Diplomarbeit Diplom-Ingenieur - Institut für Halbleiter

Transmission Electron Microscopy of self-organised
PbTe/CdTe Nanocrystals
Diplomarbeit
zur Erlangung des akademischen Grades
Diplom-Ingenieur
im Diplomstudium
Technische Physik
Angefertigt am Institut für Halbleiterphysik
Eingereicht von:
Heiko Groiss
Betreuung:
Univ. Prof. Dr. Friedrich Schäffler
Linz, Oktober 2006
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Eidesstattliche Erklärung
Ich erkläre an Eides statt, dass ich die vorliegende Diplomarbeit selbständig und ohne fremde
Hilfe verfasst, andere als die angegebenen Quellen und Hilfsmittel nicht benutzt bzw. die
wörtlich oder sinngemäß entnommenen Stellen als solche kenntlich gemacht habe.
i
Heiko Groiss

Kurzfassung
Nanostrukturierung erlaubt die Beeinflussung der elektronischen und optischen Eigenschaften
von Halbleiterstrukturen für vielfältige Anwendungen. Sogenannte Quantenpunkte (QD)
zeigen ein mit Atomen vergleichbares optisches Verhalten und sind eine vielversprechende
Methode zur Herstellung von Materialsystemen für optoelektronische Bauelemente für
Frequenzbereiche, die mit den Standardmaterialien nicht zugänglich sind.
Ein neuartiger Ansatz der QD Produktion durch Entmischung in der Festkörperphase
zweier Halbleiter mit unterschiedlichen Gitterstrukturen wurde mit CdTe/PbTe
Heterostrukturen verwirklicht. PbTe besitzt die Struktur von Steinsalz (rs), CdTe hat
Zinkblende-(zb)-Struktur. Eine in CdTe eingebettete PbTe Schicht zerfällt durch Tempern in
hochgradig symmetrische Nanokristalle mit atomistisch scharfen Grenzflächen zu dem
Umgebungsmaterial. Die entstandenen QDs zeigen starke Photolumineszenz im mittleren
Infrarot, einem Energiebereich, in dem viele Molekülanregungsenergien zu finden sind, für
den aber keine effizienten Halbleiterlaser existieren. Hauptaufgabe dieser Arbeit war die
Charakterisierung dieser QDs mit dem Transmissionselektronenmikroskop (TEM), wobei
verschieden Mikroskopiertechniken verwendet wurden.
Wie gezeigt wird, besitzen die PbTe Nanokristalle im thermodynamische Gleichgewicht
die geometrische Form von kleinen Rhomboedrischen–Kubo-Oktaeder mit {001}, {110} und
{111} PbTe/CdTe Grenzflächen, wobei auch Einblicke in die Prozesse während des
Temperschrittes gegeben werden. Die Größe der QDs kann mittels Epischichtdicke gesteuert
werden, wobei die Dichte der Quantenpunkte stark mit ihrer mittleren Größe zusammenhängt.
Der Hauptteil dieser Diplomarbeit beschäftigt sich dann mit der atomaren
Charakterisierung der PbTe/CdTe Grenzflächen und den, für die Interpretation notwendigen
TEM Simulationen. Durch die unterschiedliche Gitterstruktur der beiden beteiligten
Materialien kommt es an den Grenzflächen zu starken Verschiebungen einzelner Atome oder
ganzer Atomgruppen, um die Bindungkonfigurationen für das zb oder rs Gitter besser zu
erfüllen. Abhängig von der Terminierung der CdTe Kristallhälfte konnte die Existenz von
zwei unterschiedlichen {001} Grenzflächen am selben QD nachgewiesen werden. Die
bemerkenswertesten Effekte treten aber an den {110} Grenzflächen auf, wo die
Rekonstruktion zu einem Versatz der beiden Kristallhälften von mehr als 10% der
Gitterkonstante führt. Das Grenzflächenproblem wurde auch von R. Leitsman et al. mit ab-
initio-Rechnungen behandelt. Die theoretischen Verschiebungen und die aus hochauflösenden
TEM-Aufnahmen gewonnenen zeigen eine hervorragende Übereinstimmung.
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Abstract
Nano-structuring allows the manipulation of electronic and optical properties of
semiconductors, which is useful for various applications. So-called quantumdots (QD) reveal
optical properties comparable with atoms. They are a promising method for the production of
material systems for opto-electronic devices in frequency ranges, which are not accessible
with the standard materials.
A novel approach of QD formation was realized by decomposition of two immiscible
semiconductors with different lattice structures. The experiments were carried out at
CdTe/PbTe heterostructures. PbTe possesses the structure of rock salt (rs), CdTe has
zincblende (zb) structure. A PbTe layer, embedded in CdTe, disintegrates into highly
symmetrical nano-crystals with atomically sharp interfaces during an annealing step. The QDs
show intense photoluminescence in the mid-infrared, an energy region, where the excitation
energies of molecules are found. No efficient semiconductor lasers exist for this frequency
range. The aim of this work was a concise characterisation of these QDs with transmission
electron microscopy (TEM), for which different techniques were used.
As will be shown, the PbTe nanocrystals have a thermodynamic equilibrium shape of
small rhombi-cubo-octahedrons with {001}, {110} and {111} PbTe/CdTe interfaces. An
insight into the processes during the annealing step is given. The size of the QDs can be
controlled by the epi-layer thickness. The density of the dots depends strongly on their
average size.
The main part of this thesis is the atomic characterisation of the PbTe/CdTe interfaces and
TEM image simulations, which are necessary for the interpretation. The different lattice
structures of the two materials induce strong atomic displacement of single atoms or groups of
atoms at the interfaces. The displacements end up in bonding configurations for the zb or rs
lattice close to their respective bulk configuration. It was shown that two different {001}
interfaces exist at the same QD, depending on the termination of the CdTe crystal half. The
most remarkable effects can be found at the {110} interfaces, where the displacements lead to
a shift of more than 10% of the two crystal halves against each other. The interface problem
was also treated by R. Leitsman et al. with ab-initio calculations. The theoretical
displacements and those obtained by high resolution TEM images show excellent agreement.
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Contents
Preface i
Eidesstattliche Erklärung i
Kurzfassung iii
Abstract v
Contents vii
1. Introduction 1
1.1. Materials for mid-infrared devices and applications 1
1.2. Quantum Dot precipitation in solids 3
2. The material system and its fabrication 5
2.1. PbTe and CdTe –Two immiscible Materials 5
2.2. Sample growth with Molecular Beam Epitaxy 7
2.2.1. Growth of the CdTe/PbTe Heterostructure 9
2.3. Annealing 11
3. The Transmission Electron Microscope 13
3.1. The JEOL JEM-2011 FastTem 13
3.2. Scattering of Electrons 17
3.3. Contrast Enhancement with Bright and Dark Field Imaging 21
3.3.1. Contrast Mechanism 21
3.3.2. Dark Field and Bright Field imaging 22
3.4. High Resolution Transmission Electron Microscopy 25
3.4.1. Requirements for HRTEM 25
3.4.2. Origin of Lattice Fringes 26
3.4.3. Transferfunction and Scherzer Defocus 27
3.5. Sample Preparation 30
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4. Shape and size of the PbTe Dots 31
4.1. Available Samples 31
4.2. Precipitation steps 33
4.3. Precipitation from different layer thicknesses 36
4.3.1. Annealed 5nm layer 36
4.3.2. Annealed 1nm layer 38
4.4. Equilibrium shape 40
5. Interpretation of HRTEM Images 44
5.1. JEMS Simulation Package 44
5.1.1. Multi-Slice Approach 46
5.1.2. Simulation Procedure 47
5.2. Image simulation of the CdTe/PbTe interfaces 50
6. Interface characterization 52
6.1. Available Samples 52
6.1.1. Specimens for HRTEM imaging 52
6.1.2. Beam Damage 53
6.2. HRTEM investigation of PbTe nanocrystals 54
6.2.1. HRTEM images of single QDs 54
6.2.2. Total energy calculations 56
6.2.3. The (001) interface 58
6.2.4. The (110) interface 65
6.2.5. The (111) interface 73
7. Conclusions and Outlook 77
Appendix A Structure factors of CdTe and PbTe 82
Appendix B Simulated HR-maps of CdTe/PbTe interfaces 84
References 91
Curriculum vitae 95
List of Publications 96
Acknowledgment 98

Chapter 1
Introduction
1.1 Materials for mid-infrared devices and applications
Optical devices have a broad field of applications. The physical principle behind
most applications is the recombination of an electron-hole pair over a direct band gap
in semiconductor materials. Band gap design is a key to produce materials with fitting
band gaps. Further tuning of the optical properties is done by micro- and nano-
structuring of the optical active materials. The approach of low dimensional systems
like quantum dots (QDs) or quantum wires leads to confined electrons. Electrons
confined in a certain potential show quantized properties and behave like the electrons
in atoms or molecules with certain excitation levels [1, 2]. The confinement yields to
a blueshift and is controlled by the size of the structures used for confinement.
Optoelectronic device based on QDs are realized for different application, e.g QDs
lasers [3, 4] or single photon sources [5, 6]. But the band gaps of typical direct band
gap semiconductors are not perfectly suitable for the mid-infrared frequency range (3-
30μm). Lead salts are used for applications in this frequency range and further nano-
structuring would improve the performance of these devices. The mid infrared
frequency range can be found e.g. at the absorption energies of CO2 or other
molecules important for environmental monitoring or medical diagnosis. Improved
semiconductor-lasers and detectors would allow efficient application in these fields.
QDs can be produced by using self-organisation schemes during epitaxial growth
of strained semiconductor heterostructures. The best-known self-organisation scheme
is the Stranski-Krastanov (SK) growth mode [7-10]. This growth mode is governed by
surface energy minimisation and strain relaxation. SK growth is always starting with
the formation of a wetting layer to minimise the surface, which covers the entire
substrate. If the stored strain energy gets larger than the energy benefit of layer-by-
layer growth, the formation of QDs starts. A capping layer is needed for an
implementation of these dots, so that the dots are surrounded by a host material.
During the overgrowth, alloying and shape transitions appear [11-13]. An often
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encountered shape of SK dots is that of a pyramid, which during capping usually
changes to the shape of a truncated pyramid. Capping of the dots causes strong
alloying of the host material with the dot material, which is a disadvantage of SK dots.
A further disadvantage is the existing 2D wetting layer. Examples for Stranski-
Krastanov systems are InGaAs dots on GaAs or Ga dots on Si (see Fig. 1.1a).
Another approach is the synthesis of core-shell nanoparticles [14, 15]. During a
chemical reaction of liquid precursors the QDs precipitate out of the liquid. FeO
quantum dots produced by this method can be seen in Fig.1.1b. These dots are highly
symmetric with sharp surfaces and the size distribution can be controlled. With this
technique it is possible to produce dots in the nanometer scale. A disadvantage of this
approach is an organic shell surrounding the dots due to the chemicals that are used to
stabilize the reaction. This is an essential part of the synthesis, otherwise the
nanocrystals would agglomerate. The organic shell is not conductive and thus
hampering electronic applications. The dots can be sorted by size and produced as
powder, but the nanocrystals are not surrounded by a host material and thus difficult
to apply in optoelectronic devices.
Figure 1.1: (a) TEM image of stacked Ge Stranski-Krastanov dots on Si. The dots have
the shapes of truncated pyramids. The wetting layer can be seen on the left and right
handed side of the dots. (b) TEM image of FeO dots fabricated by core-shell synthesis.

1.2 Quantum Dot precipitation in solids
The aim of QD fabrication by precipitation in solids is the combination of the
advantages of the Stranski-Krastanov grown dots and the chemical synthesised ones.
The nanocrystals should be embedded with high shape symmetry and sharp interfaces
in a host material. There should be no alloying between the host and the dot materials.
The size of the dots should be well controllable.
Our material system consists of a CdTe/PbTe heterostructure. Earlier studies of this
material system attempted to produce a PbxCd1-xTe ternary alloy by the Bridgman
method [16-18]. The characterisation of their samples takes place in the μm range
where Cd and Pb rich grains are found. No imaging techniques were used to reveal
structures with the dimensions of nanocrystals, which are treated within this thesis.
Our heterostructures consist of a thin PbTe layer in the nanometer range, clad by
CdTe [16]. These two materials have almost the same lattice constant and
Figure 1.2: PL measurements at room temperature of CdTe/PbTe heterostructures
annealed at different temperatures. Different solid curves in (a) represent different
annealing temperatures. The intensity increases for higher annealing temperatures and
the maximum is shifted to longer wavelength of 3.2 μm for QDs. The sample was excited
below the CdTe barrier with a 1480nm pump laser with 245mW. The dotted lines show
the PL spectrum of bulk PbTe. (b) Shows the luminescent of a PbTe/CdTe
heterostructure which was excited above the CdTe barrier with a 730nm Ti:sapphire laser
with 400mW. [16]
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the heterostructures can be grown almost strain-free. PbTe and CdTe differ
fundamentally in their lattice structure. PbTe has rock salt (rs) structure, whereas
CdTe has zinc blend (zb) structure. The precipitation of the QDs in solids takes place
during an annealing step and is driven by lattice type mismatch. The novel approach
of precipitation in the solid phase should also be applicable to other semiconductor
heterosystems and was shown for the semimetals ErAs and ErSb (rs lattice) on GaAs
or GaSb substrate (zb lattice) respectively [20-23].
Our PbTe/CdTe semiconductor system was at first investigated with photo
luminescent (PL) measurements (see Fig.1.2) on CdTe/PbTe heterostructures. The
measurements were performed at room temperature with excitation below and above
the CdTe barrier for samples which were annealed at different temperatures. The PL
signal of the heterostructures increases significantly after the annealing step. First
TEM investigation showed that the 2-dimensional PbTe layer breaks up into highly
symmetric QDs (see Fig. 1.3) with sharp interface between the dot and host materials
during the annealing step. The resulting dots are higher than the original 2
dimensional quantum well (QW), which leads to a shift of the increased luminescent
peak to larger wave lengths. An in-depth characterisation by TEM of the shape, size
and interfaces of these dots was the aim of this diploma thesis.
Figure 1.3: (a) PbTe quantum dots that precipitated from a 1nm PbTe epi-layer in plan
view. (b) Two dots that precipitated from a 5nm epi-layer in a cross section view. Their
shape is highly symmetric and sharp interfaces can be seen between the PbTe and the
CdTe host material.

Chapter 2
The material system and its fabrication
Lead telluride and cadmium telluride are well-know semiconductor materials. The
narrow band gap material PbTe has rock salt (rs) structure and is used as material for
infrared detectors or as thermoelectric material. CdTe is a wide band gap material
with zinc blend (zb) structure and is used as material for thin film solar cells. Due to
its properties in the infrared, it is often used for optical windows or lenses in this
range. The combination of these two immiscible materials for QD precipitation is a
novel approach for mid infrared materials.
2.1 PbTe and CdTe –Two immiscible Materials
CdTe consists of elements from the II´s and VI´s group of the periodic table. It has a
cubic lattice structure of the zincblend type. A zb - lattice consists of two face centred
cubic (fcc) lattices, shifted by one fourth of the unit cell diagonal. Each sublattice
Figure 2.1: CdTe unit cell; each atom has four nearest neighbours which are from the
other atomic species.
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is occupied with one kind of atoms, in this case either with Cd or Te (see Fig. 2.1). In
this lattice, each atom has four nearest neighbours. There are covalent and ionic
contributions to the chemical bonding. The bonds of the atoms are four-fold
coordinated sp 3 hybridised binding orbitals. Surfaces perpendicular to the 〈100〉 or
〈111〉 crystal directions are polar surfaces and can be either Cd or Te terminated. The
surfaces perpendicular to the 〈110〉 direction is a non-polar one.
In contrast to CdTe, PbTe is an ionic crystal. The element Pb is from the IV´s
group of the periodic table, thus PbTe is an IV-VI semiconductor. The ionic crystal
has also a cubic lattice but with rs structure. This lattice consists of two fcc sublattices
which are displaced by one half of the unit cell diagonal. This configuration leads to
six nearest neighbours for each atom (see Fig. 2.2). The bonds in this crystal are p 3
binding orbital with a strong ionic character. Interfaces of a PbTe crystal
perpendicular to the 〈100〉, 〈110〉, 〈111〉 direction are non polar surfaces, where the
first atomic layer contains the same number of each atom species.
Figure 2.2: PbTe unit cell; each atom has six nearest neighbours which are from the
other atomic species.
CdTe and PbTe have a large miscibility gap [24]. The reason for this immiscibility
is the fundamental difference in the lattice structure and not a difference in lattice
constant as in the case of the miscibility gap of In1-xGaxN [25]. CdTe and PbTe have
almost the same lattice constant, the difference being smaller than 0.3% at 300K. The
lattice constant of CdTe is slightly larger but the thermal expansion coefficient is
smaller. Both materials have the same lattice constant at about 425 K. Both materials
are direct band gap materials which means that the minimum of the conduction band
and the maximum of the valence band are at the same point in the bandstructure.
CdTe is a wide band gap material with a direct band gap at the Γ point. The band gap

of PbTe is one order of magnitude smaller and its direct band gap is at the L point.
This band gap difference of about 1.2eV at room temperature allows an efficient
carrier confinement in the PbTe/CdTe material system. Important material properties
of CdTe/PbTe are shown in Tab. 2.1.
CdTe PbTe
Structure Zincblend Rocksalt
Lattice constant (300 K) [nm] 0.648 0.6462
Thermal expansion coefficient [K -1 ] 4.70E-06 2.70E-05
Direct band gap at 0 K eV Γ8-Γ6= 1.61 L6 - -L6 + = 0.187
dEg/dT [[eV/K] -3.0E-04 4.1E-04
Electron effective mass [m0] 0.11 ml= 0.24
mt= 0.024
Hole effective mass [m0] 0.41 ml= 0.31
mt= 0.022
Table 2.1: Comparison of important material constants of CdTe and PbTe [26]
An important property of the materials for the transmission electron microscopy is
the structure factor Fhkl. The structure factor depends on the lattice structure of the
material and determines which diffraction spots are allowed. Both structures consist
of fcc lattices. All diffraction spots with mixed even and odd h, k, l are forbidden for
the fcc lattice thus also for PbTe and CdTe. The structure factors of the other
diffraction spots for CdTe and PbTe can be found in the Appendix A.
2.2 Sample growth with Molecular Beam Epitaxy
All samples of the CdTe/PbTe heterostructures were grown by Molecular Beam
Epitaxy (MBE) on (001)-GaAs substrates. The MBE technique is widely used in
semiconductor research because it allows growing material layers with a controllable
thickness down to an atomic monolayer of atoms. Epitaxy means that the substrate
crystal structure determines the further growth. One disadvantage of the MBE
technique is the low growth rate, therefore semiconductor industry mainly uses other
techniques like Chemical Vapour Deposition or Metal Organic Vapour Deposition.
The essential parts of a MBE system are the molecular effusion cells and substrate
heating. These parts are placed in a vacuum chamber because ultra high vacuum
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conditions are essential for the crystal growth. A common method for in situ
characterisation is Reflection High Energy Electron Diffraction (RHEED).
The basic processes of crystal growth take place in three zones between the
effusion cell and the sample surface. Firstly, there is the molecular beam generation
zone. The vapour elements mix in the mixing zone and crystal growth takes place in
the crystallisation zone on the substrate surface. The growth itself is controlled by the
substrate temperature, the beam flux and the process time. A schematic drawing of a
MBE system with the tree process zones can be seen in Fig. 2.3.
Figure 2.3: Sketch of a MBE System [27]. The essential parts of the system are shown,
and the tree main process zones are indicated.
In general, three epitaxial growth modes driven by energy minimisation can be
distinguished. The energy terms are the surface, interface and strain energy. The
Frank-van der Merwe growth is a monolayer-by-monolayer growth. The substrate and
the epi-material have a fitting lattice constant, thus no strain is established during the
crystal growth. The interface energy is smaller than the surface energy, consequently
the epi-layer minimises its surface and grows in closed monolayer steps. The Volmer-
Weber mode refers to a pure island growth on the surface. The strain energy term
plays again no role. The surface energy is now the smaller term and the crystal grows
with the minimum interface in the shape of islands. The Stranski-Krastanov growth is

an intermediate case with a strain energy term. In the beginning, the interface energy
is smaller than the surface energy and the stored strain energy is small. It is
energetically beneficial to build up a strained epi-layer. As soon as the stored strain
energy gets lager than the difference between interface and surface energy, the growth
characteristic switches, and island growth starts to relax strain energy.
2.2.1 Growth of the CdTe/PbTe Heterostructure
All samples investigated within this thesis were grown at the Osaka Institute of
Technology, Japan [26], [28], [29]. The growth was carried out in a MBE apparatus
with solid sources of CdTe, PbTe, Cd and Pb in Knudsen cells.
Figure 2.4: Sketch of the sample Structure; The HQ buffer is necessary to provide a
good (001) CdTe surface, which is either Te or Cd terminated before the growth of PbTe.
The PbTe layer is grown with different thicknesses and the heterostructure is finalised
with a CdTe capping layer.
The basic structure of the samples consists of a high quality (HQ) buffer of CdTe
grown on (100)-oriented GaAs substrates. On top of this buffer the PbTe layers were
grown with different thicknesses. This Single Quantum Well (SQW) was than capped
again with CdTe. Some samples were also capped additionally with MnTe to prevent
the CdTe from re-evaporation during annealing. A sketch of a heterostructure can be
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seen in Fig. 2.4, where also the structure of the HQ buffer is shown. Fig. 2.5 shows a
TEM image of an annealed sample, where also the buffer structure can be seen.
Essential for the growth of a high quality PbTe SQW is a high-quality CdTe buffer
with low surface roughness and low lattice defects. The lattice constants of GaAs and
CdTe differ by ~15% which lead to CdTe growth with a high dislocation density. To
grow a high-quality CdTe buffer, fist a 100 nm thick low temperature (LT) CdTe film
was grown at 280°C on a sulphur treated GaAs substrate, followed by 300 nm CdTe
at 320°C providing a (100) oriented CdTe surface. This was capped with a 100 nm
thick MnTe layer to suppress the re-evaporation during the following thermal
annealing step at 380°C for 30min. On the CdTe/MnTe buffer a superlattice of twenty
5 nm thick MnTe / 2 nm thick CdTe sublayers were grown at 280°C and then
finalised with a CdTe layer (300nm-900nm) at 320°C [28]. Such high-quality buffers,
or similar ones, were used for all samples investigated within this thesis. The root-
mean-square roughness of such a HQ buffer is less than 0.5nm in an area of
3μm × 3μm (measured by atomic force microscopy).
Figure 2.5: A typical PbTe/CdTe heterostructure recorded with the TEM along the [110]
zone axis. The layers with Mn content are brighter and clearly visible. The HQ buffer
was finalised with 900nm CdTe. The image shows an annealed sample. The PbTe dots
can be seen beneath the surface of the sample at the top of the image.
On such high quality CdTe buffers the PbTe SQWs were grown at temperatures
from 220°C to 280°C with different thickness. The CdTe (100) surface is polar,

therefore it can be Te or Cd terminated. Roughness measurements with atomic force
microscopy showed that Cd termination before PbTe growth causes a smoother
surface [26]. The termination also determines the CdTe/PbTe interface structure as is
shown later in this thesis.
2.3 Annealing
The transformation of the heterostructure into PbTe QDs embedded in a CdTe matrix
happens during an annealing step. Annealing was performed after growth at different
temperatures above 300°C for 10min. CdTe and PbTe have the same lattice constant
at about 150°C. The strain in the PbTe SQW switches from -0.3% tensile strain (room
temperature) to 0.4% compressive strain (temperatures above 300°C). During the
annealing step the SQW breaks up into islands of PbTe with a larger thickness than
the original 2-dim layer. The process is driven by the immiscibility of the two
materials and activated by the thermal load transferred during annealing. The
separated PbTe material tries to reach a thermal equilibrium shape caused by
minimising the total energy. The PbTe islands end up in a highly symmetric shape.
First TEM investigations showed that the dots are terminated by {100}, {110} and
{111} planes (see Fig.2.6).
Figure 2.6: (a) Two PbTe dots precipitated from a 5 nm layer. The dots have a highly
symmetric shape and sharp interfaces to the CdTe host material. (b) High resolution
TEM image of a small dot. The PbTe is identifiable by the (110) and (001) lattice planes.
CdTe shows {111} lattice planes. The PbTe dot shows sharp interface to the host
material. The kinds of the interfaces are indicated.
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The equilibrium shape is constructed with these first tree Miller planes. The shape
built up with these planes is a small cubo-octahedron, or, for the special case that the
{110} and {001} interfaces are quadratic, a rhombi-cubo-octahedron (see Fig.2.7).
The definition of a cubo-octahedron is the combined shape of a cube and an
octahedron which leads to a cube with truncated edges and corners. The {001}
interfaces represent the original cube interfaces. There are manifold appearances of
the cubo-octahedron if the sizes of the chopped parts, which build the {110} and
{111} interface classes, changes. The equilibrium shape has important consequences
for interface characterisation. The interface must be parallel to the electron beam for
interface characterisation with high resolution TEM imaging. The {111} interfaces of
the QDs are of triangular shape. If this interface is parallel to the electron beam and is
focused, the projected length of the interface changes and makes it difficult to image
this interface.
Figure 2.7: A small rhombi-cubo-octahedron. The {100} and {110} surfaces have the
same area and are quadratic. Each facet has a parallel associate surface. The shape is
highly symmetric. The {111} surfaces are triangles.

Chapter 3
The Transmission Electron Microscope
The Transmission Electron Microscope (TEM) is a well-known and often used
instrument for the characterisation of nanostructures. All investigations of the QDs
were done with the TEM, thus, it is important to discuss the used techniques in detail.
This chapter provides only a brief introduction to the basic concepts and the main
components of a TEM considering the JEOL JEM-2011 FastTem that was used within
this thesis. The main part of this chapter is then about the used techniques and the
theory behind them. For more detailed information about the basics and further
information, please see [30], [31], [32] and [33].
3.1 The JEOL JEM-2011 FastTem
The basic principle of a TEM is similar to an optical transmission light microscope,
but it uses electrons for the exploration of the specimen. The manipulation of the
electrons is done by magnetic lenses. An exception is the Wehnelt electrode, which
acts as an electrostatic lens. The main parts of a TEM are the electron gun, the
condenser lens system, the specimen stage and the imaging system, consisting of
objective, intermediate and projector lens system. The task of the electron gun is the
generation of a sufficient amount of electrons with a distinct energy, which are then
formed to a parallel beam in the condenser lens system. After the interaction of the
electrons with the specimen, the imaging system reproduces an enlarged image of the
sample on the luminescent screen or a CCD camera. A schematic cross sectional
image of our TEM setup can be seen in Fig. 3.1 [34]
The mode of the electrons is no longer a single beam after the specimen stage. The
crystal structure creates a multitude of multiple scattered electron beams. One can
either image this diffraction pattern (DP) or a real image of the sample on the
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Figure 3.1: Cross sectional view through the column of the JEOL JEM-2011 [34]

screen. These are the two basic modes of imaging (see Fig. 3.2) [32]. Any of the
scattered electron beams are focused into the focal plane of the objective lens, but
they also build up a real image of the sample in the image plane of the objective lens.
Now the setting of the intermediate lens determines the image on the viewing screen.
The diffraction pattern is reproduced on the viewing screen, when the objective plane
of the intermediate lens coincides with the focal plane of the objective lens. On the
other hand, if the image plane of the objective lens is the objective plane of the
intermediate lens, a real image of the specimen appears on the screen.
Figure 3.2: The two basic operation modes of a TEM are controlled by the strength of
the intermediate lens. (a) The focal plane of objective lens and objective plane of the
intermediate lens are at the same level. The projector lens reproduces the diffraction
pattern on the screen. (b) The objective plane of the intermediate lens is in-plane with the
image plane of the objective lens and a real image of the specimen is formed on the
screen. [32]
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There are two important, adjustable apertures between the objective and
intermediate lens. The first is the objective aperture, which is located at the level of
the focal plane and allows the selection of electrons from distinct scattered beams for
image formation. The other is placed in the image plane of the objective lens and acts
as a virtual aperture to choose the area of interest on the sample. It is called field-
limiting aperture or selected area diffraction aperture (SAD).
The JEOL JEM 2011 FastTem uses a LaB6 filament as electron source and the
electrons can be accelerated up to 200keV between the Wehnelt cylinder and the
anode plates. Electrons with an energy of 200keV are in the range where relativistic
effects are playing a role. This leads to a wavelength of the particles of 2.5·10 -2 Å.
The microscope is an electron system, thus the theoretical diffraction limit is given by
the Rayleigh criterion (eqn. 3.1) [32].
The denominator of equation 3.1 is called the numerical aperture and is the product of
the diffraction-index and sin β, whereas β is the semiangle of collection. λ refers to
the wavelength of the electrons. For an electron energy of 200keV this wavelength is
2.5·10 -2 Å. The maximum resolution (the numerical aperture is set to 1) is then
1.53·10 -2 Å.
0.
61⋅
λ
δ =
n ⋅sin
β
The practical resolution is much worse than the theoretical diffraction limit. The
main reasons are lens aberrations and in particular the spherical aberration of the
magnetic lenses (see Fig. 3.3) [32]. The spherical aberration causes a stronger bend of
off-axis electrons toward the optical axis, and thus a spot is reproduced as a disk in the
image plane. The radius of this disk is given by Csβ 3 . β is again the semiangle of
collection and Cs the spherical aberration coefficient, which is an important
characteristic of a TEM. With this value and the Rayleigh criterion one can estimated
a practical point-to-point resolution (eqn. 3.2) [32] of the microscope.
r
min
≈ s
( ) 4
1
3
C
0. 91 λ
(3.1)
(3.2)

This leads with Cs = 1mm and λ = 2.5·10 -2 Å (parameters of the JEM 2011 FastTEM
at 200 keV) to a resolution of about 2 Å. This is near the specified point resolution of
the JEM 2011 FasTEM for 200keV of 2.3 Å, [35].
Figure 3.3: Ray diagram of the lens aberration. A point P is reproduced on the Gaussian
image plane as a disk by a real lens. Due to the stronger bend of an off-axis electron, a
disk with a minimum radius is found in the plane of least confusion. [32]
3.2 Scattering of Electrons
Scattering of electrons at the atoms are the interaction with the specimen. We can
characterise the scattering depending on how we look at the electron, as particle or as
a wave. The expression inelastic or elastic scattering describes whether the particle
electron transfers energy to the target or not. Coherent and incoherent scattering
distinguish between scattering without a phase shift of the incident and the scattered
electron wave and an event with a phase shift.
17

18
Elastic scattering is described by Rutherford scattering, with the important
parameter of the differential cross section which (eqn. 3.3, eqn. 3.4) [32] defines the
atomic form factor (eqn. 3.5) [32].
an isolated atom.
2
f (θ)
is proportional to the scattered intensity of
Equation (3.3) is the screened relativistic Rutherford cross section, a function of
the scattering angle θ. θ0 (eqn. 3.4) is the so-called screen parameter. λR is the
relativistic corrected electron wavelength and E0 the according electron energy. The
properties of the atom are described by the atomic number Z. a0 denotes the Bohr
radius. For a more detailed explanation of the Rutherford scattering see e.g. [32,33].
The structure of the crystal is described by the unit cell structure factor (eqn. 3.7,
detailed calculation for the zb and rs lattice in appendix A). With the Laue equation
K=kD-kI this leads to the description of a diffraction pattern. For a detailed
introduction of reciprocal space and diffraction from a crystal, see e.g. [36].
The intensities of the diffraction spots contain the information of the contrast of a
real image. Therefore, it is important to understand the mechanism behind it to
interpret the contrast of TEM images. The amplitude of an e-beam scattered at one
unit cell is given by [32]:
4
dσ ( θ )
λR
dΩ
=
4
64π
a
A
θ
0
f ( θ)
cell
F (
θ)
=
=
2
0
2
e
=
∑
i
Z
2
2
⎛
⎞
⎜ 2 θ ⎛ θ0
⎞
sin + ⎟
⎜
⎜ ⎟
2 2 ⎟
⎝ ⎝ ⎠ ⎠
0.
117
E
0
1
2
Z
1
3
dσ(
θ)
=
dΩ
2 i r k⋅ π
r
fie
2πi
F
( θ
)
( hx + ky + lz )
i
i
i
2
(3.3)
(3.4)
(3.5)
(3.6)
(3.7)

F(θ) is the structure factor of the unit cell and k is the wave vector of the scattered
beam. Summation over all unit cells leads to an expression for the amplitude of a
scattered electron beam.
This is a summation over n unit cells in an unit area plane separated by the distance t.
The extinction distance ξg (eqn. 3.9, [32]) is an important quantity to describe a
scattering event. It contains the lattice parameters (via the volume Vc of the unit cell),
the atomic number (via Fg, the structure factor of the unit cell for the Bragg angle θB)
and the wavelength λ of the electrons.
Equation 3.8 is an expression of the kinematical theory of electron diffraction,
which is only valid for a thin crystal slice. The intensity of the scattered electron beam
|φg| 2 is proportional to t 2 . If only two electron beams, the direct and one scattered
electron beam, are considered, |φg| 2 is small and the intensity |φ0| 2 of the direct beam is
approximately one. This is valid if the condition t

20
To derive the change of the beam amplitude the two-beam approximation is
applied. This means that only one diffracted beam is strong. This condition can also
be reached in a real TEM by tilting the sample until only one beam besides the (000)
reflex is strong. The other spots can then be neglected. If one writes now this equation
in terms of the change of the amplitudes when the beam passes through the specimen
along the z direction, one obtains the Howlie - Wehlan equations (eqn. 3.11, eqn.
3.12,) [32].
dφ g πi
−2
πisz
= φ 0e
dz ξ g
πi
+ φ
ξ
dφ0 πi
πi
2πisz
= φ0
+ φge
dz ξ0
ξg
This pair of coupled differential equations can be used to derive the amplitude of the
scattered beam. This gives the intensity of a diffracted beam
Whereas seff is the effective excitation error and is given by
φ
g
2
⎛ t ⎞
⎜
π
= ⎟
⎜ ⎟
⎝ ξg
⎠
s is the excitation error and expresses the deviation from the exact Laue condition and
is also a vector in reciprocal space. Many diffraction spots can be seen even if the
Laue condition is not exactly fulfilled, which is then expressed as K=kD-kI+s. The
intensity of the scattered electron beam is a periodic function of the specimen
thickness t. The period of the oscillations is πseff. seff differs for different diffraction
spots (hkl) and approaches s for very large values of s and becomes ξg -2 if s equals
zero. The periodic behaviour of the electron beams plays an important role in the
interpretability of the lattice fringes in HRTEM images (see section 3.4).
s
eff
2
=
0
g
( )
( ) 2
2
πts
eff
πts
sin
s
2
eff
+
1
ξg
2
(3.11)
(3.12)
(3.13)
(3.14)

3.3 Contrast Enhancement with Bright and Dark Field
Imaging
To get sufficient information from a TEM image it is important to know what the
origin of contrast in the image is and how one can use these mechanisms to enhance
it. The term of contrast itself is defined as a difference in intensity between to areas
(egn. 3.15), [32].
Therefore, it is not possible to increase contrast by increasing the intensity of the
electron beam. Rather one will decrease the contrast and the best condition to record
high contrast images is to do it with low intensity.
3.3.1 Contrast Mechanism
There are three main contrast mechanisms that are important for TEM imaging. The
mass-thickness (ρt, density×thickness) contrast is caused by incoherent elastic
electron scattering. The Rutherford cross section depends strongly on the atomic
number Z (eqn. 3.3). Thicker samples cause more scattering events due to the mean
free path remains constant. In a specimen region with a higher mass-thickness more
electrons are scattered, thus less electrons are collected by the objective lens in the
image plane (see Fig. 3.4), [32]. On the other hand, coherent elastic scattering causes
the diffraction contrast. This contrast is a form of amplitude contrast, because
diffraction peaks appear at the Bragg angles. The intensity of the diffraction peaks
depends on the unit cell structure factor and can be used to produce contrast between
materials with different structure.
The mass thickness effect and the diffraction contrast compete. Given that
Rutherford scattering in a thin specimen is strongly forward peaked, the primary spot
of the DP contains most of the mass thickness contrast. This spot can be used to form
a real image which is called bright field image (BF). On the other hand, collecting the
electrons of any diffraction spot with dominant diffraction contrast for imaging is
called Dark field (DF) imaging.
I
C =
2
− I
I
1
1
ΔI
=
I
1
21
(3.15)

22
The origin of the third contrast mechanism is interference of differently diffracted
e-beams. This contrast allows to resolve lattice fringes in High Resolution
Microscopy which is treated in section 3.4.
Figure 3.4: In regions with low mass thickness more electrons are forward scattered to
small angles and can be collected by the objective aperture. This causes a higher intensity
in the formed image. In higher mass thickness regions more scattering events occur
causing darker regions in the image. [32]
3.3.2 Dark Field and Bright Field imaging
Since the diffraction pattern of the crystal is reproduced in the focal plane of the
objective lens and the objective aperture is located in the same plane, a distinct
diffraction spot can be chosen in the DP mode for real image formation. To do that all
other spots are masked by the aperture and only the electrons of one beam are
collected by the intermediate lens. BF images are formed by collecting only the
electrons of the (000) peak by the objective aperture and show strong mass thickness
contrast.
On the other hand, collecting the electrons of any diffraction spot can show
contrast in the real image, whose origin are different lattice parameters or a different
structure form factor. Both of these properties are a part of the extinction distance ξg
(egn. 3.9) which is a determining factor of the amplitude of a scattered beam. This

kind of imaging is called Dark field (DF) imaging. In Figure 3.5 one can see a
comparison of dark and bright field imaging.
Figure 3.5: Sketch of (A) BF and (B) DF imaging. The electrons of a distinct diffraction
spot can be collected for image formation by alignment of a small enough objective
aperture. [32]
Since the diffraction contrast is correlated with the intensity of the Bragg reflexion,
one can increase the contrast of the real image by optimizing the amplitude of the
scattered electron wave. The intensity of the scattered Bragg reflex is periodic in the
thickness t of the sample and periodic in the effective extinction error seff, which can
be changed by tilting the sample. The best results are obtained for the two beam
condition, where only the spot of interest has a high intensity. Of course, the other
bright spot is the (000) reflex.
The DF technique is best suited for specimens with different crystal structure. For
the CdTe/PbTe heterosystem which is treated within this thesis, DF imaging is really
powerful. CdTe crystallizes in the zb lattice and the formfactor of {200} reflexes is
weak. On the other hand the formfactor F{200} for the PbTe rs structure is strong, thus
this reflex is well suited for DF images. In Figure 3.6 one can see the comparison of a
dark and a bright field image at the same position of a CdTe/PbTe sample. The
diffraction pattern of the specimen is also shown. The images were recorded slightly
away of the [001] zone axis.
23

24
Figure 3.6: (a) BF image of a PbTe/CdTe specimen, recorded slightly away of the [001]
direction. The images show the mass-thickness contrast. The PbTe dots appear darker
than the surrounding CdTe host material (mass contrast). A thickness contrast can be
seen at the top and the bottom of image (a). The diffraction contrast is dominating in the
DF image (b). The (020) spot, which is a forbidden reflex for the zb lattice, was used for
image formation. Thus, the PbTe dots appear bright in a dark background. In addition,
the dots in the thicker areas, which are not visible in image (a) are visible in image (b).
(c) shows a diffraction pattern, that was recorded slightly away from the zone axis, so
that the (020) reflex is the brightest of the {200} spots.
Figure 3.7: Sketch of the diffraction condition for CDF. (A) Common two beam
condition. The spot +g(hkl) and 000 are excited. If now the +g(hkl) spot is moved to the
position of the 000 spot it becomes weak and the +g(hkl) spot is strong (B). If the
opposite –g(hkl) spot is tilted toward the 000 position (C) the reverse two-beam
condition is now applied to this spot. [32]

Centred Dark Field
One disadvantage of the straight-forward DF imaging procedure is increased lens
aberration. Scattered e-beams are not near the optical axis of lenses, so they are
stronger bent towards this axis and it is difficult to form high quality real space
images.
To record DF images in the same quality as BF images it is necessary to bring the
e-beam of interest on the optical axis and into a two beam condition. That can be done
by tilting the incident beam in such a way that the spot of interest replaces the (000)
spot. This kind of DF imaging is called Centered Dark Field (CDF) mode. The tilting
of the incident beam changes the diffraction conditions for the electrons of the hkl-
plane and the applied two-beam condition is destroyed. Both conditions can be
reached if first the symmetric spot of the diffraction spot is tilted to the two-beam
condition and after that the incident beam is tilted. This procedure is sketch in Figure
3.7, [32]. Most TEM are able to save the alignments for the beam tilts, so it is possible
to switch simply between DF and BF imaging, once the objective aperture is well
aligned.
3.4 High Resolution Transmission Electron Microscopy
Another kind of investigation of specimens is High Resolution Transmission Electron
Microscopy (HRTEM). The main difference to DF and BF imaging is the number of
collected beams for image formation. To form a HRTEM image more than one beam
is collected by the objective aperture (see Fig. 3.8). If the resolution of the microscope
is high enough, so-called phase contrast can be obtained. This phase contrast contains
the spatial information of the lattice planes of the sample and can be exploited to
explore the crystal structure.
3.4.1 Requirements for HRTEM
There are some essential requirements for the microscope to obtain high resolution
TEM images. [33]
• High mechanical stability, low vibrations
• A goniometer of high precision
• High enough acceleration voltage to reach the necessary resolution
• High gun brightness
25

26
• Stability of the acceleration and lens currents
• On-axis alignment of the electron beam and the voltage centre of lens
current
• Low spherical aberration coefficient of the objective lens
• Parallel beam for good spatial coherence
• Low energy spread and low chromatic aberration coefficient
• Well aligned stigmators of the intermediate and objective lens to avoid
lens astigmatism
Figure 3.8: (a) Diffraction pattern of a CdTe specimen, recorded along the (110) zone
axis. The most important spots that cause the phase contrast of the lattice planes in the
real image, are indicated. The circle indicates the size of the aperture that was used for
real image recording. (b) Real image that shows phase contrast. The {002} and {220}
diffraction spots are strong for the PbTe rs structure, the {111} are strong for the CdTe
zb structure. The two materials can be distinguished by the corresponding lattice planes
in the real image. The lattice planes are indicated.
3.4.2 Origin of Lattice Fringes
The origin of the lattice fringes are the different phase factor of the scattered beams.
This can be easily shown by the solution of the Howlie - Wehlan equations. The
intensity of the solution is given for the two-beam approximation by [32]
2
2 2
I = ψT
= A + B + 2AB
sin( 2πg′
x − πst)
(3.16)

Whereas A 2 and B 2 are the intensities of the primary and scattered beam and the
term 2AB is the interference part. This equation also implements the assumption that
the specimen is thin enough to set sg equal to s. The intensity of the two beams is a
sinusoidal function of g´ (g´ = g+sg). If the term πst is a constant, one will see this
variations as lattice fringes with a periodicity of x = 1/g. If the excitation error s = 0 it
is the exact lattice plane spacing of the scattering planes. If the excitation error is not
zero and there are no variations of the thickness t it will be still the same case. For a
not entirely flat specimen the lattice fringes will be shifted as a function of πst, but the
periodicity will not change drastically.
3.4.3 Transferfunction and Scherzer Defocus
As image formation in a microscope is described in terms of a specimen function
f(x,y), the image function g(x,y) can be written as the convolution of f(x,y) with a so
called impulse response function h(x,y) (eqn. 3.17), [32]. h(x) describes the properties
of the optical system.
g( r) = ∫ f ( r′
) h(
r − r′
) dr′
= f ( r)
⊗ h(
r)
A Fourier transform of a convolution results in a multiplication of the fourier
transformed terms in the reciprocal space. This terms are the contrast transfer function
H(u), the specimen function F(u) and the image function G(u).
G( u ) = H(
u)
F(
u)
H(u) contains the properties of the optical system of the microscope as the aperture
function A(u), the envelope function E(u) and the aberration function B(u).
H( u ) =
A(
u)
E(
u)
B(
u)
A(u) and E(u) restrict the spatial frequency range, whereas A(u) depends on the
aperture size and E(u) is a fixed property of the lens system. Depending on the chosen
aperture, A(u) can be more or less restrictive. B(u) is usually given by eqn. 3.20 and
eqn. 3.21, the phase-distortion function χ(u). A point like object is imaged as disk due
27
(3.17)
(3.18)
(3.19)

28
to defocus Δf and spherical aberration, expressed by Cs. The phase-distortion function
brings that into account for all rays passing through the lens system with the angles
θ = λu.
The specimen is described as a phase object. It can be shown that the phase change
of the electrons only depend on the crystal potential V(x,y,z) if the specimen is thin
enough. The 3-dim potential is then replaced with the projected potential Vt(x,y) on
the x-y plane perpendicular to the electron beam. The so called weak phase object
approximation (WPOA, eqn. 3.22), [32] applies for very thin specimens (Vt(x,y)

Figure 3.9: Plots of the sin x(u) term for different values of Δf and Cs. The first cross
over defines the change form a positive phase contrast to a negative phase contrast. If the
spatial frequencies of the lattice distances of interest is smaller than this first cross over,
the image may be directly interpreted. The effect of the defocus Δf can be balanced
against that of the spherical aberration to optimize the first cross over. The plots are
calculated for 200keV electrons. The plot for Δf=-60nm, Cs=1mm is the optimized
transferfunction for the Jeol JEM 2011 FasTEM (Scherzer defocus)
But there is a way to improve the transferfunction and shift the first cross over to
large value. Scherzer found in 1949 that one can balance the effects of the spherical
aberration against an underfocus of the sample (see Fig. 3.9). This is known as the
Scherzer defocus (eqn.: 3.24), [32].
This leads to a resolution (eqn. 2.25), [32] that can be defined as the reciprocal
value of the first cross over sin χ(u).
Δf Sch
s
= −1.
2(
C λ)
1
2
29
(3.24)

30
For the JEM 2011 FasTEM with a Cs of 1mm and 200keV electrons with a λ of
2.5·10 -2 Å this equation leads to a resolution of 2.3 Å which is equal to the specified
resolution by JEOL [35].
3.5 Sample Preparation
The aim of sample preparation is the production of thin enough samples. Electrons
can only pass through samples thinner than about 100nm. For HRTEM imaging, the
sample must be even thinner and should be only a few nanometers thick if it should be
simple to interpret the images. The sample holder of the Jeol JEM2011 FastTem
requires samples with a diameter of 3mm. These small disks are thinned to the
necessary thickness. For a detailed description of the Sample Preparation see [40].
One distinguishes between two kinds of preparations concerning the direction of
view with respect to the layer structure of the specimen. With a cross sectional sample
(X-specimen) one looks along a direction in the plane with the layer of interest. With
a plan view (P-specimen) sample one looks along a direction perpendicular to the
layer. The material is cut with a wire saw or an ultrasonic cutting device [37]. After
the fabrication of the blank shape (for our sample holder a disk with a diameter of
3mm), it is thinned by grinding on a rotation wheel to about 150 μm. The next step is
done with the so called dimple grinder [38]. A rotating wheel grinds a dimple in the
middle of the rotating disk such that a supporting ring remains. The thinnest area is in
the middle of the dimple and is about 10 μm thick. The last step of thinning is done by
ion milling with argon ions [39] down to 10 nm or less.
The Ar ions are accelerated with 2-3kV for the sputtering process and thus result in
a heating of the sample during the thinning. The sputtering time for the thinning
process varies strongly because grinding with the dimple grinder is only accurate on
the μm scale. The transferred load of heat can cause additional annealing of the
sample. Specimens of un-annealed samples show in some case the beginning stage of
QD precipitation. But this could also be an effect of the CdTe overgrowth. The
additional transferred heat has no effect for annealed samples with QDs in the
equilibrium shape.
r
Sch = s
1
4
3
4
0. 66C
λ
(3.25)

Chapter 4
Shape and size of the PbTe Dots
For the implementation of the QDs for devices one must be able to control the size,
density, shape and position of the nanocrystals. The size of the dots should be
controlled by the layer thickness and the density dependents on the amount of
deposited material. The shape is determined by a thermodynamic equilibrium shape.
The in-depth location of the dots is well controlled by the position of the epi-layer. To
learn more about the size and shape of the dots in dependence of the annealing
conditions and the layer thickness, DF and BF images of several samples were
statistically evaluated.
4.1 Available Samples
The samples were grown at the Osaka Institute of Technology, as mention in chapter
2, and were originally intended for photoluminescence measurements. The samples
were annealed at our institute in Linz. The annealing parameters were adjusted to
optimise the PL measurements. The series of samples, grown at different conditions,
were thus not perfectly suitable for the statistical analysis.
Table 4.1 shows the series of the investigated samples. The most common
thickness of the SQWs was 5nm PbTe, but there was also one attempt of a double
quantum well (samples with series number #11). The quantum wells were grown at
different substrate temperatures from 280°C to 220°C. All PbTe layers were grown on
a Cd terminated CdTe surface, expect for series number #8. The Cd termination was
preferred, because PbTe grown on this termination show less surface roughness [26].
The annealing temperature was in the range of 320°C to 350°C. To investigate the
influence of the layer thickness on the resulting dots a series was grown with SQW
thickness from 1nm to 50nm. The samples with the highest PL intensity (#28-#31)
were used for TEM investigation. For the specimen fabrication we used in most cases
annealed samples, but also as-grown samples were used. First we prepared a cross
31

32
section specimen and, if the TEM images showed interesting features, we tried to
fabricate an additional plan view sample. Because a limited amount of material was
available, and not all attempts of sample preparation were successful, not always both
preparation kinds became available.
TEM specimen numbers
(epi-number following #)
Kind of
Preparation
Cross section(X)
/ Plan view(P)
Substrate
temperature
during SQW
growth
Annealing
temperature
Annealing
time
Termination
before PbTe
growth
PbTe
well
thickness
[°C] [°C] [min] [nm]
192X_SQW_A_CdTe X 280 as grown Cd 5
188X_SQW_B_CdTe X 280 as grown Cd 5
201X_#5_G_CdTe X 250 as grown Cd 5
227P_#5_C_CdTe P 250 cooled Cd 5
204X_#5_C_CdTe X 250 cooled Cd 5
242P_#8_G_CdTe P 280 as grown Te 5
235X_#8_CdTe_G X 280 as grown Te 5
243X_#8_C_CdTe X 280 cooled Te 5
231P_#8_A_CdTe P 280 350 10 Te 5
234X_#8_CdTe_A X 280 350 10 Te 5
223X_#11_G_CdTe X 280 as grown Cd 5
226X_#11_C_CdTe X 280 cooled Cd 5
225X_#11_A_CdTe X 280 350 10 Cd 5
254P_#28_A_CdTe P 220 320 10 Cd 1
258X_#28_A_CdTe X 220 320 10 Cd 1
253P_#29_G_CdTe P 220 as grown Cd 3
245P_#30_A_CdTe P 220 320 10 Cd 3
247X_#30_A_CdTe0 X 220 320 10 Cd 3
248X_#30_A_CdTe90 X 220 320 10 Cd 3
244P_#31_A_CdTe P 220 320 10 Cd 5
246X_#31_A_CdTe0 X 220 320 10 Cd 5
249X_#31_A_CdTe90 X 220 320 10 Cd 5
228X_CdTe_1974_1016 X
229X_CdTe_1974_1015 X implanted
257X_CdTe_Pb_1610 X
Table 4.1: List of all investigated specimens within this thesis. The # in the TEM
specimen numbers marks the epi-layer series, of which cross section and plan view
specimens were fabricated. As-grown and annealed samples were prepared. The last
three samples were an attempt to produce the PbTe/CdTe dots by implanting Pb into bulk
CdTe.

4.2 Precipitation steps
TEM images of as-grown samples showed that in most cases the 2D layer does not
exist any more after the preparation process. If the 2D layer was not breaking up
during the overgrow process, the start of the disintegration of the layer was induced
by the heat load which was transferred to the sample during the last sample thinning
process, argon ion sputtering. This fact allows some insight into the processes during
the annealing step. The sputtering time varies strongly for different samples.
Therefore, different intermediate steps can be found in these nominally un-annealed
samples, from a nearly closed 2D layer to separated material in off-equilibrium dot
sizes and shapes. The dots of the annealed specimens assume the equilibrium shape,
or they are on the way toward it, depending on the annealing temperature and the
original layer thickness. With this it is possible to demonstrate the precipitation
process from the start of up-breaking of the 2D layer to highly symmetric PbTe dots
in the thermodynamic equilibrium shape.
Figure 4.1: BF TEM image of a nominally non-annealed PbTe layer recorded along the
[001] zone axis of a plane view specimen of series #29. The 2D layer of this series was
3nm thick and disintegrates during the ion milling process. The lateral dimensions of the
wiggly lines are about 10 -15nm. The lines are orientated along the and
directions.
The breaking-up of the PbTe layer starts with a disintegration along extended lines
and building of interconnecting lines of material. Figure 4.1 shows a plan view
specimen of an as-grown sample. The image shows the contracted PbTe material with
the shape of wiggly lines. In this stage most of the PbTe is still interconnected, but
also some separated material in dot size can be found. The material contracts laterally
33

34
and increases the height of the PbTe material lines. The increase of the local layer
thickness can be seen in Fig. 4.2. The image shows a cross-sectional specimen of an
originally 5nm epi-layer sample. The PbTe wires contracts until the thickness of the
Figure 4.2: BF TEM image of an annealed PbTe layer recorded slightly away from the
[110] zone axis on a cross sectional specimen of series #31. Growth direction was along
the [001] axis. The sample was originally a 5 nm SQW and was annealed at 320°C for
10min, which was not sufficient for complete precipitation. The sample contains still
interconnected 2D part with a height form 5 to 20 nm. The lateral dimension shrinks for
thicker layers. Dot-shaped material with sharp interfaces can be seen in the 20 nm layer.
Figure 4.3: Images of several constrictions of the PbTe wires during the dot
precipitation. The images were recorded on a cross section specimen of series #5, as-
grown sample. (a) shows a DF image, (b) and (c) show BF images. The layer was
originally 5nm thick. The dot material already shows sharp interface to the host material.
The shape of the separated material shows larger in-plane dimensions than height.

lines approaches the diameter of the resulting dots. The wires began to constract at
some points to provide sufficient material for this height increase (see Fig. 4.3). At
these constrictions the PbTe wire becomes thinner and thinner and the developing
PbTe wires are separated into PbTe islands. Figure 4.4a shows TEM images of plan
view and cross sectional specimens in this stage. The dots have a elongated shape and
the lateral dimensions are larger than the height of the dots.
Figure 4.4: (a) Cross sectional (DF image) and plan view (BF image) of an annealed
3nm PbTe layer (#30). The dots are elongated and disk-shaped, and show sharp
interfaces (indicated in the plan view image). The height of the dots is about 10nm. The
longer interface in the plan view is either the (010) or the (110) interface, but also highly
symmetric dots can be found. (b) Cross sectional (BF image) and plan view (DF image)
of dots from a 1nm layer, annealed at the same conditions as (a). The dot size is
distributed over some range, but only highly symmetric dots can be found and the sample
seems to be in thermodynamic equilibrium.
The separated dots then try to reach their thermodynamic equilibrium shape (see
fig. 4.4b). The distribution of the constrictions, which separate the PbTe wires into
dots, determines the final size distribution of the QDs. The PbTe wire dimensions are
different for different thicknesses of the original epi-layer. The PbTe wire dimensions
determine the maximum distance between two constrictions which lead to a relatively
sharp upper limit of the resulting dot size. Smaller dots can be found over a larger
range.
35

36
4.3 Precipitation from different layer thicknesses
4.3.1 Annealed 5nm layer
The best specimen of an originally 5nm thick layer resulted from sample #11, which
is the double QW sample. It was possible to record more than 100 dots in one row,
which allows significant dot size statistics. The double quantum well samples were
annealed at 350°C for 10 min. The height (along the growth direction) and the width
of the dots were evaluated with the program package Gatan Digital Micrograph.
Digital Micrograph is a control and analysis software for the Gatan Multi-Scan CCD
camera employed on our TEM [41]. The specimen itself shows dots with almost the
same height, but the width of the dots varies significantly (see fig. 4.5). Smaller dots
with a decreased high show always a high symmetry with comparable height and
widths. Dots with the maximum height have lengths of up to twice their height. This
is a strong indication that not all dots have reached there thermodynamic equilibrium
shape.
Figure 4.5: (a) Cross sectional, dark field image over a large area. The sample contains a
double row of QDs. The bottom row was used to analyse the dimensions of the dots. (b)
Typical QDs found in the sample, recorded as bright field image. The left-hand image
shows two highly symmetric QDs. The crystal orientation is indicated. The QDs show
sharp interfaces. The kind of the interfaces indicated in the right-hand images, which
show two elongated, centro-symmetric dots.

Figure 4.6: The distribution of the measured QDs in sample #11. Cubic dots with
quadratic cross-sections lie on the solid line. Symmetric dots with an aspect ration from
0.8 to 1.25 are bordered by the dashed line. The TEM images in the insets show one dot
at the solid line, one at the dashed line and one dot that is of elongated shape.
Figure 4.6 shows the distribution of the measured dots. The height of the dots has
an upper limit of about 30 nm. Most of the dots show a quadratic shape in the cross
section, but for heights larger than 15 nm also elongated dots can be found. Dots,
which are smaller than 15 nm, have almost the same height and width. Figure 4.6
contains also some example, of how the dots look in detail. The dots were sorted into
classes of 2nm for the height and length to get the distributions of these dimensions.
The number of dots in one class was counted. The accuracy of the measurements with
Digital Micrograph was about 1nm. Figure 4.7 shows these distributions. The heights
of the dots are narrower distributed than the length, and show a relatively sharp upper
limit of 30nm with a maximum at 25nm. Lower limit is at 6nm, but such small dots
are also hard to see in the dark field images with low magnification. But even in HR
images no dots are found with less than 20 atomic layers, which correspond to a dot
with a size of 4.6 nm. The length of the dots is wider spread. The maximum of the
37

38
distribution is at about 30 nm and limited by 8 and 45 nm. If it is also taken into
account that the dot elongation can be parallel to the line of sight, most of the dots in
this sample are elongated. Unfortunately, no plan view specimen of this sample exists,
but it should look like the plan view image of Figure 4.4, which shows an annealed
3nm sample.
Figure 4.7: (a) Height distribution of the dots. The maximum is at 25nm. The upper limit
is at about 30nm. (b) Length distribution of the dots with the maximum at about 30nm.
4.3.2 Annealed 1nm layer
The same measurements were also performed for sample #28, with an originally 1nm
thick PbTe layer. The sample was annealed at 320°C for 10 min. The plan view
specimen of the sample was good enough for statistical evaluation. A cross sectional
specimen was also available and was used to check the highly symmetric shape,
which the dots show in the plan view sample. This can be seen in Figure 4.8. The
appearance of the dots in plan view is an octagon with longer {110} interfaces. The
distances between two parallel {110} interfaces were used to measure the size of the
dots. The cross sectional specimen shows the appearance of these dots in a line of
sight along the [ 110]
direction which confirmed the high symmetry. One interesting
point is the extended (111) interface of these small dots, which will be treated in part
4.4.
The distribution of the dot size can be seen in Figure 4.9. Figure 4.9a shows the
high symmetry of the dots, which seem to become ever better for larger dots. The
ideal case is again indicated with a solid line. The shift of the distribution to one side

Figure 4.8: The image at the top shows the cross sectional specimen of sample #28 as a
BF image. The (111) interface is most pronounced, and for small dots the other interfaces
almost disappear. The DF image at the bottom shows the plan view specimen. The
interfaces of the dots are indicated.
Figure 4.9: (a) Size distribution of the measured dots. Only highly symmetric dots are
found. (b) Classification with respect to size. The most common size is 7 to 11nm. The
size of the smallest dot was 3.5nm
39

40
of this line is due to a slight tilt away from the zone axis to increase the contrast of the
dark field image. The classification of the dots with respect to their size shows a
narrow distribution with a maximum at about 8nm. The upper limit is again sharper
than the lower one, and appears at 11 nm. The smallest dot was 3.5 nm large, but it
was strongly blurred and could also be 5 nm large. The accuracy of this measurement
was about 0.2 nm if the interfaces are sharp for larger dots and get worse for smaller
dots, which can be explained by the shrinking (110) interface down to almost zero, as
can be seen in the cross sectional image of figure 4.8.
The comparison of these two specimens showed that the size of the dots depends
strongly on the original layer thickness. Unfortunately, the cross-sectional specimen
of a 3nm layer was not good enough for statistical evaluation and comparison with the
5nm sample. A rough estimate of the mean volume of the dots from the 3nm layer
resulted in about 6000nm 3 . An accurate estimate of the mean dot volume of the 1nm
samples is 335nm 3 , which corresponds to a dot density of 3 10 11 cm -2 . The largest one
is that from the 5nm layer with a mean volume of about 8000nm 3 , which corresponds
to a dot density of about 6 10 10 cm -2 . Thinner layers break up in dots with smaller
volume. On the other hand, the larger dots of e.g. a 5nm layer, collect much more
material. The volume of the large dots of the 5nm layer is ~25 time larger than for that
ones of the 1nm layer, but the thicker 5nm layer has only 5 times more material per
unit area than a 1nm layer. Thus, one can find 5 times more small dots precipitating
from a 1nm layer than large ones from a 5nm layer.
4.4 Equilibrium shape
As shown in part 4.3, the shape appearance of the dots changes with their size. The
{111} interfaces do not seem to shrink with the same ratio as the others do, when dots
get smaller. As the {111} facets are the interfaces which are hardest to resolve in high
resolution images. The aim of this chapter is to describe the expected shape of the
dots with attention on the {111} interface.
Figure 4.10 shows the length L of the projected (111) interface of dots with
different height H. Only dots with highly symmetric shape of sample series #11 and
#28 were used, which have almost the same height and width. The cross sectional
images of these samples were evaluated. The measurements show that the length of
the {111} interface is almost independent of the size of the dot and varies in a range
of 7 to 10 nm. An exception of this can be found if the interface falls together with a

Figure 4.10: Length of the {111} interface as a function of the height of the dots. Only
dots with the same height and width were used for the measurements. The solid line
indicates a ratio {111} length/height of 0.61.
stacking fault (also along [111] direction) of the CdTe crystal. For the small dots of
sample #28 (originally an 1 nm layer PbTe) this leads to a disappearance of the other
interfaces which can be see on the small dot in the cross sectional image of figure
4.8.The projected length of the {111} interface must be smaller the 7nm for dots with
a height smaller than about 12nm. For the acute angle of the small dots (α=70.5°,
angle between a (111) and ( 1 11)
interface), the ratio of the length to the height is
−1
( 2cos(
α ) = 0.
61
L =
. The solid line in figure 4.10 is a straight line with this
H 2
slope. For dots, which only build up {111} interfaces, the data points of the (111)-
length should lie on the solid line. Also the {111} interface length of dots with all
three interface kinds should have the same behaviour as a function of the height if all
three interface of the dot increase uniformly. The line should be parallel to the solid
line in fig. 4.10. The measurement show this behaviour for small dots with
disappearing {110} and {001} interfaces and shrinking {111} interface. Larger dots
show a relatively constant projection length of the {111} interface.
Figure 4.11 shows two dots with different shapes and sizes. The left dot from series
#28 is a small one with extended {111} interfaces relative to the {001} and {110}
41

42
areas. The sketch on top shows the contours of the dot with indicated interfaces. The
same can be seen for a larger, highly symmetric dot from series #11. For these dots all
projected interface have almost the same length. It can be seen that the (111) interface
for both dots have approximately the same length of about 10 nm.
Figure 4.11: The TEM images shows a small and a bigger QD recorded along the [ 110]
zone axis as bright field images. The top of the image shows the according cubo-
octahedrons with different interface sizes.
Figure 4.12 shows three possible equilibrium shapes of quantum dots. The shapes
were calculated for different interface energies using the Wulff construction. These
calculations and the calculations of the interface energies were performed by R.
Leitsmann et al., Institut für Festkörpertherorie und -optik, Jena [42]. This group in
Jena investigates the interface problem between PbTe and CdTe theoretically. They
apply density functional theory (DFT) as implemented in the Vienna ab-initio
simulation package (VASP). More detailed description of their work can be found in
the next chapter about the interface characterization. One finding of these calculations
was that the interface energies for the three experimentally observed interfaces classes
are almost the same. They found for the {110}, {100} and {111} interfaces energies
of 0.20, 0.23 and 0.19 J/m². It is important to say that the energies of the polar
interfaces {100} and {111} contain a dipole energy correction term of the same order
as the uncorrected value. Three shapes can be seen in Figure 4.12. The outer right dot
is calculated with the aforementioned corrected energies of the DFT calculation. The
dot in the middle is one with equal interface energies of 0.20 J/m² for all three
interfaces. The dot on the left hand side has again interface energies of 0.20 and 0.23
J/m² for the {110} and {100} interfaces. The interface energy of the {111} interfaces
is 0.22 J/m², which is within the estimated error bar of the calculated value of 0.19
J/m².

Figure 4.12: Different shapes of cubo-octahedrons calculated with the Wulff
construction with different interface energies [42]. The {001}, {110} and {111}
interfaces are indicated as red, green and blue. The directions for the projected shapes are
indicated. A projection along the [ 110]
axis contains parallel interfaces of all three
kinds.
If the different shapes in Fig. 4.12 are scaled to a projected {111} length of 10nm,
then the dot in the middle corresponds to a dot height of about 25 nm. This is the
mean size of the dots in series #11. The right-hand dot represents one with a smaller
height of 20 nm, which can be found in series #28. One important conclusion of the
left dot is the increased difficulty to image the (111) interface. The first difficulty has
its origin in the triangular shape of the interface. This means that the length of the
transmitted interface changes as one focus through this interface. The second point
concerns large dots, such as the one on the left side in Fig. 4.12. In the projection the
{111} interface is too small to connect the {110} with the {001} interface. This edge
consist of the projected {111} interface, and the edge between two {110} interfaces.
The angle of these two parts is almost the same. That only a part of the edge is the
projected {111} interface, is an additional difficulty for imaging.
The interface energies of a real dot are constants and should not change with the
size of the dot. If one calculates the equilibrium shape of the dots one obtains the
same shape for different sizes. The edges and corners between the interfaces are not
considered in the Wulff construction. A system with dominating interface energies
forms an equilibrium shape, which is independent of the dot size. The real system
shows variation of the dot shape depending on the size. This is a hint for the influence
of the edge energies on the equilibrium shape. The behaviour of the real system with
the relatively stable size of the {111} interface leads to a constant edge length
between the {111} and {110} interfaces and shrinking edge between the {110} and
{001} interfaces.
43

44
Chapter 5
Interpretation of HRTEM Images
As shown in chapter 3, HRTEM images are not real images of the structure. The
formed images depend strongly on the transfer function as a function of Δf and the
thickness t via the intensity of a diffracted beam (eqn. 3.13). The first cross-over of
the transfer function changes the sign of the phase contrast. For conditions away from
the Scherzer defocus, the first cross-over moves to smaller values of reciprocal
distances. If the investigated structures are in the range of the resolution limit, small
lattice frequencies (large distances in real space) and large lattice frequencies (small
lattice distances in real space) are mixed up with positive and negative phase contrast.
The intensity of a diffracted beam is proportional sin 2 (πξg -1 t), which leads to a
maximum intensity of a diffraction beam with wave vector g at a multiple of ξg/2. The
same behaviour is then also valid for the interference of diffracted beams, which leads
to the lattice fringes. This strong dependence on Δf and the thickness t makes it
difficult to interpret HRTEM Images.
It is necessary to perform HR map simulations to interpret HRTEM images.
Firstly, one has to make an assumption of the atomic structure of the sample. The next
step is the construction of a three dimensional model of the sample structure which is
then used to simulate HR maps. HR maps are functions of the defocus and thickness
of the samples. Other parameters, which determine the quality of the maps, are, e.g.,
the microscope parameters, astigmatism, noise, etc. These HR maps are compared
with the real HRTEM images, and if they do not fit, the model is changed and the
procedure is repeated until the HR map resembles the real HRTEM image.
5.1 JEMS Simulation Package
The JEMS (Java based Electron Microscopy Software) program is a software
package that allows simulation of the diffraction and imaging of a TEM with a
standard PC. It was developed by Prof. Pierre Stadelmann from the CIME-EPFL

(Centre Interdisciplinare de Microscopie Electronique-Ecole Polytechnique Fédérale
de Lausanne) in Switzerland. A free version for students and information about this
program can be found online at http://cimewww.epfl.ch/people/stadelmann/.
The JEMS program has several helpful functions for electron microscopy. The
crystal menu allows building up the crystal cells necessary for the simulations. The
space and point group of the crystal, its basis and the lattice constant is entered to
build up the unit cells of simple crystals. More complex crystal cells with a low
symmetry are constructed by entering each atom position. The crystal files are saved
in the txt-format as lists of the atomic positions. That allows easy conversion of
calculated atomic positions to JEMS crystal files.
The microscope performance is defined by entering the following parameters:
• Acceleration voltage
• Chromatic aberration coefficient
• Spherical aberration coefficient
• 5 th order spherical aberration coefficient
• Gun energy spread
Also adjustable are the parameters which are changed during the use of the
microscope, such as the beam tilt, size and position of the apertures, the camera
length, etc.
Different functions can be applied to the crystal files and the parameters of the
microscope, such as the generation of a diffraction pattern with or without Kikuchi
lines, Convergent Beam Diffraction (CBED) patterns, or the transferfunctions of the
microscope for a distinct value of the defocus. Also a function for the simulation of
the propagating electron beam is then available. There are two common approaches
for TEM simulations to calculate the propagating electron beam, and the JEMS
program package is able to perform simulations with both methods. The bloch wave
approach is suitable for simulations where the calculation must include High Order
Laue reflections like in the case of CBED patterns. For HRTEM map simulations of
lattice defects, interfaces or large crystal unit cells the multi-slice approach is used.
The simulations concerning the PbTe/CdTe interfaces were done with the multi-slice
approach. A detailed description of all functions of the JEMS program can be found in
the online manual of the program [43].
45

46
5.1.1 Multi-Slice Approach
The calculation of the DP and HR maps is based on the dynamical theory of elastic
electron diffraction at small angles. It uses several approximations, in particular the
small angle approximation. This approximation is satisfied if the energy of the
electrons is lager than about 50 keV, but depends also on the crystal. A full dynamic
calculation would need too much computer power. The multi-slice approach uses the
fact that the crystal potential is not z-dependant and that scattering at these high
energies is strongly forward peaked. The crystal is sliced in layers of thickness Δz,
and the slice potential is replaced by a projected potential (eqn. 5.1).
The calculation starts to calculate the propagating beam through the first slice,
followed by propagation through vacuum to meet the next slice. This step takes also
the microscope behaviour into account. This is repeated until the desired thickness is
reached. In the real space approach, which is used to save computer time, it can be
written as:
Whereas P(r) is the propagator of the electron in free space and describes the
microscope and is also called Fresnel propagator. q(r) is an exponential function of
the projected potential and describes the specimen. It is called the phase grating or the
phase object function. The knowledge that P(r) is strongly forward peaked is used to
decrease the computation time.
The real space approach was used for the JEMS calculations. The program is also
able to display the Fresnel propagator, phase object function and the projected
potential individually. More details of the dynamical theory of elastic electron
diffraction with the approximations that are necessary for the bloch-wave or multi-
slice approach can be found in [44]. For more detailed descriptions of the two
methods see [32] and [33].
V
P
z+
τ
1
=
τ ∫
( r)
V ( r;
z′
) dz
z
[ ψ ( ) ⊗ P
( r)
] q ( r)
ψn+ 1 = n r n+
1 n+
1
′
(5.1)
(5.2)

5.1.2 Simulation Procedure
The standard procedure of image interpretation with HR-map simulations is done with
a HR map which contains simulations for different values of defocus and specimen
thickness. This can be done in the HR multi-slice dialog by choosing the starting
focusing condition, the focus step size and the number of focus steps. The simulated
sample thickness is controlled by the number of slice iterations. The parameters are
the start number of iterations, the number of simulated image and the increment
between these images. The value of the thickness is the number of iteration times the
slice thickness which depends on the crystal model. For instance, the models for the
simulation of bulk CdTe and bulk PbTe are simply the unit cells of these materials
(see Fig. 5.1). The orientation of the cell can be chosen: For the PbTe/CdTe samples
one looks along a direction for plan view specimens and along a
direction for cross section specimens.
Figure 5.1: The unit cells of CdTe and PbTe as models for the JEMS program. The DP
of the materials shows the diffracted beams causing the lattice fringes. The 2D projection
shows 2x2x2 unit cells along the [001] direction. The according HR simulations are
direct maps of the crystal structure and show a positive contrast (dark areas correspond to
the atomic positions). The images were simulated for the Scherzer defocus condition and
a sample thickness of 4.5nm which are 15 PbTe (001) layer for PbTe or 15 Cd-Te bi-
layer for CdTe.
47

48
Firstly, the program calculates the transmitted electron beam for the start number
of slices. With that and the transfer functions of the different values of defocus the
image maps are calculated. This is repeated until the reached iteration number equals
the multiple of the iteration step number. The outcome is then an array of HR images.
Such HR-maps can be seen in Figure 5.2 or 5.4. The image in the left bottom corner
of the HR-map is the simulation for the thinnest sample and the start defocus, the
image in the right top is for the thickest specimen and the end defocus. For the
interpretation of HRTEM images it is also important to know, how the projection of
the lattice is related to the pattern of the lattice fringes. The JEMS program allows
displaying of the atomic positions of the used model in the HR map. The multi-slice
menu point can also display the parameters which are used for the simulations, such
as the projected potential and the phase object function.
Figure 5.2: Comparison of CdTe and PbTe HR maps. The images show either positive
or negative phase contrast. One reason for the strong variation for PbTe is the small
spacing of the (110) lattice planes. This distance is comparable with the resolution limit
of the microscope and therefore strongly sensitive to the defocus. The phase contrast
switches several times. The thicknesses of 3.2, 5.5 and 7.8 nm correspond to 15, 25, 35
layers (PbTe) or bi-layers (CdTe) of (110) lattice planes.

The DP of the materials is very helpful because it is directly correlated to the real
image via the fourier transform. It helps to interpret the real image over the indices of
the diffraction spots. For the plan view (one look along a zone axis) of CdTe
the {002} reflection spots are forbidden, and the {022} spots are strong. The spacing
between the (022) lattice planes are 0.23nm and near the practical resolution of the
JEOL FasTEM 2011. For the rs structure of PbTe the {002} reflexes are the strongest.
The spacing between the (002) planes is 0.46nm. These lattice planes and their
spacing are then the dominant structures in the HR simulation for thin samples at the
Scherzer defocus (see Fig. 5.1).
For the [110] oriented materials the DP looks differently (simulation can be seen in
Fig 5.3). The CdTe DP shows the dominating {111} spots of this material. The first
two strong spots for PbTe are the {002} and the {220} reflexes. The lattice distance of
the {111} planes is 0.37nm, i.e. significantly larger than the resolution limit of
0.23nm. Also far away from the limit is the lattice spacing of the {002} reflex with
0.46nm. However, the spacing of the {220} planes is with 0.23nm again near the
practical resolution limit and in reciprocal space near the first cross over of the
transfer function. This leads to strong variation of the PbTe pattern in the HR-maps as
a function of the defocus, as shown in Fig. 5.2.
Figure 5.3: Simulated diffraction patter for CdTe and PbTe oriented along the [110]
zone axis. The patterns have the same structure but the intensities of the spots, which is
indicated by the diameters of the circles, vary.
Because the PbTe lattice fringes show much faster variation in the sign of the
phase than the CdTe contrast, it could appear for CdTe/PbTe interface that a TEM
49

50
image shows opposite contrast for the two materials. Figure 5.4 shows the small range
where PbTe shows positive phase contrast and can be directly correlated to the lattice
structure. As can be seen in Figure 5.2, the pattern of CdTe is less sensitive to the
defocus value and can be correlated over a larger range directly to the lattice structure.
In order to know during the work at the microscope in which region of defocus one is
working it is necessary to perform focus series to be sure to record HRTEM images at
the correct defocus value.
Figure 5.4: HR map of [110] PbTe at ideal defocus condition (Scherzer defocus -61nm).
The image at Δf = -64nm and t = 1.4nm shows already a differing pattern, which does not
resemble the lattice structure. The thicknesses of 0.5, 0.9 and 1.4 correspond to 3, 5 and 7
(110) PbTe layers
5.2 Image simulation of the CdTe/PbTe interfaces
Different kinds of models were used for the interface simulation, with the largest
model consisting of more than 270 atoms. This large model contains all three relevant
interfaces and was used in the beginning to get a rough overview of how the interfaces
should look in the HRTEM images. The {111} interfaces are hard to image, due to the
size and the shape of these interfaces. A condition for high quality interface imaging
is the orientation of the interface. It must be parallel to the electron beam and it should
be a continuous structure throughout the specimen. It is hard to find a continuous

interface through the whole specimen because the (111) interfaces are small. The
focused length of the interface changes as one changes the defocus because the
interface is triangular shaped. This complicates the situation additionally. Only few
high quality HRTEM images could be recorded and so no further simulations of these
interfaces were performed. For the other two interface classes, {100} and {110},
single models which contain only the interface of interest were used. The program
MATLAB was used to calculate the atomic positions of the largest model. The atomic
positions of the two single interface models were entered manually.
The line-of-sight for cross sectional specimens is a zone axis of the crystal.
This direction is favourable because all three interfaces of the Quantum dots are
parallel to this direction and can be characterised. For this view the atomic rows
parallel to a direction consist for both kinds of material of only one kind of
atoms. This situation is really helpful for interface characterisation. To simulate HR-
maps for these directions with the multi-slice approach it is necessary that the models
have a layer structure where the atomic planes are perpendicular to the
directions. The individual interface models and the according simulation are treated in
the next chapter together with a comparison with the HRTEM images.
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52
Chapter 6
Interface characterization
6.1 Available Samples
6.1.1 Specimens for HRTEM imaging.
High-resolution interface characterisation requires TEM specimens of very high
quality. The specimen must be a few nanometers thick to get well interpretable
HRTEM images, as shown by the JEMS simulation. Most of the HRTEM imaging
was performed on sample series #11 for a simple reason: Series #11 was originally a
double quantum well, which was transformed by annealing into a double QD-row
sample. Cross sectional specimens were used for the interface characterisation
because in this view all three interfaces can be found parallel to the electron beam.
After preparation, the specimen is a disk with a dimple in the middle. Cross sectional
specimens are constructed of stripes of sample material. In the middle of the dimple is
the adhesive joint of the material stripes which is sputtered away in the thinnest area.
The material is also thinned at this point of the specimen and a curved wedge
develops from the straight edge. Only in a range of about 50 nm away from the edge
the specimen is thin enough for HRTEM imaging. The wedge is steeper if it is farther
away from the former edge, which decreases the limit of 50 nm. As was shows in
chapter 5, this thickness restriction can be even narrower if the image should be easily
interpretable. A double row increases the chance to meet this condition in the sample.
A sketch of a schematic specimen edge is shown in Figure 6.1.

Figure 6.1: A schematic sketch of the specimen edge. At the thinnest area a curved edge
develops upon ion milling. The dotted lines indicated the double QDs row. The hatched
area indicates where good conditions for HRTEM imaging can be found. A double row
doubles the chance for meeting the HRTEM conditions in comparison with a single row.
6.1.2 Beam Damage
Another problem of the HR investigations is beam damage of the sample material. For
HR imaging the TEM is run in a high magnification mode. The electron beam is
strongly focused to get sufficient intensity. The transferred energy to the field of
interest is large enough to produce beam damage of the sample material. The
investigations show that, depending on the thickness of the sample, the CdTe host
material starts to dissolves after about 10 to 20 min of illumination with a 200keV
beam at the intensity needed for the HR TEM images. This makes it necessary to
work fast and to align the microscope sufficiently far away form the area of interest.
Figure 6.2 shows the effect of a strongly focused beam on the CdTe/PbTe material
system. The damage from image (a) to (b) happens during the alignment of the
microscope for HR imaging at the highest magnification, which takes about 20 min.
Image (c) is recorded after further 20 min and 10 min waiting time without
illumination. The thickness of the region near the specimen edge is in the order of the
free mean path of the electrons in CdTe or even thinner, thus less affected by damage.
53

54
Figure 6.2: Different steps of beam damage: (a) shows the original PbTe Dot at the
beginning of illumination. (b) Beam damage is visible after ~20min illumination.
Stacked material with different lattice constants (temperature differences) of the same
lattice structure show so called Moiré Patterns, which originate from the overlap of
different sized periodic structures. (c) QD after further 20min: strong beam damages can
be seen containing even areas where the material was completely evaporated by the
electron beam.
6.2 HRTEM investigation of PbTe nanocrystals
An aim of the HRTEM investigations was to learn more about the correlation between
the PbTe-rs lattice and the CdTe-zb lattice. First use of HRTEM images was the
investigation of the lattice structure of the dots to get a raw overview. The more
sophisticated part was the attempt of detailed interface characterisation.
6.2.1 HRTEM images of single QDs
The dark and bright field images, as shown in the previous chapters, reveal sharp
interfaces between the PbTe and CdTe material. The question was, if this is also the
case on the atomic scale. The analyses of the HRTEM images showed that this is

Figure 6.3: Two HRTEM examples of dots in sample series #11. (a) The dot shows
coherent interface between the PbTe and CdTe lattices, which are almost defect free. (b)
Two dots can be seen to the left (small dot) and the right (large dot) of a stacking fault.
This sample is too thick for high quality HRTEM images and gives rise to distinct mass –
thickness contrast.
Figure 6.4: Dot recorded at an annealed sample of series #11. The image is stitched
together of four HRTEM images. The growth direction is indicated and correlates with
the direction of decreasing wedge thickness. The lattice fringes of PbTe are well oriented
with respect to the CdTe fringes. The number of PbTe lattice planes is constant on both
(110) interfaces, indicating the absence of dislocations.
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indeed the case for the {001} and {110} interfaces. Only few mono-atomic height
steps can be found at the {001} interfaces at the bottom of the PbTe SQW, which is
created during MBE growth. Practically no steps are found at the {110} and {001}
interface, which are created during the annealing process. Figure 6.3 shows some
HRTEM examples of dots with these interfaces. The {001} and {110} interfaces
show perfectly coherent interfaces between CdTe and PbTe. The {111} interfaces
show different appearances. This can be explained by the triangle shape of these
interfaces. If the conditions for HRTEM images are fulfilled no mass-thickness
contrast should be visible. This is partly fulfilled for the top part of Fig. 6.3a.
Another question is the correlation between the two different lattice structures.
Figure 6.4 shows a HRTEM images stitched together of four individual images. The
resulting dot shows well-ordered PbTe lattice planes with almost no lattice defects.
The right hand (110) interface of this dot was used for the interface characterisation
below (part 6.2.4). In particular, counts of the PbTe lattice planes showed that PbTe
and CdTe lattice fringes are well aligned and there are no discrepancies in the number
of lattice planes between the PbTe and CdTe, i.e. no dislocations.
6.2.2 Total energy calculations
Total energy calculations were carried out at the Institut für Festkörpertheorie und –
optik, Jena, Germany [42] in a collaboration funded by the Spezialforschungsbereich
IRoN of the FWF, Vienna. They applied density functional theory (DFT) in local-
(spin) density approximation (L(S)DA). The calculations were carried out with the
Vienna ab-initio simulation package (VASP). The interface energies and atomic
displacements were calculated using the repeated slab approximation. For the
construction of the slabs an averaged, theoretical lattice constant of 6.41 nm was used.
The slabs, i.e. 3d models of the interface structure, were constructed like the JEMS
crystal files. A continuous Te host matrix was assumed as a starting condition. This
matrix was filled up with a Cd fcc-sublattice displaced by (¼, ¼, ¼) for the CdTe part
and a Pb fcc-sublattice displaced by (½, ½, ½) for PbTe. This leads to the two
different {001} interface spacings. The total free energy for this slab system is smaller
than for {001} interfaces with a displaced Te matrix and equal interface separations.
The slabs should be large enough, electrostatic neutral and stoichiometric. The slab
system for the (111) interface consists of a multiple of tree bi-layers of PbTe and
CdTe respectively. The (001) interface slab consists of four layer (two neutral bi-
layer) CdTe and two neutral layer PbTe. For the (110) interface two neutral layers of

PbTe and CdTe, respectively, are combined. Ionic relaxation is allowed during the
calculation until the interatomic force falls below a pre-defined cut-off.
Displacements occur in two directions, perpendicular and parallel to the respective
interface. For {111} and {001} interfaces, only displacements perpendicular to the
interfaces were found. This is obvious for the polar {001} interface, which is
symmetric around the interface normal. The different terminations lead to different
atomic relaxation. The effects are stronger at the Cd terminated interface, where the
spacing is smaller. The {111} interface shows similar behaviour as the {001}
interface. The polar interfaces show a so-called rumpling effect for the PbTe, which is
also known for bulk PbTe surfaces [45].
The main finding of the {110} simulations is a displacement of the two crystal
halves against each other, i.e. a significant modification of the original starting
condition of a continuous Te matrix. The results lead to a displacement of the Te
matrix of about 0.04nm across the interface. Figure 6.5b shows the calculated atomic
displacement in comparison with the simple starting model in Fig.6.5a of a (110)
interface between bulk PbTe and CdTe with a continuous Te matrix. In Fig 6.5b the
atomic positions of the undisturbed model are indicated as black crosses. The clear
difference is the shift of the two crystal halves against each other. The differences of
Figure 6.5: (a) shows the projected model of the (110) interface, assuming a continuous
Te matrix. (b) shows the atomic positions after total energy minimisation. This model
results in a shift of the two crystal halves against each other of 0.04nm. The black crosses
mark the atomic positions of (a).
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58
the displacements along the [001] direction and the displacements along the [110]
direction are hardly visible in this picture. The detailed displacements are discussed in
part 6.2.4, where the calculated values are compared with the displacements extracted
from the HRTEM images. The calculated values are also used to construct a JEMS
model for HR map simulations. The results can also be found in part 6.2.4.
6.2.3 The (001) interface
Few is known about the interface between rs and zb crystals. Two important points
were interesting to be investigated at this interface. The first concerns the two
different kinds of interfaces depending on the interface termination. One interface is
determined by the substrate termination before PbTe growth. The opposite interface
above the PbTe SQW should have the other kind of termination, according to atomic
number conservation. It is not obvious that this is the behaviour of the real system, in
particular for annealed samples, where the PbTe crystal part is subjected to strong
shape transitions and the (001) interface between the PbTe and the CdTe capping
layer is newly built. The substrate termination could be destroyed and both (001)
interfaces could contain both kinds of termination. It would be also possible that one
kind of interface termination is preferred and the stoichiometry is fulfilled by excess
atoms being segregated and causing lattice defects. There is one study of a rs-zb (001)
interface in a ErAs(rs)/GaAs(zb) material system, where only one kind of termination
was treated[46]. As will be shown, both kinds of interfaces can be seen in our
experiments, which can be distinguish by the spacing at the interface. SQW and dots
show both interface kinds on the opposite (001) interfaces and no intermixing of the
termination occurs. Both interfaces, the one that is terminated during the MBE growth
and the one that is newly established during the annealing process, show a low defect
density. For the interpretation of the HRTEM images JEMS HR-maps were used.
PbTe and CdTe have different rotational symmetry around the interface normal which
complicates the correlation of the HRTEM image to a lattice structures.
The second point is the rumpling effect at the interface. The DFT calculation
predicted atomic displacements at the interface. This interface rumpling possibly
should also be seen in the HRTEM maps or at least the experiments should show that
there are not other, larger displacements.
(001) interface modelling for the HR-simulations
Both lattices, the rs and the zb lattice, consist of two face centred cubic ( fcc ) lattice
of which one in each lattice consists of Te atoms. We therefore assume for the first

simulation a continuous Te matrix. The two crystal halves are then filled up with the
respective other fcc lattice (Cd or Pb). The difference is only their displacement with
respect to the Te matrix. It is ( ½, ½, ½) for the PbTe rs structure and ( ¼, ¼, ¼) for
the CdTe zb lattice. As will be shown in Chapter 6, it was necessary for the (110)
interface to change the starting condition of a continuous Te matrix. As an average
lattice constant 0.6471 nm was used.
Figure 6.6: (a) Cd terminated CdTe/PbTe (001) interface; (b) Te terminated CdTe/PbTe
(001) interface. The two possible (001) interfaces lead to 4 different images for a
projection along the directions. If one looks along the [ 11
0]
direction the top two
Cd Atoms are in a row, for a view along [ 1 10]
the two atoms at the bottom are in a row.
The appearance of PbTe in the projection does not change under this rotation of 90°. The
used JEMS models have the same structure but are extended along the [001] direction on
the PbTe and CdTe side.
For the (110) interface this leads to only one model, but the polar (001) interfaces
can be either Te or Cd terminated, which leads to two different models (see Fig. 6.6).
Aside of that, the CdTe and the PbTe crystal halves have different rotational
symmetries around the [001] axis. CdTe has a 180° symmetry, PbTe has a 90°
rotational symmetry. This led to two different appearances of the polar interface under
a 90° rotation. These two different directions are not distinguished during the
preparation process and it is necessary to perform two simulations and to allocate this
direction in combination with the grow direction.
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60
Figure 6.7 shows the four different projections of the Cd and Te terminated
interface. The HR image simulation shows clear differences between the Cd and Te
terminated interfaces. A clear separation can be seen for the Te terminated interface
between the PbTe and the CdTe crystal halves. The orientation determines whether
the CdTe pattern starts with a single or double row of atoms. It is the same behaviour
for the Cd terminated interface, but the distance at the interface is smaller so that the
first CdTe pattern is connected to the PbTe.
Figure 6.7: The four possible appearances of the (001) interface. The projection shows
three unit cells of the JEMS models projected along the directions indicated in Fig. 6.6.
The HR images are simulated for the Scherzer defocus of -61nm and for t = 1.4 nm (7
(110) lattice planes for PbTe).
These four different patterns should be found in a HRTEM image. In an annealed
sample the CdTe substrate is connected with the CdTe capping layer and no phase
discontinuity should appear in the host material of the dots. Two different appearances
of opposite {001} interfaces are possible with the assumption that both kinds of
termination can be found at one dot on opposite {001} interfaces. Figure 6.8 shows
the HR simulation of two opposite (001) interface with respect to the crystal
orientation. Figure 6.8a is a combination of the Cd terminated interface with a
projection axis [ 11
0]
and the Te terminated interface with a projection axis [ 1 10]
with respect to Fig. 6.7. The other two interfaces of Fig.6.7 result in Fig. 6.8b.

Figure 6.8: HR simulation of the (001) interface of both crystal directions. Simulation
parameters: defocus -61nm, thickness 1.4 nm. (a) shows HR simulations of a Cd and Te
terminated (001) interfaces arranged how they should be found at opposite (001)
interfaces at a PbTe SQW or QD. (a) shows the same for a 90° rotated crystal orientation.
HRTEM images of the (001) interface
Figure 6.9 shows a HRTEM image recorded on a series #5, as-grown sample. It
was originally a 5 nm SQW, but it already started breaking apart. The layer thickness,
which can be seen in the left-hand image, is about 10nm and the SQW fragment is
terminated to the left with two {111} interfaces. The zoomed-in sections in this figure
show Fourier filtered images of the two (001) interfaces. The two images are recorded
at different specimen thickness due to the wedged shape of the specimen. There is
also some uncorrected astigmatism left, which can especially be seen in the bottom
section by the preferential direction of the CdTe lattice fringes. Nevertheless, the
section shows the different behaviour of the two kinds of termination. The section at
the top shows the interface created during the annealing step and has larger lattice
spacing. The PbTe and CdTe part are well separated. The section at the bottom shows
the Cd terminated interface, which was defined by growth. The interface spacing is
smaller and the nominal interface is not as clearly visible as for the Te termination.
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62
Figure 6.9: HRTEM image of an as-grown sample (series #5). Both (001) interfaces can
be seen in the image. This sample was Cd terminated before PbTe growth. The two
zoomed-in images show the Fourier-filtered interfaces. One can see the difference of the
two interfaces, especially at the interface pattern. This pattern depends on the interface
separation, which is determined by the kind of termination. The two patterns of bulk
PbTe and CdTe are better separated for the Te terminated interface where the larger
lattice spacing can be found.
Figure 6.10 shows this behaviour for two images from sample series #5. The two
interfaces were recorded at almost the same position and ideal defocusing condition at
a SWQ. The projected JEMS model of the two different kinds of (001) interfaces on
the left hand side of this figure shows the atomic position at the interface. The
terminations determine the lattice plane distances at the interfaces. The Cd terminated
interface shows a lattice plane spacing of ¼ of the lattice constant. The Te terminated
interface has a spacing of ½ a. The two different terminations can be easily
distinguished, because ¼ a = 0.16nm is below the practical resolution limit of the
microscope. The nominal interface sits in the middle of the ¼ a distance. Thus,
HRTEM images of a Cd terminated interface show dark areas across the nominal
interface. HRTEM images of the Te terminated interface show well separated lattice
fringes of bulk PbTe and CdTe at the interface.

Figure 6.10: The images on the right-hand side show two HRTEM images recorded at
ideal defocus condition along the [ 110]
zone axis. The images were taken on an as-
grown cross sectional specimen of sample #5. They were imaged at almost the same
position on the SQW. (a) shows the (001) interface with Cd termination. On the opposite
side a Te terminated interface is found (b). The MBE growth direction and the supposed
atomic positions are indicated. The left image shows the projected crystal structure with
indications of the interface terminations and the interface spacings. The simulation for
the interface can be seen in fig. 6.8b.
The atomic displacements at the interface are too small to be measured for a
comparison with the calculations. The total energy calculations find a displacement of
the Pb atom of the first lattice plane of PbTe near the interface in direction of the
PbTe, which is comparable to the so called rumpling effect [45]. This was a finding
for both kinds of termination. Additional to this rumpling effect, displacements are
found for the Cd terminated interface with the smaller interface spacing. All atoms of
CdTe are displaced slightly into the CdTe halve and the first PbTe lattice plane is
slightly changed into a zigzag chain like the neutral Cd-Te bi-layer. This can be
interpreted as the domination of the CdTe zb lattice at the Cd terminated interface.
Small variations of the PbTe lattice fringes can be seen in Fig. 6.10a, but this variation
is too small to be evaluated from the HRTEM image. As was shown in Chapter 4, the
PbTe HR image is strongly thickness dependent. The variation resulting from the
displacement can easily be mixed up with the strong thickness variations of the PbTe
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64
pattern. This is taken into account especially for the (001) interface because the
interface normal is parallel to the direction of increasing thickness of the specimen
wedge. Given that the Cd terminated interface can be seen as being dominated by the
zb-lattice, the Te terminated interface can be interpreted as being dominated by the
PbTe rs structure. The lattice spacing of this interface is ½ a, which is also the lattice
plane spacing of the PbTe lattice planes. HR simulations of this line of sight can be
seen in Fig. 6.8b, or in Appendix B, where HR maps can be found.
The (001) interfaces have two different appearances as shown in Figure 6.8. The
characteristics of the HRTEM lattice fringes of Figure 6.10 are well reproduced with
the HR-simulation of 6.8b. The single row of Te atoms can be seen in the top HR
simulation for the Te termination. This row is followed by a bright region parallel to
the interface representing the interface spacing. This bright, interconnected lattice
fringe parallel to the interface cannot be found at the Cd terminated interface. Figure
6.11 shows the two (001) interfaces recorded along a line-of-sight rotated by 90° with
respect to the HRTEM image of Figure 6.10. The fringes of these images can be
identified as the simulated images of Figure 6.8a. Further HR maps can be found in
Appendix B. The different terminations can again be seen easily by the lattice plane
separation at the interface.
Figure 6.11: The two (001) interface in a line of sight 90° rotated with respect to Figure
6.10. They were recorded on sample #11 at almost ideal defocus conditions at the dot
that can be seen in Figure 6.2. The respective HR simulations are shown in figure 6.8a, or
can be found in Appendix B.

6.2.4 The (110) interface
The main effect to be seen at a {110} interfaces is the shift of the two crystal
halves against each others. A shift of the lattice fringes occurs, if the thickness
changes (see eqn. 3.16). Thus it is important to know that the PbTe part and the CdTe
part of the specimen have the same thickness. Differently thick material regions could
be encountered, if the thinning process by Ar - ion sputtering is differently efficient
for CdTe and PbTe. But no indication for such behaviour can be found in the
specimens. The edge of the specimen is an almost continuous line. This is also the
case, if the edge cuts through a dot, which means that the sputtering rate is widely
independent for the two materials.
(110) interface modelling for the HR-simulations
The (110) interface is from the point of view of the model simpler than the (001)
interface. The (110) interface is a non-polar one and only one model is necessary (see
Fig. 6.12). Also, the rotational symmetry around [110] is the same for PbTe and
CdTe. This leads to only one possible projection of this interface. The interface was
constructed by putting together the (110) surfaces of CdTe and PbTe with a
continuous Te matrix. Fig 6.13 shows a HR simulation of this interface. Under this
Figure 6.12: Starting model of the (110) interface between PbTe and CdTe. The (110)
surface is non-polar for both materials and also the rotational symmetry around the
[ 11
0]
axis is the same. For this assumption of the interface the sp³ hybrid bond of a Cd
atom meets two p³ orbitals of a Te atom. Rearrangement of the bonds leads to atomic
displacements at the interface which were implemented in this model for the comparison
with the HRTEM images.
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66
assumption the sp³ hybrid bond of a Cd atom meets two p³ orbitals of a Te atom.
Rearrangement of the bonds lead to atomic displacements at the interface, which were
implemented in this model for the interpretation of the HRTEM images in Chapter 6
to reproduce the interface of the experiment.
Figure 6.13: Projection of the (110) interface model with a simulated HR pattern. The
simulation parameters are Δf = -61nm t = 1.8 nm which correspond to 9 (110)–lattice
planes of PbTe. The image shows a positive phase contrast and the atomic positions are
indicated. The assumption of a continuous Te matrix can be clearly seen in the
simulation by the continuous top edge of the dark PbTe rows into the CdTe part.
HRTEM images of the (110) interface
In Figure 6.14 two examples of (110) interfaces can be seen. Both images are
recorded at almost ideal defocus conditions. Image (a) shows a dot at the specimen
edge. The amorphous region is the adhesive from sample preparation. Image (b) was
recorded at the same dot which is shown in Figure 6.2. Both images show no mass-
thickness contrast or, in other words, the phase contrast dominates, which is an
indication that the specimen is thin enough. This is a precondition for a direct
correlation of the lattice fringes with the lattice structure. Especially in image (b) no
substantial change of the lattice fringes can be seen along the [001] direction, which
corresponds to increasing thickness of the specimen wedge. This is an indication of a
wedge with a small angle. The interface normal is perpendicular to the wedge. So, no

Figure 6.14: Two example of the (110) interface recorded with high magnification at
almost ideal defocusing condition. (a) is recorded on sample #30 at the edge of the
specimen wedge. The bright area is the adhesive of sample preparation showing the
pattern of an amorphous material. (b) is recorded on series #11. The interface is part of
the dot shown in Figure 6.2. This image was used for the construction of the JEMS
model. A Fourier filtered section of the interface can be seen in Figure 6.16.
change of the lattice fringes should occur along this direction. This allows a
straightforward interpretation of these images to measure the shift of the crystal
halves.
A straightforward comparison shows a phase shift of the PbTe lattice fringes with
respect to the CdTe lattice fringes. It was not possible to simulate this phase with the
continuous Te matrix model. A shift cannot occur with this model and comparisons
with HRTEM images show pattern discrepancies of the lattice fringes at the interface.
These discrepancies concern especially visible variations of the PbTe lattice fringes
near the nominal interface. It can be seen as alternating bends of the lattice fringes
along the [001] directions. This makes it necessary to adjust the JEMS model. The
first attempt was the use of the calculated atomic displacement from the total energy
calculation. Figure 6.15a and b shows examples of HR simulations and the projected
lattice structures of these two models. The second model leads to HR simulations,
which reproduce the shift of the crystal halves, but do not resemble the characteristics
of the lattice fringes near the interface. Differences can be seen especially for the
alternating bends of the PbTe lattice fringes near the interface.
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68
Figure 6.15: Examples of HR simulations calculated with different JEMS interface
structure models. (a) HR image of the model with the continuous Te matrix without
atomic displacements. Simulation parameter: Δf=-61 nm, t=0.9nm; (b) Model with the
theoretic atomic displacements of the total energy calculations. Δf=-60 nm, t=0.9nm; (c)
Model constructed with atomic displacements extracted from a HRTEM image. Δf=-60
nm, t=0.9nm;
Figure 6.16: Comparison of a HRTEM image (a) with a HR simulation (b). The used
model for the simulation contains atom displacements extracted from the HRTEM image.
The model reproduces the shift of the crystal halves and the characteristics of the lattice
fringes near the interface. The positions of the atomic species are indicated in the
simulated image. Simulation parameters: Δf=-60 nm, t=0.9nm.

Figure 6.15c and 6.16b show examples of HR simulations with the model which
resembles the real interface best. The approach for this new model was the correlation
of the HRTEM image to the crystal structure. A section of image 6.14b can be seen in
Figure 6.16a. The section is from the middle of the image to minimise the effects of
remaining lens aberration after microscope alignment. The image was also Fourier
filter to get rid of the noise and the mass-thickness contrast. The lattice fringes in both
crystal halves show a positive phase contrast and the patterns of the bulk material at
ideal defocus (Scherzer defocus). HRTEM images were recorded along the whole dot
interface with the same ideal defocusing conditions. The difference of {001}
interfaces regarding the termination and orientation allow a correlation of the lattice
structure and the HRTEM image. The knowledge that the substrate was Cd terminated
before PbTe growth allows the adaptation of the lattice structure. This is important,
because for a non-continuous Te matrix it is important to know which orientation the
Cd-Te dimer has with respect to the dark areas in the CdTe lattice fringes. In case of
Figure 6.16a the tellurium atom rows sit at the top and the Cd atom rows at the bottom
of the dark areas. All lattice fringe structures could be allocated to atomic positions of
the interface structure with the knowledge of the crystal orientation. This makes it
possible to measure the atomic positions in the HRTEM images. This was done with
the program Gatan DigitalMicrograph [41]. Arrays of 8x8 atom positions were
measured at the (110) interface of Figure 6.10b. For the PbTe lattice fringes each
single atom is resolved, thus simply the centre of the dark areas were assigned to the
atomic positions. For the CdTe lattice, where each dark area represents a Cd-Te
dimer, the dark area was fitted by two circles. Each centre of the fitted circles were
assigned to the atomic positions. As reference to the first JEMS model the last Cd-Te
dimer, which is furthest away from the interface, was used. Their displacement was
set to one halve of the 0.04 nm shift. With these values, a new model for the JEMS
simulation was constructed. The most important change to the first JEMS model was
the abandonment of the continuous Te matrix condition. The new model contains a
shift of the CdTe and PbTe crystal halves as predicted by the DFT calculation. A
simulated HRTEM image can be seen in figure 6.16b. The simulated image shows the
same features at the interface as the HRTEM image. The model with indicated shifts
can be seen Figure 6.17.
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70
Figure 6.17: Projection of the model constructed with the measured displacements. The
shift of 0.04 nm is clearly visible. The horizontal lines indicated the Te positions for a
continuous Te matrix; the dashed line indicates the nominal interface. The origin of the
difference in the HR simulation in comparison to the calculated values is the Te atom in
the first lattice plane parallel to the interface. It has almost no displacement.
The comparison of the calculated values and the measured ones can be seen in
image 6.18. The displacements are sorted with respect to atomic species and
displacement direction. The standard error of the mean of the measured atomic
displacements is in the range of ±0.002 nm to ±0.015 nm for the individual measured
values and is indicated as dashed black lines. The calculated displacements show good
agreement with the measured ones. One difference of the calculated and measured
displacements can be seen in the HR simulations and concerns the alternating bends
of the PbTe lattice fringes near the interface. This visible discrepancy concerns the
atom row along the [110] directions. In this row Cd and Te atoms are alternating. For
the theoretical values the displacements of Te and Pb show the same tendency. In the
simulated HR images these atomic rows show slight variations, but they seem to be
parallel. The measured values for the Te atom in the first lattice plane parallel to the
interface show almost no displacement, which leads to a bending of the rows with this
atom. In the HR simulation this appears as a pattern where the bending of the atomic
rows alter, depending on the atom species in the first PbTe lattice plane near the
interface. The variation along the Te-Pb chains in PbTe can be interpreted as
continuation of the zb structure into the rs structure. One electrostatically neutral
CdTe bi-layer, orientated along [ 110]
, can be described as a Cd-Te zigzag chain.
These chains are continued in the first few lattice planes in the PbTe part. The
theoretical values predict this behaviour, but the calculated displacements are too
small to be visible in the simulated image. The measured displacements show this
behaviour more pronounced. A comparison of the two HR simulation can be seen in

figure 6.15. This displacement can also be interpreted as a domination of the zb
structure at the interface.
This behaviour emphasises that the more important measurement is the comparison
of the simulated HR images with the HRTEM images and thus the used values of the
JEMS model construction. The atomic displacements, used for the JEMS model, are
the mean values of the measured displacements which are shown in Figure 6.18. The
best agreement can be found for the displacements parallel to the [001] direction. The
measured values for the Te and Pb atoms show exactly the same behaviour as the
calculated ones, except for the Te atom of the first PbTe lattice plane, as mentioned in
the previous section. Both, the calculated and measured shift of the two crystal halves
against each other are 0.04 nm. The maximum difference can be seen in the diagram
for the Cd and Te atoms, where the difference to a undisturbed lattice is 0.06 nm for
the calculated and 0.1 nm for the measured one. This is 10% change with respect to
the lattice constant for the calculations and even more for the measured values. The
calculated displacements parallel to the [001] direction for the Cd atoms describes
also the tendency of the measured ones.
The agreement of the displacements parallel to the [110] direction is also really good
for the tellurium atoms, but measurement accuracy is in the range of the largest
feature of the theoretic values, and one has to be careful with the interpretation. The
same is valid for the displacements parallel to [110] for the Cd and Pb atoms. The
calculations find a strong effect, where the atoms of every other lattice plane show a
large displacement away from the interface. This would lead to a pairing of Cd and Pb
atoms, respectively, for the CdTe and PbTe crystal halves. Each pair consists of a not-
displaced and a displaced atom. The measurement shows the behaviour of a common
displacement of the atoms, which decreases with increasing distance to the interface.
In the diagram for the displacements parallel to [110] for Pb and Cd the measured
values show the same tendency as the calculated ones, and represent the average value
of them. The measurements for the displacements parallel to [110] were more difficult
and less accurate, because the lattice plane spacing in this direction is near the
practical resolution limit of the microscope, and the dark disks of the lattice fringes
for PbTe overlap. The same is true for the CdTe lattice spacings parallel to the
interface, even though there is no overlap.
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Figure 6.18: Comparison of the displacements calculated by total energy calculation and
the measured displacements used for the JEMS HR-map simulation. The standard error
of the mean atomic displacements, evaluated from the HRTEM image, are indicated as
dashed black lines in the diagrams. The displacements are ordered with respect to
element and displacement direction. The gridline at zero on the abscissa indicates the
nominal interface. The displacement directions are indicated in the projected crystal
structures for each diagram. The agreement of the data is very good except for the
theoretical predicted rumpling effect for the displacement parallel to [110] for the Pb and
Cd atomic rows. But the measurement shows a mean value of the displacement with the
same shift away from the interface. The shift of the two crystal halves against each other
parallel to [001] can be seen best in the diagram for the Te displacements parallel to
[001].

6.2.5 The (111) interface
It is difficult to image the {111} interfaces. The reason is the triangular shape of
these facets. If this interface is parallel to the electron beam and is focused, the
projected length of the interface changes and makes it difficult to image this interface.
Aside of that, two neighbouring {110} interfaces of a small {111} interface can form
a direct intersection line above the {111} face. If one look along a {110} direction,
this intersection line next to the small {111} interfaces complicates the identification
of the {111} interfaces. This condition can be seen in Fig 4.12. Additionally, the
{111} interfaces of larger dots are the smallest ones and the chance that the interface
penetrates all through the specimen wedge is lower than for larger interfaces. The
penetration through the wedge is an important condition for recording high quality
HRTEM images. Therefore, the imaged {111} interfaces showed no clear interface
lattice fringes.
(111) interface modelling for the HR-simulations
As mentioned before, it was difficult to investigate the (111) interface by TEM due
to the dot geometry. Nevertheless, a model with this interface was used to visualise
the pattern of this interface. The model was constructed with the conditions for the
(001) and (110) interfaces and combines the three interfaces of the PbTe nanocrystals.
This model also shows the corners between the (001), (111) and (110) interfaces (see
Fig. 6.19). It was the largest model used. It consists of about 270 Atoms and was
programmed in MATLAB. The (111) interface is polar for PbTe and CdTe. The
rotational symmetry around a axis is the same for PbTe and CdTe, and one can
build up four different (111) interfaces between CdTe and PbTe under the condition
of atom number conservation. Two of these interfaces are sorted out, because the
bond lengths of the atoms at the interface are too large or small in comparison to bond
lengths in the bulk material and the other interface models. These two interfaces
consist of the same number of atoms like the others, thus the atom number is
conserved. This leads to a corner between the polar (001) interface and the neutral
(110) interface, which contains one of the (111) interfaces defined by the crystal
orientation and not by the (001) interface termination. The corners for both
terminations along the [ 110]
direction contain a (111) interface where the PbTe is Pb
terminated and the CdTe is Te terminated. For the (111) interface along the
[ 11
0]
direction the relations are vice versa. The main difference in the HR simulation
of these two (111) interface is whether the PbTe part is completed by the CdTe or the
PbTe lattice fringes.
73

74
Figure 6.19: Projection of the JEMS atomic model with all tree interfaces for both
terminations and projection axes. The simulations are done for Δf = -61nm t = 1.4 nm (7
(110) lattice planes). As can be seen, the termination of the (001) interface does not
determine the kind of (111) interface. The orientation of the Cd-Te dimer determines the
spacing of the (111) interface. The left image shows the model for the (111) interface
parallel to the [ 1 10]
direction. The right image shows the model for the (111) interface
parallel to the [ 11
0]
direction.
Figure 6.20 shows simulated HR-maps of this model. One can see the change from a
positive phase contrast (dark areas are correlated to atomic positions) to a negative
phase contrast (bright areas are correlated to atomic positions). Images for t = 1.4 nm
and Δf = -56 and -61 nm (Scherzer defocus) show a positive phase contrast. The
images for t = 5.5 nm and a Δf = -66 and -71 show a negative phase contrast. The
simulations in between show images where lattice fringes from different lattice planes
have different phase contrast. These images show strong variations in the appearance
of the pattern.

Figure 6.20: HR-map of the model containing the Te terminated (001) interface with the
projection axis [ 1 10]
with respect to fig. 6.7. The thicknesses of 1.4, 2.7, 4.1, 5.5 nm
correspond to 7, 14, 21, 28 (110)-lattice planes of PbTe. A direct, easy correlation to the
atomic structure is only possible for very thin samples near the Scherzer defocus of -
61nm.
HRTEM images of the (111) interface
The best HRTEM images of the (111) interface were obtained at the dot shown in
figure 6.4. It is know from the analysis of the (110) and (001) interfaces of this dot
that the images were recorded at almost ideal defocus, and that the specimen is thin
enough. This holds also for the images of the {111} interface. The images can be seen
in figure 6.21 and show two (111) interfaces to the left and right of a Te terminated
(001) interface. The interfaces should have the atomic structure as shown on the Te
75

76
terminated model for the [ 1 10]
projection direction (see figure 6.19). The lattice
fringes at the interface (seen in the zoom-ins of figure 6.21) show left and right of the
Te terminated interface the same behaviour. Characteristic is the dark pattern between
the PbTe and the CdTe pattern, which could be either part of the CdTe or PbTe crystal
halves. HR simulations, depicted in figure 6.19 in connection with the used model,
show that this interface behaves like the Cd terminated (001) interface, i.e. the
interface pattern is a mixture of the CdTe and PbTe lattice fringes. This cross-over is
the stair shaped dark area in the small images of figure 6.21 along the diagonals.
Similar patterns can be seen in the HR-map of figure 6.20. Assuming that the JEMS
model of this interface is correct, these differences with respect to the simulation can
only be understood if atomic displacements at this interface occur. Unfortunately,
these two HRTEM images are the only high quality (111) interfaces available, and no
images exist of the other kind with corresponding quality.
Figure 6.21: Two images of the (111) interface. The images were recorded at ideal
defocusing conditions at the dot shown in figure 6.2. The (001) interface between the two
interfaces is Te terminated. The two zoom-ins show a Fourier filtered version of the
interface and they show almost the same lattice fringes. The CdTe and PbTe parts are
indicated left and right of the stair-shaped pattern along diagonal of the small images.

Chapter 7
Conclusions and Outlook
Conclusions
The intense study of as-grown and annealed PbTe/CdTe heterostructures by TEM
reveals many features of this material system. Firstly, it was shown that the PbTe epi-
layer clad by CdTe transform into high quality PbTe QDs embedded in CdTe host
material. The origin of this process is the large solid phase miscibility gap and the QD
formation is driven by the minimisation of the total energy between PbTe and the
CdTe host material. The origin of the immiscibility is the different lattice structure of
the participating materials. Both materials have fcc lattice symmetry. CdTe possesses
zb-lattice structure and has a partly covalent chemical bonding. Each atom in this
crystal type has four next neighbours. The ionic crystal PbTe is of the rs-lattice type,
with six next neighbour surrounding each atom. Dark and bright field investigation of
several samples allowed the construction of the equilibrium shape. All QDs are
defined by {001}, {110} and {111} interfaces. The geometric shape assembled with
these interfaces is a cubo-octahedron. The shape is dependent on the QD size which is
a hint for the influence of the edge energies on the equilibrium shape. A system with
dominating interface energies forms an equilibrium shape, which is independent of
the dot size.
Results of these studies were size distributions of QDs precipitated from different
PbTe epi-layer. The upper size limit for formed QDs is strongly dependent on the
original layer thickness. Typical QDs, developed from a 5 nm epi-layer, are ~25 nm
large. The most common dot size found in an annealed 1nm PbTe layer
heterostructure is in the range of 7 to 10nm. The lower limit is nearly independent of
the original layer thickness. The smallest QDs found in all annealed specimens consist
of about 20 PbTe (002) lattice planes which correspond to a size of 4.6 nm. The
density of the dots depends on the size distribution and the material amount of the
77

78
original SQW. Typical dot densities are e.g. 3 10 11 cm -2 for an annealed 1nm epi-layer
or 6 10 10 cm -2 for an annealed 5nm epi-layer. The SQW thickness is well controllable
and thus allows the control of the size and density distribution.
The HRTEM interface studies, combined with multi-slice HR simulation, highlight
the strong rebonding effects at the CdTe/PbTe interfaces. The {001} PbTe/CdTe
consist of the non-polar PbTe {001} face and the polar {001} faces of CdTe which
can be Cd or Te terminated. This leads to two possible {001} interfaces. The HRTEM
investigations reveal the formation of both interface kinds on opposite {001}
PbTe/CdTe interfaces. One (001) interface of the PbTe QW is terminated during MBE
growth and allow the control of the position of the two kinds of the {001} interfaces.
The main difference of these two interfaces is the lattice plane spacing at the nominal
interface. This distance is a/2 for the Te terminated interface which corresponds to the
lattice plane spacing of the parallel (002) PbTe lattice planes. The Cd terminated
interface has an interface spacing of a/4, the lattice plane spacing of the (004) CdTe
lattice planes. The PbTe crystal halves of both interfaces show a rumpling effect
comparable to free PbTe surfaces. This feature is small for the Te terminated
interface, where practically no other displacements effects occur. The rumpling is
pronounced at the Cd terminated interface and additionally strong displacements can
be found in the CdTe crystal halve of this (001) interface. These displacements allow
the Cd atoms again a fourfold coordinated binding configuration at the interface. This
behaviour allows the classification of the Te terminated interfaces as rs lattice
dominated and the Cd terminated as zb lattice dominated. The displacements are
findings of the ab-initio calculations by R. Leitsman. The two kinds of the (001)
interfaces can be easily distinguished with the TEM and also strong indications of the
displacements can be found.
The {110} interface can also be seen as zb-lattice determined. The strong effects at
this interface also lead to a better fourfold coordinated bonding configuration of the
interfaces near CdTe components. This reconfiguration ends up in a shift of the CdTe
and PbTe crystal halves against each other of 0.04nm. The Cd-Te chains of the zb
lattice are continued in the PbTe part and result in atomic displacements of Pb and Te
atoms in addition to the shift of the crystal halves. The displacements evaluated by
HRTEM were compared with the atomic positions evaluated by the ab-initio
calculations. Both methods reveal the same feature of the CdTe/PbTe interfaces and
also the absolute values of the atomic displacements agree very well. The main effect
of the displacements is again a better fulfilment of the four fold coordination of the
atomic bonds in the zb-lattice near the interface.

Figure 7.1: (a) QDs interfaces stitched together from several HRTEM images. All
interfaces are clearly visible and the main features are indicated. (b) shows a HR
Simulation and (c) shows the according crystal model of a small QD. The orientation and
the (001) terminations of the small dot correspond to the large one.
The {111} face is a polar one for both materials, which results in four possible
{111} interfaces. Two of them contain bondlengths, which are not realistic and no
indications of these two excluded interfaces can be found in the HRTEM images. The
79

80
other two show the same characteristic as the two {001} interfaces. The {111}
interface is difficult to image with the TEM, thus only one kind could identify by
HRTEM images at the right position at the PbTe QD. This is a strong indication that
the former consideration made about the {111} interface is correct and describes the
behaviour of these interface class. A summary of the feature of the QD interfaces can
be seen in Fig.7.1.
Outlook
The {111} interfaces of PbTe QDs are hardly accessible for TEM investigations,
because their triangular shape hamper correct imaging. A possible method for an
accurate characterisation of this interface class would be cross-sectional TEM on
SQWs grown on (111) CdTe substrate with continuous {111} CdTe/PbTe interfaces.
Also these SQWs should have two different kinds of {111} interfaces determined by
the substrate termination as it is the case for the SQWs grown on (001) substrate.
As the investigated samples of this thesis are optimally annealed for PL
measurements and not for obtaining the ideal annealing conditions, further annealing
studies of various samples with different epi-layer thicknesses would be necessary.
An interesting, open question is also the diffusion of the compounds in the bulk CdTe
or PbTe. There are no studies about the diffusion velocity of Pb in CdTe and only one
study of the diffusion velocity of Cd in PbTe [47], which was done without the
knowledge that PbTe forms QDs embedded in CdTe. The knowledge of the exact
diffusions processes would give a deeper insight in the QDs formation processes
during the annealing step and would allow a better controllability of the size and
density distribution.
Another attempt of QD production in the CdTe/PbTe material system was the
implantation of Pb ions into bulk (111) CdTe or CdTe grown on (111) GaAs
substrate. The implantation was done at an acceleration voltage of 200keV with
different doses (10 15 cm -2 , 10 16 cm -2 ) of Pb ions. The high acceleration voltage and the
heavy Pb ions result in an amorphisation of the CdTe bulk material. After an
annealing step and recrystallisation of the CdTe, PbTe QDs can be found. The QDs
show a broad size distribution. The found dots also show the three interfaces of the
epitaxial fabricated QDs but they have more imperfections. An interesting question of
this fabrication method is the controllability of the size and density distribution and
also the in-depth location of the QDs as a function of the dose and the acceleration
voltage. The stoichiometry is not fulfilled in this system. The excess Cd atoms must

segregate at the surface, build lattice defects or could change the Te-terminated
interfaces to Cd-terminated ones. But this would lead to QDs containing a dipole.
Further investigation of this system could give a deeper understanding of these
processes. An example of PbTe QDs, fabricated by ion implantation can be seen in
Fig. 7.2.
Figure 7.2: (a) PbTe dots in CdTe matrix produced by Pb ions implanting in bulk (111)
CdTe with 200keV and a dose of 10 16 cm -2 . The size of the QDs is distributed from about
25nm to 5nm. (b) shows a small QD from a sample with 10 15 cm -2 implanted Pb ions.
The QDs show more imperfection than the epitaxial grown ones.
The goal of all these investigation is of course an application of the QDs produced
by lattice type mismatch. Semiconductor laser in the mid infrared frequency range
would open the possibility of modern molecule spectroscopy for e.g. medical
diagnosis. The CdTe/PbTe material system grown on GaAs substrate is not suitable
for laser application, because the refractive index of CdTe is smaller than the
refractive index of GaAs. This would lead to a deflection of emitted light into the
GaAs substrate. A solution of this problem could be the use of HgxCd1-xTe as bulk
material. The refractive index of this ternary alloy is near four and is larger than the
refractive index of GaAs. HgTe is like CdTe zb structure and has also almost the same
lattice constant as PbTe. But Hg is a really difficult and highly toxic material for
utilisation in a MBE system. The approach of the lattice type mismatch QDs is also
available for other material systems. One example of another material system, which
was investigated, is ErAs on GaAs, mentioned in the introduction. However, ErAs is
not a semiconductor but a semi-metal. Another interesting material is BaF2. BaF2 is
fluorite structure, a cubic lattice structure, and has also a lattice constant near the
lattice constant of PbTe and CdTe. Therefore also the material combinations of
BaF2/PbTe or CdTe/BaF2 would be an interesting attempt for investigation. As the
refractive index of BaF2 is small (n=~1.4, for the mid infrared frequency range), it is
also a substrate candidate of CdTe/PbTe structures.
81

82
Appendix A
Structure factors of CdTe and PbTe
CdTe and PbTe can be described by a cubic unit cell. CdTe has zinc blend structure,
PbTe has rock salt structure. Both materials can be described by a face centred cubic
(fcc) unit cell with different basis. That why we first treat the structure factor of a
simple fcc lattice. A detailed description can be found in [32].
The expression for Fhkl, the structure factor for the (hkl) spot is given by:
The fi is the atomic form factor, given by the differential cross section of the atoms.
The coordinates xi, yi and zi describe the atomic positions in the unit cell. For the fcc
lattice these positions are given by ( 0, 0, 0), ( ½, ½, 0), ( ½, 0, ½) and ( 0, ½, ½). This
lead to the structure factor of the fcc lattice:
If h, k, l are all even or all odd all three e-function are one. If the values of h, k, l are
mixed even and odd, two of the e-functions are -1. This lead to following structure
factors:
hkl
• h, k, l are all even or all odd →
• h, k, l are mixed even and odd →
F
fcc
F
=
∑
i
f
2πi
ie
F
F
( hx + ky + lz )
πi(
h+
k { ) πi(
h+
l)
πi(
k+
l
=
f 1+
e + e + e
) }
i
= 4f
i
= 0
i
(3.26)
(3.27)

A1 CdTe structure factor
CdTe has zinc blend structure. This can be described by a fcc lattice with a two-atom
base and a base vector of ( ¼, ¼, ¼ ). In the origin sits a tellurium atom, at the end of
the base vector a cadmium atom. fTe and fCd describe the atomic form factor of the
atom species. The structure factor becomes:
This leads to the following rules:
• h, k, l are mixed even and odd →
• h, k, l are all odd →
• h, k, l are all even, h+k+l=2N, N is odd →
F
F
F
• h, k, l are all even, h+k+l=2N, N is even F →
A2 PbTe structure factor
= 0
= 4(fTe±ifCd)
= 4(fTe-fCd)
= 4(fTe+fCd)
PbTe has rock salt structure. This can be described by a fcc lattice with a two-atom
base and a base vector of ( ½, ½, ½ ). The base consists of a Pb-Te dimer. The atomic
form factors are again given by fPb and fTe. The structure factor becomes:
The selection rules are given by:
• h, k, l are all even →
• h, k, l are all odd →
• h, k, l are mixed →
F =
⎧
⎨f
Te + f Cde
⎩
F
F
F
π
2
= 4(fTe+fPb)
= 4(fTe-fPb)
= 0
( h+
k+
l)
⎫
⎬F
⎭
fcc
π { ( h+
k+
l
F =
f
)
Te + fPbe
} Ffcc
83
(3.28)
(3.29)

84
Appendix B
Simulated HR-maps of CdTe/PbTe interfaces
B1 The (001) interface
The four HR-maps (Figure B2 to B5) are for the two different terminations of the
CdTe crystal halve and the two different projections along a zone axes. The
crystal orientation indication relates to figure B1.
Figure B1: The (001) lattice plane through the origin represents the Te termination. The
first (001) lattice plane filled with Cd near the origin represents the Cd termination.

Figure B2: HR-map for the Te terminated (001) interface along the [ 1 10]
direction.
Figure B3: HR-map for the Cd terminated (001) interface along the [ 1 10]
direction.
85

86
Figure B4: HR-map for the Te terminated (001) interface along the [ 1 10]
direction.
Figure B5: HR-map for the Cd terminated (001) interface along the [ 1 10]
direction.

B2 The (110) interface
The tree HR-maps show simulations of the tree used models. Figure B6 is the HR-
map of the JEMS model with the continuous Te matrix. Figure B7 shows the HR-map
of the model constructed with the displacements calculated by DFT. Figure B8 shows
the HR-maps constructed with the displacements extracted from HRTEM images.
Figure B6: HR-map of the (110) interface model with the continuous Te matrix.
87

88
Figure B7: HR-map of the (110) interface model with the calculated displacements.

Figure B8: HR-map of the (110) interface model with measured displacements.
89

90
B3 The (111) interface
For the sake of completeness a HR-map of a (111) interface is shown. Only one kind
of the two different (111) interface was images with the TEM. The HR-map (see
figure B9) is the corresponding simulation to Figure 6.15, shown in chapter 6. The
used JEMS model was the model containing all tree interfaces and the corner between
these interfaces.
Figure B9: HR-map of the (111) interface model with the Te terminated (001) interface
for a projection direction along the [ 1 10]
direction.

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Curriculum Vitae
1 March 1979 born in Linz
Sept. 1985 - July 1989 Primary school in Unterweitersdorf
Sept 1989 - July 1993 Secondary school in Gallneukirchen
Sept. 1993 - July 1998 LiTec in Linz (Secondary Technical and
95
Vocational College), branch of study: mechanical
engineering, Matura (general qualification for
university entrance) July 1998
Oct. 1998 - Oct. 1999 Civilian service at the Lebenshilfe OÖ
(association for mental- and multi-handicapped
people)
Since Oct. 1999 Study of Technical Physics at the Johannes
Kepler University, Linz
Sept. 2004 - Feb. 2005 Study of Physics at the University of Groningen,
Netherlands
Since Aug. 2005 Diploma Thesis for Technical Physics at
the Institute of Semiconductor Physics,
Johannes Kepler Universität, Linz,
Univ. Prof. Dr. Friedrich Schäffler

96
List of Publications
“Centrosymmetric PbTe/CdTe quantum dots coherently embedded by epitaxial precipitation”
W. Heiss, H. Groiss, E. Kaufmann, G. Hesser, M. Böberl, G. Springholz, F. Schäffler,
K. Koike, H. Harada, M. Yano
Appl. Phys. Lett. 88, 192109 (2006)
“The coherent {100} and {110} interfaces between rocksalt-PbTe and zincblende-CdTe”
H. Groiss, W. Heiss, F. Schäffler, R. Leitsmann, F. Bechstedt, K. Koike, H. Harada, M. Yano
Submitted to JCG Proceedings for 14th International Conference on Molecular Beam Epitaxy,
MBE 2006, September3-8 2006, Tokyo, Japan
“Quantum dots with coherent interfaces between rocksalt-PbTe and zincblende-CdTe”
W. Heiss, H. Groiss, E. Kaufmann, G. Hesser, M. Böberl, G. Springholz, F. Schäffler,
R. Leitsmann, F. Bechstedt, K. Koike, H. Harada, M. Yano
Submitted to AIG Proceedings for 28th International Conference on the Physics of
Semiconductors, ICPS 2006, July 24-28 2006, Vienna, Austria
“Photoluminescence Characterization of PbTe/CdTe Quantum Dots Grown by Lattice-Type
Mismatched Epitaxy”
K. Koike, H. Harada, T. Itakura, M. Yano, W. Heiss, H. Groiss, E. Kaufmann, G. Hesser,
M. Böberl, G. Springholz, F. Schäffler
Submitted to JCG Proceedings for 14th International Conference on Molecular Beam Epitaxy,
MBE 2006, September3-8 2006, Tokyo, Japan
“Rebonding at coherent interfaces between rocksalt-PbTe/zinc-blende-CdTe”
R. Leitsmann, L. E. Ramos, F. Bechstedt, H. Groiss, F. Schäffler, W. Heiss, K. Koike,
H. Harada, M. Yano
Submitted to New Journal of Physics

Contributed talks:
“The coherent {100} and {110} interfaces between rocksalt-PbTe and zincblende-CdTe”
H. Groiss, W. Heiss, F. Schäffler, R. Leitsmann, F. Bechstedt, K. Koike, H. Harada, M. Yano
14th International Conference on Molecular Beam Epitaxy, MBE 2006, September3-8 2006,
Tokyo, Japan
Invited talks:
“Quantum dots with coherent interfaces between rocksalt-PbTe and zincblende-CdTe”
W. Heiss, H. Groiss, E. Kaufmann, G. Hesser, M. Böberl, G. Springholz, F. Schäffler,
R. Leitsmann, F. Bechstedt, K. Koike, H. Harada, M. Yano
28th International Conference on the Physics of Semiconductors, ICPS 2006,
July 24-28 2006, Vienna, Austria
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Acknowledgement
I would like to thank those who supported me during my diploma thesis and thus contributed
to the successful completion of this work.
Especially I would like to thank:
The group of Prof. Ph.D. M. Yano at Osaka institute of technology, especially
Ph.D. K. Koike, for the supply of excellent samples and valuable discussions during our
meeting at the MBE2006 conference in Tokyo;
DI G. Hesser, for carrying out excellent sample preparation, giving me a detailed
introduction into the TEM and a amicable support during my work at the TEM;
DI R. Leitsmann and Prof. Dr. F. Bechstedt for the ab-inito calculations and interesting
discussion about the PbTe/CdTe QDs project;
Prof. Dr F. Schäffler for giving me the great opportunity of this diploma thesis, the scientific
support and the suggestions for my diploma thesis;
All member of the institute working on the PbTe/CdTe project, especially Prof. Dr. W. Heiss
and DI E. Kaufmann for helpful support and valuable discussion;
Prof. Dr. G. Bauer for the possibility to write my diploma thesis at the Institute of
Semiconductor Physics;
DI D. Pachinger and Dr. H. Lichtenberger for the introduction and support concerning the
TEM;
DI M. Ratajski for the good cooperation at the TEM within the Department for Technical
Support;

All member of the institute for the friendly atmosphere, especially the members of the office
for the help at all problems concerning the diploma thesis and the creative working
atmosphere;
My parents Gertrud and Franz Groiss for financial support and general support all the years
of my studies and also my brother Stefan for his support;
The PbTe/CdTe project is part of the SFB 25 IR-ON. I would like to thank the Fond zur
Förderung der Wissenschaftlichen Forschung (Austria) for their financial support.
I would like to thank the Marubun Research Promotion Foundation for the travel grant for
the MBE2006 conference in Tokyo, Japan.
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