further sharpening of the tips [438, 439].

Ion sputtering of STM tips has already been successfully established in this group several

years ago [440]: Etched W tips [Fig. A.1(a)] were rotated in an external UHV chamber and

sputtered with 4 kV Ar+ions at a pressure of about 10−5mbar from the rear under an angle

of about 45◦. After one hour of sputtering, the acceleration voltage was decreased for a more

gentle sputtering, until finally an ultra-sharp tip was produced. During this process, the

sharpness of the tip was controlled from time to time by measuring the field emission current

(see below). The final shape of the tip was determined by transmission electron microscopy,

as shown in Fig. A.1(b), obtaining a radius of curvature of less than 3 nm.

While in that setup single tips were sputtered ex-situ and had later to be transferred into

the STM chamber through air, a corresponding sputtering stage is now being built within

the tip preparation chamber directly attached to the XSTM chamber. It offers three different

flanges for the sputtering gun, enabling sputtering under angles of either 35◦, 45◦, or 55◦,

and the tips can easily be placed at a rotatable and adjustable sputtering position using the

same tip holder system as in the XSTM.

167

168 APPENDIX A. OUTLOOK: TIP SPUTTERING AND CHARACTERIZATION

(a) (b)

200nm 200nm 20nm

Figure A.1: Transmission electron mi-

croscopy images of representative STM

tips (a) directly after electrochemical

etching and (b) after sputtering the tip

with Ar+ions; taken from [440].

Field emission current

During sputtering of the tip, an indicator is needed which can easily be measured to decide

when the acceleration energy has to be reduced and when the sputtering has to be finished

in order not to damage an already obtained good tip. Such an indicator is given by the field

emission current between the tip and a steel plate acting as counter electrode.

Between the metal tip and any conductive electrode an electric field will form under an

applied voltage. If the tip is negatively biased and the field is sufficiently large, electrons

will emit from the tip and be accelerated along the lines of electric field towards the anode.

This field emission was extensively studied by R. H. Fowler and L. Nordheim already in 1928

[441]. Considering the number of electrons being emitted from a metal surface of unit area

per unit time under the applied electric field F, they derived the following expression for the

field emission current density j(transformed to the SI system):

j=e3

2πh qEF

EF+φF2exp Ã−8π√2me

3e h

φ3

F!,(A.1)

with the electronic charge eand mass meand the metal work function φ. If φis measured

in eV and the electric field in V/m, the current density expressed in A/m2amounts to

j=6.2·10−6qEF

EF+φF2exp Ã−6.8·109φ3

F!.(A.2)

Equation A.2, known as the Fowler-Nordheim-equation for field emission, demonstrates a

strong increase of the emission current with increasing field F.

For a sharp tip with an approximatedly spherical summit, the electric field is strongest

directly at the tip apex and amounts to

F=V

κR (A.3)

for an applied voltage Vand a tip radius of curvature Rwith κ≈4. . . 8 being a geometric

factor [442, 443], which can best be approximated by κ≈5 [443, 444]. Replacing the current

density jby the total field emission current I(in A) through the emitting region Atof the

tip (with Rin m), this current finally results to

I=2.5·10−7qEF

φAtV2

EF+φ

R2exp Ã−3.4·1010 φ3

VR!.(A.4)

169

Accordingly, the easily measurable emission current increases strongly with decreasing tip

radius and can therefore be used as an indicator for the tip sharpness. For a rough estimation

of the tip sharpness it can be sufficient to measure the order of magnitude of the current at

a given voltage, or to measure the applied voltage Vwhich is necessary to induce a specific

current [440].

For a more exact measurement of the tip radius, I/V 2can be plotted logarithmically

versus 1/V , resulting in a straight line of slope −3.4·1010 φ3/2R[359, 442].

Field ion microscopy

Exceeding the approximations of the Fowler-Nordheim current, the exact radius and also the

complete geometry of the tip apex can be obtained when the current pattern is imaged by

field ion microscopy (FIM), which was invented in 1952 by E. W. M¨uller in Berlin [442, 445].

For FIM imaging, the tip is positioned within a few cm distance opposite a conductive

screen, or better, a multichannel plate within a vacuum chamber containing an imaging gas.

A typical imaging gas is He, while Ne or H can also be used, at pressures of about 10−6mbar.

When a high voltage of several kV is applied between the positively charged tip and the

screen, the atoms near the sharp tip get polarized within the very strong electric field and

are attracted towards the tip [see Fig. A.2(a)]. In sufficiently large fields directly at the tip

surface the atoms get ionized, which is occuring at a critical distance xcdetermined by

xc≈I−φ

eF ,(A.5)

with the ionization energy Iof the imaging gas atoms, the tip work function φand the

electric field F. Taking as example a W tip with a radius of curvature of 20 nm and an

applied voltage of 5 kV, an electric field of F= 5 ×1010 V

mresults, which – using He as

imaging gas with I= 25 eV – leads to a critical distance of xc≈4˚

A for ionization of the He

atoms.

Once the imaging gas atoms are ionized, they get accelerated to the screen along the lines

of electrical field. These lines originate perpendicularly at the flat screen and also at the

surface of the tip, thus a projected image of the tip geometry is present at the screen, as

depicted in Fig. A.2(b). As the bending of the tip surface and therewith the electrical field is

largest at atomic protrusions and edges of atomical terraces, such features appear as bright

spots in the FIM images of the tip.

An impressive example of an FIM image is displayed in Fig. A.2(c), showing a crystalline

W tip with a rather large radius of curvature, resulting in many surface terraces with slightly

different orientation. From characteristic symmetric spots the tip apex can be identified as

a (110) plane, with four additional {110}side facets. Also higher indexed geometries can be

recognized, as shown in Fig. A.2(d).

The magnification and the lateral resolution of the FIM are mainly determined by the

applied voltage and the radius of the tip. However, there are several effects limiting the

resolution, including the initial tangential velocity of the imaging ions due to the finite tem-

perature, the radius of the gas molecule itself, and the quantum mechanical uncertainty of

the ion position according to Heisenberg [442]. Additionally, the applied voltage and the re-

sulting electric field are restricted to avoid manipulation of the tip shape by field evaporation

[359, 442]. In conclusion, best resolution is obtained with very small tip radii, by imaging at

low temperatures, and by using imaging gases with high ionization fields and small atomic

radii, thus favoring He as imaging gas for most tip materials. Under appropriate conditions

atomic resolution down to less than 2 ˚

A can be achieved [442].

170 APPENDIX A. OUTLOOK: TIP SPUTTERING AND CHARACTERIZATION

(b)

(a)

STMtip

channel

plate

Heatoms

electric

field

(f)

[hkl]

[h'k'l']

2mm

R-ns g

(c)

(d)

(e)

Figure A.2: (a,b) Sketches of the FIM principle: Imaging gas atoms get polarized and attracted

towards the tip within the strong electric field (a), until they get ionized and are accelarated to the

channel plate, imaging the tip (b). (c-e) FIM images of W tips, showing (c) a rather blunt tip in an

wide-angle image, (d) a tip with a (211) apex, and (e) a very sharp tip with a (110) apex. The images

are taken from (c,d) [442] and (e) [359]. (f) Sketch how to evaluate the local tip radius from a FIM

image, adopted from [442].

Coming along with the increased resolution and magnification for decreased tip radii,

the distances between neighboring atomic spots on the screen increase, too. Figure A.2(e)

shows a very sharp polycrystalline W tip prepared for STM imaging, with one single atom

directly at the apex [359]: The rings around the central spot contain only a few atoms and

are considerably separated from each other. On the other hand, the angle between distinct

surface planes of the tip is constant. Therefore the number of atomic rings which can be

counted in the FIM image between characteristic neighboring spots is a measure for the

radius of curvature, as it is depicted in Fig. A.2(f) [442]: The angle γbetween the planes

(hkl) and (h’k’l’) and the step height sbetween neighboring atomic rings are determined by

the crystal structure and the lattice constant of the material. Knowing the number nof rings

171

observed between the corresponding two planes, the local tip radius Ramounts to

R=n s

1−cos γ.(A.6)

Therewith the tip radius and the geometry of tips prepared for STM imaging can nicely

be determined using FIM [356, 359].

Enhanced tip preparation setup for the XSTM chamber

The three discussed tip preparation and characterization methods – ion sputtering, measuring

the field emission current, and imaging the tip geometry by FIM – are combined within the

new tip preparation chamber, which is attached to the XSTM chamber and separated by

UHV valves.

The complete chamber is specially designed to enable a fast and easy switching between

the preparation and characterization stages and to directly transfer the readily prepared tips

to the STM. A possible procedure of tip preparation is sketched in Figs. A.3(a-c): At the

beginning, a freshly etched tip is taken from the tip storage, which can accommodate up

to 28 tips, and is positioned at the tip holder by a wobble stick. The tip holder consists of

a rotatable copper cylinder which is insulated against the UHV chamber and connected to

a high voltage supply, holding the tip by a magnet. The radial position of the tip can be

adjusted over a range of 10 cm by a linear drive at which the copper cylinder is mounted,

enabling the tip to be positioned at the center of the ion beam [Fig. A.3(a)]. For sputtering,

Ar can be supplied to the chamber via a gas dosing valve.

After the first desired duration of sputtering, the ion beam is switched off and the tip is

moved a few cm forward close to a steel plate, which simultaneously acts as a shutter protect-

ing the multichannel plate during sputtering and as an anode for field emission measuring

[Fig. A.3(b)]. Large windows in the chamber give an easy optical access for positioning the tip

at the different stages. For field emission, the tip is negatively biased by a high voltage and

the resulting emission current is measured. According to the current, the sputtering process

can be continued as before, the sputtering energy can be changed, or when the current is

satisfyingly high the sputtering is not repeated any more and the tip is imaged by FIM.

In this case the shutter is removed, releasing the small entrance to the FIM which is nearly

completely shielded by a copper frame. After the Ar has been replaced by He as imaging gas,

the sputtered tip gets positioned a few cm in front of the channel plate which is negatively

biased against the tip [Fig. A.3(c)]. At the rear side of the channel plate a phosphorus screen

is mounted at which the FIM image of the tip can be viewed (or recorded by a camera)

through a large window of the chamber.

This window and the flange containing the FIM setup including several high voltage

feedthroughs can well be seen in the photograph of Fig. A.3(d), which also shows the flange

of the shutter, a gas inlet valve, some windows for optical access, and instruments for UHV

generation and measurement. In Fig. A.3(e), opposite to the FIM flange a linear drive can

be seen. This linear drive holds a rotary drive (at the right hand of the image), to which the

tip is mounted by the long copper cylinder (in the image hidden from view within the linear

drive), thus the tip position is adjusted by the linear drive.

The exact setup of the sputtering and characterization stages can be seen in the scaled

drawing in Fig. A.4(a). Additionally, a sketch of the complete new chamber and its connection

to the XSTM system is shown in Fig. A.4(b). The tip preparation chamber is connected to

the loadlock and to the old small preparation chamber by a long magnetic transfer, which

enables an easy transfer of sputtered tips to the XSTM and also a fast supply of new tips

and samples to the tip preparation chamber or to the XSTM chamber.

172 APPENDIX A. OUTLOOK: TIP SPUTTERING AND CHARACTERIZATION

channelplate

shutter

tipstorage

copper

cylinder

holding

thetip

copper

cylinder

holding

thetip

sputtering

gun

channelplate

shutter

tipstorage

copper

cylinder

holding

thetip

sputtering

gun

sputtering

gun -

(a)

(b)

STM

unit

UHVvalve

valvefor

gasinlet

FIMflange

withHV

feed-

throughs

UHVpumps

window

tothe

FIM

screen

FIM

flange

gas

inlet lineardrive

fortip

positioning

UHV

valve

sputteringgun

positions

positionfor

wobblestick

(d) shutter

flange

Figure A.3: (a-c) Tip preparation and characterization steps, consisting of (a) ion sputtering,

(b) measuring the field emission current, and (c) FIM imaging. (d,e) Photographs of the new chamber.

Additionally to the controlled preparation of stable and sharp tips, it is possible and

important to image a sputtered tip by FIM prior to its employment in the XSTM experiment

and to characterize it again after it has aquired the STM images. In this way the changes

to the STM tip structure upon imaging get apparent. Even more, if no such changes can

be observed, one can be sure that the used tip has remained its structure analyzed by FIM

throughout the whole XSTM experiment.

In conclusion, from the tip preparation expansion at the XSTM chamber setup a better

resolution of the STM images and especially a by far increased structural and electronic

stability of the tips for aquiring STS spectra can be expected. Moreover, the possibility to

atomically characterize a tip before and after imaging in comparison with the aquired STM

data will give new insight into the imaging process itself.

The UHV chamber is readily mounted and also the main mechanical parts of the tip

preparation setup have already been finished, as can be seen in Fig. A.3(d,e). Currently the

rather complex tip positioning stage including the electrical connections is under construction,

together with some remaining mechanical feedthroughs. Once this stage is working, the

173

rotarydr.

sputter

gun

wobble

stick

FIM

UHVpumps

underneath

thechamber

load-

lock

current

prepa-

ration

chamber

magnetictransfer

tipstorage

tothe

STM

chamber

magnetictransfer

lineardrive

UHV

valve

UHV

valve

topview

lineardrive

withshutter

lineardrive

withtip,

retracted

lineardrive

withtip,

extended

rotarydrive

100mmwindow

sputter

gun

HVfeedthrough

fortipcontacting

coppercylinder

holdingthetip

alternative

sputtering

position

channel

plate shutter

copper

frame

ofthe

FIM

HVfeedthroughs

forFIMcontacts

sideview

(a)

(b)

Figure A.4: Sketches drawn to scale of (a) the stage for tip sputtering and FIM imaging and (b) the

complete tip preparation chamber.

chamber can already be used for tip sputtering and measuring the field emission current,

while the FIM itself will be assembled as a last step.

174 APPENDIX A. OUTLOOK: TIP SPUTTERING AND CHARACTERIZATION

Appendix B

Simulated distribution of

cross-sections through ring

structures

In the MBE-grown samples C and D quantum dots with a ring-like structure were obtained

(see chapter 8). Although in XSTM images QDs with a rather compact appearance, like

that shown in Fig. B.1(a), and paired features with a clear central gap, like that shown in

Fig. B.1(b), were observed, it was concluded in section 8.3.1 that both types of images can

represent a ring-shaped QD and differ only in the position where such a ring was cleaved [for

illustration see Fig. B.1(d)].

(c)

[ 10]1

[ 0]11

[00 ]1

(e)

din, cut

din

dout

dout, cut

5nm 5nm

[1 0]1

[001]

(a) (b)

experimentalhistogram

apparentratior=d /d

in, cut out, cut

( 1)11

(111)

(1 1)1 ( 11)1

different

(110)

cleavage

planes

(d)

[ 10]1

[110]

(001)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Figure B.1: Different cross-sections of cleaved ring-shaped QDs: (a,b) XSTM close-view images of

QDs in layer 3 of sample C, taken at (a) VT= -2.6 V and (b) VT= -2.3 V; (c) histogram of the

ratio of apparent inner to outer ring diameter, obtained from XSTM images of 140 QDs in sample C;

sketches of (d) different cleavage positions of a QD and (e) a resulting cross-section.

175

176 APPENDIX B. SIMULATED DISTRIBUTION OF RING CLEAVAGE

From the XSTM images of sample C data on 140 QDs could be obtained, which is still a

rather small database for statistical analysis, but is a large number of nanostructures for an

atomically resolved XSTM investigation. In order to investigate the characteristics of the ring

structure, especially the extension of the central gap, the ratio of inner to outer diameter in

the XSTM images of ring-shaped QDs was chosen as a parameter which is independent of the

total size of the QDs (see also section 8.3.2). The histogram of this parameter, obtained from

the experimental data, is shown in Fig. B.1(c). It is important to notice that the actual inner

diameter of the ring is in most cases larger than the diameter apparent in XSTM images, as

the sketches in Fig. B.1(d,e) illustrate. Therefore it has to be distinguished between the actual

ratio of inner and outer ring diameter r=din / dout and the ratio of the apparent diameters

˜r=din, cut / dout, cut. The latter one is the parameter that can directly be measured in XSTM

images [and is shown in Fig. B.1(c)], while the former one determines the actual shape of the

QD. Please note that for the assumption of a square-based outer shape of the ring with {111}

side facets [Fig. B.1(d)] the apparent and actual outer diameters are identical, dout, cut =dout.

By calculating a distribution of the apparent ring ratio ˜rand comparing this simulation

with the experimental histogram, the question should be answered if all QDs in sample C

have a ring shape, or if ring-shaped and conventional, continuous QDs coexist. The concept

of this simulation and the different steps will be introduced in the following.

In a first step the apparent ring ratios ˜rresulting from different cross sections through

one QD with a constant actual inner diameter din are simulated. Therefor a parameterization

of such a ring structure has to be chosen. For simplifiaction and using the symmetry of the

ring, the outer diameter was set to dout = 2, so the ring ratio is r=1

2din =rin with an

inner ring radius rin = (0, . . . , 1), and only one irreducible quadrant of the ring structure has

to be regarded, as sketched in Fig. B.2(a). The QD is cleaved within this quadrant at the

position x= (0, . . . , 1), with x= 0 meaning the QD being cleaved directly in the center and

x= 1 meaning exactly at the edge. Then the apparent ring ratio as a function of the cleavage

position results to

˜r=qr2

in −x2for x < rin ,˜r= 0 else.(B.1)

Due to the symmetry of the circle, Eq. B.1 can be inverted for all cleavage positions inside

the ring, i.e. for x < rin:

x(˜r) = qr2

in −˜r2.(B.2)

In order to simulate the distribution, however, not the exact value of ˜ror x(˜r) is important,

but the frequency hhow often a value within the interval [˜r, ˜r+ ∆˜r) is obtained, i.e. how

many different cleavage positions lie within the corresponding interval [x(˜r), x(˜r+ ∆˜r)) =

[x, x + ∆x), as it is sketched in Fig. B.2(b). For the frequencies of ˜rand xone can postulate

|h(˜r) ∆˜r|=|h(x) ∆x|.(B.3)

Assuming that the frequency h(x) is constant, meaning that all possible cleavage positions

have equal probability, and considering the range of the cleavage positions x∈(0,1], one

yields h(x) = 1, and the frequency of the apparent ring ratio results to

h(˜r) = ¯¯¯¯

∆x

∆˜r¯¯¯¯

.(B.4)

Coming back to Eq. B.2, for sufficiently small intervals ∆˜rand for cleavage positions

x < rin the frequency of the apparent ring ratio can now be given by

h(˜r) = ¯¯¯¯

dx(˜r)

d˜r¯¯¯¯

=˜r

qr2

in −˜r2

.(B.5)

177

0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.1

0.2

0.3

0.4

0.5

simulateddistribution

ringstructurewith

circularbase

quadraticbase

apparentratior=d /d

in, cut out, cut apparentratior=d /d

in, cut out, cut

~ ~

cleavage

position

cleavage

positionx

apparentratio

r=r /r

in, cut out apparentratio

r=r /r

in, cut out

rin

rin rin

(a) DxDx

(b)

0.0 0.2 0.4 0.6 0.8

0.00

0.01

0.02

0.03

0.04

0.05

0.25

0.50

Figure B.2: Pathway of simulating the distribution of ring cleavage: (a) Parameterization of a model

ring structure, (b) sketch how to obtain the frequency of a certain interval [˜r, ˜r+ ∆˜r). (c,d) Calcu-

lated distributions of the apparent ring ratio for (c) a structure with constant rin = 0.5 and (d) ring

structures with varying actual inner radii rin = (0.1, . . . , 0.9), weighted by a Gaussian distribution

with a maximum at 0.5 and a standard deviation of 0.2. In (d) a calculated distribution using a

model ring structure with a quadratic base, as shown in (a), is compared with a distribution using a

circular-based model.

For all cleavage positions x > rin, the apparent ring ratio is ˜r= 0, thus the frequency h(0)

is proportional to the ratio of the numbers of cleavage positions outside (rin <x<1) and

inside (0 < x < rin) the central gap and has to be normalized by the sum over all frequencies

with ˜r > 0 as follows:

h(˜r= 0) = 1−rin

rin ·Xh(˜r > 0) = 1−rin

rin ·

rin

x=0

dx(˜r)

d˜r= 1 −rin .(B.6)

A calculated distribution of the apparent ring ratio for a ring structure with rin = 0.5

is shown in Fig. B.2(c), which obviously still has no agreement with the experimental his-

togram [Fig. B.1(c)]. In a next step, it is therefore necessary to regard an ensemble of ring

structures with a distribution of inner radii rin, which is simulated by a Gaussian distribu-

tion Gwith a maximum at r0and a standard deviation σ. Thus for a set of different radii

rin = [rmin, . . . , rmax] the calculated cleavage distribution for each radius has to be weighted

178 APPENDIX B. SIMULATED DISTRIBUTION OF RING CLEAVAGE

by the Gaussian distribution as follows:

h(˜r) = X

rin

h(˜r, rin)·G(rin) =

rmax

rin=rmin

˜r

qr2

in −˜r2·exp Ã−1

2µr0−rin

σ¶2!.(B.7)

An example of such a weighted distribution is shown in Fig. B.2(d), using the parameters

r0= 0.5 and σ= 0.2 and inner ring radii from rin = 0.1 to rin = 0.9. A high peak for

˜r= 0, corresponding to cross-sections showing no central gap, and a broad distribution for

larger values of ˜rwith a maximum between 0.4 and 0.5 can be seen. The frequency h(0)

corresponding to ˜r= 0 is calculated analogously to Eq. B.6 and regarding the Gaussian

distribution of the radii by

h(˜r= 0) = X

rin

h(˜r= 0, rin)·G(rin).(B.8)

Depending on the number of different radii rin employed in the sums of Eqs. B.7 and B.8,

the weighted cleavage distribution has to be renormalized to fulfill the condition

˜r=0

h(˜r) = 1 .(B.9)

It should be noted that only the blue columns in Fig. B.2(d) represent a distribution

calculated as described above, while for the distribution shown by green columns the ring

structure was modelled differently: Instead of an outer shape with a quadratic base [as

sketched in Figs. B.1(d) and B.2(a)] a circular base was assumed here, leading to a slightly

different frequency of apparent ring ratio

h(˜r) = ˜r

qr2

in −˜r2√1−˜r2−˜rqr2

in −˜r2

q(1 −˜r2)3(B.10)

instead of Eq. B.5. Comparing both calculated results in Fig. B.2(d) it can be seen that the

choice of the model ring structure has very little influence on the distribution of the apparent

ring ratio.

For the calculated results shown in Fig. B.2(d) the variables r0and σof the Gaussian

distribution have been chosen arbitrarily. In a final step, these variables now have to be

optimized to obtain the best fit between the calculated distribution and the experimental

histogram. Thereby all values for ˜r > 0 are included in the fitting procedure, while the

peak at ˜r= 0 is not considered. In order to evaluate the agreement between simulation and

experiment, two parameters are regarded, namely the mean deviation of the experimental

data from the model and the statistical average of the apparent ring ratios ˜r. The latter

one can easily be calculated for the complete experimental data set of all QDs observed by

XSTM, and it can also straightforwardly be obtained from the calculated results by averaging

the apparent ring ratios for all used actual radii rin and cleavage positions x, weighted by

the Gaussian distribution. Obviously, the difference between both average values should be

as small as possible for a good simulation of the experimental findings.

The mean deviation χ2is calculated for the individual columns iof the experimental and

calculated distributions for ˜r > 0, regarding the number nQD of experimentally observed

QDs, by summarizing over all Ncolumns as follows:

χ2=1

N−1·

i=1 



hexp(˜ri)−nQD ·hcalc(˜ri)

qnQD ·hcalc(˜ri)



.(B.11)

179

A color map of the value of χ2for a broad parameter range of the Gaussian variables r0and σ

is shown in Fig. B.3(a). Good agreement between experiment and calculation, meaning a

small mean deviation χ2, is obtained for an average ring radius r0between 0.3 and 0.5 with

a Gaussian standard deviation σbetween 0.1 and 0.2.

Additionally to the mean deviation, the difference between the average apparent ring

ratio in experiment and calculation ∆<˜r> is displayed as a color map for the same ranges of

r0and σin Fig. B.3(b): Here, for all actual ring radii smaller than r0= 0.5 a corresponding

value of the statistical deviation with σ < 0.35 exists which leads to good agreement between

experiment and simulation.

By comparing the results for both parameters χ2and ∆ <˜r> [Fig. B.3(c)], the pair of

Gaussian variables r0and σwhich leads to the best fit can be obtained to r0= 0.42 and

σ= 0.13. The value of r0can therefore be estimated to be the average ratio of actual inner

to outer ring diameter for the ring-shaped QDs in sample C. The corresponding distribution

calculated using these parameters and considering all possible actual ring radii between 0.1

and 0.9 is shown by the blue columns in Fig. B.3(c), together with the experimental histogram

displayed in red.

While a detailed comparison of both distributions and a discussion of the resulting con-

(a) (b)

(d)

(c)

averageradius r0averageradius r0averageradius r0

standarddeviation s

c2D<r>

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.12

0.16

0.20

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.25

0.35

0.45

0.60

0.80

1.2

2.0

4.0

8.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100

experimentalhistogram[numberofQDs]

simulateddistribution[a.u.]

apparentratior=d /d

in, cut out, cut

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

experimentalhistogram

simulateddistribution

apparentratior

r =0.42 =0.13

Figure B.3: Optimizing the parameters r0and σof the Gaussian distribution to fit the experimental

histogram for ˜r > 0: Calculated values of (a) the mean deviation between experimental and simulated

data χ2, (b) the difference between the average apparent ring ratios of experiment and simulation

∆<˜r>, and (c) an overlay of (a), shown as greyscale plot, and (b), indicated by colored lines. (d) A

comparison between experimental and simulated distribution for the best fit of r0= 0.42 and σ= 0.13.

180 APPENDIX B. SIMULATED DISTRIBUTION OF RING CLEAVAGE

clusions is performed in section 8.3.2, here only the very good agreement between experiment

and simulation is emphasized, especially in regard to the rather poor statistical database and

the idealized assumptions used for modeling the ring structure.

List of abbreviations

2D two-dimensional

3D three-dimensional

AB effect Aharonov-Bohm effect

AB oscillation Aharonov-Bohm oscillation

AFM atomic force microscopy

CB conduction band

CITS current imaging tunneling spectroscopy

CV capacitance voltage

DLTS deep level transient spectroscopy

DOS density of states

DRAM dynamic random access memory

FIM field ion microscopy / microscope

FWHM full width of half maximum

GI growth interruption

HRTEM high-resolution transmission electron microscopy

LDOS local density of states

MBE molecular beam epitaxy

ML monolayer

MOCVD metalorganic chemical vapor deposition

PL photoluminescence

PLE photoluminescence excitation

QD quantum dot

QR quantum ring

QW quantum well

181

182 LIST OF ABBREVIATIONS

RHEED reflection high energy electron diffraction

SEM scanning electron microscopy / microscope

SK growth Stranski-Krastanow growth

STEM scanning transmission electron microscopy

STM scanning tunneling microscopy / microscope

STS scanning tunneling spectroscopy

tBAs tertiarbutylarsine

tBP tertiarbutylphosphine

TEGa triethylgallium

TEM transmission electron microscopy / microscope

TESb triethylantimony

TIBB tip-induced band bending

TMAl trimethylaluminium

TMGa trimethylgallium

UHV ultrahigh vacuum

VB valence band

WL wetting layer

XSTM cross-sectional scanning tunneling microscopy / microscope

XSTS cross-sectional scanning tunneling spectroscopy

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Publications and presentations

Parts of this work have been published in:

•R. Timm, H. Eisele, A. Lenz, S. K. Becker, J. Grabowski, T.-Y. Kim, L. M¨uller-Kirsch,

K. P¨otschke, U. W. Pohl, D. Bimberg, and M. D¨ahne, Structure and intermixing of

GaSb/GaAs quantum dots, Appl. Phys. Lett. 85, 5890 (2004).

•R. Timm, J. Grabowski, H. Eisele, A. Lenz, S. K. Becker, L. M¨uller-Kirsch, K. P¨otschke,

U. W. Pohl, D. Bimberg, and M. D¨ahne, Formation and atomic structure of GaSb nano-

structures in GaAs studied by cross-sectional scanning tunnelling microscopy, Physica E

26, 231 (2005).

•R. Timm, A. Lenz, J. Grabowski, H. Eisele, and M. D¨ahne, A cross-sectional scan-

ning tunneling microscopy study of GaSb/GaAs nanostructures, Springer Proceedings

in Physics 107, 479 (2005).

•R. Timm, A. Lenz, J. Grabowski, H. Eisele, K. P¨otschke, U. W. Pohl, D. Bimberg, and

M. D¨ahne, Formation and Atomic Structure of GaSb Quantum Dots in GaAs Studied by

Cross-Sectional Scanning Tunneling Microscopy, in: Proceedings of EW-MOVPE XI,

ed. by E. Kapon and A. Rudra (Lausanne 2005), p. 39.

•R. Timm, A. Lenz, H. Eisele, L. Ivanova, K. P¨otschke, U. W. Pohl, D. Bimberg, G. Bal-

akrishnan, D. L. Huffaker, and M. D¨ahne, Onset of GaSb/GaAs quantum dot formation,

phys. stat. sol. (c) 3, 3971 (2006).

Other publications:

•A. Lenz, R. Timm, H. Eisele, Ch. Hennig, S. K. Becker, R. L. Sellin, U. W. Pohl, D. Bim-

berg, and M. D¨ahne, Reversed truncated cone composition distribution of In0.8Ga0.2As

quantum dots overgrown by an In0.1Ga0.9As layer in a GaAs matrix, Appl. Phys. Lett.

81, 5150 (2002).

•H. Eisele, A. Lenz, R. Timm, Ch. Hennig, M. Ternes, F. Heinrichsdorff, A. Krost,

R. Sellin, U. W. Pohl, D. Bimberg, T. Wehnert, E. Steimetz, W. Richter, and M. D¨ahne,

Atomic Structure of InAs and InGaAs Quantum Dots Studied by Cross-Sectional Scan-

ning Tunneling Microscopy, Inst. Phys. Conf. Ser. 171, P199 (2003).

•O. Flebbe, H. Eisele, R. Timm, and M. D¨ahne, Room-Temperature Observation of

Standing Electron Waves on GaAs(110) at Surface Steps, AIP Conf. Proc. 696, 699

(2003).

205

206 PUBLICATIONS AND PRESENTATIONS

•S. K. Becker, J. Grabowski, T.-Y. Kim, L. Amsel, F. Bechtel, N. Tschirner, I. Mantou-

valou, A. Lenz, R. Timm, K. Hodeck, F. Streicher, G. Pruskil, H. Eisele, and M. D¨ahne,

Low Budget UHV STM Built by Physics Students for Use in a Laboratory Exercises

Course, AIP Conf. Proc. 696, 216 (2003).

•H. Eisele, R. Timm, A. Lenz, Ch. Hennig, M. Ternes, S. K. Becker, and M. D¨ahne,

Segregation effects during GaAs overgrowth of InAs and InGaAs quantum dots studied

by cross-sectional scanning tunneling microscopy, phys. stat. sol. (c) 0, 1129 (2003).

•H. Eisele, A. Lenz, Ch. Hennig, R. Timm, M. Ternes, and M. D¨ahne, Atomic structure

of InAs and InGaAs quantum dots determined by cross-sectional scanning tunnelling

microscopy, J. Crystal Growth 248, 322 (2003).

•A. Lenz, H. Eisele, R. Timm, S. K. Becker, R. L. Sellin, U. W. Pohl, D. Bimberg,

and M. D¨ahne, Nanovoids in InGaAs/GaAs quantum dots observed by cross-sectional

scanning tunneling microscopy, Appl. Phys. Lett. 85, 3848 (2004).

•O. Schumann, S. Birner, M. Baudach, L. Geelhaar, H. Eisele, L. Ivanova, R. Timm,

A. Lenz, S. K. Becker, M. Povolotskyi, M. D¨ahne, G. Abstreiter, and H. Riechert,

Effects of strain and confinement on the emission wavelength of InAs quantum dots

due to a GaAs1−xNxcapping layer, Phys. Rev. B 71, 245316 (2005).

•R. Timm, H. Eisele, A. Lenz, T.-Y. Kim, F. Streicher, K. P¨otschke, U. W. Pohl,

D. Bimberg, and M. D¨ahne, Structure of InAs/GaAs quantum dots grown with Sb

surfactant, Physica E 32, 25 (2006).

•A. Lenz, R. Timm, H. Eisele, L. Ivanova, D. Martin, V. Voßeb¨urger, A. Rastelli,

O. G. Schmidt, and M. D¨ahne, Structural investigation of hierarchically self-assembled

GaAs/AlGaAs quantum dots, phys. stat. sol. (b) 243, 3976 (2006).

•A. Lenz, H. Eisele, R. Timm, L. Ivanova, H.-Y. Liu, M. Hopkinson, U. W. Pohl, and

M. D¨ahne, Structure of InAs quantum dots-in-a-well nanostructures, Physica E, in

print.

Contributions at international conferences:

•12th International Conference on Scanning Tunneling Microscopy/Spectroscopy and

Related Techniques (STM2003), 21 - 25 July 2003, Eindhoven, The Netherlands:

Atomic structure and type-II band alignment of GaSb quantum dots in GaAs studied by

cross-sectional STM (oral),

Structural change of InAs quantum dots during GaAs overgrowth studied by (cross-

sectional) STM (poster).

•QD2004 Quantum Dots Conference, 10 - 13 May 2004, Banff, Alberta, Canada:

Atomic Structure and Type-II Band Alignment of GaSb Quantum Dots in GaAs Studied

by Cross-Sectional Scanning Tunneling Microscopy (oral).

•Microscopy of Semiconducting Materials (MSM XIV), 11 - 14 April 2005, Oxford, UK:

Formation, Atomic Structure, and Type-II Band Alignment of GaSb/GaAs Quantum

Dots Studied by Cross-Sectional Scanning Tunneling Microscopy (oral).

PUBLICATIONS AND PRESENTATIONS 207

•11th European Workshop on Metalorganic Vapour Phase Epitaxy (EW–MOVPE),

5 - 8 June 2005, Lausanne, Switzerland:

Formation and Atomic Structure of GaSb Quantum Dots in GaAs Studied by Cross-

Sectional Scanning Tunneling Microscopy (poster).

•International Conference on Modulated Semiconductor Structures (12 MSS), 10 - 15

July 2005, Albuquerque, New Mexico, USA:

Structure of InAs/GaAs Quantum Dots grown with Sb surfactant (poster).

•EPS - 21st General Conference of the Condensed Matter Division of the European

Physical Society, 26 - 31 March 2006, Dresden, Germany:

Atomic structure of GaSb/GaAs quantum rings and dots studied by cross-sectional scan-

ning tunneling microscopy (oral).

•4th International Conference on Quantum Dots (QD2006), 1 - 5 May 2006, Chamo-

nix-Mont Blanc, France:

Growth, Atomic Structure, and Type-II Band Alignment of GaSb/GaAs Quantum Dots

and Rings (poster).

•28th International Conference on the Physics of Semiconductors (ICPS28), 24 - 28

July 2006, Vienna, Austria:

Growth, Atomic Structure, and Electronic Properties of GaSb/GaAs Nanostructures:

Quantum Wells, Dots and Rings (oral).

•International Conference on Nanoscience and Technology (ICN+T2006), 30 July -

4 August 2006, Basel, Switzerland:

Local tip-induced band bending at type-II GaSb/GaAs nanostructures studied with cross-

sectional scanning tunneling microscopy and spectroscopy (oral).

•Microscopy of Semiconducting Materials (MSM XV), 1 - 5 April 2007, Cambridge, UK:

Growth and atomic structure of GaSb/GaAs quantum dots and rings studied by cross-

sectional scanning tunneling microscopy and spectroscopy (oral).

•International Conference on Modulated Semiconductor Structures (13 MSS), 15 - 20

July 2007, Genova, Italy: Growth, atomic structure, and type-II band alignment of

GaSb/GaAs nanostructures: Quantum wells, dots, and rings (poster).

208 PUBLICATIONS AND PRESENTATIONS

Acknowledgments

I am deeply grateful to many people who have contributed to the success of this work.

First of all, my sincere thanks go to Prof. Mario D¨ahne for giving me the opportunity

to directly “look at the atoms” and for supervising this work. His continuous support at all

times, his enthusiasm for physics and teaching, many detailed and fruitful discussions, and

his careful proof reading of the manuscript have helped and impressed me far beyond the

scope of this thesis.

Prof. Dieter Bimberg is gratefully acknowledged for refereeing this thesis and for his great

motivation and support.

Special thanks belong to Dr. Holger Eisele for introducing me into the world of STM and

for teaching me much about the details of UHV technology as well as the physics of QDs. I

have learned a lot from his knowledge and experience. During all the time of my Diploma

and Ph.D. thesis I could benefit from the cooperation with Andrea Lenz, in whom I found an

absolutely reliable and loyal colleague, and whith whom I share(d) not only our office, many

XSTM experiments, several conferences, and teaching activities, but also a close friendship.

Thank you!

I further want to thank Holger, Andrea, and also Lena Ivanova, Jan Grabowski, Vivien

Voßeb¨urger, Dominik Martin, and Sebastian Becker for assistance in XSTM measurements,

investing sleepless nights and a lot of patience. Even more, I am very grateful to them as

well as to Martina Wanke, Kai Hodeck, Angela Berner, and all other members of the D¨ahne

workgroup for a lot of help and encouragement during everyday life, for many great events,

and for a working atmosphere that let me really enjoy the time of my Ph.D.

The GaSb QDs studied in this work have been grown by Dr. Lutz M¨uller-Kirsch and

Konstantin P¨otschke in the group of Prof. Bimberg, by Dr. Ganesh Balakrishnan in the group

of Prof. Diana L. Huffaker, and by Dr. Ian Farrer in the group of Prof. David A. Ritchie. All

of them I want to thank for their cooperation in providing the samples. Special thanks also

go to Till Warming for the PL data and to Prof. Randall M. Feenstra for his calculations

and excellent suggestions on STM contrast and tip-induced band bending. Additionally, I

would like to acknowledge Martin Geller for his concern in GaSb QDs and his explanations

about the concepts of storage devices, and PD Dr. Udo W. Pohl for his enduring interest in

my work and enriching discussions on various aspects of QD growth.

This work profited from funding by the European Commission in the SANDiE Network

of Excellence and by projects Da 408/4, Da 408/8, Da 408/13, and SFB 296 of the Deutsche

Forschungsgemeinschaft, as well as from a personal grant given by the city of Berlin in the

“NaF¨oG” program.

Finally, I am particularly grateful to my parents, who inspired in me the whish to explore

nature, who encouraged me, and who enabled my physics studies. Above all, I thank my wife

Bianca for her everlasting support and for every single day.

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