Document [original]

Cubic AlGaN/GaN structures

for device application

dem Department Physik

der Universit¨

at Paderborn

zur Erlangung des akademischen Grades eines

Doktors der Naturwissenschaften

vorgelegte

Dissertation

von

J¨

org Sch¨

ormann

Paderborn, Mai 2007

Abstract

The aim of this work was the growth and the characterization of cubic GaN, cubic

AlGaN/GaN heterostructures and cubic AlN/GaN superlattice structures. Reduction of

the surface and interface roughness was the key issue to show the potential for the use of

cubic nitrides in futur devices. All structures were grown by plasma assisted molecular

beam epitaxy on free standing 3C-SiC (001) substrates.

In situ reflection high energy electron diffraction was first investigated to determine the

Ga coverage of c-GaN during growth. Using the intensity of the electron beam as a probe,

optimum growth conditions were found when a 1 monolayer coverage is formed at the sur-

face. GaN samples grown under these conditions reveal excellent structural properties.

On top of the c-GaN buffer c-AlGaN/GaN single and multiple quantum wells were de-

posited. The well widths ranged from 2.5 to 7.5 nm. During growth of Al0.15Ga0.85N/GaN

quantum wells clear reflection high energy electron diffraction oscillations were observed

indicating a two dimensional growth mode. We observed strong room-temperature, ul-

traviolet photoluminescence at about 3.3 eV with a minimum linewidth of 90 meV. The

peak energy of the emission versus well width is reproduced by a square-well Poisson-

Schr¨

odinger model calculation. We found that piezoelectric effects are absent in c-III

nitrides with a (001) growth direction. Intersubband transition in the wavelength range

from 1.6 µm to 2.1 µm was systematically investigated in AlN/GaN superlattices (SL),

grown on 100 nm thick c-GaN buffer layers. The SLs consisted of 20 periods of GaN

wells with a thickness between 1.5 nm and 2.1 nm and AlN barriers with a thickness of

1.35 nm. The first intersubband transitions were observed in metastable cubic III nitride

structures in the range between 1.6 µm and 2.1 µm.

List of abbreviations

AFM Atomic Force Microscopy

AlGaN cubic AlxGa1−xN

BEP Beam Equivalent Pressure

CL Cathodoluminescence

DAP Donor Acceptor Pair

EL Electroluminescence

FET Field Effect Transistor

FWHM Full Width at Half Maximum

GaN cubic GaN

HEMT High Electron Mobility Transistor

HRXRD High Resolution X-Ray Diffraction

ISBT Intersubband transitions

IR Infrared

MBE Molecular Beam Epitaxy

MOCVD Metal-Organic Chemical Vapor Deposition

MQW Multiple Quantum Well

PAMBE Plasma-assisted Molecular Beam Epitaxy

PL Photoluminescence

QCSE Quantum Confinement Stark Effect

QWIP Quantum Well Infrared Photodetector

SEM Scanning Electron Microscopy

SL Superlattice

SQW Single Quantum Well

rf Radio Frequency

RHEED Reflection High Energy Electron Diffraction

RSM Reciprocal Space Map

UHV Ultra High Vacuum

UV Ultraviolet

XExciton

Contents

1 Introduction 1

2 Fundamentals 5

2.1 Properties of III-nitrides . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Epitaxial growth techniques . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Molecular beam epitaxy . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Characterization methods . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 High resolution X-ray diffraction . . . . . . . . . . . . . . . . . . 12

2.3.2 Atomic force microscopy . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.3 Luminescence spectroscopy . . . . . . . . . . . . . . . . . . . . . . 17

3 MBE of cubic GaN and cubic AlGaN 21

3.1 In situ growth regime characterization of cubic GaN . . . . . . . . . . . . 21

3.1.1 Adsorption and desorption of Ga on c-GaN . . . . . . . . . . . . . 21

3.1.2 Kineticmodel............................. 26

3.1.3 Growth experiments . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Growth and characterization of cubic AlGaN/GaN heterostructures . . . 35

4 Growth of cubic AlGaN/GaN quantum wells 43

4.1 Growth and structural properties of cubic AlGaN/GaN quantum wells . 43

4.2 Photoluminescence of cubic AlGaN/GaN quantum wells . . . . . . . . . 46

5 AlN/GaN superlattices for intersubband spectroscopy 53

5.1 Intersubband transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

ii Contents

5.2 Growth of c-AlN/GaN superlattices . . . . . . . . . . . . . . . . . . . . . 60

5.3 Structural properties of AlN/GaN SLs . . . . . . . . . . . . . . . . . . . 64

5.4 Optical properties of AlN/GaN SLs . . . . . . . . . . . . . . . . . . . . . 66

6 Conclusion 71

7 Appendix 73

List of Figures

2.1 Unit cell of a) the zincblende structure and b) the hexagonal structure. . 6

2.2 Different polarities in hexagonal GaN . . . . . . . . . . . . . . . . . . . . 7

2.3 Band profiles and carrier distributions in cubic and hexagonal AlGaN/GaN

quantum wells; a) the cubic AlGaN/GaN DH structure and b) the hexag-

onal AlGaN/GaN DH structure . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Schematic cross section of an MBE setup. . . . . . . . . . . . . . . . . . 9

2.5 Schematic diagram of the RHEED diffraction geometry, showing reflection

and transmission diffraction, as well as the straight-through (0,0) beam. . 10

2.6 Typical RHEED-pattern of c-GaN during growth interruption. A (2 ×2)

reconstruction of the (-110) azimuth is observed. . . . . . . . . . . . . . . 11

2.7 Sketch of the diffraction geometry. The exact Bragg condition for (hkl)

planes is fulfilled, if the scattering vector ~

Qends at a reciprocal lattice

point(hkl). .................................. 13

2.8 Schematic drawing of the Phillips X´Pert MRD consisting of X-Ray tube,

hybrid monochromator, Euler cradle and detector. . . . . . . . . . . . . . 15

2.9 Schematic drawing of an AFM setup. . . . . . . . . . . . . . . . . . . . . 16

2.10 Schematic diagram of radiative transitions in a semiconductor; (e, h) rep-

resents intrinsic band to band, (X) free exciton,(D0, X), (A0, X) repre-

sents bound excitons to donator or acceptor and (D0, h),(h, A0) free to

bound, (D0, A0) donor to acceptor transitions. . . . . . . . . . . . . . . . 18

2.11 Schematic diagram of the photoluminescence setup. . . . . . . . . . . . . 19

iii

iv List of Figures

3.1 a) A sketch of the sample structure with the RHEED geometry. b) A

(2×2) reconstruction of a c-GaN surface during growth interruption. The

red rectangle indicates the area where the RHEED intensity was recorded. 22

3.2 The intensity of a reflected high energy electron beam (RHEED inten-

sity) versus time measured during the evaporation of Ga onto c-GaN at a

substrate temperature of TS= 720◦C. The Ga-fluxes are indicated. The

spectra are normalized to one and vertically shifted for clarity. . . . . . . 23

3.3 RHEED intensity transient for a Ga-flux of FGa = 4.3×1014 cm−2s−1and

7.5×1014 cm−2s−1............................... 24

3.4 RHEED intensity transients for Ga-fluxes of 4.3×1014 cm−2s−1and 7.5×

1014 cm−2s−1. After a transition time ∆tka kink in the transients is

observed. The estimated Ga-coverage is plotted on the right side. . . . . 25

3.5 RHEED intensity transients for a Ga-flux of 2 ×1014cm−2s−1. The red

curves show the simulations for a flux of 2 ×1014 cm−2s−1and three

different desorption fluxes as indicated in the figure. Good agreement was

achieved for a desorption flux of 1.6×1014 cm−2s−1. ........... 27

3.6 RHEED intensity transients for two Ga-fluxes together with simulations

as indicated in the figure. Good agreement was achieved within the linear

decrease of the RHEED intensity. . . . . . . . . . . . . . . . . . . . . . . 28

3.7 RHEED intensity transients measured during the growth of c-GaN, which

started after opening the N source. The RHEED intensity measured dur-

ing growth shows the amount of excess Ga (indicated in the figure) on the

c-GaN surface. Ga-fluxes are 4.4×1014, 3.2×1014 and 1.2×1014 cm−2s−1

for the coverages of 1, 0.8, and 0 ML, respectively. . . . . . . . . . . . . . 29

3.8 Root-mean-square (RMS) roughness of c-GaN layers measured by 5 ×

5µm2scans vs. Ga-flux during growth. The corresponding values of

the Ga-coverage during growth are also included. Minimum roughness is

obtained with an excess coverage of 1 ML. The line is added for better

overview..................................... 30

List of Figures v

3.9 ω−2Θ scan of the (002) reflex of sample 1287. The inset shows the ω-scan

of this sample revealing a FWHM of 16 arcmin. . . . . . . . . . . . . . . 31

3.10 Full width at half maximum (FWHM) of c-GaN layers vs. Ga-flux during

growth. The corresponding values of the Ga-coverage during growth are

also included. Minimum linewidth is obtained with an excess coverage of

1 ML. The line is a guide for the eyes. . . . . . . . . . . . . . . . . . . . 32

3.11 Line width of rocking curve (FWHM) of the (002) reflex of cubic GaN

epilayers grown on 3C-SiC(001) substrates versus thickness of the GaN

epilayers..................................... 34

3.12 Schematic sketch of an AlGaN/GaN heterostructure . . . . . . . . . . . . 35

3.13 RHEED intensity measured during initial growth of c−Al0.25Ga0.75N.

The RHEED intensity after opening the N shutter yields the amount of

excess Ga on the c-GaN surface. After opening the Al shutter RHEED

intensity oscillations are observed indicating a two-dimensional growth

mode with a rate of 177 nm/h. . . . . . . . . . . . . . . . . . . . . . . . 37

3.14 Reciprocal space map of the c-GaN (-1-13) reflex of sample 1117. The

c-AlGaN layer is pseudomorph to the c-GaN buffer layer. The Al-mole

fractionisx=0.3 ............................... 38

3.15 Reciprocal space map of the c-GaN (-1-13) reflex of sample 1360. The

c-AlGaN layer is relaxed to the c-GaN buffer layer. The Al-mole fraction

isx=0.7 .................................... 39

3.16 XRD rocking curve of the (002) reflex of sample 1117. The full width at

half maximum of the c-GaN and the c-AlGaN layer are nearly identical. . 40

3.17 Relation between the Al mole fraction x of c- AlxGa1−xN and the ratio

of Al-flux to the total metal flux for films grown under 1ML Ga-coverage.

The mole fraction x was determined by HRXRD. . . . . . . . . . . . . . 41

3.18 RMS surface roughness of different c-AlxGa1−xN/GaN heterostructures

with an Al mole fraction between x=0 and x=1. Layers were grown with

a 1 ML Ga coverage. The line is a guide for the eyes. . . . . . . . . . . . 42

vi List of Figures

4.1 Schematic Sketch of a multiple quantum well structure . . . . . . . . . . 44

4.2 Measured ω−2Θ scan of a 15-fold Al0.3Ga0.7N/GaN structure (solid line)

and simulated data (dotted line). The well and the barrier width are 3

nmand6nm.................................. 45

4.3 Reciprocal space map around the asymmetric (-1-13) reflex of sample

1372. The quantum wells are pseudomorph to the c-GaN buffer. . . . . . 46

4.4 Room temperature photoluminescence of cubic Al0.15Ga0.85N/GaN sin-

gle and multiple quantum well structures. The QW transition energy is

E=3.30 eV and the linewidth is 90 meV for the SQW and 103 meV for

theMQW.................................... 47

4.5 Low temperature photoluminescence of cubic Al0.15Ga0.85N/GaN SQW

and MQW structures. The QW transition energy is E=3.33 eV and 3.35

eV and the linewidth is 64 meV and 80 meV, respectively . . . . . . . . . 48

4.6 Schematic view of a quantum well without and with built-in field. Elec-

trons and holes are localized in opposite corners leading to a red-shift of

the lowest transition and to a reduction of the oscillator strength compared

to the flat band case in the cubic system [53]. . . . . . . . . . . . . . . . 49

4.7 Energy difference of cubic and hexagonal AlGaN/GaN QWs as a function

of well width [54]. The full curve for the cubic QWs was calculated using

the self-consistent Poisson-Schr¨

odinger model [55]. The hexagonal QWs

show a red-shift of the transition energy below the band gap of hexagonal

GaN....................................... 50

5.1 Schematic sketch of an intersubband transition in the conduction band

after absorption of a photon with equal energy to the difference between

the ground state E0and the first excited state E1[70]. .......... 54

5.2 The (a) bound-to-bound, (b) bound-to-quasi-bound and (c) bound-to-

continuum transitions of electrons in the conduction band are depicted. . 55

5.3 Band gap of AlxGa1−xN and the conduction band offset of GaN/AlxGa1−xN

as a function of the Al mole fraction. . . . . . . . . . . . . . . . . . . . . 56

List of Figures vii

5.4 Schematic sketch of transitions in quantum wells with different well thick-

nesses. The blue curve indicates case (a) the red curve case (b) and the

greencurvecase(c)[70]............................ 57

5.5 Typical quantum well design structure with two bound states. Quantum

wells are shown without bias voltage on the left side and with applied bias

voltageontherightside............................ 58

5.6 Mesa structure of a typical quantum well infrared photo detector. A bias

voltage is supplied and a photocurrent is measured. . . . . . . . . . . . . 59

5.7 Transition energies of AlN/GaN multiple quantum well versus the QW

thickness calculated by a self-consistent Poisson-Schr¨

odinger model. . . . 60

5.8 Schematic sketch of an AlN/GaN MQW structure for intersubband tran-

sitions. The thicknesses of the wells vary between 1.3 and 1.9 nm, the

thickness of the barriers is 1.5 nm. . . . . . . . . . . . . . . . . . . . . . . 61

5.9 RHEED timescan of sample 1518 on an extended scale. The shutter se-

quence and the coverage of 1 ML during c-GaN growth is indicated in the

figure. ..................................... 62

5.10 RHEED intensity versus time during the growth of an AlN/GaN super-

lattice of sample 1518. The Fig. shows the RHEED intensities of period

2 and 3 and of period 18 and 19. The shaded area indicates the growth

of the individual layer. The scans are vertically shifted for clarity. . . . . 63

5.11 ω-2Θ scan and simulated data of the (002) reflex of sample 1518. The

sample consists of a 20-fold AlN/GaN MQW structure. The simulation

reveals a barrier thickness of 1.35 nm and a QW thickness of 1.75 nm. . . 64

5.12 An SEM image of a waveguide with approximately 2 mm width and 5 mm

length[70]. .................................. 66

5.13 Illustration of light propagating through a waveguide. . . . . . . . . . . . 66

5.14 Room-temperature absorbance spectra of 4 AlN/GaN MQW structures

and of a substrate. Absorption was observed in the range of 0.6 eV to 0.8

eV (1.6 µm to 2 µm). The spectra are vertically shifted for clarity. . . . . 67

viii List of Figures

5.15 Intersubband absorption of four AlN/GaN MQWs. The spectra are plot-

ted after subtraction of the substrate background in the spectral range

between 0.5 eV and 1.1 eV (1.1 µm and 2.5 µm). A shaded area indicates

the wavelength of 1.55 µm. The FWHM of all samples is about 200 meV. 68

5.16 Simulation of the conduction band of sample 1518. Two bounded states

are observed within the quantum well. The shaded area indicates the

distribution of the first excited state E1. .................. 69

5.17 Transition energies of AlN/GaN multiple quantum wells versus the QW

thickness as shown in Fig. 5.7. The experimental data show good agree-

ment with the calculated data. . . . . . . . . . . . . . . . . . . . . . . . . 70

1 Introduction

In the last decade, the group III-nitrides AlN, GaN, InN and their alloys have become

one of the most important classes of semiconductor materials. In particular, GaN and

Ga-rich InxGa1−xN, and AlxGa1−xNthin films are used in a variety of commercial op-

toelectronic devices, including green and blue light emitting diodes (LEDs) and lasers

[1]. By combining UV-emitting GaN LEDs with phosphor it is possible to fabricate high

efficiency white light emitters which are predicted to play a crucial role in future high-

efficiency home and commercial lighting systems [2]. Group III-nitrides have also found

application in other electronic devices. For example, advanced GaN/AlGaN high-power

microwave transistors are now commercially available.

Group III-nitrides crystalize in the stable wurtzite (hexagonal) structure or in the meta-

stable zinc blende (cubic) structure. An important difference between these material

modifications is the presence of strong internal electrical fields in hexagonal III-nitrides

grown along the polar (0001) c-axis, while these “built-in“ fields are absent in cubic

III-nitrides.

These “built-in“ polarization-induced electric fields limit the performance of optoelec-

tronic devices which employ quantum well active regions. Especially the spatial sepa-

ration of the electron and hole wave functions caused by the internal fields reduces the

oscillator strength of transitions and limits the recombination efficiency of the quantum

wells [3]. To solve this problem, much attention has been given to the growth of wurtzite

structures with nonpolar orientations, e.g., growth along the a,mand Rdirections

[4][5][6].

Because of their higher crystallographic symmetry cubic nitrides grown in (001) direction

21 Introduction

offer an alternative way to produce nitride based quantum structures that are unaffected

by internal polarization fields. The zinc blende III-N are metastable and can only be

grown in a very narrow window of process conditions [7]. However, the use of nearly

lattice matched, freestanding high quality 3C-SiC substrates led to substantial improve-

ments of the crystal quality of c-III nitrides [8].

Group III-nitrides are usually grown by two different techniques, either metal-organic

chemical vapor deposition (MOCVD) or molecular beam epitaxy (MBE). All samples

included in the present work were grown by plasma-assisted molecular beam epitaxy

(PAMBE) where the chemically inert nitrogen molecule is activated by a plasma dis-

charge.

As an important step to further improve the c-GaN surface morphology in a systematic

way, it is essential to understand the surface structure and the underlying growth pro-

cess on an atomic scale. Investigations of the impact of growth temperature and surface

stoichiometry on epilayer deposition are the strength of MBE due to its in situ tools,

such as reflection high energy electron diffraction (RHEED). This technique has become

extremely valuable for the understanding of growth mechanisms of thin films.

The present work is structured in five main parts. A short introduction is given in chapter

1. In the first part of chapter 2 the basic properties of III-nitrides especially the difference

between hexagonal GaN grown along the (0001) direction and cubic GaN grown along

the (001) direction are summarized. In the second part of chapter 2 the growth technique

(molecular beam epitaxy, MBE) and the characterization methods used for this work are

described. Chapter 3 gives an overview of the structural properties (dislocation density,

roughness) of c-GaN and c-AlGaN. The growth of these structures was optimized using

reflection high energy electron diffraction (RHEED) as an in situ control method. Op-

timum growth conditions were achieved using a well defined Ga coverage during c-GaN

epitaxy. Chapter 4 describes the growth and the properties of c-AlGaN/GaN Quantum

Wells (QWs). These structures find their application as ultraviolet emitters in the 250

nm to 400 nm range. AlN/GaN superlattices can be used as infrared detectors in the

1µm to 3 µm range. The growth of AlN/GaN superlattices as well as their structural

and optical properties are described in chapter 5. First intersubband transitions in the

1 Introduction 3

near infrared region were observed with c-III-nitrides. Finally the conclusions are given

in chapter 7.

41 Introduction

2 Fundamentals

This chapter begins with a brief introduction of the most important differences between

hexagonal and cubic structures. Firstly, the impact of the huge spontaneous and piezo-

electric polarization fields on radiative recombination from quantum wells is discussed.

Secondly, a description of the molecular-beam epitaxy (MBE) system used for growth is

given followed by a description of the characterization methods which have been used.

2.1 Properties of III-nitrides

Group III-nitrides crystallize in the stable hexagonal (wurtzite) structure or in the

metastable cubic (zincblende) structure. Figure 2.1 shows a ball-and-stick model of

these two structures. The unit cell of the cubic and the hexagonal structure is shown in

Fig. 2.1 a) and b).

In both cases, each group-III atom is tetrahedrally coordinated to four nitrogen atoms.

The main difference between these two structures is the stacking sequence of closed

packed diatomic planes. The stacking sequence is ABABAB along the wurtzite (0001)

direction and ABCABC along the zincblende (111) direction.

Due to non-centro-symmetric configuration and ionic binding, the hexagonal nitrides

exhibit large piezoelectric effects under strain along the c-direction and spontaneous

polarization at hetero-interfaces. The genesis of the polarization is two-fold: the piezo-

electric effects and the difference in spontaneous polarization between AlN, GaN, and

InN even in the absence of strain.

62 Fundamentals

Figure 2.1: Unit cell of a) the zincblende structure and b) the hexagonal structure.

Polarization depends on the polarity of the crystal, namely whether the bonds along

the c-direction are from cation (Ga) sites to anion (N) sites or vice versa. As can be

seen in Fig. 2.2, the basal surface of GaN is either Ga-faced or N-faced (also known as

Ga-polarity and N-polarity), which means that the top position of a [0001] surface is

either gallium or nitrogen, respectively.

The polarity of the crystal gives rise to an internal electric field due to the interaction

between Ga cation and N anion, which is called polarization field. If strain exists in the

system, it will modify the electric field by changing the spacing between the Ga plane

and the N plane. This strain-induced additional electric field is called piezoelectric field.

On the contrary, zincblende (cubic) GaN has a symmetric configuration along the (001)

growth direction, where the polarization fields are absent.

Due to the polarization field difference in GaN and InGaN, or GaN and AlGaN, band

diagram and carrier distribution will be influenced by these electric fields. In the case of

AlGaN/GaN quantum wells, the band profile and carrier distribution difference in the

cubic and hexagonal configuration is shown in Fig. 2.3 a) and b).

In hexagonal AlGaN/GaN the polarization field in AlGaN and GaN wells results in a

net electric field EGaN , which makes the tilt of the GaN energy gap in the band profile

2.1 Properties of III-nitrides 7

Figure 2.2: Different polarities in hexagonal GaN

and separates the electron and holes to the two opposite sides of the well. This results

in a lower transition energy of the electron from the conduction band to the valence

band. The wave function overlap also decreases with increasing well thickness. This

effect degrades the emission intensity with increasing the well thickness. Both effects

are called the quantum confinement Stark effect (QCSE). Bai et al. have studied the

dependency of PL intensity with the well thickness [9]. They found that the PL intensity

decreases monotonically with the well thickness. The intensity will totally quench with a

well thickness above 5 nm. The optimum GaN well thickness in h-AlGaN/GaN multiple

quantum wells is 2-3 nm [1] [10]. Chichibu et al. have shown that the polarization field

is inactive in cubic polytypes by time-integrated and time-resolved PL measurements

on cubic InGaN/GaN MQWs [11]. The same properties described above also apply to

InGaN/GaN quantum wells. Therefore it can be expected that cubic III-nitrides will

have a different PL intensity dependence on the well thickness, which is an advantage

for the fabrication of cubic III-nitride based devices.

82 Fundamentals

GaN AlGaNAlGaN GaN AlGaNAlGaN

b)a)

Figure 2.3: Band profiles and carrier distributions in cubic and hexagonal AlGaN/GaN

quantum wells; a) the cubic AlGaN/GaN DH structure and b) the hexagonal

AlGaN/GaN DH structure

2.2 Epitaxial growth techniques

Group III-nitrides are usually grown by two different techniques, either metal-organic

chemical vapor deposition (MOCVD) or molecular beam epitaxy (MBE). In the following

the MBE growth process will be reviewed to provide the reader with an understanding

of this growth process which relate on the materials under investigation.

2.2.1 Molecular beam epitaxy

Molecular beam epitaxy (MBE) is an advanced deposition technique which is performed

in ultra-high vacuum. With MBE, atoms are delivered to a substrate through an ultra-

high vacuum atmosphere (<10−9mbar). This atmosphere allows the atoms to reach the

substrate without colliding with other atoms or molecules. The heated substrate surface

allows the arriving atoms to arrange themselves across the surface forming an almost

perfect crystal structure. Through the use of shutters and precise control of the effusion

2.2 Epitaxial growth techniques 9

cell temperatures almost any material composition and doping can be achieved.

All cubic III-nitride structures used for this work were grown by MBE in a Riber 32

system equipped with an Oxford Applied Research HD25 radio frequency plasma source

for activated nitrogen atoms. Figure 2.4 shows a schematic sketch of our MBE system.

Figure 2.4: Schematic cross section of an MBE setup.

A liquid nitrogen-cooled shroud is used to enclose the entire growth area in order to

minimize any residual vapor in the vacuum chamber during growth. To improve the

uniformity of the layer deposition, the substrate holder can be rotated. A Bayard-Alpert

gauge mounted on the back of the substrate manipulator is used to measure the beam

equivalent pressure (BEP) of the element species in the effusion cells. The MBE is

equipped with 4 ABN 35 standard effusion cells which are used for the evaporation of

Ga, Al, In and Si. The temperatures of these cells are measured by thermocouples at the

bottom of a pyrolytic boron nitride (PBN) crucible. The purity of the source material is

99.9999 %. The plasma source for activated nitrogen atoms is water-cooled and operates

with an inductive coupled radio frequency (RF) of 13.65 MHz at 130-260 W. Typical

flow rates of the N2gas were 0.2-0.4 sccm, resulting in N-background pressure of about

2·10−5mbar. More details about MBE are given in Ref. [12].

10 2 Fundamentals

A significant part of nitride growth by MBE is the ability to monitor the growing sur-

face in situ using Reflection High Energy Electron Diffraction (RHEED). RHEED is

limited to high vacuum conditions which restricts its use for other growth techniques,

e.g. MOCVD. A high energy electron beam (10-20 keV acceleration voltage) is directed

at a grazing angle (1-2◦) onto the substrate surface. The diffracted beam is forward-

scattered to a fluorescence screen. The resulting diffraction pattern on this screen is a

superposition of the contribution of electrons that have been scattered from atomically

flat regions of the crystal and those that have been transmitted through asperities rising

above the surface. Thus, the formed diffraction pattern gives information about the

symmetry and periodicity of ordered layers near the surface and the position of atoms

within the unit cell. Figure 2.5 shows a schematic diagram of the RHEED diffraction

geometry showing reflection (2D) and transmission (3D), as well as the straight-through

or (0,0) beam.

Figure 2.5: Schematic diagram of the RHEED diffraction geometry, showing reflection

and transmission diffraction, as well as the straight-through (0,0) beam.

The observed RHEED-pattern can be used to monitor the growth dynamics in real

time. RHEED is therefore capable of measuring intensity oscillations of the diffraction

pattern. These RHEED intensity oscillations can be measured on the specular reflected

2.2 Epitaxial growth techniques 11

spot in the RHEED-pattern. In our case RHEED intensity oscillations were used to mea-

sure the growth rate of c-AlGaN and c-AlN. Furthermore, the in-plane lattice parameter

of the growing surface can be determined. Figure 2.6 shows a typical RHEED-pattern of

a c-GaN surface. The pattern shows a (2×2) reconstruction during growth interruption.

(0,-1) (0,0) (0,1)

Δk

Figure 2.6: Typical RHEED-pattern of c-GaN during growth interruption. A (2 ×2)

reconstruction of the (-110) azimuth is observed.

The distance ∆kbetween the (0,-1) and the (0,1) reflex is inverse proportional to the

in-plane lattice parameter of the growing layer. This offers the possibility to measure

the distance ∆kquasi continuously during growth. Therefore this technique enables

the in situ study of the relaxation process of strained epilayers on lattice mismatched

substrates. Details about RHEED are given in [13].

Using the reflected high energy electron beam as a probe, we developed a method which

allows to measure the Ga-coverage of the GaN surface during growth with submonolayer

accuracy. Details are given in chapter 3.

12 2 Fundamentals

2.3 Characterization methods

2.3.1 High resolution X-ray diffraction

High resolution X-ray diffraction (HRXRD) is a powerful tool for the non-destructive

ex situ investigation of epitaxial layers, heterostructures and superlattice systems. The

information obtained from diffraction patterns concerns the composition and uniformity

of epitaxial layers, their thickness, the built-in strain, the strain relaxation and the

crystalline perfection related to their dislocation density.

For a single crystal the diffraction of X-rays can be described by the Bragg equation [14].

λ= 2 ·dhkl ·sin Θ (2.1)

The triplet (hkl) denotes the Miller indices, and dhkl is given by

dhkl =a0

√h2+k2+l2(2.2)

dhkl is the spacing of the lattice planes, a0is the lattice constant, λis the wavelength

of the X-ray radiation and Θ is the incident angle of the radiation. Details of X-ray

diffraction can be found in references [15], [16], [17].

It is a convenient and common way to describe X-ray diffraction in reciprocal space.

The reciprocal lattice is formed by the terminal points of reciprocal repetition vectors

b1,~

b2and ~

b3which are related to the primitive vectors of crystal lattice ~a1,~a2and ~a3by:

bi= 2 ·π·~aj×~ak

~a1·(~a2×~a3)i, j, k cycl. (2.3)

In reciprocal space the plane with the Miller indices (hkl) is described by the reciprocal

vector which is given by

Ghkl =h·~

b1+k·~

b2+l·~

b3(2.4)

2.3 Characterization methods 13

The condition of diffraction in equation 2.1 by the plane (hkl) can be transferred in

reciprocal space (see for example [15]) in the form:

Q=~

Ghkl (2.5)

Qis the scattering vector defined as ~

Q=~

kε−~

kδwhere ~

kεand ~

kδare the wave vectors

of incident and diffracted waves as indicated in Fig. 2.7.

Figure 2.7: Sketch of the diffraction geometry. The exact Bragg condition for (hkl) planes

is fulfilled, if the scattering vector ~

Qends at a reciprocal lattice point (hkl).

Thus, in reciprocal space the diffraction plane is represented as a reciprocal lattice

point and the diffraction geometry defined by the incident and by the detection angles

is represented by the scattering vector. When the scattering vector ends at a reciprocal

lattice point (hkl) the exact Bragg condition is fulfilled. Scattered X-ray intensity around

a reciprocal lattice point (RLP) is strongly influenced by the structural properties of the

crystalline material. Therefore the measurements and detailed analysis of diffracted

intensity around reciprocal lattice points is the subject of high resolution diffractometry.

14 2 Fundamentals

The variation of the incident beam allows to analyze different crystal properties. Three

types of measurements are performed: ω−2Θ scans, ωscans and two dimensional

intensity distributions in reciprocal space, e.g. Reciprocal Space Maps (RSM).

•ω−2Θ scans

This kind of scan allows measurements where the angular rotation speed of the

detector is twice that of the incident angle. The detector angle moves along a

reciprocal lattice vector. With this kind of scan geometry it is possible to get

information on lattice parameter and chemical composition of epitaxial layers.

•ωscans

In this configuration the detector angle is fixed and the sample is rotated. In

symmetrical scan geometry the ωscan is perpendicular to a ω−2Θ scan if one

describes this in reciprocal space. Using ωscans, also called rocking curve, it is

possible to get information about the layer quality and the dislocation density [32].

•Reciprocal Space Maps (RSM)

A RSM is a combination of ωscans and ω−2Θ scans. The result is a two di-

mensional distribution of intensity in reciprocal space. Using different kinds of

measurements it is possible to get information about the strain status and the

chemical composition.

For this work, a Phillips X´Pert Diffractometer was used with a copper anode emitting

the Kα1radiation of λ= 1.54056 ˚

Aand the Kα2radiation of λ= 1.54444 ˚

A. The tube

is equipped with a line focus and a hybrid monochromator, which guarantees a beam

divergence of 47 arcsec. The monochromator consists of a graded parabolic mirror in

connection with a (220) channel-cut Germanium crystal. The mirror parallelizes the

beam and the Germanium crystal blocks the Kα2line. The samples are mounted onto

an Euler cradle which allows an independent variation of the angle of incident ω, the

diffraction angle 2Θ, the rotation around the surface normal φand the incident axis ψ,

as well as a linear motion in the three directions x, y and z. A schematic sketch of the

diffractometer is shown in Fig. 2.8.

2.3 Characterization methods 15

Figure 2.8: Schematic drawing of the Phillips X´Pert MRD consisting of X-Ray tube,

hybrid monochromator, Euler cradle and detector.

The measurements were performed in double axis configuration using a 1◦

16 slit in front

of the detector resulting in a resolution of 1.8 arcmin. Another configuration is the so

called triple axis configuration where a second (220) Germanium crystal is placed in

front of the detector. The resolution in triple axis configuration is 0.084 arcmin.

2.3.2 Atomic force microscopy

Atomic force microscopy (AFM) offers a way to get information about the surface mor-

phology of epitaxial layers. This method allows measuring the surface roughness on an

atomic scale.

Figure 2.9 shows the schematic diagram of an AFM setup. A tip consisting of SiN is

mounted at the end of a cantilever.

The tip is moved towards the investigated surface so that only atomic forces are

relevant. The tip is approached to the surface by piezoelements and then starts scanning

the surface. The distance between the tip and the surface will be held constant by

theses piezoelements and an optical measurement yields the height profile. A laser beam

is focused on top of the tip where it is reflected and detected with a photo diode which

is sensitive to changing positions. If the tip is linked during scanning the position of the

laser beam on the photo diode will change. The amplitude is proportional to the surface

morphology.

16 2 Fundamentals

Figure 2.9: Schematic drawing of an AFM setup.

Surface Roughness

A quantity for the roughness is the so-called Root Mean Square (RMS) roughness. The

RSM in one dimension is defined as

RMS ="1

LZL

(z(x)−¯z)2·dx#1

(2.6)

where L is the scan width, z(x) the line profile and ¯zis the median value of the height.

However, the roughness is not determined in real space, it is determined via Fourier

transformation in frequency space. In frequency space the RMS is

RMS ="ZL2

P(f)·df#1

(2.7)

P is the power spectral density, which is defined as the square of the Fourier trans-

formed line profile. For the line profile z(x) follows

P(f) = 1

LZL

e−i·2·π·f·x·z(x)·dx

(2.8)

As the topography of the scanned area is 2-dimensional and consists of discrete data

2.3 Characterization methods 17

points the power spectral density in two dimensions is calculated by the Fast-Fourier

Transformation (FFT) [18].

2.3.3 Luminescence spectroscopy

Luminescence is the emission of electromagnetic radiation in excess of thermal radiation.

In general the high energy part of the spectrum is determined by the gap energy of the

semiconductor. Excitation of the luminescent material is necessary to achieve radiative

recombination of excess carriers. The luminescence is specified according to the mode of

excitation. Three types of excitation for semiconductors are listed below.

•Photoluminescence (PL), excited by incident photons, e.g. a LASER

•Cathodoluminescence (CL), excited by incident electrons, e.g. a scanning electron

microscope which allows position-sensitive measurements.

•Electroluminescence (EL), excited by application of an electric field, e.g. a power

supply

After excitation the carriers in the semiconductor are in a non-equilibrium state. To

achieve thermal equilibrium carrier recombination processes have to occur and radiative

recombination results in light emission. Different optical properties can be observed [19]

[20] [21]. In bulk semiconductors different kinds of optical transitions are present. In

films of high purity, e.g. intrinsic semiconductor band to band (e,h) and free exciton (X)

transitions are dominating. A schematic drawing of the various radiative recombination

processes leading to emission in semiconductors is shown in Fig. 2.10.

The most common radiative transitions in c-GaN are described below and for example

in references [22], [23], [24], [25].

Band to band (e, h) transitions are described by the difference of the conduction and

the valence band edges where an electron from the conduction band recombines with a

hole in the valence band.

The free exciton transition (X) is important in photoluminescence and is a typical indica-

18 2 Fundamentals

Figure 2.10: Schematic diagram of radiative transitions in a semiconductor; (e, h) rep-

resents intrinsic band to band, (X) free exciton,(D0, X), (A0, X) represents

bound excitons to donator or acceptor and (D0, h),(h, A0) free to bound,

(D0, A0) donor to acceptor transitions.

tor for a high sample quality. In case of a high-purity semiconductor the Coulomb inter-

action between the generated electron and hole can bind them into the quasi-hydrogenic

exciton. High doping or defect levels can reduce the probability of exciton formation,

because the free charges tend to screen out the Coulomb interaction.

Donor to acceptor transition (D0, A0) occurs when a semiconductor is doped or an im-

purity related level is introduced. According to the hydrogen model the binding energy

ED(EA) of the electron (hole) to the donor (acceptor) impurity can be estimated with

the effective mass approximation.

The PL setup used for this work enables the realization of temperature- and intensity-

dependent measurements. A sketch of the PL setup is given in Fig. 2.11.

The luminescence was excited by the 325 nm (3.81 eV) line of a continuous-wave

single-mode HeCd laser with an output power of about 4 mW. The laser plasma lines

were suppressed by an interference filter. The laser light was then focussed onto the

mirror reflecting the light onto the sample. The PL signal was dispersed by a grating

monochromator and detected using a GaAs photomultiplier and a photon counting sys-

2.3 Characterization methods 19

Figure 2.11: Schematic diagram of the photoluminescence setup.

tem. A computer system served for data collection and visualization. A He bath cryostat

allowed temperature-dependent measurements in the range from T=2 - 300 K.

20 2 Fundamentals

3 MBE of cubic GaN and cubic AlGaN

In this chapter, the synthesis of cubic GaN layers on free standing 3C-SiC (001) substrates

is discussed. These layers serve as buffer for subsequent growth of heterostructures and

quantum structures. Hence, the simultaneous accomplishment of a high morphological

and structural quality of the GaN layer is required in order to realize heterostructures

with smooth interfaces and low dislocation densities.

3.1 In situ growth regime characterization of cubic GaN

using reflection high energy electron diffraction

3.1.1 Adsorption and desorption of Ga on c-GaN

As an important step to improve the c-GaN surface morphology in a systematic way, it is

essential to understand the underlying growth process on an atomic scale. In particular,

the kinetics of adsorption and desorption on the surface are considered as key param-

eters that govern the surface morphology, incorporation kinetics and consecutively the

overall material quality. In molecular beam epitaxy of hexagonal GaN, two-dimensional

surfaces are commonly achieved under slightly Ga-rich conditions with theoretical [26]

and experimental [27], [28] evidences suggesting that the growth front is stabilized by a

metallic adlayer. The optimum growth conditions for the epitaxial growth of c-GaN are

mainly determined by two parameters, the surface stoichiometry and the substrate tem-

perature [7]. Both parameters are interrelated; therefore an in situ control of substrate

22 3 MBE of cubic GaN and cubic AlGaN

temperature and surface stoichiometry is highly desirable. The study of the surface

reconstruction by RHEED was one of the key issues in understanding the c-III-nitride

growth [7], [22], [29]. First principle calculations by Neugebauer et al. [30] show that all

energetically favoured surface modifications of the nonpolar (001) c-GaN surface are Ga

stabilized and therefore optimum growth conditions are expected under slightly Ga-rich

conditions. It is shown quantitatively that a 1 monolayer (ML) Ga-coverage favours

two-dimensional growth and yields c-GaN layers with a minimum surface roughness [31].

Cubic GaN layers used for the RHEED experiments were grown under Ga-rich condi-

3C-SiC

c-GaN

d=800nm

T=720°C

reflected

electron beam

(2 x 2) reconstruction during

growth interruption (-110)

Recorded RHEED intensity

(0,-1) (0,0) (0,1)

a) b)

Figure 3.1: a) A sketch of the sample structure with the RHEED geometry. b) A (2 ×

2) reconstruction of a c-GaN surface during growth interruption. The red

rectangle indicates the area where the RHEED intensity was recorded.

tions [32] on 3C-SiC (001) substrates [33]. The substrates were chemically etched and

backcoated with silicon for efficient heat incoupling. Prior to growth the substrates were

subjected to an Al deoxidation process at TS= 800◦Cusing Al BEP of 8 ×10−8mbar

in order to remove native oxides. The substrate temperature during growth was kept

constant at TS= 720◦C. The adsorption and desorption of metal Ga layers on the

3.1 In situ growth regime characterization of cubic GaN 23

0.4

0.6

0.8

0 50 100 150 200 250

intensity (a.u.)

time (s)

Ga open Ga close Ga flux

60sec

Tsubs=720°C

4.3 x 1014 cm-2s-1

3.4 x 1014 cm-2s-1

4.7 x 1014 cm-2s-1

2.0 x 1014 cm-2s-1

2.5 x 1014 cm-2s-1

7.5 x 1013 cm-2s-1

Figure 3.2: The intensity of a reflected high energy electron beam (RHEED intensity)

versus time measured during the evaporation of Ga onto c-GaN at a substrate

temperature of TS= 720◦C. The Ga-fluxes are indicated. The spectra are

normalized to one and vertically shifted for clarity.

c-GaN surface was investigated using the intensity of a reflected high energy electron

beam (short RHEED intensity) as a probe. The transient of the RHEED intensity of the

(0,0) streak was recorded versus time. A sketch of the sample structure and the RHEED

geometry is given in Fig. 3.1 a). Figure 3.1 b) shows a RHEED pattern of the (-110)

azimuth of a c-GaN surface with a (2 ×2) reconstruction. The picture was taken during

growth interruption. The red window indicates the area of the (0,0) streak where the

RHEED intensity was recorded.

The calibration has been performed as follows: All experiments used for the RHEED

24 3 MBE of cubic GaN and cubic AlGaN

intensity observations were started on a Ga-free c-GaN surface established by a 5 min

growth interruption. After 5 min the c-GaN surface was exposed to different Ga-fluxes

for 60 s. Figure 3.2 shows the variation of the RHEED intensity versus time measured

after exposing c-GaN at TS= 720◦Cto Ga fluxes between 7.5×1013 cm−2s−1and

7.5×1014 cm−2s−1. For the lowest flux of 7.5×1013 cm−2s−1no change in the RHEED

intensity was observed indicating the re-evaporation of Ga from the surface. At higher

0.20

0.40

0.60

0.80

1.00

1.20

0 50 100 150 200

RHEED intensity (a.u.)

time (s)

TS=720°C

Ga on Ga off

kink

FGa=7.5x1014 cm-2s-1

FGa=4.3x1014 cm-2s-1

Figure 3.3: RHEED intensity transient for a Ga-flux of FGa = 4.3×1014 cm−2s−1and

7.5×1014 cm−2s−1.

fluxes ≥2.5×1014 cm−2s−1the RHEED intensity exhibits a clear drop after the Ga shut-

ter was opened. In the following, we discuss the adsorption kinetics in more detail. After

opening the Ga shutter we observe a steep decrease of the RHEED intensity between I0

and a kink position (Ik) which is clearly visible in Fig. 3.3. We would like to point out

that the kink position is always at the same relative intensity for Ga-fluxes exceeding

4×1014 cm−2s−1. The further decrease of the RHEED intensity below Ikhas a different

gradient. After closing the Ga shutter an increase of the RHEED intensity is observed

3.1 In situ growth regime characterization of cubic GaN 25

0.70

0.80

0.90

1.00

1.10

19 20 21 22 23 24 25

RHEED intensity (a.u.)

FGa=7.5x1014 cm-2s-1

open Ga shutter TS=720°C

time (s)

Δtk

FGa=4.3x1014 cm-2s-1

Δtk

1 ML

0 ML

Figure 3.4: RHEED intensity transients for Ga-fluxes of 4.3×1014 cm−2s−1and 7.5×

1014 cm−2s−1. After a transition time ∆tka kink in the transients is observed.

The estimated Ga-coverage is plotted on the right side.

which is due to desorption of accumulated Ga. Again two different slopes which change

at Ikare observed. The last desorption stage corresponds to the desorption of a fixed

amount of Ga and this amount seems to be identical to that adsorbed during the time

the intensity reached the kink. Finally the RHEED intensity reaches the starting value

I0indicating a Ga-free surface. Figure 3.4 shows the RHEED intensity on an extended

scale of the two Ga-fluxes shown in Fig. 3.3 just after opening the Ga shutter. A linear

decrease of the RHEED intensity during the time interval ∆tkup to the kink position

Ikis observed. The gradient of the RHEED intensity drop is related to the impinging

Ga-flux and is inverse proportional to the Ga flux.

In order to explain these adsorption kinetics we assume first a certain reflectivity of

the GaN surface (I0) and a lower reflectivity of a Ga-covered surface. A linear decrease

26 3 MBE of cubic GaN and cubic AlGaN

of the RHEED intensity up to the kink position was observed and second we assume an

adsorption of a fixed amount of Ga during the time interval ∆tk. This amount seems to

be 1 monolayer (ML) based on the flux times ∆tkproduct which is equal to the number

of lattice sites on a GaN surface. Therefore we plotted the estimated Ga-coverage on the

right side in Fig. 3.4. The kink position is always at the same relative intensity for Ga

fluxes exceeding 4 ×1014 cm−2s−1. To show that our assumptions are correct we had to

develop a model which confirms the adsorption of 1 ML Ga at the kink position.

3.1.2 Kinetic model

In the preceding section we have seen a decrease of the RHEED intensity if Ga is supplied.

To understand the adsorption kinetics a model is required to account for adsorption and

desorption of Ga. Our model is described by the following equation, which takes into

account ad- and desorption of Ga.

dΘ(t)

dt =FGa −FdesΘ(t) (3.1)

where Θ(t) is the coverage of the surface, FGa is the impinging Ga-flux and Fdes is the

desorption flux which depends on the coverage of the surface. The RHEED intensity

itself was assumed to decrease linearly, due to the decreased reflectivity of a metal covered

surface.

Fig 3.5 shows one adsorption curve for a Ga-flux of 2 ×1014 cm−2s−1together with

simulations based on equation 3.1. The RHEED intensity drops to a certain value

and saturates. As shown in the figure the situation corresponds to a balance between

impinging and desorbing flux. A steady-state Ga-coverage is established at the surface

which is independent of deposition time. This can be described by eq. 3.1. For these

calculations desorption was taken into account. Three different desorption fluxes of 9.8×

1013 cm−2s−1, 1.6×1014 cm−2s−1and 1.8×1014 cm−2s−1were used for the simulation.

The desorption flux Fdes can be estimated to a value of 1.6×1014 cm−2s−1due to the

3.1 In situ growth regime characterization of cubic GaN 27

0.70

0.80

0.90

1.00

1.10

0 50 100 150

RHEED intensity (a.u.)

time (s)

TS=720°C

Ga on Ga off

FGa=2 x 1014 cm-2s-1

Fdes=1.6 x 1014 cm-2s-1

Fdes=9.8 x 1013 cm-2s-1

Fdes=1.8 x 1014 cm-2s-1

1 ML

0 ML

Figure 3.5: RHEED intensity transients for a Ga-flux of 2×1014cm−2s−1. The red curves

show the simulations for a flux of 2 ×1014 cm−2s−1and three different des-

orption fluxes as indicated in the figure. Good agreement was achieved for a

desorption flux of 1.6×1014 cm−2s−1.

good agreement between experimental and calculated data. On the right side of Fig. 3.5

the estimated values of the Ga-coverage are indicated (see Fig. 3.4). The figure clearly

shows that with Ga-fluxes below 4 ×1014 cm−2s−1it is not possible to establish a fully

Ga-covered surface.

Corresponding simulations were done for fluxes exceeding 4×1014 cm−2s−1taking the

desorption flux of 1.6×1014 cm−2s−1into account. Figure 3.6 shows the RHEED intensity

versus time for two different Ga-fluxes of 4.3×1014 cm−2s−1and 7.5×1014 cm−2s−1

together with simulations based on equation 3.1. The Ga-fluxes are the same as in

Fig. 3.4. In Fig. 3.6 the RHEED intensity decreases linearly to the kink position

Ik. The simulation also shows a linear decrease during the time interval ∆tk. Based

28 3 MBE of cubic GaN and cubic AlGaN

0.50

0.60

0.70

0.80

0.90

1.00

1.10

19 20 21 22 23 24 25

RHEED intensity (a.u.)

open Ga shutter TS=720°C

time (s)

Δtk

FGa=4.3 x 1014 cm-2s-1

Δtk

FGa=7.5 x 1014 cm-2s-1 2

Ga coverage Θ (ML)

Figure 3.6: RHEED intensity transients for two Ga-fluxes together with simulations as

indicated in the figure. Good agreement was achieved within the linear de-

crease of the RHEED intensity.

on equation 3.1, the simulation reveals a Ga-coverage of 1 ML at the kink position

(Ik). The calculated Ga-coverage Θ is indicated on the right side of Fig. 3.6. This

confirms our assumption that during ∆tk1 ML Ga is adsorbed. The further decrease

of the RHEED intensity after reaching the kink position is probably related to another

adsorption mechanism (Ga-Ga bonds), which change the reflectivity of the electron beam

most likely due to increasing interface roughness. This is not considered in our model

and therefore the simulated intensity exceeds the kink position.

Using in situ reflection high energy electron diffraction, the drop of the RHEED inten-

sity has been calibrated to allow direct measurements of the Ga-coverage. This process

established a new method to quantitatively verify the amount of adsorbed Ga on a c-GaN

surface between 0 and 1 ML taking Ikas reference.

3.1 In situ growth regime characterization of cubic GaN 29

3.1.3 Growth experiments

In case of c-GaN growth the RHEED intensity transient is different to the experiments

described above. An example is plotted in Fig. 3.7 which shows the RHEED intensity

measured after opening the Ga shutter.

0 ML coverage

1 ML coverage

0.8 ML coverage

40 50 60 70 80 90 100

RHEED intensity (a.u.)

time (s)

open Ga shutter

open N shutter

TS=720°C

Figure 3.7: RHEED intensity transients measured during the growth of c-GaN, which

started after opening the N source. The RHEED intensity measured during

growth shows the amount of excess Ga (indicated in the figure) on the c-GaN

surface. Ga-fluxes are 4.4×1014, 3.2×1014 and 1.2×1014 cm−2s−1for the

coverages of 1, 0.8, and 0 ML, respectively.

After the RHEED intensity reached the kink position, the N shutter was opened, too

(see Fig 3.7. We then observed an increase of the RHEED intensity which is due to

the formation of c-GaN. A part of the additional Ga is incorporated into the crystal.

During continuing growth the RHEED intensity saturates at a certain value. From the

30 3 MBE of cubic GaN and cubic AlGaN

saturation value the Ga-coverage can be calculated using Ikas reference. This procedure

allows measuring the Ga-coverage in the range between 0 and 1 ML with an accuracy of

0.1 ML. We reached a Ga-coverage during c-GaN growth of 0, 0.8 and 1 ML, by varying

the Ga-flux. Growth with a coverage of 0 ML is defined as stoichiometric growth, where

the incorporation of Ga and N is equal and no adsorbed Ga adlayer exists.

The influence of the Ga-coverage during growth on the surface roughness of c-GaN

is depicted in Fig. 3.8. The diagram shows the root-mean-square (RMS) roughness

measured on a 5 ×5µm2AFM scan range of several c-GaN layers versus the Ga-flux

used during MBE.

1x1014 2x1014 3x1014 4x1014 5x1014 6x1014

RMS roughness (nm)

Ga flux (cm-2s-1)

TS=720°C

0 ML

0.4 ML

0.8 ML

0.85 ML

1 ML

Figure 3.8: Root-mean-square (RMS) roughness of c-GaN layers measured by 5 ×5µm2

scans vs. Ga-flux during growth. The corresponding values of the Ga-

coverage during growth are also included. Minimum roughness is obtained

with an excess coverage of 1 ML. The line is added for better overview.

The nitrogen flux was almost identical for all samples and the thickness of these sam-

ples is about 1 µm. The corresponding values of the Ga-coverage during growth, as

3.1 In situ growth regime characterization of cubic GaN 31

measured by the procedure described above, are indicated in Fig. 3.8. Only values be-

low 1 ML can be measured, because this can be calibrated by the linear decrease of the

RHEED intensity up to the kink position. A minimum roughness of 2.5 nm is obtained

with 1 ML Ga-coverage during growth. This is in contrast to what has been observed

with h-GaN, where optimum growth conditions with regard to surface morphology are

related to the formation of Ga bilayer (cplane [34], [35] or trilayer (mplane [28])).

It has variously been suggested that excess Ga acts as surfactant during epitaxy of hexag-

onal GaN [34], [36], [37]. We believe that the data shown in Fig. 3.8 clearly demonstrate

that this effect exists also on the (001) surface of c-GaN.

The structural properties of these samples were derived from high resolution X-ray

diffraction measurements. An ω−2Θ scan of the (002) reflex of sample 1287 is de-

picted in Fig. 3.9. The reflexes at 41.2 ◦and 39.9 ◦correspond to the 3C-SiC substrate

and the c-GaN layer, respectively.

10-1

100

101

102

103

104

105

106

34 36 38 40 42

intensity (counts/s)

2Theta [°]

3C-SiC

c-GaN

500

1000

1500

2000

19 19.5 20 20.5 21 21.5

intensity (counts/s)

Omega (°)

FWHM=16arcmin

Figure 3.9: ω−2Θ scan of the (002) reflex of sample 1287. The inset shows the ω-scan

of this sample revealing a FWHM of 16 arcmin.

No additional peak of the hexagonal (0002) reflex (34.4 ◦) was detected confirming

the absence of h-GaN in growth direction. However, it is well known from c-GaN that

32 3 MBE of cubic GaN and cubic AlGaN

hexagonal inclusions mainly grow on (111) facets and cannot be detected in ω−2Θ scans

of the (002) reflex. Therefore reciprocal space maps (RSMs) of the GaN (002) Bragg

reflex were measured. The RSMs confirm the absence of hexagonal inclusions on the

(111) facets of the cubic layer. Assuming equal X-ray scattering factors of hexagonal

and cubic GaN a phase purity >99% was estimated from the measurements. In the

inset of Fig. 3.9 the rocking curve (ωscan) of sample 1287 is shown. The measured full

width at half maximum (FWHM) is about 16 arcmin. The FWHM of ωscans provides

information of the dislocation density of the film [32].

The influence of the Ga coverage during growth on the FWHM of the ωscan of c-GaN

layers is depicted in Fig. 3.10. The diagram shows the FWHM of the rocking curve of

the c-GaN samples shown in Fig. 3.8 versus the Ga-flux used during MBE.

1x1014 2x1014 3x1014 4x1014 5x1014 6x1014

FWHM RC (arcmin)

Ga flux (cm-2s-1)

TS=720°C

0 ML

0.8 ML

0.85 ML

1 ML

Figure 3.10: Full width at half maximum (FWHM) of c-GaN layers vs. Ga-flux during

growth. The corresponding values of the Ga-coverage during growth are

also included. Minimum linewidth is obtained with an excess coverage of 1

ML. The line is a guide for the eyes.

3.1 In situ growth regime characterization of cubic GaN 33

The corresponding values of the Ga-coverage during growth, as measured by the pro-

cedure described above, are also included in Fig 3.10. The diagram shows a minimum

FWHM of the rocking curve for samples grown with a 1 ML Ga-coverage. Among our

c-GaN layers with equal thickness, 16 arcmin is a minimum value. Ga-fluxes which are

equivalent to a Ga-coverage exceeding 1 ML lead to a pronounced increase of the rough-

ness (see Fig. 3.8) and the full width at half maximum of the X-ray rocking curve.

By comparing the rocking curve linewidth (ωscan) of all our cubic GaN epilayers with

the best values cited in literature, the dependence of the FWHM on film thickness has to

be taken into account. We found that the linewidth dependence indicates that a defect

annihilation process is effective during growth similar to that observed in cubic GaN

grown on GaAs (001) substrates [38]. Since in the zinc blende structure the stacking

faults (SFs) are on the (111) planes, an annihilation mechanism is possible, when two

SFs, for example on the (111) and the (-1-11) planes intersect and annihilate simultane-

ously with the creation of a sessile dislocation along the [110] direction.

The line width of the rocking curve of the (002) reflex is plotted versus the layer

thickness in Fig. 3.11 of cubic GaN epilayers. The red triangles represent our own data,

the black dots and the blue squares are data reported by Okumura [39] and Daudin

[40]. Both groups used 3C-SiC/Si (001) pseudosubstrates about 3-5 µm thick grown by

chemical vapor deposition. As can clearly be seen with improved structural properties

of the c-GaN we were able to reach and even exceed under the best cited values. In the

case of 3C-SiC, where the lattice mismatch is only -3.7% to cubic GaN, the full green

line shows the theoretically calculated FWHM as a function of layer thickness using the

dislocation glide model by Ayers [41]. This model implies that the dislocation density

Ndisl is inverse proportional to the layer thickness d and that the FWHM is proportional

to 1/d2.

The roughness of cubic GaN grown by MBE on freestanding 3C-SiC (001) substrates

was significantly reduced by growth under controlled Ga-excess conditions. A minimum

RMS roughness of 2.5 nm was achieved using a Ga-coverage of 1 ML during c-GaN

growth. Cubic GaN layers grown under these conditions on 3C-SiC substrates have

34 3 MBE of cubic GaN and cubic AlGaN

100

100 1000 104

FWHM (arcmin)

layer thickness (nm)

Okumura

Daudin

own

Figure 3.11: Line width of rocking curve (FWHM) of the (002) reflex of cubic GaN epilay-

ers grown on 3C-SiC(001) substrates versus thickness of the GaN epilayers.

narrow X-ray (002) rocking curves (16 arcmin) indicating also a low density of extended

defects in these layers. Since the method described above yields the best structural

quality of c-GaN epilayers, it was used for the growth process in all further samples.

3.2 Growth and characterization of cubic AlGaN/GaN heterostructures 35

3.2 Growth and characterization of cubic AlGaN/GaN

heterostructures

After optimizing the c-GaN buffer layer, we focus on growth and structural properties

of cubic AlGaN. AlGaN is used as barrier layer in AlGaN/GaN quantum well structures

and high electron mobility transistors (HEMTs). For the realization of distributed Al-

GaN/GaN bragg reflectors (DBR) high quality AlGaN is required. For the fabrication

of optoelectronic or electronic devices it is essential to realize AlxGa1−xN epilayers with

a well-defined Al mole fraction x which determines e.g. the barrier height of hetero-

junctions and quantum wells. Therefore a series of heterostructures was grown to check

strain, dislocation density, mole fraction and roughness of these heterostructures. The

structural parameters were determined by HRXRD and AFM.

A sketch of the grown AlGaN/GaN heterostructures is depicted in Fig. 3.12. On top

of a c-GaN buffer an AlxGa1−xN layer with a thickness between 50 and 400 nm was

deposited. The mole fraction of the AlGaN film was varied between x=0.15 and x=0.74.

3C-SiC

c-GaN

c-AlxGa1-xN

T=720°C

d=800nm

T=720°C

d=50…400nm

Figure 3.12: Schematic sketch of an AlGaN/GaN heterostructure

The influence of the Ga-coverage on the AlGaN surface during growth was also inves-

tigated.

Firstly we will focus on the adjustment of the metal fluxes needed for the growth of c-

36 3 MBE of cubic GaN and cubic AlGaN

AlGaN. As known from the growth of c-GaN, optimum growth conditions were achieved

with a well defined Ga-coverage of 1 ML during growth. This knowledge will be trans-

ferred to the growth of AlGaN. We will start with the total impinging Ga-flux for c-GaN

which is given by

Fimp

Ga,1ML(GaN) = Fimp

Ga,0ML(GaN) + F1Ml,cover

Ga =Finc

Ga (GaN)

sGa

+F1ML,cover

Ga (GaN) (3.2)

where Fimp

Ga,1ML is the impinging Ga-flux for c-GaN growth with 1 ML coverage as

described above, Fimp

Ga,0ML is the corresponding Ga-flux for stoichiometric growth (see

Fig. 3.7), F1ML,cover

Ga is the Ga-flux necessary for the formation of an additional Ga-

coverage of 1 ML during growth. Finc

Ga is the incorporated Ga-flux and sGa is the sticking

coefficient of Ga. The Ga sticking coefficient strongly depends on the growth temperature

and the value is about 0.5 for a growth temperature of 720◦C. Details are discussed in

Ref. [42]. We get the impinging Ga-flux Fimp

Ga,0ML for stoichiometric growth conditions

from Fig. 3.7. This metal flux (Fimp

Ga,0ML ·sGa =Finc

Ga ) has to be used to calculate the Al

and Ga-fluxes for AlxGa1−xNgrowth. Therefore we have to split Finc

Ga into the following

eq.

Fimp

Al (AlGaN) = x·Finc

Ga (GaN)

sAl

(3.3)

and

Fimp

Ga (AlGaN) = 1−x·Finc

Ga (GaN)

sGa

(3.4)

where x is the Al mole fraction, sAl the sticking coefficient of Al (1 for TS= 720◦C)

and Fimp

Ga,Al(AlGaN) are the Al and Ga-fluxes needed for AlGaN growth. These fluxes

are for stoichiometric AlGaN growth. For c-AlGaN we have to add the Ga-flux which

is necessary to establish a 1 ML Ga-coverage during growth, thus eq. 3.4 has to be

modified to

Fimp

Ga (AlGaN) = 1−x·Finc

Ga (GaN)

sGa

+F1ML,cover

Ga (3.5)

3.2 Growth and characterization of cubic AlGaN/GaN heterostructures 37

140 175 210 245 280

RHEED intensity (a.u.)

time (s)

open Ga

open N

open Al

c-AlGaN

TS=720°C

growth rate: 177 nm/h

0.1 ML

Figure 3.13: RHEED intensity measured during initial growth of c−Al0.25Ga0.75N. The

RHEED intensity after opening the N shutter yields the amount of excess

Ga on the c-GaN surface. After opening the Al shutter RHEED intensity

oscillations are observed indicating a two-dimensional growth mode with a

rate of 177 nm/h.

Figure 3.13 shows the RHEED intensity during initial growth of a c-AlGaN layer using

the fluxes described above (eqs. 3.3 and 3.5). When the nitrogen shutter was opened

with Ga on, an increase of the RHEED intensity was observed, indicating a Ga-coverage

of about 0.1 ML (see Fig. 3.13. This is due to the reduced Ga-flux in comparison to

pure c-GaN growth. Then the Al shutter was opened and the RHEED intensity dropped

revealing a surface coverage of about 1 ML. The increase of the coverage is given by the

additional metal flux and contains an exchange process in which the Ga incorporation

in the layer is depleted by the Al. This process is driven by the higher bond energy

of Al-N which is about EAlN = 2.88eV [43] in comparison to Ga-N bond energy of

EGaN = 2.24eV [43]. Weakly damped RHEED oscillations were observed, indicating

38 3 MBE of cubic GaN and cubic AlGaN

-2.1 -2.0 -1.9

4.0

4.1

4.2

4.3

4.4

c-Al0.3Ga0.7N

AlN

3C-SiC

(-1-13)-Reflex

#1117 AlN strained

c-GaN

q⏐⏐ [Å-1]

q⊥ [Å-1]

Figure 3.14: Reciprocal space map of the c-GaN (-1-13) reflex of sample 1117. The

c-AlGaN layer is pseudomorph to the c-GaN buffer layer. The Al-mole

fraction is x=0.3

a two-dimensional AlGaN growth at a substrate temperature of TS= 720◦Cwith a

growth rate of 177 nm/h. These are the first RHEED oscillations observed in cubic

AlGaN epitaxy.

For the growth of quantum wells it is essential to achieve the correct alloy composition.

Therefore XRD reciprocal space maps (RSMs) of the c-GaN (-1-13) reflex of different

AlGaN layers were measured to check the composition. Within these RSMs it is also

possible to measure the strain of the heterostructures. Strain is another parameter

which influences the dislocation density. With increasing relaxation of the lattice the

defect density increases. Figure 3.14 shows a RSM of the c-GaN (-1-13) reflex of sample

1117. The thickness of the c-AlGaN layer is about 100 nm. The reflexes plotted in the

figure correspond to the 3C-SiC substrate, the c-GaN buffer and the c-AlGaN layer. In

addition, the position of the Bragg reflexes of c-GaN, strained c-AlN and relaxed c-AlN

3.2 Growth and characterization of cubic AlGaN/GaN heterostructures 39

are indicated. They were calculated with the lattice parameters of 4.38 ˚

A for c-AlN. The

parameters of c-GaN and c-AlN are given in the appendix. The position of the c-AlGaN

reflex relative to the c-GaN reflex indicates that the c-AlGaN layer is pseudomorph to

the c-GaN buffer layer. The Al mole fraction of this layer is x=0.3.

The strain strongly depends on the thickness and the composition of the AlGaN layer.

Details are described in Ref. [44], [45]. With increasing thickness the strain energy

increases and with increasing Al mole fraction the critical thickness (see Ref. [45], [46])

decreases.

-2.2 -2.1 -2.0 -1.9 -1.8

4.0

4.1

4.2

4.3

4.4

4.5

AlN

3C-SiC

(-1-13)-Reflex

#1360 AlN strained

c-Al0.69Ga0.31N

c-GaN

q⏐⏐ [Å-1]

q⊥ [Å-1]

Figure 3.15: Reciprocal space map of the c-GaN (-1-13) reflex of sample 1360. The c-

AlGaN layer is relaxed to the c-GaN buffer layer. The Al-mole fraction is

x=0.7

An example for a relaxed AlGaN layer is shown in Fig. 3.15. The RSM of the c-

GaN (-1-13) reflex is plotted. The thickness of the AlGaN layer is 80 nm and the layer

is nearly relaxed. The Al mole fraction of this layer is x=0.69. With increasing mole

40 3 MBE of cubic GaN and cubic AlGaN

fraction of the AlxGa1−xNlayer the defect density also increases due to the increasing

lattice mismatch between the c-GaN buffer and the c-AlxGa1−xN layer.

Figure 3.16 shows the XRD ωscans of the c-GaN buffer and the c-AlGaN layer of

sample 1117. The c-Al0.3Ga0.7Nlayer is pseudomorph to the c-GaN buffer which means

that no more dislocations are created at the heterointerface (see Fig. 3.14). This was

confirmed by measuring the XRD ωscan of both layers.

0.5

1.5

-1.8 -0.9 0 0.9 1.8

intensity (a.u.)

Δω (°)

c-GaN

c-Al0.3Ga0.7N

FWHM=25arcmin

FWHM=26.6arcmin

(002) reflex

Figure 3.16: XRD rocking curve of the (002) reflex of sample 1117. The full width at

half maximum of the c-GaN and the c-AlGaN layer are nearly identical.

The measured values of the FWHM are 25 arcmin for the c-GaN buffer and 26.6

arcmin for the c-AlGaN layer. These values are nearly identical indicating the same

dislocation density in both layers. For relaxed AlGaN the FWHM of the XRD rocking

curve is about two times higher than in strained layers.

A series of samples was grown using a Ga-coverage of 1 ML at a substrate temperature

of 720◦C. The relation of the Al mole fraction to the flux ratio of the Al-flux to the total

metal flux is depicted in Fig. 3.17.

3.2 Growth and characterization of cubic AlGaN/GaN heterostructures 41

0 0.2 0.4 0.6 0.8 1

0.0

0.2

0.4

0.6

0.8

1.0

Al mole fraction

FAl/(FAl+FGa)

1ML

Figure 3.17: Relation between the Al mole fraction x of c- AlxGa1−xN and the ratio of

Al-flux to the total metal flux for films grown under 1ML Ga-coverage. The

mole fraction x was determined by HRXRD.

We found that the Al mole fraction x is directly proportional to the Al mole fraction

in the vapor phase for the samples grown with a 1 ML Ga-coverage, indicating that Al

is preferentially incorporated.

The RMS roughness of different AlxGa1−xN alloys versus the Al mole fraction is plotted

in Fig. 3.18. The diagram shows that the RMS roughness measured on a 5×5µm2scan

is constant with a value of about 5 nm for AlxGa1−xNin the range of x=40% to x=70%.

However, these values are slightly above the minimum value of c-GaN which may be due

to the lower surface diffusion of Al in comparison to Ga, because AlGaN is normally

grown at higher substrate temperatures. The RMS value for pure AlN is about 1 nm.

Similar observation were also made with GaAs and AlAs where the ternary compound

shows a higher roughness than the two binary layers. The roughness of AlGaN layers

exceeding 1 ML coverage are about a factor of two higher [44], [45].

42 3 MBE of cubic GaN and cubic AlGaN

0 0.2 0.4 0.6 0.8 1

Al mole fraction x

c-AlGaN RMS roughness (nm)

Figure 3.18: RMS surface roughness of different c-AlxGa1−xN/GaN heterostructures with

an Al mole fraction between x=0 and x=1. Layers were grown with a 1 ML

Ga coverage. The line is a guide for the eyes.

Based on the results described in this chapter, we assume that AlGaN layers up to a

thickness of 80 nm and a Al mole fraction up to x=0.5 are pseudomorph to the c-GaN

buffer layer. The dislocation density is equal to that of the buffer layer. AlGaN layers

of that thickness can be used for the growth of AlGaN/GaN-based quantum structures

where the thickness of the AlGaN layer is less than 100 nm. The growth and the

properties of AlGaN/GaN quantum wells will be discussed in the next chapter.

4 Growth of cubic AlGaN/GaN

quantum wells

This chapter deals with AlGaN/GaN single (SQW) and multiple quantum wells (MQW)

grown on c-GaN buffer layers. Firstly the growth and the structural properties of these

quantum wells are discussed. Then the optical properties of these structures are in-

vestigated. The optical properties of nonpolar cubic quantum wells are compared to

their hexagonal counterparts grown along different growth directions. We found that

c-AlGaN/GaN QWs are unaffected by internal piezoelectric and polarization fields.

4.1 Growth and structural properties of cubic

AlGaN/GaN quantum wells

Two types of c-AlGaN/GaN quantum wells, i.e. single and multiple quantum wells

(SQWs and MQWs) were grown. Figure 4.1 shows a schematic sketch of a multiple

quantum well structure.

Before the quantum structure was grown a 800 nm thick c-GaN buffer layer was

deposited on the 3C-SiC substrate. The buffer and the c-AlGaN/GaN quantum wells

were grown at a substrate temperature of 720◦C. The layers were deposited using a 1

ML coverage as described in the previous chapter [31]. The MQWs consist of 6 nm

thick AlxGa1−xN barriers and GaN wells with a thickness of 2.5 to 7.5 nm, and were

sandwiched between 50 nm AlGaN cladding layers. The metal fluxes were adjusted using

44 4 Growth of cubic AlGaN/GaN quantum wells

3C-SiC

c-GaN

c-AlGaN

3nm/6nm

d=50nm

d=800nm

c-AlGaN

TSubs=720°C

Figure 4.1: Schematic Sketch of a multiple quantum well structure

equations 3.3 and 3.4 given in chapter 3. During change between GaN well and AlGaN

barrier the growth was stopped for 5 min to change the temperature of the Ga source

to adjust the correct flux. The surface was continuously monitored during growth by

RHEED. At the initial growth of the c-AlGaN layers weakly damped oscillations of the

intensity of the RHEED specular spot were observed.

The structural characterization was performed by HRXRD. We measured ω−2Θ scans

of the symmetric (002) reflex and reciprocal space maps of the (-1-13) reflex of the c-

AlxGa1−xN quantum structures. Figure 4.2 shows an ω−2Θ scan of the (002) reflex of

sample 1372. This sample consists of a 15 period AlxGa1−xN/GaN MQW structure.

The reflexes of the 3C-SiC substrate and of the c-GaN buffer as well as several su-

perlattice peaks are clearly resolved. The broadening of the peaks is mostly dominated

by the interface roughness, which is in the order of 2-3 nm. Experimental data have

been fitted using the dynamic scattering theory [47], yielding a well width of 3 nm, a

barrier width of 6 nm and an Al mole fraction of x=0.3. The values of the thickness are

4.1 Growth and structural properties of cubic AlGaN/GaN quantum wells 45

100

101

102

103

104

105

106

35 36 37 38 39 40 41 42

intensity (a.u.)

2Theta (°)

SL-2

SL-1

c-GaN 3C-SiC

SL+2

SL +1

SL 0

simulation

exp. data

Figure 4.2: Measured ω−2Θ scan of a 15-fold Al0.3Ga0.7N/GaN structure (solid line)

and simulated data (dotted line). The well and the barrier width are 3 nm

and 6 nm.

in excellent agreement with the data, obtained from growth rate measurements using

RHEED oscillation period. The full width at half maximum (FWHMs) of XRD rocking

curves of the c-GaN buffer and the AlGaN cladding layers were almost identical, reveal-

ing that the density of dislocations does not increase at the AlGaN/GaN interface. The

reciprocal space map around the asymmetric (-1-13) reflex depicted in Fig. 4.3 shows

that the quantum structure is pseudomorph to c-GaN buffer. Clear superlattice peaks

of the c-AlGaN/GaN quantum structure are observed and indicated in the figure. The

peaks of the c-GaN buffer and the 3C-SiC substrate are also indicated.

46 4 Growth of cubic AlGaN/GaN quantum wells

-2.2 -2.1 -2.0 -1.9 -1.8 -1.7

3.9

4.0

4.1

4.2

4.3

4.4

4.5

SL -1

SL+2

q⏐⏐ [Å-1]

q⊥ [Å-1]

(-1-13)-Reflex

#1372

3C-SiC

AlN

AlN strained

c-GaN

SL +1

Figure 4.3: Reciprocal space map around the asymmetric (-1-13) reflex of sample 1372.

The quantum wells are pseudomorph to the c-GaN buffer.

4.2 Photoluminescence of cubic AlGaN/GaN quantum

wells

The optical transition energies of our QW structures were derived by room and low (2

K) temperature photoluminescence spectroscopy using the 325 nm line of a HeCd laser.

Figure 4.4 shows the room temperature PL spectra of a single quantum well (SQW)

structure (left) and a 5 period multiple quantum well (MQW) structure (right). The

quantum structure has 3 nm thick wells and 6 nm thick barriers and is sandwiched be-

tween two 50 nm thick cladding layers. The Al mole fraction of the AlGaN barriers

is x=0.15 [48]. Strong emission at 3.28 eV for the SQW and at 3.30 for the MQW is

observed. The emission lies between the c-GaN emission at 3.20 eV and the emission of

the Al0.15Ga0.85N cladding layer at about 3.48 eV [23]. Therefore we related the observed

strong ultraviolet emission to radiative recombination of electron-hole pairs in the QWs.

4.2 Photoluminescence of cubic AlGaN/GaN quantum wells 47

2 2.4 2.8 3.2 3.6

intensity (a.u.)

energy (eV)

SQW

T=300K

90meV

2 2.4 2.8 3.2 3.6

intensity (a.u.)

energy (eV)

5 x QW

T=300K

103meV

Figure 4.4: Room temperature photoluminescence of cubic Al0.15Ga0.85N/GaN single and

multiple quantum well structures. The QW transition energy is E=3.30 eV

and the linewidth is 90 meV for the SQW and 103 meV for the MQW.

The emission of the AlGaN barriers is suppressed due to an efficient collection of excess

carriers from the barriers in the well region indicating a diffusion length of about 50 nm

in the AlGaN barriers, which is in good agreement with earlier results of cathodolumi-

nescence investigations [49]. No additional yellow luminescence at about 2.25 eV which

is related to defects in nitrides was observed [4]. The linewidths of the room temperature

QW emission are 90 meV for the SQW and 103 meV for the MQW. The low temperature

(2 K) Pl spectra of the SWQ and MQW structures are shown in Fig. 4.5. The emission

of the SQW lies at 3.33 eV and at 3.35 for the MQW. The linewidth is 64 meV for the

SQW and 80 meV for the MQW. The additional peaks indicated as (D0A0) and (X)

originate from the donor-acceptor pair transition and the free exciton transition of the

underlying cubic GaN layer. This is most likely due to the penetration depth (about

400 nm) of our HeCd laser, which excites electron-hole pairs in the underlying c-GaN

48 4 Growth of cubic AlGaN/GaN quantum wells

3 3.1 3.2 3.3 3.4 3.5 3.6

intensity (a.u.)

energy (eV)

D0A0X

SQW 3nm

64 meV

3 3.1 3.2 3.3 3.4 3.5 3.6

Intensity (a.u.)

energy (eV)

D0A0X

MQW 3nm

80 meV

Figure 4.5: Low temperature photoluminescence of cubic Al0.15Ga0.85N/GaN SQW and

MQW structures. The QW transition energy is E=3.33 eV and 3.35 eV and

the linewidth is 64 meV and 80 meV, respectively

layer. The difference in the peak energies is due to the temperature shift between room

and low temperature [50]. We suppose that the difference of the SQW and the MQW

linewidths at room temperature and at low temperature is due to fluctuations of the

width of individual quantum wells in the MQW structure. Notably, the linewidth of

the c-Al0.15Ga0.85N/GaN QW emission is close to values recently reported for hexagonal

AlGaN/GaN quantum wells grown on a-plane substrates [4] [51]. This indicates the

potential of cubic quantum structures for application in nonpolar devices. However, the

PL linewidth of our QWs exceeds that of the emission from polar (c-plane) hexagonal

AlGaN/GaN QWs [52], this is most likely due to the higher density of dislocations in

metastable cubic structures.

The presence of internal piezoelectric fields in hexagonal nitride based quantum struc-

tures give rise to a strong quantum confinement Stark effect (QCSE) leading to a red-shift

4.2 Photoluminescence of cubic AlGaN/GaN quantum wells 49

of the quantum well emission. The energy band diagram of a cubic quantum well and of

a state-of-the-art hexagonal quantum well grown along the polar c-axis is plotted in Fig.

4.6. In the case of cubic nitrides the electron and hole wave functions are localized in

Figure 4.6: Schematic view of a quantum well without and with built-in field. Electrons

and holes are localized in opposite corners leading to a red-shift of the lowest

transition and to a reduction of the oscillator strength compared to the flat

band case in the cubic system [53].

the center of the quantum well whereas for the hexagonal counterpart the electron and

hole wave functions are separated and localized opposite side of the quantum well edges.

Due to the spatial separation of electrons and holes the oscillator strength is strongly

reduced and as a result the recombination probability of electron and hole pairs will be

severely lowered [3] resulting in a weak luminescence intensity.

The room temperature PL peak energies of our cubic Al0.15Ga0.85N/GaN MQWs are

plotted versus well width in Fig. 4.7 together with hexagonal Al0.17Ga0.83N/GaN quan-

tum wells [54]. The figure shows the energy difference ∆Eof the transition energies

of the quantum wells to the bulk GaN versus the quantum well thickness. We find a

decrease of the transition energy with increasing well width.

The full curve in Fig. 4.7 is calculated using a square well self-consistent Poisson-

50 4 Growth of cubic AlGaN/GaN quantum wells

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

02468

ΔE = EQW - Egap (eV)

well width (nm)

Al0.15Ga0.85N / GaN

electric field=710 kV/cm

cubic QW

hexagonal

Al0.17Ga0.83N QW

Figure 4.7: Energy difference of cubic and hexagonal AlGaN/GaN QWs as a function of

well width [54]. The full curve for the cubic QWs was calculated using the

self-consistent Poisson-Schr¨

odinger model [55]. The hexagonal QWs show a

red-shift of the transition energy below the band gap of hexagonal GaN.

Schr¨

odinger calculation of the quantum well [55]. We assume a 70:30 ratio of the con-

duction and the valence band discontinuities [56]. The effective masses of electrons and

holes in c-GaN and c-Al0.15Ga0.85N are me= 0.15m0[57], mh= 0.8m0and me= 0.156,

and mh= 0.86 [58], respectively. We find excellent agreement between experimental

and calculated data indicating that, unlike in polar h-group III-nitride based quantum

structures, polarization and piezoelectrical fields are absent in c-III-nitrides with a (001)

growth direction [59]. The shift of the emission energy versus the width of cubic QWs is

almost identical to that of nonpolar a-plane hexagonal AlGaN/GaN QWs with similar

composition [51]. The transition energies EQW in the hexagonal case are lower than the

band gap of hexagonal GaN due to the quantum confinement Stark effect. The strength

4.2 Photoluminescence of cubic AlGaN/GaN quantum wells 51

of the electric fields in hexagonal GaN increases with increasing Al content and is about

710 kV/cm for an Al mole fraction of x=0.17 [54].

52 4 Growth of cubic AlGaN/GaN quantum wells

5 AlN/GaN superlattices for

intersubband spectroscopy

AlN/GaN superlattices were grown on c-GaN buffer layers. These structures are used

for intersubband spectroscopy in the infrared (IR) region and can be used as detector

for this kind of radiation. A brief introduction on intersubband spectroscopy is given

below. The main part of this chapter will focus on the growth of AlN/GaN superlattices

followed by optical investigation of these structures. The optical transition energies were

calculated and compared to experimental results. First intersubband transitions were

observed in cubic III-nitrides.

5.1 Intersubband transitions

While most of the applications of III-nitride materials are in the visible and the ultra-

violet spectral region, there has been increasing interest in this class of materials for

the infrared spectral range. This interest stems from the fact that AlN/GaN systems

exhibits a large conduction band offset that allows to optically design structures with

intersubband transitions. Additionally, the intersubband transition relaxation time in

GaN/AlGaN was predicted theoretically [60] [61] to be 100 fs at 1.55 µm, which is one

order of magnitude shorter than the relaxation time in InGaAs multiple quantum wells.

Intersubband transitions in AlN/GaN multiple quantum wells have been investigated for

their application possibilities in the near infrared spectral region by several groups [62],

54 5 AlN/GaN superlattices for intersubband spectroscopy

[63], [64], [65], [66], [67], [68], [69].

AlxGa1−xN/GaN or AlN/GaN multi quantum wells are suitable for detection of near

infrared light. To make this possible the size of the wells must approach the size of the

exciton Bohr radius of the well material. The effective Bohr radius in GaN is about 28

A due to the large effective mass. The small size of the Bohr radius in GaN materials

necessitates the use of small well sizes to achieve quantization of energy levels. One dif-

ference between quantum well infrared photodetectors (QWIP) and other IR detectors is

that optical absorption takes place within sub-bands in the conduction or valence band.

Transitions in the wells due to photon absorption are commonly called intersubband

ΔEc

AlN AlN

GaN

hν

conduction band

Figure 5.1: Schematic sketch of an intersubband transition in the conduction band after

absorption of a photon with equal energy to the difference between the ground

state E0and the first excited state E1[70].

(or intraband) transitions. These transitions take place in the conduction band if the

semiconductor is n-type doped or in the valance band if the semiconductor is p-type

doped. Due to the fact that we used only n-type GaN we will focus on the conduction

band to illustrate the intersubband transition. Figure 5.1 shows a schematic sketch of

an intersubband transition in the conduction band. The quantized states are E0and E1

5.1 Intersubband transitions 55

as indicated. The ground state is populated by electrons due to n-type doping which

means that the Fermi energy has to be above the ground state energy. If an electron

in the ground state E0absorbes a photon it can induce a transition to the first excited

state E1if the photon energy is equal to the energy difference between E0and E1. This

transition is called bound-to-bound transition. However, this is not always the case.

Two other types of intersubband transitions have to be considered (see Fig. 5.2). The

ΔEc

hν

ΔEc

hν

ΔEc

hν

a) b) c)

Figure 5.2: The (a) bound-to-bound, (b) bound-to-quasi-bound and (c) bound-to-

continuum transitions of electrons in the conduction band are depicted.

bound-to-quasi-bound transition occurs between the ground state and an excited state

at the upper limit of the quantum well. The bound-to-continuum transition occurs be-

tween a ground state to an unbounded state in the continuum.

Due to the selection rules in quantum mechanics, the absorption strength in these n-

doped quantum wells is proportional to an incident photon´s electric field polarization

component normal to the quantum well. If light is polarized in the x-y plane of the

quantum well, the electron-photon coupling is zero [71]. But if light has a component

parallel to the growth axis (z axis), then the electron-photon coupling is nonzero and

intersubband transitions can be observed [72]. Because of the small thickness of the

quantum wells, the measured optical absorption of the intersubband transition is usu-

ally very small. One way to increase the absorption intensity is to fabricate a waveguide

through which the light will make multiple passes (see section optical properties). A

detailed description of waveguide preparation is given in Ref. [70].

As already mentioned, it is possible to use wide band gap materials to detect light in the

56 5 AlN/GaN superlattices for intersubband spectroscopy

infrared region from 1 to 3 µm. The epitaxial growth of two semiconductors with differ-

ent band gaps allows the fabrication of such structures. This work focused on AlN/GaN

quantum structures. The conduction band offsets provided in Fig. 5.3 are very impor-

tant to achieve wavelengths shorter than 3 µm. Since the conduction band offsets in

GaAs [73] and InP [74] is less than in AlN/GaN, the shortest detectable wavelengths

with these materials are 3 and 8 µm, respectively. However, the large conduction band

offset between c-GaN and c-AlN allows intersubband transitions in the IR range from

1 to 3 µm. Figure 5.3 shows the conduction band offset as a function of the Al mole

0.5

1.5

2.5

0 0.2 0.4 0.6 0.8 1

conduction band offset (eV)

Al mole fraction x

c-GaN c-AlNc-AlxGa1-xN

Figure 5.3: Band gap of AlxGa1−xN and the conduction band offset of GaN/AlxGa1−xN

as a function of the Al mole fraction.

fraction. The conduction band offset is assumed to be 70 percent [56] of the total gap

discontinuity for these calculations. The energy gap of AlxGa1−xN is calculated by the

following equation:

5.1 Intersubband transitions 57

Eg(x) = xEg(AlN) + (1 −x)Eg(GaN) (5.1)

where Eg(AlN), Eg(GaN) are the band gaps of c-AlN and c-GaN (5.1 eV and 3.2

eV [7]), respectively, taking linear interpolation into account [75]. For this work only

AlN/GaN quantum wells were grown to achieve the desired wavelength.

As mentioned before, the separation between the ground state E0and the first excited

state E1, which can be bound or unbound, corresponds to a particular wavelength. In

the case of AlN/GaN quantum wells, the wavelength of interest is 1.55 µm which is used

in optical communication. The only variable parameter for AlN/GaN quantum wells

investigated for this work is the quantum well width. As reported by Gmachl et al. [76]

intersubband transitions in the near infrared were observed when narrow wells and high

aluminum compositions are used. Figure 5.4 shows the transition wavelength dependence

of three quantum wells with decreasing well width (Lw) and identical conduction band

ΔEc

hν

ΔEc

hν

ΔEc

hν

c) b) a)

Figure 5.4: Schematic sketch of transitions in quantum wells with different well thick-

nesses. The blue curve indicates case (a) the red curve case (b) and the green

curve case (c) [70].

58 5 AlN/GaN superlattices for intersubband spectroscopy

offsets (∆Ec). As the size of the quantum well is decreasing both E0and E1shift to higher

energies, and the difference ∆Eis increasing. This corresponds to decreasing wavelength

needed to excite an electron to the first excited state. It should be noted that the green

curve in Fig. 5.4 is slightly skewed with a tail, which is typical for a transition occuring

outside the bounded states of the quantum well (bound-to-continuum transition). The

other bound-to-bound transitions show a Lorentzian line shape [71].

The two major categories of infrared detectors are thermal and photonic (quantum)

detectors. Quantum detectors operate on the principle of electron-photon interaction.

Thus, these detectors are much faster than thermal detectors. For example Iizuka et

ΔEc

hν

electric field

Vb=0

Vb≠0

Figure 5.5: Typical quantum well design structure with two bound states. Quantum

wells are shown without bias voltage on the left side and with applied bias

voltage on the right side.

al. [77] report an intersubband relaxation time of 150 fs in AlGaN/GaN MQWs. There

are two basic processes involved in quantum detectors. Firstly, conduction electrons or

electrons bound to the lattice atoms absorb light and thus get excited to higher energy

levels. Secondly, the excited electrons are swept by an applied bias voltage and collected

as an electrical signal. The quantum well infrared photodetector (QWIP) is based on

intersubband transition, as shown in Fig. 5.5. The applied bias voltage shown on the

right side in Fig. 5.5 causes the conduction band to bend and the excited state is than

located near the edge of the barrier conduction band. Electrons in the ground state can

5.1 Intersubband transitions 59

be excited by illuminating the sample with infrared light. They can tunnel through the

barrier and then contribute to a photocurrent under the influence of the external field

(bias voltage). The tunneling probability through the barrier is proportional to the bias

voltage. The detector output signal is usually called a photocurrent. Photoconductivity

measurements of a photodetector require fabricating a mesa so that electrodes can ba

attached to the mesa and a bias voltage is applied. A typical mesa structure is shown

in Fig. 5.6 where a quantum well structure is sandwiched between two ohmic contact

layers.

n+GaN

3C-SiC

Figure 5.6: Mesa structure of a typical quantum well infrared photo detector. A bias

voltage is supplied and a photocurrent is measured.

60 5 AlN/GaN superlattices for intersubband spectroscopy

5.2 Growth of c-AlN/GaN superlattices

As a first step to test a material system´s suitability for application in IS-based devices,

straightforward IS-absorption measurements are performed. As we are investigating the

growth of c-AlN/GaN MQWs we are foremost interested in the observation of bound-

to-bound transitions. In order to be able to observe bound-to-bound transitions in

the range of 0.8 eV (1.55 µm), the transition energies were calculated using a square

well self-consistent Poisson-Schr¨

odinger model. The simulation was done for quantum

wells embedded between 1.5 nm thick c-AlN barriers. We assume a 70:30 ratio of the

conduction and valence band discontinuities [56]. The effective masses of c-GaN are

me= 0.15 m0[57] and mh= 0.8m0and for c-AlN me= 0.19 m0and mh= 1.2m0

[58], respectively. A net donor concentration of ND= 6 ×1018 cm−3was used for c-GaN

0.50

0.60

0.70

0.80

0.90

1.00

1 1.2 1.4 1.6 1.8 2 2.2

transition energy (eV)

well width (nm)

Figure 5.7: Transition energies of AlN/GaN multiple quantum well versus the QW thick-

ness calculated by a self-consistent Poisson-Schr¨

odinger model.

5.2 Growth of c-AlN/GaN superlattices 61

and ND= 7 ×1019 cm−3for c-AlN. These values are obtained by CV-measurements of

thick GaN and AlN layers. Figure 5.7 shows the transition energies from E0to E1versus

the QW thickness in the range of 1.3 nm to 2.1 nm. With increasing well thickness

the transition energy is decreasing. A transition energy of 0.8 eV (1.55 µm) is expected

for a QW thickness of 1.5 nm. Therefore we decided to realize the following structures.

Figure 5.8 shows a schematic sketch of a c-AlN/GaN MQW structure.

1.5 nm AlN

c-AlN

x 20 c-GaN

100 nm c-GaN

c-AlN

100 nm c-GaN

3C-SiC TSubs=720°C

dGaN=1.3…1.9 nm

dAlN=1.5 nm

Figure 5.8: Schematic sketch of an AlN/GaN MQW structure for intersubband transi-

tions. The thicknesses of the wells vary between 1.3 and 1.9 nm, the thickness

of the barriers is 1.5 nm.

A 100 nm thick c-GaN buffer was deposited on a 3C-SiC substrate using the growth

process described in chapter 3 and Ref. [31]. Then a 20 period AlN/GaN superlattice

was grown with well widths ranging from 1.3 nm to 1.9 nm and a barrier width of 1.5

nm. The growth temperature was 720◦C. We fabricated four samples with varying QW

thicknesses to see the shift in transition energy. After each layer the growth was stopped

for 30 seconds to allow excess metal to evaporate from the surface. The RHEED intensity

was recorded versus time when the superlattice was started. The shutters were opened

and closed using a computer program to guarantee the same thickness of the wells and

the barriers.

62 5 AlN/GaN superlattices for intersubband spectroscopy

A typical RHEED timescan of sample 1518 after opening of both the Al and the N

shutter is shown in Fig. 5.9. Clear RHEED oscillations of c-AlN are seen after opening

100

120

140

160

180

200

0 50 100 150

intensity (a.u.)

time (s)

open Al, N open Ga, N

close Al, N

close Ga, N

1 ML

Figure 5.9: RHEED timescan of sample 1518 on an extended scale. The shutter sequence

and the coverage of 1 ML during c-GaN growth is indicated in the figure.

the Al and N shutter. Using the number of deposited AlN monolayers a barrier thickness

of 1.5 nm was calculated, assuming a lattice constant of aAlN = 4.38 ˚

A. The GaN wells

were grown for a certain time (depending on the well thickness) taking a growth rate

of 210 nm/h into account. This growth rate was obtained using optical interference

spectroscopy with thick c-GaN layers. After a growth interruption of 20 sec. we opened

the Ga and N shutter simultaniously. The RHEED intensity decreases and saturates at

a Ga-coverage of 1 ML. After closing the Ga an N shutter the intensity increases and

saturates indicating a Ga free surface. The growth rate of the AlN barrier observed by

RHEED oscillation is 87 nm/h. We found that the growth rate of AlN is lower than that

of GaN, which is due to nitrogen rich growth conditions. Nitrogen-rich growth conditions

5.2 Growth of c-AlN/GaN superlattices 63

are required due to the small growth window for c-AlN at 720◦C. Similar results were

obtained by Heying et al. [79] for growth of GaN. By comparing the RHEED timescan

100

150

200

250

300

0 50 100 150 200 250 300

intensity (a.u.)

time (s)

AlN AlN GaNGaN

period 2 period 3

period 18 period 19

Figure 5.10: RHEED intensity versus time during the growth of an AlN/GaN superlat-

tice of sample 1518. The Fig. shows the RHEED intensities of period 2 and

3 and of period 18 and 19. The shaded area indicates the growth of the

individual layer. The scans are vertically shifted for clarity.

obtained during growth of different periods we found a growth mode which is highly

reproducible as shown in Fig. 5.10. The Fig. shows the RHEED intensity versus time

for the second and the third period and for periods 18 and 19. For clarity the time scans

of period 18 and 19 has been shifted both in time and in position in Fig. 5.10. The

shaded area indicates the growth of the individual layer. These timescans are identical

revealing a high reproducible growth process within the superlattice.

64 5 AlN/GaN superlattices for intersubband spectroscopy

5.3 Structural properties of AlN/GaN SLs

The structural properties were investigated by HRXRD and AFM. The ω-2Θ scan of

sample 1518 is shown in Fig. 5.11 together with a simulation using a dynamic scattering

model [47]. The reflexes of the 3C-SiC substrate, of the c-GaN buffer as well as of two

superlattice peaks are clearly resolved.

100

101

102

103

104

105

106

36 37 38 39 40 41 42

intensity (a.u.)

2 Theta (°)

3C-SiC

c-GaN

SL 0

SL -1

simulation

exp. data

Figure 5.11: ω-2Θ scan and simulated data of the (002) reflex of sample 1518. The sample

consists of a 20-fold AlN/GaN MQW structure. The simulation reveals a

barrier thickness of 1.35 nm and a QW thickness of 1.75 nm.

The thickness of a SL period (consisting of one QW and one barrier) is given by eq.

d=n·λ

2(sin Θm−sin Θn)(5.2)

where Θmand Θnare the positions of the superlattice peaks and λis the wavelength

5.3 Structural properties of AlN/GaN SLs 65

of the X-ray beam. From the difference of the superlattice peaks a periodicity of 3.1

nm was calculated [16]. Due to the unknown strained lattice parameter of AlN the

QW and barrier thicknesses were determined from dynamic simulation. The thickness

is 1.75 nm for the QW and 1.35 nm for the barrier. These values differ slightly from

the calculated data obtained by RHEED oscillation period for the AlN barrier. The

thickness of the AlN barrier is thinner than estimated, which can be explained by the

strain of the AlN layers. Strain reduces the vertical lattice constant which results in a

smaller lattice parameter than included in our calculations. The QWs are thicker which

is due to uncertainties in growth rate calculations and a second reason may be growth

rate fluctuation caused by our plasma source.

The surface roughness of these structures was investigated by AFM. The RMS roughness

of sample 1518 is 2.6 nm on a 5×5µm scan area, which is in the order of the best values

reported for bulk c-GaN layers (see Fig. 3.8). The QW thicknesse, the FWHM of the X-

ray rocking curves and the RMS roughness of the investigated structures are summarized

in table 1

sample number QW thickness (nm) RMS roughness (nm) FWHM X-ray (arcmin)

1518 1.75 2.6 36

1544 1.6 4.2 36

1545 1.65 5.9 37

1547 2.1 3.2 36

Table 1: Structural parameters of AlN/GaN MQW samples.

The surface roughness of sample 1518 is the lowest within this series of samples. The

FWHMs of the XRD rocking curve are identival for all samples.

66 5 AlN/GaN superlattices for intersubband spectroscopy

5.4 Optical properties of AlN/GaN SLs

The absorption measurements were performed in a waveguide geometry at the University

of Arkansas, group of Prof. Dr. M.O. Manasreh. The samples were cut into 5 mm ×2

mm wide pieces. The 45 degree facets were fabricated by lapping using various grades

of lapping material. Details are given in Ref. [70]. Figure 5.12 shows the SEM image

of a waveguide with two 45 degree facets. Figure 5.13 illustrates the propagation of

light through the waveguide. The angles of total reflection for the SiC-air and GaN-air

interfaces are 23.09◦and 25.3◦, respectively.

Figure 5.12: An SEM image of a waveguide with approximately 2 mm width and 5 mm

length [70].

2 mm

45°

AlN/GaN

Figure 5.13: Illustration of light propagating through a waveguide.

5.4 Optical properties of AlN/GaN SLs 67

The optical measurements were performed using a Bomen DA8 FTIR spectrometer.

The light was detected by a HgCdTe detector, cooled by liquid nitrogen. The optical

range for this detector is 1 to 12 µm (0.1 to 1.24 eV) and has a detectivity greater than

4×1010 cmHz1/2W−1[70].

The room-temperature optical absorbance spectra of samples 1518, 1544, 1545, 1547 and

a 3C-SiC substrate are plotted in Fig. 5.14. All four samples show a clear absorption

peak in the range of 0.6 eV to 0.8 eV (1.6 µm to 2 µm). These structures consist of

AlN/GaN MQWs with a well width between 1.6 and 2.1 nm. The absorption below 0.4

eV (3.2 µm) is due to absorption bands from the 3C-SiC substrate. The spectra are

vertically shifted for clarity. Figure 5.15 shows the absorbance of the same four samples

0.2

0.4

0.6

0.8

0.2 0.4 0.6 0.8 1 1.2

absorbance (a.u)

energy (eV)

#1544

#1545

#1518

#1547

substrate

0.62 eV

0.71 eV

0.75 eV

0.77 eV

Figure 5.14: Room-temperature absorbance spectra of 4 AlN/GaN MQW structures and

of a substrate. Absorption was observed in the range of 0.6 eV to 0.8 eV

(1.6 µm to 2 µm). The spectra are vertically shifted for clarity.

in the spectral range from 0.5 eV to 1.1 eV (1.1 µm to 2.5 µm) with the absorbance of

68 5 AlN/GaN superlattices for intersubband spectroscopy

the substrate subtracted. A shaded area indicates the communication wavelength of 0.8

eV ( 1.55 µm). The IS-transition of sample 1544 is nearly located at the favored wave-

length of 0.8 eV (1.55 µm). The lineshape of the absorption of samples 1518 and 1544

0.01

0.02

0.03

0.04

0.05

0.5 0.6 0.7 0.8 0.9 1 1.1

1545

1547

1544

1518

absorbance (a.u.)

energy (eV)

~1.55 µm

Figure 5.15: Intersubband absorption of four AlN/GaN MQWs. The spectra are plotted

after subtraction of the substrate background in the spectral range between

0.5 eV and 1.1 eV (1.1 µm and 2.5 µm). A shaded area indicates the

wavelength of 1.55 µm. The FWHM of all samples is about 200 meV.

is symmetrical which is an indicator for a bound-to-bound intersubband transition. The

lineshape of sample 1545 and 1547 is asymmetrical, which is most likely due to interface

fluctuations in the quantum well. The absorption peak energy is inverse proportional to

the quantum well width and lies between 0.6 eV and 0.8 eV (1.6 µm to 2 µm). The line

width (FWHM) of the absorption peaks is about 200 meV. The FWHM is larger than

in hexagonal AlGaN/GaN MQW structures (130 meV) [80]. This is most likely related

to the interface roughness of the AlN/GaN interfaces.

5.4 Optical properties of AlN/GaN SLs 69

In the following I discuss the transition energies of sample 1518 by comparing the ex-

perimental data with theoretical calculations. Figure 5.16 shows a simulation of the

conduction band of sample 1518. In this calculation a square well self-consistent Poisson-

Schr¨

odinger model [55] was used with the parameters given above and in table 1. For

simplicity we only used five quantum wells to calculate the transition energies. At

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

90 100 110 120 130

energy (eV)

distance from surface (nm)

EFE0

Figure 5.16: Simulation of the conduction band of sample 1518. Two bounded states are

observed within the quantum well. The shaded area indicates the distribu-

tion of the first excited state E1.

least ten quantized energy levels were observed in this structure. The first five states

are located below the Fermi energy. They form a miniband due to the overlap of the

wave functions. The excited states also form a miniband above 0.7 eV. The transition

energy is 0.712 eV (1.76 µm) as indicated by an arrow in the figure. The thickness of

the quantum well used for this calculation was 1.75 nm. This is in good agreement with

the experimental results given in Fig. 5.15. The miniband of the first excited state has

70 5 AlN/GaN superlattices for intersubband spectroscopy

0.50

0.60

0.70

0.80

0.90

1.00

1 1.2 1.4 1.6 1.8 2 2.2

transition energy (eV)

well thickness (nm)

Figure 5.17: Transition energies of AlN/GaN multiple quantum wells versus the QW

thickness as shown in Fig. 5.7. The experimental data show good agreement

with the calculated data.

a distribution of about 200 meV and is indicated by the shaded area in Fig. 5.16, which

is in good agreement to the observed line widths in the absorbance spectra. Figure 5.17

shows the calculated and the measured transition energies as a function of the well width

in the range between 1.3 nm an 2.1 nm. The experimental data show excellent agreement

with the calculated values. To reach the target wavelength of 1.55 µm thinner quantum

wells are required, which will be one of the next steps for epitaxy.

20 period c-AlN/GaN SL structures grown by MBE serve as first demonstration that

IS-transitions in the communication wavelength range can be achieved with metastable

cubic group III-nitrides. This result is an extremely important milestone towards the

demonstration of a high performance intersubband detector at the telecommunication

wavelength of 1.55 µm.

6 Conclusion

Metastable cubic GaN layers were grown on free standing 3C-SiC (001) substrates. The

main focus of this work was the investigation of the growth process of cubic III-nitrides

by plasma assisted molecular beam epitaxy to reduce the surface and the interface rough-

ness. We studied the adsorption of Ga on c-GaN using in situ reflection high energy

electron diffraction. The drop of the RHEED intensity after growth was started had

been calibrated to allow direct measurements of the Ga-coverage at growth conditions

with an accuracy of 0.1 ML. The roughness of cubic GaN was significantly reduced by

growth under controlled Ga-excess conditions. A minimum RMS roughness of 2.5 nm

was achieved using a Ga-coverage of 1 ML during c-GaN growth. Cubic GaN layers

grown under these conditions have narrow x-ray (002) rocking curves (16 arcmin) in-

dicating also a low density of extended defect in these layers. Our data show that the

epitaxy of c-GaN with high structural quality is only possible if the amount of excess

Ga on the surface is monitored with high accuracy during growth.

Cubic Al0.15Ga0.85N/GaN single and multiple quantum wells were grown on top of c-

GaN buffer layers. During growth of Al0.15Ga0.85N/GaN QWs clear RHEED oscillations

were observed allowing a stringent control of the growth rate and indicating a two-

dimensional growth of the respective layers. The peak energy of the emission from our

cubic Al0.15Ga0.85N/GaN QWs follows the square-well Poisson-Schr¨

odinger model and

demonstrates the absence of polarization-induced electrical fields. The FWHM of c-QW

luminescence is almost identical to values reported for nonpolar hexagonal AlGaN/GaN

quantum wells. Our results obtained with quantum wells grown on 3C-SiC substrates

indicate that the well-known thermodynamic metastability of the cubic nitrides does not

72 6 Conclusion

necessarily limit their application for polarization-free structures.

First intersubband transitions in 20 period c-AlN/GaN multiple quantum wells were

observed in the near infrared region. The c-GaN well widths were estimated from

X-ray simulations. 1.6 nm to 2.1 nm thick quantum wells show intersubband transi-

tions between 1.6 µm and 2.1 µm. Simulation of transition energy using self-consistent

Poisson-Schr¨

odinger model show excellent agreement to experimental data. The ab-

sence of built-in fields in these structures will simplify the design of polarization-free

intersubband devices.

7 Appendix

Table A.1 gives a short overview of the physical properties of c-GaN and c-AlN. The

parameter for the ternary compounds are calculated by linear interpolation of the binary

compounds.

Parameter c-GaN c-AlN Reference

lattice constant (˚

A) 4.52 4.38 [81] [82]

Band gap (eV) 3.2 5.1 [58]

effective conduction band mass

m00.15 0.19 [58]

effective hole mass

mhh

m00.8 1.2 [58]

mlh

m00.18 0.33 [58]

Deformation Potential (eV)

ac-2.77 -6.8 [83] [84]

b-2.67 -1.5 [84] [85]

Elastic coefficients (GPa)

c11 296 304 [84]

c12 154 152 [84]

The Poisson ratio which is defined as ν=c11

c11−c12 was used to calculate the strain and

the transition energies in our AlGaN/GaN heterostructures.

74 7 Appendix

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List of samples

Sample No Date of growth Structure Al content

1117 12.12.03 AlGaN/GaN MQW 0.25

1132 05.02.04 AlGaN/GaN SQW 0.15

1138 12.02.04 AlGaN/GaN SQW 0.15

1143 16.02.04 AlGaN/GaN MQW 0.15

1204 07.06.04 GaN

1221 15.07.04 GaN

1286 15.12.04 GaN

1287 16.12.04 GaN

1304 07.02.05 GaN

1310 12.12.12 GaN

1314 12.12.12 AlGaN/GaN HS 0.3

1360 23.05.05 GaN

1372 21.06.05 AlGaN/GaN MQW 0.3

1397 25.08. 05 AlGaN/GaN 0.33

1398 26.08.05 AlGaN/GaN 0.49

1403 02.09.05 AlGaN/GaN 0.57

1426 11.10.05 AlGaN/GaN 0.14

0.25

0.38

0.67

1436 31.10.05 AlGaN/GaN 0.18

0.32

0.52

82 Bibliography

Sample No Date of growth Structure Al content

1437 02.11.05 AlGaN/GaN 0.8

1441 10.11.05 AlGaN/GaN 0.74

1447 19.11.05 AlGaN/GaN 0.48

1448 20.11.05 AlGaN/GaN 0.54

1452 24.11.05 AlGaN/GaN 0.54

1455 27.11.05 AlGaN/GaN 0.65

1459 01.12.05 AlGaN/GaN 0.82

1518 21.11.06 AlN/GaN MQW

1544 05.02.07 AlN/GaN MQW

1545 06.02.07 AlN/GaN MQW

1547 08.02.07 AlN/GaN MQW

Publication List

1. A. Pawlis, D.J. As, D. Schikora, J. Sch¨

ormann, and K. Lischka, Photonic de-

vices based on wide gap semiconductors for room temperature polariton emission

phys. stat. sol. (c), 1, 202 (2004)

2. S. Li, J. Sch¨

ormann, A. Pawlis, D.J. As, and K. Lischka, Cubic InGaN/GaN

multiple quantum wells and AlGaN/GaN Bragg reflectors for green resonant cavity LED

in IEEE Proceedings SIMC-XIII, Bejing, p.61 (2004)

3. S. Li, J. Sch¨

ormann, A. Pawlis, D.J. As, K. Lischka, Cubic InGaN/GaN multi-

quantum wells and AlGaN/GaN distributed Bragg reflectors for application in resonant

cavity LEDs

Microelectronics Journal 36, 963 (2005)

4. M. Abe, H. Nagasawa, S. Potthast, J. Fernandez, J. Sch¨

ormann, D.J. As, and

K. Lischka, Cubic GaN/AlGaN HEMTs von 3C-SiC substrate for normally-off operation

IEICE Transactions on Electronics, E89-C (7), 1057 (2006)

5. D.J. As, S. Potthast, J. Fernandez, J. Sch¨

ormann, and K. Lischka, Ni Schottky

diodes on cubic GaN

Appl. Phys. Lett. 88, 1521112 (2006)

6. J. Sch¨

ormann, S. Potthast, M. Schnietz, S.F. Li, D.J. As, and K. Lischka, Growth

of ternary and quaternary cubic III-nitrides on 3C-SiC substrates

phys. stat. sol. (c) 3, 1604 (2006)

84 Bibliography

7. S. Potthast, J. Sch¨

ormann, J. Fernandez, D.J. As, K. Lischka, H. Nagasawa, M. Abe,

Two-dimensional electron gas in cubic AlxGa1−xN/GaN heterostructures

phys. stat. sol. (c) 3, 2091 (2006)

8. D.J. As, S. Potthast, J. Sch¨

ormann, S.F. Li, K. Lischka, H. Nagasawa, M. Abe,

Molecular beam epitaxy of cubic group III-Nitrides on free-standing 3C-SiC substrates

Matrials Science Forum Vols. 527-529, 1489 (2006)

9. J. Sch¨

ormann, S. Potthast, D.J. As, and K. Lischka, Near UV emission from

nonpolar cubic AlxGa1−xN/GaN Quantum Wells

Appl. Phys. Lett. 89, 131910 (2006)

10. D.J. As, M. Schnietz, J. Sch¨

ormann, S. Potthast, J.W. Gerlach, J. Vogt and

K. Lischka, MBE growth of cubic AlxIn1−xNand AlxGayIn1−x−yNlattice matched to

GaN

phys. stat. sol. (c) (2006) (accepted)

11. J. Sch¨

ormann, D.J. As, K. Lischka, P. Schley, R. Goldhahn, S. Li, W. L¨

offler,

M. Hetterich, and H. Kalt, Molecular Beam Epitaxy of phase pure cubic InN

Appl. Phys. Lett. 89, 261903 (2006)

12. J. Sch¨

ormann, S. Potthast, D.J. As, and K. Lischka, In situ growth regime char-

acterization of cubic GaN using reflection high energy electron diffraction

Appl. Phys. Lett. 90, 041918 (2007)

13. J. Sch¨

ormann, D.J. As, and K. Lischka, MBE Growth of cubic InN

MRS Symp. Proc. Vol. 955E, I8.3 (2007)

14. S.F. Li, J. Sch¨

ormann, D.J. As, and K. Lischka, Room temperature blue and

green light emissions from nonpolar cubic InGaN/GaN multi-quantum-wells

Bibliography 85

Appl. Phys. Lett. 90, 071903 (2007)

15. F.Y. Lo, A. Melnikov, D. Reuter, A.D. Wieck, V. Ney, T. Kammermeier, and

A. Ney, J. Sch¨

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Appl. Phys. Lett. (submitted)

16. R. Goldhahn, P. Schley, J. Sch¨

ormann, D.J. As, K. Lischka, F. Fuchs, F. Bechst-

edt, C. Cobet, and N. Esser, Dielectric function and band structure of cubic InN,

Bessy - Annual Report 2006, p. 529 (2007)

Acknowledgement

Firstly, I would like to thank Apl. Prof. Dr. D. J. As. My work was performed

under his direct supervision and he has given a lot of valuable advices.

The same gratitude goes to Prof. Dr. K. Lischka who gave me the opportunity to work in

this group. Plenty of valuable discussions and advices from him support this challenging

work on the research of cubic nitrides.

Thanks also goes to Dr. D. Schikora for his help and discussion about the growth.

Next I have to mention my college, friend and office partner during the last four years,

Dr. S. Potthast. I am really sorry that the world best MBE dreamteam will be splitted.

I thank him for all the helpful discussions (not only physics) and the after work beers.

Specially I have to thank him for playing my taxi driver during my torn ligament.

In addition I would like to thank my other fellow Ph. D. students C. Arens, S. Preuss,

Dr. S. Li, Dr. A. Pawlis and especially our ladies E. Tschumak, M. Panfilova and Olga

Kasdorf, for the helpful physical and technical discussions.

Of course I am also grateful for the (not only technical) help of our optoelectronics staff,

I. Zimmermann, B. Vollmer and S. Igges.

I would like to thank H. Nagasawa and M. Abe from SiC Development Center, HOYA

Corporation, for supplying the 3C-SiC substrates.

I have to thank E. A. Decuir Jr. from the University of Arkansas for the collaboration

and the nice time during his stay at the University of Paderborn.

I want to thank Dr. A. Khartchenko for his help regarding the X-Ray simulations.

Moreover I have to thank my girl friend Teresa for her love and encouragement she gave

me during the last 10 years.

Last but not least I would like to thank my parents for their love, encouragement and

financial support during my whole life.