Kinetic and Strain-Induced Self-Organization of SiGe ...

J O H A N N E S K E P L E R
U N I V E R S I T Ä T L I N Z
N e t z w e r k f ü r F o r s c h u n g , L e h r e u n d P r a x i s
Kinetic and Strain-Induced Self-Organization of SiGe
Heterostructures
Dissertation
zur Erlangung des akademischen Grades
Doktor der Technischen Wissenschaften
Angefertigt am Institut für Halbleiterphysik
Betreuung:
Univ. Prof. Dr. Friedrich Schäffler
Eingereicht von:
DI Herbert Lichtenberger
Gutachter:
1. Univ. Prof. Dr. Friedrich Schäffler
2. Dr. Detlev Grützmacher
Linz, August 2006
Johannes Kepler Universität
A-4040 Linz · Altenbergerstraße 69 · Internet: http://www.jku.at · DVR 0093696

Preface
Eidesstattliche Erklärung
Ich erkläre an Eides statt, dass ich die vorliegende Doktorarbeit selbstständig 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
Herbert Lichtenberger

ii PREFACE
Kurzfassung
Eine kinetische Wachstumsinstabilität in der Silizium-Germanium Molekularstrahlepitaxie
(SiGe-MBE) wurde dazu verwendet, Si-Substrate mit periodisch modulierter Oberflächen-
struktur zu erzeugen. Diese kinetische ”Step-Bunching” Instabilität führt für die verwendeten
vizinalen Si(001) Substrate mit 4 ◦ Verkippung entlang [110] zu einer Welligkeit mit einer
Periode von ungefähr 100 nm und einer Amplitude von etwa 4 nm.
Im ersten Teil dieser Arbeit werden Aspekte selbstorganisierten Wachstums im Si/SiGe
System behandelt. Die spezielle ”Step-Bunching”-Oberflächenstruktur wurde benutzt, um
das Zusammenspiel zwischen Kinetik, Oberflächenenergie und Verspannung zu untersuchen.
Diese ”Step-Bunching”-Morphologie ist eine ein-dimensionale Oberflächenstruktur, die be-
vorzugte Keimzentren für SiGe-Inseln entlang der asymmetrischen Wellenflanken bietet. Dies
ermöglicht uns, kinetische und Verspannungs-induzierte Selbstorganisations-Phänomene im
Si/SiGe Heterosystem zu kombinieren. Bei gemäßigten Wachstumstemperaturen um 425 ◦ C
wurden Verspannungs-induzierte Hügelketten beobachtet, die die Flanken senkrecht zur ”Step-
Bunching”-Struktur dekorieren. Die gesamte sich ergebende Morphologie wird dann nur
von (001)-orientierten Oberflächen und {105}-Facetten gebildet. Diese {105}-facettierten
Hügelketten sind anscheinend energetisch bevorzugt und zeigen sich geometriebedingt an
geneigten Substratflächen, deren Ausrichtung in etwa der einer {1 1 10}-Ebene entspricht.
Diese Strukturen weisen eine relativ gute Ordnung auf, die gänzlich auf Selbstorganisati-
on beruht. Derartige morphologische Strukturen bilden die Basis für das Verständnis des
Ge-Insel Keimbildungsmechanismus auf zwei-dimensional vorstrukturierten Si-Substraten.
Im zweiten Teil werden Magneto-Transport Messungen an p-modulationsdotierten Si/SiGe
Heterostrukturen diskutiert, die auf ”Step-Bunching” Si-Puffer gewachsen wurden. Die kurz-
periodische Oberflächenstruktur des Si-Puffers führt zu einer wohldefinierten Modulation im
SiGe-Kanal, was die Anzahl der Streuprozesse im p-dotiertem Quanten-Topf (p-MODQW)
steigern müsste. Daraus resultiert eine Asymmetrie in der Ladungsträgerbeweglichkeit senk-
recht und parallel zur wellenartigen Modulation des elektrisch leitfähigen Kanals, die dazu
beitragen könnte, die verschiedenen Streumechanismen, insbesondere Legierungs- und Grenz-
flächenrauhigkeitsstreuung, zu unterscheiden. Obwohl erst wenige Messungen hierfür durch-
geführt wurden, zeigen erste Ergebnisse eine verminderte Tief-Temperatur Beweglichkeit quer
zur Oberflächenmodulation, und zwar um einen nennenswerten Faktor zwei. Weitere die-
ser Messungen in Kombination mit zusätzlicher Modellierung könnten einen neuen Zugang
eröffnen, um die lang anhaltende Debatte beizulegen und den Mechanismus zu eruieren, der
die Ladungsträgerbeweglichkeit der Löcher in p-MODQW Strukturen limitiert.

PREFACE iii
Abstract
A kinetic growth instability of silicon-germanium molecular beam epitaxy (SiGe-MBE) was
used to generate periodic Si-ripple-templates. By increasing the substrate miscut to 4 ◦ the
ripple period could be tuned to smaller periods towards the nanometer scale. At Si growth
rates of 0.2 ˚A/s a ripple pattern with few defects develops within a small temperature window
around 425 ◦ C. For our vicinal Si(001) substrates with 4 ◦ miscut along [110] this step-bunching
instability provides undulations of about 100 nm periodicity and 4 nm amplitude.
In the first part of this work several aspects of self-organized growth in the Si/SiGe system
could be addressed. The special morphology of step-bunching was used to investigate the
interplay between kinetics, surface energy and strain. The step-bunching templates provide
a one-dimensional pattern with preferable nucleation sites for SiGe-islands along the ripple
flanks, and thus allow us to combine kinetic and strain-driven self-organization phenomena
in the Si/SiGe heterosystem. At moderate temperatures around 425 ◦ C strain-driven ridges,
which decorate the ripple flanks perpendicular to the step bunches, were observed. The
whole morphology is only made up with (001)-surfaces and {105}-facets. These {105}-faceted
ridges appear to be energetically preferable for geometrical reasons at slopes, which are close
to {1 1 10}-planes. These structures show a fair degree of ordering entirely based on self-
organization. Furthermore, such morphological features are the basis for understanding the
mechanism of Ge-dot nucleation on 2D pit-patterned Si-templates.
In the second part magnetotransport measurements on p-modulation doped Si/SiGe het-
erostructures grown on top of a step-bunched Si-buffer are discussed. The short-scale peri-
odic height fluctuations of the Si-buffer form well-defined undulations in the SiGe-channel.
This should increase scattering in the remotely p-doped quantum well (p-MODQW). Thus
an asymmetry in mobility perpendicular and parallel to the undulations is expected, which
might help to uncouple the different scattering mechanisms. These, namely alloy scattering
and interface-roughness related scattering, are conversely discussed as predominant hole-
mobility limiting factors for p-modulation doped structures. Although still at the beginning,
the first measurements confirm a decreased low-temperature mobility across the undulations
by a remarkable factor of two. Further measurements combined with additional modeling
are expected to provide a new approach toward settling the long-lasting dispute on the hole-
mobility-limiting scattering mechanisms in p-MODQW structures.

iv PREFACE

Contents
Preface i
Eidesstattliche Erklärung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Kurzfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
I Basics 1
1 Silicon-Germanium Material System 3
1.1 Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.1 Crystal Orientation and Miller Indices . . . . . . . . . . . . . . . . . . 5
1.2 Vicinal Si(001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Step Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.2 Step Types in Different Miscut Angle Regimes . . . . . . . . . . . . . 8
1.3 Electronic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Silicon Germanium Alloys (Si1−xGex) . . . . . . . . . . . . . . . . . . . . . . 12
1.4.1 Bandstructure of SiGe-Heterostructures . . . . . . . . . . . . . . . . . 12
2 Molecular Beam Epitaxy (MBE) 15
2.1 MBE-Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Fundamentals and Prerequisites . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 Physical Processes in the Growth-Chamber . . . . . . . . . . . . . . . 17
v

vi CONTENTS
2.1.3 Growth-Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.4 Heteroepitaxy versus Homoepitaxy . . . . . . . . . . . . . . . . . . . 20
2.1.5 Relevant Temperatures in MBE . . . . . . . . . . . . . . . . . . . . . 21
2.2 Cleaning Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Pre-Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 RCA-Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.3 HF-Dip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.4 Oxide-Desorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 MBE-System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1 Vacuum System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.2 Evaporation and Rate Measurement . . . . . . . . . . . . . . . . . . . 26
2.3.3 Heating and Temperature Measurement . . . . . . . . . . . . . . . . . 26
2.3.4 Controlling and Monitoring . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Methods of Investigation 29
3.1 Transmission Electron Microscopy (TEM) . . . . . . . . . . . . . . . . . . . . 30
3.2 Scanning Electron Microscopy (SEM) . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Atomic Force Microscopy (AFM) . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 Scanning Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.2 AFM-Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.3 Imaging Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.4 Data Types and Data Representation . . . . . . . . . . . . . . . . . . 36
II Main Research 41
4 Self-Organized Growth – Step-Bunching 43
4.1 Introduction to Step-Bunching . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1.1 Dependence on Temperature, Rate, Thickness, Ge-content and Miscut 45
4.1.2 Kinetic vs. Strain-Induced Step-Bunching . . . . . . . . . . . . . . . . 47
4.2 Optimization of Step-Bunching for Ripple-Patterns . . . . . . . . . . . . . . . 48

CONTENTS vii
5 Self-Organized Growth 2 – Kinetics and Strain 55
5.1 Introduction to State-of-the-Art Ge-Dots . . . . . . . . . . . . . . . . . . . . . 55
5.2 Kinetic Step-Bunching and Strain-Driven Island Growth . . . . . . . . . . . . 57
5.2.1 Influence of Ripple-Template Annealing . . . . . . . . . . . . . . . . . 57
5.2.2 SiGe-Overgrowth of Step-Bunching Template – Strain-Effects . . . . . 57
5.3 Ordering and Size of SiGe-Islands . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.4 Closer Look on Surface Energy Effects – Facetting . . . . . . . . . . . . . . . 70
5.4.1 Surface Energy Minimization via Excessive Facetting . . . . . . . . . . 77
5.4.2 Step-Bunching Templates for p-Modulation Doped SiGe-Structures . . 83
6 p-Modulation Doping and Mobility Analysis 85
6.1 Introduction to p-Modulation Doping . . . . . . . . . . . . . . . . . . . . . . 86
6.2 Experimental Aspects and Mobility Analysis . . . . . . . . . . . . . . . . . . 90
6.2.1 Processing of Hall-Bars . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2.2 Cryo-Measurements and Data Evaluation . . . . . . . . . . . . . . . . 93
6.2.3 Data Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3 Outlook and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
III Additional Work 113
7 Transient-Enhanced Si Diffusion 115
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.2 Template Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.4 Detailed Characterization and Discussion . . . . . . . . . . . . . . . . . . . . 121
8 Germanium Source Reconstruction 125
A Calibration and Characterization of Sources 133
A.1 Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.2 Photoluminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

viii CONTENTS
B General Physical Data 145
B.1 Stereographic Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.2 Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Bibliography 147
Postface 159
Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Part I
Basics
1

Chapter 1
Silicon-Germanium Material
System
Within this chapter some basic facts of the SiGe-material system are covered which are
essential for the understanding of the present work. This introductory part is reassembled
from the diploma-thesis [1] and based on standard text books [2] and data collection volumes
[3, 4, 5]. To get a more detailed insight into SiGe-heterostructures and for further reading
overview articles such as Ref. [6, 7] may be considered valuable.
The beginning of semiconductor studies reaches back to the early nineteenth century. One
of the most studied elemental semiconductors, that are composed of single species of atoms,
is silicon (Si). Like germanium (Ge) and carbon (C), silicon can be found in column IV of
the periodic table.
Prior to the invention of the bipolar transistor in 1947, semiconductors have been used only
as two-terminal devices, such as rectifiers and photodiodes. In the 1950s germanium has been
the most used semiconductor material. But due to various disadvantages of germanium, such
as high leakage currents at moderately elevated temperatures, and its water soluble germa-
nium oxide, germanium has widely been substituted by silicon in the 1960s.
There are several convincing reasons for the use of Si. Silicon offers – compared with ger-
manium – much lower leakage currents and a stable natural oxide. Thermally grown silicon
dioxide can be achieved with high quality. Another reason is that device-grade silicon is much
cheaper than any other semiconductor material. Silicon in the form of silica and silicates is
next to oxygen the most widespread element in the earth crust.
Many of the compound semiconductors have electrical and optical properties that surpass the
properties of silicon or are even absent in silicon. These semiconductors, especially gallium ar-
3

4 CHAPTER 1. SILICON-GERMANIUM MATERIAL SYSTEM
senide (GaAs) and heterostructures based on it, are used mainly for microwave and photonic
applications. Nevertheless silicon is one of the most investigated elements in the periodic
table and the whole silicon technology is by far the most advanced among all semiconductor
technologies. [2]
1.1 Structural Properties
Silicon and germanium crystallize in a diamond lattice structure. This structure belongs to
the cubic-crystal family and can be seen as two interpenetrating fcc sublattices with one sub-
lattice displaced from the other by one quarter of the distance along the diagonal of the cube
(i.e. a displacement of √ 3/4 along [111]). In a diamond lattice all atoms are identical, and
each atom in the diamond lattice is surrounded by four equidistant nearest neighbors that
lie at the corners of a tetrahedron (see Fig. 1.1, refer to the spheres connected with darkened
bars [2]).
In a hard sphere model only 34% of the available space is filled, and therefore the diamond
lattice structure is not very compact. Si and Ge have, like any other group IV element,
four electrons in the outer orbit, and each atom shares these valence electrons with its four
neighbors. This sharing of electrons is called covalent bonding and occurs between atoms of
either the same element or between atoms of different elements that have similar outer-shell
electron configurations (in our case: Si, Ge, C). [2].
Figure 1.1: Diamond lattice structure of Si and Ge [2].
� Source: SiGe crystalstructure.jpg

1.1. STRUCTURAL PROPERTIES 5
Figure 1.2: Schematical picture of a (211)-crystal plane [2].
� Source: SiGe crystalplane.jpg
1.1.1 Crystal Orientation and Miller Indices
The usual method of defining the different crystal planes is to use Miller indices. This is
achieved in the following way, demonstrated with an example: As one can see in Fig. 1.2
[2] the depicted plane intercepts the Cartesian coordinates (x, y, z) at a, 2a, 2a. Taking
the reciprocals of the intercepting numbers (in terms of the lattice constant) yields 1, 1 1
2 , 2 .
Multiplying with 2 gives the smallest three integers and the plane is written in Miller indices
notation as (211)-plane.
Some conventions for the Miller indices notation are:
(hkl) : For the plane that intercepts the x-axis on the negative side of the origin, such as
(100), (110).
Figure 1.3: Miller indices of most important planes in a cubic crystal [2].
� Source: SiGe Miller-indices.jpg

6 CHAPTER 1. SILICON-GERMANIUM MATERIAL SYSTEM
{hkl} : For planes of equivalent symmetry – such as {100} stands for (100), (010), (001),
(100), (010), (001) in cubic symmetry.
[hkl] : For a crystal direction, such as [100] for the x-axis-direction. Therefore the [hkl]-
direction is perpendicular to the (hkl)-plane.
〈hkl〉 : As for the planes for a full set of equivalent directions – such as 〈100〉 stands for [100],
[010], [001], [100], [010], [001].
In Fig. 1.3 [2] there are some important planes in cubic crystals depicted. In a Si-crystal
the {111}-surface is the energetically favored surface-plane.
1.2 Vicinal Si(001)
Generally Si-surfaces are never flat on a long scale. There are always steps even at nearly
singular or low-index surfaces. These tilted surfaces are named ”vicinal” as the average
surface orientation is usually close to the respective low-index surface and deviates only
by a small miscut angles from the specific crystal-direction (Fig. 1.4). This is not always
unwanted as a finite miscut provides several steps which enables ”step-flow” growth even
at lower temperatures due to the large number of favored nucleation sites (”kinks”): the
steps proceed by incorporation of adatoms at these kink sites along the step edges (red
circle in Fig. 1.4) whereas on-terrace nucleation events are suppressed (blue circle in Fig. 1.4).
Figure 1.4: Schematic visualization of vicinal Si(001) surface with a miscut angle
between the nominal (001)-crystal direction and the average surface orientation.
The high step-edge density offers favored nucleation sites in form of steps and
”kinks” on steps.
� Source: SiGe miscut.jpg

1.2. VICINAL SI(001) 7
Vicinal substrates are in principal available with any miscut angle α and arbitrary azimuthal
orientation φ. Commercial use is actually only made of Si(001) with a miscut of up to
± 4 ◦ . [8]
1.2.1 Step Structure
Terraces on vicinal Si(001) which are separated by an odd number of mono-atomic steps show
dimer rows which are oriented perpendicular to each other. These dimer rows are (2×1) and
(1×2) reconstructed domains which are oriented along the [110] and [110] direction. This
reconstruction reduces the number of dangling bonds and thus lowers the surface energy.
There are two different types of step segments with mono-atomic height: the upper-terrace
is either reconstructed with dimer rows parallel to the step edge (SA) or perpendicular to it
(SB) [9]. Step edges with arbitrary direction according to their different azimuthal miscut
orientations are assembled from such segments. For SB-steps two kinds have to be distin-
guished depending on the registry of the step edge with the dimer row reconstruction on the
lower-terrace. For rebonded SB step edges the number of dangling bonds is reduced which
makes them energetically favorable compared to non-rebonded SB-steps. Double steps are
observed primarily in form of DB-steps and here again mainly in the rebonded type [10, 11].
They separate terraces which expose dimer rows running perpendicular to the DB step edges.
Figure 1.5: Schematic model of the most common step types on Si(001) showing
SB and DB steps in their rebonded configuration [8].
� Source: SiGe vicinal-surface dimers.jpg

8 CHAPTER 1. SILICON-GERMANIUM MATERIAL SYSTEM
DA double steps have a by far subordinate abundance. Fig. 1.5 (after [8]) depicts a schematic
model of the most common step types on Si(001) showing SB and DB steps in their rebonded
configuration. [8].
1.2.2 Step Types in Different Miscut Angle Regimes
For small miscuts below 1 ◦ only mono-atomic steps with a height of 0.136 nm (i.e. aSi/4)
are found. Both single-step types are present but reveal a different nature. Whereas the
SA-steps are rather straight and smooth, the SB-steps appear rugged. There are many SA-
kinks in SB-steps and few SB-kinks in SA-steps as it costs less energy to create an SA step
segment [11].
Fig. 1.6 [12] shows an STM image (∼ 350 ˚A × 350 ˚A) of such a typical vicinal Si(001) surface
with a low miscut of 0.66 ◦ along [110]. Equally spaced A- (orange) and B-terraces (violet) can
be clearly discerned. The regular (2×1)-reconstruction is revealed as dimer-rows spanning
along the 〈110〉-directions over the terraces with an altered orientation parallel (A-terrace)
and perpendicular (B-terrace) to the step-edges. Thus the B-terraces are defined by rugged
SB-steps at the lower side and rather straight SA-steps at the upper boundary.
Figure 1.6: STM image (∼ 350 ˚A × 350 ˚A) of a vicinal Si(001) surface with a
miscut of 0.66 ◦ along [110] revealing equally spaced A- (orange) and B-terraces
(violet). The regular (2×1)-reconstruction is revealed as dimer-rows spanning along
the 〈110〉-directions over the terraces with an altered orientation parallel (A-terrace)
and perpendicular (B-terrace) to the step-edges. Thus the B-terraces are defined
by rugged SB-steps at the lower side and rather straight SA-steps at the upper
boundary. [12]
� Source: SiGe STM stepped-surface.jpg

1.3. ELECTRONIC PROPERTIES 9
Monoatomic height steps separate surface stress domains due to the anisotropic in-plane
stress linked to the dimerization of the terraces [13, 14]. Especially for low miscuts (< 0.03 ◦ )
a slightly wavy surface morphology is established which shrinks the size of stress domains
by introducing reverse steps and increasing the step density over the necessary value to
accommodate the miscut [15, 16, 17]. Therefore the local miscut partially exceeds the overall
”averaged” substrate miscut.
For miscut angles exceeding 1 ◦ along [110] the evolution of double-atomic steps sets in
and the fraction of these mainly DB-steps is increased with increasing miscut (between 1 ◦
and 10 ◦ ) [18]. The formation of the surface structure is a complex interplay of strain fields
associated with step rebonding, step-step interactions, and energy differences between an
SA-SB step pair and rebonded DB-steps [19].
In the current work the main emphasis was directed to vicinal Si(001) substrates with a
miscut of 4 ◦ along [110]. Hence the average terrace lengths can be estimated with 1.94 nm
(3.88 nm) assuming purely mono-atomic (di-atomic) surface steps. [8].
1.3 Electronic Properties
1.3.1 Band Structure
Silicon is like Germanium and Carbon (Diamond) an indirect semiconductor, which means
that the lowest minima of the conduction band and the highest maxima in the valence band
are not located at the same position in � k-space. In Fig. 1.7 [12] the Brillouin zone of the
diamond lattice structure is depicted.
Figure 1.7: Brillouin zone of the fcc lattice [12].
� Source: SiGe Brillouin-zone.jpg

10 CHAPTER 1. SILICON-GERMANIUM MATERIAL SYSTEM
Silicon (Si)
Figure 1.8: Band structures for the most prominent group IV semiconductors
Si (a) and Ge (b), both featuring an indirect bandgap [12, 20].
� Source: SiGe bandstructure.jpg
In Si the conduction band is characterized by six equivalent minima along the 〈100〉-directions
of the Brillouin zone located at about k0 = 0.85 (2π/a). The constant energy surfaces are
ellipsoids of revolution with major axes along 〈100〉. The valence band of Si has its minimum
at the Γ-point where the warped heavy and light hole bands are degenerate. The indirect
gap energy Eg,ind is 1.12 eV (300 K). In Fig. 1.8 [12, 20] the Si band structure and the indirect
band gap are shown. [3]
Germanium (Ge)
In Ge the conduction band is characterized by eight equivalent minima at the end points of
the 〈111〉-directions of the Brillouin zone and the constant energy surfaces are ellipsoids of
revolution with major axes along 〈111〉. The valence band of Ge has its minimum, like Si, at
the Γ point. The indirect gap energy of Ge is with Eg,ind = 0.66 eV (291 K) smaller than in
Si (see also Fig. 1.8 [12, 20] for the Ge band structure).
In Tab. 1.1 some important properties for Group IV elements are listed. For the sake of
completeness additionally to Si and Ge also values for carbon (diamond) are tabulated. [3]

1.3. ELECTRONIC PROPERTIES 11
Silicon (Si)
Germanium
(Ge)
atomic number 14 32 6
Carbon (C)
diamond
relative atomic mass [amu] 28.0855(3) [21] 72.64(1) [21] 12.0107(8) [21]
density d [gcm −3 ] 2.329002 5.3234 3.51525 [22]
(25 ◦ C) [23] (298 K) [24]
lattice parameter a [˚A] 5.43102018(34) 5.6579060 3.56683(1)
(295.7 K) [25] (298.15 K) [26] (298 K) [27]
relative lattice mismatch f [%] 0 +4.2 -34.3
indirect energy gap Eg,ind [eV] 1.1242 0.664 5.50(5)
(300 K) [28] (291 K) [29] (RT) [30]
direct energy gap Eg,dir [eV] 4.135 0.805(1) 6.5 [31]
effective electron masses:
(190 K) [32] (293 K) [33]
me,|| 0.1905(1) 0.0807(8) 1.4
me,⊥ 0.9163(4) 1.57(3) 0.36 [34]
(in units of m0)
effective hole masses:
(1.26 K) [35] (30...100 K) [36]
mhh 0.537 0.284(1) † 1.08
mlh 0.153 0.0438(3) † 0.36 [37]
(4.2 K) [38] (4 K) [39]
mso 0.234 0.095(7) 0.15 [37]
(in units of m0) (4.2 K) [38] (30 K) [40]
electron mobility µe 1450 3900 ≈ 2000
[cm 2 V −1 s −1 ] (300 K) [41] (300 K) [42] (RT) [34]
hole mobility µh 505 1800 2100
[cm 2 V −1 s −1 ] (300 K) [43] (300 K) [44] (RT) [45]
melting point Tm [K] 1685(2) [46] 1211.4 [21] 4100 [47]
→ Tm [ ◦C] 1412 938.3 3800 (subl.)
thermal conductivity κ 130 [48] 60 [49] 7 × 105 [50]
@ 300 K [Wm −1 K −1 ]
Table 1.1: Properties of frequently used group IV elements [3, 21].
† constant energy surfaces for the VB are represented by ”warped” spheres; hence the effective masses mh
depend on the crystal direction – values are listed for B parallel to [100] only

12 CHAPTER 1. SILICON-GERMANIUM MATERIAL SYSTEM
Figure 1.9: Lattice parameters of Si1−xGex alloys and deviation from Vegard’s
rule [51].
� Source: SiGe Vegards-rule.jpg
1.4 Silicon Germanium Alloys (Si1−xGex)
Silicon and germanium form a continuous series of solid solutions Si1−xGex providing a grad-
ual change in some parameters (e.g. lattice parameter a) with x ranging from 0 to 1 [3].
The lattice parameter aSiGe of Si1−xGex alloys shows a small deviation from Vegard’s rule,
i.e. from the linearity between the lattice constants of pure Si and Ge. According to ex-
periments by Dismukes et al. [51] (see Fig. 1.9) and theoretical Monte Carlo simulations of
Si1−xGex alloys the lattice constant for Si1−xGex alloys aSiGe lies below Vegard’s rule [5].
1.4.1 Bandstructure of SiGe-Heterostructures
The lattice mismatch (4.2%) strain between Si and Ge enables band engineering for SiGe-
heterostructures. Due to the different symmetries in Si- and Ge-band structure the SiGe-
alloy bandstructure shows a cross-over in the lowest conduction band edge from Si-like [100]-
symmetry to Ge-like [111]-symmetry at x ∼ 0.85 [3]. Fig. 1.10 [6, 52] shows the compositional
dependence of the indirect energy gap for unstrained Si1−xGex alloys with the change from
the conduction band (CB) minimum at the ”∆”-point (Si-like) to the L-point (Ge-like) (upper
curve in Fig. 1.10). The two lower curves show the vast influence of strain for pseudomorphic
SiGe-layers on a Si-substrate. The in-plane compressively strained SiGe-layers show a signif-
icantly lowered bandgap with a splitting of the valence band (VB) maximum in heavy-hole
(HH) and light-hole (LH) band. [6, 52]

1.4. SILICON GERMANIUM ALLOYS (SI1−XGEX) 13
Figure 1.10: Compositional dependence of the indirect energy gap for Si1−xGex
alloys. The upper curve reveals the change from the Si-like (CB-minimum at the
”∆”-point) to Ge-like (CB-minimum at the L-point) for unstrained SiGe-bulk material
and x ∼ 0.85. The in-plane compressively strained SiGe-layers on a Si-substrate
show a significantly lowered bandgap with a splitting of the valence band (VB)
maximum in heavy-hole (HH) and light-hole (LH) band [6, 52].
� Source: SiGe bandgap.jpg
Fig. 1.11 (after [7]) depicts the strain-induced band modification of a SiGe-epilayer on a
Si-substrate and a strained Si-epilayer on a relaxed SiGe-substrate. The six-fold degenerate
conduction band is split into two groups of two-fold degenerate ∆(2) and four-fold degenerate
∆(4)-bands. The degenerate heavy-hole and light-hole bands are also split with increasing
strain. Whereas a compressively strained SiGe-epilayer can be used to confine hole-type
carriers (HH), a tensilely strained Si-channel provides confinement for high mobility ∆(2)
electrons. The second row of images in Fig. 1.11 depicts the constant energy surfaces for the
conduction band of strained epilayers. There are six ellipsoids of revolution with the longi-
tudinal effective mass m e,|| for the symmetry axis along the X-direction and the transversal
effective mass me,⊥ perpendicular to that. Along with the strain-induced change in band-
structure also the effective masses are influenced. [7]

14 CHAPTER 1. SILICON-GERMANIUM MATERIAL SYSTEM
Figure 1.11: Strain-induced band modification of a SiGe-epilayer on a Sisubstrate
and a strained Si-epilayer on a relaxed SiGe-substrate. Whereas a compressively
strained SiGe-epilayer can be used to confine hole-type carriers (HH), a
tensilely strained Si-channel provides confinement for high mobility ∆(2) electrons.
(after [7])
� Source: SiGe strained layers Si-SiGe.jpg

Chapter 2
Molecular Beam Epitaxy (MBE)
This chapter is mainly based and transferred from the preceding diploma-thesis [1]. Compa-
rable descriptions and contents are also found from the preworkers [12, 53, 54].
The first successful use of a molecular beam apparatus for the crystallization and inves-
tigation of GaAs epilayers by Cho and Arthur dates back to the late 1960s [55]. Since then
ultra-high-vacuum epitaxial growth techniques developed rapidly and nowadays molecular
beam epitaxy is a powerful means of growing layers and films with high purity and preci-
sion. MBE provides several key advantages over CVD (Chemical Vapour Deposition), LPE
(Liquid Phase Epitaxy) or MOVPE (Metal-Organic Vapour Phase Epitaxy), such as the abil-
ity to control growth reproducibly to atomic monolayer dimensions and even the ability to
monitor and study the growth process itself via RHEED (Reflection High Energy Electron
Diffraction), XPD (x-ray Photoelectron Diffraction), AES (Auger Electron Spectroscopy)
and ellipsometry. It is a far off equilibrium deposition technique and features growth with
arbitrary supersaturation. MBE also provides the possibility to control the composition and
doping of the grown structures and yields material with impurity levels below ten parts per
billion [56].
2.1 MBE-Growth
2.1.1 Fundamentals and Prerequisites
MBE-grown thin films crystallize via reactions between the impinging atomic or molecular
beams of the constituent elements and the substrate that is kept at an elevated tempera-
15

16 CHAPTER 2. MOLECULAR BEAM EPITAXY (MBE)
Figure 2.1: The relationship between the fundamental units encountered in vacuum
technology [56].
� Source: MBE vacuum.jpg
ture in ultra-high-vacuum (UHV). Total pressures of the residual gas in the reactor below
p ≤ 1.33 × 10 −7 Pa (10 −9 Torr) are called UHV. The composition of the grown epilayer and
its doping level is adjusted via the relative arrival rates of the different constituents by con-
trolling the beam fluxes of the various sources. Usual growth rates are in the range of about
1.5 monolayer (ML) per second (i.e. ∼ 1.5 ˚A/s). This moderate growth rate ensures sufficient
surface migration of the impinging particles and therefore provide a smooth surface (also
depending on the substrate temperature TS; higher TS enhances surface mobility). With the
help of simple mechanical shutters in front of each of the beam sources the whole growth
procedure or just the deposition of single constituents or dopants can be started, stopped
or interrupted; that guarantees sharp borders or changes in composition and doping on an
atomic scale, at least as long as segregation effects are thermally suppressed.
In order to preserve one of the major characteristic features of MBE-growth – that is
the beam nature of the mass flow towards the substrate – it is an indispensible requirement
that ultra-high vacuum conditions are ensured. There are another two parameters closely
related to the pressure p of the residual gas in the growth-chamber, namely the mean free
path lmfp and the concentration nconc of the gas molecules travelling through the volume
towards the target-substrate. Mean free path is the average distance of a molecule between
two successive collisions, whereas the concentration is simply the number of species per unit
volume. Large values for lmfp are not only necessary to avoid high scattering rates (that
would destroy the beam-like nature), but also to minimize atoms from the residual gas to

2.1. MBE-GROWTH 17
hit the substrate surface and get incorporated into the epilayer. These contaminants and
impurities would accumulate lattice imperfections or unintentional impurity levels, and could
therefore also cause problems in the sensitive crystallization-process. All this would end up in
unpredictable epilayers of low quality and usefulness. In Fig. 2.1 [56] the relationship between
fundamental units in vacuum technology are compared.
2.1.2 Physical Processes in the Growth-Chamber
The growth process in a MBE-chamber can be divided into three zones, where different
physical reactions take place [57]:
1. In the first zone the molecular beams are generated under UHV conditions from electron-
beam evaporators (for Si, Ge, partly for C) and sources of the Knudsen-type effusion
cells (mostly used for dopants in SiGeC-MBE-technology). The temperatures of the
effusion-cells are accurately controlled using proportional-integral-derivative (PID) con-
trollers together with thermocouples for a feedback loop to enable flux-stabilization
better than ± 1% [58]. By choosing appropriate temperatures for the effusion-cells and
the substrate, the desired structural composition of the epilayers can be realized.
2. The second zone in a MBE vacuum reactor is the ”mixing” region in which the different
molecular beams – originated at various sources – interpenetrate each other and form
a more or less uniform beam. In case of a large enough mean free path there should
not occur many collisions between the different species of molecules traversing towards
the substrate, and interactions among these particles should be negligible.
3. The actual epitaxial growth process takes place on the substrate surface that forms the
third zone. Here is a series of surface processes that can be distinguished:
(a) Adsorption of the incoming molecules or constituent atoms impinging on the sub-
strate surface
(b) Surface migration and diffusion on the substrate
(c) Incorporation of the adsorbed species into the crystal lattice of the substrate or
grown epilayers
(d) Thermal desorption of atoms that have not been incorporated into the lattice
In Fig. 2.2 [12] the most important surface processes are illustrated.
Atoms or molecules arriving at the substrate surface have an energy corresponding to the

18 CHAPTER 2. MOLECULAR BEAM EPITAXY (MBE)
Figure 2.2: Schematic illustration of surface processes occurring during MBEgrowth
[12].
� Source: MBE surface-kinetics.jpg
temperature of the region of their origin (source temperature). This initial temperature Ti is
usually higher than the substrate temperature TS; hence they have to loose energy via energy
exchange with the substrate until thermodynamic equilibrium at TS is reached. When the
impinging species stays adsorbed due to a lack of energy for desorption (re-evaporation into
vacuum) the particles diffuse along the surface in order to find an energetically favored lattice-
site, such as a kink-position, where one half of the bonds is occupied. Other possibilities for
reactions on the surface are inter-diffusion (two atoms exchange sites) or nucleation processes
that appear, when migrating atoms aggregate and form a new island on a flat part of the
substrate surface. [55]
2.1.3 Growth-Modes
As mentioned at the end of the last section, atoms preferentially become incorporated at kink-
sites. Incorporation itself has been experimentally documented [59] and can be understood
as a two-step condensation process in which the chemisorbed state is reached via a precursor
physisorbed phase [60]. According to the model in Ref. [61, 62, 63] the atom as physisorbed
species is allowed to diffuse over the surface with a rate constant kdiff to find an energetically
favored site. The interaction potentials as seen by an atom approaching the surface are
schematically depicted in Fig. 2.3 [55, 64]. It is evident from Fig. 2.3 that the physisorbed

2.1. MBE-GROWTH 19
Figure 2.3: The interaction potential due to the surface, as seen by an atom
impinging perpendicularly to the surface for chemisorbed (curve 1) and physisorbed
precursor (curve 2) states [55, 64].
� Source: MBE physi-chemisorb.jpg
atom has to overcome a lower barrier to become chemisorbed at the surface, than to evaporate
back into the vacuum because Ea < Edp [55].
There are three growth-modes in crystal-growth that may be distinguished (see Fig. 2.4
[55, 65, 66]). In the island growth-mode (Vollmer-Weber) small clusters nucleate directly on
the substrate surface and build the base to islands of the condensed phase. This growth type
appears when the molecules for deposition are more strongly bound to each other than to
Figure 2.4: Schematic illustration of the three crystal-growth-modes. (a) Layerby-layer
or Frank-Van der Merve; (b) layer plus island or Stranski-Krastanov;
(c) island or Vollmer-Weber mode. θ represents the coverage in monolayers [55, 65].
� Source: MBE growth-modes.jpg

20 CHAPTER 2. MOLECULAR BEAM EPITAXY (MBE)
Figure 2.5: Pseudomorphic epilayer (left) and partially plastically relaxed epilayer
introducing misfit dislocations (right) [12].
� Source: MBE relaxation.jpg
the substrate material (e.g. in growing metals on insulators).
In contrast, the layer-by-layer (Frank-Van der Merve) growth mode happens in the opposite
case, i.e. when the impinging atoms are more strongly bound to the substrate than to each
other. In consequence, the first atoms to condense form a complete monolayer (ML) on the
surface, which is covered with ongoing deposition with a slightly less bound second layer. For
the case in which – during further deposition and an increasing number of layers – the binding
energy shows a monotonic decrease towards the value of the bulk crystal of the deposit, this
layer-by-layer mode is obtained (e.g. often observed in semiconductor on semiconductor
growth).
The Stranski-Krastanov, or layer plus island growth, is an intermediate case. When the first or
a few monolayers (”wetting-layers”) have been formed subsequent layer growth is energetically
unfavorable and islands form on top of these intermediate layers. The accumulation of strain
energy with increasing epilayer thickness disturbs the monotonic decrease in binding energy
that is necessary for a layer-by-layer growth. Therefore the epilayer morphology gets three-
dimensional to enhance stress relaxation at expense of surface energy. [55]
2.1.4 Heteroepitaxy versus Homoepitaxy
There are two main categories distinguished in epitaxy, namely homoepitaxy and hetero-
epitaxy. In homoepitaxy the grown crystal consists of one main compound that can be
additionally doped. In heteroepitaxy, which is exploited for bandstructure engineering, the
crystal, or parts (layers) of it, is a mixture of different compounds (e.g. Si/SiGe).
In heteroepitaxy the lateral lattice parameters of the underlying substrate or epilayers are
continued in pseudomorphic overgrowth (see Fig. 2.5 [12]). Due to deviating lattice parame-
ters (e.g. aGe > aSi) the pseudomorphic epilayers contain tensile or compressive strain, which
can have significant influence on growth. For pseudomorpic growth the most relevant pa-

2.2. CLEANING PROCEDURE 21
rameter is the critical thickness tc. This tc is an equilibrium parameter that defines the film
thickness at which the strain relaxation by the generation of misfit dislocations begins [67, 68].
Films with thicknesses below tc cannot relax, because the elastic energy stored in the strained
layer is lower than the energy associated with the local distortion around a misfit dislocation.
For films thicker than tc it becomes energetically favorable for the system to form misfit
dislocations in order to provide partial strain relaxation (see Fig. 2.5 [12]) of the film. Under
non-equilibrium conditions there is another critical thickness parameter t ∗ c, that defines a
metastable thickness range between tc and t ∗ c. In this parameter range the nucleation and
propagation of misfit dislocations is kinetically suppressed [69, 70]. Growth temperature
has a strong influence on the maximum available critical thickness t ∗ c, as strained layers of
metastable thickness can partly relax during later heat treatment. In Fig. 2.6 [68] the theoret-
ical critical thickness for equilibrium tc, and the experimental critical thickness t ∗ c measured
with films grown by MBE at 550 ◦ C (metastable limit) on Si are shown for Si1−xGex [6].
2.1.5 Relevant Temperatures in MBE
Temperature affects all aspects of the epitaxial crystal quality. Surface diffusion, incorpora-
tion and redistribution of impurities and lattice defects strongly depend on temperature.
Crystal growth by MBE systems is a non-equilibrium process. Usually growth temperatures
are far below the melting temperatures Tm of the different constituents. For Si-MBE sub-
strate temperatures around 550 ◦ C are used. But there is a wide temperature range in which
layer-structures are grown, depending on the intended device properties. To achieve high
crystal quality and to keep the defect-density in the epilayers low, higher temperatures up
to ∼ 750 ◦ C are used. To minimize diffusion and segregation of dopants even lower temper-
atures down to ∼ 300 ◦ C can be of practical interest. The substrate temperature influences
the whole surface kinetics and controls interface roughness and surface morphology [56].
Sometimes high-temperature steps up to 1000 ◦ C and more are introduced to growth proce-
dures to heal out crystal defects or to adjust doping profiles via diffusion. Also, after chemical
cleaning procedures outside the MBE-chamber the substrates are annealed in a short-time
annealing step at 900–1000 ◦ C inside the MBE-system to remove silicon-oxides.
2.2 Cleaning Procedure
It is obvious that a clean substrate surface is essential to make high quality epitaxial growth
possible. A clean and smooth surface on an atomic scale is the requirement for perfect

22 CHAPTER 2. MOLECULAR BEAM EPITAXY (MBE)
Figure 2.6: Critical thickness versus Ge-content for Si1−xGex on Si [68].
� Source: MBE Matthews-Blakeslee.jpg
epitaxial crystal growth. In our case the Si-substrates have undergone several precursor
processing steps and have been exposed to air. Thus, the Si-surface is covered with metallic
or organic impurities or just the amorphous natural silicon-dioxide SiO2. On a slightly
contaminated surface epitaxial growth would be inhibited or at least the properties of the
epilayers – electrical, optical or structural – would be poor. Without oxide desorption the
growth on Si-wafers that are covered by an amorphous SiO2 layer (natural oxide (∼ 20 ˚A) or
chemical oxide caused by the cleaning procedure (RCA: ∼ 60 ˚A)) would produce amorphous
Si epilayers.
In the following sections some relevant cleaning procedures are discussed [53].
2.2.1 Pre-Cleaning
Small substrate-pieces that have been processed before (especially the etched wire substrates,
Ch. 7) are successively cleaned in Trichloretylen, Acetone, Methanol using an ultrasonic
bath (US), 5 min per step. After that the substrates are rinsed with deionized water (DI-
H2O) and dried using the flow of a nitrogen (N2) nozzle. Additionally, the Si-pieces are
cleaned with sulphuric acid (H2SO4, 96%) and hydrogen peroxide (H2O2, 30%) for 15 min at

2.2. CLEANING PROCEDURE 23
H2SO4 : H2O2 = 5:1. In this acidic cleaning step organic impurities on the surface are oxidized
and removed. This cleaning procedure closes with rinsing the samples in DI-H2O for another
15 min.
2.2.2 RCA-Cleaning
The RCA-cleaning procedure is again a multi-step procedure that provides extraordinary
clean surfaces and makes good crystalline quality of the epilayers possible. Although the
cleaning sequence that has been developed by the Radio Corporation of America [71, 72]
is time consuming, the good results (much better than with a short HF-Dip) speak for
themselves.
In the first part of the cleaning procedure the Si-substrates are lowered into a boiling alkaline
bath (80 ◦ C) for 15 min. Subsequently the pieces are rinsed in a DI-H2O water-bath for
another 15 min or at least till the resistivity extends values of 10–15 MΩcm. In the second
part the substrates are immersed in an acidic mixture (80 ◦ C) for 15 min. Afterwards, in the
final step, the pieces are rinsed again in the DI-H2O water-bath for 15 min to wash away
residual ions of the acid. For better handling the pieces are kept during the whole RCA-
cleaning procedure in a polypropylene basket. Small pieces (17.5 mm × 17.5 mm) are cleaned
in quartz glasses standing in a temperature regulated water-bath. Whole 4”-Si-wafers are
cleaned in suitable quartz basins and are handled with special clamp-holders.
The alkaline mixture consists of NH3 (25%), H2O2 (31%) and DI-H2O in parts of 1:1:5. HCl
(30%), H2O2 (31%) and DI-H2O in parts of 1:1:5 are the ingredients of the acid. Whereas
the acid removes organic impurities, the basic bath should take away metallic contamination.
Although the original recipe for RCA-cleaning includes three HF-Dips (in the beginning, after
the acidic and the alkaline treatment) in our ”HF-free RCA-cleaning” procedure no HF-Dip
is implemented. Hence, this variation of RCA-cleaning generates a chemical oxide with a
thickness of some tens of ˚Angstroms and a hydrophilic substrate surface. [53]
2.2.3 HF-Dip
An HF-Dip is used to remove the natural SiO2 from the Si-substrate surface immediately
before the Si-pieces or Si-wafers are put into the load-lock chamber. Usually an HF-Dip
is a mixture of HF (40%) and DI-H2O with a ratio between 1:5 and 1:10. The substrates
are put into the HF-solution for about 30 s and dried with the N2-nozzle. When the Si has
been ”dipped” long enough the liquid drips down. The so cleaned surface shows hydrophobic
characteristics due to a temporary hydrogen-passivation, and inhibits new oxidation for some

24 CHAPTER 2. MOLECULAR BEAM EPITAXY (MBE)
time (several minutes or even up to a few hours).
All that seems to be promising but hydro-carbons from the ambient air pollute the HF-acid
and after an HF-Dip organic residuals stay behind. Even after high-temperature annealing
in the MBE-chamber – where the organic hydro-carbons are cracked and desorb mainly
from the substrate – some carbon is left, contaminates the surface and reacts with silicon to
silicon-carbide (SiC) precipitates that can generate growth defects and dislocations.
2.2.4 Oxide-Desorption
Since SiO2 forms an amorphous layer, mono-crystalline epitaxial growth is impossible on
SiO2. In order to desorb the oxide, the substrate is heated up to temperatures above 900 ◦ C.
Due to the temperature dependence of the oxide-desorption rate, even higher temperatures
(1035 ◦ C) are preferred and used, if possible. Although noteworthy oxide-desorption starts
at about 875 ◦ C, it has been experimentally shown that for higher annealing temperatures
better growth quality can be achieved [53]. It is suggested that some impurities leave the
surface only at higher temperatures.
Not only in the case of a precursor RCA-cleaning an oxide-desorption is necessary to remove
the relatively thick chemical oxide, but even after an HF-Dip the time span can be too long
until the substrate is brought into UHV. In usual oxide-desorption cycles the substrates are
kept for ∼ 5 min (depending on the maximum achieved temperature within this cycle) at the
high temperature.
2.3 MBE-System
In this work a Riber SIVA 45-chamber with a base pressure of 5 × 10 −11 mbar has been used.
The MBE-system consists of the main growth chamber, a load-lock chamber for wafer loading
and storage in UHV, and an additional chamber for special evaporation processes. In this
SiGeC-facility wafers of 125 mm diameter as well as 100 mm-wafers and smaller pieces can
be used directly or in all-Si adapters (Fig. 2.7), respectively. The latter can adapt substrates
sawed to a size of 9.0 mm × 9.0 mm and/or 17.5 mm × 17.5 mm. Growth parameters are mon-
itored with a Sentinel flux sensor, and controlled by a commercial software via PC. [12, 53]
2.3.1 Vacuum System
In addition to clean substrates and pure evaporation materials, ultra-high vacuum conditions
are absolutely necessary to obtain epitaxial layers of the best quality with a minimum of

2.3. MBE-SYSTEM 25
Figure 2.7: All-Si adapter to accommodate two 17.5 mm × 17.5 mm substrates.
� Source: MBE all-Si-adapter.jpg
impurities and defects. The two small chambers are pumped with a turbo-molecular-pump
and an associated rotary pump. In order to achieve the lowest possible pressures in the
main growth chamber during growth, a 520 l turbo-pump, an ion getter pump and a titanium
sublimator cooled with liquid nitrogen (LN2) are installed. Additionally, all sources and
surfaces inside the chamber becoming hot during growth are water cooled.
Vacuum conditions are checked using standard Convectron (Pirani) and Bayard-Alpert
vacuum gauges; a residual gas quadrupole mass spectrometer (HIDEN) in the growth chamber
completes vacuum monitoring. [12]
Figure 2.8: Schematic principle of an e-beam evaporator assembly and the flux
measurement [12].
� Source: MBE e-beam-evaporator.jpg

26 CHAPTER 2. MOLECULAR BEAM EPITAXY (MBE)
2.3.2 Evaporation and Rate Measurement
In this MBE-system electron beam evaporators for silicon, germanium and carbon are used
for the deposition of the main epilayer constituents. In the course of this thesis the two
formerly small e-beam evaporators for Ge and C were replaced by a larger Ge-source (see
Ch. 8). Effusion cells for boron (B, p-type doping) and antimony (Sb, n-type doping) are
used and also a carbon sublimation cell is installed. The chamber for special processes is
equipped with a C60-effusion cell and can be upgraded and supplied with additional sources,
such as for manganese (Mn), in the future.
The evaporation rates of the resistively heated effusion cells are temperature controlled. The
temperature is measured with tungsten-rhenium thermocouples (Rh 5%/26%) mounted di-
rectly below the radiativly heated crucible, and can be stabilized using feed-back loops to
adjust the heating currents.
Since in this work mainly epilayers consisting of silicon and germanium were grown, in the
following the description is restricted to these sources. The schematic principle of an elec-
tron beam evaporator is sketched in Fig. 2.8 [12]. A resistively heated hot filament emits
thermionic electrons that are accelerated to an energy of 10 keV. This electron beam is de-
flected by a static magnetic field following a 270 ◦ arc. The beam strikes the target material
which is heated up and evaporated locally. With moderately high power (∼ 1 kW) growth
rates of typically ∼ 0.4 ˚A/s for Si and ∼ 0.025 ˚A/s for Ge can be realized. In the case of Si
and Ge the evaporation material is located in a crucible of pure silicon that is mounted in
a water-cooled copper hearth. A water-cooled roof (stainless steel) that is screened towards
the evaporator by Si shields confines the molecular beam.
The growth rates are measured using a Sentinel III controller (Leybold Inficon). The mea-
suring principle is based on electron impact emission spectroscopy (EIES). This is an optical
technique, where the emission intensities of element-specific atomic transitions that are exited
via electron impact, are measured. The signal intensity depends on the density of atoms and
therefore on the flux of the evaporated specimen. Growth rates ranging from 0.01 ˚A/s up
to 2 ˚A/s can be conveniently measured, but have to be calibrated by the evaluation of thick
Si homoepitaxial and SiGe heteroepitaxial epilayers using x-ray diffraction (see Ch. A) and
step-height measuring systems (Alpha-Stepper). [12, 53]
2.3.3 Heating and Temperature Measurement
Directly above the substrate holder a resistively heated graphite meander serves as thermal ra-
diation source. The substrate is heated by absorbing the radiation emitted from the graphite

2.3. MBE-SYSTEM 27
Figure 2.9: Schematic picture of the Riber SIVA 45 MBE system [12].
� Source: MBE system.jpg
heating system. In order to minimize the radial temperature distribution and to improve the
temperature homogeneity over the whole wafer a peripherical silicon ring is mounted in be-
tween. Two thermocouples are mounted close to the middle of the substrate-backside (one for
reserve). These thermocouples have been calibrated against an additional thermocouple that
has been cemented into a Si-wafer. To be flexible in measuring the substrate-temperature at
any position a pyrometer has been installed. It has been calibrated against the thermocou-
ple and can be used to monitor temperatures in a range between 550 ◦ C to 1050 ◦ C with a
measurement spot of about 1 cm 2 .
Within this MBE the substrate can be heated up to a temperature of ∼ 1050 ◦ C. The sub-
strate can also be rotated and biased with voltages up to -2000 V during growth. Fig. 2.9 [12]
shows schematically the MBE-system used in this work. [12, 53]
2.3.4 Controlling and Monitoring
Usually the sources and substrate-temperature are controlled and monitored via PC using
the ”EPICAD-software” (Episoft). Using this software process parameters can be changed
manually or automatically according to a programmed growth sequence. Several Eurotherm
controllers read in the actual values that are provided by the thermocouples and Sentinel
sensors. The computer passes the programmed ideal values to the Eurotherm units which
calculate the new setpoints and control the sources.
The program provides convenient process control and graphical parameter visualization.
It provides the possibility of setting calibration functions for temperatures and fluxes and
watches vacuum conditions and flow rates of the water-cooling system for an eventually

28 CHAPTER 2. MOLECULAR BEAM EPITAXY (MBE)
necessary emergency stop. Single and complex epilayers can be programmed; the software
controls all shutters, and regulates the sources to the appropriate temperatures in order to
get the desired atomic fluxes and growth rates. Growth control parameters such as actual
and nominal values are automatically recorded and saved for later re-view.
The growth chamber is equipped with a RHEED-system (Reflection High Energy Electron
Diffraction) for growth monitoring. It consists of a RHEED gun and a fluorescence screen
that can be used to study or check the surface morphology during growth. [12, 53]

Chapter 3
Methods of Investigation
This chapter is thought to give just a brief introduction to TEM and AFM, mainly on the
basis of Ref. [73] regarding TEM, and basically summarizing the contents of Ref. [74] for the
AFM related section. A more detailed overview, but still in a compact and comprehensive
form are elaborated in the diploma-thesis [1].
In this work various experimental techniques have been used for investigating surface mor-
phology and characterizing changes between different preparation steps. As small structures
in the nanometer range will be characterized, standard optical microscopy faces its limits
and therefore other experimental means – providing higher spacial resolution – have to be
applied.
For studying the structures in more detail, electron (optical) microscopy – namely Scanning
Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) – and Atomic
Force Microscopy (AFM) are suitable tools. However, each of these different methods for
characterization has several advantages and disadvantages. With TEM the highest reso-
lution can be obtained and TEM images additionally reveal structures below the surface,
however, this technique requires a time-consuming sample preparation and provides small
effective regions for analysis (sample-thickness ≤ 100nm!). For SEM the preparative effort is
smaller and for AFM measurements almost no preliminary steps are required. Since in AFM
measurements the surface morphology is probed using tips with physical dimensions that
cannot be neglected, AFM images have to be regarded as image of the surface in convolution
with the shape of the tip.
29

30 CHAPTER 3. METHODS OF INVESTIGATION
3.1 Transmission Electron Microscopy (TEM)
Optical microscopes are limited in image resolution due to the long wavelength of visible
light. Historically, this has been the reason for the introduction of electrons into microscopy.
After de Broglie’s famous equation (Eq. 3.1), in which particle momentum p and its wave-
length λ are related via Planks’s constant h,
λ = h
p
(de Broglie) → λ[nm] ∼ 1.22
� E[eV ]
(3.1)
and from a simple transformation, high energy 200 keV-electrons (accelerated by a corre-
sponding voltage of 200 kV) have a wavelength λ of about 2.5 pm (0.0025 nm), which is sub-
stantially smaller than atomic diameters. This diffraction limit of resolution is out of reach,
mainly due to electron lenses. These are the crucial and limiting point in electron microscopy
since electromagnetic lenses are by far not perfect. Compared to glass lenses that can be pro-
duced with perfect quality the best electromagnetic lenses would correspond to ”the bottom
of a Coke bottle as magnifying glass” (cite Williams and Carter [73]). Typical values for the
practical resolution of a TEM are 0.15–0.3 nm and therefore the maximum useful magnifica-
tion in the best high-resolution TEM is about 10 6 (resolution of eye approximately 0.1 mm).
For thick samples these limit of resolution cannot be obtained due to the increased energy
spread ∆E resulting in chromatic aberration. The mean free path for inelastic scattering
depends on the electron energy, and therefore with higher acceleration voltages good high
resolution can even be achieved with relative thick samples (50 nm) [73, 75, 76].
Sample preparation has to be performed carefully and is probably the most important step in
order to obtain good high-resolution images. It demands great skill to prepare thin electron-
transparent (→ 50–100 nm!) specimen over a wide area. Ideally, the volume considered for
TEM-analysis should be free of defects and artifacts originated by the time consuming prepa-
ration.
In order to image the corrugation of buried interfaces (see Ch. 6), or the wire profile of the pro-
cessed Si-samples (see Ch. 7), cross-sectional specimen have to be prepared. The preparation
cycle for cross-sectional (Si-)samples is outlined in Ref. [1].
The specimen in this work were investigated with a JEOL-2011 FasTEM (HR type) trans-
mission electron microscope [77] with an acceleration voltage of 200 kV using a LaB6-cathode.
For this TEM facility a point image resolution of 0.23 nm is specified; the magnification can be
chosen from 2000 to 1.5 million. Images are either recorded with a conventional photo-plate
camera, or, nowadays, mainly with a Gatan CCD-camera (1 megapixel).

3.2. SCANNING ELECTRON MICROSCOPY (SEM) 31
3.2 Scanning Electron Microscopy (SEM)
Scanning electron microscopy can be used to study and analyze (mainly the surface of) bulk
specimen. The information is derived from the interaction between the probe electrons and
the specimen. The focussed electron beam is deflected by scan coils and the probe is scanned
across the specimen in a raster mode. Synchronous to this scanning process, the signals
generated by the probe beam interaction with the specimen are detected. The recorded in-
tensity modulation gives the contrast in SEM images. The scanning process can be applied
to generate a magnified image of the sample.
The newly commissioned LEO (ZEISS) SUPRA� 35 FESEM provides access to nanoscale
resolution images without an elaborate sample preparation (specified resolution: 1.7 nm
@ 15 kV). It is well-suited to characterize the surface after critical processing steps, or to
investigate etched profiles in cross-sectional view (Sec. 7.2). An SEM combines the possibili-
ties to give a fast overview over the whole specimen area and to zoom-in for a more-detailed
inspection of the surface morphology. It provides a large magnification range of typically
20x–500 000x).
For more facts the reader is referred to the diploma-thesis (Ref. [1]) and the PhD-thesis
written by T. Berer [78].
3.3 Atomic Force Microscopy (AFM)
Atomic Force Microscopy (AFM) is a further development on the basis of scanning probe
microscopy (SPM) implemented in the mid 1980’s. The AFM is an imaging tool with a vast
dynamic range, spanning the realms of optical and electron microscopes, and is operated as a
surface profiler with unprecedented 3D-resolution [74]. In atomic force microscopy the surface
of a sample is scanned with a sharp tip that is several micrometers long and has a smallest
diameter of typically 10 nm. It is located on the free end of a cantilever (∼ 100–200 µm in
length). Forces between the sample and the tip cause the cantilever to bend or deflect. As
the tip scans across the surface, these deflections are measured with a detector and allow a
computer to generate topographic maps [74].
The force most commonly associated with cantilever deflection in atomic force microscopy is
the interatomic van der Waals force. The dependence of this van der Waals force upon the
distance between the tip and the sample surface is depicted in Fig. 3.1 [74]. Three distance
regimes are labelled in Fig. 3.1: 1) Contact regime, 2) Non-contact regime (NC), and, in
between, 3) Intermittent-contact regime (IC). In the so-called contact mode the tip is held

32 CHAPTER 3. METHODS OF INVESTIGATION
less than a few ˚Angstroms above the sample surface, and the van der Waals force between tip
and sample is repulsive. In non-contact mode the tip is held tens or hundreds of ˚Angstroms
from the surface, and therefore the intermittent force is attractive due to long-range van der
Waals interactions. [74]
3.3.1 Scanning Modes
Contact Mode
In this repulsive mode the AFM tip makes soft ”physical contact” with the sample. The
tip is attached to the cantilever with a low spring constant, and therefore the contact force
causes the cantilever to bend and accommodate the changes in topography, as the scanner
traces the tip across the sample (or the sample under the tip).
Usually, the position of the cantilever (degree of deflection) is detected with optical tech-
niques. A laser beam is reflected from the back of the cantilever onto a position-sensitive
photodetector (PSPD). A change in the bending of the cantilever results in a shift of the
laser beam on the detector. This system is suited to resolve the vertical movement of the
cantilever tip with sub-˚Angstrom resolution.
The AFM can be operated either in constant-height or constant-force mode. In constant-
height mode the height of the tip is fixed, and the spatial change in cantilever deflection is
Figure 3.1: Dependence of interatomic force on tip-to-sample separation [74].
� Source: AFM van-der-Waals.jpg

3.3. ATOMIC FORCE MICROSCOPY (AFM) 33
used to generate the topographic data. In constant-force mode a feed-back loop moves the
scanner up and down in z-direction, responding to the local topography, and thereby keeping
the force and thus the deflection of the cantilever constant. In this case the topographic map
can be directly drawn using the z-motion of the scanner as height-information.
Due to the ”hard contact” between tip and sample, soft surfaces may be deformed, tips may
collect dirt or are rubbed off and become blunt.
Non-contact Mode
In NC-mode, the system vibrates a stiff cantilever with an amplitude of a few tens to hundreds
of ˚Angstroms near its resonant frequency (several 100 kHz). Using a sensitive AC detection
scheme, the changes in resonant frequency of the cantilever are measured. Since the resonant
frequency is a measure of the force gradient (i.e. derivative of the force versus distance
curve), the force gradient reflects the tip-to-sample spacing [74, 79, 80]. Comparable with
the constant-force mode in contact regime, a feed-back system moves the scanner up and
down in order to keep the resonant frequency or amplitude constant. Again this corresponds
to a fixed tip-to-sample distance, and the motion of the scanner is used to generate the
topographic data set (see Fig. 3.2 [81]).
NC-AFM does not suffer from tip or sample degradation effects and is suited to scan even
soft samples and to keep the tips sharp.
Intermittent-contact Mode
IC-AFM is similar to NC-AFM, except that in this mode the vibrating cantilever tip is
brought closer to the sample, so that it barely hits (”taps”) the surface. The changes in
cantilever oscillation amplitude responding to the tip-to-sample separation are monitored to
obtain the surface topography.
This mode is usually preferred as it combines the high resolution of contact mode, and the
low wear and tear of the tip in NC-mode. [74]
3.3.2 AFM-Probes
The AFM-tips are the crucial point in AFM as they are in contact with the surface and probe
the sample. The sharpest tips that are commercially available have a tip radius as small as
50 ˚A. Due to the fact, that the interaction area of tip and sample is just a fraction of the
tip radius, these tips would result in a lateral resolution of at least 20 ˚A. In this case the

34 CHAPTER 3. METHODS OF INVESTIGATION
Figure 3.2: Schematic view of hardware components and signal pathways in noncontact
(NC) AFM-mode [81].
� Source: AFM schematic-principle.jpg
resolution is usually limited to the step size according to the number of image data points
(e.g. 512 × 512) [82]. [74]
3.3.3 Imaging Artifacts
Atomic force microscope images are among the easiest-to-interpret of all images generated
by any microscopy technique. With these 3-dimensional AFM images it is easy to determine
whether a feature is protruding from the surface or recessed into it [74].
Tip Convolution
In scanning probe microscopy most imaging artifacts arise from the tip imaging, i.e. the
imaging of the convolution of the sample surface and the tip. As the tips are not ideal,
in case of features that are sharper than the tip, the image is dominated by the shape of
the tip, rather than by the true edge profile of the structure. In Fig. 3.3 the origin of tip
convolution is demonstrated. Many samples have features with steep sides and therefore tip
imaging is a common occurrence in images. As a consequence, sidewall angles should be
measured routinely in order to check, whether the imaged slope is limited to the shape of the

3.3. ATOMIC FORCE MICROSCOPY (AFM) 35
Figure 3.3: a) Path of the AFM-tip proving the topography and (b) the effect of
tip convolution on the resulting image.
� Source: AFM tip-path.jpg
tip, or really represents the topography of the sample. At least the height of features can be
measured and reproduced accurately as long as features are separated wide enough so that
the tip touches the bottom between these features. The lateral dimensions of the imaged
features provide just a maximum value, i.e. if one measures a protruding tip-imaged feature
giving a width of 250 ˚A, it is clear that the feature is at most 250 ˚A wide.
Feedback Artifacts
SPM images are also affected by feedback artifacts, if the feedback loop is not optimized. In
the case of high feedback gains the system may oscillate, generating high frequency periodic
noise in the image, either throughout the image or just localized to structures with steep
slopes.
For feedback gains that are too low, the tip cannot track the surface well and the images
loose detail and appear smooth. Another effect in the low gain case that is less obvious is
”ghosting”. On sharp slopes, an overshoot can occur in the image as the tip scans up the
slope, and an undershoot can occur as the tip scans down the slope. This artifact can usually
be seen on steep features, imaged as bright ridges on the uphill side and/or dark shadows on
the downhill side of the structure.
Image Processing Capabilities
Commercial SPMs are usually equipped with sophisticated image-processing software, pro-
viding curvature enhancement algorithms, filters for environmental noise, or giving the op-
portunity for retouching areas of bad data, etc.

36 CHAPTER 3. METHODS OF INVESTIGATION
Figure 3.4: For miscut Si(001) substrates the average orientation usually deviates
from the specific (001)-crystal direction. a) Short terrace segments are hard to
resolve by AFM which impedes accounting for the tilted surface via the miscut angle.
b) The step-bunching morphology exhibits flat and wide (001)-oriented terraces
which enables tilt-correction.
� Source: AFM tilt-correction.jpg
Although there are some benefits of image-processing software, it may not be used care-
lessly, as it could lead to data misrepresentation. Careless flattening could change structure
curvature or could make features even disappear, as well as irresponsible filtering could add
artificial structures to the image. Usually a tilted surface cannot be identified as such directly
from the height-scale AFM-data. Just with additional structure-related knowledge about the
orientation of intrinsic morphological features, e.g. facet angles, the correct surface orienta-
tion can be deduced which provides thereafter angle measurements with meaningful values
(see Fig. 3.4). [74]
3.3.4 Data Types and Data Representation
In this work a Digital Instruments Veeco Dimension 3100 AFM with Nanoscope IV controller
[83] was employed with Olympus TESP tips [84] in the ”tapping” mode to map highly resolved
surface images.
There are two signals or data types that are collected by the AFM-system which are
exploited for the thesis at hand.
The ”height” data, which give directly the topographic information of the surface morphol-
ogy, correspond to the change in piezo height (z-direction) needed to keep the amplitude of
the cantilever vibration constant. Thus for the acquisition of the ”height” data the feedback
gains must be high enough, so that the sample surface can be tracked and the change in
oscillation amplitude of the tip is minimized.
The ”amplitude” data measure the change in amplitude relative to the amplitude setpoint.
Using high feedback gains for collecting ”amplitude” data gives the derivative of the to-
pographic height in scan-direction. Hence the ”amplitude” data are often also referred to

3.3. ATOMIC FORCE MICROSCOPY (AFM) 37
Figure 3.5: Schematic illustration of the evaluation of AFM data for the surfaceorientation-map
(SOM). a) 3D-model of a faceted wire profile with surface normal
vectors (”1”, ”2”, ”3”). For each surface point (black spot) the normal orientation
[hkl] (here shown for ”2”) is calculated with the nearest-neighbor points (red spots)
to determine the local plane (rectangle colored orange). b) The intersection points
of the local normal vectors and a half-sphere seen from top as projection gives a
2D-plot in polar coordinates (ρ, φ). c) Whereas ρ indicates the angle between the
respective local surface normal [hkl] and the (001)-surface (growth direction), φ
denotes the in-plane azimuthal angle of [hkl] with respect to [100] (seldom [110]).
The intensity at each point (ρ, φ) in the surface orientation histogram is a measure of
the abundance of a respective surface orientation. Marker circles which correspond
to specific surface angles are introduced as guidance for the characteristic facets in
the SiGe-system.
� Source: AFM SOM schematic.jpg
as ”derivative” data or data acquired in ”derivative” mode. The ”amplitude” mode pro-
vides a sensitive edge-detection technique which reveals facets with a better signal-to-noise
ratio. [83]
The topographic AFM data (”height” mode) can be also utilized to calculate special data
representation plots to point out special morphological features or arrangements. Espe-
cially useful to evaluate faceted morphologies are the surface-angle-plots (SAP) and surface-
orientation-maps (SOM). These are introduced to visualize the local surface inclination in
each AFM data point itself or to depict a histogram of the involved surface orientations,
respectively. Fig. 3.5 demonstrates the evaluation of AFM ”height” data for the surface-

38 CHAPTER 3. METHODS OF INVESTIGATION
orientation-map (SOM). For each surface point (black spot in Fig. 3.5a) the normal orien-
tation [hkl] (in Fig. 3.5a shown for ”2”) is calculated with the nearest-neighbor points (red
spots) to determine the local plane (rectangle colored orange). The intersection points of
the local normal vectors and a half-sphere seen from top as projection gives a 2D-plot in
polar coordinates (ρ, φ) (Fig. 3.5b). Whereas ρ indicates the angle between the respective
local surface normal [hkl] and the (001)-surface (growth direction), φ denotes the in-plane
azimuthal angle of [hkl] with respect to [100] (or sporadically [110]). The intensity at each
point (ρ, φ) in the surface orientation histogram is a measure of the abundance of a respective
surface orientation. Marker circles which correspond to specific surface angles are introduced
as guidance for the characteristic facets in the SiGe-system (Fig. 3.5c).
In the SAP representation the local slope is plotted. This is defined as the angle between the
normal orientation vector [hkl] and the reference orientation of Si(001), namely [001]. It is
extracted again via the nearest-neighbor points in analogy to the SOM evaluation.
Fig. 3.6 gives an overview of the different AFM-data types and their visualization. In this
exemplary illustration a calculated model of a faceted wire-profile is utilized. The shape of
the investigated profile can be clearly seen from the 3D-AFM view (Fig. 3.6a). Fig. 3.6c de-
picts a line scan along the fast scan-direction (x-direction). From this cross-sectional view the
faceted nature of the wire gets obvious. Surface regions of the (001)-, {113}- and {111}-type
can be easily distinguished from each other.
The conventional, topographic 2D-AFM representation for which the data are usually ac-
quired in ”height”-mode, deliver only a rough ”feeling” for the morphology. It provides
rather qualitative information about a feature, whether it is recessed into the surrounding
surface or juts out. Usually topographic 2D-AFM data do not reflect the detailed structure
and shape (Fig. 3.6b).
In this respect the ”amplitude” data provide a more detailed access compared to the ”height”
data since the ”derivative”-signal shows high contrast and reveals sensitively changes in slope
along the scan-direction (Fig. 3.6c). Usually the ”amplitude”-signal features less noise than
the calculated derivative of the ”height” data, and thus can give meaningful information es-
pecially about micro-facets with small lateral extensions.
Fig. 3.6e shows a surface-orientation-map (SOM) with the relative abundance of the promi-
nent surface angles ((001) ≡ 0 ◦ , {113} ≡ 25.2 ◦ , {111} ≡ 54.7 ◦ ). This plotting scheme is well-
suited to quickly reveal special surface orientations even from slightly noisy AFM-data mea-
sured in ”height”-mode. Extracting representative facet angles is often hardly possible by
analyzing line scans. The marker circles in the SOM images correspond to surface angles ρ
(see Fig. 3.5) which are known for the {113}-, {111}-, and {110}-orientation.

3.3. ATOMIC FORCE MICROSCOPY (AFM) 39
Figure 3.6: Overview of different AFM-data types and their visualization illustrated
for a faceted wire-profile. a) 3D-AFM view and d) line scan in the fast
scan-direction (x-direction). b) Compared to the conventional topographic 2D-
AFM image (”height”-mode) the c) ”derivative”-mode signal reveals changes in
slope along the scan-direction. e) The surface-orientation-map (SOM) shows the
relative abundance of prominent surface angles and the f) surface-angle-plot (SAP)
indicates quantitatively the local inclination angle for the AFM-probed area.
� Source: AFM data-types.jpg
The surface-angle-plot (SAP) indicates quantitatively the local inclination angle in every
point separately, but again for the whole AFM-probed area (Fig. 3.6f). Such plots are again
calculated from the ”height” data and evidence hence a noisier slope representation than im-
ages depicting the ”derivative” signal. Nevertheless this evaluation scheme is the only chance
to get quantitative information of the local slope in any direction, and not only towards the
fast scan-direction (x-direction in the present case). So would a ”derivative”-mode image
with the fast scan-direction exactly along the wire-profile (i.e. in y-direction for the discussed
case) exhibit purely uniform data without any contrast.

40 CHAPTER 3. METHODS OF INVESTIGATION

Part II
Main Research
41

Chapter 4
Self-Organized Growth –
Step-Bunching
In this and the following chapter (see Ch. 5) various sub topics of self-organized growth in the
Si/SiGe system are discussed. The first introductory part gives a compact summary on the
preparatory work and the PhD-theses by Christoph Schelling [12] and Michael Mühlberger
[54]. The results on step-bunching presented there serve as starting point for the work at hand.
Transferring this know-how to high-miscut samples should yield periodic ripple templates
which are feasible for self-organized growth of SiGe islands [85, 86, 87, 88]. Anyway, these
structures on the nanometer scale open up an ample playground to study several aspects of
growth and especially the interplay between kinetics, surface energy and strain [88, 89, 90].
The epilayer morphology encountered here is closely related to the features seen for seeded Ge
dot growth on pre-structured Si templates [91, 92, 93]. Thus these experiments may help to
reveal the pathway of island formation in the pits of 2D pre-patterned Si substrates [94, 95].
In the following chapters a different notation is used for measured values and growth
related parameters. Period and height readings especially encountered in AFM data analysis
are listed in nanometers (SI-units), whereas for the MBE-intrinsic parameters, such as layer
thickness and growth rate, the more natural Angstrom units are ought to be used consistently.
4.1 Introduction to Step-Bunching
In this section ”step-bunching” is briefly discussed to sketch the actual status and under-
standing of the community for this basic growth instability. The results of the pre-workers
are summarized here only in a very compact form. For a more comprehensive and detailed
43

44 CHAPTER 4. SELF-ORGANIZED GROWTH – STEP-BUNCHING
Figure 4.1: Typical AFM image showing step-bunching of a 3300 ˚A thick Si-buffer
(Si @ 0.2 ˚A/s, 490 ◦ C) grown on a Si-substrate with 0.66 ◦ miscut along [110]. The
data represent the ripple-morphology for low-miscut Si-substrates as investigated
by the preworkers Christoph Schelling [12] and Michael Mühlberger [54] (data from
[54]).
� Source: Stepbunching AFM low-miscut preworkers.jpg
view on these experimental findings the reader is referred to the PhD-theses written by
Christoph Schelling [12] and Michael Mühlberger [54]. Fig. 4.1 shows a typical AFM im-
age demonstrating step-bunching of a 3300 ˚A thick Si-buffer (Si @ 0.2 ˚A/s, 490 ◦ C) grown
on a 0.66 ◦ [110] miscut sample. The data represent the ripple-morphology for low-miscut
Si-substrates as investigated by the preworkers (data were taken from [54]).
In general the evolution during growth and final morphology of an epitaxial film is governed
by the interplay between thermodynamics and kinetics. The competition can be described
with the concept of local equilibrium [96]. The slowest kinetic rate defines the finite range of
equilibrium. For extended length scales the kinetics always win over thermodynamic processes
which is thus reflected in the layer morphology. The borderline can be tuned by appropri-
ately choosing the growth rate, substrate temperature and miscut. For low growth rates and
high temperatures the equilibrium properties will dominate over a wide range, whereas for
very rapid growth at low temperatures thermodynamics are spatially restricted by kinetic
limitations. A high miscut provides more step edges offering a large number of preferential
nucleation sites and therefore corresponds to a higher effective substrate temperature.
Kinetic growth instabilities can be explained by adatom currents on the surface during growth.
Especially the behavior of an adatom encountering a downward step edge has to be consid-
ered. The adatom can either jump to the lower terrace or can be reflected at the step edge
which is described with the help of an Ehrlich-Schwoebel barrier [97, 98, 99]. For growth
on vicinal surfaces the Schwoebel barrier has a stabilizing effect. The migrating adatoms
are mainly incorporated at the upward step edge. The cross-section for impinging atoms is
proportional to the terrace length which helps to shrink the respective terrace by adjusting its

4.1. INTRODUCTION TO STEP-BUNCHING 45
size towards the average. For the inverse behavior and incorporation from the upper terrace
the large terraces grow even further on cost of the small terraces leading to a destabilized
situation. The step edges of the small shrinking terraces are finally collected in bunches
which leads to the name ”step-bunching”. Instabilities can also occur parallel to the miscut
direction where a slight initial waviness of the step edges is exaggerated to pronounced un-
dulations due to the incorporation from the lower terrace (Bales-Zangwill instability [100]).
The kinetic stability of the surface can be analyzed in terms of the surface mass current � j as
a function of the local miscut �m of the surface [101, 102]. The surface morphology perpen-
dicular to the miscut direction is determined by the sign of the derivative of the surface mass
current � j after the miscut �m, whereas the surface parallel to the miscut direction is correlated
to the sign of the current � j itself. Therefore both variables ∂� j
∂ �m and � j( �m) together fully determine
the overall evolution of an epitaxial surface. The different scenarios are schematically
visualized in Fig. 4.2 [54]. Step-bunching (with straight step-edges) occurs for a downward
current and preferential adatom incorporation from the upper terrace which makes broad
terraces grow faster. [12, 54]
4.1.1 Dependence on Substrate-Temperature, Growth-Rate, Layer-Thick-
ness, Ge-content and Miscut
Many experiments were performed to examine the vast parameter space and to check the de-
pendence of the kinetics on substrate temperature, growth rate, layer thickness, Ge-content
and miscut orientation on the surface morphology of step-bunching. Manifold results are
reported in the literature by various groups. Not only miscut orientations close to the tech-
nologically most important Si(001) surface were extensively investigated, but also further
surface orientations, such as Si(111), Si(113) and Si(118), were examined for their stability
against step-bunching and instabilities in general (see e.g. [103, 104, 105]).
Although for vicinal substrates near thermodynamically stable facets the free surface ener-
gies may strongly influence the morphology of the grown Si/SiGe epilayers, in the following
the general behavior for the nearly singular Si(001) surface (close to the wafer standard spec-
ification, i.e. < 0.5 ◦ ) is explained. This part is intended to summarize the results gathered
by the preworkers for slightly miscut Si(001) (0.66 ◦ along [110], see PhD-theses [12, 54] and
related publications [106, 107, 108, 109, 110, 111]).
The above mentioned experiments revealed that step-bunching for a miscut of 0.66 ◦ along
[110] occurs only in a very small temperature window and shows its maximum around 490 ◦ C
with a flux of 0.2 ˚A/s (see Fig. 4.1). For slightly higher or lower substrate temperatures the
regular ripple structure fades away. Post-growth annealing even at the growth temperature

46 CHAPTER 4. SELF-ORGANIZED GROWTH – STEP-BUNCHING
Figure 4.2: Stability analysis in terms of surface mass current � j( �m) [101, 102, 54].
� Source: stability analysis 01.jpg
generally leads to a reduction in the amplitude of the instability [106]. The steps tend to
rearrange to evenly spaced monoatomic and diatomic height steps [18].
The growth-rate influences the evolution of the ripples indirectly via the diffusion length.
Higher rates perturb the unhindered adatom current thus giving less pronounced step-bunching.
Increased flux corresponds therefore to a decreased effective substrate temperature.
The third important parameter is the layer-thickness. With increasing layer-thickness t the
period Λ and the peak-to-valley height H of the ripples is increased according to a power-law
dependence Λ ∝ t α (α ∼ 0.25) and H ∝ t β (β ∼ 0.5), respectively. For a Si epilayer thickness
of 1000 ˚A deposited at 490 ◦ C and a rate of 0.2 ˚A/s the measured values read Λ ∼ 450 nm for
the period and H ∼ 1.8 nm for the ripple height.
The miscut vector plays a very important role. It can be separated into the inclination angle
θ with respect to the singular surface and into φ, which is the azimuthal angle measured rel-
ative to a specific in-plane direction. The miscut angle θ defines the average terrace length,
which is an important quantity considering step-flow growth, and thus has to be seen in the
context of the diffusion length. Thus, it is not surprising that an increased miscut results in
shorter terraces and shifts the maximum of pronounced step-bunching to lower temperatures.

4.1. INTRODUCTION TO STEP-BUNCHING 47
The ripple period does not depend on the azimuthal miscut orientation but shows strong in-
fluence on the corrugation of the step edges along the bunches. Straight ripples parallel to
the DB double steps were found for a miscut along the [110] direction, whereas a triangular
morphology was observed for a miscut along the [100] direction. In the latter case the DB
double step segments are oriented ± 45 ◦ out of the miscut direction, which can be used to
explain the experimental data seen with AFM [12].
The experiments providing the dependence of the various parameters listed above were based
on Si homoepitaxy only. Further studies employing heteroepitaxial SiGe layers proved that
the amplitude of step-bunching is drastically reduced in the presence of Ge. Nevertheless,
the influence of the Ge-content and the resulting strain is discussed controversially in the
literature (see 4.1.2). [12, 54]
4.1.2 Kinetic vs. Strain-Induced Step-Bunching
Although step-bunching is experimentally extensively explored, it is still not fully understood.
There is ongoing interest in step-bunching to learn more about surface step dynamics, which
is approved by the appearance of new theoretical models and computer simulations.
Various speculations and theories on the origin of step-bunching were published. In the
early days strain-induced step-bunching was proposed [112, 113]. According to this one-
dimensional theory on a vicinal surface under stress, elastic relaxation at steps produces a
long-range attractive interaction between these steps. As a result, the surface should be
unstable against step bunching, driven by the energetics of the system rather than by the
kinetics of step flow [112]. Strain-induced step-bunching has also be claimed to be experi-
mentally evident [114, 115, 116].
More recent considerations propose kinetic step-bunching as an explanation for the evolv-
ing ripple structure during growth. Several microscopic models evolved describing the step-
bunching instability with the help of an inverse Schwoebel barrier [99], step edge diffusion [117]
or the combination of attachment and detachment at the step edges and anisotropic diffu-
sion [118, 119, 120]. Each of these processes can be characterized by specific critical exponents
to characterize the correlation between layer-thickness t, ripple-height H and period Λ [105]
(see also 4.1.1). Recapitulatory, there is a huge variety of different models, e.g. some models
include elastic interactions of the terraces [121] whereas other descriptions do not [122].
The results gathered in our group [106, 107, 108, 109, 110, 111, 118, 119, 120] strongly fa-
vor kinetic step-bunching. In these experiments the exotic influences of electromigration,
impurities, multispecies coupling by chemical reactions (see [123] and references therein)
can be ruled out. Furthermore, the influence of strain has to be at least widely neglected

48 CHAPTER 4. SELF-ORGANIZED GROWTH – STEP-BUNCHING
as the most pronounced ripple patterns were achieved by Si homoepitaxy. SiGe heteroepi-
taxial layers showed a reduced peak-to-valley height regarding step-bunching and even in
Si/SiGe superlattice structures the amplitude of the resulting ripple morphology appeared
to be rather diminished. With increasing Ge-content the amplitude of the step-bunching
instability decayed continuously although strain increases. This behavior can be explained
with Ge segregation [124, 125, 126], which is significant at the employed temperatures, and
the alteration of the adatom dynamics due to the presence of even small amounts of Ge
on the surface [127, 128]. Another strong indication against strain-driven step-bunching is
that after-growth annealing does not enhance the ripple structure but leads to an attenu-
ation of the step-bunching instability. The opposite behavior and an enhancement of the
instability had to be expected if the effects were ruled by strain since its influence should be
thermodynamically enhanced. [12, 54]
4.2 Optimization of Step-Bunching for Ripple-Patterns with
Small Periodicity
It was already outlined in the previous part that the kinetic step-bunching instability is ex-
tremely sensitive to the growth temperature [106, 108, 120]. For the experiments discussed
in the following we used substrates with 4 ◦ miscut in [110] direction (ø 3”, 375 µm thick, CZ,
(001)-orientation, 4.0 ◦ [110] miscut; n-doped, As, 1 – 10 Ωcm) that were cut to a practical
size of 17.5 mm × 17.5 mm. All growth procedures started with a high temperature Si-buffer
which should ensure a flat surface and reproducible starting point for the study.
With increasing substrate miscut from 0.66 ◦ to 4 ◦ the ripple period could be tuned to
smaller periods towards the nanometer scale. At Si growth rates of 0.2 ˚A/s a ripple pattern
with few defects develops within a small temperature window around 425 ◦ C. Although the
layers are grown under UHV-conditions in our MBE-system (base pressure < 10 −10 mbar),
at slightly lower temperatures many defects are incorporated and the ripples decompose into
islands, which are aligned in chains (Fig. 4.3, 400 ◦ C). For marginally higher temperatures the
ripple structure fades away (Fig. 4.3, 450 ◦ C). This behavior is visualized in Fig. 4.4 where the
ripple height of the step-bunching structure is plotted as a function of substrate temperature
for a 1000 ˚A Si-buffer. Data for growth temperatures below 400 ◦ C were not evaluated since
already for 400 ◦ C the ripple morphology changes gradually to a hillock pattern. Generally,
the transition from hillocks, appearing at low temperatures, to elongated ripples through lat-
eral bunch expansion leads to bifurcations at optimized temperatures . These are caused by
ripples which originate from different parts of the sample, and thus can be accidentally out-of-

4.2. OPTIMIZATION OF STEP-BUNCHING FOR RIPPLE-PATTERNS 49
Figure 4.3: AFM images showing the growth temperature dependence of stepbunching.
The series of 500 ˚A thick Si-buffers grown on 4 ◦ [110] miscut samples
confirms that only within a small temperature range (here at around 425 ◦ C) a
pronounced ripple structure evolves [89, 106]. (miscut vector points upwards!)
� Source: Stepbunching AFM Temp-series.jpg
phase. This opens up a 2D-pathway for ”transversal” coarsening (proposed as ”ripple-zipper”
mechanism by C. Schelling et al. [12]) which increases the period of step-bunching for increas-
Figure 4.4: Evaluation of the step-bunching ripple height as a function of substrate
temperature for a 1000 ˚A Si-buffer. The maximum of the instability for 4 ◦
miscut and a Si-rate of 0.2 ˚A/s occurs around 425 ◦ C.
� Source: Stepbunching temp eval.jpg

50 CHAPTER 4. SELF-ORGANIZED GROWTH – STEP-BUNCHING
Figure 4.5: AFM images showing the layer thickness dependence of step-bunching
at 425 ◦ C. The series of 250, 500, 1000 and 3000 ˚A thick Si-buffers grown on 4 ◦ [110]
miscut samples demonstrates that the ripple structure gets more pronounced with
increasing layer thickness [89].
� Source: Stepbunching AFM Thick-series.jpg
ing layer thickness. For perfect ripples spanning over several micrometers only ”longitudinal”
coarsening with the dissolution of intermediate bunches and excessive material transport can
Figure 4.6: Evaluation of the step-bunching ripple period (a) and height (b) on
the thickness of the Si-buffer for 4 ◦ [110] miscut. Both values gradually increase
with layer-thickness but show seemingly a reduced gain for thicker layers.
� Source: Stepbunching period-height eval.jpg

4.2. OPTIMIZATION OF STEP-BUNCHING FOR RIPPLE-PATTERNS 51
Figure 4.7: AFM image (a) and Fourier transform (b) of optimized 1000 ˚A thick
Si-buffer grown with a Si-rate of 0.2 ˚A/s at 425 ◦ C on a 4 ◦ [110] miscut substrate
resulting in a regular ripple template.
� Source: Stepbunching AFM FFT.jpg
lead to continuously growing ripples [112] (see also [12] for a discussion). Therefore also the
influence of the Si-buffer layer thickness was explored systematically (Fig. 4.5). In the early
stage of step bunching (Fig. 4.5, 250 ˚A) there are many uncorrelated localized step bunches.
With increasing layer thickness (500 ˚A) the individual bunch segments merge and form well-
pronounced elongated ripples (500 ˚A), which finally span several micrometers (1000 ˚A). The
low growth temperature of 425 ◦ C leads to an increasing number of accumulated defects with
increasing layer thickness. These show up occasionally as holes and constricted bunches
(Fig. 4.5, 3000 ˚A). For this reason the layer thickness was not further increased within this
series, which impedes an extraction of reasonable coefficients for the power-law dependence
and scaling of step-bunching (see 4.1.1). Nevertheless, the evaluation of the ripple period and
height of the step-bunches as a function of the Si-buffer thickness for 4 ◦ miscut along [110] is
depicted in Fig. 4.6. Both values gradually increase with layer-thickness but show seemingly
a reduced gain for thicker layers.
Fig. 4.7 shows an extended AFM image (5 µm scan-size) and the corresponding Fourier trans-
form of the optimized 1000 ˚A thick Si-buffer grown with a Si-rate of 0.2 ˚A/s at 425 ◦ C on
typical 4 ◦ [110] miscut substrates resulting in a regular ripple template and providing the
base for further experiments. The measured parameters are Λ ∼ 105 nm for the period and
H ∼ 4 nm for the ripple height. Fig. 4.8 and Fig. 4.9 show tilt-corrected AFM data for the
same optimized Si-buffer with a scan-size of 500 nm. From the line scan (Fig. 4.8) and the
surface-angle-plot (SAP, Fig. 4.9) the typical morphology of step-bunching is revealed. In
the corner regions between the lower ends of the slope and the adjacent terraces seemingly
also retrograding steps become visible. It is not really clear whether this is an artifact of
the measurement or due to applying tilt-correction. Similar line-scans were also reported

52 CHAPTER 4. SELF-ORGANIZED GROWTH – STEP-BUNCHING
Figure 4.8: AFM image and corresponding line-scan in miscut direction for a
nominally 4 ◦ [110] miscut sample with the optimized 1000 ˚A thick Si-buffer. By
correcting the AFM data for the miscut (3.86 ◦ ) the line-scan reveals extended terraces
in (001)-orientation.
� Source: Stepbunching linescan.jpg
Figure 4.9: Analysis of local surface inclination from the tilt-corrected AFM
image with a scan-size of 500 nm (see Fig. 4.8). The plot illustrates the surface
landscape with the flat terraces and the steep ripple flanks which is typical for stepbunching.
� Source: Stepbunching surfangles.jpg

4.2. OPTIMIZATION OF STEP-BUNCHING FOR RIPPLE-PATTERNS 53
Figure 4.10: AFM images giving a comparison between a 4 ◦ [110] miscut substrate
(a) and a flat reference sample (b) grown simultaneously. The epilayer consists
of a 1000 ˚A thick Si-buffer grown at 425 ◦ C and a rate of 0.2 ˚A/s.
� Source: Stepbunching miscut-dummy.jpg
by the preworkers [12]. The overall landscape consists of flat extended terraces with (001)-
orientation and steep ripple flanks with typical slopes slightly above 10 ◦ . In the central part
of the surface inclination visualization a region of out-of-phase bunches can be seen, whereas
in the outer right part a constriction gets clearly visible.
In all sample series growth was performed on a miscut sample and a flat reference sample
simultaneously. The morphologies of the grown epilayers were compared by AFM (Fig. 4.10).
For the flat reference, Fig. 4.10b reveals that in the low growth temperature regime around
425 ◦ C step-flow growth is suppressed and ”islanding” occurs. The small sharp dot-like
features in the 2 µm AFM data of the reference sample can be attributed to the onset of
oxidation. The samples were taken out from the UHV-system right before the AFM char-
acterization. Still, such artifacts could not be prevented since the time consuming AFM
Figure 4.11: AFM images point up the importance of sample cleaning. Scan
sizes of 2 µm (a) and 20 µm (b) show many holes and line defects in the optimized
1000 ˚A thick Si-buffer grown at 425 ◦ C.
� Source: Stepbunching defects.jpg

54 CHAPTER 4. SELF-ORGANIZED GROWTH – STEP-BUNCHING
characterizations were performed on air.
It cannot be pointed out with enough emphasis that a proper sample preparation is of great
importance. A failed cleaning procedure due to problems with the DI-water system can
have significant consequences as evidenced in Fig. 4.11. AFM images with different scan-
sizes of 2 µm (Fig. 4.11a) and 20 µm (Fig. 4.11b) show many holes and line defects in the
otherwise – especially regarding growth parameters – optimized 1000 ˚A thick Si-buffer grown
at 425 ◦ C. This again justifies our elaborate cleaning procedures especially applied to the
17.5 mm × 17.5 mm sample pieces. [89, 90]

Chapter 5
Self-Organized Growth 2 –
Combination of Strain-Effects and
Kinetic Phenomena
This chapter deals with several aspects of self-organized growth in the Si/SiGe system as al-
ready outlined in the preamble of the preceding chapter (see Ch. 4). The special morphology
and periodic surface modulation of step-bunching provide a versatile basis for the investiga-
tion of the interplay between kinetics, surface energy and strain. Varying the parameters for
the SiGe-epilayers grown on top of these ripple templates delivers insight and better under-
standing on the nucleation and evolution of SiGe-islands. In an introductory discussion the
self-organized SiGe-islands found as byproduct here are linked to state-of-the-art perfectly
organized SiGe-dots on pre-patterned substrates.
5.1 Introduction to State-of-the-Art Ge-Dots
In recent years self-organized SiGe/Ge dots attracted increased interest and are regarded
promising candidates for nano-electronic and optoelectronic applications due to quantum size
effects [129, 130, 131, 132]. This is supported by the compatibility of these feasible devices
with the sophisticated and well-established Si microelectronic technology [133]. Conventional
deposition of self-assembled Ge-dots leads to a heterogeneous growth and thus fluctuations
in size and random positioning of the islands. Although the exact positioning is not of direct
interest for optical properties, the size homogeneity is usually improved along with lateral
55

56 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
ordering. Otherwise, for electronic applications the direct access to individual dots and a
controlled spatial arrangement is inevitable for functional devices. [93, 134]
Under optimized growth conditions also for conventional unpatterned Si(001) substrates
uniform self-assembled Ge-dots were achieved [135]. Surfactant-mediated growth turned out
to yield homogeneous high-density Ge-dots (see Sec. 5.3). Furthermore, processes based on
natural substrate pre-patterning via growth instabilities on vicinal substrates [85, 104] also
resulted in the formation of purely self-organized Ge-dot growth and therefore without special
ex situ substrate preparation steps. Nevertheless the SiGe-system does not deliver perfect 3D-
ordering of quantum dots based on strain fields alone as found for other material systems [136].
Therefore different approaches were adopted to achieve organized Ge-dot nucleation and
lateral positioning. Vertical ordering of Ge-dots in growth direction gets accessible via residual
strain from the dot-layers beneath, which favors nucleation above the buried islands, and thus
results in stacking for Si/SiGe multi-layer structures. In these superlattices strain-filtering
can improve the size homogeneity for the upper Ge-dot epilayers [137]. Various attempts to
achieve 2D ordering include selective epitaxial growth within the windows of SiO2-masks [138,
139, 140], buried stress centers from oxygen implantation [141], implementation of intended
defects in general [142] or misfit dislocation networks [143]. Also, conventional lithographic
means with subsequent etching are employed to generate templates with modulated surfaces,
such as mesa structures [144, 145, 146, 147] or pits [148], offering preferential nucleation
sites for Ge-islands [149]. The periodicity of 2D pit-patterned substrates is ever shrunk by
optimization and introduction of new lithographic means such as e-beam lithography [91],
nanoimprinting [150], focused ion beam (FIB) etching [134] and x-ray interference lithography
(XIL) [151]. These high-density pit-patterns with a typical pitch well below 100 nm provide
well-defined periodic nucleation sites. For every pit the same amount of Ge-atoms contribute
to 3D growth. Thus equal material catchment areas for each single Ge-island enable state-
of-the-art Ge-dot growth with high homogeneity and a narrow size distribution. [93, 134]
Novel x-ray techniques are developed to characterize the growth mode, strain state and
shape of Ge islands during their growth on Si(001) in situ [152]. Up to now real-time Ge-dot
growth analyses were mainly reserved to STM experiments [153], which were especially suited
to explore the strain-driven transition from 2D- to 3D-growth of Ge on Si [154] with high
resolution. 2D-pit-patterned substrates are not only promising candidates for the realization
of seeded and organized growth for future applications, but also open the opportunity for basic
research to get a deeper insight and a detailed understanding of the underlying mechanisms
of Ge-dot formation.

5.2. KINETIC STEP-BUNCHING AND STRAIN-DRIVEN ISLAND GROWTH 57
Figure 5.1: AFM images of the optimized Si-ripple template (Sec. 4.2) as grown
(a) and after annealing at 550 ◦ C for 15 min (b). The ripple amplitude was decreased
during the post-growth heat treatment from ∼ 5 nm to less than ∼ 2 nm.
� Source: Kinetics n Strain annealing.jpg
5.2 Interplay between Kinetic Step-Bunching and Strain-
Driven Island Growth
5.2.1 Influence of Ripple-Template Annealing
In the following especially the growth-temperature dependence of SiGe-epilayers is evaluated.
For most SiGe-deposition procedures the temperature has to be ramped up to promote strain
effects and pronounced facet formation by approaching thermodynamic equilibrium. Hence
the growth temperature for the SiGe-epilayer has to be adjusted and stabilized within a
short growth interrupt directly after the preparation of the periodic Si-ripple template. As
the temperature ramp is known to affect the integrity of the ripple template the dependence
of annealing has to be checked to ensure a remaining 2D-pattern to be present at least in the
initial stage of SiGe-deposition. The AFM data in Fig. 5.1 show the decrease in amplitude of
the optimized Si-ripple template (Sec. 4.2) after annealing at 550 ◦ C for 15 min. The ripple
height was diminished during the post-growth heat treatment from ∼ 5 nm to less than ∼ 2 nm.
This result confirms again the kinetic origin of step-bunching but it unambiguously makes
clear that the ramp-up to the SiGe-epilayer deposition temperature has to be performed
as fast as possible to avoid loosing the ripple-structure completely. Especially for high-
temperature SiGe-epilayers the thermal volatility of the template might be a problem.
5.2.2 SiGe-Overgrowth of Step-Bunching Template – Strain-Effects
All further experiments were conducted with the optimized 1000 ˚A thick Si-buffer (at 425 ◦ C,
0.2 ˚A/s Si), which show typical dimensions of 100 nm for the ripple period and 4 nm for

58 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
the ripple height (miscut 4 ◦ [110]). By increasing the substrate miscut to 4 ◦ the period of
the evolving step-bunching structure was reduced to such an extent that the spacing of the
pronounced ripple morphology complies with the average distance of SiGe-islands deposited in
the Stranski-Krastanov growth mode. The step-bunching templates supply a one-dimensional
pattern with preferable nucleation sites for SiGe-islands along the ripple flanks, and thus
allows us to combine kinetic and strain-driven self-organization phenomena in the Si/SiGe
heterosystem.
The deposition parameters for the SiGe-epilayer were varied to find parameters where regular
strain-driven features appear. Fig. 5.2 shows the comparison of two different strained SiGe-
epilayers grown on top of the rippled Si-buffer at 425 ◦ C. The excessive strain in the 50 ˚A
Si0.55Ge0.45 top-layer (1506LSG) leads to more pronounced and regular features compared to
the 150 ˚A Si0.75Ge0.25 epilayer (1497LSG). The morphology of the SiGe-layer shows the onset
of 3D-growth with additional ridges in miscut direction and perpendicular to the elongated
bunches. The layer sequence and deposition parameters for the rippled Si-buffer and SiGe-
epilayers are listed in Tab. 5.1.
For the following investigations the thinner highly strained SiGe-epilayer (50 ˚A Si0.55Ge0.45)
was used to check the influence of the deposition temperature on the evolution of the ridge
structure. The strain is limited to < 2% to avoid plastic relaxation but high enough to get
access to the underlying mechanism.
Fig. 5.3 and Fig. 5.4 show data based on Atomic Force Microscopy (AFM) for a pure, 1000 ˚A
Sample 1497LSG 1506LSG 1539LSG
High T Buffer – – 240 ˚A Si
Si @ 0.2 ˚A/s
750 ◦ C → 425 ◦ C
Rippled Buffer 1000 ˚A Si 1000 ˚A Si 1000 ˚A Si
Si @ 0.2 ˚A/s Si @ 0.2 ˚A/s Si @ 0.2 ˚A/s
425 ◦ C 425 ◦ C 425 ◦ C
Growth interrupt – – 425 ◦ C → 625 ◦ C
(5 min)
SiGe epilayer 150 ˚A Si0.75Ge0.25 50 ˚A Si0.55Ge0.45 50 ˚A Si0.55Ge0.45
Si @ 0.2 ˚A/s Si @ 0.2 ˚A/s Si @ 0.2 ˚A/s
Ge @ 0.0667 ˚A/s Ge @ 0.1636 ˚A/s Ge @ 0.1636 ˚A/s
425 ◦ C 425 ◦ C 625 ◦ C
Table 5.1: Growth sequence for ripple-template preparation and SiGe-deposition.

5.2. KINETIC STEP-BUNCHING AND STRAIN-DRIVEN ISLAND GROWTH 59
Figure 5.2: AFM data for SiGe-epilayers grown on top of the rippled Si-buffer
at 425 ◦ C. The increased strain in the 50 ˚A Si0.55Ge0.45 top-layer (b, d, 1506LSG)
leads to more pronounced and regular features compared to the 150 ˚A Si0.75Ge0.25
epilayer (a, c, 1497LSG).
� Source: Kinetics n Strain Ge-cont var.jpg
thick Si-buffer, and the same Si-buffer covered with 50 ˚A Si0.55Ge0.45 at temperatures ranging
from 350 ◦ C to 625 ◦ C. The epilayer morphology for various temperatures is illustrated with
3D-AFM data (Fig. 5.3c and Fig. 5.4c).
Only at very low temperatures around 350 ◦ C the Si0.55Ge0.45 film replicates the underlying
ripples of the Si-buffer in a conformal manner. At 425 ◦ C the stress in the top-layer leads to the
formation of the aforementioned ridges at the ripple flanks decorating the main structure. A
slight increase of the substrate temperature leads to the development of {105}-faceted islands,
which are known from the hut-clusters of SiGe- and Ge-films [155]. Due to the high miscut of
our substrates the islands are bound by two {105}-facets and the (001)-facet on top, while the
underlying ripple pattern is widely conserved. The Fast Fourier Transform (FFT) evaluations
in Fig. 5.3b and Fig. 5.4b reveal a period of approximately 100 nm for the step bunches on the
Si-buffer under the chosen growth conditions. At medium temperatures around 550 ◦ C the
Si0.55Ge0.45 islands decorate the kinetic step bunches with a single dot row per step bunching
period, but have a somewhat smaller spacing of ∼ 70 nm along the bunches. Nevertheless there
is no clear lateral ordering discernible for 550 ◦ C, as can be seen from the broad halo that

60 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
Figure 5.3: AFM data for a pure Si-buffer, and Si-buffers covered with 50 ˚A
Si0.55Ge0.45 at various temperatures. Conventional 2D-AFM images (a), are complemented
with FFTs (b), 3D-AFM (c) and SOM representations (d), to illustrate
the transition from pure step bunching to {105}-faceted islands (see also Fig. 5.4).
� Source: Kinetics n strain SiGe45 varT01.jpg

5.2. KINETIC STEP-BUNCHING AND STRAIN-DRIVEN ISLAND GROWTH 61
Figure 5.4: AFM data and evaluation in continuation of Fig. 5.3 [89, 90].
� Source: Kinetics n strain SiGe45 varT02.jpg
appears in the FFT in addition to the well-defined signal of the periodic ripples. The ripple
flanks are preferable nucleation sites which can be used to achieve at least one-dimensional
ordering of the SiGe-islands [105]. The adatom diffusion length, which depends exponentially

62 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
on the substrate temperature, rules the spacing of the SiGe-islands along the ripples, whereas
in an appropriate temperature window the perpendicular dot distance in miscut direction is
given by the ripple period only. At 625 ◦ C (see Tab. 5.1, 1539LSG) the adatom diffusion length
is sufficiently high, so that the SiGe-island spacing matches the period of the ripples well and
an homogeneous ordering, both along and perpendicular to the ripple pattern is found. The
respective FFT shows pronounced ordering already for a single SiGe-layer. Although hard to
distinguish from a distorted hexagonal ordering, the four-fold symmetry of the hut clusters
on Si(001) and mutual island repulsion along the [100]-directions make it more likely that
the islands order anti-correlated in a face-centered rectangular fashion as already reported
by Zhu et al. [85].
The individual facets of the islands are determined from a surface-orientation-histogram,
which is derived from tilt-corrected AFM-data (Fig. 5.3d and Fig. 5.4d). For each surface
point the normal orientation [hkl] is calculated with the nearest-neighbor points to deter-
mine the local plane and then plotted in polar coordinates (ρ, φ). Whereas ρ indicates the
angle between the respective local surface normal [hkl] and the (001)-surface (growth direc-
tion), φ denotes the in-plane azimuthal angle of [hkl] with respect to [100]. The intensity
at each point (ρ, φ) in the surface orientation histogram is a measure of the abundance of a
respective surface orientation (see also Sec. 3.3.4). The marker circles correspond to surface
angles ρ of 11.3 ◦ and 25.2 ◦ , which are introduced as guidance for the characteristic {105}-
and {113}-facets in the SiGe-system [155, 156]. Both the pure Si-buffer and the buffer over-
grown with 50 ˚A Si0.55Ge0.45 at 350 ◦ C show just a streak spanning from (001) to (1 1 10)
along the [110]-direction with an average slope of 10±2 ◦ . Obviously, the surface consists of
(001)-oriented stripes and more and less inclined regions in the flanks of the step-bunches
which indicates a rounding of the ripple edges. For growth temperatures between 425 ◦ C
and 550 ◦ C the surface orientation signal extends from the center – corresponding to (001) –
towards the [105]- and [015]-directions. The asymmetry in the appearance of the {105}-facets
is based on the high miscut (Fig. 5.5) causing the shape elongation due to the vicinality of the
surface [157] and resulting in a rhombic base of the pyramids [158] (see also Sec. 5.3). The
(105)- and (015)-facets can easily grow out of the ripple-flanks whereas the formation of the
retrograding (105)- and (015)-facets occurs only for an extension of the ”downhill”-facets and
elevation beyond the upper terrace, which is kinetically suppressed at lower temperatures.
At 625 ◦ C the height of the dots drastically increases forming rather symmetric dots with
{105}- and higher-index facets. Although the underlying ripple pattern of the Si-buffer is
now hardly visible, since it has already begun to dissolve thermally (see also 5.2.1), still, the
nucleation sites of the SiGe-dots are obviously influenced by the ripple pattern: reference

5.2. KINETIC STEP-BUNCHING AND STRAIN-DRIVEN ISLAND GROWTH 63
Figure 5.5: 3D-AFM data and schematic drawings for a rippled Si-buffer covered
with 50 ˚A Si0.55Ge0.45. The distorted AFM-data representation (b) of the 3Ddata
(a) helps visualizing the faceted zigzag pattern of the step-bunching areas.
The dominant facets for the SiGe-layers deposited at 425 ◦ C and above 550 ◦ C are
depicted schematically in (c) and (d), respectively [89, 90].
� Source: Kinetics n strain model.jpg
samples on substrates with no miscut show a clear 4-fold symmetry in the FFT, which can
be easily explained with the typical hut-cluster networks (see Sec. 5.3). The SiGe top-layer is
decomposed into uniform pyramids and most of the signal is evenly distributed over all four
{105}-facets. Also, at these high growth temperatures signs of high-index facets, which are
known from Ge-domes, are found (see also Sec. 5.4).
Fig. 5.5 illustrates schematically how, and where, island nucleation commences: The SiGe-
film does not completely disintegrate into individual islands. Instead, upon SiGe-deposition
the flanks of the step bunches are converted into a zigzag train of adjacent (105)- and (015)-
facets, which is in fact a strain-driven step-meandering instability (Fig. 5.5a-b) that was
already reported by Teichert et al. [115, 116]. The originally smooth flanks with typically
10±2 ◦ inclination with respect to (001) are energetically favorable nucleation sites for the
strained SiGe-epilayer leading to the pronounced {105}-faceted ridge structure. These su-
perimposed features are oriented perpendicular to the step bunches and mark the transition

64 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
from conformal Si/SiGe epilayer growth [88] to strain-driven 3D-island growth, where the
epilayer completely decomposes into separated islands (T ∼ 550 ◦ C). For 425 ◦ C the ridge
structure consists only of the (105)- and (015)-facets that emerge easily out of the ripple-
flanks and are bound by the upper (001)-terrace to the top (Fig. 5.5c). Higher temperatures
favoring strain are needed to overcome the kinetic limitation and finally enable the formation
of the retrograding (105)- and (015)-facets (Fig. 5.5d). This is realized with the extension of
the ”downhill”-facets and elevation beyond the upper terrace, which is confining the ridges
for lower temperatures. Obviously, the Ge-rich epilayer material avoids nucleation on the
(001)-terraces in favor of 3D-growth on the ripple flanks [86]. The distorted AFM-data rep-
resentation (Fig. 5.5b) of the 3D-data (Fig. 5.5a) helps visualizing the faceted zigzag pattern
of the step-bunching areas.
The measured slope of the ripple flanks corresponds well with the 8.05 ◦ inclination with
respect to the (001)-surface of the [551] intersection line between two adjacent {105}-facets.
Therefore a special situation is expected for substrate areas with a local miscut of ∼ 8–
10 ◦ . There the {105}-faceted ridges can extend over larger distances in [110]-direction.
Such structures were demonstrated with SiGe-wires in extended holes with slowly varying
Figure 5.6: Visualization of strain relaxation. The compressively strained
Si0.55Ge0.45 epilayer can easily relief stress perpendicular to the {105}-faceted ridges
(broad black arrows). Due to the tilted base plane of these ridges (i.e {1 1 10}) there
are densely stepped edges of the wire-like structure along the [551]-direction which
enables strain relaxation along the wire direction (broad red arrows).
� Source: Kinetics n strain relaxation.jpg

5.3. ORDERING AND SIZE OF SIGE-ISLANDS 65
slope [159, 160], and with Ge-wires where STM-measurements were used to resolve the recon-
struction of the {105}-facets [105]. For these extended ridges the surface energy is minimized
with {105}-facets, which is immediately plausible. For strain energy relaxation the wire
structures might not seem that ideal right from the beginning. Clearly the one-dimensional
structure can easily relax strain in perpendicular direction. But also the densely stepped
{105}-facets are not completely inadequate for relieving strain energy along the wire direc-
tion. This is visualized in Fig. 5.6. Due to the tilted base plane of the {105}-faceted ridges (i.e
{1 1 10}) there are densely stepped edges in the wire-like structure along the [551]-direction.
This enables strain relaxation also along the wire direction (broad red arrows in Fig. 5.6).
The experiments clearly demonstrate that a reduction of the step-bunch spacing to a
value approaching the average spacing of the Si0.55Ge0.45 islands under the chosen growth
conditions couples the two otherwise independent mechanisms of kinetic (homoepitaxial) step
bunching [118, 120] and of strain-induced 3D island growth [88]. This way long-range ordering
of self-organized SiGe-dots is achieved that is entirely based on self-organization phenomena.
By optimizing the growth parameters, and by introducing strain filtering [137, 161], further
improvements in size-uniformity and ordering are possible [85, 105, 110] which will be required
for any potential applications (also see Sec. 5.1). [89, 90]
5.3 Ordering and Size of SiGe-Islands
In this section the ordering of the SiGe-islands found in Sec. 5.2.2 is picked up again. Addi-
tional experiments with different Ge-content, layer-thickness and growth temperature docu-
ment the influence of strain on ordering and size of the SiGe/Ge islands. The main intention is
again to clarify the importance of the ripple template for the nucleation of the SiGe-epilayers
on the 4 ◦ miscut substrates in comparison with flat standard Si(001).
Fig. 5.7 shows the comparison of ordering for a 50 ˚A Si0.55Ge0.45 epilayer deposited at
625 ◦ C (1539LSG) on a 4 ◦ miscut sample (Fig. 5.7a) and a flat Si(001) reference substrate
(Fig. 5.7b). As already stated in Sec. 5.2.2 for the step-bunching template a seemingly hexag-
onal ordering is found [85]. The moderate strain in the Si0.55Ge0.45 islands adjusts the island
size towards the ripple period resulting in a single-island-row arrangement per bunch. This
leads to a mean island distance of 95 nm and a density of 8×10 9 cm −2 . For the flat standard
substrate the usual simple 4-fold arrangement along the 〈100〉-directions is revealed. The
importance of the periodic ripple template with respect to ordering gets clear from Fig. 5.8.
In the growth procedure of the samples presented here a flat high-temperature (HT) Si-buffer
was used that lacked the periodic ripples. Thus there is no ordering in miscut direction which

66 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
could be associated with the periodicity of step-bunching. Instead, the 50 ˚A Si0.55Ge0.45 epi-
layer deposited at 625 ◦ C on a flat HT Si-buffer reveals a comparable hut-cluster network
along the 〈100〉-directions for the 4 ◦ miscut sample as for a flat ”dummy” substrate. The
guiding lines in Fig. 5.8a indicate the distorted 4-fold ordering due to the large miscut. Ob-
viously several islands group together and share {105}-facets which is typical for hut-clusters
on flat substrates. The missing peak in the FFT (Fig. 5.8a) points out the lack of ordering in
miscut direction for the SiGe-dots grown on top of the HT Si-buffer. For growth on the opti-
mized ripple template the two ordering trends together, namely the network formation along
the 〈100〉-directions and the island nucleation along the step-bunches, establish the basis for
a fair degree of ordering of the SiGe-islands already in the first SiGe-epilayer (Fig. 5.7a).
The AFM images in Fig. 5.9 show a comparison of the initial coarsening process in island
growth with a 25 ˚A thin Si0.55Ge0.45 epilayer deposited at 650 ◦ C (1623LSG). The slightly
higher growth temperature favors strain and a symmetric shape which can be seen with the
square base of the pyramids (flat reference sample, Fig. 5.9b) and the regular rhombic shape
due to the miscut on the tilted substrates (Fig. 5.9a). Both samples show poor ordering
and size uniformity. Thus it is startling that growth continuation to the usual thickness
of 50 ˚A can result in the well-pronounced ordering and acceptable size homogeneity for the
Si0.55Ge0.45 islands on the optimized step-bunching buffer (compare Fig. 5.7a). Obviously a
coarsening process, such as Ostwald ripening, in this case improves the homogeneity of the
islands.
The considerably increased strain in a 25 ˚A thin Si0.25Ge0.75 epilayer leads to an early onset of
3D-growth of dome-shaped SiGe-islands grown at a temperature of 600 ◦ C. Fig. 5.10 demon-
strates the striking ordering of these Si0.25Ge0.75 islands along the step-bunches indicated
Figure 5.7: AFM images and FFTs showing a fair degree of ordering in the 50 ˚A
Si0.55Ge0.45-epilayer deposited at 625 ◦ C (1539LSG) on a 4 ◦ miscut sample (a) and
a flat dummy substrate (b).
� Source: Ordering n shape 1539LSG.jpg

5.3. ORDERING AND SIZE OF SIGE-ISLANDS 67
Figure 5.8: AFM images and FFTs demonstrating the importance of the ripple
buffer. Growth on a flat HT Si-buffer reveals a comparable hut-cluster network
along the 〈100〉-directions for the 4 ◦ miscut sample (a) as for a flat dummy substrate
(b). The high miscut only results in a simple distorted 4-fold ordering with a lack
of ordering in miscut direction – as indicated by guiding lines and the missing peak
in the FFT (a).
� Source: Ordering n shape 1616LSG.jpg
by the sharp peak in miscut direction (FFT in Fig. 5.10a) in comparison to the faint 4-fold
ordering for the reference sample (Fig. 5.10b).
Alignment of Ge islands on faceted Si(001) surfaces and high-index-planes is already widely
investigated and documented in literature [86, 162, 163, 164]. The AFM data in Fig. 5.11
for pure Ge-dots demonstrate the effect of the increase in strain to its ultimate extent. The
Ge-dots (6 ML, @ 0.05 ˚A/s) deposited on top of the optimized rippled Si-buffer at 575 ◦ C
Figure 5.9: AFM images and FFTs depicting the initial coarsening process of
island growth. The slightly thinner Si0.55Ge0.45-epilayer (25 ˚A) deposited at an
increased temperature of 650 ◦ C (1623LSG) shows poor ordering and a wide size
distribution but a symmetric shape for the hut clusters with a rhombic base for the
miscut sample (a) and a square base for the flat substrate (b).
� Source: Ordering n shape 1623LSG.jpg

68 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
Figure 5.10: AFM images and FFTs revealing a proper ordering in miscutdirection
for a 25 ˚A thin Si0.25Ge0.75-epilayer deposited at 600 ◦ C. The FFT proves
a rather perfect ordering along the step-bunches for the miscut substrate (a).
� Source: Ordering n shape 1624LSG.jpg
show good size homogeneity with a mean island size of ∼ 25 nm, island distance of ∼ 35 nm
and thus a density of ∼ 2.5×10 10 cm −2 . Preferential island nucleation takes place in the ripple
flanks whereas the flat (001)-terraces of step-bunching do not show 3D-growth but exhibit flat
denuded zones (zoom-in: Fig. 5.11c). Against first expectations, there are no small Ge-wires
spanning down the ripple-flanks but there are only these small separate islands. Obviously
the local miscut in the ripple-flanks is not high enough, so that the dots cannot merge to
wires. The temperature ramp-up to 575 ◦ C is already too high and thus the amplitude of the
ripple pattern and the steep flanks degrade. On the other hand for the nucleation of Ge-dots
the growth temperature of 575 ◦ C is quite low and causes a high density of small islands.
Figure 5.11: AFM data in the usual height representation (a) and in derivative
mode (b). The Ge-dots (6 ML, @ 0.05 ˚A/s) deposited on top of the optimized rippled
Si-buffer at 575 ◦ C show good size homogeneity. Preferential island nucleation takes
place in the ripple flanks whereas the flat (001)-terraces of step-bunching do not
show 3D-growth but exhibit flat denuded zones (c).
� Source: Ordering n shape 1549LSG miscut.jpg

5.3. ORDERING AND SIZE OF SIGE-ISLANDS 69
Figure 5.12: Series of AFM images for Ge-dot growth at various temperatures
and a different layer thickness. The 4 ◦ miscut substrates (a-e) provide compared
to untilted Si(001) substrates (f-j) a slightly wider temperature window where homogeneous
Ge-dots can be found. The deposition of 6 ML Ge at a rate of 0.05 ˚A/s
shows the best size homogeneity for the ripple template around 575 ◦ C (c).
� Source: Ordering n shape Ge-dots miscut n dummy.jpg

70 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
Fig. 5.12 shows a series of AFM images for Ge-dot growth at various temperatures and a
different layer thickness. The deposition of 6 ML Ge at a rate of 0.05 ˚A/s shows the best
size homogeneity for the ripple template around 575 ◦ C (Fig. 5.12c). For increasing deposi-
tion temperatures the influence of the step-bunching template fades away and the ordinary
coarsening and multi-modal size distribution is found (Fig. 5.12a-d). As for the flat reference
substrate (Fig. 5.12f-i) pyramids, domes and super-domes showing the usual asymmetries due
to the substrate miscut are already seen for a moderate Ge-layer thickness of 6 ML. The in-
creased strain in a 8 ML thick Ge-layer leads to an irregular 3D-growth for the flat ”dummy”
substrate (Fig. 5.12j) and for the miscut sample (Fig. 5.12e) as well, even at a growth temper-
ature lowered to 550 ◦ C. The densely stepped miscut sample offers plenty of equally favorable
nucleation sites in a kinetically dominated growth regime. On flat substrate regions only a
few seeds as attractive sites for material incorporation are available. Whatever substrate is
used for higher temperatures and increased diffusion lengths the existing seeds capture most
of the Ge-adatoms. The competition of the large attractive islands leads to the inordinate
coarsening when thermodynamics rule. In summary, miscut substrates provide compared
to untilted Si(001) a slightly wider temperature window around 575 ◦ C where homogeneous
Ge-dots can be found.
Miscut Si(001) may be exploited to achieve small, regular and very dense Ge-dots which
are of interest for optical applications. In this approach neither use of surfactant-mediated
growth [165, 166, 167, 168, 169, 170, 171] nor of extremely low growth temperatures [172, 173]
is made to shrink down the dot size.
5.4 Closer Look on Surface Energy Effects – Facetting
This illustrative part comprises several AFM-images which show different states of facetting
for various epilayers. Not only details and morphological features in well-known standard
structures like pyramids and domes were revealed. Further examples demonstrate effects
of energy minimization and facetting found by chance, when unexpected sample cleaning
problems were encountered.
Fig. 5.13 depicts AFM data of 50 ˚A thick Si0.55Ge0.45 epilayers grown at 625 ◦ C (1580LSG)
and 700 ◦ C (1581LSG), respectively. These AFM images show the morphology of the untilted
reference substrates. Details regarding the layer structure of sample 1580LSG are summarized
in Tab. 5.2. The smooth Si buffer was grown with the usual ”optimized” parameters (see
Tab. 5.1). Sample 1580LSG was especially grown to check the reproducibility with our MBE-
system after updating our Ge-evaporation assembly (see Ch. 8).

5.4. CLOSER LOOK ON SURFACE ENERGY EFFECTS – FACETTING 71
Figure 5.13: AFM data of 50 ˚A thick Si0.55Ge0.45 epilayers grown at 625 ◦ C
(1580LSG) and 700 ◦ C (1581LSG), respectively. Conventional topographical data
(a, e) and data recorded in derivative mode (b, f, i) are complemented with facet
evaluation plots (SOM: d, h; SAP: c, g, j) for the flat reference samples.
� Source: Facetting d1580 d1581.jpg

72 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
Sample 1580LSG (1539LSG) 1636LSG 1635LSG
Growth interrupt 425 ◦ C → 625 ◦ C 425 ◦ C → 625 ◦ C 425 ◦ C → 575 ◦ C
(5 min) (5 min) (5 min)
SiGe/Ge epilayer 50 ˚A Si0.55Ge0.45 150 ˚A Si0.75Ge0.25 6 ML Ge
Si @ 0.2 ˚A/s Si @ 0.2 ˚A/s
Ge @ 0.1636 ˚A/s Ge @ 0.0667 ˚A/s Ge @ 0.05 ˚A/s
625 ◦ C 625 ◦ C 575 ◦ C
Table 5.2: Growth parameters for SiGe/Ge-dot layers on ”optimized” buffer.
The conventional AFM data give the usual topographical view with height information
(Fig. 5.13a), whereas the derivative recording mode during AFM operation is more sensi-
tive to height fluctuations and offers a better signal-to-noise ratio (Fig. 5.13b). Nevertheless,
from these data only the changes in slope along the scan-direction are accessible. For this
reason the topographic AFM data are exploited to evaluate facetting. In Fig. 5.13c the calcu-
lated local slope in each AFM data point is visualized in a surface-angle-plot (SAP), whereas
the already introduced histogram of specific orientations (see Sec. 5.2.2) is presented in a
surface-orientation-map (SOM) Fig. 5.13d. The upper series of images (Fig. 5.13a-d) for the
50 ˚A thick Si0.55Ge0.45 epilayer grown at 625 ◦ C shows bimodal islands with typical facetting
for the flat reference Si(001) substrate. Although {105}-facets are dominant, also {113}- and
{15 3 23}-facets can be clearly identified [156, 174, 175, 176, 177]. Steeper facets, such as
the {111}-type, are not observed here since these are usually found only for diluted Si1−xGex
islands (x < 0.2) [178]. The circles in Fig. 5.13d serve as guides to the eye and indicate surface
orientation angles for the well-known facets (from out to in: {15 3 23}, {113}, {105}). At the
higher temperature of 700 ◦ C (1581LSG) the islands grow larger and are no longer in touch
at the base (Fig. 5.13e-j), as is the case for the 625 ◦ C sample (1580LSG). The presence of
extended denuded zones around the widely separated islands results in an intensified central
x y z x y z angle [�]
0 0 1 1 1 1 54.74
15 3 23 33.63
substrate 1 1 3 25.24
(reference) 1 0 5 11.31
1 1 10 8.05
Table 5.3: Relevant facets and angles in the SiGe-system.

5.4. CLOSER LOOK ON SURFACE ENERGY EFFECTS – FACETTING 73
Figure 5.14: Topographical (a) and derivative mode AFM data (b) of a 25 ˚A thin
Si0.55Ge0.45 epilayer grown at 650 ◦ C (1623LSG). The evaluation of the local slope
is visualized in a surface-angle-plot (c) and a histogram of specific orientations is
presented in a surface-orientation-map (d). A remarkable morphological feature is
the splitting of the down-hill edge at the base of the predominantly {105}-faceted
pyramids.
� Source: Facetting m1623.jpg
spot in the SOM image indicating the (001)-orientation of the Si(001) substrate. Generally
the spots get more distinct for the higher growth temperature as the facet areas increase to-
gether with the island size. The zoom-in images for 700 ◦ C (Fig. 5.13i-j) show several stages in
the pyramid-to-dome transition. Although the upper part is typically dome-like at the base
extended foothills and remainders of pyramids are present [179]. The edges of the pyramids
exhibit partially a fringy shape. Seemingly, this is the way the pyramidal edges are dissolved
at the base, and the boundary lines are moved in and converted from a pure 〈100〉- to a
finally achieved 〈110〉-orientation (compare Fig. 5.15 and subsequent discussion). Steepening
occurs mainly near the pyramid top where steps on {105}-facets bunch and {113}-facets can
be formed [180]. The surface angles of the islands (Fig. 5.13j) agree well with the calculated
values listed in Tab. 5.3.
The fringy structure correlated with the shape transition was also observed for a 25 ˚A thin
Si0.55Ge0.45 epilayer grown at 650 ◦ C (for details see Tab. 5.4, 1623LSG). The 4 ◦ miscut of the

74 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
Figure 5.15: Model of {105}-faceted pyramid with one split edge. A region
offering a steep slope is generated automatically where the pyramidal edge meets
the groove between the fringes which could be an alternative growth center for a
{113}-facet.
� Source: Facetting edge-splitting model.jpg
sample is the reason for the rhombic distortion of the pyramidal base [158, 181, 182] as already
discussed for Fig. 5.9. This asymmetry causes the higher intensity for the larger down-hill
{105}-facets in the SOM-representation (Fig. 5.14d) compared to the small upper facets. Es-
pecially from the derivative-mode AFM data (Fig. 5.14b) and the SAP-image (Fig. 5.14c) the
remarkable morphological feature, namely the splitting of the down-hill edge at the base of
the predominantly {105}-faceted pyramids, gets obvious. The edge is split up in two fringes
which are again {105}-faceted. It is indisputable that the longer down-hill edge would show
up further steepening to relief excessive strain first. Developing this splitting gives an easy
access to transform the main base-orientation from 〈100〉 to 〈110〉 which is necessary to form
the next steeper {113}-facet in the base region. By the splitting a region of steep slope has to
be generated where the pyramidal edge meets the groove between the fringes. This could be
seen as a growth center for a {113}-facet which has to be nucleated to proceed with the tran-
sition from a pyramid- to dome-shaped island. Fig. 5.15 schematically depicts a 3D-model for
this proposed mechanism. Nevertheless there is no evidence from the AFM data (Fig. 5.14d)
which clearly supports this idea, and, as stated above, it is quite obvious from more detailed
STM images that the main pyramid-to-dome transition takes place via bunching of steps and
growth from top to bottom [180]. Nevertheless the proposed model minimizes surface en-
ergy and enables strain relief during the process of pyramidal edge dissolution. Additionally
material is provided for the rearrangement of atoms also for the upper part of an island to

5.4. CLOSER LOOK ON SURFACE ENERGY EFFECTS – FACETTING 75
realize finally an energetically stable dot shape.
Facet generation and evolution is also found for Si-overgrowth of already formed SiGe-islands.
Fig. 5.16 shows AFM data illustrating the morphological changes of buried SiGe-dots with
dependence on Si-cap thickness and growth temperature (details in Tab. 5.4, 1609LSG). Low-
temperature Si-capping results in a reversed island transition from dome- to pyramid-type
shape [179, 183, 184, 185]. With increasing Si-layer thickness the truncated pyramids ex-
tend mainly in lateral size whereas the height decreases slowly (Fig. 5.16a-b, d-e). On both
substrate types the extending islands partially merge. For the miscut samples this leads to
a formation of bunches, which exhibit still numerous constrictions (Fig. 5.16a-b). By ap-
plying a temperature ramp up to 550 ◦ C during Si-capping the structure height is strongly
reduced due the increased adatom diffusion giving faint step-bunches for the 4 ◦ miscut tem-
plate (Fig. 5.16c) and a flat surface with step-flow growth along the 〈110〉-directions for the
”dummy” Si(001) substrate (Fig. 5.16f). The change in facetting is revealed by small-scale
AFM data in the early stage of Si-capping after the deposition of 50 ˚A Si at 425 ◦ C on top of
the optimized SiGe-island epilayer for a flat untilted substrate (Fig. 5.16g). The AFM-data in
derivative mode (Fig. 5.16h) and the surface-orientation-map (Fig. 5.16i) indicate a seemingly
octagonal base shape with facets along 〈110〉- and 〈100〉-directions. For an increased Si-cap
thickness (250 ˚A) the transition from Ge-like to Si-favored high-index {11n}-type facets is
completed and the base adopts a square shape (Fig. 5.16j-l). These truncated pyramids are
thus arranged along a 〈110〉-direction, which is rotated by 45 ◦ with respect to the usual
orientation of Ge pyramids or hut-clusters.
Sample 1684LSG 1623LSG 1609LSG
Growth interrupt – 425 ◦ C → 650 ◦ C 425 ◦ C → 625 ◦ C
(5 min) (5 min)
LT-Si Buffer / 50 ˚A Si 25 ˚A Si0.55Ge0.45 50 ˚A Si0.55Ge0.45
SiGe epilayer Si @ 0.2 ˚A/s Si @ 0.2 ˚A/s Si @ 0.2 ˚A/s
Ge @ 0.1636 ˚A/s Ge @ 0.1636 ˚A/s
425 ◦ C → 350 ◦ C 650 ◦ C 625 ◦ C
Growth interrupt – – 625 ◦ C → 425 ◦ C
(5 min)
Si-cap – – 100 ˚A + 50 ˚A + 100 ˚A Si
Si @ 0.2 ˚A/s
425 ◦ C → 550 ◦ C
Table 5.4: LT-Si buffer and SiGe-epilayer growth with optional Si-capping.

76 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
Figure 5.16: AFM data illustrating the morphological changes of buried SiGedots
with dependence on Si-cap thickness and growth temperature for 4 ◦ miscut
(a-c) and flat reference substrates (d-f). For increased Si-cap thickness facets change
from Ge-like (g-i) to a Si-favored {11n}-type (j-l).
� Source: Facetting Si-capping.jpg

5.4. CLOSER LOOK ON SURFACE ENERGY EFFECTS – FACETTING 77
No clear facets can be assigned, which indicates the existence of stepped mounds [183].
Steep slopes offering angles up to those of {113}-facets are measured. Slight distortions and
imperfections in the 500 nm AFM-images and the calculated data based thereon are caused
by sample drift during the AFM measurements (see e.g. Fig. 5.16j-l).
5.4.1 Surface Energy Minimization via Excessive Facetting
It was already discussed in Sec. 5.2.2 that at moderate temperatures the ripple flanks of
step-bunching are decorated by {105}-faceted ridges (see Fig. 5.5). There the whole surface
is purely made up with (001)- and {105}-facets. Already from this, the assumption is very
close, that any 3D-object, whether it is protruding from the Si-surface or recessed into it, can
be fully lined with {105}-faceted features. The only condition, which has to be met, is, that
the inclination angle of the surfaces, which confine the rough overall shape of these struc-
tures, are close to {1 1 10}-planes. Meanwhile, such a behavior and comparable morphological
features were found for overgrown 2D-pit-patterned templates by G. Chen [91, 186] and Z.
Zhong [93] or for Ge-deposition on large-scale spherical dimples demonstrated by Watanabe
et al. [159, 160]. Pit-patterned Si-templates are currently studied to explore the influence of
the faceted ridges at the slopes of the pits on the mechanism of Ge-dot nucleation [186].
In this thesis, by chance, such faceted structures were found due to failed sample pre-
cleaning procedures. Although it took quite a while to locate the origin of the problem in the
DI-water system, this was finally not so unfortunate, as this way interesting morphologies
could be investigated. Fig. 5.17 presents AFM data in conventional and derivative mode of a
150 ˚A thick Si0.75Ge0.25 epilayer deposited on flat reference sample (see Tab. 5.2, 1636LSG).
Surface contamination hinders perfect 2D layer-by-layer growth and several extended hills
and holes are created instead. The flanks of the elevated structures exhibit angles around
∼ 10 ◦ which gets clear from the SOM- and SAP-image representation of the plain AFM-data
(see Fig. 5.17a-b, e, g). The same is seen for zoom-in AFM-data and its corresponding facet
evaluation plots (Fig. 5.17c, f, h) revealing the morphological details of a pyramid located in
the center of a pit. The major contribution of the surface is made up with {105}-facets
which is typical for Ge-rich epilayers. The low Ge-content, however, promotes also Si-type
facets at the edges of the pyramids and in the corners of the pits. Obviously sharp edges are
energetically less favorable and flattened edges exhibiting {1 1 10}-facets are preferable for
large SiGe-structures formed within a low-Ge-alloy.
The sample substrate deficiencies originating from improper cleaning are also manifested in
the AFM images of an epilayer consisting of 6 ML Ge grown at 575 ◦ C (Fig. 5.18 and Fig. 5.19).
Fig. 5.18 gives with a 5 µm AFM scan an overview of the interesting morphology on a flat

78 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
Figure 5.17: AFM data in conventional (a, d) and derivative mode (b-c) of 150 ˚A
Si0.75Ge0.25 epilayer on flat reference sample (1636LSG). The morphology evidences
the cleaning problems at that time with faceted hill and hole structures. Due to the
low Ge-content the pyramid edges are not sharp but flattened and exhibit {1 1 10}facets.
This gets clarified by surface-angle-plots (SAP: e-f) and surface-orientationmaps
(SOM: g-h).
� Source: Facetting SiGe-features.jpg
reference Si(001) substrate influenced by the failed pre-cleaning procedure. The Ge-film dec-
orates the hills and holes in the underlying Si-buffer (for layer details see again Tab. 5.2,
1635LSG). Small-scale AFM based data captured in conventional and derivative-mode are
complemented with SAP-images representing hill- (Fig. 5.19a-f) and hole- (Fig. 5.19g-l) struc-
tures that are fully lined with {105}-faceted ridges to minimize energy. The large truncated

5.4. CLOSER LOOK ON SURFACE ENERGY EFFECTS – FACETTING 79
Figure 5.18: AFM image of 6 ML Ge grown at 575 ◦ C on a flat reference Si(001)
substrate (1635LSG). The 5 µm scan gives an overview of the interesting morphology
influenced by the failed cleaning procedure. The Ge-film decorates the hills and
holes in the underlying Si-buffer.
� Source: Facetting Ge-features01.jpg
pyramids featuring {1 1 10}-faceted flanks are well suited for the nucleation of {105}-faceted
ridges (compare Fig. 5.5). The flat Si-substrate surrounding the hills and the wide plateaus
on top of the Si-pyramids are decorated by the usual small Ge-pyramids. According to the bi-
modal growth regime also Ge-domes are found. The small holes in the Si-buffer yield perfect
nucleation sites for Ge-dots as can be seen in Fig. 5.19g-i. The side-walls of the pits are only
made up of {105}-facets and therefore exhibit the same but inverted structure which is found
for the hills (Fig. 5.19j-l). A similar behavior and comparable morphological features were
found for overgrown 2D-pit-patterned templates by G. Chen [91, 186] and Z. Zhong [93] or for
Ge-deposition on large-scale spherical dimples demonstrated by Watanabe et al. [159, 160].
Fig. 5.20 shows AFM results of an Sb-mediated Ge-dot double-layer which was grown together
with a guest scientist, M. M. Rzaev (layer details are listed in Tab. 5.5, 1680RSG). Although
the original intent of this layer was to generate small Ge-dots for photoluminescence studies
the layer reveals also in the respect of facetting interesting features which again originate
from the failed wafer cleaning procedure. On the overall flat parts many small Ge-islands are
formed because the diffusion length is reduced by the surfactant antimony (Sb) and the rel-
atively low growth temperature for Ge-deposition (500 ◦ C). Although quite at the resolution
limit of the AFM, the islands exhibit the usual pyramidal shape (Fig. 5.20b) which is already
well-experienced [167]. A closer look on the deep, almost circular holes with a diameter of
about ∼ 150 nm reveals different remarkable details (Fig. 5.20c-e). The conventional AFM
image (Fig. 5.20c) shows densely packed Ge-dots at the rim of a hole, which seem to extend
down the upper part of the hole with probably {105}-faceted ridges forming a radial structure
in the derivative-mode AFM image (Fig. 5.20d).

80 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
Figure 5.19: Small-scale AFM-based data of the 6 ML Ge film grown at 575 ◦ C
(Fig. 5.18, 1635LSG). Conventional, derivative-mode AFM data and surface-angleplots
of hill- (a-f) and hole- (g-l) structures lined with {105}-facets to minimize
energy.
� Source: Facetting Ge-features02.jpg

5.4. CLOSER LOOK ON SURFACE ENERGY EFFECTS – FACETTING 81
Figure 5.20: AFM data of the Sb-mediated Ge-dot top-layer grown at 500 ◦ C
together with M. M. Rzaev (1680RSG). The defective growth arising from failed
substrate cleaning leads to faceted holes featuring ”inverted” dome-like shapes.
� Source: Facetting GeSb.jpg
The inner part of the hole is also purely faceted and offers facets usually found on domes. All
the major facets as {105}, {113} and {15 3 23} can clearly be distinguished (Fig. 5.20e). The
presented hole is obviously in its structural appearance an inverted dome. The formation of
this structure is remarkable as strain relaxation seems to be not evident for a hole. Clearly
convex surface parts are more favorable for strain relaxation compared to concave regions.
But on the microscopic scale the effect of surface curvature is also important for the surface
energy in terms of atomic bonding. In a concave region an atom has, on average, more
neighbors, which reduces the local surface energy [149]. Obviously in the present case the
(”inverted”) dome structure, which was also found by G. Chen and Z. Zhong, is dominated
by the surface energy, and strain plays a subordinate role.
The experimentally observed multi-faceted hill- and pit-structure is visualized in Fig. 5.21
with 3D-models. For comparison Fig. 5.21a shows the 3D-representation of the AFM data
already presented in Fig. 5.19a-c next to the simplified hill structure which is modeled as an
extruding truncated pyramid (Fig. 5.19b, left). The underlying shape is bound by {1 1 10}-
oriented side walls, has thus a square base along the 〈110〉-directions and is fully decorated

82 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
Figure 5.21: 3D-AFM data of a multi-faceted hill (see Fig. 5.19a) and models. An
extruding truncated pyramid (b, left) with {1 1 10}-oriented side walls, and thus a
square base along the 〈110〉-directions, is fully decorated with {105}-faceted ridges.
The whole surface is only made up with (001)- and {105}-facets. Also the inverted
pit-like structure (b, right) was found experimentally (see Fig. 5.19j).
� Source: Facetting model.jpg
with {105}-faceted ridges. The whole surface is purely made up with (001)- and {105}-
facets (see especially the encircled edge in Fig. 5.19a). The same is true for the inverted
pit-like structure (Fig. 5.19b, right) that was also found in experiments (compare Fig. 5.19j-l).
These structures are currently investigated systematically on periodically 2D pit-patterned
Sample 1680RSG
Si Buffer 250 ˚A + 500 ˚A + 250 ˚A Si
Si @ 1.0 ˚A/s
750 ◦ C → 500 ◦ C
Ge-dot layer 1 4 ML Ge + 2 ML Ge:Sb
Ge @ 0.05 ˚A/s
Sb @ 310 ◦ C (see Fig. A.4)
500 ◦ C
Si Spacer 200 ˚A + 800 ˚A Si
Si @ 1.0 ˚A/s
450 ◦ C → 500 ◦ C, 500 ◦ C
Ge-dot layer 2 4 ML Ge + 2 ML Ge:Sb
Ge @ 0.05 ˚A/s
Sb @ 310 ◦ C
500 ◦ C
Table 5.5: Growth parameters for Sb-mediated Ge-dot layers.

5.4. CLOSER LOOK ON SURFACE ENERGY EFFECTS – FACETTING 83
Figure 5.22: AFM images of 2D pit-patterned Si(001) templates with 4 ML Ge
(@ 0.03 ˚A/s) deposited at 620 ◦ C. (a) 3D-AFM image showing an array of six pits
with faulty lithography which led to a spread in the depth of the etch pits. (b)
Laplace transformation revealing the {105}-faceted morphology for the side-walls
and corners of the pits as schematically shown in Fig. 5.21b. (taken from [186])
� Source: Facetting pit-patterned substrates.jpg
substrates by G. Chen (see Fig. 5.22 taken from [186]). They are attributed to play an
important role in the initial stage of the 2D-3D transition of a strained SiGe layer on a pit-
patterned Si(001) template. Fig. 5.22 depicts an array of six pits from a part of an overgrown
pit-patterned Si(001) substrate. Fig. 5.22a shows a 3D-AFM image of these pits for 4 ML Ge
(@ 0.03 ˚A/s) deposited at 620 ◦ C with faulty lithography leading to a spread in the depth of
the etch pits. The Laplace transformation in Fig. 5.22b reveals that in the lower pit row Ge
pyramids have already developed in the center, and the full symmetry of the morphological
features both on the pit walls and in the corners has formed. The upper pits are shallower
and show merely the staircase-like surface corrugations in the corners of the pits. This
inhomogeneous region of the pit-pattern already demonstrates several stages at the 2D-3D
transition where the {105}-faceted ridges seem to be important (compare schematic view
in Fig. 5.21b). [186]
5.4.2 Step-Bunching Templates for p-Modulation Doped SiGe-Structures
A major goal of the thesis was also to investigate p-modulation doped SiGe-structures on step-
bunching templates to measure an expected anisotropy in mobility (see Ch. 6). The carriers,
holes confined in the SiGe-channel, should feel an additional scattering potential due to the
corrugation of the step-bunches for the current-flow perpendicular to step-bunching. As pre-
experiments showed the SiGe-channel has to be deposited at rather low temperatures around
350 ◦ C to suppress strain-driven morphological features and to form a smooth conformal
SiGe-layer (see Fig. 5.3). To avoid a growth interruption the Si-shutter was kept open during

84 CHAPTER 5. SELF-ORGANIZED GROWTH 2 – KINETICS AND STRAIN
temperature ramp-down to 350 ◦ C and this way a 50 ˚A thin low-temperature Si-layer was
grown on top of the optimized ripple buffer (details are listed in Tab. 5.2, 1684LSG). The
AFM measurements (Fig. 5.23) and especially the evaluation with the corresponding surface-
orientation-map (SOM, Fig. 5.23d) and surface-angle-plot (SAP, Fig. 5.23e) revealed that the
step-bunching structure on the 4 ◦ miscut sample exhibits in the ripple flanks regions of
increased slope approaching {113}-facets. This steepening obviously occurred during the
growth of the 50 ˚A LT-Si layer as the optimized Si-buffer grown at 425 ◦ C exhibits only step-
bunches with angles reaching up to 15 ◦ (Fig. 4.9). As artifacts again holes appear in the
Si-buffer which mark unintentional nucleation sites caused by bad sample pre-cleaning. The
small holes are in the center of extended humps as the incoming adatoms cannot escape the
vicinity of the holes due to the lowered diffusion length at 425 ◦ C (Fig. 5.23a).
Several experiments in this part show that pronounced facetting can also occur for low
growth temperatures (Fig. 5.23, Fig. 5.20c-e). This happens whenever surface energetics rule
at least locally and thermodynamical disorder or kinetics do not smoothen the morphology.
Figure 5.23: AFM data of a 50 ˚A LT-Si layer grown on top of the optimized
ripple buffer (1684LSG). Conventional height (a-b) and derivative-mode (c) data
are complemented with a surface-orientation-map (d) and a surface-angle-plot (e).
Especially the latter reveal that the step-bunching structure on the 4 ◦ miscut sample
exhibits in the ripple flanks regions of increased slope approaching {113}-facets (de).
Again detrimental cleaning artifacts are visible as holes in the Si-buffer (a).
� Source: Facetting LT-Si.jpg

Chapter 6
p-Modulation Doping and Mobility
Analysis
In this chapter first results on p-modulation doped Si/SiGe heterostructures grown on top of
a rippled step-bunching Si-buffer are outlined. The short-scale periodic height fluctuations
of the Si-buffer – which were extensively discussed in the previous chapters – are intended
to form well-defined undulations in the SiGe-channel of the remotely p-doped quantum well
giving rise to increased scattering. Thus an asymmetry in mobility perpendicular and par-
allel to the undulations is expected which might help to uncouple the different scattering
mechanisms which are conversely discussed as predominant hole-mobility limiting factors for
p-modulation doped structures, namely alloy scattering and interface-roughness related scat-
tering.
Earlier experiments in this direction were published by Waltereit et al. [187] for n-modulation
doped Si/SiGe heterostructures grown on vicinal Si(001) substrates on top of a composition-
ally graded strain-relaxed Si0.72Ge0.28 buffer. Also by Neumann et al. [188, 189] anisotropic
hole transport measurements on p-modulation doped SiGe channels on step-bunched vicinal
Si(113) surfaces were reported. These however were performed on Si(113) which shows strong
step-bunching but will hardly become of technical relevance. Our investigations are based on
Si(001) substrates with a miscut of 4 ◦ which are also used commercially [8].
The modulation-doped quantum well structures (MODQW) grown on a step-bunching tem-
plate enables surface roughness dependent measurements on one and the same sample which
makes the experiment and interpretation less sensitive to other growth-process- or sample
processing-induced artifacts: especially background impurity scattering is known to be hard
to control giving unpredictable results.
85

86 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
Figure 6.1: Layer sequences typically employed for (a) n-type MODQWs with
Si-channel and strain-adjusting SiGe buffer layer, (b) pseudomorphic p-MODQWs
with SiGe-channel, and (c) p-MODQWs with pure Ge (or Ge-rich SiGe) channel on
relaxed SiGe buffer layer. Depicted is the conventional architecture with frontside
doping. [6]
� Source: p-mod MODQW.jpg
Although still at the beginning, the first measurements confirm a decreased low-temperature
mobility across the undulations by nearly a factor of two. Such a remarkable effect was
beyond expectations for the Si(001) surface. Further measurements with altered parameters
such as carrier density ps, ripple period Λ and ripple amplitude H and especially Ge-content
x remain to be done. The reported results, and their continuation combined with additional
modeling are expected to provide a new approach toward settling the long-lasting dispute on
the limiting scattering mechanisms of the hole mobility in p-MODQW structures.
6.1 Introduction to p-Modulation Doped Si/SiGe Heterostruc-
tures and Hole Mobility Limitations
Modulation-doped Si/SiGe heterostructures were first realized in 1984 with a SiGe quantum
well sandwiched between the Si substrate and an unstrained Si-cap layer [193]. Selective
p-type doping in the Si cladding layers leads to an enhanced hole mobility for the estab-
lished two-dimensional hole gas (2DHG) in the SiGe-channel which is formed according to
the valence band offset. Historically later, n-doped structures featuring a two-dimensional
electron gas (2DEG) were fabricated. Employing relaxed virtual Si1−xGex substrates, an
in-plane tensilely strained Si-channel is formed due to the conduction band offset. Such re-

6.1. INTRODUCTION TO P-MODULATION DOPING 87
Figure 6.2: Valence-band (VB) and layer structure of a p-modulation doped
sample with conventional architecture. The wave-function (Ψhh) clearly shows that
the carriers are confined close to the upper Si/SiGe interface in the triangularly
shaped potential. At cryogenic temperatures only the lowest sub-band of the heavyhole
band (HH) is occupied.
� Source: p-mod structure.jpg
laxed SiGe-buffers are nowadays also used in p-type structures with Ge-rich or even pure
Ge-channels. All three structures depicted in Fig. 6.1 consist of a high mobility channel,
which is separated from the remote doping layer with a spacer layer to suppress remote im-
purity scattering. Frontside doping is the conventional architecture for modulation-doped
heterostructures having the doping layers at the side of the channel-controlling gate. This
structure is usually preferred over the ”inverted” design where the doping layer is positioned
beneath the channel at the substrate-side. There segregation of dopants can lead to undesir-
able impurity scattering and secondly the adjusting influence of an optional gate is weekend
by automatically increasing the distance between doping layer and top-gate. However, in
both architectures the contributing carriers are confined in a triangularly shaped potential
at the dopant-facing Si/SiGe interface (see also Fig. 6.2). For a well-chosen doping concen-

88 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
tration all dopants are ionized, all the free carriers are restricted to the channel, and only the
lowest sub-band is occupied. Therefore, in this ideal case conduction takes only place in the
narrow confining potential of the channel (2DEG or 2DHG) and there is no parasitic parallel
conduction path with low-mobility inside the doping region, at least not for sufficiently low
temperatures (typically < 4.2 K).
Whereas for n-MODQW structures extremely high mobilities were observed reaching values
beyond 500 000 cm 2 V −1 s −1 , p-MODQW structures seem to be restricted to hole mobilities
around 20 000 cm 2 V −1 s −1 for SiGe-channels [190, 194], and well below 100 000 cm 2 V −1 s −1
even for pure Ge-channels [195, 196] with a strongly reduced effective hole mass [197] and
absent alloy scattering. The origin of the vast difference in low-temperature mobilities is still
not clear. At least for n-doped strained-silicon heterostructures no intrinsic limitations are
Figure 6.3: Calculated 2DHG hole mobilities for a 200 ˚A Si1−xGex QW and
a carrier density of ps = 2 × 10 11 as a function of Ge-content x. The solid lines
demonstrate the estimated limitations for scattering based on deformation potential
µDP , surface roughness µSR, alloy disorder µAD, piezoelectric charges µP E.
The calculated total mobility µtot nicely fits the reported experimental 4 K data
(filled [6, 190] and open squares [191]; data of flat reference sample 1663LSG p
(see Tab. 6.1 and 6.2) is marked with a red circle). The dashed line clearly demonstrates
that alloy disorder alone without screening is not able to reproduce the
observed monotonic decrease in mobility even with an unjustifiable high alloy potential
ual = 0.74 eV (for details see text). [192]
� Source: p-mod scattering hole-mobility.jpg

6.1. INTRODUCTION TO P-MODULATION DOPING 89
found, which would impede mobilities well over 1 000 000 cm 2 V −1 s −1 , as long as uncontrolled
background doping and unintentional alloying in the quantum well can be suppressed during
growth [198]. Alloy scattering and interface-roughness scattering together with strain fluctua-
tions arising from smeared-out Si/SiGe interfaces coming along with Ge-segregation [126, 199]
and interface charges are discussed as the ultimate limitations regarding mobility. How-
ever many theoretical treatments are found in literature which usually adjust numerous
parameters to fit the experimentally observed low-mobility results for p-modulation-doped
structures. Thus often the predictions for the dominant limiting scattering mechanism are
different. [6, 7]
It seems that in the early years high relevance was attributed to alloy scattering regard-
ing low-temperature mobility [200]. Especially by accounting for screening [201], even with
utilizing unjustifiably high values of the alloy potential, the experimental data were not repro-
duced theoretically on the basis of predominant alloy scattering [202]. Also, unrealistically
high interface impurity levels were introduced into numerical calculations to explain the low-
mobility observed in hole transport [203, 204]. Other investigations favor interface roughness
scattering as limiting factor [191, 205, 206, 207].
A more recent theory claims to solve the deficiencies of earlier explanation attempts [192].
This model is not based on the ill-defined concept of interface impurity charges, but tries to
adequately include all possible scattering sources, such as alloy disorder, surface (interface)
roughness, deformation potential, and piezoelectric charges in a full treatment of the hole
mobility. Deformation potential scattering is regarded herein as the limiting mechanism,
which results from the combination of lattice-mismatch strain and surface roughness. The
latter gives random, nonuniform valence band shifts which are experienced by the holes and
subjected to non-vanishing off-diagonal components of the strain field in the SiGe layer [192].
These theoretical predictions are visualized in Fig. 6.3, where the hole mobilities limited by
individual scattering mechanisms and the calculated total mobility versus Ge-content are
plotted. The overall mobility µtot nicely fits the reported experimental 4 K data [6, 190, 191]
for the plotted range of raising Ge-content x. Alloy disorder alone without screening is ob-
viously not able to reproduce the observed monotonic decrease in mobility even with an
unjustifiable high alloy potential ual = 0.74 eV (i.e. the VB offset between Si and Ge used as
a natural choice), since there appears a calculated minimum in 2DHG alloy disorder mobility
µAD around x ∼ 0.4, which is inconsistent with experimental findings. However, this is not
such a hard proof, since the calculated minimum is very shallow and it is hard to grow 2D
layers at higher Ge-content x. According to the model at hand a surface roughness domi-
nated mobility µSR is expected only for a very low Ge-content x � 0.05, whereas just for high

90 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
Ge-contents exceeding x � 0.5 piezoelectric charges get important. The commonly experi-
mentally utilized Ge-content region (0.1 � x � 0.4) seems to be limited in low-temperature
mobility predominantly by deformation potential scattering (see Fig. 6.3). For comparison
the mobility data of the flat reference sample 1663LSG p (see Tab. 6.1 and 6.2 (page 102))
was added to Fig. 6.3 and is marked with a red circle. [192].
6.2 Experimental Aspects and Mobility Analysis
The first p-modulation-doped structures grown within this work were fabricated by MBE on
standard 4” Si-wafers to check the 2DHG transport parameters for flat substrates and to
compare the achieved results to values reported in literature. These procedure also delivers
plenty of material for testing and optimization of the Hall-bar samples. All the structures
used in the following are based on the conventional p-MODQW architecture with the doping
layer at the frontside within the Si-cap layers. The relevant valence band and layer structure
of the employed p-MODQW architecture is sketched in Fig. 6.2. The conductive 2DHG is
confined in the triangular potential within the SiGe-channel at the upper Si/SiGe interface.
The growth temperature for the Si0.75Ge0.25 channel and the subsequently deposited Si-spacer
Sample 1663LSG p 1682LSG p
Si Buffer 700 ˚A + 100 ˚A + 200 ˚A Si 240 ˚A + 1000 ˚A + 75 ˚A Si
Si @ 0.7 ˚A/s → 0.2 ˚A/s Si @ 0.2 ˚A/s
550 ◦ C → 450 ◦ C 750 ◦ C ↘ , 425 ◦ C, ↘ 350 ◦ C
SiGe Channel 100 ˚A Si0.75Ge0.25 100 ˚A Si0.75Ge0.25
Si @ 0.2 ˚A/s, Ge @ 0.0667 ˚A/s Si @ 0.2 ˚A/s, Ge @ 0.0667 ˚A/s
450 ◦ C 350 ◦ C
Si Spacer 100 ˚A Si 50 ˚A + 50 ˚A Si
Si @ 0.2 ˚A/s Si @ 0.2 ˚A/s
450 ◦ C 350 ◦ C → 425 ◦ C, 425 ◦ C
p-doping 200 ˚A Si:B (p2.5e18 #/cm 3 ) 200 ˚A Si:B (p2.5e18 #/cm 3 )
Layer Si @ 0.2 ˚A/s, B @ 1717.9 ◦ C Si @ 0.2 ˚A/s, B @ 1717.9 ◦ C
450 ◦ C 425 ◦ C
Si Cap 100 ˚A + 600 ˚A Si 100 ˚A + 100 ˚A + 500 ˚A Si
Si @ 0.2 ˚A/s → 0.7 ˚A/s, 0.7 ˚A/s Si @ 0.2 ˚A/s → 0.7 ˚A/s
450 ◦ C → 550 ◦ C, 550 ◦ C 425 ◦ C → 500 ◦ C → 550 ◦ C, 550 ◦ C
Table 6.1: Layer sequence of conventional p-modulation doped structures.

6.2. EXPERIMENTAL ASPECTS AND MOBILITY ANALYSIS 91
layer is chosen as compromise between good crystal quality and a sharp Si/SiGe interface.
The growth parameters for such a structure grown on a flat Si-substrate (1663LSG p) are
listed in Tab. 6.1. For the actual samples with predefined modulations in the SiGe-channel
the growth temperatures had to be lowered even further (Tab. 6.1, 1682LSG p). This be-
came necessary to suppress unwanted, strain-driven corrugations at the Si/SiGe interface
(see Fig. 5.2). Otherwise, additional fringes perpendicular to the periodic ripples pattern
could interfere with the desired surface roughness which should involve just step-bunching.
According to the usual practice (Sec. 4.2), the samples on small pieces of miscut substrates
were grown simultaneously with a flat reference sample (both: 17.5 mm × 17.5 mm) mounted
in an all-Si substrate adapter for direct comparison. The low growth temperature should
not be that detrimental for the miscut sample because the high step density still enables
step-flow growth. In contrast for the flat substrates the crystal quality is expected to be
strongly reduced. Nevertheless, for a first set of samples the used, but not yet optimized pa-
rameters regarding layer thickness, growth temperature, doping level and SiGe-composition
are envisaged to show at least the principle functionality of the approach to implement a
step-bunching-induced modulation in the SiGe-channel for a mobility analysis.
6.2.1 Processing of Hall-Bars
The usual procedure starts with the preparation of the substrates that are intended for Hall-
bar processing. The first step is cutting the samples to an adequate size. From full-size
grown wafers ∼ 2 cm × 2 cm pieces are cleaved from the central region by using a diamond
scribing table, whereas small substrates can be used directly. After protecting the sample
surface with a thin photoresist layer the respective piece is glued with a special wax to a
glass microscope slide and the chuck of the diamond wire saw [208]. This precision saw is
used to cut the sample to a useful size of about 5 mm × 4 mm. A rectangular size is especially
useful for miscut samples to document the orientation of the ripple pattern. After cutting
and releasing the samples from the wax on a hot plate (∼ 120 ◦ C) the residues of wax and
photoresist are stripped in acetone (ultrasonic bath, 5 min). Further cleaning continues with
the usual pre-cleaning sequence and subsequent ultrasonic cleaning steps in trichlorethylene,
acetone, and methanol for 3–5 min each. A final Piranha-etch (H2SO4 : H2O2 = 5 : 1, 15–
20 min) and DI-H2O rinse concludes the required cleaning procedure, and the samples are
blown dry (N2).
In all subsequent masking steps Shipley S1818 photoresist was used as follows. The spinning
parameters were ∼ 3 sec at a rotation speed of 2000 rpm and ∼ 40 sec at 4000 rpm to realize a
homogeneous photoresist layer. A softbake at 90 ◦ C in an oven was applied to outgas exces-

92 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
Figure 6.4: (a) Photograph of processed Hall-bar on structure 1682LSG p (miscut
substrate) mounted and bonded onto a ”Stycast” sample carrier. (b) The zoomin
shows the two perpendicular branches of the Hall-bar structure together with
the pin numbers assigned for the measurements. (c) Schematics of metal contact
pads (red color) and etched Hall-bars (blue color). The line pattern indicates the
elongation direction of step-bunching. Thus the upper branch of the Hall-bar is
used to measure the conductivity σ || parallel to the bunches and the lower branch
σ⊥ perpendicular to the ripple structure.
� Source: p-mod Hall-bar 1682LSGp miscut01.jpg
sive solvents. A chromium-quartz mask with a Hall-bar lay-out featuring two perpendicular
branches for anisotropy measurements was used. The mask was designed by T. Berer during
his diploma thesis for AlGaAs-samples (see [209], p. 104, Fig. 8.13e-f). Thus a self-aligned
top-gate was not implemented and is therefore not available. The photoresist was exposed
in a Süss MJB3 mask-aligner for 8 sec and subsequently developed (MF319, 60 sec). Rinsing
the sample for ∼ 2 min in DI-H2O stops the developing procedure.
In the first masking step the contact pads are defined and the photoresist covers the inverse
areas. A 20 sec short ashing-step in an O2-plasma (200 W, 1 torr) is applied to remove rem-
nants of the photoresist or solvents. Immediately before the samples are transferred into the
vacuum environment of the evaporation chamber an HF-dip (HF : DI-H2O � 1 : 10, 20–30 sec)
is adopted to strip the natural SiO2 from the exposed contact areas. The sample are again
dried with the N2-nozzle. 1000 ˚A aluminum (Al) is evaporated which is the common material
for p-type contacts. In the ultrasonic bath acetone is used to lift-off the photoresist and the
metal layer above. Methanol concludes the cleaning sequence (US-bath, 3–5 min), and the
samples are again blown dry. The Al-contacts are alloyed in a special annealing oven in an
ambient of forming gas (Ar/H2, 0.25 bar). The annealing step at nominally 450 ◦ C for 6 min
enables a Al-Si inter-diffusion providing ohmic contacts. During this heat treatment the sam-
ple is separated from the heater furnace with a plain Si-wafer piece to prevent contamination

6.2. EXPERIMENTAL ASPECTS AND MOBILITY ANALYSIS 93
from the back-side.
The same masking procedure is executed a second time to adapt the metal contacts. This
time after the O2-ashing step no HF-dip is applied and onto the contact pads 150 ˚A chromium
(Cr) as undercoating and 1250 ˚A gold (Au) are evaporated to provide solid contact pads for
wire-bonding.
After lift-off and cleaning the photoresist mask for mesa-etching is created in a working pro-
cedure analogous to the steps listed above. The asher [210] is exploited a last time before
the samples are placed in the reactive-ion-etching machine (RIE) [211]. The etching process
defines the ”Hall-bar” structure since outside the mesa-structure the 2DHG-layers are com-
pletely removed. For this purpose the employed etching parameters (2 min @ 5 mtorr; 90 W;
5% O2, 25% SF6) provide an etch depth of ∼ 200 nm. Subsequent photoresist stripping yields
a completely processed Hall-bar without top-gate.
The samples are mounted on exchangeable ”Stycast” sample holders with a special adhesive † .
Afterwards, the contact pads are inter-connected with the pins of the sample carrier using
a wire-bonding machine with Au-wire. The bonded wire-ends stick nicely to the Au-covered
contact pads but not so well to the pins of the self-made ”Stycast” sample holder. Therefore,
the wires are additionally soldered with indium (In) at the pin-side to secure the mechanical
and essential electrical connection.
The samples are now prepared and ready for the electrical characterization in a 7 T super-
conductivity magnet. In Fig. 6.4a a photograph of the finally processed Hall-bar on structure
1682LSG p (miscut substrate) mounted and bonded onto a ”Stycast” sample carrier is repre-
sented. The zoom-in (Fig. 6.4b) shows the two perpendicular branches of the Hall-bar struc-
ture together with the pin numbers assigned for the cryo-measurements. Fig. 6.4c depicts
schematically the metal contact pads (red color) and the Hall-bars defined by the mesa-etch
(blue color).
6.2.2 Cryo-Measurements and Data Evaluation
The electrical characterization was performed in a 4 He-immersion cryostat with an adjustable
magnetic field up to B = 7 T. The inner reservoir where the sample is located can be pumped,
which extends the temperatures available for measurements from the standard liquid 4 He tem-
perature (TLHe � 4.2 K) down to ∼ 1.6 K. A sample heating unit provides the possibility to
perform temperature-dependent measurements up to room temperature (∼ 300 K). Further
details of the 4 He-system can be found in Ref. [212].
† also known as ”Pudalov-glue” at the institute

94 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
The basics of electronic transport and measurements regarding the Shubnikov–de Haas (SdH)
and the Integer Quantum Hall (IQH) effect can be found in standard semiconductor physics
text books [213, 214, 215]. For further reading on data evaluation from electrical and magneto-
transport experiments the reader is advised to have a look at Ref. [216].
All transport data presented in this section were gathered by a dc-measurement technique.
A dc-current of I = 1 µA was established along the branches of the Hall-bar structure. Al-
though the current was usually driven between pin 5 and pin 12 (see Fig. 6.4c) a homoge-
neously current flow along each branch was realized, which is fully equivalent to currents
directed separately between contacts 5 and 9 or 9 and 12, respectively. The realization of
the conventional 4-point measurement setup decouples the detected longitudinal resistivity
RL from the quality of the contacts. Thus the normalized longitudinal resistivity ρxx can
be precisely calculated from the longitudinal voltage drop between the inner contact pads,
e.g. between 6 and 8 or 10 and 11, which is measured with a high impedance voltage meter.
The geometry of the Hall-bar, in fact the ratio between the width W and the length L, has
to be considered to extract the correct value for ρxx according to Eq. 6.1. The length L is
the distance between the contacts applied for measuring the longitudinal voltage drop VL.
Therefore the geometry factor is G = 1 for neighboring contacts such as 6 and 7, and G = 0.5
for the preferred longitudinal voltage measurements such as between 6 and 8.
G = W
L , RL = VL
I
ρxx = RL · G
(6.1)
The Hall-voltage VH picked up at contacts located across the Hall-bar, e.g. between pins 3
and 6 or 1 and 11, is a direct measure for the Hall-resistivity ρxy after Eq. 6.2.
ρxy = VH
I
(6.2)
At sufficiently low temperatures T , where thermodynamical broadening does not conceal the
energy splitting of the Landau levels, and at a reasonably high magnetic fields B the two-
dimensionality of the hole gas (2DHG) gets obvious from the Shubnikov–de Haas oscillations
in ρxx and the Integer Quantum Hall effect in ρxy. For all investigations the samples were
orientated in the cryostat in such a way that the magnetic field was aligned in perpendicular
direction to the 2DHG. Thus, the relevant perpendicular magnetic field component B⊥ is
equal to the absolute value of the applied magnetic field B (B⊥ ≡ B).
Fig. 6.5 shows the measured data gathered from a magnetic field sweep for the extracted
resistivity along (ρxx) and across (ρxy) the upper branch of the Hall-bar of sample 1663LSG p,
which was grown on a flat standard Si-substrate. Although not shown here, the transport
investigation for the lower branch produced comparable curves since there is no intrinsic

6.2. EXPERIMENTAL ASPECTS AND MOBILITY ANALYSIS 95
anisotropy in the structure. The Hall-bars are oriented along the two perpendicular 〈110〉-
directions. The B-sweep at ∼ 1.7 K yields pronounced SdH-oscillations in ρxx and extended
plateaus featuring the Integer Quantum Hall effect in ρxy. The increase of the resistivity
ρxx around B = 0 T can be attributed to a phenomenon called weak localization effect. This
is a quantum-mechanical interference effect arising from coherent backscattering of single
electrons, which is associated with an additional contribution to resistivity (see also [212,
216]).
Fig. 6.6 represents the same data depicted in the previous figure (Fig. 6.5) but plotted as a
function of the inverse magnetic field 1/B at the abscissa, and with the Hall-resistivity ρxy
normalized to the universal resistance 25 812.8 Ω (h/e 2 ) [217]. The quantized Hall resistance
gives integer filling factors ν of the Landau levels according to Eq. 6.3.
ρxy = 1 h
ν e2 (6.3)
Fig. 6.6b demonstrates the filling factor ν of the Landau levels with extended plateaus for
even values due to spin degeneracy gs = 2 and valley degeneracy gv = 1 in the valence band.
For magnetic fields exceeding ∼ 5 T the spin degeneracy is already slightly lifted, which gets
obvious from the faintly appearing plateau at ν = 5.
The transport parameters of the holes confined in the SiGe-channel were predominantly
calculated from longitudinal resistivity ρxx and especially via the SdH-oscillations. These
deliver information which is based purely on the electronic properties of the 2DHG and
do not account for the carriers in a potential parasitic channel in the doping region. The
hole sheet carrier density ps in the 2DHG, therefore often also referred to as p2D, is either
calculated from the periodicity of the SdH-oscillations as a function of inverse magnetic field
∆(1/B) (Eq. 6.4) or directly from the position of an SdH-minimum with regard of magnetic
field B, whenever the filling factor ν is known (Eq. 6.5).
ps = e
h gsgv
�
∆ 1
�−1 B
(6.4)
ps = ν e
B (6.5)
h
The mobility µ can be recalculated from the longitudinal conductivity σxx or the resistivity
ρxx for zero magnetic field (B = 0 T). Since the mobility µ depends on the carrier density
(Eq. 6.6) an accurate determination of the hole density ps is necessary for a reliable assessment
of the mobility µ.
σxx = (ρxx) −1 = pseµ → µ = 1 −1
(ρxx)
pse
(6.6)

96 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
Figure 6.5: Measured data of (a) Shubnikov–de Haas (SdH) and (b) Integer
Quantum Hall (IQH) effect at ∼ 1.7 K in a perpendicular magnetic field for a flat
p-modulation doped SiGe-structure (1663LSG p).
� Source: p-mod Hall-bar 1663LSGp SdH QH B.jpg
In this work the measured data point ρxx(B=0T) was not directly extracted from the B-
sweep. Instead, the additional resistivity contribution of the weak localization effect was
neglected by extrapolating the resistivity curve from finite magnetic fields towards B = 0 T.
This leads generally to slightly reduced resistivity values and finally results in enhanced mo-
bility readings. The extracted transport properties of sample 1663LSG p characterized at
4.2 K and 1.66 K are summarized in Tab. 6.2 (see page 102). The recalculated values for ps

6.2. EXPERIMENTAL ASPECTS AND MOBILITY ANALYSIS 97
Figure 6.6: Representation of the same experimental data from Fig. 6.5 plotted
as a function of the inverse magnetic field. The equidistant SdH-oscillations in this
plot (a) are used to derive the carrier concentration ps. The lower graph (b) shows
the filling factor ν of the Landau levels with extended plateaus for even values (spin
degeneracy gs = 2, valley degeneracy gv = 1).
� Source: p-mod Hall-bar 1663LSGp SdH nu invB.jpg
and µ have to be considered with an uncertainty or error bar of up to 10–15%. The achieved
mobility is comparable to literature values for a Si0.75Ge0.25 channel although clearly below
the reported record mobilities [6, 190, 191] (see again Fig. 6.3).
After the pre-experiments with flat ”high”-mobility p-modulation doped material the ac-

98 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
Figure 6.7: Schematic drawings of p-SiGe conventional modulation-doped structure
with frontside doping where the conduction takes place at the upper interface
of the SiGe-channel. The modulation of the channel yields expected differences in
conductivity for measurements parallel (σ ||) and perpendicular (σ⊥) to the ripple
structure.
� Source: p-mod conductivity model.jpg
tual measurements were addressed. Here the p-MODQW structures grown on step-bunching
templates were envisaged for measuring a mobility anisotropy. Again, the branches of the
Hall-bar structure were processed with orientation along the 〈110〉-direction. This way the
buried ripple structure – giving a modulation at the upper Si/SiGe-interface, and thus of the
2DHG – is aligned parallel to the upper branch and perpendicular to the lower branch of the
Hall-bar (see Fig. 6.4c). The modulation of the channel yields expected differences in con-
ductivity for the measurements parallel (σ ||) and perpendicular (σ⊥) to the ripple structure.
Fig. 6.7 depicts schematic drawings of p-SiGe modulation-doped structure with frontside dop-
ing where the conduction takes place at the upper interface of the SiGe-channel. The electrical
properties were investigated in detail for two sets of samples (1882LSG p, 1883LSG p), each
a sample on miscut substrate and on a flat reference substrate. The growth sequence for
p-MODQW structure 1883LSG p is identical to 1882LSG p except for the lowered doping
concentration (p1.0e18 #/cm 3 ) in the Si:B doping layer.
Fig. 6.8 shows selected B-sweep measurement curves of the longitudinal resistivity ρxx
(Fig. 6.8a) and the transversal resistivity ρxy (Fig. 6.8b) for the Hall-bars parallel (solid
curves) and perpendicular (dashed curves) to the periodic modulations in the SiGe-channel
due to step-bunching. A LED mounted near the sample is utilized to illuminate the sample.
The light generates electron-hole pairs which modifies the carrier concentration depending on
the illumination level. This is a poor, but successful, substitute to tuning the carrier density

6.2. EXPERIMENTAL ASPECTS AND MOBILITY ANALYSIS 99
Figure 6.8: Plots of the longitudinal resistivity ρxx (a) and transversal resistivity
ρxy (b) for the Hall-bars parallel (solid curves) and perpendicular (dashed curves)
to the periodic modulations in the SiGe-channel due to step-bunching. The data
for miscut sample 1682LSG p recorded at 4.2 K and ∼ 1.6 K are plotted for different
stages of sample illumination.
� Source: p-mod Hall-bar 1682LSGp miscut01 SdH QH B.jpg
with a top-gate. Data recorded at 4.2 K and ∼ 1.6 K at different stages of sample illumination
are plotted for miscut sample 1682LSG p (see Fig. 6.8). Tab. 6.2 gives a complete overview on
the measurement parameters and the extracted values for carrier density and mobility of the
investigated samples. Again it has to be remarked that the confidence of the data evaluation

100 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
Figure 6.9: Evaluated data from Fig. 6.8 summarized in a plot showing mobility
µ versus carrier concentration ps for miscut sample 1682LSG p. The data clearly
prove a lower carrier mobility perpendicular to the ripples due to increased scattering.
� Source: p-mod Hall-bar 1682LSGp miscut01 mu p.jpg
is estimated to be within a 10–15% uncertainty. From Fig. 6.8a it can clearly be seen that the
resistivity ρxx for the investigation along (||) and across (⊥) the ripple modulation forms two
groups of curves in the resistivity plot. Obviously, the conductivity µ || is by nearly a factor of
two higher in the upper branch of the Hall-bar structure although the carrier densities ps are
comparable (see Fig. 6.8b). This indicates a strong influence of the step-bunching structure
on the 2DHG mobility. The evaluated data of the miscut sample 1682LSG p are summarized
in a plot showing the mobility µ versus carrier concentration ps (Fig. 6.9). The data clearly
prove a lower carrier mobility perpendicular to the ripples due to increased scattering.
The change in temperature from 4.2 K to ∼ 1.6 K does not affect the carrier concentration or
mobility remarkably. Nevertheless, the lowered temperature clearly enhances the oscillation
amplitude of the SdH-effect and produces well-pronounced IQH-plateaus (Fig. 6.8). As pre-
dicted for a considerable illumination level, the carrier concentration in the SiGe-channel is
increased which directly lowers the resistivity. Additionally, the raised level of free carriers
favors higher mobilities due to the effect of screening where perturbing scattering potentials
are partially shielded (Fig. 6.9). This second effect further lowers the classical longitudinal
resistivity ρxx on which the quantum-mechanical Shubnikov–de Haas oscillations are over-

6.2. EXPERIMENTAL ASPECTS AND MOBILITY ANALYSIS 101
layed. In ρxy the overall slope is decreased along with enhanced carrier density since this
slope is a direct measure in conventional Hall characterization to evaluate the carrier density
ps. For all the involved illumination levels the detected ps is nearly identical for both Hall-bar
branches, which is proved by the positions of the SdH-minima in the ρxx-plot (Fig. 6.8a) and
the almost congruent ρxy-curves (Fig. 6.8b).
6.2.3 Data Interpretation
In all investigated samples the doping level was rather high so that already without illu-
mination the SiGe-channel was almost fully populated with carriers (ps ∼ 5 ×10 11 cm −2 , see
Tab. 6.2). Therefore the lower doped samples 1883LSG p showed carrier densities compara-
ble to 1882LSG p. Long-lasting permanent effects arising from previous sample illumination
were not observed. Usually, some minutes decay time provided, the recorded data before and
after illumination were comparable.
Some inconsistencies with the results are found for the flat reference sample 1882LSG p
(referred as 1882 (d) as abbreviation for 1882LSG p dummy) itself and furthermore by com-
parison with the lower doped sample 1883LSG p. Although no intrinsic anisotropy should be
involved for the two branches of the flat 2DHG-sample 1882LSG p (dummy), the character-
ization showed an extremely low mobility value for the upper branch (see Tab. 6.2: 1682 (d)
before illumination and at 4.2 K). Since a contact problem was suspected, the sample was
unmounted, the contacts were checked and the sample was reinstalled into the measurement
set-up, rotated by 90 ◦ . After the involved warm-up and cool-down procedure the sample
behaved differently (1682 (d)*) and more reasonably. The unexpected anisotropy observed
before was gone (or even slightly inverted). This indicates fluctuations in the sample which
might be attributed to structure induced defects. It was not further investigated whether
this anomalousness arises from growth defects or from post-processing.
More interestingly, the observed mobilities for the different samples do not fit into a simple
systematics. Whereas the lower doped miscut sample 1883LSG p (m) shows unpredictable
results except for high illumination, the corresponding dummy sample (1883LSG p (d)) per-
forms well already without illumination. This flat reference sample even outperforms the
nominally higher doped dummy 1882LSG p (d), except for high illumination where the latter
sample seems to recover performance. A decrease in carrier density with increasing illumi-
nation is found for sample 1882LSG p (d) and 1883LSG p (m) (see Tab. 6.2) which is an un-
expected result. Generally the samples 1882LSG p (d), 1883LSG p (m), and 1883LSG p (d)
would benefit definitely from top gates, which should give more reproducible and reliable
measurement results since surface potentials are then well defined.

102 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
Sample
upper branch (Pin 5-9) lower branch (Pin 9-12)
mobility µ || hole conc. ps mobility µ⊥ hole conc. ps
[cm 2 V −1 s −1 ] [×10 11 cm −2 ] [cm 2 V −1 s −1 ] [×10 11 cm −2 ]
illum. temp.
1663 2690 5.65 2670 5.65 – 4.2 K
1663 2880 5.60 2830 5.60 – 1.66 K
1682 (m) 1350 5.00 745 5.00 before 4.2 K
1682 (m) 1330 5.00 685 5.00 before 1.64 K
1682 (m) 1190 4.80 630 4.80 after 1.64 K
1682 (m) 1360 5.20 695 5.30 5 nA 1.64 K
1682 (m) 1450 5.50 845 5.70 50 nA 1.61 K
1682 (m) 1500 5.80 875 5.85 250 nA 1.61 K
1682 (m) 1280 4.85 690 4.85 after 1.59 K
1683 (m) 340 5.00 290 6.10 before 1.64 K
1683 (m) 390 5.30 540 4.20 after 1.67 K
1683 (m) 1230 4.40 695 4.40 50 nA 1.68 K
1683 (m) 1300 4.70 760 4.60 250 nA 1.69 K
1682 (d) 590 4.95 900 4.95 before 4.2 K
1682 (d) 2400 4.55 2400 4.55 250 nA 4.2 K
1682 (d)* 950 4.60 860 4.70 – 4.2 K
1682 (d)* 940 4.60 850 4.70 – 1.65 K
1683 (d) 1300 5.40 1300 5.30 – 4.2 K
1683 (d) 1300 5.40 1300 5.30 – 1.65 K
Table 6.2: 2DHG transport parameters evaluated from SdH-measurements. The
mobilities parallel (µ ||) and perpendicular (µ⊥) to step-bunching are listed for the
upper and lower branch of the different Hall-bar samples, respectively. The different
samples are specified in abbreviated notation: (m) denotes miscut and (d) flat
reference (”dummy”) samples. Sample 1663 was grown on a flat standard 4”-Si-
wafer. The ”*” indicates a second measurement after sample reinstallation (rotated
by 90 ◦ ), and associated warm-up/cool-down procedure for sample 1682 (d).

6.2. EXPERIMENTAL ASPECTS AND MOBILITY ANALYSIS 103
The highest mobility was found for the flat sample 1663LSG p. This is not surprising
as in the growth procedure of this sample a more appropriate growth temperature could be
applied (see Tab. 6.1). Especially for the flat reference samples 1682LSG p and 1683LSG p
the crystal structure suffers from the reduced substrate temperature, which became necessary
to prevent strain-driven features at the Si/SiGe-interface perpendicular to step-bunching (see
also preamble of Sec. 6.2). For another reason it is not possible to directly compare the mis-
cut and reference samples. Although these were grown simultaneously they were grown at a
slightly different location in the MBE-system with regard to the sources. The samples were
oriented in the growth chamber with the miscut substrate at the Ge-rich side and the reference
dummy substrate at the Si-rich side. Therefore, some differences in the SiGe-composition –
layer thickness and Ge-content – and doping concentration (see Ch. A) are always present.
These are complications which impede a direct comparison of several measurement results.
According to the evaluation of calibration data (see Ch. A, especially Tab. A.3) deviations
from the nominal parameters of the SiGe-channel were estimated and are listed in Tab. 6.3.
The differences in doping level should play only a subordinate role since in all cases the chan-
nel seems to be highly filled with hole-type carriers. The SiGe-channel thickness can also
be neglected because the carriers are confined at the upper Si/SiGe interface in a triangular
potential anyway. Presumably the most significant restriction is in this sense probably the
Ge-content, since its value deviates from the nominal value, which is calibrated for the center
position in the growth chamber, by x = 0.25 ± 0.05 for the Ge-rich and Si-rich side, respec-
tively (Tab. 6.3). Although the dependence of Ge-content on the mobility is already weak
around x = 0.25 (see Fig. 6.3), the Ge-content is next to the growth temperature the major
complication for a direct data comparison.
Therefore, the following considerations are mainly related to miscut sample 1682LSG p.
Although there was the justified expectation to measure an anisotropy in mobility for a
Hall-bar oriented parallel to the ripple modulation (upper branch) and perpendicular (lower
branch), such a remarkable effect with a factor of two difference in µ seemed to be well out
of scope. To rule out severe constrictions in the SiGe-layer, cross-sectional transmission elec-
tron microscopy (XTEM) investigations were conducted on miscut sample 1882LSG p (m).
growth position center (calibr.) Si-rich side Ge-rich side
SiGe-channel thickness Lz [˚A] 100.0 102.4 93.7
Ge-content x 0.250 0.225 0.275
B doping conc. p [#/cm 3 ] 2.5e18 2.9e18 1.8e18
Table 6.3: Deviations of the SiGe-channel parameters for different positions.

104 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
Figure 6.10: XTEM images stiched together depicting the dark Si0.75Ge0.25
channel of miscut sample 1682LSG p, embedded between Si-buffer and Si-spacer
layer. The view along the ripple direction [110] reveals a seemingly homogeneous
Si0.75Ge0.25 layer thickness. The Si/SiGe interface is only partially smeared out due
to slight modulations along the bunches lying within the finite sample thickness in
view direction.
� Source: p-mod XTEM 1682LSGp Imag10-14.jpg
Fig. 6.10 presents a set of XTEM images stiched together depicting the dark Si0.75Ge0.25
channel embedded between Si-buffer and Si-spacer layer. The view along the ripple direction
[110] reveals a seemingly homogeneous Si0.75Ge0.25 layer thickness. The SiGe channel repli-
cates the underlying step-bunched Si-buffer in a conformal manner. The Si/SiGe interface
is partially smeared out due to slight modulations along the bunches lying within the finite
sample thickness in view direction. The contrast in the presented XTEM data was strongly
enhanced and optimized to reveal the morphological details of the sandwiched SiGe-layer.
Therefore the epoxy glue, which would appear on top is not visible within the shown gray
scale. The top part of the Si-cap layer is clearly amorphous which is an artifact generated by
ion-sputtering and sample thinning during the TEM-preparation procedure. Fig. 6.11a shows
another more detailed XTEM image of the Si0.75Ge0.25 channel of miscut sample 1682LSG p.
The red box serves as guide to the eye to help resolving the periodic modulations (Λ ∼ 100 nm)
of the Si0.75Ge0.25 channel. The modulation amplitude of the SiGe quantum well is clearly
on the nanometer scale. For comparison the SiGe-channel thickness reads ∼ 10 nm. As far

6.2. EXPERIMENTAL ASPECTS AND MOBILITY ANALYSIS 105
Figure 6.11: (a) More detailed XTEM image of the Si0.75Ge0.25 channel of miscut
sample 1682LSG p. The red box serves as guide to the eye to help resolving the
periodic modulations (Λ ∼ 100 nm) of the Si0.75Ge0.25 channel grown on top of the
step-bunching template. (b) Representation of the same image squeezed together
in lateral direction to emphasize the modulation of step-bunching for the SiGechannel.
The red arrows indicate the minima of the undulations with ∼ 100 nm
periodicity.
� Source: p-mod XTEM 1682LSGp Imag09.jpg
as can be seen in these XTEM images both Si/SiGe interfaces are rather sharp (except for
aforementioned sporadic undulations of the SiGe-channel in view direction) and do not in-
dicate significant intermixing or Ge-segregation. As expected, the doping layer cannot be
identified from these views. The interface between substrate and epitaxial layers is located
∼ 130 nm below the SiGe-channel and is not decorated with defects. This proves a proper
crystal growth based on a successfully performed precleaning procedure. In Fig. 6.11b the
XTEM image of Fig. 6.11a is represented squeezed together in lateral direction to emphasize
the modulation of step-bunching for the SiGe-channel. The red arrows indicate the minima
of the undulations with ∼ 100 nm periodicity.
It seems to be straightforward that the strongly reduced mobility is due to roughness scatter-
ing events as the holes experience the modulation of the Si/SiGe interface when drifting across
the step-bunches. To confirm this it is necessary to compare the length scales of typical trans-
spin degeneracy gs
valley degeneracy gv
effective mass m ∗ 0.28 m0 [kg]
carrier density ps 5.0×10 11 [cm −2 ]
mobility (perp.) µ 700 [cm 2 V −1 s −1 ]
Table 6.4: Parameters employed for the estimation of scattering.
2
1

106 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
port related parameters and the period of the undulations of step-bunching. The thickness
fluctuations of the SiGe quantum well are characterized in terms of correlation length Λ and
amplitude ∆ of the surface roughness. Usually only short-range surface roughness is treated
(kF · Λ ≪ 1) and used as fitting parameter to experimental mobility data [192, 218, 219]. In
the present case the roughness parameters for the SiGe-channel are Λ ∼ 100 nm and ∆ ∼ 4 nm.
According to simple transport related formulas and typical parameters for the characterized
p-modulation doped structures on miscut samples (Tab. 6.4) the Fermi wave number (Eq. 6.7)
kF =
� 4πps
gsgv
(6.7)
and the mean free path lmfp (Eq. 6.8) are calculated. The latter is a product of the Fermi
velocity and the momentum relaxation time which is also known as transport lifetime.
vF = �kF
m∗ µ = eτm
m∗ → τm = m∗ µ
e
lmfp = vF · τm = �kF
µ
e
(6.8)
The estimated values are listed in Tab. 6.5. The comparison of the Fermi wave number kF and
the interface roughness correlation length Λ shows that the condition for short-range surface
roughness (kF · Λ ≪ 1) is not fulfilled in the present case. The reciprocal Fermi wave number
k −1
F
is by an order in magnitude smaller than the period of step-bunching Λ. Interestingly, the
mean free path is by more than a factor of 10 smaller than the ripple distance as well. This
means that on average several scattering events occur between two adjacent ripples. Along the
bunches the mean free path is just by the discussed factor of two larger and reaches estimated
values around lmfp ∼ 15 nm. Hence, generally the travel paths between successive scattering
events are too small to understand the huge anisotropy in mobility for conduction along (σ ||)
and perpendicular (σ⊥) to the ripple pattern. A sophisticated model has to be developed
and theoretical calculations have to be performed for an interpretation and to eventually
understand the underlying physics. For now it can only be speculated whether long-range
Fermi wave number kF 1.8×10 8 [m −1 ]
reciprocal Fermi wave number k −1
F 5.6×10 −9 [m] → 5.6 [nm]
momentum relaxation time τm 1.1×10 −13 [s] → 0.11 [ps]
Fermi velocity vF 7.3×10 4 [ms −1 ]
mean free path lmfp 8.2×10 −9 [m] → 8.2 [nm]
Table 6.5: Estimated values for scattering related parameters.

6.2. EXPERIMENTAL ASPECTS AND MOBILITY ANALYSIS 107
Figure 6.12: Schematic visualization of ideas to explain the differences in mobility
measured parallel and across the ripple structure. The transport anisotropy is
assumed to be related to an inhomogeneous distribution of scattering centers. These
increased scattering potentials could dominantly be active at the bending edges of
the 2DHG (a). Overall conduction has to be seen as parallel and series connection
of different ohmic resistances (b). According to the ripple structure in the 2DHG
(c) different resistivity regions can be assumed: d) terraces and ripple flanks, e)
low- and high-curvature regions, f) continuous model for (e).
� Source: p-mod mobility model1.jpg
surface roughness scattering directly or strain-induced scattering potentials correlated with
the periodically modulated SiGe-channel limit the mobility so strongly across the bunches.
Even strain-induced fluctuations in the SiGe-composition aiming at alloy scattering cannot
be ruled out completely [220, 221, 222]. The origin and nature of the relevant scattering
potentials involved in the presented structures remain unrevealed by now.
With the present data at hand it can only be speculated about the microscopically dom-
inant scattering mechanisms. Just one thing seems to be clear by now: there are different
”channels” contributing unequally to the overall measured total conductivity σtot and the
derived mobility µtot. The scattering centers are supposed to be aligned along the ripple
pattern forming stripes of different mobility parallel to these step-bunches. The lateral ex-
tension and even the position with respect to the ripples of these less-conducting paths in

108 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
Figure 6.13: Two simple macroscopic models to explain the measured mobility
anisotropy. Different conductivities for the flat terraces and the steep flanks of the
step-bunching structure are assumed. a) anisotropic mobility for the parallel and
perpendicular direction; b) isotropic mobility within the terrace regions and the
flanks, respectively.
� Source: p-mod mobility model2.jpg
the 2DHG are unclear. Several geometries of the high-resistivity stripes can be assumed.
Fig. 6.12 schematically visualizes some ideas to explain the different mobilities measured par-
allel and across the ripple structure. The electrically evidenced anisotropy is assumed to be
related to an inhomogeneous distribution of scattering centers. These numerous scattering
potentials could be dominantly be active at the bending edges of the 2DHG (Fig. 6.12a).
Overall conduction σtot has to be seen as parallel and series connection of different ohmic
resistances (Fig. 6.12b). The grey-scale in Fig. 6.12c-f is used to illustrate the different resis-
tivity regions in the 2DHG. Bright colors are used for higher conductivity regions and dark
colors symbolize lower conductivity. A rather unrealistic model assumes different mobilities
for the flat terraces and the steep ripple flanks (Fig. 6.12d), whereas low and high curvature
regions at intermediate zones seem to be more realistic regions for increased resistivity. This
is shown in Fig. 6.12e with a homogeneously lower conductivity at the edges. A more compli-
cated assumption would invoke a continuous model (Fig. 6.12f) with a continuous variation
of (isotropic) conductivities σi.
Simple mathematical considerations are applied to discuss the plain macroscopic approach
with a two-stripe-phase conductivity. For simplicity the width of the two channels of different
conduction are supposed to be the same. For Fig. 6.13 the different channels are related to
the flat terraces and the ripple flanks (compare Fig. 6.12d). The more realistic splitting and
re-allocating of the low-conduction areas to the high curvature regions in the 2DHG (edges
in the SiGe-channel, Fig. 6.12e) is for the mathematical treatment absolutely equivalent. Ac-

6.2. EXPERIMENTAL ASPECTS AND MOBILITY ANALYSIS 109
cording to Fig. 6.13 two simple macroscopic models are discussed to explain the measured
anisotropy in mobility. The overall mobilities for the parallel µ ||
tot and perpendicular µ⊥ tot
direction are calculated using the basic formulas to analyze ohmic resistivity circuits with
parallel and series connections of different ohmic resistances (Eq. 6.9).
||: µ || 1
tot = 2 ·
�
µ ||
⊥:
�
1 + µ|| 2
µ ⊥ �
µ ⊥
1 ·µ
tot = 2 ·
⊥ �
2
(6.9)
µ ⊥ 2 +µ⊥ 1
In case 1 an anisotropic mobility for the parallel and perpendicular direction with respect
to step-bunching is assumed. This is motivated by interface-roughness- (parallel to step-
bunching) induced scattering, which reduces the mobility only for the perpendicular direction.
In a different scenario (case 2) the mobility could be isotropic within the terrace regions and
the flanks of the ripple pattern, respectively. Slightly different growth conditions in the
steep ripple flanks could locally increase or decrease the crystal quality or at least modify
the Si/SiGe interface in a way which gives differing mobilities for the different areas. The
resulting formulas to estimate the mobilities for the different zones under both assumptions
are comprised under Eq. 6.10.
case 1: case 2:
µ ||
tot = µ|| 1 = µ|| 2
µ ⊥ tot = µ ⊥ 1 = µ⊥ 2
For case 1 the calculated mobilities µ ||
1
µ1,2 = µ± = µ ||
tot ±
� �
µ ||
tot
� 2
− µ ||
tot · µ⊥ tot
for equal width of conduction paths (σ1- and σ2-regions)
and µ||
2
(6.10)
coincide with the measured anisotropic mo-
bilities (µ ||
tot and µ⊥ tot) in both regions. Only in the second case the averaged mobilities
overestimate or underestimate the mobilities for the distinct conduction paths. Hence, as-
suming an equal width for the conduction channels (σ1- and σ2-regions) typical measurement
results (1882LSG p: µ⊥ = 700 cm 2 V −1 s −1 , µ || = 1340 cm 2 V −1 s −1 ) lead to calculated values of
µ+ ∼ 2266 cm 2 V −1 s −1 and µ− ∼ 416 cm 2 V −1 s −1 (see Eq. 6.10). The higher value µ+ could be
assumed for the flat (001)-oriented terrace part, whereas the lower value µ− may be used to
estimate poor conduction in the steep ripple flanks. The higher value would nicely coincide
with the measured mobility value for the optimized 2DHG-sample grown on a flat untilted
Si(001)-substrate (1663LSG p: µ ∼ 2750 cm 2 V −1 s −1 ). However, also case 1 should not be
discarded hastily, since with the assumption of low-mobility ”edges” (see Fig. 6.12e-f) the
period of the correlation length Λ is reduced by a factor of two. Thus the discrepancy to the
values for the mean free path perpendicular to the bunches l⊥ mfp ∼ 8 nm and the new reduced
Λr ∼ 55 nm is relativized and appears more meaningful again. Furthermore, the mean free
path parallel to the undulations in the SiGe-channel (l ||
mfp ∼ 16 nm) is merely less than a

110 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
factor of four smaller than the interface roughness correlated length Λr. Since lmfp is just an
averaged value more than a negligible portion of holes could travel across the wide terraces
and reach the edges of the neighboring flanks where severe scattering occurs.
6.3 Outlook and Perspectives
For future investigations several new experimental setups are proposed. First, a p-modula-
tion-doped structure could be grown onto a highly miscut substrate on top of a flat high-
temperature Si-buffer. Thus a highly miscut substrate could be utilized to match extensively,
over its whole surface area, the inclination angle with the slope of the ripple flanks of the
4 ◦ miscut samples showing step-bunching. With this additional reference experiment the
found decrease in mobility perpendicular to the ripples could be unambiguously linked to
the mesoscopic periodic undulations of step-bunching. Although the higher density of closely
spaced atomic steps in miscut direction is not expected to cause a significant detectable
mobility anisotropy, this way it should be possible to rule out a transport anisotropy for a
planar 2DHG on tilted substrates definitely.
Up to now, only electrical measurements for the two prominent directions – parallel and
perpendicular to the ripple structure – were conducted. The Hall-bars could be oriented in
any arbitrary direction to analyze the angle dependence of the mobility. This way according
to the chosen angle α any corrugation period along the measurement path can be adjusted
after Eq. 6.11.
Λα (α, Λ) =
Λ
cos (α) , Λα > Λ (6.11)
The effective distance between the undulations Λα depends on the ripple period Λ and the
rotation angle α, where an angle α = 0 represents the measurement direction perpendicular
to the ripples. Generally p-MODQW grown on ripple templates featuring different periods
and amplitudes would be interesting to compare. Especially short-periodic ripple templates
(Λ < 50 nm) would be favorable for further experiments. However, it can be doubted whether
the realization of such structures based on fully self-organized means is possible.
New optical masks have to be designed which employ the opportunity to put self-aligned gates
on top of the Hall-bars. This would be essential to precisely adjust the carrier density ps in
the SiGe-channel and to get reliable results. Although the position of the wave-function is
shifted with respect to the Si/SiGe-interface by making use of the top-gate, still, ps-dependent
mobility data could help to identify the dominant scattering mechanisms.
Maybe the most important goal should be to optimize the p-modulation doped structure to
achieve higher mobilities. Accordingly, the relevant parameter, namely the mean free path

6.3. OUTLOOK AND PERSPECTIVES 111
lmfp, would be enhanced. In an ultimately ideal case the mobility would thereafter only be
limited for the hole transport in perpendicular direction and all the scattering events would
occur due to the interface-roughness-induced scattering potential extending along the ripple
structure. Several ways are assumed to achieve this mobility improvement. The layer thick-
ness of Si-spacer and SiGe-channel may require optimization. So an increase in thickness
towards 150–200 ˚A might be beneficial. Of course, also the growth temperature in relation
with the growth rates are crucial parameters for the final quality of the structures and have
to be reconsidered.
Switching to the inverted p-MODQW architecture with the doping region beneath the chan-
nel could also be advantageous. In this approach an, at a short scale, smoother Si/SiGe
interface is expected, since Ge-segregation should be less pronounced for the lower interface
when compared with the upper Si/SiGe-interface [6].
However, lowering the Ge-content x in the SiGe-channel should give the largest contribution
for the desired increase in mobility (see Fig. 6.3). Estimated Ge-contents as low as x ∼ 5–10%
should give a boost in mobility by a factor of 10. Too low Ge-contents are not useful as the
carriers are no longer well-confined in the shallow SiGe quantum well, and the wave-function
is less defined at the interface, which is a drawback for the characterization of the surface
roughness related scattering.
Also with the currently available samples further measurements could be performed at lower
temperatures in a different cryostat. Thus cooling down the samples to 300 mK in the 3 He-
refrigerator or even to 30 mK in the dilution refrigerator should significantly suppress thermal
effects and enhance significantly the otherwise blurred quantum effects. Especially the onset
of SdH-oscillations is expected to be shifted to lower magnetic fields. There, spin splitting
does not distort the periodic pattern, and hence, the position and amplitude of the SdH-
oscillation can be evaluated according to the Dingle analysis to extract the quantum lifetime
τq [216]. The ratio of the transport lifetime and the quantum lifetime τm/τq is known to re-
veal information on the nature of the scattering potential and the scattering mechanism [6].
Low-temperature magnetoresistance experiments with tilted magnetic fields are also inter-
esting to study the edge-channel transport in the Si/SiGe QH-system [223]. The existence
of stripe phases causing a strong transport anisotropy at half filled Landau levels (LL) was
found first for high-mobility GaAs/AlGaAs heterostructures [224, 225, 226]. There a signifi-
cantly high in-plane magnetic field increases the Zeeman splitting and causes a cross-over of
adjacent Landau levels, i.e. the spin-down configuration of the higher Landau level (N+1, ↓)
crosses the energetic position of the spin-up state (N, ↑). For the edge-channel transport
of electrons in Si/SiGe heterostructures it was revealed that inter-edge-channel scattering is

112 CHAPTER 6. P-MODULATION DOPING AND MOBILITY ANALYSIS
strongly suppressed over macroscopic distance between (0 ↓, 0 ↑) edge channels, whereas it is
promoted between (0 ↓, 1 ↓) edge channels [227]. Thus, it could be interesting to study the
influence of the anisotropic ripple structure, which is present in our 2DHG-samples, on such
a stripe-phase formation and the inter-edge-channel scattering.
In conclusion, more measurement data have to be collected from different electrical ex-
periments to develop a more sophisticated model. In a second step, based on the extracted
parameters, theoretical simulations have to be applied to fit the experimental results and
to learn more about the microscopic physics of the limiting scattering mechanisms for p-
modulation doped structures.

Part III
Additional Work
113

Chapter 7
Transient-Enhanced Si Diffusion on
Natural-Oxide-Covered Si(001)
This chapter comprises the work on ”Transient-enhanced Si diffusion on natural-oxide-covered
Si(001) nanostructures during vacuum annealing”, which was started in the course of the
diploma thesis [1]. Further experiments proposed as outlook there were conducted here in
continuation. Thus all the related results are discussed here in compact form on the basis of
the two resulting publications [228, 229] in order to keep the context.
The morphology of patterned Si(001) wire-templates after annealing was studied by several
techniques. An enormous Si-mass-transport on the Si-surface at usual oxide desorption tem-
peratures around 900 ◦ C under UHV-conditions was found. Heat treatment of 5 min trans-
forms the initially rectangular wire profiles with a height of 300 nm to flat (< 100 nm) and
faceted triangular ridges exhibiting thermodynamically preferred {111}- and {113}-facets.
It was found that the natural SiO2 on the predefined wire pattern must be responsible for
the degradation of the wire structure. Removing the SiO2-layer from the Si wires ex situ
with an HF-dip preserves the rectangular structures during high temperature annealing. The
Si/SiO2-interface was investigated with high-resolution transmission electron microscopy to
image the Si wire surface and the natural-oxide-layer in detail.
The new experiment employed low-temperature Ge-deposition to generate in situ a Ge-
contrast layer which conserved the Si/SiO2 interface for later HRXTEM studies (high reso-
lution cross-sectional transmission electron microscopy). This way the role of the SiO2-cover
in the vast transient Si surface diffusion process could be enlightened.
115

116 CHAPTER 7. TRANSIENT-ENHANCED SI DIFFUSION
Figure 7.1: (a) HRXTEM image of the outer edge including zoom-in of a Si-wire
after RIE. (b) Cross-sectional SEM image of 800 nm Si-wire template tilted slightly
out of the wire-direction. (c) Schematic drawing indicating the respective location
of image (a) with regard to the complete wire cross sections.
� Source: TEM n SEM rect.jpg
7.1 Introduction
State-of-the-art semiconductor devices have reached critical dimensions well below 100 nm.
For shrinking the device dimensions it becomes increasingly important to control the shape
and size of small structures during subsequent processing. Our investigations concentrate
on the shape stability of Si nanostructures during vacuum annealing at around 900 ◦ C for a
few minutes. Such thermal steps are typically employed for natural oxide desorption prior
to epitaxial growth, but similar thermal budgets are frequently required during device pro-
cessing, e.g. after ion implantation. While the shape evolution of structured Si surfaces into
thermodynamically stable facets ({111} and {113}) is well described [230, 231], most of the
experimental studies employed long-term, high-temperature anneals. Also, quite often exotic
annealing procedures (e.g. a flash to 1200 ◦ C [232]) and direct current heating (prone to
electro-migration artifacts [233]) were used. The discussed experiments here only employed
cleaning and annealing procedures adapted from standard Si device processes.
7.2 Template Preparation
For our experiments Si wire-arrays were processed on 17 mm × 17 mm Si-wafer pieces that
were cut from (001)-orientated standard Si-wafers supplied by Wacker Siltronic (4”, p-doped,

7.3. EXPERIMENTAL RESULTS 117
> 1000 Ωcm resistivity, 525 µm thick). Stripe-patterns with a period of typically 800 nm along
the [110]-direction were produced by holographic lithography (λ = 457.9 nm) and subsequent
reactive ion etching in an SF6 process. Typical etch depths were 250–300 nm. The residual
photoresist-mask was removed by plasma-ashing. The homogeneity of the fabricated wire-
structures was checked with a Park Scientific atomic force microscope (AFM) operated in a
non-contact mode with Olympus TESP tips. The shape of the etched profiles was controlled
with cross-sectional views in a JEOL JSM 6400 scanning electron microscope (SEM) or at
200 keV with a Jeol 2011 FasTEM transmission electron microscope. The wire-templates
show rectangular profiles with small corner rounding of < 5 nm (see Fig. 7.1).
7.3 Experimental Results
The wire-templates that had been pre-characterized with AFM were successively cleaned in
trichlorethylene, acetone, methanol using an ultrasonic bath, rinsed with deionized water (DI-
H2O) and dried using the flow of a nitrogen nozzle. Additionally, the Si-pieces were cleaned
with a mixture of sulphuric acid (H2SO4, 96%) and hydrogen peroxide (H2O2, 30%) for 10 min
(H2SO4 : H2O2 = 5 : 1) to remove organic impurities, and again rinsed with DI-H2O. The con-
ventional cleaning procedure was concluded with the standard RCA clean [71, 72] without any
HF-treatments. The RCA-clean leaves a passivating SiO2-layer of ≈ 2 nm on the Si-surface.
Additionally, for some experiments the samples were HF-dipped (HF 40% : DI-H2O ≈ 1 : 5)
immediately before substrate-transfer into the UHV of our Riber SIVA 45 MBE-system.
This optional HF dip removes the oxide and provides a hydrogen terminated surface that is
stable against oxidation for a few hours. After introduction of the samples into the UHV-
environment of the MBE-chamber the prepatterned substrates were annealed to desorb the
SiO2 from the Si-surface and to provide a clean surface for epitaxial overgrowth. After sample
degassing at 550 ◦ C the temperature was ramped up to 900–950 ◦ C at 230 ◦ C/min, kept at
this maximum temperature for 1–5 min, and was then rapidly quenched to room temperature.
The substrate temperature was controlled by a calibrated thermocouple (≈ 15 ◦ C), located in
the radiation area between wafer and heater, and additionally monitored with a pyrometer.
The samples were characterized before and after annealing on air by AFM to reveal structural
changes. Selected samples were imaged by high-resolution cross-sectional transmission elec-
tron microscopy (HRXTEM). Fig. 7.2 and Fig. 7.3 show 3D-AFM data and AFM line scans
of a sample covered with natural oxide before and after annealing at 950 ◦ C for 4 min. It is
obvious that a dramatic morphological change has taken place that converted the originally
300 nm high, almost rectangular wire structures into multiple faceted wires that have lost up

118 CHAPTER 7. TRANSIENT-ENHANCED SI DIFFUSION
Figure 7.2: 3D-AFM images of a natural-oxide covered sample before (a) and
after (b) annealing at 950 ◦ C for 4 min.
� Source: Wire-Samples 3D-AFM.jpg
to 75% of their original height (see Fig. 7.3a). The central, triangular part of the wires is
made up of {113}-facets, whereas the lower part of the cross section is inclined against the
[100]-direction by about 4.5 ◦ (see Fig. 7.3b). To uncouple the oxide-desorption process from
the Si-mass-transport phenomenon the experiment was repeated with an identical sample
that had the natural oxide removed in 4% HF. In that case no noticeable change of the wire
cross section was observed after annealing. To further investigate the relation between oxide
desorption and surface diffusion, the shape evolution of the wire arrays was studied. Fig. 7.4
shows the normalized wire height after annealing at 900 ◦ C and 950 ◦ C versus annealing time
for samples with and without a final HF dip. The upper curve in Fig. 7.4 indicates that there
is no visible change of the wire-height without an initial SiO2-layer. Especially the data point
for 4 min annealing at 950 ◦ C proves that after an HF-dip also an extended heat-treatment
Figure 7.3: AFM line scans of a natural-oxide covered sample before (broken line)
and after annealing at 950 ◦ C for 4 min (solid line). (a) Direct comparison of AFM
line scans of wire-templates before and after annealing. (b) The central, triangular
part of the annealed wire is made up of {113}-facets
� Source: Wire-Samples Linescans.jpg

7.3. EXPERIMENTAL RESULTS 119
Figure 7.4: Normalized wire height vs. annealing time for samples with (RCA),
and without (HF) natural-oxide. The arrow links the data points from a sample
that was annealed first without, and then again with natural oxide coverage.
� Source: Annealing plot.jpg
does not affect the Si-nanostructures. The lower curve for thermal oxide-desorption reveals
that the wire height of the oxide-covered samples initially decreases with increasing annealing
time, and then saturates after about 3 min. The onset of saturation agrees well with the time
required for complete oxide desorption at 900 ◦ C [234]. The saturation behavior is consistent
with the results of the oxide-free samples, which do not show any structural changes. To rule
out that possible hydro-carbon contaminations from the HF treatment had interfered with
Si surface diffusion, a control experiment was performed: A sample that had been annealed
after an HF-dip underwent another RCA clean to generate a natural oxide layer. Repeating
the annealing step on this recycled sample resulted in the same loss of height as expected
for an RCA-cleaned sample (arrow in Fig. 7.4). It can be ruled out that possible hydrocar-
bon contaminations after HF treatment have impeded the surface migration of Si after an
HF dip. These would have reacted with Si during the first annealing step to SiC, which is
stable against the RCA-clean for the second experiment. Thus the greatly enhanced surface
mass transport on Si(001) can unambiguously be associated to the presence of a thin layer
of natural oxide. It is also interesting to note that annealing at 950 ◦ C leads to a saturated
wire height that is significantly lower than the saturation height after a 900 ◦ C anneal. This
is a clear indication that the activation energies for the oxide desorption mechanism and for
the Si mass transport are different. HRXTEM images with the viewing direction along the

120 CHAPTER 7. TRANSIENT-ENHANCED SI DIFFUSION
Figure 7.5: HRXTEM images of a natural-oxide covered sample after annealing
for 60 s at 900 ◦ C. Faceted wire-top (a) and wire-edge (b) showing thermodynamically
stable facets. (c) Multiple faceted wire flank. (d) Schematic drawings indicating
the respective location of the HRXTEM images with regard to the complete
wire cross sections.
� Source: TEMs facet-evolution.jpg

7.4. DETAILED CHARACTERIZATION AND DISCUSSION 121
[110]-oriented wires were recorded to study details of facet formation. The samples were
covered ex-situ with a polycrystalline Ti-film to enhance contrast. Fig. 7.5a shows the cross
section of the uppermost part of a wire after 60 s at 900 ◦ C. A top (001)-facet still exists, but
the former {110}-sidewall facet (compare Fig. 7.1) has been transformed into a lower {111}-,
and an upper {113}-facet (see Fig. 7.5b). We also found some regions with multiple facet
orientations (see Fig. 7.5c), and transitions regions that cannot be assigned to known low
energy facets. The respective location of the HRXTEM images with regard to the wire cross
sections is sketched in Fig. 7.5d.
7.4 Detailed Characterization and Discussion
The vast Si-self-diffusibility on the Si-surface was also found with other experiments. Fig. 7.6a
shows an XTEM-image of a SiO2 wire structure on Si(001) annealed for 6 min at 950 ◦ C. It can
be clearly seen that a large amount of Si has diffused towards the SiO2 structures, resulting
in a bowed Si-surface between two neighboring SiO2-ridges [12]. The SiO2 wires seemingly
Figure 7.6: (a) XTEM image of a SiO2 wire-structure on Si(001) after annealing
for 6 min @ 950 ◦ C. As indicated with the schematic graph (b) the Si surface atoms
diffuse towards the ridges and react with the SiO2 to volatile SiO molecules. This
process provides the lateral undercut of the SiO2 wires and leads to the bowed Sisurface
between neighboring oxide wires. The dashed line indicates the Si-surface
before annealing [12].
� Source: TEM oxide-wires.jpg
attract the Si-atoms. Evaluating the contact-angles between the SiO2-structures and the Si-
surface yields values slightly exceeding 90 ◦ . Apparently, wetting cannot be attributed as the
driving force for the Si pile-up next to the SiO2-wires. The transport of the large amount of Si
within a short period of time at relatively low temperatures is a proof for the high Si-surface
mobility. The lateral undercut of the SiO2-structures can be explained using the well-known
oxide-desorption reaction at elevated temperatures around 900 ◦ C. This mechanism for oxide-
desorption for the patterned SiO2-template is illustrated in Fig. 7.6b and follows the reaction

122 CHAPTER 7. TRANSIENT-ENHANCED SI DIFFUSION
path [235]
SiO2 + Si → 2 SiO ↑ . (7.1)
In contrast to SiO2, SiO is volatile at typical annealing temperatures around 900 ◦ C. As long
as a continuous oxide film exists, SiO forms predominantly at the interface to the oxide [236].
Thermal desorption would then require SiO diffusion through the SiO2 film. It was, how-
ever, found that oxide desorption occurs mainly via the expansion of voids that form during
an early stage in the oxide [237, 238]. Surface diffusion on the Si surface, which becomes
exposed within these voids, is high even at 900 ◦ C [239]. This allows Si transport towards
the periphery of the voids, were reaction Eq. 7.1 and the desorption of SiO can readily oc-
cur. On flat substrates no correlation between void formation and interface structures has
been found [237]. Instead, void nucleation has been associated with contaminations on or
in the oxide [238, 240]. It is, however, not clear whether this applies to our wire-structured
substrates, which expose almost atomically sharp intersections between facets. Such a large
perturbation might be expected to affect the nucleation and anisotropy of void formation.
Therefore XTEM decoration experiments were conducted to visualize the location of the
voids with respect to the wire structures. For that purpose natural-oxide covered samples
with a wire period of 400 nm that had undergone an annealing cycle for 1 min at 900 ◦ C were
covered in-situ by a 20 nm thick Ge layer at a deposition temperature < 100 ◦ C to passivate
the underlying Si/SiO2 interface. Under these conditions the Ge film becomes amorphous on
areas above the Si surface with intact SiO2-film, and forms polycrystalline Ge-grains in the
voids where the deposited Ge is in direct contact with the crystal-order of the Si-surface (see
Fig. 7.7a). Because of the large mass contrast, the residual natural oxide is clearly visible as
a lighter stripe between the crystalline Si-substrate and the amorphous Ge-cap. The darker
appearance of the poly grains decorates the void regions even in the lower resolution images
in Fig. 7.7b, which show cross sections of several {113}-faceted wires. It is obvious that the
voids are not correlated with the period of the wire template. It is especially striking that
most of the ridges are still completely covered by oxide despite their shape transformation
from an originally rectangular cross section. This clearly indicates that the strongly enhanced
diffusion occurs predominantly underneath the oxide, and even more, that the oxide follows
the shape transformation. The voids do have some influence, as can be seen at the arrow-
marked ridge in Fig. 7.7b that coincides with a void, and has become even flatter than the
neighboring oxide-covered ridges. A similar effect might have caused the height fluctuations
in Fig. 7.2b. Nevertheless, most of the mass transport takes place beneath the oxide, and is
most likely associated with the SiO phase that forms with substantial partial pressure [236]
at the Si/SiO2 interface upon annealing.

7.4. DETAILED CHARACTERIZATION AND DISCUSSION 123
Figure 7.7: HRXTEM images of an annealed sample that was in-situ covered
with Ge. (a) Voids in the oxide are decorated by polycrystalline Ge (p-Ge), which
appears darker than the amorphous Ge (a-Ge) that forms on SiO2. (b) Lower
resolution images of several Si wires.
� Source: TEMs Ge-cover.jpg
The presented study shows that the initially rectangular profiles of periodic Si-wire-arrays
are degraded during radiative annealing in UHV for 1–5 min at 900–950 ◦ C to {113}-faceted
trapezoids concomitant with a loss of up to 75% of the structure height. This shape trans-
formation requires drastically enhanced mass transport, which occurs only in the presence of
SiO2 on the surface, and consequently ceases after complete oxide desorption.

124 CHAPTER 7. TRANSIENT-ENHANCED SI DIFFUSION

Chapter 8
Germanium Source Reconstruction
The initial MBE-system as supplied by RIBER consisted of 3 single-crucible e-guns. A large
Temescal SFIH-270-3 canon with a crucible volume of 156 cm 3 was and is still used as electron
beam evaporator for silicon, which is the main matrix material in our SiGeC apparatus.
Two small Temescal SFIH-270-2 canons with a capacity of 40 cm 3 were originally used for the
other two matrix materials, germanium and carbon, respectively. Therefore the evaporable
amount of germanium was fairly limited and even further diminished as the source material is
not evaporated directly from the copper hearth of the e-gun, but out of a Si-liner. This action
is taken to prevent Cu in-diffusion into the Ge material, which is known to be detrimental es-
pecially for photoluminescence results. The carbon e-beam evaporator was shut down a long
time ago and a carbon sublimation cell, which was better to control, was used instead. Thus
there was enough space for a larger Ge evaporator which could provide several improvements:
The larger amount of germanium expands the refilling cycle and therefore there should be no
need to open the growth chamber frequently, which improves the vacuum conditions and also
the quality of the grown layers. Especially for n-modulation-doped structures, where thick
graded buffers with up to 30% germanium are involved, a lot of material is needed. Addi-
tionally, with the larger crucible higher growth rates are feasible. Instead of about 0.2 ˚A/s in
the small evaporator, with the new large e-gun 1.2 ˚A/s can be readily realized. Due to higher
available growth rates it is now possible to speed up growth and cut down growth times
from > 12 hours to about 4 hours for n-modulation doped structures involving thick graded
buffers. As our group started up in a new field with growth on Ge-substrates, excessive use
of Ge-material is made especially for pure Ge-buffers. The maximum Ge-rate is chosen to
be 1.25 ˚A/s to keep a meaningful relation to the maximum available Si-rate (2.5 ˚A/s). The
limited sensor range yields an optimized sensitivity and resolution in the low growth-rate
125

126 CHAPTER 8. GERMANIUM SOURCE RECONSTRUCTION
region, which is extremely important for Ge-dot growth with sub-monolayer accuracy.
As already mentioned, there were several good reasons for updating our machine with a pow-
erful Ge-source. We decided to buy another Temescal SFIH-270-3 e-gun for Ge-evaporation
to stay compatible with our electronics, and to keep our stock of spare-parts small. On the
basis of original 2D-drawings of our whole MBE-system supplied by Episerve (i.e. the lo-
cal distributor for RIBER products) 3D-drawings had to be generated to fit all parts into
our apparatus. Although the former water-cooled roof of the Ge/C-assembly and the Si-
evaporation assembly were used as model for the new Ge-assembly, several aspects had to
be taken into account. The water-cooled roof was designed to reach a maximum of thermal
shielding with regard to the chamber walls. The roof was extended to block excessive heat
radiation from the melt and to keep the surrounding temperature as low as possible, which
improves the growth pressure. Baffle plates inserted into the hollow space of the roof ensure
Figure 8.1: Top-view of rendered 3D-drawings of most important parts in our
SiGeC MBE-system with new Ge-evaporation assembly.
� Source: GC Drawing51 3d 2 new07Feb2006 3a label.jpg

Figure 8.2: Elevated front-view of rendered 3D-drawings of most important parts
in our SiGeC MBE-system with new Ge-evaporation assembly.
� Source: GC Drawing51 3d 2 new07Feb2006 3c.jpg
proper water-flow and cooling. Most important were the openings and bores in the roof to
ensure an unobstructed intervisibility between crucible and substrate, viewport window and
flux sensing units (Sentinel, QMS), respectively. Additionally, the space for the installation
of a long-term planned phosphorous effusion cell had to be provided. Therefore, to check all
the details, and to perfectly tailor the new evaporation assembly into the existing system the
elaborate designing in 3D of all involved parts was inevitable.
The 3D-drawings of the growth-chamber were generated with AutoCAD R14 with as many
details as required. Only the parts of the Ge-roof assembly had to be constructed with every
detail. Rendered 3D-views of the most important parts in our SiGeC MBE-system already
with the new Ge-evaporation assembly are shown in Fig. 8.1 and Fig. 8.2.
In Fig. 8.3 various rendered 3D-views of the final Ge-roof assembly are depicted. The images
include all parts of the custom-made construction including main-flange, water-cooled roof,
underframe for e-beam source mounting and all waterlines. The main flange was provided
with several flanges for various feedthroughs, such as the high-voltage connection, electron
127

128 CHAPTER 8. GERMANIUM SOURCE RECONSTRUCTION
Figure 8.3: Various rendered 3D-views of the Ge-roof assembly. The images
include all parts of the custom-made construction including main-flange, watercooled
roof, underframe for e-beam source mounting and all waterlines.
� Source: Ge-roof02.jpg
beam sweep control, water-cooling and linear shutter-motion. The hole in the underframe is
necessary to connect the electron beam source with the high-voltage cables.
Fig. 8.4 presents a photograph of the new Ge-evaporation unit and two group members ad-
justing the Ge-shutter. Fig. 8.5 shows the fully assembled Ge-assembly mounted on the
”service-trolley” with installed electron gun, shielding plates, shutter mechanics, electric and

water lines.
Figure 8.4: Photograph taken during assembling of Ge-evaporation unit showing
two group members adjusting the Ge-shutter.
� Source: Photo Ge-roof01.jpg
Due to software incompatibilities, the company, which was assigned with manufacturing, had
to redraw the construction drawings. Fig. 8.6 and 8.7 show the final drawings of VTS-Schwarz
that match our 3D-drawings and thus were accepted for fabrication.
Figure 8.5: Photograph of Ge-evaporation assembly ready to slide into the growth
chamber.
� Source: Photo Ge-roof03.jpg
129

130 CHAPTER 8. GERMANIUM SOURCE RECONSTRUCTION
Figure 8.6: Part 1 of final construction drawings for Ge-evaporation assembly redrawn by VTS-Schwarz.
� Source: Ge-evaporation-assembly Schwarz04Mar04 2 ok 1.jpg

Figure 8.7: Part 2 of final construction drawings for Ge-evaporation assembly redrawn by VTS-Schwarz.
� Source: Ge-evaporation-assembly Schwarz04Mar04 2 ok 2.jpg
131

132 CHAPTER 8. GERMANIUM SOURCE RECONSTRUCTION

Appendix A
Calibration and Characterization of
Sources
In this part the influence of the Ge source reconstruction (see Ch. 8) on the SiGe calibration
is discussed. Photoluminescence measurements on single SiGe quantum wells were performed
to verify the cleanliness of the new Ge source material.
A.1 Calibrations
The substitution of the two small electron guns (for Ge and C) with the larger Ge gun re-
sulted in a new position of the Ge crucible. The whole geometry of Ge evaporation is therefore
changed, which significantly alters the distribution of Ge in grown epilayers across a wafer.
For SiGe calibration it is now standard to grow a single SiGe epilayer with about 750–1000 ˚A
thickness and a Ge-content between 10% and 20% (see Tab. A.1 for details). The parameters
of the pseudomorphic epilayer are calculated from x-ray data. A single ω-2θ scan around the
symmetric (004)-reflex of Si reveals the sharp Si substrate peak and the SiGe peak shifted
to lower angles. The peak positions indicate the perpendicular lattice constants a⊥ of Si
and the pseudomorphic SiGe epilayer. The position of the SiGe peak is used to extract the
Ge-content x. This is accessible due to the monotonic relation of the Ge-content x and the
fully strained pseudomorphic lattice constant of the epilayer aSiGe,⊥. The thickness of the
epilayer can either be derived from the width of the SiGe peak, or, alternatively, from the
spacing of the thickness oscillations [241].
The measured x-ray data were compared and fitted with simulated spectra calculated by the
Matlab-program ”simx” developed and maintained by our X-Ray group. This is a convenient
133

134 APPENDIX A. CALIBRATION AND CHARACTERIZATION OF SOURCES
way to extract the Ge-content and the total SiGe epilayer thickness. From these two values
the Si and Ge rate can easily be computed.
Usually the calibration is only actualized for the wafer center. Nevertheless, all sources show
a distinct flux distribution across the substrate. Therefore, also growth on larger substrates,
e.g. on a whole 4”-wafer, does not yield identical sample material. Out-of-center regions do
not supply that high quality material due to glide lines arising from thermal stress during
the high temperature oxide desorption step at the wafer rims.
Often, not much material is needed for later experiments or special substrate miscuts are
used. So, we save substrate material by growing on small pieces, which are mounted in all-Si
adapter wafers (see Sec. 2.3). Several adapters are available which usually can hold several
pieces. The position of the samples is sometimes off-center in the growth chamber. Therefore
the calibration data and the distribution across the substrate should be available for all the
different sources.
To get the distribution of the SiGe composition the MRD x-ray system is used, where a whole
4”-wafer can be mounted and the measurement spots can be easily adjusted due to the wide
accessible range of the motorized x-y-stage. At each position an ω-2θ scan can be recorded
fully automated for later data evaluation.
Fig. A.2 shows the evaluation of the x-ray data of Sample 1536LSG which was grown with
the old Ge-evaporation-assembly, that means, before the small Ge source was replaced with
the new larger electron gun for Ge. The comparison of the distribution of the normalized Ge
Sample 1536LSG 1823LSG 1653LS n 1661LS p
Buffer 700 ˚A Si 700 ˚A Si 840 ˚A Si 500 ˚A Si
Si @ 1.5 ˚A/s Si @ 1.5 ˚A/s Si @ 0.7 ˚A/s Si @ 1.0 ˚A/s
550 ◦ C → 500 ◦ C 550 ◦ C → 500 ◦ C 550 ◦ C 550 ◦ C
+
840 ˚A Si
Si @ 0.7 ˚A/s
550 ◦ C → 350 ◦ C
Epilayer 1000 ˚A Si0.90Ge0.10 1000 ˚A Si0.90Ge0.10 300 ˚A Si:Sb 1000 ˚A Si:B
Si @ 1.5 ˚A/s Si @ 1.5 ˚A/s Sb pre-dep.: 120 s B @ 1850 ◦ C
Ge @ 0.1667 ˚A/s Ge @ 0.1667 ˚A/s Sb @ 310 ◦ C Si @ 1.0 ˚A/s
500 ◦ C 500 ◦ C Si @ 0.7 ˚A/s 550 ◦ C
350 ◦ C
Table A.1: Typical structure and growth parameters of several calibration layers.

A.1. CALIBRATIONS 135
Figure A.1: X-Ray data (ω-2θ scan) of a SiGe-epilayer grown for calibration of Si
and Ge sources. Nominally, the epilayer consists of 1000 ˚A Si0.90Ge0.10. Using our
MRD x-ray system, the whole 4”-wafer can be mounted and the measurement spots
can be easily adjusted due to the wide accessible range of the motorized x-y-stage.
The plotted graph shows x-ray data recorded at the wafer center (green solid line)
together with the fitted, simulated curve (red dashed line).
� Source: 1823LSG xpos0 ypos0 2.jpg
flux between the old and the new Ge-evaporator shows, as suspected, a significant change.
This can be seen from Fig. A.3, where the evaluated data from sample 1823LSG are visual-
ized.
To get reproducible results, or to compare different samples within a growth series, it is es-
sential to be aware of the layer distribution. This is especially the case for growth on small
substrate pieces using all-Si adapters. Whenever samples of consecutive growth processes
should be directly compared, one has to take care to rotate them to the same growth posi-
tion.
The calibration data were completed with measuring the flux distribution of our Sb and
B effusion cells used for doping. These sources are calibrated with doped epilayers which are
grown with direct doping for p-doped layers (B) or pre-deposition of Sb and subsequent Si

136 APPENDIX A. CALIBRATION AND CHARACTERIZATION OF SOURCES
Figure A.2: Normalized Si and Ge distribution across a grown wafer (1536LSG)
evaluated via x-ray measurements. The different measurement positions are
marked with black spots. The black circle indicates the circumference of a 100 mm
wafer. The layers were grown with the old Ge-evaporation-assembly.
� Source: wafercalibration 1536Si fig01.jpg, wafercalibration 1536Ge fig02.jpg
overgrowth with Sb incorporation for n-doped layers. The n-doped layers have to be grown at

A.1. CALIBRATIONS 137
Figure A.3: Normalized Si-distribution on calibration layer 1823LSG grown
with the new Ge-evaporation-assembly. Markers point up the side in the growth
chamber from which the different sources emit.
� Source: wafercalibration 1823Si fig05.jpg, wafercalibration 1823Ge fig06.jpg
lowest possible substrate temperatures to suppress the Sb-segregation but still to guarantee
good crystalline quality of the epilayers. More details of the layer structure can be found

138 APPENDIX A. CALIBRATION AND CHARACTERIZATION OF SOURCES
Figure A.4: Sb and B flux distribution of calibration layer 1653LS n and
1661LS p, respectively. The plotted data are based on 4-point measurements which
take into account only the active doping concentration which contributes to the
electrical conductivity.
� Source: wafercalibration 1653Sb fig10.jpg, wafercalibration 1661B fig14.jpg
again in Tab. A.1.
The epilayers are characterized electrically by measuring the sheet-resistance with a 4-point

A.2. PHOTOLUMINESCENCE 139
Sample 1596LSG
Buffer 1000 ˚A Si
Si @ 1.0 ˚A/s; 750 ◦ C → 550 ◦ C
+
1000 ˚A Si
Si @ 1.0 ˚A/s → 0.45 ˚A/s; 550 ◦ C → 450 ◦ C
SiGe quantum-well 25 ˚A Si0.75Ge0.25
Si @ 0.45 ˚A/s, Ge @ 0.15 ˚A/s; 450 ◦ C
Cap 500 ˚A Si
Si @ 0.45 ˚A/s → 1.0 ˚A/s; 450 ◦ C → 650 ◦ C
+
1500 ˚A Si
Si @ 1.0 ˚A/s; 650 ◦ C
Table A.2: Layer structure and growth parameters of a typical PL structure.
measurement setup across the central region of a 4”-wafer. Therefore the calculated fluxes
presented in Fig. A.4 for boron (1661LS p) and antimony (1653LS n) take into account only
the active doping concentration which contributes to the electrical conductivity. SIMS mea-
surements are known to give significantly different fluxes for the Sb source in particular.
Nevertheless for electrical applications only the activated dopants are relevant and although
the absolute values for the fluxes may vary, the distribution of the doping concentration
remains unaffected.
A.2 Photoluminescence
As already mentioned in this chapter’s preamble, photoluminescence measurements (PL) on
single SiGe quantum wells were performed to verify the cleanliness of our source material.
The layer structure and growth parameters of a typical photoluminescence structure are listed
in Tab. A.2. The PL data presented in this chapter were acquired together with our optics
group. The samples were irradiated with an Ar + laser (λ = 514.5 nm) with a power of 58 mW
and measured at a temperature of 4.2 K with an InGaAs CCD-line detector. Fig. A.5 shows
a typical spectrum of a single Si0.75Ge0.25 quantum well with a well width of 25 ˚A grown with
the new Ge-evaporation assembly. Sample 1596LSG shows well-behaved photoluminescence
signal from which can be stated that the first crucible filling of our new Ge source is not
contaminated. The comparison of the PL-signal of structure 1596LSG with the reference

140 APPENDIX A. CALIBRATION AND CHARACTERIZATION OF SOURCES
Figure A.5: Photoluminescence spectrum of single Si0.75Ge0.25 quantum well
with a well width of 25 ˚A grown with the new Ge-evaporation assembly (sample
1596LSG). The labels indicate the different PL-signals.
� Source: photolum fig09.jpg
data of sample 1080MSG, which was grown long ago with the old small Ge evaporator,
Figure A.6: Schematic drawing indicating various measurement positions used
for recording photoluminescence spectra.
� Source: PL measure points2.jpg

A.2. PHOTOLUMINESCENCE 141
Figure A.7: Photoluminescence spectra taken at different wafer positions indicating
a significant variation of the Si and Ge thickness. Origin of PL signals with
regard to sample position can be seen in Fig. A.6.
� Source: photolum fig08.jpg
shows, that the samples match regarding PL intensity (see Fig. A.7). In principle the peaks
of samples 1080MSG and 1596LSG at measurement spot ”D” (central wafer position) should
coincide. The significant offset between the positions of the SiGe no-phonon (NP) peak can
be deduced from slight SiGe calibration deficiencies. Various PL measurements (Fig. A.6
and Fig. A.7) were performed on sample 1596LSG across the wafer from the ”Si-rich” to
the ”Ge-rich” region. The significant shift of the SiGe NP-peak can be explained by the
distribution of Si and Ge and the resulting changes in Ge-content and layer thickness. For
the relatively thin SiGe quantum well examined here the shift of the no-phonon line depends
on quantum confinement and on the reduced SiGe energy gap (which is coupled to the Ge-
content) in about equal parts. Obviously, either the quantum well thickness of the grown
layer is gradually increasing from the ”Si-side” towards the ”Ge-side” or the the Ge-content
is heavily increased. Both trends would red-shift the SiGe NP-line as a wide well yields low
quantum confinement energy having the energy levels near the bottom, and a high Ge-content
results in a lower excitonic bandgap. The Si and Ge flux distribution known from x-ray
analyses of SiGe calibration layers reveal that the maximum thickness has to be expected
rather at the ”Si-side”. Therefore, the observed red-shift has to be attributed to a noticeable

142 APPENDIX A. CALIBRATION AND CHARACTERIZATION OF SOURCES
Ge gradient.
Figure A.8: Calculated SiGe NP-line position as a function of Ge-content and
quantum well width. The computation includes the approximation of the SiGe
excitonic bandgap and the quantum confinement energy in an ideal rectangular
quantum well only.
� Source: NP SiGe position fig03c.jpg
The position of the SiGe NP-line can be estimated by considering only the SiGe excitonic
bandgap E SiGe
GX and the quantum confinement energy ∆Equant in the valence band (VB)
Eq. A.1.
E SiGe
NP = E SiGe
GX + ∆Equant (A.1)
Calculating the energy levels for a textbook-like rectangular box gives a good approximation
for the confinement energy of the single SiGe quantum well. Only the out-of-plane heavy hole
masses m⊥ hh have to be taken into account. The whole bandgap difference is assumed to occur
in the VB and is used as barrier height of the quantum well Vb (see Wachter pp. 27 [242]).
Values for the excitonic SiGe bandgap are taken from a fit to measured SiGe NP-line positions
for thick SiGe quantum wells of known Ge-content x, which show no significant quantization
effect Eq. A.2
EGX(x) = 1.155 − (0.848 ± 0.029)x + (0.173 ± 0.108)x 2
[eV] (A.2)

A.2. PHOTOLUMINESCENCE 143
Figure A.9: Zoom-in into Fig. A.8 for better comparability of the measured SiGe
NP-lines presented in Fig A.5. The calculated data (well width Lz = 2.5 nm, Gecontent
x = 0.25) match the measured PL-data of 1596LSG B (central wafer position)
nicely. This indicates an accurate SiGe calibration.
� Source: NP SiGe position fig04c.jpg
(after Wachter pp. 53 [242]).
In Fig. A.8 the thus calculated SiGe NP-line position as a function of Ge-content and quan-
tum well width is depicted. It is clearly visible that the SiGe NP-line position is dominated
by the Ge-content for broad wells which give no significant confinement energy contribution,
whereas for thin quantum wells the Ge-content plays a subordinate role. Fig. A.9 shows a
zoom-in into Fig. A.8 for better comparability with the measured SiGe NP-lines presented
in Fig. A.5. The calculated data (well width Lz = 2.5 nm, Ge-content x = 0.25) match nicely
PL measurement position 1596LSG B 1596LSG D 1596LSG A
recalculated well thickness Lz [˚A] 25.59 25.00 23.43
recalculated Ge-content x 0.225 0.250 0.275
measured SiGe NP-energy ESiGe NP, meas [meV] 1039.0 1025.5 1015.0
calculated SiGe NP-energy ESiGe NP, calc [meV] 1041.0 1025.0 1016.0
Table A.3: Comparison of the measured and calculated SiGe NP-lines E SiGe
NP .

144 APPENDIX A. CALIBRATION AND CHARACTERIZATION OF SOURCES
x m ⊥ hh Vb [meV]
0.00 0.2778 0.0
0.05 0.2729 38.6
0.10 0.2681 77.4
0.15 0.2635 116.1
0.20 0.2591 155.0
0.25 0.2548 193.9
0.30 0.2506 232.9
0.35 0.2466 272.0
Table A.4: Values used for quantum confinement energy calculation ∆Equant.
with the measured PL-data of 1596LSG D (central wafer position), as the calculated SiGe
NP-transition energy ESiGe NP, calc ≈ 1025 meV is quite close to the measured value, which reads
E SiGe
NP, meas
≈ 1025.5 meV. Additionally the experimentally found SiGe NP-line positions from
the off-center measurements (1596LSG A and 1596LSG B) can be reproduced with the cal-
culations. By applying corrections for the quantum well thickness and Ge-content according
to the distribution of the Si and Ge source (known from x-ray calibration, Sec. A.1) the dis-
crepancy between measured and calculated data is negligible (see Tab. A.3). This actually
proves the accurate SiGe calibration of our MBE-system.
The calculation is partly based on a Matlab-program developed by T. Fromherz [243]. For
more details on that program and parameters involved see also the diploma thesis written by
P. Rauter (pp. 17) [244] and references therein [245, 246, 247]. Several values computed with
the aforementioned program and used for the calculation of the quantum confinement energy
∆Equant, namely the perpendicular heavy hole mass m ⊥ hh and the barrier height Vb for the
SiGe quantum well as function of Ge-content x, can be found in Tab. A.4.

Appendix B
General Physical Data
B.1 Stereographic Projection
Figure B.1: Stereographic projection of important Si-crystal planes relative to the
(001)-surface [12].
� Source: Stereographic Proj.jpg
145

146 APPENDIX B. GENERAL PHYSICAL DATA
B.2 Physical Constants
International System of Units (SI) From: physics.nist.gov/constants
Fundamental Physical Constants – Frequently used constants
Quantity Symbol Value Unit
speed of light in vacuum c, c0 299792458 m s−1 magnetic constant µ0 4π × 10−7 N A−2 = 12.566370614... × 10−7 N A−2 electric constant 1/µ0c2 ε0 8.854187817... × 10−12 F m−1 Newtonian constant
of gravitation G 6.673(10) × 10−11 m3 kg−1 s−2 Planck constant h 6.62606876(52) × 10 −34 J s
h/2π � 1.054571596(82) × 10 −34 J s
elementary charge e 1.602176462(63) × 10 −19 C
magnetic flux quantum h/2e Φ0 2.067833636(81) × 10 −15 Wb
conductance quantum 2e 2 /h G0 7.748091696(28) × 10 −5 S
electron mass me 9.10938188(72) × 10 −31 kg
proton mass mp 1.67262158(13) × 10 −27 kg
proton-electron mass ratio mp/me 1836.1526675(39)
fine-structure constant e 2 /4πε0�c α 7.297352533(27) × 10 −3
inverse fine-structure constant α −1 137.03599976(50)
Rydberg constant α 2 mec/2h R∞ 10973731.568549(83) m −1
Avogadro constant NA, L 6.02214199(47) × 10 23 mol −1
Faraday constant NAe F 96485.3415(39) C mol −1
molar gas constant R 8.314472(15) J mol −1 K −1
Boltzmann constant R/NA k 1.3806503(24) × 10 −23 J K−1
Stefan-Boltzmann constant
(π 2 /60)k 4 /� 3 c 2 σ 5.670400(40) × 10 −8 W m −2 K −4
Non-SI units accepted for use with the SI
electron volt: (e/C)J eV 1.602176462(63) × 10 −19 J
(unified) atomic mass unit
1 u = mu = 1
12 m(12 C) u 1.66053873(13) × 10 −27 kg
= 10 −3 kg mol −1 /NA
Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental
Physical Constants: 1998, Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999
and Reviews of Modern Physics, Vol. 72, No. 2, 2000.

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Postface
Curriculum Vitae
⋄ ∗ 13. 09. 1976 born in Linz
⋄ Sept. 1983 – July 1987 VS Ottensheim (primary school)
⋄ Sept. 1987 – July 1995 Akademisches Gymnasium Linz Spittelwiese (secondary
school)
⋄ Oct. 1995 – Sept. 1996 alternative (military) service
⋄ Oct. 1996 – Sept. 2002 Technical Physics studies at the Johannes Kepler Uni-
versity Linz
⋄ May 2001 – July 2002 Diploma thesis at the Institute of Semiconductor and
Solid State Physics on ”Characterization and Over-
growth of Prestructured Silicon-Substrates”
⋄ from Oct. 2002 PhD thesis at the Institute of Semiconductor and Solid
State Physics and composing the thesis at hand
159

160 POSTFACE
List of Publications
� H. Lichtenberger, M. Mühlberger and F. Schäffler, ”Transient-enhanced Si diffusion on
native-oxide-covered Si(001) nanostructures during vacuum annealing”, Appl. Phys.
Lett. 82, 3650–3652 (2003)
� Z. Zhong, A. Halilovic, H. Lichtenberger, F. Schäffler, G. Bauer, ”Growth of Ge islands
on prepatterned Si(001) substrates”, Physica E 23, 243–247 (2004)
� H. Lichtenberger, M. Mühlberger, C. Schelling, W. Schwinger, S. Senz and F. Schäffler,
”Transient-enhanced Si diffusion on natural-oxide-covered Si(001) nano-structures dur-
ing vacuum annealing”, Physica E 23, 442–448 (2004)
� C. Schelling, J. Mysliveček, M. Mühlberger, H. Lichtenberger, Z. Zhong, B. Voigtländer,
G. Bauer and F. Schäffler ”Kinetic and Strain-Driven Growth Phenomena on Si(001)”,
Phys. stat. sol. (a) 201, 321–328 (2004)
� J. P. Leitão, A. Fonseca, N. A. Sobolev, M. C. Carmo, N. Franco, A. D. Sequeira,
T. M. Burbaev, V. A. Kurbatov, M. M. Rzaev, A. O. Pogosov, N. N. Sibeldin, V. A.
Tsvetkov, H. Lichtenberger and F. Schäffler, ”Low-temperature molecular beam epitaxy
of Ge on Si”, Mat. Sci. Semicond. Proc. 8, 35–39 (2005)
� H. Lichtenberger, M. Mühlberger, C. Schelling and F. Schäffler, ”Ordering of self-
assembled Si0.55Ge0.45 islands on vicinal Si(001) substrates”, J. Cryst. Growth 278,
78–82 (2005)
� T. M. Burbaev, V. A. Kurbatov, M. M. Rzaev, A. O. Pogosov, N. N. Sibel’din, V. A.
Tsvetkov, H. Lichtenberger, F. Schäffler, J. P. Leitão, N. A. Sobolev and M. C. Carmo,
”Morphological Transformation of a Germanium Layer Grown on a Silicon Surface by
Molecular-Beam Epitaxy at Low Temperatures”, Phys. Solid State 47, 71–75 (2005)
� H. Lichtenberger, M. Mühlberger and F. Schäffler, ”Ordering of Si0.55Ge0.45 Islands on
Vicinal Si(001) Substrates: The Interplay between Kinetic Step Bunching and Strain-
Driven Island Growth”, Appl. Phys. Lett. 86, 131919 (2005)
� W. Jantsch, H. Malissa, Z. Wilamowski, H. Lichtenberger, G. Chen, F. Schäffler and
G. Bauer, ”Spin Properties of Electrons in Low-Dimensional SiGe Structures”, Journal
of Superconductivity 18, 145–149 (2005)

POSTFACE 161
� D. Gruber, D. Pachinger, H. Malissa, M. Mühlberger, H. Lichtenberger, W. Jantsch
and F. Schäffler, ”g-Factor tuning of 2D electrons in double-gated Si/SiGe quantum
wells”, Physica E 32, 254–257 (2006)
� T. Berer, D. Pachinger, G. Pillwein, M. Mühlberger, H. Lichtenberger, G. Brunthaler
and F. Schäffler, ”Single-electron transistor in strained Si/SiGe heterostructures”, Phys-
ica E 34, 456–459 (2006)
� Z. Zhong, H. Lichtenberger, G. Chen, M. Mühlberger, C. Schelling, J. Mysliveček, A.
Halilovic, J. Stangl, G. Bauer and W. Jantsch and F. Schäffler, ”Ordered SiGe islands
on vicinal and pre-patterned Si(001) substrates”, Microelectronic Engineering 83, 1730–
1735 (2006)
� G. Chen, H. Lichtenberger, F. Schäffler, G. Bauer and W. Jantsch, ”Geometry depen-
dent nucleation mechanism for SiGe islands grown on pit-patterned Si(001) substrates”,
Materials Science and Engineering: C 26, 795–799 (2006)
� H. Malissa, W. Jantsch, G. Chen, D. Gruber, H. Lichtenberger, F. Schäffler, Z. Wil-
amowski, A. Tyryshkin and S. Lyon, ”Investigation of the spin properties of electrons
in zero-dimensional SiGe structures by electron paramagnetic resonance”, Materials
Science and Engineering B 126, 172–175 (2006)
� T. Berer, D. Pachinger, G. Pillwein, M. Mühlberger, H. Lichtenberger, G. Brunthaler
and F. Schäffler, ”Lateral quantum dots in Si/SiGe realized by a Schottky split-gate
technique”, Appl. Phys. Lett. 88, 162112 (2006)
� G. Chen, H. Lichtenberger, G. Bauer and W. Jantsch, F. Schäffler, ”Initial stage of the
2D-3D transition of a strained SiGe layer on a pit-patterned Si(001) template”, Phys.
Rev. B 74, 035302 (2006)

162 POSTFACE
Acknowledgements
I would like to thank all the people who have supported me with my PhD thesis and have
contributed a lot to the success of this work:
� Prof. Dr. Friedrich Schäffler for the interesting topic, for the productive discussions
and for his ongoing support in every respect.
� Dr. Detlev Grützmacher for taking on the second report.
� All other members of the institute and the people in the office for the friendly atmo-
sphere and the good collegiality. I cannot name all the people personally here, as the
list would be simply too long. However, I am deeply grateful for their assistance in
different respects. They offered technical or administrative support, helped handling
computer problems or contributed in valuable physical discussions.
� My family for the encouragement and making all this possible.

POSTFACE 163
Abbreviations
AFM Atomic Force Microscope
HRXTEM High Resolution CrossSectional Transmission Electron Microscope
MBE Molecular Beam Epitaxy
MODQW Modulation-doped Quantum Well
PL Photoluminescence
SAP Surface Angle Plot
SEM Scanning Electron Microscope
SOM Surface Orientation Map
TEM Transmission Electron Microscope