Document [original]

Phonons and excitons in colloidal

CdSe/CdS quantum dots with wurtzite

and zincblende crystal structure

vorgelegt von

Diplom-Physikerin

Amelie Laura Biermann

geb. in Berlin

von der Fakult¨at II - Mathematik und Naturwissenschaften

der Technischen Universit¨at Berlin

zur Erlangung des akademischen Grades

Doktor der Naturwissenschaften

– Dr. rer. nat. –

genehmigte Version

Promotionsausschuss:

Vorsitzender: Prof. Dr. Lehmann

Gutachterin: Prof. Dr. Axel Hoffmann

Gutachter: Dr. Anna Rodina

Tag der wissenschaftlichen Aussprache: 01.12.2017

Berlin, 2018

1 Abstract

This thesis presents a thorough analysis of the optical and vibrational prop-

erties of colloidal II-VI-semiconductor quantum dots, focussing on the effects

of crystal structure differences and the interplay within core-shell QDs on

the lattice vibrations, temperature dependent lattice parameters the exciton-

phonon coupling and the exciton fine structure. Here, spherical CdSe/CdS

QDs of different sizes are studied. The nano-scale confinement not only al-

lows the growth in the wurtzite structure – the default for bulk CdSe – but

also in the zincblende structure. Since these two structures are fundamen-

tally different, it is one of the main objectives of this work to analyze the

influence of the crystal structure on the properties of the QD.

The lattice parameters of core-shell QDs are investigated and strain and

temperature dependent effects are separated by comparison with reference

samples at the same temperature. This leads to the extraction of purely

temperature dependent lattice expansion coefficients thus becomes possible

for each material, revealing different expansion behaviors for the wurtzite

and zincblende structured cores, as well as a dependence on the core size.

The exciton-phonon coupling within the QD is studied with Raman spec-

troscopy, in dependence of the QD diameter and the effect of zincblende and

wurtzite crystal structure, revealing a size dependent minimum in coupling

strength. Additionally, the influence of the addition of a CdS shell on the

coupling is investigated with Raman spectroscopy and resonance PL, finding

decreasing coupling for increasing shell thickness.

The difference in crystal structure, i.e. the anisotropy of the wurtzite struc-

ture with it’s piezo- and pyroelectric fields, should strongly influence the

charge carriers and their band structure. Using photoluminescence excita-

tion spectroscopy, the band edge fine structure is revealed to be different

for zincblende and wurtzite CdSe QDs, as well as diameter dependent. This

is mainly achieved by evaluating the energetic distance between the lowest

bright and dark exciton states, which becomes larger both for smaller QDs

and in wurtzite structures. For comparison, the excitonic states are cal-

culated according to a established formalism. The results reveal that the

existence of this dark state in zincblende structures can only be explained

by a oblate deformation of about 10%, which induces an anisotropy large

enough to cause the observed splitting.

In the final section of this thesis, a more complex hybrid structure is studied,

namely a CdSe/CdS core-shell system which is enclosed in a thick shell of

protective silica against a reactive environment, that is present in biological

applications. Through a combined approach of TEM and Raman analysis,

this study reveals that a successful silica encapsulation employing loosely

bound ligands leads to the formation of an interface between QD and silica.

This interface between the CdS shell and the silica shell, is proposed to be

formed via the formation of Cd-O-Si bonds at the QD surface.

2 Zusammenfassung

Diese Arbeit befasst sich mit optischen und vibronischen Eigenschaften kol-

loidaler Quantenpunkten aus II-VI-Halbleitern. Dabei werden die Auswir-

kungen unterschiedlicher Kristallstrukturen und der Wechselwirkung inner-

halb von Kern-H¨

ulle-Systemen auf die Gitterschwingungen, die Exziton-

Phonon-Kopplung und die Exzitonische Feinstruktur der Quantenpunkte

(QD). Hierf¨

ur werden sph¨

arische CdSe/CdS Quantenpunkte verschiedener

Gr¨

oßen und Kristallstrukturen mit Hilfe von Ramanspektroskopie und Photo-

lumineszenz-Anregungsspektroskopie (PLE) untersucht. Durch ihre geringe

Gr¨

oße ist es m¨

oglich diese Strukturen nicht nur in der fr Bulkmaterialien

ublichen Wurtzitstruktur, sondern auch in Zinkblendestruktur herzustellen.

Da sich die beiden Strukturen fundamental in ihrer Polarit¨

at unterscheiden,

ist es von besonderem Interesse heraus zu finden, welche Auswirkungen dies

auf die Eigenschaften der QD hat.

Aus der Temperaturabh¨

angigkeit der Phononenmoden in Kern-H¨

ulle-Sys-

temen werden die rein temperaturabh¨

angigen linearen thermischen Ausdeh-

nungskoeffizienten bestimmt. Daf¨

ur werden Verspannungseffekte, die durch

das Zusammenspiel von Kern und H¨

ulle entsetehen, von der eigentlichen

Temperaturabh¨

angigkeit separiert. Dies f¨

uhrt zu Ausdehnungskoeffizienten,

die sich f¨

ur CdSe und CdS unterscheiden, aber auch von der Kristallstruktur

und vom QD-Durchmesser abh¨

angen.

Desweiteren wird die Exziton-Phonon-Kopplungsst¨

arke in Abh¨

angigkeit des

QD-Durchmessers f¨

ur QDs mit Wurtzitstuktur und Zinblendestruktur mit

Hilfe von Ramanspektroskopie untersucht. Dabei wird f¨

ur beide Kristall-

strukturen festgestellt, dass es ein Minimum in Kopplungst¨

arke bei einen

bestimmten Durchmesser gibt. Der Einfluss einer CdS H¨

ulle um den CdSe

Kern reduziert die Kopplung, wie mit Ramanspektroskopie und resonanter

Photolumineszenz beobachtet wird. Außerdem wird eine h¨

ohere Kopplung

bei QDs mit Wurtzitstruktur beobachtet, was mit h¨

oheren internen Felder

zu erkl¨

aren ist.

Der Einfluss der unterschiedlichen Kristallstruktur wird ein weiteres Mal

klar, wenn die elektronischen Bandkantenzust¨

ande betrachtet mit Hilfe von

PLE werden. Bei der Analyse von Zinkblende und Wurtzit QD mit ver-

schiedenem Durchmesser wird beobachtet, dass die Aufspaltung zwischen

den Bandkantenzust¨

anden gr¨

oßer wird je kleiner der Durchmesser des QDs.

Außerdem wird beobachtet, dass die Separation zwischen den beiden unter-

sten elektronischen ¨

Uberg¨

angen generell f¨

ur Wurtzitstruktur h¨

oher ist.

Die elektronischen Bandkantenzust¨

ande werden mit Hilfe eines etablierten

Formalismus ermittelt, daf¨

ur muss um eine entsprechende Aufspaltung zu

erlangen f¨

ur Zinkblende eine Deformation in Richtung abgeflacht angenom-

men werden, da ansonsten auf Grund der Isotropie des Kristalls keine Auf-

spaltung entsteht.

Zum Schluss wird das Hybridsystem bestehend aus einem von einer Sili-

kath¨

ulle umgebenen CdSe/CdS QD analysiert, dass wegen seiner hohen

chemischen Stabilit¨

at nachgefragt ist. Die Silikatumh¨

ullungssynthese wird

in situ mit Ramanspektroskopie beobachtet. Hier wird gezeigt, dass das

amorphe Silikat direkt mit dem QD wechselwirkt, ohne eine Ligandenzwi-

schenschicht wechselwirkt. Als m¨

ogliche Bindung zwischen den Materialien

wird eine Cd-O-Si Br¨

ucke vorgeschlagen.

iii

3 List of publications

Some of the results included in this thesis have been published:

Ghazarian, N., Biermann, A., Aubert, T., Hens, Z., and Maultzsch, J.

“Thermal Expansion of Colloidal CdSe/CdS Core/Shell Quantum Dots”,

in preparation (2017)

Biermann, A., Aubert, T., Baumeister, P., Drijvers, E., Hens, Z., and

Maultzsch, J. “Interface formation during silica encapsulation of colloidal

CdSe/CdS quantum dots observed by in situ- Raman spectroscopy.” J.

Chem. Phys., 146(13):134708-7, April 2017.

Cirillo, M., Aubert, T., Gomes, R., Van Deun, R., Emplit, P., Biermann, A.,

et al. (2014). “Flash” Synthesis of CdSe/CdS Core-Shell Quantum Dots.

Chemistry of Materials”, 26(2), 1154-1160.

http://doi.org/10.1021/cm403518a

Norman Tschirner, Holger Lange, Andrei Schliwa, Amelie Biermann, Chris-

tian Thomsen, Karel Lambert, Raquel Gomes, and Zeger Hens. “Interfacial

Alloying in CdSe/CdS Heteronanocrystals: A Raman Spectroscopy Analy-

sis.” Chem. Mater., 24(2):311-318, January 2012.

C. Friedrich, A. Biermann, V. Hoffmann, M. Kneissl, N. Esser and P. Vogt,

“Preparation and atomic structure of reconstructed (0001) InGaN surfaces”,

J. Appl. Phys. 112, 033509 (2012); http://dx.doi.org/10.1063/1.4743000

Contents

1 Abstract i

2 Zusammenfassung ii

3 List of publications v

4 Colloidal Nanocrystals, an introduction 1

4.1 Applications and resulting demands on the QD’s properties . 4

4.2 Properties of core-shell QDs . . . . . . . . . . . . . . . . . . . 6

5 Theoretical background: Raman spectroscopy 11

5.1 Raman effect in bulk crystals, Raman spectroscopy setup and

interpretation........................... 11

5.2 Strain determination from Raman spectroscopy . . . . . . . . 13

5.3 Exciton-phonon coupling strength determined from Raman

spectroscopy ........................... 14

6 Experimental methods 16

6.1 Raman spectroscopy setup . . . . . . . . . . . . . . . . . . . . 16

6.2 Photoluminescence excitation spectroscopy (PLE) setup . . . 18

7 Synthesis of CdS/CdSe colloidal QDs and subsequent Silica

encapsulation 21

7.1 Synthesis of colloidal QDs . . . . . . . . . . . . . . . . . . . . 21

7.1.1 Exemplary CdSe QD syntheses . . . . . . . . . . . . . 24

7.2 Semiconductor shell addition methods for bare colloidal QDs

and properties of the core-shell QDs . . . . . . . . . . . . . . 25

7.2.1 Exemplary SILAR and flash synthesis and comparison

of resulting properties . . . . . . . . . . . . . . . . . . 25

7.3 Silica encapsulation for biological applications . . . . . . . . . 28

8 Structural and electronic properties of CdSe/CdS quantum

dots 31

8.1 Crystal lattice and optical properties of CdSe/CdS QDs . . . 31

8.2 Raman spectra of pure CdSe QDs and CdSe/CdS core-shell

structures ............................. 34

9 Temperature dependent lattice contraction in

wurtzite and zincblende core-shell QDs 42

9.1 Temperature dependence of Raman modes in wurtzite and

zincblende core-shell NC . . . . . . . . . . . . . . . . . . . . . 42

9.2 Separation method of thermal and epitaxial strain effects . . 47

9.3 Linear temperature coefficients for heterostructures . . . . . . 49

10 Exciton-phonon coupling 55

10.1 QD diameter dependent Huang-Rhys factor from Raman spec-

troscopy.............................. 57

10.2 Huang-Rhys factor in CdSe/CdS core-shell QDs . . . . . . . . 61

11 Excitonic fine structure of CdSe QD 64

11.1 CdSe QDs in PLE measurements . . . . . . . . . . . . . . . . 66

11.2 Determination of the energy to size conversion at low tem-

peratures ............................. 69

11.3 Temperature dependence of the near band-edge states . . . . 71

11.4 Fine structure dependence on QD size, emission energy and

crystalphases........................... 74

11.5 Excitonic fine structure in CdSe/CdS core-shell QDs . . . . . 80

12 Effect of a silica shell on the encapsulated QD 85

12.1 Previous studies by TEM, PL and absorption . . . . . . . . . 85

12.2 Synthesis of silica particles and the synthesis reaction mech-

anism in the reverse micelle microemulsion . . . . . . . . . . . 88

12.3 The in situ Raman setup and synthesis of silica shell on

CdSe/CdSQDs.......................... 91

12.4 Raman analysis of the silica encapsulation of CdSe/CdS QDs 94

12.5 Dynamics of the silica encapsulation reaction analyzed by in

situ RamanandTEM ...................... 97

12.6 Origin of the change in Raman frequency during silica synthesis101

12.7 The evolution of the Raman intensity observed during silica

encapsulation...........................105

12.8 QD A and QD B’s diverging evolution of the Raman spectrum

during silica encapsulation . . . . . . . . . . . . . . . . . . . . 109

13 Conclusions 113

14 Bibliography 116

15 Acknowledgments 130

vii

viii

4 Colloidal Nanocrystals, an introduction

Colloidal nanocrystals (NC), or colloidal quantum dots (QDs), are crys-

tals in the nanometer size range that are in a stable solution with an organic

or inorganic solvent. The solution is stabilized by ligands (surfactants) which

are molecules with a polar and a non-polar part. Often the non-polar part

consists of one or several long carbon chain, which is attached to a polar

functional group at one end. They organize around the polar surface of the

colloidal NC, orienting their polar part towards the NC surface and to non-

polar part towards the solvent (Fig. 1). This construct is called a micelle

and enables to keep the NCs in stable solution with a non-polar solvent (e.g.

toluene, hexane).

Figure 1: Right: Colloidal QD inside a micelle of ligands in solution of

a non-polar solvent, such as toluene. Non-polar objects and areas are

shown in blue, whereas polar ones are red. The example ligand shown,

is TOPO (trioctylphosphinoxid, three carbon chains (non-polar) depicted

as blue lines, with the red phosphinoxid end (polar)). The ligand molecules

arrange around the QD with the polar end oriented in direction of the polar

crystal surface, while the non-polar carbon chains ensure the suspension of

the QD in the non-polar solvent. Left: TEM image of spherical zincblende

CdSe/CdS QDs (CdSe diameter 3.4 nm, total diameter 7.4 nm) as an ex-

ample for the QDs examined in this work.

In this way, using the correct ligand for each combination of specific

NC and solvent, the NCs are prevented from settling at the bottom of the

containment and/or agglomerating at the same time. The ligand needs to

be chosen specifically to fulfill the demands of the intended application.

Electronic conductive ligands for instance, are mandatory and performance

limiting for applications like electrically driven LEDs or solar cells. In those

applications, the colloidal NCs are used as the active element. Charge carri-

ers need to be injected in the NC in the case of LEDs and the separated and

subsequently extracted in the case of the solar cells. For those applications,

colloidal NCs would be an interesting and promising candidate, since due to

their small size, they exhibit quantum confinement effects (hence the name

quantum dot), which enables to tune the emission wavelength with the NC

size. Many colloidal QDs are shown to offer a very high quantum yield and

high absorbance. Additionally, the possibility to apply an active layer for

a device from solution would open up completely new fabrication methods.

Hence, finding the optimal ligand for such applications is a subject of great

interest in research. [1–4]

The NC itself contains a few hundred until a few thousands of atoms, ar-

ranged in approximately regular patterns that are often similar to structures

known from bulk semiconductors. Other than those well-known bulk ma-

terials or epitaxial quantum dot-structures, grown in metal-organic vapor

phase epitaxy (MOVPE) or molecular beam epitaxy (MBE), colloidal NCs

are synthesized in a wet-chemical reaction in solution. Different syntheses

of CdSe/CdS QDs used in this work, will be addressed in detail in Section

7.1.

While the NCs have a regular crystal structure on the inside, the crystal

symmetry is broken at the surface due to the lack of bonding partners.

Open bonds are energetically unfavorable and hence surface reconstructions

are formed or bonds to molecules in the NC‘s proximity to reduce the surface

energy. This means the surface has inherently different properties than the

corresponding bulk material; how big the influence of this surface is on the

QD and how exactly the surface is influenced by the surrounding medium

is widely unknown, despite being researched for many years.

The outer form of the NC can be varied by the choice of precursor, ligand

and reaction condition, which can selectively favor the growth at different

reactive crystal surfaces. This gives rise to a wide variety of forms rang-

ing from spheres to triangular/rectangular pyramids and cubes to elongated

sticks, rods or wires. Nevertheless, many authors found indications that the

influence of the surface on the QDs properties are considerable

Figure 2: Colloidal zincblende CdSe QDs of different sizes (between 2.5 and

5.5 nm), emitting light at their corresponding lowest electronic transition

because of UV illumination. This highlights the broad spectrum of wave-

lengths that can be reached depending on the QD size. From Sofie Ab´e,

private communication

Due to their finely tunable size, colloidal QDs can be synthesized to a

wide range of wavelengths because of electronic confinement in two or three

dimension, depending on the shape of the QD. Because of their different

bulk emission wavelength, different materials are used to produce colloidal

QDs in different wavelengths. Among the widely used II-VI semiconductors

alone, the range in wavelength varies from PbSe, which is used for the in-

frared and red region to CdSe for visible wavelengths, and to CdS for blue

and UV. In Fig. 2 solutions of differently sized zincblende CdSe QDs are

shown. Under UV illumination, the QDs shown in the figure emit at the

energy of their lowest electronic transition. Thus, the figure shows the di-

versity of emission wavelength available by size variation alone.

CdSe QDs (like CdS, ZnS etc.) can be synthesized in two basic crystal sym-

metries; zincblende and wurtzite structure. The two symmetries have very

similar bond lengths, hence the formation of both symmetries is possible

in the same inter-atomic potential. In colloidal QDs, zincblende structure

forms comparatively easy in syntheses using lower temperatures and differ-

ent precursors and surfactants than wurtzite, however, it is not found as a

bulk material. The diverging properties caused by the different symmetry

are often neglected as similar emission wavelength with similar character-

istics can be produced for the two configurations. However, the wurtzite

structure is a polar structure, and such has pyro- and piezo-electric fields.

This leads to a polar moment along the c-axis, which on the one hand en-

hances light absorption (or generally interaction with light) in this direction,

and on the other hand also influences surface states, causes surface charge

accumulation at interfaces and band bowing. Additionally, effects like for

example the Quantum Confined Stark Effect should be present in wurtzite

material.

In summary, while colloidal QDs are a promising and interesting material

for different applications (see also following Sections), it is especially out of

interest to analyze the surface of the QDs in general, influences of changing

surface chemistry and the influence of the crystal anisotropy.

In this Section, general properties of colloidal QDs in application prospects

(Sec. 4.1), as well as core-shell QDs, which are heterostructures combining

different materials will be addressed. Heterostructures combining different

crystalline semiconductor materials, will be covered in Sec. 4.2, focussing

on CdSe/CdS QDs as they are the subject of this work. Beyond those

crystalline structures, it is also possible to enclose the QDs in different, non-

crystalline materials to modify the QDs surface (Sec. 7.3). This becomes

especially necessary for application of the QDs as biological labels, to provide

a chemical barrier towards the reactive environment in the application.

4.1 Applications and resulting demands on the QD’s prop-

erties

Colloidal QDs are a promising candidate for many application, especially in

opto-electronics, due to their great luminescent brightness, high absorption

and finely tunable emission wavelength, with bandgaps in the visible and

infrared spectral region. The first working diode based on colloidal CdSe

QDs has been demonstrated already in 1994 by Colvin et al.[5], followed by

further well-known proof of principle publications on the electro lumines-

cence of CdSe QDs in 1996 and 1998[6, 7] And the first working diode based

on colloidal CdSe QDs has been demonstrate already in 1994 by Colvin et

al.[5]

In general, there is different basic sorts of optoelectronic applications, one is

based on the as efficient as possible emission of light, like LEDs or lasers, and

one that relies on absorption and subsequent charge separation, solar cells

for instance. For the first, a high emission, high QY and finely controlled

emission wavelength is of high importance. Here, an additional challenge

is posed by the complexity of electronically contacting the QDs, which is

necessary to drive the devices electrically. This originates from the surface

stabilization with ligands, as the conventionally used ones are electrically

isolating, like TOPO (trioctylphosphinoxid), TOP (trioctylphosphine) or

oleic acid (see Fig.8) for instance. Hence, the search for conductive ligands

provides a great field of research in order to reduce losses at the surface and

optimize the device efficiency. Nevertheless, working colloidal QD LEDs

have been demonstrated by several groups already. [8–10] Even white LEDs

have been demonstrated, combining different colloidal QDs.[11] Here, the

“green gap” can be covered more easily than with conventional semiconduc-

tor materials like InGaN.

Whereas Dang et al show optically pumped red, green and blue lasing col-

loidal quantum dot films[12], using QDs showing single-exciton gain and an

efficiency exceeding 80%, which show constant efficiency over 2000h and are

hence interesting as backlight of displays.

But also efficient solar cells are demonstrated frequently. A good overview is

given by Talapin et al..[1] Here, a great advantage compared to conventional

materials is the simpler realization of multi-junction architectures that can

potentially boost the power conversion efficiency greatly, by proving efficient

absorption over the whole solar spectrum and low energetic loss. Lunt et al.

analyze different architectures and combination possibilities in detail and

find that single junction solar cells should be able to reach power conversion

efficiencies up to 17% and tandem cells (combination of two different QD

films) even could achieve 24%. Those structures can potentially have life-

times of about 10-15 years, and thus should be of great interest for generation

of solar energy.[13] Already during the past years efficiencies have increased

rapidly and are now exceeding 10%. Lan et al. for instance reached 10.6

% with PbS QDs by engineering the polarity of the halide QD passivation

with the solvent.[14] In the infrared region, efficient and stable photovoltaics

with an external QY of 46% have been demonstrated by Koleilat et al. by

employing linker molecules within the QD film to enhance the electric con-

ductivity.[15]

However many of the realized concepts are based on the so-called Gr¨atzel-cell

[16], originally conceptuated to use dye-molecules in a solar cell and pub-

lished in 2000. Although different architectures and even devices produced in

an all-solution process are thinkable. For the Gr¨atzel-cell, the dye-molecules

(now colloidal QDs) are adsorbed on a mesoporous TiO2(titanium dioxide).

The TiO2functions as an electrode, offering a large surface area for cover-

age with QDs, which can absorb the generated electrons at high speed and

efficiency. The transport of holes is realized by an electrolyte surrounding

the QD-covered TiO2.

During the past years, colloidal QDs have raised interest in a different area

of application entirely: biology. In biology, there is great demand for mak-

ing biological processes visible by monitoring the position of specific cells or

molecules in cells or in the body. This applies to a broad spectrum of ap-

plication from monitoring cancer cells and stretches to understand different

aspects of the metabolism. Conventionally organic fluorophores are used

as emitters. The emitters are attached to a marker molecule with a large

affinity to doc to the specific cell-type to be monitored, so the position is

visualized by emission of the fluorophore close to the marked cell under illu-

mination. However these fluorophores, as they are molecules, fluorophores

defined and discrete electronic states. This means in order to excite them

efficiently, the light source has to match one of the higher excited electronic

states. This makes it hard to use different markers to see different types

of cells at the same time and excite at once. Here, colloidal QD offer the

advantage of a overall higher absorption, and broader absorption spectrum.

At the same time, they exhibit intense and long-term stable luminescence,

providing the opportunity of long-term observation and fast/easier detection

because of the higher intensity.[17, 18] Further information can be found in

several reviews like for instance Pietryga et al. or Jing et al..[2, 3]

However, in order to use the QDs in biological applications, they must be

adapted to be stable in aqueous environments. Therefore, the encapsulation

of the QDs in different materials has been researched for years, creating a

chemical barrier between the QD and the environment while offering solu-

bility. The shell material in question need to be optically transparent for

the makers to be visible. Additionally, these materials should optimally be

biocompatible and offer possibilities for functionalization, as it must be pos-

sible to couple the encapsulated QD to molecules that target specific cell.

For this, different polymers and silica have been suggested for use. The use

of a silica shell has been investigated during the past years [18, 20–22] and

research has shown that it offers higher stability in water and other polar

Figure 3: Example of a QD dec-

orated human (epithelial) cell, using

five different colors: Cyan corresponds

to 655-QDs labeling the nucleus, ma-

genta 605-QDs labeling Ki-67 protein,

orange 525-QDs labels mitochondria,

green 565-QDs labels microtubules,

and red 705-QDs labels actin fila-

ments. Taken from [19].

solvents and different harsh conditions, like pH.[23]

In this work we investigate silica capped QDs and analyze the encapsulation

synthesis in detail. In Section 12, we address the effects of silica encap-

sulation on the QD. While the state of the art of silica encapsulation is

presented in Sec. 7.3, the procedure of in situ Raman measurements during

the synthesis is described in Sec. 12.3 and the results are presented in Sec.12.

4.2 Properties of core-shell QDs

Due to differently strong confinement, colloidal QDs can be synthesized with

almost any desired emission wavelength, however when a single material is

applied, e.g. CdSe or HgTe, the surface of the QD is in direct contact with

the surrounding environment, which has been shown to reduce chemical and

luminescent stability. On the one hand, this direct contact to the environ-

ment can result in surface defects. This is because the open, unsaturated

bonds on the QD surface are likely to bind to molecule in their vicinity or

form reconstructions, which can trap charge carriers and thus reduce the

quantum yield by non radiative recombination. Or on the other hand the

uncovered surface provide defect centers that emit at another wavelength

entirely. Overall theses surface trap states lead to a strongly reduced photo-

luminescence quantum yield (PLQY) and enhance photo bleaching, as well

as reducing the chemical stability against the environment and thus compli-

cate post synthesis processing steps such as atomic layer deposition, which

are mandatory for some device concepts.

Additionally, the surface is prone to interaction with the environment and

chemical reactions are probable, which could hinder the application of those

QDs in certain environments. For instance, it has been shown that an acidic

environment or an oxidative environment (like water for instance) reduces

the QD lifetime drastically. [24–26]

One way to saturate the open surface bonds of the optically active part of

the QD is to cover the QD in a material with the same crystal structure and

similar lattice constant. In case the chosen shell material has a larger band

Figure 4: Schematical image of a colloidal

core shell QD surrounded by its ligand shell

and solvent, below schematic cross section

along the QD symmetry axis of the ground

and lowest excited state of core and shell for

QD with type-I band alignment, including

the surrounding ligand shell (“high energy

gap”/isolator) and solvent/air (≈ ∞) for vi-

sualization of confining potentials at play in

a core shell structure. Band offset and abso-

lute energy differences not to scale.

gap than the enclosed QD (now called core), depending on the band-off set,

the structures can have type I or type II band alignment. For type I band

alignment (Fig.4) the potential minimum for electrons and holes is in the

core of the QD, hence both charge carriers locate in close spacial proximity.

This leads an efficient recombination of free charge carriers, as opposed by

type II alignment, where the electrons accumulate in the core and holes in

the shell of the QD or vice versa. Thus the free charge carriers are spa-

tially separated in type II QDs. Hence for the recombination an additional

momentum is needed, which makes the recombination less probable and in

consequence reduces the QY. This renders type II alignment unfavorable

for applications that demand high emission intensity and efficiency. The

CdSe/CdS core-shell structures, that are discussed in the work, show a type

I alignment. This also means, that the core, the part of the QD where the

free charges accumulate plays the dominating role in the emission.

The coverage of the crucial part of the QD propels the reactive QD surface

further away from the optically active material and thus reduces trapping of

charge carriers at the surface and improves the PLQY widely.[27–29] Since

this encapsulation of the QD core changes the environment from a mix-

ture of ligands and solvent (mostly non-polar solvents, such as toluene) or

ligands and air, an essentially isolating environment, to a semiconducting

environment, this effectively relieves the electronic confinement in the core

by reducing the step height in the surrounding potential form near infinity

to a finite height (see schematics Fig.4). As a consequence, the electronic

transition energies are shifted towards lower energies after capping. This

has to be taken into account when configuring a QD for a specific applica-

tion with a determined emission wavelength; however since there has been

extensive research connecting emission wavelength, and core and shell size

and the correlation with growth conditions and times, this is not an obsta-

cle.[27–29]

Apart form the electronic properties, the shell also influences the atomic lat-

tice of the core. For an epitaxial growth, the two lattice constants need to

be similar, with as small a mismatch as possible. At the interface of the two

materials, each material needs to deviate from their respective “ideal”, bulk-

like lattice constants to accommodate direct bonds. This distortion of the

lattice is called strain (Fig. 5). The lattice that has a reduced bond length

as compared to the bulk bond length shows compressive strain, whereas the

lattice that stretches the bonds in comparison to bulk shows tensile strain.

Strained materials not only exhibit changed phononic properties , but can

also have altered optical properties compared to their unstrained state, in

particular in polar structures.

Looking at the bulk lattice constants of zincblende CdSe a=6.13 nm [30]

Figure 5: Core shell QD with examplary lattice constants for CdSe as core

and CdS as shell material. The zoom to the interface of core an shell material

shows the deviation of bond length from the “ideal” that each material has

to undergo to form direct bonds. While the CdSe core needs to reduce the

mean bond length, the CdS shell stretches the mean bond length, therewith

the core shows compressive and the shell tensile strain.

and CdS a=5.83 nm[31], and wurtzite CdSe a=4.37 nm and c=6.97 nm [30]

CdS a=4.16 nm and c=6.61 nm [32, 33], it becomes clear that CdSe consis-

tently has the larger bulk lattice constant. Hence in a CdSe/CdS core-shell

QD this means that the CdSe core is under compressive strain and the CdS

shell under tensile strain.

The amount of strain depends strongly on the geometry of the QD, for

spherical QDs this breaks down to the relation between core radius and shell

thickness. As a rule of thumb, the material that occupies the highest vol-

ume, is the least strained and concomitantly puts the other material under

heavy strain. So for one specific CdSe core, the compressive strain increases

for increasing CdS shell thickness, at the same time the shell’ s strain is

reduced. However, the growth temperature also play a role, because during

growth the atoms arrange themselves to reach the minimal potential energy

at this temperature, which can differ for different temperature due to dif-

ferent thermal expansions (see also Sec. 9). Since the strain in materials

influences the materials electronic properties and also influences the overall

crystal quality (for instance structural defects can be caused by relaxation

of heavy strain), it is important to understand this quantity. These depen-

dencies will be discussed in more detail in Sec. 8.2, including the differences

between the two crystal structures as well as the temperature dependency

of the strain.

The improvement of the QY for core-shell QD has been found to be es-

pecially large for high shell thicknesses, and so-called “giant” shell QDs,

which show a strong reduction of blinking behavior during emission.[34–37]

This “blinking” can be identified in the observation of the emission of single

QDs; the observed QD doesnt emit continually, but shown times without

luminescent recombination in between, so-called “off” times. In ensemble

measurements this behavior manifests itself by an effective reduction of QY.

The origin of the blinking is often explained by recombination of electrons

ans holes through an Auger process.[38, 39]

For instance Cragg and Efros have provided a description of the process, and

find that the Auger recombination rate depends on the size and the shape

of the confinement potential. A soft potential barrier should reduce the

amount of Auger recombinations drastically by three orders of magnitude.

This soft barrier can be achieved by a graded interface layer between the

core and the shell material, and would lead to a slow transition in electronic

properties between the two materials. This points out the importance of

a precise knowledge of the interface. Additionally, they find strong oscilla-

tions in Auger recombination rate, when the potential size is reduced. So

in principle, it is possible to suppress Auger recombination by choosing the

right “magic size”. [40]

Already in 2011 Garc´ıa-Santamar´ıa et al. found a strong reduction in blink-

ing behavior and a decreased Auger recombination for their CdSe/CdS core-

shell QDs (also called dot-in-dots) and attributed their findings to a graded

interface between core and shell. Which they see evidenced by the obser-

vation of CdSe and CdS LO phonon replica as well as a mixed overtone in

fluorescence line narrowing measurements (FLN) and interpret those as an

alloyed phonon modes at the interface.[41] Even though, his assignment of

the phonon modes might be debatable, since second-order mixed CdSe-CdS

modes yield similar energies, the resulting conclusion is in line with previous

ideas. Wang et al. for instance have come to a similar interpretation of their

results on CdZnSe/ZnSe QDs where they attribute the reduction in Auger

recombination rate to the presence of a graded transition between core and

shell.[42]

Furthermore, Tschirner et al. demonstrated evidence of an alloyed inter-

face layer by Raman spectroscopy combined with ab initio calculations.[43]

In a series of different shell thicknesses added to the same QD, they find

a mode in the Raman spectrum that increases in intensity for higher shell

thicknesses and correlate this with calculation on alloyed bulk material fre-

quencies, while also addressing the occuring strain in the hetero structure

in the paper.

Finally, Mourad et al. find effects of an randomly alloyed interface layer

for CdSe/CdS QDs which is visible in absorption measurements. In the

measurements additional transitions appear for alloyed CdSexS1−xQDs[44]

and they interpret those states to deeper valence band states to the lowest

conduction band. The absorption measurements reflect their findings form

tight-binding calculations. The corresponding absorption lines shift between

the lowest main transitions of the alloyed QD. The breaking of symmetry of

the charge carrier wave function compare to the pure binary QDs leads to

a relaxation selection rules, so that formerly prohibited transition become

relevant and observed.

In 2016 this view is completed by a study from Vaxenburg et al (with Efros

and Rodina), who find the Auger recombination rate originates from the non

radiative recombination of the biexciton (BX) ground state in the CdSe/CdS

QDs. Taking into account the biexciton fine structure, that is caused by the

asymmetry of the QD (caused by crystal field or non-spherical shape) and

the hole-hole interaction, they find these BX are energetically identical to

negative trion states. The negative trion recombination channel however is

suppressed when the hole is stronger localized than the electron. The height

of the Auger recombination rate depends on the core size as well as the

shell thickness and shows an oscillatory behavior depending on both quan-

tities, which originates from the overlap between of the three single-particle

states and the wave function (oscillation) of the excited charge carriers. An

additional influence is posed by the temperature, which generally enhances

Auger recombination rate.[45]

All those works imply a very strong dependence on the interface and the

surface of the QD. If it is not intentionally grown, the question is where

this alloyed interface layer stems from and how to enhance it. A possible

origin of an alloyed interface can be interdiffusion of atoms due to elevated

temperature during the synthesis. The issue demonstrates that a deeper

understanding and knowledge on the interplay between core and shell in

mandatory to improve the QDs on all fronts.

5 Theoretical background: Raman spectroscopy

In this Section the theoretical ground work will be introduced, that will be

used for the evaluation of Raman spectra presented in the work. First the

theoretical description of Raman effect in bulk crystals will be addressed, as

the effect lays ground to many of the measurements presented here. This will

followed by two Sections focussing on properties, which can be determined

from the observed Raman spectra. The strain on the crystal lattice, which

can be determined via an energetic shift of the phonon mode on the one hand

and the coupling strength between excitons and phonons, which manifests

in the higher order Raman intensities observed on the other hand.

5.1 Raman effect in bulk crystals, Raman spectroscopy setup

and interpretation

The Raman effect is based on the scattering of photon with the collective

vibrations, the phonons, of a crystal lattice of a solid. In the process of this

interaction of the photon with the solid, a lattice vibration is either gener-

ated or exterminated fulfilling momentum- and energy-conservation. Thus,

when analyzing the change energy experienced by the light, the effect pro-

vides direct information on the lattice vibrations of the examined solid. This

process occurs additionally to the elastic scattering of photons at the matter

without energy transmission, which is called Rayleigh-scattering, and leads

to photons with the same energy but different momentum after scattering as

compared to the initial photon. Due to higher probability, the elastic scat-

tering process dominates the spectrum of scattered light, with an intensity

higher by the order of magnitude of 106than the Raman scattered light.

In the macroscopic theory the interaction of light with a material is de-

scribed as an interaction between the electronic wave with the polarization

of a solid medium via the susceptibility.

P(r, t) = χ(ki, ωi)Ei(ki, ωi) (1)

Where χ(ki, ωi) is the susceptibility of the medium, P(r, t) polarization of

the medium (at position rand time t), and Ei(ki, ωi) electromagnetic field

as a harmonic wave with the field vector kiand frequency ωi.

This susceptibility however depends on the position of the atoms within

the solid, which in return is altered by the vibration of the lattice. The

interaction can then be consider as a perturbation of susceptibility, caused

by phonons.

Q(r, t)m=Q(q, ω0)·cos(qr −ω0t) (2)

The influence of the phonons on the crystal lattice is well described using

the normal coordinates of the vibrations Q(r, t)m(q wave vector and ω0the

eigen frequency of the harmonic phonon mode m) and the effect of a phonon

on the susceptibility can be approximated with Taylor series on dependence

of Q(r, t):

χ(ki, ωi) = χ0(ki, ωi) + (δχ

δQ)⏐⏐⏐⏐0

Q(r, t) + ... (3)

This splits the polarization in to parts, one unperturbed, which corresponds

to the part of the Rayleigh scattered light and one part induced by interac-

tion with phonons, which is the Raman scattered part of the light:

P0(r, t) = χ0(ki, ωi)Ei(ki, ωi)·cos(kir−ωit) (4)

Pinduced(r, t) = (δχ

δQ)⏐⏐⏐⏐0

Q(r, t)Ei(ki, ωi)·cos(kir−ωit) (5)

Together with Eq. ,this can be reformulated as:

Pinduced(r, t) = 1

2(δχ

δQ)⏐⏐⏐⏐0

Q(q, ω0)Ei(ki, ωi) (6)

[cos{(k+q)r−(ωi+ω0)}+cos{(k−q)r−(ωi−ω0)t}] (7)

For the electromagnetic wave, this means the incoming wave is split into one

wave with the wavevector ks(AS) = ki+qand the frenquency ωs(AS) =

ωi−ω0, and another wave with ks(S) = ki−qand ωs(S) = ωi−ω0. In case

of ks(AS) the wave gains the momentum qand the energy of one phonon (in

the form of ω0), for ks(S) the wave gives a momentum qand the energy of one

phonon to the lattice, and hence creates one phonon. These formula show

that momentum and energy conservation are intact in the Raman process.

In case a vibration is created, the process is called Stokes, when a vibration

is exterminated the process is called Anti-Stokes, while ω0corresponds to

the Raman shift.

Since the wavevector of the incoming electromagnetic wave (after kphoton =

2π/λphoton) is about two orders of magnitude larger than the size of first

Brillouin zone, as a result of the momentum conservation, the interaction

with one phonon at the center of the Brillouin zone, the Γ-point is possible.

For Raman processes of higher order, so including more than one phonon, in

principle the interaction can take place with phonon from the whole Brillouin

zone. In the macroscopic description those processes are captured by the

development of the Taylor series in Eq. 3 to higher orders.

Additionally Equation 3 leads to the definition of the Raman tensor R,

R=(δχ

δQ)⏐⏐⏐⏐0

Rij =(δχij

δQm)⏐⏐⏐⏐0

(8)

which is the derivative of the susceptibility in all dimensions from normal

coordinates of all phonon modes m. It represents the symmetry of a given

crystal structure and can be determined under consideration of group the-

ory. It is used to calculate the measurable intensity of the Raman scattered

light I∝ |ei·R·es|, for an experimental geometry, given by eiand esas

the polarization of the incoming and the scattered light. This results the

selection rules, that show under which an interaction between incoming light

and the matter can be observed.

When the energy of the incoming light corresponds to an electronic state of

the analyzed material, the Raman process becomes resonant and the inten-

sity of Raman scattered light becomes dramatically increased due to a much

higher interaction cross section. This is also true for a process where the

energy of the Raman scattered light equals an electronic transition. This

effect become even more important, when the analyzed subject is not a cys-

talline bulk material, but a molecule since their electronic states are much

further separated. Also the vibrations of molecules can be investigated with

Raman spectroscopy, in fact the Raman effect was originally discovered for

molecules (Nobel price in 1930).

In this way, Raman spectroscopy can be applied to many different fields.

Here it is used for the investigation of nanocrystals, where it reveals size de-

pendences for the lattice phonons, the different strain conditions that occur

for core-shell crystals and even surface modifications on the nanocrystal can

be observed.

5.2 Strain determination from Raman spectroscopy

Generally, the change in phonon frequency ∆ωin relative to the phonon

frequency of the corresponding unstrained material ωcaused by a change of

lattice constant (∆a) relative to the optimal, unstrained lattice constant a,

can be described according to Scamargio et al., using the Gr¨uneisen param-

eters for the LO phonon of CdSe and CdS γCdSe = 1.1 [46] and γCdS = 1.37

[47].

∆ω

ω=(1+3∆a

a)−γ

−1 (9)

[48] This uses ∆ω=ω−ω0, the relative Raman frequency shift of a sample

(ω) compared to an unstrained reference(ω0), such as the corresponding

bare core for CdSe or bulk material for CdS, and gives ∆a=a−a0, the

epitaxial strain due to the lattice mismatch (a0is the free-strain and ais

the strained lattice parameter). The choice of unstrained reference here, in

contrast to bulk-like structures, is complicated by the fact that the phonon

should be affected by confinement. An overview over results of different

studies is given by Dzhagan et al. [49] and illustrates that independently of

the method used for determination of the phonon frequency, the variation

for diameters smaller than 10 nm is non neglegable. The majority of studies

find a variation of 203 to 211 cm−1just between the diameters between 2

and 7 nm. This overview can be found and be discussed in more detail in

Sec.8.2 and 9.

5.3 Exciton-phonon coupling strength determined from Ra-

man spectroscopy

The coupling between excited carriers and the crystal lattice can be under-

stood as Fr¨ohlich interaction[50]. It describes the interaction of the polar-

ization caused by an electron-hole pair in a dielectric environment with the

exciton itself. A local point charge causes a force on the ions in its surround-

ing and the resulting displacement creates a polarization which acts on the

charge itself. A longitudinal optical (LO) vibration of a chain of atoms in

a polar crystal results in a polarity which can e.g. couple to photons. This

vibration is changed, when the equilibrium positions of the atoms are dis-

placed due the presence of a point charge. But also the point charge feels a

force, induced by the polarization caused by the LO vibration and hence its

properties are influenced, resulting in a complex entanglement.

Huang and Rhys addressed the problem of the change of an electronic tran-

sition, when it is coupled to a lattice with perturbation theory[51]. They

introduced a dimensionless parameter Sto adjust their equations to exper-

imental observations. This parameter is now called Huang-Rhys factor and

is used to quantify the coupling strength. The Huang-Rhys factor can be

estimated from Raman spectra, but a quantum mechanical description is

needed to translate observations of the measurement.

The interaction of point charge and lattice is different for vibrations of dif-

ferent symmetry, higher-order vibrations. This results in different-order

phonon processes being disturbed differently, which is reflected in changed

intensities of the related Raman bands[52]. This then allows the calculation

of the coupling strength from the intensities in a Raman spectrum. For

a system with electronic transitions, in a certain lattice configuration, the

energy of the ground state reads as:

Ei=1

2mω2

LOq2,(10)

while the energy in the excited state is

Ej=Eij −√2∆ωLO (mωLO

¯h)1

2q+1

2mω2

LOq2(11)

with the excited state energy Eij, the phonon frequency ωLO and qas the

normal mode coordinate of the lattice vibration. The overlap between the

wavefunctions of the lattice vibration and the electronic exitation can then

be calculated following Frank-Condon theory. The corresponding eigenfunc-

tions to the energies of excited and ground state are given by

φn(p) = (√mω/¯h

√π2n!)1

¯h

mω q2Hn(√¯h

mωq)(12)

Hα(q) being Hermite polynomes. In general, the overlap between the wave-

functions of two linearly displaced harmonic oscillators can be expressed by

⟨n|m⟩=∫∞

−∞

φm(q)φn(q)dq (13)

Following the works of Keil et al. and Martin et al.[52, 53], this integral

can be solved using the following relation between Hermite- and Laguerre-

polynomes: ∫∞

−∞ e−x2Hm(x+y)Hn(x+z)dx = 2n√π m!zn−mLn−m

m(−2yz)

[54], which leads to:

⟨n|m⟩=(m!

n!)1

e−1

2∆2∆n−mLn−m

m∆2.(14)

with ∆ being a dimensionless parameter describing the displacement of the

excited harmonic oscillator potential caused by the lattice vibration.

This Frank-Condon overlap is part of the Raman scattering cross section in

scattering theory. Following Klein et al. and Albrecht et al., the Raman

scattering cross section for an n-order process at temperatures near 0 K

is[55, 56]:

|σn(ω)|2=µ4⏐⏐⏐⏐⏐

∞

∑

m=0

⟨n|m⟩⟨m|0⟩

Eij +m¯hωLO −¯hω +iΓ⏐⏐⏐⏐⏐

(15)

with the incident photon energy ¯hω, the homogeneous linewidth Γ of the

optical transition, the electronic transition dipole moment µand mas inter-

mediate vibrational level in the excited state. It can be shown that S=∆2

applies. The ratio of the intensities of different-order LO Raman bands then

yields an expression that only depends on the value of ∆ and known quan-

tities and thus allows an evaluation of the coupling strength.

Many publications follow this proceeding, first introduced by Merlin et al.

and Alivisatos et al.[57, 58]. However, a factor in the reported equations is

inverted. The Frank-Condon overlap (14) differs in numerator and denomi-

nator of the factor m!

n!and in the upper index of the Laguerre polynomial.

Furthermore, a recent calculation based on a Brownian oscillator model by

Kelley et al.[59] suggests that this expression might be underestimating the

influence of the spectral broadening of the electronic bands. It is represented

as Γ in the Raman-cross section in (15) and mainly varies due to size- and

shape variations. This could give rise to changes in the absolute value of the

Huang-Rhys factor. However, relative comparisons should be appropriate

and general quantitative comparisons should not be inhibited[59].

6 Experimental methods

As mentioned before, a big part of this work is the characterization of the

CdSe/CdS QDs by means of Raman spectroscopy. This method provides

a wide range of information on the crystal properties through probing the

phonons of the examined QD sample. Like this, it is possible to gain in-

formation like lattice strain for core and shell, that are not easily available

by other techniques. Determining the influence of a shell on the core lattice

parameter could otherwise only be performed by HRTEM, which would en-

tail high evaluation effort and statistics. Especially the lack of possibility to

align the spherical QDs according to their crystal axis, makes it difficult to

measure atomic distances accurately.

Although optical techniques such as PL and absorption also provide an in-

direct indication of strain in the structure in form of a strain-induced shift

of transitions, they predominately show the cores properties because of the

higher carrier concentration and lower transition energies in the core. Addi-

tionally, to the investigation of everything that influences the lattice phonons

in the sample, the intensity in Raman spectroscopy can be used to determine

the exciton-phonon coupling or electronic density of states through analysis

of resonant conditions.

An additional method used in this work for the characterization of the QDs

is photoluminescence spectroscopy, which provides insights on the electronic

fine structure, which will be presented in chapter 11. As well as the obser-

vation of phonons under resonance conditions.

6.1 Raman spectroscopy setup

In order to analyze the Raman signal of a sample, a coherent light source

with high intensity is needed, which is provided by a laser. This is necessary

to on the one hand gain the a high signal intensity and on the other hand to

be able to separated the elastically scattered from the inelastically scattered

light to be analyzed. In some setups this separation is realized with the help

of a notch filter, that is reflective for a corresponding laser wavelength but

transmissive for all other light, which is positioned to suppress the excita-

tion laser wavelength in the scattered signal coming from the sample. Since

the quality of the filters is limited to a certain width, the edge of the filter

can’t be infinitely close to the laser wavelength, so only Raman signals can

be observed that aren’t too close to the excitation and thus suppressed can

be observed.

Figure 6: Experimental Raman setup using a triple monochromator, used

for several measurement within this work. The optical path way marked

with blue dashed belongs to the macro setup, the red dashed line show the

pathway of the micro setup. The makro setup is used for the in situ Raman

measurements in particular because of the higher spatial demands for the

synthesis. Taken from [60]

Here however, a triple monochomator (Dilor XY) is used instead. The

first two monochromators are used in substrative mode and act as a bandfil-

ter for the excitation wavelength and suppress stray light. This filter can be

finely tuned and even signals close to the excitation can be separated, de-

pending on the quality of alignment and the hole widths. This is in contrast

to the notch filter which is specific for the excitation wavelength. The third

monochromator is used to disperse the signal for energetic resolution. The

dispersiveness is determined by the grating used and the spectral region to

be analyzed. Fig. 6 shows the setup used for the majority of the Raman mea-

surements presented in this work. It uses a grating with 1800 grooves/mm

and neon and argon lines are are used for calibration to absolute energies.

The scattered and dispersed light is detected with a nitrogen cooled silicon

based charge coupled device, positioned behind the third monochromator.

The setup provides a resolution of 0.4 cm−1and in principle can be used in

two different modes.

Either the sample is placed under a microscope (Fig. 6, optical pathway in

blue), which provides the opportunity to excite and detect locally with a

focus laser spot with down to µm width and thus gives lateral resolution on

the sample for observation of small samples or microstructures. The other

mode, here called macro-mode (Fig. 6, optical pathway in red), instead of

the microscope uses a lens with a focus distance of 5 cm. This leads to a

wider spot on the sample that is illuminated and hence a larger area that the

signal is collected from. In this way the local power density is lower and the

risk of damage is reduced. At the same time the Raman signal is averaged

over larger areas of the sample. This mode can be used for samples without

local structures or samples that are dissolved. Since in this work focusses

on colloidal QD with sizes far below optical resolution, most measurements

presented here are recorded using this mode.

For excitation an Ar-Ion laser (Coherent Innova, Spectra Physics Stabilit)

was used, offering different laser lines between 457 and 647 nm. For sup-

pression of plasma lines, originating from the laser tube, a prism pre-mono-

chromator is used as a filter.

For low-temperature measurements, the samples are cooled in an Oxford

microcryostat with liquid helium in an isolating vacuum, or with a Linkam

stage with liquid nitrogen for higher temperatures. We estimate the tem-

perature accuracy to account to ±5 K for both cryostats.

6.2 Photoluminescence excitation spectroscopy (PLE) setup

The extensive investigation with Raman spectroscopy in this work will be

completed with photoluminescence excitation spectroscopy (PLE), to add

the analysis of electronic properties of the QDs to the more structural in-

formation gained from observation of the phonons.

Regular photoluminescence (PL) measurements use a fixed excitation wave-

length and analyze the light that is emitted by the investigated sample

under this given excitation. Especially when the excitation is close to reso-

nance with states with high occupation probability such as the ground state,

the PL spectra are strongly dependent on the excitation wavelength. The

analysis of this dependency can be performed with a method called pho-

toluminescence excitation spectroscopy (PLE). By variation of excitation

wavelength, this method can reveal insights in the electronics states of the

sample beyond the ground state, including information on electronic states

bi- and triexcition states, different trap or defect states, or states induced

by doping.

Figure 7: Setup used for the PLE measurements in this work. As light

source the XBO lamp was used in combination with a double monochro-

mator (red lines) for monochromatization. The samples were cooled in a

self-stabilized cryostat with liquid helium. The collected signal was analyzed

with a spex monochromator and CCD(left). Image from Gordon Callson,

private communication.

Additionally, energy dependent modulations in intensity give informa-

tion on the exciton phonon coupling strength to state in resonance. This

quantity can simply be determined comparing the intensities of the tran-

sition and the phonon replica. Thereby the probabilities of the process of

excitation and subsequent emission of a photon with and without generation

of a phonon are compared, which directly gives a measure of the interaction

probability of the generated exciton with the phononic system. This means

the method provides complementary information to results gained from Ra-

man measurements, where the monitored process is different, as described

in Sec.5.3. Additionally coupling factors derived from Raman spectroscopy

are seldom determined under resonant excitation in the ground state as for

many systems under these conditions the Raman signal is overpowered by

a highly efficient PL and hence hard to decipher.

The PLE setup (see Fig. 7) is similar to a regular PL setup, but with an exci-

tation source, which has to offer continuously tunable excitation energy and

a high power output. The light must be either monochromatic or go through

a monochromator, for a high resolution of the excitation energy dependence.

Here, a Hg high-pressure lamp with parallelization optic and monochroma-

tor combination is used. With a slit width of 1 mm and a grating 150 1

mm of

the monochromator, the excitation axis can reach resolutions up to 5 meV in

the spectral range used in this work. The monochromatized light is focussed

on the sample, which is positioned in a self-stabilized liquid He flow cryostat.

The resulting signal from the sample is collected under a small angle (about

10◦) in relation to the excitation (approximately back-scattering geometry)

and subsequently spectrally decomposed in a monochromator (1800 1

mm , slit

180 µm) and detected with a CCD. For the measurement, the excitation

energy is tuned stepwise and spectra are recorded with a fixed detection

monochromator position. This results in 2d data, with the detected signal

in one axis, stacked according to their excitation energy.

7 Synthesis of CdS/CdSe colloidal QDs and sub-

sequent Silica encapsulation

Colloidal QD are QD synthesized and kept stable in a solution. This synthe-

sis however has an impact on the properties of the final sample. For instance

the synthesis conditions can be used to tune the size of the QD, as well as

the crystal structure and the shape of the QD. An Additional challenge is to

achieve a size distribution within the ensemble, that is as small as possible.

These subjects have undergone a lot of research during in past years, in

many parts by the group of Z. Hens, who also provided our samples.

Here, the syntheses and influences of synthesis conditions on CdSe QDs will

be presented in the first subsection, focussing on comparable QDs to the ones

used in this work. This will be followed by the different synthesis options for

a subsequent CdS shell addition for the synthesis of core-shell QDs, which

are favored for application because of improved properties. Those synthesis

options and influence on the final QDs are then compared (new syntheses

from Z.Hens group), including measurements that were performed in the

context of this work.

Finally the synthesis of a silica shell around the QD, as needed for applica-

tion in bio-labelling, will be presented as it is performed for the silica shelled

QDs in Sec. 12. The observations on the silica encapsulated QDs presented

in this part are based on samples comparable to those used in this work as

a prerequisite.

7.1 Synthesis of colloidal QDs

Colloidal QDs of various forms can be synthesized in a setup that is, com-

pared to MOVPE or MBE, less laborious. It consists basically a temperature

controlled vessel for temperatures typically between 200 and 400◦C, that is

sealed to reduce desorption of the solvent into the environment, and syringes

for controlled precursor injection (example see Fig. 8 left). The vessel is filled

with a mixture of solvent and ligands, both with boiling points above syn-

thesis temperature. Often chloroform, hexane or toluene are used as solvent

and oleic acid, trioctylphosphine (TOP), trioctylphosphine oxide (TOPO)

or oleic acid (OA) as ligand (molecules see Fig.8 left). The precursor con-

sists of the inorganic constituents of the intended QD, bond to an organic

surfactant, that mediates the growth. As precursor for CdSe QDs, cadmium

oleate and selenium is dissolved in octadecene (ODE-Se) are widely used.

The choice of solvent, ligand and precursor, as well as the temperature and

time of the synthesis determines the crystal structure, shape and size of the

final QD. By adjusting these parameters, the properties of the final QD can

be finely tuned.[61–64]

For QDs, consisting of a single material, the procedure of choice is the seeded

growth method, which consists of two main steps. First, there is the nu-

Variable temperature

Injection of constituents

Micropipette,

variable volume

500µl

Synthesis

solution

Oleic Acid (OA)

H3C

Trioctylphosphinoxid (TOPO)

Cyclohexane

Tolouene

CH3

Figure 8: Left: Schematics of a vessel used for synthesis of colloidal QDs.

The vessel is sealed of with stopper, but provides the possibility to inject

the constituents of the synthesis. The volumes each ingredient is precisely

measured with a micropipette with appropriate volume and interchangeable

tip to prevent contaminations. The vessel is heatable and the temperature

is constantly observed. Right: Chemical structure of ligand and solvent

molecules typically used for colloidal QD stabilization.

cleation of the crystal seeds, followed by a subsequent growth phase in the

second step. The nucleation takes place, when the temperature of the react-

ing solution exceeds a critical temperature. At this temperature, the both

precursors convert to active monomers efficiently. After surpassing a certain

level of supersaturation, the monomers spontaneously start to form crystal

nuclei, which consumes energy and causes the temperature to drop and stops

the nucleation. A high degree of supersaturation is reached by applying the

“hot injection” method [65–68], where the precursors are injected to a hot

reaction solution of solvents and ligands. This concentrates the nucleation

to a short time frame, thus this effect is called “burst nucleation”.

The remaining active monomers in the solution can now deposit on the nu-

clei, growing the crystal. The effect that smaller QDs grow faster leads to a

smaller and smaller size distribution and is called “focussing”. When the de-

sired size is reached, the reaction can be stopped by rapidly cooling down the

solution. If the solution remains at growth temperature, once the monomers

have been incorporated, a ripening process begins. This causes some crystals

to grow, while others shrink and provide active monomers for the growing

crystals. This process is called “Oswald ripening” (also present for MOVPE

or MBE growth of QDs) and is essentially a “defocussing”-influence on the

size distribution, as it increases the halfwidth of the distribution. For a

small size distribution at optimum, this ripening growth regime should be

avoided. The reaction chemistry and how it can be engineered to tune final

size and broadness of the size distribution has been the subject of many

studies.[61–64]

Figure 9: Left: Concentration distribution c(r,t) obtained with the initial

parameters as given in the Supporting Information. The color scale indicates

an increase of c in the direction yellow orange red black. The gray line marks

the critical radius (rc). Right: diameter in dependence of the synthesis time

with clear focussing of the diameter [62]

Ab´e et al.[62] for instance have investigated the size development with

a combined approach of experiments and numeric modeling with a rate

equation model. This lead to a description of the size distribution during

synthesis time, as shown in Fig. 9 left, with the before mentioned phases of

nucleation (1), reaction driven growth (2a) and ripening driven growth (2b).

The findings accentuate the necessity to choose the right time to stop the

reaction in order to achieve a sharp size distribution. Figure 9 right shows

the mean diameter and the dispersion as a function of reaction time, with

the growth phases marked as in Fig. 9. This shows well, that for minimal

dispersion, the growth should be stopped before the ripening phase starts, as

a clear minimum in size dispersion is visible due to the “focussing”-process.

They also find that the nucleation can be tuned by the rate of active

monomers or the solute formation, whereas the exact temperature of in-

jection and growth doesnt influence the diameter after focussing much, as

the change in temperature automatically modifies the growth rate. The di-

ameter however is increased by decreasing the monomer formation rate, as

Ab´e et al. [62] found that the CdSe formation rate depends in first order on

the Cd and Se precursor concentrations. In the following year they find yet

a different way in crease the QD size and show that increasing the amount

of free acids in the synthesis effectively has the same influence on the reac-

tion as the increase of solute solubility.[63] As the free acids are responsible

for the coordination of the cation precursors, Ab´e et al. conclude that the

increased size is due to an increased solute consumption that leads to the

formation of fewer QDs and thus larger final sizes. This, however, reduces

the “focussing”-effect and thus increases the size distribution of the final

QD, and hence should not be the preferred method of increasing the QD‘s

final size.

These results lay the fundament for a well-controlled growth of QDs with

predetermines final sizes, which in essential for any application. They also

provide simulation models that can be applied to study the synthesis and

predict the outcome of a set synthesis. Since for applications of colloidal QDs

on a larger scale, upscaling and automation is essential, the optimization of

the synthesis for an optimal postfocussed diameter and optimal chemical

yield, as well as a precise control over the crystal structure, is an absolute

prerequisite.

7.1.1 Exemplary CdSe QD syntheses

Looking at a procedure that is often followed or used slightly adapted, a

more detailed insight into the chemical procedure can be gained. This pro-

cedure was described first by Jasienak et al. and produces zincblende CdSe

QDs. First the Se precursor needs to be prepared by dissolving selenium

in octadecene (forming ODE-Se). In preparation of the synthesis, the cad-

mium oleate Cd(OA)2precursor is liquified at 100◦C, and added to further

octadecene (ODE). The mixture is degassed for 1 h at 100◦C under (dry) ni-

trogen atmosphere. Afterwards the temperature is increased to 265◦C, and

the ODE-Se is injected to start the synthesis. This procedure is also called

“hot injection”, as the precursors are injected to the hot reaction solution.

The temperature of the mixture drops after injection automatically (ODE-

Se is at room temperature). The CdSe QD growth continues at 235◦C until

it is stopped by rapid cooling. The zincblende CdSe NCs produces by this

method are stabilized by oleate ligands on the surface.

For wurtzite CdSe QDs a similar procedure is used, as described in Ref-

erences [69, 70]. Here, the Cd precursor is prepared by mixing CdO with

TOPO and ODPA and heating the mixture for one hour under vacuum.

The solution is subsequently heated to 345◦C under nitrogen atmosphere

and TOP is injected in preparation for the synthesis. Then, the Se pre-

cursor (Se disolved in TOP) is added to the solution to start the synthesis,

which just as for zincblende QDs can be stopped again by rapid cooling.

The wurtzite QDs resulting from this synthesis are stabilized by a mixture

of TOP and TOPO.

After the synthesis, the both types of QDs need to be purified to remove

the excess precursor and ligand molecules. This is realized by precipita-

tion through the addition of solvent, which is followed by centrifugation to

achieve a separation of the QDs from the solution (including residue pre-

cursors and ligands) due to their higher density. The separated QDs are

resuspended by addition of further solvent. This leads to a QD solution

with reduced, but not fully removed content of remaining synthesis prod-

ucts. Hence these purification steps are repeated several times (often 3), to

successively purify the QD solution.

However, the synthesis of single material QDs usually only represents the

first step in fabrication. The subsequent addition of a semiconductor mate-

rial will be discussed in the following Section 7.2.

7.2 Semiconductor shell addition methods for bare colloidal

QDs and properties of the core-shell QDs

To create colloidal core-shell QDs which show widely improved luminescent

properties (as discussed in Sec.4.2), first the bare core QDs are grown, as

described in 7.1, then a shell is build around the QD. For this subsequent

addition of a shell materials of similar crystal structure, two different op-

tions can be found in literature. On the one hand, the Successive Ionic

Layer Adsorption and Reaction (SILAR) method is widely used and works

on zincblende, as well as wurtzite QDs. The method provides a very precise

control over the shell thickness as the atomic layers are deposed one after

another. This is realized by the addition just one of the shell-constituents

precursor at growth temperature to saturate the surface, subsequently fol-

lowed by the other constituent, forming monolayer after monolayer. For a

CdSe QD to be covered by CdS, this would be the Cd precursor followed

by S precursor. The added amounts need to be calculated exactly to reach

complete coverage of the QD, otherwise a uniform shell cannot be formed.

After each precursor injection, there must be enough time left to ensure

complete coverage (often about 10 minutes is used). An alternative to this

waiting time would be to use higher concentrations of precursor than needed

followed by a rinsing step to remove excessive precursor between each addi-

tion of each monolayer. This option however is even more time-consuming

and therefore rarely applied. Instead often an annealing step is carried out

between to the steps, which is believed to ensures good crystal quality, espe-

cially for QDs with high shell thickness (“giant shells”). In order to reduce

the synthesis time, different ways have been investigated. The “flash” syn-

thesis, as shown by Cirillo et al., provides a faster shell addition with high

crystal quality.

7.2.1 Exemplary SILAR and flash synthesis and comparison of

resulting properties

For a typical SILAR synthesis for the S precursor, the S is dissolved in

octadecene (forming S-ODE). For the Cd precursor, CdO is dissolved in a

mixture of OA and/or ODE. Before the reaction, n-octadecylamine (ODA)

and ODE were mixed and degassed for 1 h at 100◦C under nitrogen flow.

Afterwards the prepared CdSe cores in hexane are added and solution of

ODA and ODE and the mixture is degassed for another hour at 100◦C.

Then the temperature is raised to 225◦C and the successive addition of Cd

and S precursor is started, with breaks to account for reaction time and

possible additional annealing steps for higher crystalline quality.

As before mentioned the advantage of this method is the precise control of

the shell thickness (monolayer-accuracy), the downside is labour intensity

and time. The synthesis of “giant shell”-QDs is reported to take between 30

min per monolayer[36] and up to 4 hours for low defect materials with inten-

sive annealing steps. Often for optimal morphological and optical properties

each step needs to be followed by annealing for 3.5-4h [36], which results in

a total synthesis time of over two days for a 15 ML shell thickness.

Avoiding this, Cirillo et al. [69] have demonstrated a method, which enables

the direct growth of a wurtzite CdS shell in one single step. The synthesis

of the shell takes 3 minutes only and results in good crystal quality and a

regularly formed shell, as shown in the TEM images and size dispersion in

Fig. 10. The method uses a different Cd precursor, carboxylic acid (OA) and

phosphonic acids as surfactant, which lays ground to the isotropic growth

of the shells. They also found that an excess amount of OA compared to

cadmium is necessary to prevent the formation of individual CdS QDs. The

shell thickness can be directly determined by adjusting the Cd amount of-

fered in the synthesis, as it is fully converted in the reaction.

For a typical synthesis, as used in [69, 70], the Cd precursor is prepared

Figure 10: a), b) and c) TEM images

of 8.9±1.3, 13.0±1.4, and 15.8±2.7 nm

total diameter QDs, bases of 2.5 nm

CdSe cores and synthesized with the

“flash” method, showing uniform shells

and no byproducts of the synthesis like

smaller CdS QDs, although the distribu-

tion for the highest shell thickness be-

comes broad, d) visualizes the diameter

distribution of the samples in a, b, and c,

taken from [69]

by heating in oleic acid and in TOPO dissolved CdO to 120◦C for one hour

while flushing with nitrogen. Subsequently the temperature is raised to

330◦C, and TOP is injected as soon as the solution turns clear. This is

followed by the addition of the previously prepared QDs (wurtzite) and the

S precursor, which consists of S dissolved in TOP. The reaction is stopped

after a few minutes by rapid cooling and addition of toluene to accelerate

the cooling. Finally the finished core-shell QDs are purified repeatedly by

the addition of isopropanol and methanol, centrifugation and redispersion

in toluene.

This entails that the shell synthesis with the “flash” instead of the SILAR

method on the one hand is faster, and on the other hand is conducted at

higher temperatures. Regarding the finished resulting QD, this could either

lead to a sharper interface between core and shell, since the time span is

much shorter during which diffusion of core and shell molecules can take

place in comparison to SILAR. Or since the temperature of the “flash” pro-

cedure is much higher and diffusion of atoms is essentially a temperature

activated process, this could lead to a more intense diffusion for a shorter

period of time. If this method also results in a smooth graded interface

between core and shell, that is comparable to SILAR produced samples, is

a question of which of the influences, temperature or time, has a stronger

influence on the interface. Since this interface has mainly been investigated

for core-shell QDs, that were produced with the SILAR method (see also

Sec,4.2) and a smooth transition between to two materials seems favorable

for the QD QY, this property should be addressed in particular, additional

to the more general luminescent attributes of the “flash” produced QDs.

Figure 11 shows absorption and PL spectra of the QDs already depicted

Figure 11: Right: a) Absorption and b) PL spectra of the same QDs shown

in Fig. 10, Left: a)+b) Raman spectra of the QD with thinnest shells in the

publication together with a close up on the CdSe phonon region including

underlining fits for comparison with Tschirner et al. [43], measurement

within this context of this work, images taken from [69]

in Fig. 10, revealing a red shift with increasing shell thickness, as expected

(Sec. 4.2), and an increasing halfwidth of the energetically lowest transition,

as can be expected from the size distributions shown in Fig. 10. The absorp-

tion spectra are dominated by the CdS shells absorption, as it represents the

highest volume fraction in the QDs. This shows, that regarding the lumines-

cence “flash” grown QDs can have similar properties to those produced with

the SILAR method. In order to find out about the interplay between the

two lattices, we analyzed the samples with Raman spectroscopy, as previ-

ously evidence for an interface formation in SILAR CdSe/CdS QDs has been

found in the low energetic shoulder of the CdSe phonon mode (Tschirner et

al. [43], see also Sec. 4.2). Of course apart from a possible interface forma-

tion, the interplay of the two lattices causes strain in the core-shell system

(Sec.4.2), which can also be analyzed by Raman spectroscopy, but will be

discussed Sec. 8 and 9. Figure 11 left shows Raman spectra of the thiner

shelled “flash” QDs presented in the publication of Cirillo et al. [69], which

are investigated as part of this work. The spectra reveal very similar overall

spectra compared to Tschirner et al. [43]. Additionally, a similar interface

mode to the one proposed by Tschirner et al. is observed, which again shows

the great similarities between the products of this two very different synthe-

sis. Even though the width of the interface cannot be quantified by Raman

spectroscopy, due to difficult quantitative interpretation of intensities, the

similar Raman spectra show that the QDs do have similar structures and

that the much faster “flash” synthesis is most probably a good approach for

a simplification of the QD growth.

While in this Section, we addressed the coverage of QDs in crystalline mate-

rial with similar lattice parameters, predominantly semiconductor materials,

in the following Section a different encapsulation entirely will be discussed.

The encapsulation of a QD with polymers or silica and other more or less

inert materials is primarily used in biological labeling applications and poses

a largely different interaction on the QD as the interaction between QD and

outer shell is less direct and not completely elucidated yet.

7.3 Silica encapsulation for biological applications

For biological applications, the colloidal QDs need to be covered in a material

that provides a chemical barrier to the aqueous and often non PH-neutral

environment, while being optically transparent. One of the most promising

candidates for encapsulation is silica, a well known and relatively biocom-

patible material. Silica has been shown to improve stability in polar solvents

under various harsh conditions, concerning pH and ionicity for instance. For

further discussions on this topical complex, see Sec. 4.1 and chapter 12)

One additional, important advantage of silica as capping material is that

the surface of silica can be functionalized with a wide range of chemical

groups, including amines and thiols, providing the possibility to couple the

biomolecules of interest and for specific targeting of cells or intracellular

structures.[71–75] These silica shell-QD complexes will be studies in the fi-

nal part of this work, together with a detailes analysis of the encapsulation

process.

Eventhough there has been much progress in this field of research during the

past year, it is unclear in which cases the silica encapsulation preserves or

even improves the PL of the QD and how exactly this is influenced. Many

groups find indications that differences in PL QY must stem from different

surface chemistries, but this surface chemistry and extent of interaction an

the surface of the QD is subject to speculations mainly.[73, 74, 76]

In this Section the aim is to address the previous results of the encapsulation

Figure 12: a) normalized PL spectra under UV illumination (454 nm) of a

flash-synthesized CdSe/CdS QD with and without silica shell. b) PL QY of

different QDs over time. c) normalized PLQY and absorption of the same

encapsulated QD as in a over time. Taken from [70] (cooperation partner),

The QDs are directly comparable to those used in this work.

synthesis that is also used in the in situ Raman experiment conducted in

this work. Aubert et al. have optimized the silica encapsulation for applica-

tion to “flash” synthesized core-shell QDs and show the resulting composites

have a high physicochemical stability. Those “flash” QDs can, opposite to

the conventionally used SILAR QDs[77], maintain their high luminescence

quantum yield after encapsulation and even after long periods of time in

aqueous solution and long term UV irradiation. This is shown in Fig. 12,

where Fig. 12a shows the emission wavelength remains approximately the

same and Fig. 12b shows the comparative intensities of SILAR and “flash”

QDs in water under UV illumination. While the SILAR QDs PLQY is

strongly reduced after less than 5 hours, the “flash” QD only reduces to

60% of the original PLQY after 100 h≈4days and seems to saturate there

(stays constant for over 14 days), as shown in Fig. 12c. This renders the

“flash” QD after encapsulation with the described procedure the perfect

candidate for long term cell observations. The origin of the different results

for SILAR and “flash” synthesized QDs might lie in their very different sur-

face chemistries[78].

The encapsulation synthesis will be described in the Section on the proce-

dure of the in situ Raman experiment (Sec.12.3). It is usually finished by a

purification step of precipitation, centrifugation and resuspension, just like

for the QD syntheses described in the previous chapters (not covered in in

situ Raman). Also technical details about the Raman observation of the

synthesis are presented in Sec. 12.3. Finally the results of the experiments

are presented in Sec.12, showing the formation of an interface between silica

and the QD and giving rise to the possibility of a more detailed analysis of

influences on the reaction, which could lead to further improvements of the

synthesis or at least a better understanding.

8 Structural and electronic properties of CdSe/CdS

quantum dots

In the following section, we take a closer look into the properties of the

material investigated in this work. Therefore, first the crystal structures

and optical properties of CdSe and CdS will be discussed, followed by an

overview of the properties unique for colloidal QDs based on those materials.

Then, we present typical Raman spectra, we regularly observe for those QDs,

and discuss the present phonon modes together their respective origins and

show in which way Raman spectroscopy can be used for the analysis of the

present material.

8.1 Crystal lattice and optical properties of CdSe/CdS QDs

Cadmium Selenide (CdSe) and Cadmium Sulfide (CdS) can be found in

wurtzite as well as zincblende (face-centered cubic, fcc) crystal structure,

hence it can crystallize in the hexagonal or the cubic close-packed form.

However bulk material can only be found in wurtzite structures; The zinc-

blende structure is found exclusively in nanostructures, usually with a syn-

thesis at lower temperatures and using different surfactants from the wurt-

zite growth.

Figure 13 shows the two crystal structures schematically for CdS. For the

Figure 13: Crystal lattice of wurtzite (left) and zincblende (right) CdS in a

ball and stick model. Taken from Narine Ghazarian private communication.

zincblende structure, the atomic distances are the same in all directions,

such the structure is isotropic. In contrast to this, the wurtzite structure

has one symmetry axis (the c- axis) with a larger lattice constant compared

to the other. Along this axis, the layers of the different atom species are

arranged in alternating sequence. The covalent bonds between the atoms

cause a higher charge density around the S atoms. This means that if the

structure ends (surface) with such an atomic layer, there is an unsaturated

particular charge that can influence the interaction with the environment lo-

cally. This surface can e.g. provide a reactive surface in the synthesis which

is used for the synthesis of elongated crystals. Additionally, this anisotropy

leads to pyro- and piezo electricity in the structures, which influence the

electronic properties and strongly effects strained core-shell structures.

The lattice constant of zincblende CdSe is a=0.613 nm [30] while the zinc-

blende CdS marterial has a slightly smaller constant of a=0.583 nm[31]. For

wurtzite bulk CdSe, the lattice constants are a=0.437 nm and c=0.697 nm

[30], and for wurtzite CdS a=0.416 nm and c=0.661 nm [32, 33]. Hence CdSe

consistently has a larger lattice constant compared to CdS. In a CdSe/CdS

core-shell QD this results in compressive strain for CdSe cores and tensile

strain for CdS shells (see also Sec 4.2, especially Fig. 5) and will cause pro-

nounced influences on the Raman spectrum, as will be shown later on.

Looking at the bonding potentials of the atoms often helps to understand

12345678

-10

-5

) (eV)

rkl (Å)

VCdS

VCdSe

dzb

dwz





Figure 14: Left: A plot of two-body inter-atomic potential energy for CdSe

and CdS as a function of inter-atomic distance. The function of the Lennard-

Jones-like inter-atomic potential Vij(r) and the potential parameters were

taken from Ref. [79]. T indicates the influence of increasing temperature.

Right: TEM image of a wurtzite 5.12 nm diameter CdSe QD without shell.

(Part of the WZ core series used in this work).

basic properties such as temperature dependence of a materials. Fig. 14

shows the two-body interatomic potentials for Cd and Se, as well as Cd and

S. The potentials are Lennard-Jones-like inter-atomic potentials which con-

sist of a long-range Coulomb interaction term (attractive) and a short-range

potential (repulsive) and are modified by parameters to reflect the char-

acteristics of the interaction between the atomic species. The parameter

shown here are taken form Gr¨unwald et al.[79]. Those potentials describe

the interaction between the two sorts of atoms and show the energetic min-

imum at the optimal interatomic distance, as well as how much energy is

needed to break the bond and how strong the interaction is in general. A

deep minimum means a strong interaction, a shallow potential curve means

the material has a high temperature dependence. This will be used and

discussed in more detail in Sec. 9.

500 550 600 650

400 450 500 550 600 650

total diameter

3.4 nm

4.7 nm

6.0 nm

7.4 nm

Wavelength (nm)

b) zincblende CdSe/CdS

core-shells, CdSe core 3.4nm

Absorption (norm.)

Wavelength (nm)

core diameter

3.0 nm

3.6 nm

4.2 nm

4.6 nm

4.9 nm

5.4 nm

6.2 nm

a) zincblende CdSe cores

Figure 15: Absorption spectra (room temperature) with UV excitation

(λ= 454 nm) of a) a series of colloidal zincblende CdSe QD with varying

diameter without shell measured on QDs in solution at room temperature

with UV excitation (λ= 454 nm). The intensities are normalized to the

first transition. As the diameter increases, the first transition shifts to-

wards lower energies because of reduced confinement. b) a series of colloidal

zincblende CdSe QD with varying CdS shell thickness on the same core

(diameter 3.4 nm) in solution. The intensities are normalized to the first

transition. As the shell thickness increases, the first transition shifts towards

lower energies because of reduced confinement.

As mentioned in Sec. 4.2, these colloidal QDs are especially interesting

because of their well-controllable size dependent properties, most promi-

nently visible in the energy of the lowest electronic transition. This size de-

pendence is caused by the quantum confinement effect and enables to tune

the wavelength of emission and absorption. The smaller the “box” (the QD)

the charge carriers are confined in, the higher the energetic ground state and

the more separated the excited states. This leads to a size dependence of the

absorption spectrum, which is examplarily shown in Fig. 15a) for a series

of differently sized zincblende QDs (same QDs as used in Sec 11) at room

temperature. As the QD diameter decreases and the confinement grows,

the absorption edge shifts (lowest energetic electronic transition) towards

higher energies. Since this dependency is well researched and reproducible

regarding the synthesis conditions, the size of synthesized QD is mostly de-

termined from absorption spectra, using a before constructed sizing curve.

The effect of an additional CdS shell on a CdSe QD on the absorption spec-

trum is shown in Fig. 15b). When a shell is added to the QD, the confine-

ment is partially relieved and the states are shifted towards lower energies.

The higher the shell thickness, the more pronounced is this effect, which

leads to the shift in absorption edge towards lower energies as depicted in

Fig. 15b). This means the shell not only stabilizes the QD’s surface by way

of saturating the surface bonds (Sec.4.2, but it also effects the optical prop-

erties through the confinement effect and the phononic properties by causing

strain. In the next section (8.2) the phononic properties of CdSe/CdS QDs

will be presented and analyzed.

8.2 Raman spectra of pure CdSe QDs and CdSe/CdS core-

shell structures

Since the phonon properties play an important role in this work, the Raman

spectrum of pure CdSe QDs and CdSe/CdS core-shell structures, wurtzite

and zincblende, should be addressed in particular.

100 200 300

zincblende core 4.2 nm

ωLO=207.5 cm-1

FWHM 6.7 cm-1

≈25.73 meV

Intensity (arb. units)

Raman shift (cm

-1

)

wurtzite core 4.2 nm

=204.7 cm

-1

FWHM 8.6 cm

-1

≈25.38 meV

Figure 16: First order Raman spec-

tra of two 4.2 nm diameter CdSe

QDs (T=10K), one with wurtzite,

one with zincblende structure. The

phonon frequency of the wurtzite QD

is lower than for zincblende and at

the same time it exhibits a slightly

larger halfwidth, which most proba-

bly originates form the crystals struc-

ture‘s anisotropy.

Showing the influence of the different crystal structures on the Raman

spectrum of a CdSe QD, Fig. 16 gives the first order Raman spectra of one

zincblende and one wurtzite QD of the same diameter d=4.2 nm. Despite

the difference in symmetry, the spectra appear very similar between the

two samples and are dominated by one single phonon mode. In principle,

the Raman spectrum of a wurtzite structures should consist of the A1, the

E1and the E2mode, which can be observed in the experiment under con-

ditions given by the Raman tensor(Sec. 5.1). However, for a sample with

randomly distributed QD, as used in Fig. 16 and measurement in backscat-

tering geometry without polarization, all should be allowed. Nevertheless,

those modes are neither visible here, nor have they been reported in other

previous studies. Instead an “LO-like” mode is observed, very close to the

LO mode of the zincblende structure, but with a slightly lower frequency.

Considering the different atomic distances of the two symmetries in the same

bonding potential (Fig. 14), it becomes apparent that the phonons must be

very similar. The “LO-like” phonon mode must, because of the energetic

proximity to the LO mode of zincblende, be a phonon mode that mainly

vibrates along the c-axis, as the lattice constant along this axis is close to

that of the zincblende structure. This has also been found in measurements

regarding the size dependence of phonon modes combined with calculation

by Trallero-Giner et al.[80]. Additionally, to the energetic position of the

phonon modes in the Raman spectrum, the halfwidth provides further in-

formation. For the wurtzite compared to zincblende QDs, we consistently

find similar, but slightly larger halfwidth for wurtzite “LO-like” mode (sim-

ilar to the A1(LO) in wurtzite nomenclature). This should originate from

the higher anisotropy of the wurtzite structure, which results in a broader

distribution of phonon energies.

According to selection rules in zincblende crystals additionally to the LO

mode, a TO mode can be observed. For wurtzite CdSe a similar “TO like”

phonon can be found, similar to the A1(TO) in wurtzite nomenclature, com-

parable to the appearance of the LO mode. For zincblende CdSe the TO

modes is reported to appear at about ≈170 cm−1[81], but most often van-

ishes in the other Raman signal.

Figure 17: Size dependent phonon

frequency of CdSe QDs, collected

from several publications. The fre-

quency decreases with decreasing

QD size starting from a diameter

of 6 nm. Data origins: 8→[80],

7→[82], 11→[83], 15→[84] , 34→[85],

14→[86], 9→[87], 10→[88], 27→[89],

Taken from Ref.[49]

Furthermore, the observed phonon frequency of the investigated QD

varies according to the QD size. This dependence has been observed in

many publications and, like the size dependence of the optical properties,

is a confinement effect. The dependence is shown in Fig. 17 and reveals a

decreasing phonon frequency for decreasing QD diameter, consistently for

all shown data an calculations. The frequency saturates in the bulk fre-

quency depending on the model from a QD diameter of 5-10 nm (see Fig. 17

and Ref.[80]). This results in different unstrained phonon frequencies for

differently QD sizes, which has to be taken into account in strain analysis

by comparison to a suitable reference sample.

When a shell is added to the QD, the Raman spectrum becomes more com-

plex and reflects the two materials as well as the interaction between them.

Hence, Raman spectroscopy is widely used as a sensitive characterization

technique to study semiconductor materials like theses structures. Since a

precise knowledge on the structural properties and the interplay between

core and shell is mandatory, because of the direct influence on the optical

properties which are responsible for the effectiveness of the QDs in appli-

cations, Raman spectroscopy is therefore an interesting tool for the analysis.

HFS

224

a) zincblende

CdSe Ø 3.4 nm

434

2SO

394

3LOCdSe

619

2LOCdSe

412

LOCdSe

204

180

CdSe

CdSe/CdS Ø 4.7 nm

521

2LOCdS

590

mixed

overtones

490

267

LOCdS

288

CdS

181

LOCdSe

208

194

2SO

394

2LOCdSe

415

c) CdSe/CdS Ø 6.0 nm

2IP

583

2LOCdSe

400

286

LOCdS

300

259

2LOCdS

603

mixed

overtones

484 499

17 19 Si

521

LOCdSe

209

Intensity (arb. units)

189

202

200 300 400 500 600

d) CdSe/CdS Ø 7.4 nm

2IP

558

2SO

524

mixed

overtones

494

LOCdS

301

2LOCdS

605

LOCdSe

210

Raman shift (cm

-1

)

203

189

287

255

Figure 18: Raman spectra for one wurtzite and one zincblende CdSe QD

with a diameter of 3.4 nm, that is covered by a differently thick CdS shell.

As the shell thickness increases, the intensity of the CdS increases, the CdSe

decreases, the position of CdS shifts to higher energies

The typical spectra of zincblende CdSe/CdS core shell QDs (shown

Fig.18) are dominated by the Raman signals of both separate materials,

CdSe at around 210 cm−1and CdS around 302 cm−1. The room tempera-

ture bulk phonon frequencies are usually given as ωCdSe, bulk=210 cm−1and

ωCdS, bulk=302 cm−1[90].

Within the shell thickness series in Fig.18, the intensity of those two modes

varies strongly. The higher the CdS shell thickness the more intense the CdS

phonon mode becomes in comparison to the CdSe phonon mode, because

the CdS volume increases and there is simply more CdS material contributes

to the Raman scattering. Additionally, depending on the wavelength of the

measurement, the light can be absorbed by the CdS shell and hence not

reach the CdSe core und such reduces Raman scattering in the CdSe core.

Of course this effects incoming and outgoing light and leads to a further

reduction in intensity of the CdSe core for increasing CdS shell thickness.

The effect, however, is strongly dependent on the wavelength used for the

Raman measurement and the absorption characteristics of the CdS shell,

which vary according to the shell thickness particularly for thin shells due

to confinement. This makes an interpretation of absolute and relative inten-

sities within such a series complex and emphasizes the necessity for a careful

analysis when such questions are addressed.

202

204

206

208

210

212

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8

285

290

295

300

305

310

zincblende

wurtzite

CdSe cores

Raman shift (cm-1)

bulk CdS

CdS shells

CdS shell thickness (nm)

Figure 19: Raman

freqencies for the

shell thickness series

from Fig.18 for the

CdSe and CdS modes

in dependence of

the CdS shell thick-

ness. (wurtzite and

zincblende CdSe QD

with 3.4 nm diameter)

More straight forward observations can be made by analyzing the posi-

tions and occurrence of the various modes in the spectrum. Investigating

the positions of the high intensity phonons within the shell thickness se-

ries (Fig. 19), we find that the thicker the CdS shell on the QD, the closer

the CdS Raman mode shifts towards the unstrained bulk frequency of CdS

at around 303 cm−1(at room temperature, 306 cm−1at 7K), which is vi-

sualized shown the phonon frequency dependence on the shell thickness in

Fig. 19. This shows that the CdS shell that previously showed tensile strain,

relaxes the thicker it becomes.

For the CdSe core however, the behavior is the opposite (Fig. 19, with fre-

quencies determined from Fig. 18). The thicker the CdS shell becomes, the

further away the CdSe phonon mode shifts in comparison with the uncov-

ered QD. This means the core in contrast to the shell becomes more and

more compressively strained and is reflected in the Raman spectrum as a

shift of the phonon mode toward higher frequencies. This trend is very

similar for wurtzite and zincblende QDs, as shown in Fig. 19. Using Eq. 9

in the previous Section, the strain can be calculated for each material in

dependence of the shell thickness, as shown in Fig. 20. The figure clearly

shows the increasing and decreasing strain for growing shell thickness, for

the CdSe core and CdS shell respectively.

-1.0

-0.5

0.0

0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8

0.0

0.5

1.0

1.5

2.0

zincblende

wurtzite

CdSe cores

Δa/a (%)

CdS shells

CdS shell thickness (nm)

Figure 20: Strain ∆a

for the shell thickness

series from Fig.18 for

the CdSe and CdS

modes in dependence

of the CdS shell

thickness determined

with frequencies in

Fig. 19. (wurtzite and

zincblende CdSe QD

with 3.4 nm diameter)

For some core-shell QDs, the core is not visible in the Raman spectra

for some excitation energies, due to the before mentioned absorption of the

light in the shell. In those cases, the information depth of the measurement

becomes smaller then the shell thickness and no information on the core can

be gained.

Additionally to the CdSe and CdS phonon mode in first order Raman scat-

tering, each mode has overtones visible in the spectrum, which can be found

at approximately the doubled frequency of the first order phonon. They

originate from higher order Raman processes and their intensities are of-

ten used to determine the exciton-phonon coupling strength, as described

in Sec. 5.3. Also mixed overtones, combinations of two or more different

phonon modes, are present in the spectrum. These modes are allowed un-

der energy and momentum conservation and can stem from anywhere in the

Brillouin zone. This means depending on the materials phononic dispersion,

the assignment can be difficult as the frequencies can vary strongly over the

Brillouin zone. For the CdSe and CdS overtones however, the second order

Raman frequencies correspond to approximately Γ-point frequencies.

In addition to the phonon modes of each material and overtones, more com-

plex phonons can be found taking a closer look at the lower intensity regions

and the line shapes of the high intensity modes. Around 180-190 cm−1for

instance, a peak to the lower frequency side of the CdSe LO is visible. The

mode has been first shown to exist in Raman experiments in 1974 for CdS

micro crystallites[91]. It was predicted occur as it is part of the solution of

Maxwell’s equation, when a damping at the surface of the structure is taken

into account, and is named “surface optical”(SO) phonon after it’s supposed

origin.

Since then, many groups have observed this mode and investigations have

been published regarding dependence of this mode on the form of the QD

and the dielectric environment. These factors both influence the damping

at the QD’s surface on the phonons and hence change the solution of the

Maxwell’s equation. For spherical QDs the size dependence has been investi-

gated by modeling [87] [92] and experimentally by Raman spectroscopy [93].

While calculations regularly find different phonon branches for this phonon,

in experiments usually only one mode is observed. But they coherently find

a larger separation of SO and LO mode, the higher the surface area be-

comes. For elongated structures, such as rods or nanowires this geometry

dependence has been shown by many groups and for a number of materials,

auch as GaP[94], ZnS nanowires[95] and CdS nanorods [96] for instance.

Often the influence of the dielectric environment is automatically discussed

in the publications, as it is substantial for the calculation of the SO. In this

context, the construction of core-shell structures merely presents itself as a

special environment with a dielectric constant different from the usually as-

sumed solvent or vacuum. This can be found in Ref. [97] and experimentally

for ZnS capped CdSe QDs.[98] For an increasing ZnS shell, the SO phonon

near the CdSe LO shifts towards lower frequencies (higher separation from

the LO), which shows the growing influence of the ZnS with a lower dielec-

tric constant than the previous environment. Guigni et al. even show a

dependence of the arrangement for CdSe/CdS nano rods samples.[99]

Recently Lin et al.[100] have claimed that the intensity of the feature is

strongly dependent on the resonance conditions of the measurement. They

say that the peak becomes intense when higher energetic transitions, like

1Pe-1P3/2, come into resonance. However, their calculation does not ex-

plain the geometry dependent energetic shifts, which where observed in ear-

lier publications. Additionally they calculate the localization of the phonons

and find that the modes in this energetic region are not localized at the sur-

face, but include atoms in the whole QD. This however is in strong contrast

to atomistic calculations that were performed in this group by Steffem West-

erkamp (as yet unpublished), where we find that in this region the vibrations

exhibit the highest amplitude in the volume near the surface of the QD.

For sufficiently narrow LO modes (here at the CdSe mode) an additional

mode becomes distinguishable, between the LO and the SO signal. This

mode has been shown to increase in intensity, when the shell thickness is

increased and is correlated with the formation of an interface between the

core and the shell of the QD [101] (see also Sec. 4.2, 7.2) Hence this mode

is called interface mode (IF in the spectra).

Furthermore additional broader features are observed frequently. In several

others publications for instance, Dzhagan calls a broader feature the high

frequency shoulder (HFS) of the LO mode of CdSe. However this feature is

present in most studies, but has not been assigned to an origin yet. Besides

this, there have been reports of a broad feature at about 250 cm−1, which

is correlated with the signal of amorphous Se structures[102], resonant with

the excitation wavelength of 633 nm.[103] This is however not visible in our

samples and should generally be avoidable by purification of the QD solu-

tion after the synthesis, as described in Sec. 7.1.

Possibly Raman modes originating from the substrate can become visible

in Raman measurements of QD films. In this work, Si substrates are used,

which is visible in some spectra with a sharp Raman peak at 521 cm−1. With

an intensity that is lower by more than an order of magnitude than the peak

at 521 cm−1, the much broader feature around 300 cm−1(characteristic three

peak structure), is not visible in any spectra presented here.

Based on this knowledge, in the following Section, the temperature depen-

dence of the Raman signal will be analyzed and discussed for core-shell QDs

with different geometries and crystal structures. The observation of the

temperature dependent phonon modes will be used to extract temperature

expansion coefficients for each material in the QD, proposing a method to

separate the pure temperature dependence from the interplay of core and

shell.

9 Temperature dependent lattice contraction in

wurtzite and zincblende core-shell QDs

This chapter will focus on the influence of temperature on the crystal lattice

of the QD, leading to the determination of lattice expansion coefficients.

For core-shell structures, extracting the expansion coefficient is complicated

by the interplay between core and shell, especially when expansion coeffi-

cients differ between the two materials. This difference in thermal expansion

causes one material to expand/contract at a different temperature than the

other, and thus change the strain it applies to the other material.

This temperature dependent interplay will be analyzed by Raman spec-

troscopy using a set of core-shell QDs consisting of two shell thickness se-

ries with zincblende crystal structure with two different core sizes and one

wutzite series with the same core size as one of the zincblende series to en-

able a direct comparison of the two crystal structures. Table 1 shows the

crystal structure, core sizes and shell thicknesses for the samples used. For

zincblende QDs, the CdS shell is grown with the SILAR method, which

automatically provides information the shell thickness with monolayer pre-

cision (see. Sec. 7.2). For wurtzite QDs, the FLASH method is used for

the shell growth and shell thicknesses are determined with TEM. Here the

mentioned number of monolayers are estimated from the shell thicknesses.

9.1 Temperature dependence of Raman modes in wurtzite

and zincblende core-shell NC

Generally, when a solid body is exposed to changes of temperature, it ex-

pands or contracts because the bond lengths defining the lateral dimension

of the crystal lattice change. For most solids, above a certain temperature,

increasing temperature leads to higher bond length and thus expansion of

the material. For temperatures near 0K however, the transport of heat is

governed by transversal acoustic phonons, which due to their vibrational

geometry effectively reduce the projection of the bond length. Hence for

low temperatures, the thermal expansion coefficient can become negative.

For CdSe this should be observable around 50K [104], and since our mea-

surements start form 70K should not be observed here.

The thermal expansion above this certain temperature can be easily under-

stood considering the pair-potentials for a bond between two atoms, which

is given in Fig.14 for bond between Cd and Se and a bond between Cd and

S, as those two bond define the QDs studied in this work. A temperature

increase also means an increase in potential energy, via an increase in ther-

mal energy, for the involved species which allows larger distances between

the atoms. How much this distance and therewith the lattice parameter

changes, in dependence of the temperature, is directly dependent on the

structure core diameter total diameter shell thickness shell

(wz/zb) (nm) (nm) (nm) (ML)

wz 3.4 - -

wz 3.4 4.4 0.5 2

wz 3.4 5.9 1.25 4

wz 3.4 7.8 2.2 7

wz 3.4 9.9 3.35 10

wz 3.4 13.3 4.95 15

zb 3.4 - -

zb 3.4 5.3 1 2

zb 3.4 6.0 1.3 4

zb 3.4 7.3 1.95 6

zb 4 - -

zb 4 5.1 0.55 2

zb 4 5.6 0.8 3

zb 4 6.8 1.4 5

Table 1: List of CdSe/CdS core-shell QDs with wurtzite and zincblende

crystal structure used for analysis of the influences if the CdS shell thickness

on the phonon modes (Sec. 8.2), thermal expansion properties (Sec. 9) and

on the band edge states (Sec. 11, thin shells only). For all wurtzite QDs,

the shell thickness in monolayer is approximated, as opposed to zincblende,

where it is determined by the number of synthesis steps. (Sec. 7.2)

bonding potential between its components. Hence the thermal expansion

is material specific property. This property is mostly described with the

linear thermal expansion coefficient, which corresponds to the derivative of

the relative change in bond lengths in dependence of temperature.

Taking closer look at the pair potentials in Fig.14, the difference in depth

and slope between CdSe and CdS suggest different dependencies on tem-

perature for the materials. Since we are discussing not bulk material, but

nanometer-sized heterostructures, where there is an interaction between the

different materials of the core and the shell of the QD, the expansion will dif-

fer from ideal bulk crystals. The interaction between core and shell induces

strain, and since the lattices show different temperature dependencies, this

strain is dependent on the temperature. This underlines the necessity to

compare temperatures, when comparing strain results from different mea-

surements or even theory. Furthermore it shows that a detailed knowledge

on the thermal expansion as well as the temperature dependent interaction

between the materials is required.

For bulk materials, this thermal expansion can be determined simply by

measuring the change in spatial dimension of a defined sample for different

temperatures. However, for nanostructures, this is much harder because

with a size being below optical resolution, the size can only be determined

by electron scattering. Furthermore, the separation between change of core

and shell size would be difficult as the contrast between the materials is small

and hard to determine. Using the total size of the structure determined by

TEM, doesnt reveal the effect of the temperature on each material, which

defeats the purpose of this investigation of heterostructures. Additionally

this method would only work for low temperatures. Another method to

determine the coefficient is the determination of the bond length with XRD

at different temperatures. [105, 106]

Here we propose the use of Raman spectroscopy, which enables to observe

both materials at the same time, as each material has a distinct phonon

frequency. The phonon frequency reflects the temperature dependence of

bond length, bond strength and strain / geometry of the atoms in a crystal.

Generally, in a solid the atoms vibrate round their equilibrium positions in

the asymmetric lattice potential (for comparison see pair-potential Fig.14).

When the temperature increases, the potential energy of the lattice is in-

creased, which leads to increased interatomic distances and hence expansion,

depending on the form of the potential. This increase on bond length di-

rectly influences the frequency of a lattice phonon and results in a decrease

in frequency (red shift), which can be observed by Raman spectroscopy. Ad-

ditionally, due to the increase in bond length the collective vibrations can

oscillate with a higher amplitude. [107]

180 200 220 260 273 286 299 312

LO-like

300 K

250 K

200 K

180 K

160 K

140 K

120 K

80 K

60 K

40 K

20 K

Intensity (arb. units)

Raman shift (cm

-1

)

CdSe

core

CdS

shell

7 K

10 K

Figure 21: Tem-

perature dependent

Raman spectrum of

wurtzite CdSe/CdS

QD with 3.4 nm

CdSe and diameter

of 4 nm from 83 K

to 298 K. Left: fre-

quency range of the

CdSe core. Right:

frequency range of

the CdS shell. CdSe

and CdS LOs show-

ing a characteristic

redshift with increas-

ing temperature,

visualized by the

dashed lines. (CdSe

frequency decreases

from 210.7 cm−1to

207.0 cm−1)

However, independent of the method used for the determination of the

bond lengths in the QD, the measured bond length are the result of the

combined effects of temperature and of the interaction between core and

shell. Therefore a suitable description of the expansion and the interplay of

the lattices is required. In order to achieve this, we analyze the temperature

dependent shifts in Raman frequency (which include temperature and strain

effects) for different core-shell QDs including the pure, uncovered core and

find a suitable fit function. Then we propose a linear model for the sepa-

ration of the strain related frequency shift and the temperature dependent

properties of the pure materials, assuming negligible interaction between the

effects.

Fig. 21 shows typical Raman spectra for a wurtzite CdSe/CdS QD (with a

core size 3.4 nm CdSe core and total diameter of 4 nm) in the temperature

0 50 100 150 200 250 300

280

290

300

310

200

210

220

(b) CdS Wurtzite bulk CdS

Raman shift (cm

-1

)

Temperature (K)

5.9 nm

4.0 nm

(a) CdSe Wurtzite

bare CdSe

5.9 nm

3.4 nm

4.0 nm

Figure 22: Raman shift as a function of QD diameter and temperature

for Wurtzite CdSe/CdS. The samples have the same sizes of CdSe cores

3.4 nm and several different thicknesses of CdS shells. With increasing shell

thickness (QD diameter is increasing from 4 to 5.9 nm) the Raman values are

significantly shifted in frequency, relative to bare CdSe core ((a), blueshift),

bulk CdS shell ((b), redshift) and between the samples. Additionally, the

CdSe core and CdS shell LOs showing a characteristic redshift with increase

of temperature. Their temperature-dependency were describe well by the

calculated curves (solide lines) using equation 16. (bulk CdS blue solid line

taken from Neto et al. [104]).

range between 7 K and 298 K. In agreement with a general lattice expan-

sion as described above, we find a redshift in phonon frequency for both

materials. The temperature dependent frequencies of the CdSe and CdS

phonon are displayed in Fig. 22 for a series of different shell thicknesses on

the same wurtzite QD core (3.4 nm, the same as in Fig. 21). For reference,

the temperature dependence of the pure, uncovered CdSe core and bulk CdS

are included in the Fig. The frequency shift for all phonon modes is fitted

with an empirical formula proposed by Cui et al. [108], which describes the

data well and will be used for the following calculations to have continuous

data. For the fitting procedure A, B and ω0at 7 Kelvin where used as free

fit-parameters, resulting in the displayed functions.

ω(T) = ω0−A

eB¯hω0/kBT−1.(16)

Equation after Cui et al.[108]

Additionally to the generally decrease in frequency with increasing tempera-

ture, Fig. 22 visualizes the differences within the shell thickness series, which

are induces by strain in the core-shell structure. With increasing shell thick-

ness, the CdSe LO modes shift to higher frequencies (blueshift) compared to

bare CdSe core. For the CdS LO mode, the trend is opposite: For increasing

shell thicknesses, the phonon frequency of the CdS LO shifts towards lower

energies (redshift) compared to bulk CdS.

The strain of those materials, which is defined as the relative contortion

of the lattice constant (∆a

a0), can now be calculated form the relative shift

of the phonon frequencies compared to an unstrained value using the for-

mula (Equation 9) introduced in Section 5.2, with γCdSe = 1.1 [46] and

γCdS = 1.37 [47] the Gr¨uneisen parameters for wurtzite CdSe and CdS. Con-

sidering the strain resulting from our Raman measurements, we see that for

increasing CdS shell thickness, the tensile strain of the CdS shell relaxes,

while the compressive strain of the CdSe core is increases, as shown in Fig.22.

These results are in good agreement with other studies by Tschirner et al.

[43] and Dzhagan et al. [109] for instance. Additionally it become apparent,

that the strain is different at different temperatures.

Based on these findings, in the following Sections the separation between

pure temperature-related effects and strain effects due to the interplay be-

tween core and shell will be addressed.

9.2 Separation method of thermal and epitaxial strain effects

For the separation of epitaxial and temperature induced strain effects, we

first address the calculation of strain and insert equation 16 into equation 9,

to gain a formula which allows for a direct calculation of the strain from the

relative change in phonon frequency. This results in equation 17:

∆a(T)

a=1

3[(1 + ∆ω(T)

ω)−1

−1](17)

Within this formula, the change in Raman frequency can be defined in sev-

eral different ways. On the one hand, the shift in frequency can be deter-

mined relative to the frequency at the lowest possible temperature (here

7K). This gives the effectively measured phonon frequency shift, that hence

will be called ∆ω(T)

ω⏐⏐eff , and is defined as shown in equation 18. The strain

calculated from this frequency shift includes influences from temperature

and epitaxial strain related effects and will be called ∆a(T)

a⏐⏐eff analogue to

the frequency.

∆ω(T)

ω⏐⏐⏐⏐eff

=ω(T)s−ω(T= 7K)s

ω(T= 7K)s

.(18)

Where ω(T)sis the temperature-dependent phonon frequency of the corre-

sponding sample (index s).

On the other hand, the strain component of the effectively measured tem-

perature dependent strain, is cause by the interaction between core and shell

(epitaxial strain, index strain), is of high interest. This component can be

determined by calculating the strain of the sample in comparison with an

unstrained reference sample for each temperature (Eq. 19).

∆ω

ω(T)⏐⏐⏐⏐strain

=ω(T)i−ω(T)ref

ω(T)ref

(19)

Where ω(T)ref is the temperature-dependent function of the phonon fre-

quency of an unstrained reference sample (index ref). For the CdSe cores,

we use the bare core as unstrained reference, for the CdS shell the reference

is provided by bulk CdS, because a shell without a core cannot be synthe-

sized. The bulk CdS reference is taken from data published by Neto et al.

[104] and fitted with equation 9. Those references are then compared to

ω(T)s, the temperature-dependent function of the phonon frequency of the

analyzed sample.

These distinct strain functions for both materials, CdSe core and CdS shell

are shown in Fig. 23 for one exemplary QD of the series in Fig. 22 (details in

the caption). Generally, due to smaller lattice parameters of the CdS crys-

tal structure in respect to CdSe, we find the CdSe core to be compressively

strained (CdSecompressive, negative ∆a

a), while the CdS shell exhibits tensile

strain (CdStensile, positive ∆a

a). The amount of strain is higher for the core

indicating a higher influence of the shell inside the heterostructure.

The temperature dependence of the epitaxial strain (index strain) of the

CdSe core reveals decreasing strain for increasing temperature, which is op-

posed by the effect the increasing temperature has on the CdS shell, where

0 50 100 150 200 250 300

-1.0

-0.5

0.0

0.5

1.0

1.5

Δa

(%)

Temperature (K)

CdStensile

CdSethermal

CdSthermal

CdSecompressive

Figure 23: Strain

∆a

aas a function of

temperature and shell

thickness for one QD

for the shell thickness

series shown above.

The compressive

stain of the core

(CdSecompressive) in-

creases as the temper-

ature decreases, while

the tensile strain of

the shell (CdStensile)

decreases. Due to

different thermal

expansion between

CdSe and CdS, they

show temperature-

dependent strain.

the tensile strain increases. This shows that higher temperatures favor the

relaxation of the CdSe core due to its temperature expansion properties,

and underlines the necessity to think about temperature dependence when

comparing results on strain gained by different groups and methods. For in-

stance, results gained from room temperature Raman measurements cannot

directly be used to explain shifts in low temperature PL.

The effectively observed thermal strain ∆a(T)

a⏐⏐eff for CdSe and CdS is neg-

ligible (≈0) between 7K and 75K, where the temperature apparently has

little effect on the lattice parameters only. But above 75K (onset depends

a little on the sample), we find an increase in lattice parameter for both

materials, which is in fact stronger for CdSe. Both increases in effectively

measured ∆a(T)

a⏐⏐eff are steeper and higher than the change observed for the

pure epitaxial strain. So it becomes apparent, that the effectively observed

temperature dependence of the lattice is largely influenced by temperature

expansion and epitaxial strain. The different behavior in temperature de-

pendent change of the lattice will lead to different expansion coefficients of

the two materials, as will be discussed in the next Section.

9.3 Linear temperature coefficients for heterostructures

For the analysis of the pure thermal expansion and hence the separation

of thermal and strain effects in heterostructures in general, and CdSe/CdS

-10

0 50 100 150 200 250

-10

0 50 100 150 200 250

-10

(a) CdSe core

wurtzite

thermal (T)

(

10-6K-1

)

α(T)effective

α(T)strain

(d) CdS shell

zincblende

α(T)strain

α(T)effective

(b) CdSe core

zincblende

α(T)effective

α(T)strain

α(T)effective

wurtzite

Temperature (K)

Figure 24: Shows a comparison of the coupled effects of the thermal expan-

sion coefficient α(T) as a function of the temperature exemplary fore two

Wurtzite and zincblende QDs. α(T)effective originates effective from different

thermal expansion and α(T)strain from lattice mismatch.

QDs in particular, we first introduce a definition of the linear temperature

coefficient in order to then propose a method to separate thermal and strain

effects in heterostructures.

The linear thermal expansion coefficient (LTEC, α(T)) of a material is de-

fined as the change in length per unit (usually nm) with the change in

temperature per K. The magnitude of the LTEC depends on the struc-

ture, symmetry and bonding potential of the material. To determine this

coefficient from our experimentally measured data, we use a temperature-

dependent function (Eq. 20), based on the formula published by James et

al. [106] and Okada and Tokumaru [110], which essentially is the differenti-

ation of the strain with respect to the temperature. Hence, as a more visual

description, the LTEC can be obtained from the slopes of the strain function

(see Section 5.2) at any temperature:

α(T) = d

dT(∆a(T)

a)(20)

Applying this formula for the LTEC to our results from previous sections,

we find two different coefficients: One originates from the lattice mismatch

between CdSe and CdS (shell thickness) - the epitaxial strain, α(T)strain,

an another one that is the effectively observed thermal dependency of the

latticeα(T)effective, which includes strain effects.

Fig. 24 shows the calculated results of this two effects as a function

of the temperature, α(T)strain and α(T)effective, exemplarily for one wurtzite

and one zincblende QD for CdSe and CdS. While there are strong differences

for the wurtzite and zincblende cores, the CdS shells only differ marginally.

The function α(T)effective for the zincblende core (Fig. 24 b) shows a steeper

increase with temperature increase and overall higher values for the LTEC

compared to the wurtzite core (Fig. 24 a). In the low-temperature region,

we find an additional difference, α(T)effective for zincblende core remains

constant for higher temperatures, up to 35 K, than for the Wurtzite core.

Overall, the α(T)strain of the cores with different crystal structures are dis-

tinct and differ strongly especially for low temperatures, whereas it is almost

the identical for the different shells over the whole temperature range (trend,

values), see Fig. 24 c,d.

α(T)⏐⏐thermal =α(T)effective −α(T)strain (21)

However, in order to obtain the pure thermal expansion coefficient α(T)⏐⏐thermal,

these effects need to be separated. As an approximation, we calculate the

difference between the two functions, separating the thermal strain from

epitaxial strain (equation 21). This assumes that the two effects can be

separated linearly and do not have any higher order interaction.

Applying this method, we find thermal expansion coefficients for CdSe and

CdS, shown in Fig. 25 for all samples (see Table 1). Within one series,

the LTECs of the CdSe core and CdS shell converge independent of the

shell thickness of the corresponding sample. This underlines that the linear

interpolation approximation, we made for the separation of the different in-

fluences on the lattice constant, is reasonable and sufficiently removes the

effect of the epitaxial strain from the pure thermal properties of the mate-

rial. All calculated LTECs (Fig. 25) increase with increasing temperature,

which merely reflects that the material expands for increasing temperature,

as expected.[107]

For all CdS shells, the resulting LTECs coincide, which reflects the fact

we only found small differences in their temperature dependent behavior,

already in the Raman spectra. The coinciding temperature expansion coef-

ficients manifest in the parallel shift of the temperature dependent Raman

frequency of all CdS shell Raman modes. As the LTEC can be viewed as

the derivative of the lattice constant in dependence of the temperature, and

since the lattice constant is described with ∆a(T)

a∝∆ω

ω(T)−1

γ, with γ≈1

(CdS, CdSe), it is a good approximation to use parallel shifts of the phonon

frequency in dependence of temperature as an indication for similar LTEC.

A direct comparison between the thermal expansion coefficients of the CdSe

cores and the CdS shells (Fig. 25), provides smaller overall expansion for

the shells, which can be explained using the inter-atomic pair potentials

(Fig. 26) for the two materials. The potential curve of CdS has a deeper

0 50 100 150 200 250 300

αthermal (T) (10-6K-1)

Temperature (K)

Wurtzite CdSe Ø 3.4 nm

zincblende CdSe Ø 3.4 nm

zincblende CdSe Ø 4.0 nm

Wurtzite/zincblende CdS

Figure 25: Thermal expansion coefficient αthermal(T) as a function of tem-

perature for wurtzite and zincblende CdSe/CdS QDs as determined with

Eq. 21 from the measured temperature dependent Raman spectra.

and steeper (smaller width) minimum at lower distances compared to CdSe,

which indicates a stronger bond between Cd and S, than between Cd and

Se. Generally, materials with strong bonds typically have a lower thermal

expansion coefficient [107] than materials with weaker bond and flatter po-

tential, expectation in congruent with our findings. This can be understood

by comparing how much thermal energy needed to increase the equilibrium

distances between the atoms within the potential. This leads to the con-

clusion that for steeper potential minima, the same additional amount of

thermal energy, increases the equilibrium position of the atoms and there-

with the lattice constant less than for a flatter minimum. This matches our

results of smaller temperature expansion for CdS compared to CdSe well.

Additionally to the different materials, we have analyzed different crystal

phases, and find a steeper and higher increase for the zincblende phases

compared to the wurtzite phase, looking at the CdSe cores with 3.4 nm

diameter with different crystal structures (Fig. 25). This demonstrates the

different temperature dependent behavior of the two phases, which can be

understood, when considering the corresponding interatomic distances in

the pair-potential (see Fig. 26, marked dwz,dzb). Since the wurtzite phase

consists of smaller interatomic distances as the zincblende phase, it’s atoms

equilibrium positions are closer to the minimum of the interatomic potential,

2.0 2.2 2.4 2.6 2.8 3.0 3.2

-8

-7

-6

-5

Vkl(rkl) (eV)

rkl (Å)

CdS

CdSe

dzb

dwz

Figure 26: A plot of two-body

inter-atomic potential energy for CdSe

and CdS as a function of inter-

atomic distance. The function of the

Lennard-Jones-like inter-atomic po-

tential Vij(r) and the potential param-

eters were taken from Refs. [79].The

distance between nearest neighbor

atoms for the Wurtzite (dwz =

0.263 nm[111]) and zincblende (dzb =

0.265 nm, dzb = 1/4√3a) CdSe are

marked on the potential curve.

which only allows for smaller changes upon increase of thermal energy than

for the zincblende phase. The onset of the expansion however, is different

for the two phases. For wurtzite, the crystal starts expanding at lower tem-

peratures than for the zincblende structure, which might originate in the

crystal structure’s anisotropy. Trallero-Giner et al. have confirmed that the

lattice vibration observed in Raman spectroscopy is a vibration along the

c-axis by comparison of temperature dependent Raman measurement and

ab initio lattice dynamical calculation.[80] This vibration in c-direction has

a stronger temperature dependence than a vibration in a-direction would

have. The atomic distances along the c-axis in the crystal are larger than

for the a-direction, which could explain an onset of expansion at lower tem-

peratures for this direction, as in the interatomic potential (Fig. 26) becomes

less steep for higher distances, allowing larger changes in atomic distance

per added thermal energy. But the onset of thermal expansion also depends

on the size of the core, comparing 3.4 nm and 4 nm zincblende core in Fig.

25.

Moreover, different CdSe core sizes with the same crystal structure, show

differently high total thermal expansion (Fig. 25). This, together with the

different onset of expansion, indicates a size dependence of this property, as

found for so many other attributes for particles in this size range, as the

frequency of the phonon mode or the lowest optical transition for instance

(see Sec.4, 7)

In conclusion, through the analysis of temperature dependent Raman mea-

surements of colloidal CdSe/CdS core-shell QD of different crystal struc-

tures, we show that the epitaxial strain-related temperature effects can be

separated from the temperature dependence of the pure materials by com-

parison with the temperature dependence of an unstrained reference mate-

rial. Thus we demonstrate that with this approach it is possible to retrieve

the temperature expansion coefficients of the pure materials from interca-

lated heterostructures.

Analyzing the resulting thermal expansion coefficients, we find different co-

efficients for differently sized QDs, which points towards a yet another size

dependent effect in the low nm-regime. Furthermore we find a generally

higher temperature dependence for the zincblende crystal phase compared

to the wurtzite phases, which can be explained by their different interatomic

distances in the pair-potential. This confirms that the crystal structure plays

an important role for the temperature expansion coefficient, and thus must

always be considered. Additionally, material specific different coefficients

are found for CdSe and CdS. Here, CdS shows lower LTECs and thus tem-

perature dependent expansion than CdSe, which is in agreement with the

differences in the respective inter-atomic pair-potentials.

10 Exciton-phonon coupling

The magnitude of the coupling of excited charge carriers to phonons con-

tributes to the time scales of different photophysical processes[112] of high

significance for various light emitting applications. Although there are sev-

eral studies on the coupling strength in colloidal II-VI semiconductor QDs,

experimentally as well as theoretically, no consensus is found on the order

of magnitude of the Huang-Rhys factor S. Furthermore, the dependence of

the coupling strength on the QD size is much debated with diverging re-

sults.[113]

While some groups report a size-independent exciton-phonon coupling[55],

other groups find a decreasing[114, 115] or increasing[83, 116, 117] coupling

strength for decreasing QD size. Nomura et al.[118] report a minimum of

coupling strength at a radius of 7 nm for spherical CdSe QDs and an in-

crease for both decreasing and increasing size based on their calculations.

According to them the increase in coupling strength for increasing QD size

after the minimum is caused by an increase in coulomb interaction, whereas

the enhanced coupling toward decreasing QDs size originates form valence

band mixing in the strong confinement regime. For PbS quantum dots,

on the other hand, Krauss find a maximum in similar calculation, but in

measurements they observe Sto be 4 orders of magnitude larger than their

calculations indicate. Salvador et al.[119] find for CdSe a size independent

coupling constant in the oder of 0.10-0.12 to the optical phonon, but a strong

diameter dependence for the coupling to acoustic phonons with a maximum

at about 2 nm diameter. They explain this by, on the one hand the increase

in phonon energy for decreasing particle size, and on the other hand by the

increasing reorganization energy at small sizes, which reduces the coupling.

However in this work, we focus on the coupling to optical phonons.Opposing

the size independent exciton-phonon coupling, Oshiro et al. [120] confirm

the existence of a minimum, claiming that the increase at small diameters

is due to the difference in polaron effect on electron and hole, while the

decrease at larger diameters stems from the large polaron effect on the elec-

tron, which decreases with decreasing size. Their calculated minimum is

estimated to lye between 1.5 to 2.5 nm radius, depending on the assumed

band offset. The Huang-Rhys factor “S”, they conclude to be around around

0.6. This minimum is also found by Zheng et al [121] for zinc-compound

materials, where the minimum position is found to vary dependent on the

crystal composition.

Another, more recent, theoretical approach has been taken by A.M. Kelley

[122], who combined atomistic calculations (GULP) of the phonons in CdSe

NCs with electronic potentials calculated p(article in a sphere) with a de-

formation potential approach to estimate the coupling strength. Resulting

values of the Huang-Rhys factors are between 0.6 and 1.2. They also find an

increasing coupling strength for decreasing particle size, for particles smaller

than 2.6 nm diameter, which is the size limit of their atomistic calculation.

But they also point out, that the coupling strength in bulk CdSe is higher,

which points towards a minimum in somewhere between 2.6 nm diameter

and the bulk crystal.

In conclusion, the diameter dependence of the exciton-phonon coupling in

spherical CdSe QD remains a subject of research and discussion. Hence,

using a series of spherical zincblende CdSe QD with sizes between 3.0 and

6.4 nm, the size dependence of this quantity is analyzed. Furthermore, us-

ing a diameter series of spherical wurtzite QD between 3.6 and 5.2 nm are

analyzed for comparison of the exciton phonon coupling strength for the two

different crystal structure. The effects of the addition of the CdS shell on

the exciton phonon coupling will be discussed, based on Raman and FLN

measurements.

Amongst the experimental method, Raman spectroscopy is the most com-

monly applied to evaluate the coupling strength between excitons and the

crystal lattice. While many used calculation like presented in Sec. 5.3, some

authors use the intensity ratio between first and second order Raman peak

directly, or alternatively insert the intensity ratio directly as the displace-

ment parameter (∆) of the harmonic oszillator in equation (Eq. 15), which

leads to |I1LO/I2LO|2

However, Kelley et al. present calculations based on a Brownian oscillator

model, that suggest a dependence on the experimental conditions, namely

the wavelength used in the experiment and the resonance condition there-

with.[59] Comparing zincblende and wurtzite CdSe QDs in Raman spec-

troscopy, suggests that the energy difference between the electronic transi-

tion and the exciting photon energy generally changes the estimated Huang-

Rhys factor Sbecause of resonant enhancement near lowest energy excitonic

states[59]. Which is why excitation wavelength dependent Raman measure-

ments are include in the following Section to address this aspect.

However, the conclusion of Kelley et al. is not supported by full resonant Ra-

man measurements, as the Raman signal even just coming close to resonance

with the ground transition is drowned out by the intense luminescence of the

QD. Hence, no measurement in full resonance is presented. Additionally, to

achieve Raman spectra with low luminescence back ground, they used hole-

accepting ligands to quench the QD’s luminescence. However, this surely

deforms the hole wavefunction and makes comparability questionable.

Another, more direct method of determination of this coupling strength is

posed by close analysis of resonant PL measurements, by comparison of the

intensities of phonon replica of the ground transition. However, one must

carefully consider the coupling to which state is determined in the mea-

surements, as for low temperatures, the spectrum is actually dominated by

phonon replica of the “dark” state, which becomes optically active for tem-

peratures close to 0K (see also Sec. 11).

10.1 QD diameter dependent Huang-Rhys factor from Ra-

man spectroscopy

150 200 250 300 350 400 450

Raman Shift (cm-1)

Intensity (arb. units)

d=2.98nm

d=4.0nm

d=4.86nm

d=6.24nm

Figure 27: Exemplary Raman

spectra for several QD of the

zincblende diameter series with

the fit used to extract the 1LO

an 2LO intensities. The back

ground varies widely over the

whole series, becoming more in-

tense for both very small and

large sizes. At the same time

the second order Raman intensi-

ties increases, indicating a higher

coupling. However this coupling

seems to enhance all observed fea-

tures, not only the LO mode. The

intensities are normalized to the

CdSe first order Raman signal.

Intensities used for the determi-

nation of Sare areas under the

fitted peaks.

As demonstrated in Sec. 5.3, it is possible to determine the Huang-Rhys

factor by comparison of the intensities of different order Raman processes.

Here, the intensities of first and second order LO are compared, but a com-

parison with third or forth order should lead to equally valid observation.

However the observation of third or higher order Raman signal is limited due

to low intensity, especially for low coupling strengths. Entering these inten-

sity ratios in Eq. (15), using Eq. (14), the energy of the electronic transition

for each QD and Γ = 20 µeV for the linewidth, as mean values[123] allows

the calculation of the parameter S. Additionally the LO-phonon frequency

and the excitation energy, are measured or set by the experimental condi-

tions and inserted into the equation. Additionally, a different measure of

the exciton-phonon coupling will be shown used, which also repeatedly ap-

pears in literature. Here it is assumed that the intensity ratio approximately

equals the displacement parameter ∆, which leads to S′=|I1LO/I2LO|2

To investigate the dependency of the electron-phonon coupling strength on

the QD size, a series CdSe NCs of different diameters between 3 nm and

6.4 nm were analyzed (same series, as used for analysis of the band edge fine

structure in Sec. 11). Fig. 27 shows a selection of Raman spectra differently

sized zincblende QDs together with the fits used for the determination of

the HR factor. Over the size range, the background changes as well as the

half width of the LO mode, which decreases for larger QDs, as should be ex-

pected from confinement. Other modes beside the LO become more intense

for both very small and large sizes, at the same time as the second order

Raman intensities increases. This indicates that a higher coupling seems to

enhance all features, not only the LO mode. Atomistic calculation on the

phonon frequencies within this kind of structures have shown that the spec-

tra actually consist of a very broad, continuous spectrum, providing all kinds

of frequencies apart from the well know bulk-like LO frequencies. However

it is suspected that strong selective coupling leads to the well-known spec-

trum, dominates by one phonon mode only.[100, 122, 124, 125]

3456

0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18 S' direct from intensity ratio

Huang-Rhys factor S

after Sec. 2.3

Exciton-phonon coupling

QD diameter (nm)

Figure 28: Huang Rhys factor S(af-

ter Sec. 5.3) and S′=|I1LO/I2LO|2

2for

the zincblende CdSe QD diameter se-

ries in comparison. Both determined

from Raman spectra at 10K with a

488 nm excitation. Sand S′vary

between 0.1 and 0.2, showing a dis-

tinct minimum in coupling strength

at about 4.7 nm QD diameter. The

lines are added as a guide to the eye,

the indicated errors merely represent

the error of the measurement, fitting

errors are not included.

The Huang-Rhys factors Sand S′, determined for the zincblende CdSe

diameter series are shown in Fig. 28, showing only a small offset between

the two values. With coupling factors between 0.1 and 0.2, the observed

values are with previously reported S(see above). However, the diameter

dependence reveals a distinct shape including a minimum around 4.7 nm

and an increasing coupling strength towards increasing as well as decreasing

QD size.

As described in the introduction of this section, the resulting HR factors are

discussed to be dependent of the wavelength of measurement. To address

this issue, the excitation wavelength is varied. Fig. 29 displays the Raman

spectra of the 4.6 nm zincblende QD, excited with 465 nm, 488 nm and

514 nm. The measurement at 514 nm is closer to the bandgap and shows

a more prominent background. The determined parameter Sfor several

Figure 29: Raman spectra of

4.6 nm diameter CdSe NCs excited at

465 nm (violet), 488 nm (blue) and

521 nm (green). The spectra were

normalized to the fundamental Ra-

man peak. Inset: Determined Sfor

the 4.6 nm diameter zincblende QD,

for varied excitation wavelength with

errors based on measurement inaccu-

racy. Within measurement error, S is

constant over the observed excitation

energy range.

200 300 400 500

521 nm

488 nm

465 nm

Intensity

Raman shift (cm -1)

2.4 2.5 2.6 2.7

0.14

0.15

Huang-Rhys factor S

Excitation energy (eV)

further wavelength for this sample is displayed in the inset and reveals only

small changes in the resulting coupling strength, which is extracted from fits

to the spectrum. However, with a diameter of 4.6 nm, this sample is near

the minimum of the size dependence of S(Fig. 28) and for small coupling

strengths, the variation with excitation energy might be small. Still, the

measurements indicate, that the minimum remains fix for the investigated

excitation energy range.

Hence, Fig. 30 displays Sfor QDs with different diameters, determined with

0.1

0.2

0.3

Huang-Rhys factor S

QD diameter (nm)

Figure 30: Huang-Rhys factors S,

estimated from Raman spectra of

zincblende CdSe QDs with different

diameters, measured with 488 nm

and 514 nm as excitation wavelength.

The curves roughly follow the same

trends, however the scale differs be-

tween the two excitations. Sis con-

sistently larger for excitation with

514 nm. The dotted lines are a guide

to the eye.

488 nm and 514 nm as excitation wavelength. Starting from the largest di-

ameter, Sdecreases for decreasing QD size until a minimum value is reached

around d=4.7 nm, then increases consistently for both wavelength, the val-

ues however being larger for 514 nm excitation wavelength. This confirms

the existence of a minimum in electron-phonon coupling, independent from

measurement energy. But the figure also shows, that the influence of the

excitation wavelength on the observed coupling factor is not sufficiently ac-

counted for in the calculations presented in Sec. 5.3. This indicates that

the calculation doesn’t provide advantages compared to S′, which shows

the same dependency and only marginally larger values, but can be directly

determined from measurement. Hence S′can be easier determined and com-

pared.

Figure 31 displayed S′for the wurtzite and the zincblende series in de-

3.0 3.5 4.0 4.5 5.0 5.5 6.0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

wurtzite QDs

zincblende QDs

Exciton-phonon coupling factor S'

QD diameter (nm)

Figure 31: Exciton-phonon coupling

factors S′, estimated from Raman

spectra of zincblende and wurtzite

CdSe QDs with different diameters,

at 10K with an excitation wavelength

of 488 nm. For the wurtzite QDs,

the minimum lies between 3.8 and

4.4 nm diameter, for zincblende QDs

at 4.7 nm. Outside of the minimum,

the wurtzite QDs show a stronger

coupling by a factor of 2-4, size de-

pendently.

pendence of the QD diameter. There are less data points for the wurtzite

series, due to generally broader and less defined features of the wurtzite Ra-

man spectrum and hence more difficult evaluation of intensities. However,

the coupling strength for wurtzite QD also indicates a minimum just like

for zincblende structure, but a smaller sizes between 3.8 and 4.4 nm. The

coupling strength outside of the minimum is larger than for the zincblende

series, by a factor of 2-4 (size dependently) under the experimental condi-

tions used. This, shows once again the fundamental differences between the

crystal structures. The higher polarity of the wurtzite lattice should induce

a higher interaction of the lattice with excitons and hence a higher exciton-

phonon coupling is expected of the wurtzite structure. Although it should

be noted, that this higher coupling could also be an effect similar to the

observation on the excitation energy dependence of the coupling strength

for zincblende QDs. There the coupling is higher for excitation closer to the

ground state. Since the ground state of the wurtzite QDs is at higher en-

ergies compared to zincblende (see Sec. 11.2), the excitation energy used is

automatically closer to the ground state, which could increase the coupling

and lead to an overestimation.

The shape of the curves (Fig. 28 and 30) strongly supports the existence of

a minimum as postulated by Normura et al. [118], albeit the minimum is

predicted for a diameter of 14 nm. However the diameter at which the min-

imum is obseved here for both crystal structures, is closer to the findings of

Oshiro et al. [120], who find a minimum in coupling strength around 4-5 nm

diameter, depending on the assumed band offset to the environement. Ap-

plied to the present case, where the observed minimum in coupling is lower

for wurtzite QDs compared to zincblende QDs, this could indicate that the

band offset is smaller for the wurtzite QDs[120]. This is possible consider-

ing that the QDs are measured in equal environments and but have different

ground state energies (Sec. 11.2). Oshiro et al. explain the strong increase

of the coupling with further decreasing particle size after the minimum, with

the difference in polaron effects on the hole and the electron in the strong

confinement regime.

Normura et al. see the general decrease in coupling with decreasing QD size

as a decrease in influence of the Coulomb interaction, whereas the increase

following the minimum originates from increasing confinement.[118]

Because of the observed variation of absolute value of S, it is reasonable to

leave comparison beyond the order of magnitude aside. The magnitude of

coupling strength however is the same for Oshiro et al. (0.6 for the low-

est value), but compared to Nomura et al.[118] is larger by an order of

magnitude. However the same order of magnitude has been observed in

measurement several times, as can be found in a good overview over previ-

ously found orders of magnitude of the Huang-Rhys factor.[126]

10.2 Huang-Rhys factor in CdSe/CdS core-shell QDs

The Huang-Rhys factor has previously been found to decrease once a shell

is added to the QD.[43] Figure 32 gives an overview over the Huang-Rhys

factors determined for a zincblende series with different shell thicknesses

on the same core size of 4 nm. The coupling strength drops dramatically

upon shell addition of 2 ML only and further decreases for increasing shell

thickness. This seems reasonable, as the addition of a CdS shell effectively

reduces the overlap of the hole and electron wave function, as the electron’s

wave function leaks into the shell.

Since, as described in the previous Section, we found that the strength

012345

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Huang-Rhys factor S

CdS shell thickness (ML)

bare core

4 nm

diameter

Figure 32: Huang-Rhys factor S

determined by Raman spectroscopy

at 10K for a series of zincblende

CdSe/CdS core-shell QDs with var-

ied shell thickness. The core diame-

ter remains constant at 4 nm and the

shell is successively added by SILAR

method (Sec. 7.2). Sdecreases dra-

matically upon CdS shell addition.

of the coupling observed by Raman spectroscopy depend on the resonance

of the QD’s transition and the excitation wavelength used for the measure-

ment. Here the excitation wavelength is fixed, while the shell addition shifts

the transition toward the red (see Sec.7). Hence, the condition changes con-

tinually and it is possible that the reduction of Soriginates from the shift of

the QD’s transition further away from resonance. This leads to the idea to

measure the coupling in resonance with the main transition of each sample

to ensure consistent conditions.

Therefore, with the setup described in Sec. 6.2, PLE measurements were

performed on two sets of CdSe/CdS core-shell QD with varied shell thick-

ness (extracts from the series’ used in Sec. 8,9 and 11), based on a wurtzite

and a zincblende CdSe core with a diameter of 3.4 nm. Figure 33a shows

the resonant PL spectrum of the wurtzite core together with two differ-

ent shell thicknesses added to the core (displayed relative to the excitation

energy). The corresponding spectra of the zincblende series are shown in

Sec. 11, Fig. 46, where both spectra are discussed in the context of band

edge states. Here, again the Huang-Rhys factor can be estimated from the

intensity ratio between second and first order of the phonon-replica. Since

the process that is observed in this kind of measurement is different from

Raman spectroscopy, it allows the direct determination of the intensity ratio

is sufficient.

The shell thickness dependent Huang-Rhys factor for the examined wurtzite

and zincblende series is shown in Fig. 33b. Here too, the coupling goes down

upon shell addition, for both wurtzite and zincblende structure. However

the effect isn’t nearly as pronounced as it appeared observed by Raman

spectroscopy. This indicates that the effect observed in Raman, definitely

is enhanced by the shift in electronic transitions caused by the addition of

shells, but the overall reduction in exciton-phonon coupling remains true.

Additionally it can be observed that the coupling in the wurtzite QDs is gen-

erally larger than for zincblende QDs, by about a factor of 1.5, as was also

observed in Raman (Fig. 31). As the wurtzite structure exhibits internal

pyro- and piezo-electric fields, a larger coupling of the electronic system to

lattice vibrations is to be expected. However the difference is smaller than

anticipated, assuming a completely field-free and symmetric zincblende QD.

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0.00

3.0 3.5 4.0 4.5 5.0 5.5 6.0

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

Intensity (arb. units)

Energy rel. to excitation (eV)

QD diameter

4.4nm (ca.2MLCdS)

5.9nm (ca.4MLCdS)

3.4nm bare CdSe core

a) zincblende QDs

wurtzite QDs

Huang-Rhys factor S

QD diameter (nm)

Figure 33: a) Resonant PL spectra (5K) of the wurtzite CdSe/CdS core-

shell series, displayed relative to the excitation energy for comparison. The

2-3 phonon replica are visible, the zero phonon line lies several meV below

the excitation indicating a transfer mechanism. b) Huang-Rhys factors de-

termined from fits to the FLN measurements for zincblende and wurtzite

core-shell. Wurtzite QDs have consistently higher coupling factors and for

both structures the coupling reduces for addition of a CdS shell.

Despite revealing these very interesting coupling factors for different

core-shell QDs, one problem with this method of measurement at low tem-

peratures becomes obvious upon close inspection of the spectra in Fig. 33a.

The phonon replica are replica of the bright state, but of the “dark” state

that is located several meV below the bright state and becomes activated

at low temperatures. This can be seen by the zero-phonon-line that doesn’t

coincide with the excitation, but is a separate feature. Hence the observa-

tion made here, reveal the coupling factors to a different state. This could

be avoided using higher temperature during measurement.

It is notable, that the order of magnitude is indeed the same as observed

by Raman spectroscopy (0.1-0.2), despite the wide range discussed in the

literature. While the coupling factors determined by Raman spectroscopy

indicated a higher coupling when the measurement would be closer to reso-

nance, the Huang-Rhys factor S’ observed by PLE, with values around 0.2

for zincblende, is slightly higher but close.

11 Excitonic fine structure of CdSe QD

The band edge fine structure of wurtzite colloidal CdSe QDs was studied

by Nirmal et al.[127], using a combination of photoluminescence excitation

spectroscopy (PLE) and fluorescence line narrowing (FLN), already in 1995.

A theoretical description followed soon after by Norris et al.[128] and Efros

et al.[83], in cooperation with each other. They showed a size dependent

fine structure splitting for wurtzite colloidal CdSe QDs, together with a

theoretical description based on the crystal field splitting in the wurtzite

structure. This crystal splitting field is induced by anisotropy and results in

at least five states lying close together at the band edge, of wich only three

should be optically active due to selection rules.[129–131] The optically ac-

tive transitions are called ±1L,±1Uand 0Uin order of ascending energy for

prolate structures. For oblate structures however, the order of ±1Uand 0U

is interchanged. Additionally, energy levels related to forbidden transitions,

which should be optically inactive, the ±2 and the 0Lare present. The low-

est excitonic state in oblate structures is the 0Lstate, as opposed to prolate

structures, where it is the ±2 state. Hence both forms have in common

that the lowest excitonic state belongs to a optically forbidden transition.

Despite being forbidden or “dark” – as this characteristic is often called –

the ±2 transition is clearly visible in measurements as a zero-phonon line

(ZPL) in FLN spectroscopy.

Why this “dark” state becomes optically active, however, has been widely

speculated over time. Recently, Rodina et al. have presented a comprehen-

sive study discussing the possible activation processes and what consequently

should be observable in measurements.[132, 133] The optical activation of

the “dark” exciton is discussed in connection with dangling bond spins at

the QD surface, phonons and the magnetic field. The resulting temperature

dependencies of the recombination probability are presented, which provides

an option to experimentally determine the activation process. In our exper-

imental conditions, only recombination via interactions with dangling bond

spins or phonons are possible, as no magnetic field is present.

On the other hand, Sercel et al. have just recently presented calculations

showing that the dark state can be activated by the breaking of symmetry

introduced by doping.[134] As impurities, introducing a charge to the QD

are possible principally, this could also provide an explanation for the opti-

cal active “dark” state observed in our measurements.

Biadala et al. recently presented – together with Rodina – the formation of

a magnetic polaron in colloidal CdSe QDs under the influence of high power

excitation at cryogenic temperatures[135]. This, on one hand, increases the

splitting between dark and bright states, which can be observed in measure-

ments. This was explained by the formation of a dangling bond magnetic

polaron, consisting of about 60 oriented dangling bond spins and one dark

exciton. On the other hand, the dangling bond spins assist in the radiative

recombination of the forbidden “dark” exciton.

Beyond the wurtzite crystal structure, the zincblende structure should not

exhibit crystal splitting because of its high symmetry. However, an aniso-

tropy can be induced in zincblende QDs by any deviation from a perfectly

spherical form. Here, deformations on the order of a few percent could cause

an observable splitting of the band edge state. Since most published stud-

ies so far either focussed on wurtzite QDs – or did not mention the crystal

structure at all – this is a very interesting aspect for the understanding of

the electronic states in colloidal QDs.

In this chapter, we will analyze series of both wurtzite and zincblende CdSe

QDs with varying diameters by PLE (for the experimental setup, see sec-

tion 6.2), in order to investigate and compare the size dependent electronic

fine structure near the band edge for both crystal structures. These series

consist of 9 samples each, varying in diameter between 3.0 nm and 6.3 nm

for the zincblende structure, and between 3.4 nm and 5.4 nm for wurtzite. A

broad diameter range is thus covered for both crystal structures. For all QD

samples, the mean diameter distribution within one sample is about ±5%.

The observed transitions will be compared with calculations of the electronic

fine structure, taking into account the electron-hole exchange interaction,

the influence of the different lattice types and possible shape anisotropy of

the QDs. In order to observe which influence a CdS shell has on the elec-

tronic fine structure, an analysis of both zincblende and wurtzite series of

core-shell QDs with different shell thicknesses will be given.

11.1 CdSe QDs in PLE measurements

In this section, PLE spectra of colloidal CdSe QDs (setup see Sec. 6.2) will

be presented, followed by a discussion of the observed features. Furthermore

it will be demonstrated how the measured PLE and FLN can be used to ex-

tract transitions for a broad diameter range of wurtzite and zincblende QDs.

2.1 2.2

2.1

2.2

2.3

Excitation energy (eV)

Detection energy (eV)

Excitation energy (eV)

Detection energy (eV)

2.185

2.3

excitation

Intensity

(arb. units)

Intensity

(arb. units)

FLN

PLE

detection

Figure 34: PLE measurement of

3.6 nm zincblende CdSe QDs at 5K.

a) Contour plot of PL intensities (log-

arithmic scale) for varied excitation

energies. b) Profile for a fixed exci-

tation energy, non-resonant PL (red

line, 2.300 eV). In resonance (vi-

olet line, 2.185 eV) this profile is

called FLN (fluorescence line narrow-

ing) due to the strongly enhanced sig-

nal of the resonant states. c) Excita-

tion profile for a fixed detection en-

ergy, here 2.185 eV.

Figure 34 shows a PLE contour plot of zincblende CdSe QDs with an

average diameter of 3.6 nm. The color reflects the intensity for each energy,

going from low intensity (violet) to high intensity (red). Evaluating a pro-

file through the color plot in the x-direction yields a regular PL spectrum,

as shown in Fig. 34 b). Along the y-axis, on the other hand, this results

in an intensity profile for a fixed detection energy under varying excitation

(Fig. 34c)). If the excitation energy becomes resonant with a distinct state,

the PL process becomes very efficient, thus the intensity increases. Looking

at the different PL profiles in more detail (Fig. 35), very different spectra

can be observed in and off resonance. When excited off resonance (red), the

QD ensemble emits a Gaussian-shaped signal, which is broadened due to the

diameter distribution within the sample. This changes dramatically when

the the sample is excited in resonance, see profile shown in violet (Fig. 35).

As there is resonance only with a certain sub-sample of QDs, the line width

is strongly reduced; hence this is commonly called fluorescence line narrow-

ing (FLN). This effect is especially noticeable at energies which are smaller

than the mean emission energy of the sample, as this limits the number of

excited QDs.

The FLN profile evidently reveals a more complex structure than the off-

resonant PL spectrum, including a zero phonon line and subsequent phonon

replica. The phonon energy is in agreement with the phonon energy we

observed in Raman experiments. The zero-phonon line corresponds to the

2.1 2.2

2.1

2.2

2.3

Excitation energy (eV)

Detection energy (eV)

2.15

2.182

2.292

towards

higher excited states

off-resonance PL

PL in resonance

1LO

3LO

2LO

2.1 2.2

excitation=1

PLE-excitation profile

FLN

off-resonance PL

0LO

3LO

2LO

1LO

Intensity (arb. units)

Energy (eV)

1LO

Figure 35: PLE contour plot of ≈3.6 nm sized zincblende CdSe QDs. Line

profiles at 2.182 eV (FLN, violet) and “classical”, off-resonant PL 2.292 eV

(red) are given on the left. Text labels indictate the positions of the zero-

phonon line and the phonon replica. Additionally, the PLE profile detected

at the position of the 1LO in the resonant FLN profile is displayed (blue).

dark state. Additionally, the excitation profile along the y-axis is given in

Fig. 35 (blue), which includes several resonant states when going towards

higher energies. For a better overview, the position of each state is given

in dependence of excitation energy (FLN profiles) and the 1Lenergy (PLE

profiles) in Fig 36. While this scatter plot combines all 9 QD samples of

the zincblende series, the shown states still line up and evidently give a

clear energy dependence, albeit within a small statistical spread. This in-

dicates that we can retract information on QDs of different sizes more or

less continuously simply by tuning the excitation energy, and it highlights

that in resonant excitation, the FLN spectrum is dominated by a small sub-

ensemble of QDs. Energies below zero correspond to states identified from

the FLN spectra (i.e. along the x-axis in Fig. 35. Here we find the zero-

phonon line, which marks the position of the “dark” state ±2. Furthermore,

the first, second, and third phonon replica of this state can be seen. De-

pending on the QD diameter, the phonon replica shift more or less parallel

to the “dark” state. Even though there is a small diameter dependence of

the Raman shift (Sec. 8.2), a shift is not visible in these measurements, as

it is far below the resolution of the measurement.

1.92.02.12.22.3

-60

-40

-20

ELO

extra (PLE)

1U/ 0U (PLE)

ZPL (PLE)*

1PL (PLE)

ZPL (FLN)

1PL (FLN)

2PL (FLN)

Energy rel. to 1 L transition (meV)

Energy of the 1 L state (eV)

Figure 36: Overview of all near band edge states observed by taking profiles

in PLE and FLN for the whole zincblende diameter series. The states are

displayed relative to the 1Ustate, i.e. the bright state, which is observed as

the main transition in off-resonant measurements. Energies above zero are

observed in PLE, those below in FLN profiles. Two band edge states with

energies above the 1Lstate emerge, one of which can be attributed to the

mixture of 1Uand 0Ustates, analogous to Norris and Efros. Below the 1L

state, a zero-phonon line (ZPL) and the subsequent first and second phonon

replica (1PL/2PL) are observed. The displayed values for the ZPL are col-

lected from FLN profiles (ZPL(FLN)) and from PLE profiles (ZPL(PLE))*.

The ZPL(PLE)* values shown are calculated from the observed location of

the feature above the detection energy in the PLE profile, identifying this

feature to a ZPL belonging to the known excitation energy(both values are

known quantities). In this way, the ZPL observed in PLE is displayed ana-

logue to the ZPL observed in FLN. The ZPL corresponds to the “dark”

state, the ±2 state, that is evidently optically active for these structures.

The 1PL observed in PLE profiles matches with the 1PL observed in FLN.

Combining the observed states of all samples leads to continuously energy

dependent states, without any steps; hence extrapolations between the dis-

crete, average diameters of the series are evidently allowed.[83, 128]

Towards positive relative energies, we find two higher states with weak

diameter dependence, of which the lower energetic one was attributed by

Norris and Efros to be a combination of 1Uand 0U. As the 1Uand 0Ustates

are energetically very close, they overlap and are often indistinguishable in

measurements. Note that they did, however, observe separated features for

larger QDs, above 6.2 nm in diameter. Since our wurtzite QD series ends at a

diameter of 5.4 nm, we can unfortunately not verify this separation of states.

From consultations with our cooperations partners – who synthesized the

samples – it has become clear, however, that the size distribution becomes

quite broad at larger diameters, and the QD are prone to show ripening

effects, which can lead to non-spherical QDs. In the wurtzite crystal struc-

ture, QDs tend to form elongated (prolate) forms in case of ripening. For

spherical zincblende QDs, this deformation is usually not observed by TEM,

which means that only oblate deformation is possible. A oblate deformation

would not be difficult to observe by TEM due to the orientation of the QDs,

the images being predominantly perpendicular to the deformation. This

would subsequently lead to a diverging anisotropy within the series, hence

make a complementary description very difficult.

To compare the different crystal structures with each other, one can either

compare the different transitions in dependence of the 1Lenergy, or in depen-

dence of the corresponding QD diameter. For the latter, a relation between

the emission energy and the QD diameter at the temperature of the mea-

surement needs to be found. Such a conversion is presented in the following

section 11.2, and applied thereafter. The successful conversion of emission

energies into QD diameters entails the additional benefit of the possibility

of simulating the electronic fine structure, which was kindly performed by

Anna Rodina and Alexandr Golovatenko, and will be presented in Sec. 11.4

of this work.

For the accuracy of these calculation, we must first ensure that the measure-

ment itself does not influence the energy of the observed states. As shown

by Biadala et al.[135] – together with Rodina – the high power excitation

(e.g. by laser irradiation) leads to increased magnetic polaron effects, which

would need to be accounted for in the calculations. In contrast to an ener-

getic splitting which is based on fine structure only, theses polaron effects

should be strongly dependent on the temperature. Consequently, we show

the temperature dependence of the observed states in Sec. 11.3, and reveal

that no temperature dependent shifting of the states can be observed in our

experimental conditions.

11.2 Determination of the energy to size conversion at low

temperatures

In order to compare the band edge states of the wurtzite QD series with

those from the zincblende series, it is necessary to compare the band edge

states in dependence of the QD size. Here, a relation is required to trans-

late the transmission energies at the temperature of the measurements (5K)

into corresponding QD sizes. Since the mean diameters of our samples are

known either from TEM measurements or – via subsequent consultation of

known size relations – from room temperature absorption measurements, we

merely need to connect these with our measured lowest energetic transitions

for each sample at 5 K.

Fig. 37 shows the mean diameter dependence of the lowest energetic tran-

sition for off-resonance excitations in wurtzite and zincblende QDs. Both

zincblende and wurtzite QDs exhibit lower transition energies for larger QD

diameters, which originates from the lower quantum confinement present in

larger QDs. For similar sizes, the wurtzite QDs show higher lowest tran-

sition energies than the zincblende QDs. This originates from the internal

fields in the crystal structure, which further separate the electron and the

hole states.

2.0 2.1 2.2 2.3 2.4

Avarage QD diameter

Off-resonant PL maximum (eV)

wurtzite QDs

zincblende QDs

polynominal fit

theoretical

cut off

Figure 37: Average

QD diameter as a

function of the main

optical transition in

off-resonant PL, as

determined from our

PLE measurements.

The fits required for

a sucessfull energy-

diameter-conversion

are displayed and

discussed in the text.

In the strong confinement regime, the transition energy dependence on

the QD size can in principle be described with a classic:

Eg=Eg,bulk +Econf =Eg,bulk +2¯h2χ2

m∗

eD2+2¯h2χ2

m∗

hD2(22)

with Das the effective diameter, m∗

e/h the effective mass of hole/electron,

χnl the roots of the Bessel function solving the corresponding Schr¨odinger

equation. (After [136])

For simple cases, it should hence be possible to describe the diameter de-

pendence of the lowest energetic transition with a quadratic function E=

E0+A

D2. Here the fit parameter c(c > 0) represents the influence of con-

finement on the structure and E0is the base energy. Even though this

works for the zincblende QDs, as shown in Fig. 37, this equation does not

describe wurtzite QDs well. This might originate in their more complex

crystal structure, which has a lower symmetry and also includes internal

pyro- and piezo-electric fields, which influence in electronic and hole states.

This is often compensated with the the introduction of an additional −B/D

term, to account for the coulomb attraction (Bpositive, B << A). This

term has successfully been used, for instance, by Moreels et al. for rock-

salt PbSe[137]. It does, however, not improve our fit sufficiently. For very

small QDs, an additional influence of the fine structure splitting might be

observable, which could be described with an additional −C/D3term. For

the present wurtzite CdSe QDs at low temperature, however, the inclusion

of all these extra terms yields unphysical values, and hence should neither

be used for physical interpretations nor the size conversion.

To have a consistent procedure, we therefore use polynominal fits (also used

by Moreels et al.[137], for instance) to describe the relation between energy

and QD diameter for both crystal structures. These polynominal fits, shown

in Fig. 37, only deviate marginally from the measured data points and hence

represent the data well. Note that for the zincblende QDs, the polynominal

fit and the fit based on confinement energy show only very small deviation.

For the intended conversion of the measured transition energies of sub-

ensembles to their respective mean QD diameters, it is necessary to reverse

the function. To avoid an extrapolation too far beyond the present size data,

we use 3 nm as a cut-off for the diameter conversion (see Fig. 37), since the

deviation between the theoretical fit and the polynominal fit is small above

this point. This will be applied to our experimental findings and results will

be discussed in section 11.4.

11.3 Temperature dependence of the near band-edge states

A high excitation energy can lead to a polaron formation at low tempera-

ture for CdSe QDs, which induces an increased Stokes shift to the “dark”

exciton.[135] Since this effect is strongly temperature dependent and breaks

down easily, the temperature dependence of the observed states is investi-

gated in this section.

-0.08 -0.06 -0.04 -0.02 0.00

Intensity (arb. units)

Energy rel. to excitation (eV)

80 K

70 K

60 K

50 K

40 K

30 K

25 K

20 K

15 K

10 K

ZPL

1PL

2PL

Figure 38: Temperature de-

pendence (between 5 K and

80 K) of FLN spectra for

≈3.6 nm sized zincblende

QDs at a fixed excitation en-

ergy (off resonant PL maxi-

mum at 5K).

Figure 38 shows FLN spectra of ≈3.6 nm zincblende QDs in the range

between 5 K and 80 K for a fixed excitation energy. It becomes clear that

the zero-phonon line can not be observed anymore at temperatures above

60 K. Unfortunately, the exact location is difficult to identify from direct

observation, yet also can’t be easily calculated from the first phonon replica

(1PL) position, since the phonon frequency is also temperature dependent

(Sec. 9). The intensity of all features reduces for increasing temperature,

while the one of the features of the polaron is, that it increases the relative

ZPL intensity with T. The fact that the ground state also shifts over tem-

perature is however not taken into account in this picture, which could mean

that a sub-ensemble of QDs is actually analyzed at higher temperatures is

a different sub-ensemble, due the temperature induced shift of electronic

transitions.

To overcome the influence of different sub-ensembles on the temperature

dependence, we analyzed the observable states in Fig. 39 for a number of

samples (4) at the “elevated” temperature of 60 K, the highest temperature

where the ZPL is still observed. These energy dependent states can now be

directly compared with the states observed in measurements at 5 K.

Comparing the points for 5 K and 60 K in Fig. 39, we find no dependence

on temperature for the zero-phonon line, as well as for the state above the

bright state. The phonon replica, however, show a small shift toward lower

energies, which is in good agreement with previous observations by Raman

spectroscopy (see Sec. 9).

2.0 2.1 2.2 2.3

-60

-50

-40

-30

-20

-10

2.0 2.1 2.2 2.3

-60

-50

-40

-30

-20

-10

60 K

5 K

Energy relative to 1 L (meV)

Energy of the 1 L state (eV)

1L=0!

2PL

1PL

ZPL/0L

0U/1U

Figure 39: Comparison of states of 3 exemplary zincblende QD samples

(3.6 nm, 4.0 nm and 4.2 nm) for 5K (blue) and 60K (black): apart from a

smaller phonon energy at higher temperatures (agreement with Sec. 9) no

shifts visible. The higher lying states are not observed anymore at 60 K and

are hence not shown.

This temperature independence of the dark state energetic position in-

dicates that we don’t observe effects caused by the formation of a polaron,

but rather a purely exchange interaction based splitting of the band edge

state. This is possibly due to the low excitation intensity employed in this

experiment, where we use a lamp instead of a laser for excitation. Addition-

ally the excitation and detection is distributed over an area of about 1 cm2,

which further reduces the power density.

In summary, polaron effects can be neglected when describing the states

observed in this work.

11.4 Fine structure dependence on QD size, emission energy

and crystal phases

After having found a suitable function to convert emission energies to the

corresponding QD diameters in Sec. 11.2 for the two different crystal struc-

tures, it is now possible to compare the fine structure of the diameter series.

Figure 40 shows the near band edge states – which were extracted from the

PLE measurements of the wurtzite diameter series – as a function of the

1Lstate and of the calculated QD diameter. As mentioned in the previous

chapter, the conversion is reasonable down to a diameter of 3 nm, which

causes a small reduction of usable data points in this region. The fact that

the energetic splitting between the 1Lstate and the ±2 state increases for

higher excitation energies automatically results in and increase of splitting

for decreasing QD diameter.

3452.1 2.2 2.3 2.4

-60

-40

-20

Calculated diameter (nm)

Energy rel to 1 L state (eV)

Energy 1L (eV)

2PL

1PL

ZPL/0L

0U/1U

extra

state

Figure 40: Transitions extracted from the PLE measurements for the

wurtzite CdSe QD diameter series a) as a function of the 1Lenergy and

b) as a function of the calculated QD diameter (conversion see Sec. 11.2).

Energies are shown relative to the 1Lenergy, the transitions are labeled on

the right side.

An overview of the different observed states for the wurtzite and zinc-

blende phase is given in Fig. 41 as a function of of the 1Lstate and the

calculated QD diameter. In the energy dependence as well as the diameter

dependence, most prominently the separation between the 1Lstate and the

±2 state (bright and dark state) is higher for the wurtzite QDs and increases

for higher energies (smaller diameters). However this different behavior of

the crystal structures is strongly increased, looking at the diameter depen-

dence, highlighting the differing electronic properties of the zincblende and

the wurtzite structure. This splitting between “bright” and “dark” state

is accentuated by the equally distanced phonon replica to the dark state,

showing the same offset between the structures. However, it becomes clear,

that the conversion to QD diameter changes the outward appearance of the

figure and must be carefully considered. Additionally, wurtzite QDs show

more scattering in the observed transitions in PLE than the zincblende QDs,

indicating less homogeneous samples.

1.9 2.0 2.1 2.2 2.3 2.4

-50

-40

-30

-20

-10

1.9 2.0 2.1 2.2 2.3 2.4

-50

-40

-30

-20

-10

34563456

wurtzite QDs

zincblende QDs

Energy relative to 1 L (eV)

Energy of the 1 L state (eV)

extra

state

0U/1U

ZPL/0L

1PL

Calculated diameter (nm)

Figure 41: Transitions extracted from the measured PLE contours for the

wurtzite and zincblende CdSe QD diameter series in comparison a) in depen-

dence of the ±2 energy and b) in dependence of the calculated QD diameter

(conversion see Sec. 11.2). Energies are shown relative to the 1Lenergy, the

transitions are labeled on the right side.

Based on these findings, it is our goal to find a coherent description for

the observed states for both structures. Therefore, fine structure calcula-

tions were performed in the group of Anna Rodina. To achieve a description

of the states in zincblende QDs, a possible deformation of the QD has to be

taken into account. For perfectly spherical QDs, there should be no dark

state observable; a small distortion in QD form, however, already leads to a

splitting between bright and dark state.[138]

Figure 42 shows the results of this calculation for wurtzite QDs, including

only a purely spherical form. The best fit to our data is achieved using an ex-

change strength constant ϵexch = 500 meV(for nomenclature, see [83]), which

corresponds to a singlet-triplet splitting equivalent for a bulk semiconductor

to ¯hωST = 0.2 meV. Norris and Efros found a good fit for ¯hωST = 0.13 meV

and ϵexch = 320 meV [128, 139], which is lower than the parameter deter-

mined from our data and equals the previously determined singlet-triplet

splitting in bulk CdSe. But also higher values for the exchange parame-

ter have been determined, up to 500 to 1000 meV for 1-2 nm sized CdSe

QDs[140]. This shows that the parameters observed here are well within

the range of previous findings. Additionally these parameters might even be

influenced by sample specific properties like crystal quality, growth condi-

tions or sample preparation. Furthermore, the calculation only focusses on

short-range exchange interaction, the addition of long-range interaction to

the calculation, as done by Goupalov and Ivchenko[141] could improve the

model.

3456

-60

-40

-20

3456

1L=0

QD diameter (nm)

Energy relative to 1

excitation

in FLN (eV)

ZPL

1PL

2PL

zincblende QDs

QD diameter (nm)

wurtzite QDs

Figure 42: Observed transitions of wurtzite (a) and zincblende (b) CdSe

QDs, shown as a function of the calculated QD diameter. Also shown are

calculated transitions (lines), using the following parameters: a)¯hωST =

0.2 meV, ϵexch = 500 meV for wurtzite and b)¯hωST,zb = 0.13 meV, ϵexch =

160 meV for zincblende. For the latter, the fit can only be realized by

introducing a variation to the deformation of the QD shape. This ranges

from 10% oblate to 50%, the variation is displayed in Fig. 43.

The resulting fit identifies the state right above the bright state as a

combination of the close-lying states 1Uand 0U. Note that the energetically

highest stat is not included in the fine structure, and must originate else-

where.

For the zincblende QDs, this calculation is more complicated due to the

necessary variation of form deformation, which leads to more adjustment

possibilities. On one hand, we can expect only moderately deformed QDs,

else one would clearly see the deformation in TEM measurements. This can

reasonably assumed to be less than 15-20% deviation of QD height compared

to the QD width (see inset of Fig. 43). On the other hand, any deviation

from the perfect sphere must be great enough to facilitate a bright-dark

splitting of up to 12 meV, which is in the same order of magnitude as that

of wurtzite QDs. Furthermore, in order to reach a description comparable

to that of the wurtzite QDs, the 1Uand 0Ustate should be located close

to the lower energetic upper state. But as it turns out, this fit can only be

realized for the zincblende QDs by considering a varying anisotropy between

10% for small QDs, to up to 50% for large QDs, going from slightly oblate

to very oblate. The shape variation is shown in Fig. 43, and the fit resulting

from the variation is displayed in Fig.42.

3456

0.0

-0.1

-0.2

-0.3

-0.4

-0.5

QD diameter (nm)

εexc=160 meV

μ=c/b-1

Figure 43: Deviation from the ideal

spherical form of the QD, which

is used to calculate near band-edge

states as shown in Fig. 42 in depen-

dence of the QD diameter. The defor-

mation µ=c/b−1 is given as a func-

tion of the diameter, where c is de-

fined as the height and b as the width

of an ellipsoidal QD (see inset sketch,

arrow indicating rotational symme-

try).

Such a high shape deviation from that of a sphere should be readily

visible in TEM measurement and was not observed for the samples. This

shows, that different possible origins of the observed higher states must be

explored.

Consequently, we must revisit the possible processes which can result in

the intensities observed in the FLN and PLE profiles given in Fig. 44. Since

most visible features are already identified as phonon replica of what was

previously attributed as the “dark” state, assigning the other processes is

more or less straight forward for the FLN profile. This “dark” state shows

a strong coupling to the phononic system, as can be seen in the presence of

up to three phonon replica. In the PLE profile (vertical profile in Fig. 44),

there can thus be different explanations for the areas of higher intensity

in the PLE contour. On one hand, a possible resonance to a higher en-

ergetic state of the electronic structure (for the lower one: fine structure)

might cause increased intensities; on the other hand, this could also be a

result from phonon replica of resonantly excited smaller QDs (i.e. larger

Figure 44: Possible processes that can lead to the observed lines of higher

intensity in the PLE contour plot. Left: a photon with discrete energy

excites a state and relaxes to the ZPL, the observed emission along the FLN

profile stems from ZPL and phonon replica. Right: PLE profile for fixed

detection energy. Areas of high intensity can originate from the phonon

replica of excited QDs which have a smaller size/higher ground state energy,

as indicated by filled black circles.

band gap), as shown in Fig. 44. Such phonon replica would result in 2-

3 equally separated features in the PLE profile, depending on how many

phonon replica are visible in the FLN profiles.

Figure 45 shows where these phonon replica would appear in the PLE state

diagram (see Fig. 44). While this model predominately addresses features

appearing in PLE profiles (i.e. those with energies above the bright state 1L),

the fine structure must still be calculated for a full description of observed

states, as it causes the bright-dark exciton splitting that was observed in

FLN profiles. The calculated states in Fig. 45 are determined with the same

parameters as previously used for wurtzite QDs. For zincblende QDs, this

allows us to assume a more realistic deformation of 10% in oblate direction,

and still find a suitable fit to the data. Figure 45 shows the best fit for the

zincblende QDs, which uses an exchange strength of ϵc

exch = 160 meV (corre-

sponding to bulk singlet-triplet splitting equivalent of ¯hωST,zb = 0.13 meV).

It can be assumed that the exchange constant is the same for zincblende and

wurtzite structure, the exchange strength constants need to be scaled ac-

cording to the volumes of the unit cells of the structures, ϵc

exch =ϵw(vw/vc)),

with vw/c as the volume of the unit cells. This, combined with the two-fold

larger unit cell volume of the zincblende crystal structure, should lead to

twice smaller exchange constants for zincblende structures. Here, the ex-

change strength of the zincblende QDs is smaller than half the exchange

strength of the wurtzite QDs, which could hint toward a different exchange

constant for the two crystal structures.

Evidently, features emerging from phonon replica of excited QDs with a

higher ground state energy within the ensemble appear at energies that co-

incide with the two observed higher states for the zincblende QD. For the

wurtzite QDs, the energetically lower feature lies at the same energy as the

1Uand 0Ustates, thus it is impossible to differentiate between those two

possible explanations. Remarkably, the previously unexplained feature at

higher energies can now be successfully attributed to the second phonon

replica of QDs excited with higher energetic ground state.

2.5 2.4 2.3 2.2 2.1

100

2.3 2.2 2.1 2.0

Detection energy E

det

(eV)

Detection energy E

det

(eV)

Energy relative to E

det

(meV)

a) wurtzite CdSe QDs

+ 3LO

+ 2LO

+ 1LO

+ 3LO

+ 2LO

+ 1LO

b) zincblende CdSe QDs transition

from QD

with size

Figure 45: Transitions observed in PLE profiles as a function of the de-

tection energy, for the complete wurtzite a) and zincblende b) series. The

phonon replica of the 1Lstate from smaller QDs coincide with the observed

features in PLE.

This model can explain both observed PLE states for wurtzite and

zincblende QDs, and predict the size dependence using realistic parame-

ters for simulation. It, however, raises the question why the rest of the fine

structure is not visible. This can only originate form a very efficient and

very fast relaxation into the lower energetic states. Indeed, browsing the lit-

erature, we consistently find intra-band relaxation rates in the nano second

range observed by time resolved PL (TRPL)[142–144]. Those relaxation

rates have been shown to strongly depend on the surface ligand, of which

TOPO and TOP, the ones present in this work, lead to the fastest relaxation

time of about 6 ps.[144] Others found a femto- to picosecond time scale for

intraband-relaxation.[142, 143]

The diameter dependent fine structure observed by PLE reveals a generally

higher splitting between the transitions for smaller QDs. Differences, how-

ever, can be found between wurtzite and zincblende QDs. The separation

between the observed states is larger for wurtzite QDs, which makes sense

considering the crystal field splitting within this structure. This trend is

visible in the diameter dependence, as well as in the dependence on ground

state energy; as the relation between energy and size is different for wurtzite

and zincblende QDs. The calculation of band edge states for zincblende QDs

is possible by taking a deformation in oblate direction into account. The

1Uand 0Ustates, however, can only be the origin for the observed PLE

transitions if a high, variated deformation is assumed. Hence a different

interpretation is presented, which not only coherently explains observed fea-

tures both in wurtzite and in zincblende QDs, but also an additional feature

which is observed for both of them. Especially the latter provides a clear

advantage over previous calculations. All features above the 1Lstate can be

explained by considering LO replica from excitations in smaller QDs within

the ensemble. This indicates a very fast relaxation process to the “dark”

exciton and emphasizes the importance of phonons and the apparently very

efficient coupling to them.

11.5 Excitonic fine structure in CdSe/CdS core-shell QDs

In addition to the diameter dependent analysis of the electronic fine struc-

ture of wurtzite and zincblende QDs, we have investigated the influence of

the addition of a CdS shell on the bright state - dark state splitting. For

this, we analyzed different core-shell QDs with varied CdS shell thickness.

The two shell thickness series were both based on a core with a diameter of

≈3.4 nm, one wurtzite and one zincblende. Note that the same cores were

ones used in Sec. 9 and 8.2. Here, only those with comparable and thin shell

thicknesses were investigated in PLE, because of their clearly visible CdSe

phonon replica. Figure 46 shows the FLN profiles for each sample series, res-

onantly excited in the respective bright state. Note that this state depends

on the shell thickness, see Sec. 8.1. To compare the relative locations of the

ZPL and phonon replica, the data is displayed relative to their excitation

energies. The most prominent difference between the spectra is that the

whole phonon structure is much better separated in the zincblende series,

where the separate CdSe and CdS LO replica are clearly visible. While the

CdS phonon should be primarily confined to the shell and the exciton is

mainly located in the core, this clearly demonstrates that the exciton cou-

ples with both core and shell phonons. Here, it is possible that the exciton

mainly couples to CdS phonon modes localized to the interface between

-0.08 -0.06 -0.04 -0.02 0.00-0.08 -0.06 -0.04 -0.02 0.00

1PLCdS

1PLCdSe

Intensity (arb. units)

Energy rel. to res. excitation (eV)

3.4 wurtzite core

4.4 nm (+ca. 2Ml CdS)

5.9 nm (+ca. 4Ml CdS)

1PLCdS

3.4 zincblende core

+ 2 Ml CdS (4.8 nm)

+ 4 Ml CdS (6.0 nm)

ZPL

Figure 46: Resonant PL spectra (5K) of a) wurtzite and b) zincblende

CdSe/CdS core-shell series, displayed relative to the excitation energy to

compare relative locations of the ZPL and its phonon replica. Phonon replica

are visible from the CdSe LO phonon and the CdS phonon for the QDs with

shell. The zero phonon line lies several meV below the excitation, which

highlights the splitting between bright (1L) and dark state (±2).

CdSe core and CdS shell; this could induce lower frequencies than expected

from Raman measurements, since the lattice constant in the interface region

transitions between CdSe-like and CdS-like.

Only for small CdS coverages, the direct observation of the zero-phonon

line is possible, especially for the wurtzite QDs. The Raman frequencies

are, however, known for all samples from previous Raman experiments (see

table 2) and are used to determine the location of the dark state despite

the lack of direct observation. The subsequently uncovered relations be-

tween the states are shown in Fig. 47. In order to uncover the average fine

structure for each ensemble, each QD is analyzed for excitations in the off-

resonant PL maximum. For both crystal structures, the dark state shifts

closer towards the bright state for increasing shell thickness. On one hand,

this could be an effect of the effectively increased QD diameter; on the other

hand, it could be an effect of the interaction between core and shell, such as

changed atomic bonds at the QD surface or strain induced by the shell.

In case the recombination of the dark exciton functions via dangling bond

spins [133], the recombination should become less and less likely, the fur-

ther the surface dangling bonds are moved away from the QD core. For the

present samples, the ZPL is not visible anymore for the 4ML shell thick-

ness. Here, it is however not possible to determine whether this is due to

a dampened recombination, or whether the ZPL is shifted too close to the

excitation to be observed with the given resolution.

structure core diameter shell thickness ωLO CdSe ωLO CdSe

(wz/zb) (nm) (nm) (cm−1) (cm−1)

wz 3.4 - 202.9 -

wz 3.4 0.3 204.3 285.7

wz 3.4 1.3 208.2 295.4

zb 3.4 - 203.7 -

zb 3.4 0.7 207.6 289.0

zb 3.4 1.3 209.2 300.0

Table 2: Phonon frequencies of the CdSe and CdS LO mode, as determined

by Raman spectroscopy at a temperature of 7K for all QDs studied in Fig. 46

and Fig. 47, given to compare the phonon replica shifting with respect to

the strain in the QD’s core and shell. All Raman frequencies ±0.5 cm−1(see

also Sec. 8.2)

3456

wurtzite QDs (direct obs.)

calc wurtzite QDs (CdSe LO)

calc wurtzite QDs (CdS LO)

zincblende QDs (direct obs.)

calc zincblende QDs (CdSe LO)

calc zincblende QDs (CdS LO)

Splitting between bright and dark state (meV)

Total QD diameter (nm)

pure core:

∅ 3.4nm

Figure 47: Splitting between bright (1L) and

dark state (±2) (meV), as a function of total

QD diameter. The latter is calculated from

the 1PL line observed in resonant FLN via

the phonon frequencies determined by Raman

spectroscopy(Table 2). In tendency, the two

states shift closer together upon shell addi-

tion, indicating a strong influence of the shell

on the electronic states of the QD.

Not only the CdSe phonon couples to the “dark” exciton, the CdS

phonon shows an energetic offset compared to the “bright” state of the

CdSe core too. This energetic splitting however, is lower for the CdS than

for the CdSe phonon replica. For the wurtzite QDs, the energy is the same

as for the CdSe phonon; for the zincblende QDs, however, the phonon seems

to couple to a state with lower energetic distance to the bright state. On

one hand, this could indicate strong differences in the electronic properties

in core-shell structures. On the other hand, for the recombination via the

dark exciton, an interaction between the hole and the phonon is needed.

The hole of the exciton is located in the CdSe core, hence the phonon must

be as close as possible to the core to be able to interact. Those phonons,

right at the interface between the CdSe core and CdS shell, should exhibit a

higher strain compared with the rest of the shell. This would lead to a strain

induced shift in frequency (lower frequency), rendering phonons observed in

PLE inequivalent to those measured by Raman spectroscopy (see Sec. 8.2, 8).

2.05 2.10 2.15 2.20 2.25 2.30

-40

-30

-20

-10

Energy of the 1 L state (eV)

zincblende core:

ZPL

1PL CdSe LO

+2 ML CdS:

ZPL

1PL CdSe LO

1PL CdS LO

+4 ML CdS:

1PL CdSe LO

1PL CdS LO

Energy relative to 1 L transition (meV)

Figure 48: Excitation energy dependent ZPL and 1PL (CdSe, CdS) transi-

tions, as evaluated for the three samples of the zincblende core-shell series

shown in Fig. 46b), given here relative to the excitation energy. While each

sample shows continuous shifts for the observed transitions, the shifts are,

however, not continuous over the whole series.

For a better comparison of the states between bare core and core-shell

QDs in Fig. 46, the energy dependence of the ZPL and its phonon replica is

analyzed, just as for the diameter series in the previous section (11.4). This

energy dependence is shown in Fig. 47 for the zincblende series, as those

QDs exhibit an overall better separable phonon replica signal, possibly due

to the smaller halfwidth which was also observed in Raman spectra.

Compared to the uncovered QD, the ZPL of the core-shell QD with the

lowest shell thickness is less dependent on the excitation energy, while also

having an overall smaller separation from the bright state, as already ob-

served above. This completely different trend in energy dependence em-

phasizes that the CdS shell must not only decrease the confinement of the

QD (Sec. 8), but also completely changes the QD. As discussed in Sec. 8.2,

the CdS shell causes compressive strain in the CdSe core, which can cause

a different anisotropy or deformation of the initial QD. This strain effects

on the phonon energy alone, however, can’t explain the observed trends, as

the phonon energy of the CdSe and CdS LO both increase with increasing

shell thickness. The 1PL of the thickest shell is actually even closer to the

bright state than that of the bare core, which is in stark contrast with the

observed trend in phonon energy. This indicates further mechanisms at play

and highlights that this would be an excellent subject for further investiga-

tions.

12 Effect of a silica shell on the encapsulated QD

In this chapter, the effect of a silica shell addition on a CdSe/CdS Qd will

be discussed. These shells are employed to make the QDs water-soluble and

enable applications like the use as biological markers by creating a more or

less inert and biocompatible shell that protects both, the biological cell form

the potentially poisonous QD as well as the QD from a reactive environment.

The chapter will begin picking up from the more motivational section 7.3

(and 4.1) where the application possibilities are described, and start of with

a discussion of the state of the art and previous studies. This will be followed

by our findings before and after silica coverage and the combined approach

of in situ Raman and TEM measurements. The findings reveal an interface

formation during the nucleation of silica on the QD surface, which will be

discussed in detail in section 12.6, and demonstrate they can be used as

visualization of the dynamics of this process.

Finally, we present the additional observation (section 12.8 and 12.7), that

the Raman intensity can be used to follow the transition of the QD from

one environment to the other during the encapsulation synthesis due to the

changes in dielectric constant of the environment. This enables for the first

time, to observe the transition of the QD into a water micelle within the

reverse micelle growth of the silica encapsulation.

12.1 Previous studies by TEM, PL and absorption

A good overview over various synthesis routes for the silica encapsulation of

various particles including metal particles, magnetic particles and inorganic

semiconductor particles and synthesis of larger meta structures combining

silica with particles is presented by Guerrero Martnez et al..[23] They claim

that a precise control over the synthesis and especially the thickness of the

isolating shell is the key to ensure a good response of the particles of an

external stimulation by incoming light or applied magnetic fields and un-

derline that once this has been optimized the payoff will be considerable due

to the high functionality for electronic and bio-sensing applications. Hence a

better knowledge of the properties of the hybrid particles and the synthesis

in which they are formed is mandatory.

Many groups have demonstrated well working syntheses, that produce evenly

sized silica shells around single QDs, and leave the QD intact. [70–76]

Acebron[76] et al., Gerion et al [72] and Aubert et al.[70], like other au-

thors, demonstrate that for successful syntheses of silica encapsulation of

CdSe/CdS QDs, the quantum yield can be preserved or in some cases even

improved. Additionally, the QDs show a very high and stable QY under UV

illumination over weeks or even month, rendering them a magnificent probe

for long term cell observation. However they, like other groups[73, 74], find

a small redshift (of the oder of magnitude of 10 nm) of the PL signal after

encapsulation which has yet to be explained.

The effect of a silica shell on a colloidal QD is previously predominantly an-

Figure 49: left to right: TEM of silica coated QDs, luminescence of a bottle

of QDs under UV irradiation, and application: cells marked with differently

colored silica covered QDs under UV lighting, taken from [70] The QDs

shown are produced by our cooperation partners and are comparable to

those used for this work.

alyzed by TEM, absorption and PL. However TEM only yields information

on shell thickness, homogeneity of coverage, possible agglomerations (num-

ber of enclosed QDs), and an overall impression on the presence on generally

intact QDs. Whereas smaller, more intricate changes in the structure of the

QD, e.g. a change in bond length or a rearrangement on the surface, or

even the formation of an interface are very hard (and time consuming) to

determine by TEM. Even in high resolution TEM those small changes of

the surface at the atomic length scale are hard to resolve, rendering the

observation of a rearrangement nearly impossible.

In contract to this, in PL and absorption measurements, effects of changes

on the electronic structure of the QD can be observed. It is generally used

assuming that when the PL or absorption of a sample goes down, the syn-

thesis of the silica shell has destroyed the samples and hence was not suc-

cessful. Those methods, especially PL, mostly address the properties of

the optically active transitions with a high occupation probability (apart

form experiments with very high excitation densities). In the case of the

CdSe/CdS core-shell QDs, the charge carriers are have a high overlap of

their respective wavefunctions in the CdSe core, so PL experiments result

in information on the core. Thus they only peripherally provide informa-

tion on the effect of silica capping, because the core does not have a direct

interface with the silica (outer) shell and hence should show a only a weak

dependence on the interaction of the silica. A possible interface between

silica and QD would form at of the outermost part of the QD, between the

CdS shell and silica shell. On the one hand, this presents an advantage for

the QY of the QD, as the core is protected from influences on the surface of

the QD. On the other hand, this complicates the analysis of the influence of

the silica shell, which potentially, with higher knowledge on the interaction,

could even improve the QD’s properties.

In contrast to this, in absorption the absorption levels of both CdSe core

and the CdS shell should be visible. However the problem is the overlap-

ping of the CdS shell absorption lines with higher energetic broad features

of the CdSe cores in same the energetic region. This causes the CdS shell

related absorption lines to mostly vanish within the absorption band of close

lying levels of the CdSe core and makes the assignment and interpretation

extremely complex and thus rarely done.

In conclusion, both methods are mainly used to monitor changes in the main

optical transition, the lowest energy level on the CdSe core and are used to

confirm the QD is still intact, through demonstrating it has a comparative

quantum yield and emission wavelength after the silica encapsulation com-

pared to before. Since the QDs in the analyzed samples always have a size

distribution, the emission signal is broadened accordingly, and hence smaller

changes induced by the silica capping might not be visible anyway.

As a further method of investigation, 1H NMR spectroscopy, has been ap-

plied by Acebron et al [76]. they follow which chemical species interact

with the organic ligands that cover the QD initially and find that under

the conditions applied the ligands stay linked to the QDs even after the

encapsulation. Therewith they demonstrate that the silica forms on top of

a ligand shell that remains on the QD. However this method cannot provide

direct microstructural information on the QD’s surface. Additionally, the

ligands used in the experiment are strongly bound to the surface (see Sec.

12.2), which means the experiment can lead to different results when differ-

ent conditions are used.

At the same time, the synthesis of the silica shell in the reverse micelle solu-

tion is often regarded as a black box. Samples are analyzed before and after

the encapsulation, but the process in between is mostly guess-work between

those two points, which makes it an interesting subject for in situ analysis

for a more detailed investigation. not only indication, but real evidence of

the changes the undergo.

As Raman spectroscopy provides structural details that can potentially un-

veil the interaction between the QD and the changing surrounding. It has

been shown to reveal details on the interface in core-shell QDs [43] as well

as possible influences of the surface on the QD[91, 95, 124, 145] (see also

Section 8.2). However, it has rarely been applied to the silica encapsulation

before, only Ethiraj et al.[146] used Raman spectroscopy to prove that the

QDs remain intact after silica encapsulation. Additionally, they compare

their silica encapsulated QDs with pure silica samples and find similar fea-

tures in the spectra. However the silica features consist of broad features in

the low frequency region (250-500 cm−1) and more discrete signals at higher

energies (around 1500 cm−1), which probably originate from molecule vi-

brations while the broad low energy feature should stem from collective

vibrations of the amorphous structure of the silica. However, the Raman

spectra are mainly used to evidence the presents of both structures and are

not analyzed in much detail.

This leaves room for a more detailed Raman spectroscopy-based study of

silica-QD compound particles. Here, due to the long duration of the syn-

thesis, and the sharp and intense Raman signal of the CdSe/CdS QDs, even

the in situ observation of the synthesis is possible. Which should provide

valuable information on the process of the silica formation on the QD.

12.2 Synthesis of silica particles and the synthesis reaction

mechanism in the reverse micelle microemulsion

The use of silica for the encapsulation of QDs for biological or medical ap-

plications provides many advantages, as it is a comparatively well known

biocompatible material. One very important aspect is that it provides the

water solubility to the QD, which is the basis for any biological application.

The synthesis of nano sized spherical silica structures is usually performed in

a water-in-oil solution. Using a silica precursor, often TEOS, the synthesis

takes place under the addition of ammonia and a surfactant. Together with

the surfactant, the water forms micelles in the oily solution. Those micelles

are used as nano-reactors for silica, as well as for a wide variety of other

nanoparticles. With the addition of ammonia the synthesis is started, as

it enables the TEOS molecules (or other alkoxysilane precursor) to be hy-

drolyzed and available for reaction. Such an amorphous silica structure can

from within the water micelles form condensation of the hydrolyzed silica

precursor (classical sol-gel reaction).[75, 147] However the actual mecha-

nism for the silica encapsulation of the hydrophobic nanocrystals in the

microemulsion is not completely understood. It is however often assumed,

that the previously hydrophobic nanocrystals, initially in the oily phase, can

migrate into the water micelles, enabled by an exchange of the organic lig-

ands for hydrolyzed silica monomers and/or surfactant molecules. [73, 74]

This process is schematically depicted in Fig. 50.

Osseo-Asara and Arrigada[148] find that the evolution of average size of a

silica particle formed in a microemulsion can be described by first order ki-

netics with a growth rate k. This rate kcan, under the assumption that the

change in concentration of silica precursor is directly gives with the amount

of newly formed silica, be described as k=d[TEOS]/dt =d[SiO2]/dt.

Using TEOS as a precursor, the silica builds spherical particles, which means

that when analyzing the particle size, it can be assumed that the TEOS is

converted to a spherical volume. The speed of TEOS conversion is deter-

mined by the relation water to surfactant, which Osseo-Asara and Arri-

gada[148] studied in detail and find that a higher surfactant concentration

enables faster growth. Within the first 30 hours of the experiment the size

distribution is represented well by the description based on the amount of

hydrolized TEOS, but afterwards another growth mechanism might be at

work. For instance after a certain point, the statistics of a silica particle

even getting in contact TEOS molecule must play a role. However, for a

benign synthesis the evolution of average spherical particle size < d > over

time tthus can be described with the function <d>= (1 −e−kt)1/3·dfinal,

where kis the TEOS hydrolyzation rate and dfinal is the diameter of the

particle at the end of the described growth step (not the converged diameter

when the growth has saturated naturally). This just reflects the fact that

for the growth of a 3 dimensional structure, the TEOS converted to silica

needs a fill a volume and hence the TEOS consumption for the growth goes

by the power of 3 of the particle radius.

Looking at the synthesis in a more general way, it becomes clear the solu-

Figure 50: left to right: Model of the so-called “inverted micelle”: A micelle

of hydrophilic liquid in hydrophobic liquid (water in oil, instead of the usual

oil in water), kept stable by a shell of ligands. Schematic of the growth

mechanism of a silica (hydrophilic) shell around colloidal hydrophobic QDs:

The synthesis starts with a QD covered in amphiphilic ligands. Once the

silica precursor molecules, the TEOS, hydrolizes and silica can be formed.

This can be either directly on the surface of the QD, thereby removing

the ligands or on top of the ligand shell (not shown). The silica forms a

hydrophilic shell around the QD, that favors solution in water. Hence QD

transfers to water micelles, which provided in the synthesis solution, where

the silica shell proceeds to grow until all hydrolized TEOS is used up. image

taken from Tangi Aubert, private communication.

bility plays an important role as the CdS/CdS QDs that are to be capped

are hydrophobic, while the silica that will encapsulate them in the end is hy-

drophilic. Hence during the synthesis the solubility changes an the QD must

travel from one solvent to another. Consequently the synthesis must take

place in a microemulsion, containing both water (or a different hydrophilic

solvent for the silica) and a hydrophobic solvent like toluene or cyclohex-

ane (for the QD covered with amphiphilc ligands; often TOPO, TOP or

oleic acids). The emulsion is kept stable by a nonionic surfactant, in our

case Brij, a polyalkylene glycol ether, that is widely commercially available.

This microemulsion is schematically shown in Fig.50, where a water micelle

is shown in cyclohexane solution surrounded by surfactant molecules. Dur-

ing the course of the synthesis, the QD which were previously surrounded

by it’s ligands and diluted in cyclohexane, will be covered by the first of

silica have to travel into the water micelle because of solubility.

Figure 51: TEM measurements of CdSe/CdS QDs before (a) and after silica

encapsulation (b-c), with increasing silica shell thickness c-b-d. For better

visibility, the QD is highlighted in red, the silica shell in blue. Figure after

Aubert et al.[70]

The exact mechanism of silica incorporation is debated in the literature

currently. One possibility is that the ligands on the Qd surface are replaced

by hydrolyzed TEOs molecules which allows the QD to travel into the water

micelle (Fig.50).[73, 74] Others believe that the ligands on the QD are ex-

changed by surfactant molecules to enable the travel into the micelle before

the hydrolyzed TEOS attaches to the surface and the growth of the shell

starts.[73] Darbandi et al. base this assumption on TEM measurements,

where no surfactant filled gap found between silica and QD. Koole el al con-

clude the direct interaction of silica and the QD surface from time-resolved

PL measurements following the different stages of the synthesis. This is

opposed by thiol bound ligands, have been shown to remain on the QD

surface after silica encapsulation, as reported by Acebron et al.[76] (bases

on NMR meassurements). Those ligands however have been shown to be

more tightly bound to the QD surface than oleic acid for instance, which

have demonstrated to be easily removable from the surface by Hassinen et

al.[149]. For further information on the surface chemistry of the QDs used

in this work, see Sec. 7 and Drjivers et al. [78].

Since the bond between QD surface and attached ligand can be this diverse,

it is out of outmost importance to analyze the surface chemistry and the dif-

ferent outcomes of the silica encapsulation synthesis in more detail. This can

result in several different mechanisms of coverage and surface functionaliza-

tion, the understanding of which could be a key to improving the quality of

the final capped QD. Eventually varying the QD’s ligands, microemulsion

surfactant or pH conditions, would certainly be of interest for the design

of an optimized synthesis towards the production of materials with greater

optical properties.

Until now, very few of these theories have been supported by actual mea-

surements to determine the exact surface reaction on the QD surface. Hence

the question is left open if the silica shell is formed directly on the QD sur-

face, or on top of or incorporating the ligand shell around the QD. Between

those cases, the intensity of interaction between the two materials would

surely be very different and should influence the properties of the QD in-

side. Consequently, we analyze the silica encapsulation of CdSe/CdS QDs

in order to find evidence regarding the nature of interaction between silica

and QD in the following Section.

12.3 The in situ Raman setup and synthesis of silica shell

on CdSe/CdS QDs

In order to realize in situ Raman measurements during a silica encapsula-

tion reaction, the reaction is performed in a cuvette placed in the macro

setup (shown in Sec. 6.1). The cuvette must be stirred continuously during

the whole process by a magnetic stirrer to ensure a constant temperature

in the whole vessel due to possible laser induced heating. The cuvette used

(Torlabs) has a volume of 2.5 mL, to facilitate sufficient mixing and optimal

for transmission of light in the visible range.

Since the reaction takes place in the course of two to three days, the system

needs to be stable and CCD cooling needs to be ensured. The stability of

the solution is temperature sensitive and best kept constant at 20◦C, as at

temperatures above 32◦C the microemulsion separates irreversibly. This is

caused by the temperature instability of Brij. We found that some stirrers

develop heat after operating for a few hours, so as a result the cuvette is

positioned above the stirrer separated with ca. 2 cm styrofoam and is cooled

with cooling fan additionally. To keep laser induced heating low, the laser

power was kept below 10mW. Intensity fluctuations due to small changes in

laser power can be corrected by normalizing to the solvent intensity.

For the encapsulation, wurtzite CdSe/CdS QDs are synthesized with the

flash procedure as published by Cirillo et al. [69] (Sec. 7.2.1). These QDs

have been shown to retain good luminescent properties ans high stability

after encapsulation by Aubert et al.. [70] (see also Sec. 7.3 and Sec. 12) We

employ a reaction based on this synthesis, only the solvent is substituted

with cyclohexane for a better separation of the Raman signal of solvent and

QDs.

200 250 300 350 400 450

293.0

210.3

382.5

Cyclohexane

CdS

Intensity (arb. units)

Raman shift (cm-1)

CdSe 425.2

Figure 52: Left: photo of a QD solution post silica encapsulation within the

Raman setup, illuminated with the Raman laser. Right: Raman spectrum

of CdSe/CdS QDs in cyclohexane solution with the phonon modes of CdSe

and CdS cleary visible, as well as two modes originating form the solvent

that remain stationary over the whole synthesis.

First the prepared QDs, which are in solution with cyclohexane, are

mixed with an additional 1ml of cyclohexane with 0.32 ml Brij (Polyethy-

lene glycol hexadecyl ether) and stirred for at least 5 minutes. Then, 50 µL

water and 5 µL ammonia (NH4OH are added and after 1 hour of stirring,

the solution is ready for silica precursor injection to start the synthesis.

This step is crucial to ensure the formation of a microemulsion needed for

the reaction, as an isotropic growth of silica shells, which each enclose one

QD only, is not possible otherwise. We vary the TEOS amount to compare

different reaction speeds and final silica shell thicknesses during and after

the experiment. The TEOS amounts used in the three separate synthesis

are listed in Tab.3 and are given in the TEOS to QDs molar ratio in the

following to give a more universal value that is independent of the QD con-

centration in the initial mixture. The QD concentration of the QD solution

is determined based on their absorbance in toluene under the use of intrinsic

absorption coefficients, calculated with Maxwell-Garnett effective medium

theory in dependence of the CdSe/CdS volume ratio.

For the in situ measurement, the TEOS injection marks the beginning of

Sample TEOS-volume TEOS/QD final silica thickness

(µL) molar ratio (after 72h) (nm)

QD A-1 13 2.86·10526.7±1.5

QD A-2 25 5.51·10533.4±1.7

QD A-3 50 7.71·10535.8±1.5

Table 3: Varied TEOS amounts used in the in situ Raman observation for

three different synthesis‘ presented in Sec. 12

the reaction and thus has to be conducted with the cuvette in place inside

the Raman setup. Measurements need to be started simultaneously and be

repeated in defined intervals of time (with Labspec), and resulting in the

time axis for the in situ observations. We used an integration time of 180s

and repeated the measurements every 10 minutes for the duration of the

whole synthesis of up to tree day. Since changes in the Raman spectra have

saturated well before 24 h, in some cases the observation was stopped af-

ter 48 h. The resulting Raman spectra are subsequently analyzed and the

different phonon modes are fitted with Lorentzian functions, as shown in

Fig.52, to extract precise positions and integrated intensities of each mode.

To correlate the findings from Raman spectroscopy with a silica shell thick-

ness, in separate syntheses the thickness is analyzed by TEM after defined

intervals of time. This is done by taking aliquots from the reacting solu-

tion and subsequently stopping the shell growth by removing the remaining

TEOS molecules by centrifugation.

Name CdSe core total CdS shell thickness surface area / volume

(nm) (nm) (nm) of CdS shell(1/nm)

QD A 4 7.4 1.7 2.8

QD B 3.6 9.1 2.8 0.8

Table 4: Different QD geometries, that where observed during silica encap-

sulation with in situ Raman with diverging results presented in Sec. 12.8

Additionally to the silica encapsulation synthesis with varied silica pre-

cursor amount on the same QD, we have conducted a similar encapsulation

on a QD with a different geometry (see Tab. 4) to be able to analyze how

the effect in the Raman spectrum in influences by the surface to volume

ration of the QD. At the same time this QD B has a less strained CdS shell,

and hence the initial phonon frequency of the QDs diverge.

Theses experiments are shown and discussed in Sec. 12, giving an interest-

ing insight into the silica encapsulation reaction and the interaction with

the enclosed QD.

12.4 Raman analysis of the silica encapsulation of CdSe/CdS

QDs

In the previous Sections we established that there is an interest to find out

about the nature and strength of interaction between the QD and the silica

shell in such an silica encapsulated compound and described the experimen-

tal setup and synthesis condition to be used in the in situ Raman analysis

of the encapsulation process.

The Raman spectra of pure and silica encapsulated CdSe/CdS QDs are

shown in Fig. 53 left. The fact that the Raman signal of the QD is still

present after the shell addition, demonstrates that the crystal remains in-

tact after the reaction. The frequency of the CdS phonon mode of the shell,

however, appears shifted compared to the uncovered QD. The FWHM of

this mode is slightly reduced. Generally, in such a CdSe/CdS core-shell QD,

the frequency of the phonon modes is mainly influenced by the strain caused

by the lattice mismatch between core and shell. Within the QD, the CdSe

core and CdS shell are under compressive and tensile strain, respectively.

This results in shifted Raman frequencies compared to the undisturbed bulk

phonon mode towards blue for compressive strain, and red for tensile strain.

As a first investigation of the influence of the silica shell thickness, the re-

150 200 250 300 350

0.2

0.4

0.6

0.8

1.0

Normalized intensity (arb. units)

Raman shift (cm -1)

pure CdSe/CdS QD

same QD with Silica shell

Figure 53: Left: First silica experiment: Raman spectra of one QD, pure

and with a thick silica shell. The CdSe core is barely visible, but the CdS

shell shows a shift towards higher frequencies and a decreased halfwidth.

Right: Raman frequencies of the CdS shell of a pure QD and after coverage

with a differently thick silica shell. Within scattering, the frequencies after

capping are independent of the shell thickness.

sulting shell phonon mode is displayed in Fig. 53 right for one exemplary

QD, pure and covered with different silica shell thicknesses. For this QD, the

CdSe core Raman frequency doesn’t change upon silica shell addition. For

all silica shell thicknesses shown, the shift in Raman frequency compared to

the uncovered QD is the same, which evidences that the shift is independent

of shell thickness above 8 nm. Hence, to find the dependence of the shift

from the silica shell, the investigation needs to start at far lower thicknesses,

as the shift has saturated already above 8 nm thickness.

Nevertheless, the direction of the shift is the same direction for all exam-

ined samples. The CdS shell phonon mode always shifts towards the bulk

frequency, starting an initial red shifted CdS shell phonon frequency due

to tensile strain in the QD. This direction in combination with the small

decrease in halfwidth of the phonon mode, indicates a reduction of strain

combined (shift) with an improvement of the long range order of the crystal

(low halfwidth of Raman mode). Thus a reduction of strain due to defect

induced relaxation is unlikely. However the origin of the shift in Raman

frequency will be discussed in more detail in Sec.12.6, after the analysis of

the dynamics in Sec.12.5.

The total difference between initial and final frequency depends on the ge-

ometry of the initial QD. A QD with a thin CdS shell is under heavy tensile

strain and thus starts at with lower initial phonon frequency and in ten-

dency shows a higher change when a silica shell is added. Additionally it

will become clearer in the following chapter that a dependence of surface

area compared volume of the shell is also likely to have an impact, as we

demonstrate that, under our experimental conditions, the shift is caused by

interaction with the surface(see Sec.12.6).

In order to find out at which state of the synthesis the shift occurs, we

monitor the formation of the silica shell in situ during the synthesis with

Raman spectra every 10 minutes with an accumulation time 180 s. A typical

spectrum of the QD microemulsion, that is used for the synthesis, is shown

in Fig. 54a. The peaks of main interest, the CdSe core and the CdS shell

phonon, are visible at 210 cm−1and 293 cm−1for this QD (QD A). Addi-

tionally, the solvent Cyclohexane has two peaks at 383 cm−1and 425 cm−1,

which can be used for reference as the solvent is unaffected by the reaction,

hence the position and intensity remain constant and are used for normaliza-

tion. All spectra are analyzed and fitted with Loretzian functions, as shown

in Fig.54a with peak-o-mat and in the following, the LO-peak positions,

FWHM and intensities (peak areas) are collected from the fits are used for

analysis in the following.

In Fig.54 a and b, the evolution of Raman frequencies of the CdSe core and

CdS shell (of QD A) is displayed during the synthesis of a silica shell over

synthesis time. The time 0 corresponds to the injection of silica precursor,

the start of the synthesis. While the CdSe signal of the core only shifts

towards a higher frequency by approximately 0.5 cm−1, the CdS shell fre-

210

211

212

213

200 250 300 350 400 4500 6 12 24 36 48

Raman shift

(cm-1)

Silica shell synthesis time (h)

CdSe-mode position

292

293

294

295

Raman shift

(cm-1)

CdS-mode position

292.3

210.3

382.5

Cyclohexane

CdS

Intensity (arb. units)

Raman shift (cm-1)

CdSe 425.2

FWHM of

CdS LO (cm-1)

Figure 54: a) Raman spectra of CdSe/CdS QDs in cyclohexane solution.

Peaks from the CdSe core and the CdS shell can be seen at 210 cm−1

and 292 cm−1, respectively. The solvent cyclohexane has peaks at 382 and

425 cm−1. Position of the CdSe b) and CdS c) LO-like modes depending on

time passed during silica synthesis. Time =0 corresponds to time of TEOS

precursor injection. Break in time axis to highlight “early” hours of the ex-

periment, d) FHWM of the CdS shell LO fit during the course of synthesis.

[150]

quency increases by as much as 2.2 cm−1. Additionally, the FWHM of the

CdS shell Raman mode reduces from 20.5 cm−1to 19.5 cm−1, about 1 cm−1

in total, which has already been observed in the ex situ meassurement.

Hence the in situ measurement reproduces results from the comparison be-

tween pure and final silica covered QD, but also reveals that this shift only

takes place in a very early stage of the synthesis. While the final silica

thickness is reached after several days, the Raman frequency shift saturates

already after 2 hours in this synthesis. This indicates that the shift is not

primarily a function of the silica shell thickness, but of the formation of the

very first silica layers. Considering that silica is an amorphous material, the

prospect that it doesn’t cause an epitaxial strain on the QD makes sense,

since it would increase for increasing thicknesses far beyond a few nm.

In the following, we examine the dynamics of the synthesis in more detail.

For this experiment, we vary the concentration of the silica precursor in

order to vary the speed of the silica formation. This should lead to direct

information on the dynamics of the evolution of the Raman signal and the

synthesis. Additionally we compare the effects of the silica shell on two QDs

with different geometries to see if this influence the extend of influence of

the silica on the QD.

12.5 Dynamics of the silica encapsulation reaction analyzed

by in situ Raman and TEM

Since in Sec. 12.4 it was established that the shift in CdS phonon mode

upon silica capping develops at low silica shell thicknesses and saturates

fast. These finding shall now be connected with the silica shell thickness’

function of time during the synthesis. The growth speed is varied to find the

relation between the shift in Raman frequency and the speed of the silica

growth.

Thus to further investigate the dynamics of the shift, we have designed the

following experiment: the same QD (QD A) is encapsulated in three separate

synthesis under the same conditions, same water, Ammonia and surfactant

concentration, apart from silica precursor concentration. For a detailed list

of used amount of each chemical see Section 12.3. Three different TEOS

concentrations, 2.86·105, 5.51·105and 7.71·105TEOS to QD molar ratio,

are employed. These three reactions are monitored by in situ Raman and

in a separate experiment under the same conditions, the evolution of av-

erage particle size is analyzed by TEM. The TEM analysis is realized by

taking aliquots from the reacting solution after defined periods of synthesis

time. Those aliquots are subsequently cleaned from TEOS by centrifuga-

tion to stop the reaction and then analyzed by TEM. A small selection of

theses TEM measurements is shown Fig. 55. The QDs in their developing

silica shell for all three syntheses are displayed for two different synthesis

times; after 2 hours of synthesis and after 72 hours, when the experiment

was stopped. With increasing TEOS amount in the synthesis, both the final

silica thickness as well as the growth speed increases.

The the development of the average particle size over time gained from these

measurements is shown in Fig.56 for the three syntheses. The employed

TEOS concentrations of 1.73·103nm−2, 3.33·103nm−2and 4.66·103nm−2

result in different final silica shell thickness after 72 hours, as well as diverg-

ing speed of shell growth. In general, the higher the TEOS concentration,

the faster the speed of silica growth and the higher the final shell thickness.

As mentioned in Section 12.2 the growth of pure silica particles in water-in-

oil microemulsion can be well describe by a simple function. It should be

noted that the shell thickness after 72 hours of growth still hasn’t saturated

and would proceed if the reaction isn’t stopped by washing the particles and

thus we can assume, the growth does not go beyond the TEOS hydrolization

rate limited regime as described in Section 12.2. However, for the descrip-

tion of the silica encapsulation, the non-zero initial silica particle size has to

Figure 55: TEM-analysis as a function of the synthesis time for

different TEOS amounts in TEOS molecules per QD surface area

(QD A11.73·103nm−2, QD A23.33·103nm−2and QD A34.66·103nm−2),

in TEOS to QD molar ratio QD A12.86·105, QD A25.51·105and

QD A37.71·105

be taken into account, since the minimal particle size here is the QD size.

To account for the presence of initial CdSe/CdS seeds, which will influence

the initial growth rate, introduced a time offset to their equation. Looking

at the data, we find that the formula gives a good fit when approximately

the first 5 hours of experiment are excluded. This means that within those

first 5 hours the growth mode differs from that of pure silica particles. After

the synthesis of more than 2 nm of silica, it becomes the same as for pure

silica particles.

During those first few hours of the experiment, the first layers of silica

from on the surface of the QD. This heterogeneous nucleation is slower than

the growth later on, as can be seen in Fig.56a. Because this coincides with

the time frame of the change in Raman frequency, it is necessary to inves-

tigate this region in as much detail as possible. To quantize the nucleation

speed, we fit the average silica shell thickness approximating with a linear

fit. It may be noted that for the lowest TEOS concentration, we find no

trace of the silica in TEM after 1 hours, so for this synthesis the point 0,0

is removed from this fit. This could be an effect of low accuracy in the

determination of silica thickness by TEM, which is especially high for low

thicknesses (resolution, contrast), or a very slow start of nucleation due to

the low concentration of TEOS. The linear fit of the average silica shell

Figure 56: a) silica shell thickness as determined by TEM-analysis as a

function of the synthesis time for different TEOS amounts (2.86·105, 5.51·105

and 7.71·105TEOS to QD molar ratio in black, blue and green respectively)

The final size, as well as the speed of the reaction increases with higher

TEOS concentration, Inset in a): TEM of final silica shelled QD, b) linear

fit of 0-5 hours (formation of the first silica on the QD) of data in a), c)

slopes resulting in b) over TEOS concentration. part of this work and from

[150]

thickness within the first 5 hours is shown in Fig. 56b). To connect this

depedence with the synthesis condition, the slopes resulting from the fits

are shown in 56c) in dependence of the corresponding TEOS concentration

in the synthesis. This clearly shows a linear correlation between the speed

of silica growth in this starting phase and the TEOS concentration in the

reaction. Fig. 57 shows the CdS Raman frequencies during the course of the

three synthesis. For all syntheses, the change in phonon frequency saturates

below the duration of 5 hours. 90% of the final shift has been reached after

4.4 hours, 3 hours, and 1.8 hours in order of decreasing TEOS concentration.

Already this indicates a correlation similar to the linear dependence of the

nucleation speed on the TEOS concentration. The final Raman frequency

is the same for all synthesis, independent of final silica shell thickness or

Figure 57: Raman shift of the CdS mode as a function of the synthesis time

for different TEOS amounts per QD surface (2.86·105, 5.51·105and 7.71·105

TEOS to QD molar ratio in black, blue and green respectively). The final

shift remains the same between the different conditions, while the speed of

the shift increases with higher TEOS concentration. The red ticks mark the

time where 90% of the final shift is reached. part of this work and from [150]

the speed of heterogeneous nucleation. This essentially reflects our findings

from ex situ measurements as mentioned in Section 12.2.

To analyze dynamics of the shift, we find that the Raman shift can be well

described using Af−∆Ae−kt, where Afis the final Raman frequency reached

during synthesis, ∆Ais the total change in Raman signal over t(time) with

the exponential parameter kthat represents the rate of saturation. The

shift of the Raman frequencies together with the fits are shown in Fig. 57a.

The growth rates kresulting from this fits, are displayed in Fig. 57c in de-

pendence of the TEOS concentration in the synthesis. Again, we find an

approximately linear dependency on the TEOS concentration. This is also

supported by Fig. 57b, which shows the Raman shift in dependence of the

approximated silica shell thickness, which was calculated with the linear fits

to the TEM determined sizes. It demonstrates, that the shift in phonon

frequency is actually the same for all synthesis, when the shift is analyzed

in dependence of the shell thickness instead of synthesis time and shows this

shift is fundamental.

Additionally since the speed of silica nucleation on the QD surface is linearly

100

dependent on the silica precursor concentration, as discussed above, this is

a new method to monitor the nucleation right during the synthesis, without

the necessity of stopping the reaction or taking aliquots. Thus monitor-

ing the Raman signal enables the silica shell growth process to be studied

in more detail and optimized more rapidly than conventional spectroscopic

techniques or TEM allow. This method provides a new approach to ana-

lyze the reaction mechanism of the nucleation of silica on the QD surface

and how it is influenced by the water-to-surfactant ratio, TEOS/QD surface

relation, temperature or Ammonia concentration. As before mentioned the

influence of differently strong bound ligands on the surface of the initial QD

should have a strong influence on the synthesis.

12.6 Origin of the change in Raman frequency during silica

synthesis

In the previous Sections, the change in Raman frequency of the CdS LO

phonon mode during the encapsulation of a CdSe/CdS QD with silica has

been discussed, establishing that the shift is independent of the shell thick-

ness when the coverage exceeds 2 nm and correlating the dynamics of the

shift in Raman frequency with the nucleation of silica on the surface. If

the silica would be interacting with remaining organic ligands only, it would

not affect the structure of the QD and thus could not explain the observed

changes in the Raman spectrum. Thus, the extent of the effect of the silica

on the Raman signal of the CdS shell implies a close interaction between the

two materials. The reduction in halfwidth of the phonon line excludes mas-

sive structural defects caused by the reaction. This leaves the question open,

what the origin this shift actually is. In general, shifts in Raman frequency

mean that the vibrational properties of the material have changed. This can

happen due to a change in bond length, bond strength and/or geometry, for

instance. All of those change the conditions for a lattice vibration and thus

the phonon energy.

Scenarios with a complete exchange of bond partners in the whole sample

are unlikely in many experiments, hence shifts or deviations from reference

samples in Raman frequency are often discussed in the context of strain.

This can, for example, be epitaxial strain, that occurs when two materials

with different crystal lattices are grown on top of each other. In order to

form a bond, the unit cells at the interface need to deform to make a fit. For

the material with the smaller lattice constant this means it must stretch,

while the larger lattice constant is compressed. This puts the two materials

under tensile and compressive strain, respectively. Thinking of the lattice

vibration, this can be compared to a stressed system of springs (elastic con-

stant model). Compressive stress changes the eigenfrequency of the spring

towards higher energy, tensile stress leads to lower eigenfrequencies. The

101

same is valid for the phonon energies measured in Raman spectroscopy. To

make claims about strain however it is necessary to have a strain-free ref-

erence system, for colloidal QD in most cases a bulk reference at a defined

temperature would be used. In this context it is also important to think

about different temperature expansion coefficients of different materials, as

this influences the interplay strongly, depending on the temperature the ma-

terials were brought in contact (grown) and the temperature at which the

measurement is performed. This temperature dependence is addressed in

more detail in Section 9.

Considering the CdSe/CdS QD in silica shell, we are presented with ma-

terials that possess very different lang-range order. Two materials in the

compound form a periodic crystal lattice CdSe and CdS, while silica is an

amorphous material, which has a short-range but no long-range order. The

atomic structure of silica is shown in Fig. 58. So before the the addition

of the silica, the QD is strained depending on the correlation between CdSe

core and CdS shell, this leads to Raman frequencies that are smaller than

for bulk materiel for the CdS shell, and ones that are larger than in bulk

material for the CdSe core. The addition of the amorphous silica shell re-

sults in a shift to higher frequencies for both signals at different extents. For

the CdSe core, the shift is either very small or for not detectable (depending

on the exact geometry of the QD), this would mean a small isncrease in

compressive strain. This is opposed by the shift to higher frequencies for

the CdS shell, which shifts the shell closer to CdS bulk configuration. At the

same time, the halfwidth of the CdS LO phonon mode decreases and thus

indicates an improved ordering in the shell and an improved, overall more

bulk-like condition. Since silica is an amorphous material, this shift cannot

be because by a lattice mismatch inducing strain. As this silica is formed,

it is energetically unfavorable to grow in a way that it applies additional

(compressive) strain to the QD and because it is not constrained to crys-

tallize in an ordered lattice, it will arrange in the position with the lowest

potential energy. Furthermore since the temperature of the synthesis is the

same as for the measurement, thermal expansion can be excluded as a cause

of further strain. Additionally to the position of the phonon mode, strain

influences the halfwidth of the mode because the distribution of bond length

increases when stress is applied. The fact that the halfwidth of the CdS LO

phonon mode has a tendency to decrease, suggests that additional epitaxial

strain applied to the QD is not the explanation for the shift in phonon fre-

quency, as it would increase the distribution width of bond lengths.

At the same time, atomistic ab initio calculations done by Han et al. [124,

125] find that the whole CdSe/CdS QD structure, should be under compres-

sive strain. For the phonon frequencies for both, CdSe core and CdS shell,

this would lead to a blue shift compared to the bulk phonon frequency. How-

ever, according to their calculation the shell still has a redshifted phonon

frequency. The reason for this redshifted signal of the shell is the surface. At

102

the surface. the symmetry of the crystal is broken; the atoms lack bonding

partners. This surface under-coordination, according to Han et al., overcom-

pensates the effect of the compressive strain on the phonon frequency and

results in a signal that is red shifted compared to the bulk phonon frequency.

So the final outcome of phonon energies is coherent with that predicted by

the epitaxial strain model. Since this shift of the CdS shell is a pure surface

effect, it strongly depends on the ratio between surface area and volume of

the shell material. When the surface area is small in comparison to the vol-

ume, the influence on the resulting signal becomes negligible. This indicates

that at very small surface-to-volume ratios, the phonon frequency should

become higher for the CdS shell than for bulk material. This is where the

calculation differs from results of our measurements. Even for shells as thick

as 15 nm, the phonon frequency doesn’t become higher than the bulk fre-

quency. The same is evidenced by other groups based on measurements of

dot-in-dot or dot-in-rod structures. This shows that the overall compressive

strain in the QD that they predict can’t be found in experiments. Even

though this points out boundaries that the calculation faces, the findings

still point out the high relevance of surface symmetry breaking in a QD and

the great effect the surface has on the phonon frequency.

In our experiment, the initially red shifted CdS shell shifts towards bulk fre-

quency during the nucleation of silica on the surface of the QD, as shown in

section 12.4 and 12.5. In the comparison between two different QDs, QD A

and QD B, we will find and indication that the total shift during the synthe-

sis is in fact surface related, as it depends on the surface area compared to

volume of the CdS shell (Section 12.8). All this is evidence that during the

synthesis, the surface of the QD is modified by the formation of an interface

with the silica. This interface would reduce the surface under-coordination

by providing bonding partners to the CdS shell with bond lengths similar

to those present in CdS bulk material. This at the same tome explains the

blue shift of the CdS LO phonon towards the bulk frequency, and elucidates

the reduction of the CdS LO phonon’s halfwidth. As opposed to additional

strain, the reduction in under coordination should decrease the distribution

of bond length in the structure and hence reduce the halfwidth in Raman

signal.

Although there is no direct evidence on the nature of the bond, that is

formed at the interface of the QD and silica, the direction of the shift in

Raman frequency points towards a bond similar to those present in bulk

material. Generally, QDs are known to have dangling bonds on their sur-

face[151], thus for the formation of covalent bonds with the silica monomers

during coverage is possible. Since the reactive species formed during the

hydrolysis of TEOS are silanol groups, we assume that a Cd-O-Si bridge

is more likely to form with a dangling bond on Cd rather than a Cd-S-Si

bond. This would mean that an O bind to a Cd dangling bond, at a site

where in bulk there would be a S atom, as shown in Fig.58. Since O and S

103

Figure 58: Left: Schematic display of the atomic structure of amorphous

silica, Right: Si-O-Cd bridge als possible bound of silica to the QD CdS

surface. A Cd dangling bond at the surface is bound to a O atom, which

has Si as second bonding partner and forms a connection to the silica.

are in the same chemical group, they have a similar electronegativity and so

should form similar bonds. Hence this Cd-O-Si bridge would fulfill required

condition to be similar to the bond present in the bulk material.

Although such a reaction step has been proposed as part of the encapsula-

tion process before,[73, 74] the in situ Raman investigations thus provide a

direct observation of this tight interaction for the first time.

In conclusion, the shift of the CdS Raman mode is most likely not caused by

external strain induced by the silica shell. Instead, considering the model

proposed by Han et al.[124, 125], the blue shift can be attributed to a re-

duction of the surface under-coordination. This is caused by the formation

of an interface based on strong, direct interactions between silica and the

QD (Cd-O-Si bridge for instance) and is supported by the shift occurring

at a very “early” stage of the synthesis. Thus, the strong influence of the

silica on the CdS shell demonstrates the close interaction between the two

materials, confirming the removal of the ligands during the microemulsion

process for the synthesis condition in the work.

Although this step of the encapsulation process was already predicted by

other authors [73, 74], the in-situ Raman investigations provide here the first

direct observation of this strong interaction and insight in the microstruc-

ture of this interface.

104

12.7 The evolution of the Raman intensity observed during

silica encapsulation

An additional aspect to the change in Raman frequency during the silica

encapsulation reaction (Section 12.4) is provided by monitoring the Raman

intensity of the signal during the synthesis. Fig. 59 displays the Raman

intensity (integrated intensity) gained from the Lorentzian fits to the cor-

responding peaks. The peak areas are normalized to the solvent peaks in

order to account for any changes in laser power during the synthesis, which

is monitored over the duration of two days. It is important to note that

the changes in intensity are due to an increase in amplitude, not halfwidth.

This is shown in Fig. 54, where the halfwidth decreases over synthesis time.

In Fig. 59 a) and b) the evolution of the intensity of CdSe and CdS LO

0.58

0.60

0.62

0.64

0.66

0.68

0612

0.72

0.74

0.76

0.78

0.80

0.82

0.84

0.86

Relative intensity

CdS/Cyclohexane

Relative intensity

Synthesis time (h)

CdSe/Cyclohexane

200 300 400

Relative Raman intensity

Raman shift (cm

-1

)

496 nm

488 nm

465 nm

458 nm

Figure 59: Relative Raman intensities for the CdS (a) and CdSe (b) modes

compared to the cyclohexane peak(383 cm−1) depending on synthesis time.

The intensity equals the area under the Lorentzian fits of the peaks. (c)

Raman spectra of the same QD measured with different laser wavelength,

normalized to the intensity of the Cyclohexane peaks according to Trulson

et al.[152]. For higher excitation energies the intensity of the CdS mode

increases, while the CdSe mode decreases. [150]

mode (QD A) during the synthesis with medium TEOS concentration are

shown. This is the same synthesis, as in Fig.57 and 56 displayed in blue.

Despite the different magnitudes of change in Raman frequency between

105

CdSe and CdS, the change in intensity is an comparable range. While the

intensity of the CdS LO decreases, the intensity of the CdSe LO increases

over the course of 6 hours. This change is not at the same time scale as the

frequency shift of the signal, indicating a different origin.

Generally, the intensity of a signal in Raman spectroscopy is determined

by several factors; apart for experimental influences like laser power or the

setup efficiency, the intensity is determined by the strength of electron-

phonon coupling, resonance conditions with electronic transitions, and by

the strength of the local electric field. Amongst others, these quantities

depend on the dielectrical environment. Since in our case we can exclude

experimental origin, because we are analyzing the signal change in relation

to the stable solvent signal in one continuous experiment, the change in

intensity must originate either from a change in resonance condition by a

shift of the optical transition energy or a change in electron-phonon cou-

pling. Thinking of the mechanism of the synthesis (Section 12.2), we are

faced by a not insignificant change in environment. Before the start of the

synthesis, the QDs are in a solution of Cyclohexane with a dielectric con-

stant of ϵ≈2.0[153] and ligands. After the synthesis, the QD is surrounded

by silica, which has a higher constant of about ϵ≈2.4[154]. This can have

different effects; The screening of the optical field depends, for example, on

the local dielectric environment and so do the transition energies between

valence- and conduction-band states. Both properties influence the inter-

action between the QDs and the laser light and thus the intensity of the

Raman signals. Unfortunately, the precise effect of dielectric confinement

on the optical band gap of QDs is difficult to predict, especially in the case

of complex heterostructures.[155–157] To explain the experimental findings,

the effect must be such that the states of the CdS shell are shifted closer to

resonance with the laser wavelength of 488 nm, while the states of the CdSe

core should be shifted further away from resonance.

This can be analyzed by finding in which energetic direction in relation to

the laser wavelength the density of states of core and shell increases. There-

fore the laser wavelength was varied. The intensities of the Raman modes

are normalized to the solvent intensity at the corresponding wavelength af-

ter Trulson[152] for comparability. This results in a small resonance profile,

as shown in Fig. 59c. With increasing excitation energy the intensity of

the CdS LO increases, and the CdSe LO intensity decreases. Hence a shift-

ing of transition energies, induced by a changing dielectric environment, is

supported by our experimental observations. The fact that the CdSe mode

on the other hand displays the opposite behavior both in resonance Ra-

man measurements (Fig.59c), as well as during synthesis (Fig. 59b), further

supports our hypothesis of states shifting towards lower energies. It does

however not exclude influences of the local field factor modification by silica

encapsulation.

The dielectric confinement has been addressed by many different groups,

106

especially in theory, because calculated electronic states often differed from

experimental values. One reason is the assumption vacuum as a surround-

ing medium. For instance Franceschetti et al.[155] present a very simple

model, taking polarization properties into account. This model should help

us reveal the tendencies for shifts of electronic transitions for changes in

dielectric environment. The smaller the surrounding dielectric constant, the

higher the influence of polarization energy and self energy of hole and elec-

tron on the QD’s electronic energies, effectively increasing the energy gap. In

our experiment, the dielectric constant is increased, reducing the energy gap

effectively through reducing influence of surface polarization. This should

lower the energy of higher excited states near our laser wavelength. Com-

paring this finding with the intensities in Fig. 59c), where higher intensities

for the CdS Raman mode can be found for higher excitation energies, it

seems reasonable to explain the increase during the synthesis with a ener-

getic lowering of the transition energies, moving a higher density of states to

the Raman laser energy. The same explanation fits for the CdSe signal; The

CdSe Raman intensity decreases for higher excitation energy, hence when

the energy is lowered the intensity is reduced.

This not only explains the changes in Raman intensity of the materials,

but also shines a light on the shift of emission wavelength, which has been

found by several groups, but could not be explained until now. Additionally

it means, that the intensity can in principle be used to measure the silica

thickness. However, in contrast to the shift in Raman frequency, the in-

terpretation requires a precise knowledge on the transition energies of each

QD near the excitation wavelength. It could then be used to reveal the ex-

act distance in which the dielectric interaction takes place, which would be

interesting. Here, the intensity of the CdS saturates after about 10 hours,

which corresponds to a silica shell thickness of ≈12 nm. The CdSe intensity

appears to saturate already after about 6 hours, ≈10 nm silica thickness.

Since the CdSe core is separated from the silica by a CdS shell of about

1.6 nm, the total distance is comparable.

107

0.1 0.2 0.3 560 580 600 620 640 660 680 700

Intensity (arb. units)

Energy rel. to excitation (eV)

QD B

QD B with silica shell

Intensity (arb. units)

Wavelength (nm)

QD B pure

QD B with

silica shell

Figure 60: a) PLE measurements of the electronic transition of QD B (pure

in black, silica covered in red) at 5K with detection energy in resonance

with the main transition, shown relative to the lowest energy transition.

Arrows indicated the possible reorganization of higher states due to the

silica shell. b) PL spectra of QD B at room temperature before and after

silica encapsulation at 365 nm excitation wavelength. The emission of QD B

shows a small shift of about 5 nm towards higher wavelength, from 617 nm

622 nm, after silica encapsulation, which indicates a change in the electronic

states of the QD

This shows that the changes of transition energies are certainly out of

interest and relevant for the analysis of Raman intensities during the synthe-

sis. Therefore PLE measurements of a pure and a silica covered QD (QD B)

are shown in Fig. 60a), relative to the lowest transition energy (which is

at a higher energy for the pure QD) and shows that the higher electronic

transitions are closer after the QD was covered by the silica shell. The

lowest energetic transition is shifted towards red. This is confirmed in room

temperature PL measurements, where the lowest transition energy is shifted

from 617 nm for the pure QD to 622 nm at room temperature for the sil-

ica covered QD, Fig. 60b). Hence the encapsulation has led to an effective

reduction of lowest energy transition, which as mentioned above has been

observed by many groups. Looking at Fig. 60a), it becomes visible that the

distance between the higher energetic transitions is reduced by the addition

of the silica shell, which is in agreement with a reduction in confinement as

discussed above.

108

12.8 QD A and QD B’s diverging evolution of the Raman

spectrum during silica encapsulation

As as result of Section 12.4 and 12.5, we found that the shift in Raman fre-

quency during the silica encapsulation reaction occurs during the nucleation

of silica on the Qd’s surface until the silica layer has reached a thickness

3 nm. Thereafter the Raman frequency becomes independent of the shell

thickness. This was attributed to the formation of an interface between

the QD’s surface and the silica capping (Section 12.6). What hasn’t been

addressed yet, is how the amount of shift is changed and what happens if

the synthesis is performed on a different QD. For this investigation, two QD

with different geometries, QD A and QD B, will be compared. Different

aspects of these comparative measurements are shown in Fig. 61.

QD A has a CdSe core with a diameter of 4 nm and a relatively thin CdS

shell of 1.6 nm (total diameter 7.2 nm), whereas QD B’s core is 3.6 nm in

diameter and the CdS shell with 2.8 nm (total diameter 9.1 nm) is much

thicker. This, because of strain, causes the Raman modes of the two QDs

to have very different initial phonon frequencies. While QD A has Raman

frequencies of 210 cm−1and 292 cm−1for core and shell respectively, QD B

has frequencies of 212 cm−1and 298 cm−1. So on the one hand, QD A

has a shell that has a higher surface area (2.8) compared to volume than

QD B(0.8). On the other hand the CdS shell of QD A is under more intense

tensile strain than the shell of QD B. The CdSe cores of the QD in con-

trast are compressively strained, while the strain inside the core is higher

for QD B.

Fig.61 shows two different silica synthesis’ under different conditions, one

for QD A and QD B. The final silica thickness is 13.1 nm for QD nm and

8.6 nm for QD B. The change in Raman frequency with 2.2 cm−1is higher

f¨ur QD A than for QD B, which only shifts by 1 cm−1. The CdSe core of

QD B remains unchanged(not shown), QD A’s core shifts by a small amount

towards higher frequencies as discussed in Sec. 8, Fig. 54, so the focus is on

the shift caused in the CdS shell. How much the addition of the silica influ-

ences the Raman signal of core and shell, seems to directly depend on the

QD’s geometry.

109

0 6 12 18 24

297

298

299

300

0 6 12 18 24

292

293

294

295

0 6 12 18 24

2.0

2.5

3.0

0 6 12 18 24

0.5

0.6

200 250 300 350

QD B

∅CdSe=3.6 nm, ∅total=9.1 nm

QD A

∅CdSe=4 nm, ∅total=7.2 nm

Synthesis time (h)

200 250 300 350

Rel. Raman

intensity

Rel. Raman intensity

of the CdS LO

Raman shift

of CdS LO (cm

-1

)

Raman shift (cm-1)

496 nm

488 nm

465 nm

458 nm

Figure 61: (a)/(b)Raman frequencies of the CdS mode in the course of

the silica synthesis for QD A/ QD B; (c)/(d) Raman intensity ratios (peak

area) for the CdS mode in the course of the silica synthesis for QD A/

QD B, normalized to solvent intensities to exclude influences of the laser

power; (e)/(f) Raman spectra of QD A/QD B for different laser energies,

intensity normalized to solvent as indicated above. [150]

However, this is not the only difference between the two samples. The

evolution of intensity during the synthesis, displayed in Fig. 61, diverges

greatly between the two QDs. While the intensity of the CdS Raman mode

increases for QD A, QD B shows a distinct dip in intensity after two hours

of synthesis, accompanied by a faster and stronger change in Raman inten-

sity than for QD A (compare Fig. 61c and d). The steep rise in intensity

110

indicates a higher sensitivity to the dielectric environment for QD B, which

is also supported by the stronger change in intensity upon excitation with

higher energies (see Fig. 61f and for comparison with QD A 61e). The higher

dependence of the Raman intensity on excitation energy makes sense, since

the shell of QD B is thick ans thus should have electronic properties similar

to bulk CdS which has an absorption edge at around 500 nm[158] close to

the excitation wavelength (of 488 nm). As right at the absorption edge, the

density of electronic states dramatically changes in dependence of energy,

a strong dependence of Raman intensity on energy logically follows. The

shell of QD A, with a thickness of 1.6 nm only, is very much in the con-

finement regime and hence the electronic states should be shifted towards

higher energies and therewith further away from the excitation laser used in

this experiment.

The dip in intensity that occurs during silica encapsulation of QD B (at a

silica thickness of 2.5 nm after 3h of reaction), cannot be be explained in the

by the increase of surrounding dielectric constant as above. To further un-

derstand this dip in intensity, we have to remind ourselves of the mechanism

of the synthesis, as discussed in Section 12.2. The dielectric environment

of the QD changes over the whole synthesis changes from a mixture of lig-

ands and cyclohexane to silica, but as a transitional stage the QD has to

travel into to a micelle of water. Water however has a lower dielectric con-

stant ϵ≈1.8[159] than both, Cyclohexane and silica. Hence, when in close

proximity to the QD, it should have the opposite effect on the electronic

transitions of the QD than the silica. So, as long as the silica shell is thin

or only partially covers the QD, the effective dielectric constant of the en-

vironment is lowered by the introduction of water in the environment. This

temporarily leads to a shift of the electronic transitions of the QD (shell)

towards higher energies. This environment is then successively moved fur-

ther and further away from the QD as the silica shell grows until the QD is

surrounded by silica only and the electronic transitions shift to their final

position at lower energies. Thus for the thicker shelled QD B, it is possible

to observe the transition of the QD from the solution of Cyclohexane into

the water micelle and therewith delivers an observation, that can’t be made

by any other method.

This once more underlines the complexity of interpretation of the trend in

Raman intensity and the necessity of a very precise knowledge on the reso-

nance conditions and electronic transitions of the sample, as QD A and QD B

yield very different observations. However, these observation are strongly

energy-dependent, hence an in situ measurement with different excitation

energies must give different results, and every different QD dependent on

their electronic transitions will have a distinct resonance condition. Nev-

ertheless the observations made by monitoring the Raman intensity during

the encapsulation are unique and can potentially offer intricate details on

the synthesis mechanism. Additionally, the influence of the use of differ-

111

ently bound ligands on the surface of the QD should reflect in the dip in

intensity as they should influence the introduction of water in the proxim-

ity of the QD. The transition of the QD into the water micelle should also

be influence by the type of and concentration surfactant, which should be

observable monitoring the Raman intensity.

112

13 Conclusions

In this work, the vibronic and electronic properties of spherical, colloidal

CdSe QDs were studied, as well as CdSe/CdS core-shell QDs. The depen-

dence on crystal symmetry was evaluated using experimental methods like

Raman spectroscopy, TEM and PLE.

The Raman-based strain analysis of spherical core-shell QDs agrees well with

previous publications[43, 160]: compressive strain is found in the CdSe core

while tensile strain is exerted on the CdS shell. It was demonstrated that

the strain depends on the geometry of the QD, and that an increasing shell

thickness on a constantly sized core results in an increasing strain within the

CdSe core, while it reduces strain in the CdS shell. Additionally, the shell

addition leads a to shift in emission frequency towards red, as observed in

absorption and PL measurements, partially relieving the confinement of the

charge carriers.

Two different methods of shell synthesis, SILAR and FLASH, were com-

pared; where the former is the well-established method, the latter allows a

much faster synthesis using a higher temperature. An analysis of the inter-

face mode – which resides in the sideband of the CdSe LO mode – revealed

no significant reductions in intensity and shape of the mode between both

synthesis methods. This shows that the faster reaction method (FLASH)

can also provide a graded interface, which is highly favorable as it improves

the radiative recombination efficiency.

The lattice parameters, therefore also the strain values that were published

so far are found to differ strongly from each other, as they are highly de-

pendent on the precise ambient temperature during measurement. These

persummably temperature dependent differences indicate diverging temper-

ature coefficients for the two materials. The analysis of temperature de-

pendent Raman measurements and subsequent separation of strain effects

allows access to temperature coefficients for the two materials. Careful ex-

amination thus reveals different thermal expansion coefficients for CdSe and

CdS, which are independent of the CdS shell thickness, and thus evidence a

correct separation of effects. The thermal expansion coefficient of the CdS

shell is independent of the crystal structure and shows only a small, slow in-

crease with temperature. The CdSe core’s temperature dependence however

shows a steep increase at low temperatures, hinting at a size dependence,

which should be checked in further studies. For zincblende QDs it is shown

that smaller dots exhibit a stronger temperature dependence.

CdSe cores that have a wurtzite structure expand fast and at lower tem-

perature than zincblende structures with equivalent diameter; they however

show an overall smaller temperature dependence. This is shown to originate

from the distinct crystal structure.

The exciton-phonon coupling within the QD is studied with Raman spec-

troscopy, revealing a size dependent minimum in coupling strength for QD

113

with a zincblende structure at a diameter of about 4.7 nm, for wurtzite QDs

between 3.8 and 4.4 nm, which indicates a lower band offset to the environ-

ment for wurtzite QDs. The coupling strength of 0.1-0.2 for zincblende QDs

is in line with previous findings. However wurtzite QDs exhibit, outside

of the minimum exhibit a larger coupling strength by factors 2-4, diameter

dependently. This shows again the different properties for the two crystal

structures. The coupling strength is found to decrease upon addition of a

CdS shell, both in Raman and resonance PL.

Further differences between the two crystal structures are revealed in the

diameter dependent band edge fine structure, which is examined with ex-

citation spectroscopy. It is shown that the obtained PL signal is strongly

dependent on resonances, which are unique for each QD diameter. Dedi-

cated analysis on samples with a broad range of diameters shows that while

the inherent diameter distributions results in overlapping signals, the over-

all dependence on the excitation energy can still be extracted nicely. This

demonstrates that ensemble measurements can well be used to extract the

continuous band edge fine structure over a broad range of diameters.

For both crystal structures, well separated bright and dark states are ob-

served, the latter having a slightly lower energy. For instance for a QD with

3 nm in diameter, the wurtzite structure has an energetic separation be-

tween dark and bright state of 16 meV, zincblende only 10 meV. As shown,

the splitting between the bright-dark splitting decreases with an increasing

QD diameter. This splitting of band-edge states was already observed for

wurtzite QDs, and explained with the inherent crystal fields in the QDs.

For the zincblende structure, however, this splitting is shown here for the

first time for such a broad diameter range, and is additionally completed

with an analysis of the band edge states above the bright state, which are

only revealed by excitation spectroscopy. A shape anisotropy is considered

as potential reason for the induced splitting, analyzed with a model already

used by Efros [83]for the description of the band edge states of wurtzite

CdSe QDs, based on the A-B exciton splitting in the bulk semiconductor.

The splitting between the bright and the dark state can be well described

with this model, considering a deformation of 10% in oblate direction. Such

deformation, however, can’t explain the high energetic separation of the

next higher band edge states compared to the bright state, if keeping in line

with the original assignment. The large separation of states can only be

achieved, assuming a broad deformation gradient of 10% to 50% over the

diameter range, which seems unrealistic.

An alternative explanation is given here, where the higher lying band edge

states are phonon replica of those excited QDs, that have a higher ground

state energy. This theory completely changes the view on the interpretation

of measurements that has been used for 20 years. It also highlights how

important the coupling between excitons and the phononic system is, espe-

cially in these kind of nano-structures, and should be carefully considered

114

in the analysis of future experiments.

After analyzing the basic physical properties of QDs, this thesis turns its

focus to the more complex structure of colloidal silica encapsulated QDs.

These hybrid systems are currently highly investigated for their potential

use as biological cell-labels, due to their potentially high, long-term quan-

tum yield and biocompatibility. Additionally, they exhibit a high stability in

aqueous solution, which has been successfully demonstrated for certain syn-

thesis conditions [70, 74, 76, 147], depending on the QD surface chemistry.

However much investigated, no direct evidence has been found regarding

whether the silica interacts directly with the QD surface, or if the ligand

shell remains on the QD surface and the silica is formed on the outside.

Using Raman spectroscopy during the encapsulation reaction in combina-

tion with TEM analysis for determination of the silica shell thickness, it is

revealed that using loosely bound ligands, an interface between silica and

QD is formed during the first hours of synthesis (1-4h of 48h of synthesis

in total). In fact, the in situ analysis of the changing Raman spectra indi-

cates that the interface reduces the surface undercoordination, and that the

overall crystal quality is surprisingly even increased. Out of the many pos-

sible bonds that could constitute his interface, Cd-O-Si bonds are closest in

length and electronegativity to the optimal Cd-S bond; this would then ex-

plain the shift in Raman frequency toward the relaxed bulk value. Through

observation of the intensities of the individual Raman modes, changes in the

dielectric environment can be directly monitored, which can potentially be

used to derive silica shell thicknesses directly during of the synthesis.

In summary, Raman spectroscopy is a useful tool for the analysis of the silica

encapsulation reaction, and can be used in investigations of varying QD lig-

ands, microemulsion surfactant, or pH condition. This thesis then provides

a highly interesting tool to design an optimized synthesis route towards the

production of materials with ideal optical properties.

This work highlights the versatility of Raman spectroscopy in the analy-

sis of colloidal QDs, and emphasizes that it should be used in addition to

the conventionally used TEM, absorption and PL measurements. It shines

light on information that would be complicated to assess otherwise, e.g. the

strain, temperature dependent lattice expansion, and even information on

interfaces within the QD and the respective surface chemistry. Complimen-

tary PLE measurements offer an in-depth view on the electronic states, the

band edge fine structure and demonstrate that those observations are also

governed by phonon assisted recombination and an overall strong coupling

to the lattice phonons.

115

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15 Acknowledgments

Finally, I want to thank all my colleagues from the AG Thomsen, AG Hoff-

mann and AG Maultzsch for the exceptionally nice working atmosphere and

many discussions, which were a good mix of fruitful / about physics and just

plain ridiculous. Additionally, there are a few people I want to thank in par-

ticular:

•For the QD syntheses, great discussions and help regarding all ques-

tions on chemistry: the whole group of Zeger Hens (and Zeger Hens

himself, of course), especially Tangi Aubert and Sofie Ab´e

•For their help and involvement with measurements and great team-

work, my students Narine Ghazarian and Philipp Baumeister

•For introducing me to CdSe QDs and for many discussions on their

Raman spectra: Holger Lange, Norman Tschirner, Christian Thomsen

and Janina Maultzsch

•For great discussions and for exciton fine structure calculations: Anna

Rodina, Alexandr Golovatenko and Alexander (Sasha) Efros

•For an introduction to PLE and help addressing the PLE setup, and for

useful discussions of results and analysis of the acquired data: Gordon

Callsen, Nadja Jankowski, Steffen Westerkamp, and Stefan Kalinowski

•For chaotic help in chaotic labs: Christian Nenstiel, Thomas Kure,

Felix Nippert and Max B¨ugler

•For working together, trying to teach students at least something

about physics and for dealing with the stressful Kirchberg organiza-

tion: Hans Tornatzky, Dirk Heinrich, and Harald Scheel

•For general organisation and help with the TU bureaucracy: Anja

Sandersfeld and Sabine Morgner

•For their high spirits: Sarah Schlichting and Markus Wagner

•For many thing listed above and so much else: Asmus Vierck

Now, as this project comes to an end, I would like to thank Anna Rodina

and Axel Hoffmann for their kind review of this thesis and Micheal Lehmann

for chairing the examination.