Design and Growth of Group IV Laser Structures

Design and Growth of Group IV

Laser Structures

Denis Rainko

Design and growth of group IV

laser structures

Von der Fakultät für Mathematik, Informatik und

Naturwissenschaften der RWTH Aachen University zur Erlangung

des akademischen Grades eines Doktors der Naturwissenschaften

genehmigte Dissertation

vorgelegt von

M.Sc. Denis Rainko

aus Herne

Berichter: Prof. Dr. Detlev GrützmacherProf. Dr. Jeremy WitzensProf. Dr. Matthias Wuttig

Tag der mündlichen Prüfung: 24.04.2020

Diese Dissertation ist auf den Internetseiten der Universitätsbibliothek verfügbar.

"Did you hear about the rose that grew

from a crack in the concrete?

Proving nature’s law is wrong it

learned to walk without having feet.

Funny it seems, but by keeping it’s dreams,

it learned to breathe fresh air.

Long live the rose that grew from concrete

when no one else ever cared!"

-Tupac Amaru Shakur

Der kleinen Kämpferin im Inkubator, deren Hand meinen Finger und

mein Herz mit voller Kraft gepackt hat.

Abstract

The development of information technology during the last century was substan-

tially pushed forward by silicon technology. The rapid growth of the need for inter-

connected devices requires the optimization of the energy efficiency of information

transfer. Therefore, there is a great endeavor to replace the data transfer by elec-

trons with transfer by photons, with a laser source as the key device. One proposed

approach to achieve a laser in so-called Opto-electronic integrated circuits (OEICs),

is the monolithic integration of silicon technology compatible group IV alloys. GeSn

alloys with their potential to achieve a direct bandgap are here highly interesting.

In this work, possibilities to optimize group IV laser materials are investigated.

Starting from bulk GeSn, 8-Band k · p band structure calculations show a large

achievable gain. In this regard, the influence of strain and composition on band

structure is evaluated, demonstrating advantages of low Sn content GeSn under

tensile strain.

Following the development of III-V laser materials, the opportunities and chal-

lenges of quantum structures were investigated. GeSn/SiGeSn multi quantum wells

(MQWs) were found to be promising, in this respect, showing strong carrier con-

finement and material gain. Limitations in the well thickness and n-type doping

concentration, due to quantization effects and absorption losses, were studied.

Compared to MQWs, substantially lower lasing thresholds can be achieved with

quantum dots (QDs). Therefore, GeSn QDs were studied experimentally and the-

oretically. Using transmission electron microscopy and atom probe tomography the

morphology and composition of Sn-rich precipitates obtained by thermally treated

thin GeSn layers embedded in Ge were investigated. Based on the promising find-

ings for GeSn/SiGeSn MQWs, band alignment calculations were performed for cone

shaped GeSn QDs in an SiGeSn matrix. High energy barriers are found for hydro-

statically and biaxially strained direct bandgap QDs.

iii

At the end of this thesis, several approaches are discussed which could, additionally,

improve the laser performance. First, a GeSn/SiGeSn MQW LED was grown by

reduced-pressure chemical vapor deposition, where a grading in doping concentra-

tion was integrated into bottom and top contacts. This design could substantially

reduce losses of the lasing mode in highly doped regions. A powerful approach to

separate the growth of e.g. photodetectors and waveguides is the selective epitaxial

growth. Using different substrates, growth temperatures and adding HCl, growth

parameters guaranteeing selectivity were evaluated for GeSn.

As a last concept, the ternary CGeSn was considered. Using the precursor tetra-

bromomethane (CBr4), CGeSn layers were grown at different flow rates and growth

temperatures. C contents exceeding the solid solubility of C in Ge were found,

while still maintaining high crystal quality. Band energy calculations predict a di-

rect bandgap for ternaries grown at low temperatures. For all layers a displacement

of Sn atoms from lattice sites and a significant increase in the defect density was

measured. CGeSn alloys could represent a new way to tune the band structure of

group IV alloys.

iv

Zusammenfassung

Die Entwicklung der Informationstechnologie des letzten Jahrhunderts wurde maß-

geblich durch die hochentwickelte Siliziumtechnologie getragen. Der rasant wachsen-

de Bedarf an vernetzten Geräten erfordert eine hohe Energieeffizienz zur Übertra-

gung von Information. Daher gibt es großes Bestreben die Informationsübertragung

elektronischer Chips durch Photonen an Stelle von Elektronen zu realisieren. Als

wichtigstes Grundbauelement wird eine Laserlichtquelle benötigt. Ein Konzept zur

Realisierung eines Lasers in optoelektronischen integrierten Schaltkreisen (OEICs)

ist die monolithische Integration von Gruppe IV Elementen, welche mit der Silizi-

umtechnologie kompatibel sind. GeSn Legierungen sind hier von großem Interesse,

da in diesen eine direkte Bandlücke erzeugt werden kann.

In dieser Arbeit wurden Möglichkeiten untersucht, die Effizienz von Gruppe IV La-

sern zu optimieren. Beginnend bei dicken GeSn Schichten wurde mittels der 8-Band

k · p Methode gezeigt, dass hohe optische Verstärkungen erzielt werden können.

In diesem Zusammenhang wird der Einfluss von Verspannungen und der Material-

komposition auf die Bandstruktur berechnet, wobei Vorteile von tensil verspanntem

GeSn mit niedrigen Sn Konzentrationen demonstriert werden.

In Hinblick auf die Entwicklung von III-V Lasermaterialien wurden die Möglichkei-

ten und Herausforderungen durch die Nutzung von Quantenstrukturen untersucht.

GeSn/SiGeSn Vielfachquantentöpfe (MQWs) zeigen hier großes Potential, Ladungs-

träger in der aktiven Schicht zu konzentrieren und hohe optische Verstärkungen zu

erzeugen. Weiterhin wird die Limitierung der Schichtdicke und der n-Typ Dotierung

aufgrund von Quantisierungseffekten untersucht.

Im Vergleich zu MQWs können deutlich niedrigere Laserschwellen mit Quanten-

punkten (QDs) erreicht werden. Daher wurden QDs experimentell und theoretisch

untersucht. Mittels Transmissionselektronenmikroskopie und Atomsondentopogra-

phie wurden die Topographie und Komposition von Ausscheidungen mit hoher Sn

v

Konzentration analysiert, welche durch die thermische Nachbehandlung von dünnen

GeSn Schichten umgeben von Ge erzeugt wurden. Aufbauend auf den vielverspre-

chenden Ergebnissen für GeSn/SiGeSn MQWs wurden Energiebarrieren zwischen

konischen GeSn QDs umgeben von einer SiGeSn Matrix berechnet. Hier konnten

hohe Energiebarrieren für hydrostatisch und biaxial verspannte QDs gefunden wer-

den.

Den Abschluss dieser Arbeit beschreiben experimentelle Untersuchungen von Opti-

mierungsmöglichkeiten für Laser-Bauelemente. Zunächst wurde mittels chemischer

Gasphasenabscheidung bei reduziertem Druck eine GeSn/SiGeSn MQW LED ge-

wachsen, deren Kontaktschichten eine Konzentrationsrampe in der Dotierung auf-

weisen. Dieses Konzentrationsprofil könnte die Abschwächung der Lasermode in der

aktiven Schicht durch hochdotierte Regionen signifikant reduzieren. Ein substanziell

wichtiger Ansatz, um zum Beispiel Photodetektoren von Wellenleitern zu trennen,

ist die selektive Epitaxie. Die Selektivität von deponierten GeSn Schichten wurde

daher untersucht, wobei der Einfluss verschiedener Substrate, Wachstumstempera-

turen und des Gases HCl miteinbezogen wurden.

Als letztes Konzept wurde die ternäre Legierung CGeSn vorgeschlagen. CGeSn

Schichten wurden unter Nutzung des Kohlenstoffpräkursoren Tetrabrommethan bei

verschiedenen Flüssen und Temperaturen gewachsen. Kohlenstoffgehälter, die die

Löslichkeit von Kohlenstoff in Ge übertreffen, wurden inkorporiert, wobei hohe kris-

talline Qualitäten erzielt wurden. Bandenergierechnungen prognostizieren eine di-

rekte Bandlücke für Legierungen, die bei niedrigen Temperaturen gewachsen wur-

den. Das Wachstum bei hohen C Flüssen, bewirkt jedoch eine Verdrängung von Sn

Atomen von Gitterplätzen und einen deutlichen Anstieg der Defektdichte. CGeSn

Legierungen könnten eine weitere Möglichkeit bieten, die Bandstruktur von Gruppe

IV Legierungen anzupassen.

vi

Contents

1 Introduction 1

2 Bulk Si-Ge-Sn alloys 5

2.1 Direct bandgap GeSn . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Band energies and directness . . . . . . . . . . . . . . . . . . . 6

2.1.2 Biaxial strain . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.3 Band dispersions and effective masses . . . . . . . . . . . . . . 13

2.1.4 Optical properties of GeSn bulk alloys . . . . . . . . . . . . . 17

2.1.5 Low Sn content GeSn under tensile strain . . . . . . . . . . . 25

2.2 SiGeSn as a barrier material . . . . . . . . . . . . . . . . . . . . . . . 30

2.2.1 Band energies and directness . . . . . . . . . . . . . . . . . . . 30

2.2.2 Bandgap bowing at Γ . . . . . . . . . . . . . . . . . . . . . . . 35

2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3 GeSn/SiGeSn Quantum Wells 39

3.1 Group IV heterostructures . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2 Carrier confinement in GeSn/SiGeSn MQWs . . . . . . . . . . . . . . 41

3.2.1 Influence of strain and Si content . . . . . . . . . . . . . . . . 48

3.2.2 Strain balancing and critical thickness . . . . . . . . . . . . . 49

3.2.3 Material gain calculations . . . . . . . . . . . . . . . . . . . . 54

3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4 GeSn Quantum Dots 59

4.1 Approaches to achieve GeSn QDs . . . . . . . . . . . . . . . . . . . . 60

4.2 GeSn QDs embedded in SiGeSn . . . . . . . . . . . . . . . . . . . . . 65

4.2.1 Hydrostatically strained QDs . . . . . . . . . . . . . . . . . . 65

4.2.2 Biaxially strained QDs . . . . . . . . . . . . . . . . . . . . . . 68

vii

Contents

4.2.3 High Sn content QDs . . . . . . . . . . . . . . . . . . . . . . . 72

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5 Optimization of group IV photonic devices 75

5.1 In-situ growth of graded contact layers . . . . . . . . . . . . . . . . . 76

5.2 Selective epitaxial growth of GeSn . . . . . . . . . . . . . . . . . . . . 78

5.3 CGeSn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.3.1 CBr4 flow rate dependence . . . . . . . . . . . . . . . . . . . . 84

5.3.2 Temperature dependence . . . . . . . . . . . . . . . . . . . . . 88

5.3.3 Interpretation of CGeSn epitaxy . . . . . . . . . . . . . . . . . 91

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6 Conclusion and Outlook 95

A Appendix I

A.1 Band alignment calculation of SiGeSn heterostructures . . . . . . . . I

A.2 8-band k ·p calculations . . . . . . . . . . . . . . . . . . . . . . . . . V

A.2.1 Bulk semiconductors . . . . . . . . . . . . . . . . . . . . . . . V

A.2.2 Heterostructures . . . . . . . . . . . . . . . . . . . . . . . . . XII

A.3 Free carrier absorption . . . . . . . . . . . . . . . . . . . . . . . . . . XVI

A.4 Selective epitaxial growth . . . . . . . . . . . . . . . . . . . . . . . . XIX

A.5 Annealing of GeSn SQWs . . . . . . . . . . . . . . . . . . . . . . . . XX

Bibliography XXIII

viii

1 Introduction

The last century development of information technology put a large part of the world

population in a position to utilize and enjoy a variety of options for networking and

communication. Both the desire to exploit or extend the current possibilities and

the increasing average prosperity of the world population require a constant techno-

logical progress. By the year of 2022 the annual global internet protocol (IP) traffic

will be 4.8 ZB (4.8 billion TB) per year (threefold increase since 2017), which is

strongly influenced by an increasing video traffic and the nascent internet of things

(IoT).1 On the technological side, a performance bottleneck for on-chip and chip-

to-chip data communication becomes perceivable due to limitations in bandwidth

and power density caused by the interconnection through wires.2–4 These limita-

tions can be overcome by the realization of data transmission through photons.

Opto-electronic integrated circuits (OEICs) describe the monolithic integration of

photonic devices on semiconductor microchips promising low power consumption,

propagation losses and higher bandwidths. In this regard, the main focus is put on

silicon photonics due to its compatibility with the highly matured complementary

metal-oxide-semiconductor (CMOS) technology, guaranteeing high volume produc-

tion at low costs.5

With its potentially low absorption losses in the mid infrared (MIR) region, sili-

con photonics is of high interest for biosensors.5 It enables a real-time detection of

gases like CO, CO2 and CH4 on low cost, compact platforms6 and light detection

and ranging (LiDAR) systems.7 The outstanding maturity of CMOS technology also

qualifies silicon photonics for quantum photonic integrated circuits (QPICs), where

extremely low processing tolerances have to be met.8

However, all these platforms rely on an efficient laser source, preferably integrated

on-chip. In the last decades sophisticated OEICs have been developed with an

amount of 70 million transistors and 850 photonic devices using either an exter-

1

1 Introduction

nal light source4 or a laser bonded to the microchip.9 In this regard laser devices

based on III-V materials are commonly discussed, showing excellent characteristics.5

As a prominent representative, Quantum cascade lasers (QCLs) were demonstrated

showing multiwatt room temperature lasing.10,11 The integration of III-V lasers on

Si is, yet, a challenging task due to the large lattice mismatch between both mate-

rials. Nevertheless, room temperature lasing from monolithically integrated devices

was demonstrated, using e.g. thick buffer layers12,13 or selective epitaxial growth in

grooves and trenches.14,15 The industrial integration of these approaches has to face

the need of large investments and high process development efforts.2

A more convenient solution could be the integration of a group IV laser. Ge is here

of high interest, due to its direct bandgap being energetically close to the indirect

bandgap, which dominates charge carrier recombinations. By applying high tensile

strain to the lattice, a direct bandgap semiconductor can be achieved, needed for

interband lasers.16 In this context promising results were reported demonstrating

high strain17,18 and optical output.19–22 However, applying tensile strain is, similar

to III-V semiconductors, a challenging task and met by elaborate processing of com-

plex device structures, decreasing its advantage over III-V lasers.

A similar effect as high tensile strain is achieved by alloying Ge with Sn. Theo-

retically and experimentally, for cubic binaries, a transition from an indirect into a

direct bandgap semiconductor at ∼7 at.% Sn was shown.23,24 Although epitaxially

very challenging, high Sn content (>12.6 at.%) GeSn was grown, demonstrating las-

ing from GeSn for the first time in 2015.24,25 Since then, plenty publications report

lasing from GeSn, increasing the range of lasing wavelengths from 2.2 µm to 3 µm

(corresponding Sn content range of 12.6–22 at.%) and lasing temperatures from 90 K

to 230 K.26–29

Recently, the focus of GeSn research shifted. Based on the historical development of

III-V lasers, a strong improvement of the low-temperature optical performance and

lasing at low thresholds is achieved by implementing GeSn/SiGeSn heterostructures,

especially multi quantum wells (MQWs).30–33 Here, confinement of charge carriers

in the active region of the laser device supports its efficiency. Based on the achieve-

ments for bulk and group IV heterojunctions, the following thesis investigates several

possibilities to improve the optical performance of group IV lasers.

Starting from bulk Si-Ge-Sn alloys, chapter 2 presents band structure calculations

2

using the 8-band k · p method. The influence of strain and material composition on

effective masses and gain will be outlined, leading to a discussion about the benefits

of low Sn content GeSn layers under tensile strain. In chapter 3 GeSn/SiGeSn

MQWs are designed guaranteeing strong carrier confinement and net material gain.

The influence of n-type doping, well/barrier thicknesses and absorption losses from

free carrier absorption are evaluated using experimental constraints given by chemi-

cal vapor deposition (CVD). Related to this, an insight into GeSn QDs will be gained

in chapter 4 by annealing of GeSn single quantum wells (SQWs) surrounded by Ge

and theoretical calculations on GeSn QDs embedded in an SiGeSn matrix.

In the end, several independent approaches will be evaluated in chapter 5 to im-

prove the performance of group IV light emitting devices and tune their bandgap.

At first, an MQW light emitting diode (LED) will be presented, exhibiting a grading

in the doping content of the contact layers towards the active region. The design is

suggested to decrease absorption losses of the lasing mode in highly doped regions.

The second concept investigates the selective epitaxial growth of GeSn on struc-

tured Si and Ge, which would allow separately grow devices with different designs

and laser structures. In order to extent the horizon of possibilities in terms of tun-

ing the GeSn bandgap, carbon will be epitaxially incorporated. Applying different

growth conditions, the influence on the crystal quality and incorporated C content

will be investigated.

All calculations, presented in this thesis and first-author publications, if not declared

differently, were performed by the author of this work.

3

2 Bulk Si-Ge-Sn alloys

Contents

2.1 Direct bandgap GeSn . . . . . . . . . . . . . . . . . . . 6

2.1.1 Band energies and directness . . . . . . . . . . . . . . 6

2.1.2 Biaxial strain . . . . . . . . . . . . . . . . . . . . . . 9

2.1.3 Band dispersions and effective masses . . . . . . . . . . 13

2.1.4 Optical properties of GeSn bulk alloys . . . . . . . . . 17

2.1.5 Low Sn content GeSn under tensile strain . . . . . . . . 25

2.2 SiGeSn as a barrier material . . . . . . . . . . . . . . . 30

2.2.1 Band energies and directness . . . . . . . . . . . . . . 30

2.2.2 Bandgap bowing at Γ . . . . . . . . . . . . . . . . . . 35

2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

The following chapter introduces the group IV alloy SiGeSn. Based on the band

structure of each constituent, the influence of alloying the semiconductor germanium

(Ge) with the semimetal α-tin (Sn) on bandgap and band splitting of Γ and L

valley of GeSn is studied. The latter will be referred to as the "directness". Band

dispersion calculations using an 8-band k · p model allow a study of effective masses

of conduction and valence bands (c.b. and v.b.). Especially, the concept of heavy

hole (HH) and light hole (LH) effective masses is discussed in-depth. The case of

a perfectly cubic lattice is experimentally rather scarce for hetero epitaxial layers,

so that the influence of biaxial compressive and tensile strain ε|| on band dispersion

and bandgap is evaluated. Since the major purpose of this work is the exploration

of group IV alloys as suitable lasing material, gain calculations of bulk GeSn are

5


presented. Here, the rather unexplored field of low Sn content GeSn under tensile

strain will be studied in detail. By adding the semiconductor silicon (Si) to GeSn,

another group of alloys becomes accessible that is suitable for efficient energy barriers

in GeSn heterostructures. Therefore, calculations for SiGeSn ternaries will be shown

with regard to their bandgaps, directness and controversial bowing parameter at

the Γ valley of the conduction band. Considering SiGeSn as a barrier material, the

influence of strain is studied by investigating pseudomorphic SiGeSn ternaries on

different GeSn substrates. The code for every calculation performed in this work,

if not declared differently, was provided by Dr. Zoran Ikonić from the University

of Leeds. Parameters and detailed descriptions about the calculations performed

in this work can be found in Appendix A. The temperature for all calculations

(again if not declared differently) was kept at 300 K. Parts of these results have

been previously published in Ref. [34].

2.1 Direct bandgap GeSn

2.1.1 Band energies and directness

SiGeSn alloys are of high interest for electronic and optoelectronic applications, due

to the possibility of tuning the electronic bandgap to a great extent and to achieve

a direct bandgap semiconductor. Fig. 2.1 shows the band dispersion of Si, Ge and

Sn in the Brillouin zone for several high symmetry points (L-, Γ- and X-points).35

For the sake of simplicity, the binary alloy GeSn will be first discussed. Ge itself is

an indirect bandgap semiconductor with the lowest bandgap Eg,L of 0.744 eV at the

L-point and the direct bandgap Eg,Γ of 0.898 eV only 150 meV above the former.36–38

Its crystal structure is the diamond cubic lattice. Sn, on the other hand, is a

semimetal, which below 13 ◦C stabilizes in the α-Sn phase (also called gray Sn).39

α-Sn has a diamond lattice structure with a zero bandgap at the Γ-point.40–42 The

solid solubility of Sn in Ge is below 1 at.%,39 but due to optimized processes for

molecular beam epitaxy (MBE) and chemical vapor deposition (CVD) – and in the

case of the latter the usage of new precursors – Sn concentrations beyond the thermal

equilibrium of up to 20 at.% can be achieved.43–48

By alloying Ge with Sn, the high symmetry point bandgaps will be in between

6


α-Sn

XL Γ

Ge

XL Γ

Si

XL Γ

6

-8

-6

-4

-2

0

2

4

En

erg

y (e

V)

(a) (b) (c)

alat

= 5.4307 Å alat

= 5.6573 Å alat

= 6.4892 Å

Figure 2.1 – Electronic band structures of (a) Si, (b) Ge and (c) α-Sn as calculatedin Ref. [35] with corresponding lattice constants and conduction and valence bandsas discussed in this work. ©IOP Publishing. Reproduced with permission. All rightsreserved.

those of each constituent. The incorporation of Sn on Ge lattice sites decreases the

bandgap at the Γ-point faster than at the L-point, so that a critical Sn content can

be found, required for a transition into a direct bandgap semiconductor.

Assuming a linear change of the band structure, as a simple approach, a transition

into a direct bandgap semiconductor is expected for Sn contents above 55 at.%.49,50

However, the bandgaps of GeSn do not have to evolve linearly.51 Early theoretical

calculations using the virtual crystal approximation method (VCA) affirm that the

linear approach does not resemble experimental findings.52,53 In this method, the

potential of a unit cell is modeled by placing virtual atoms on diamond lattice

sites, where the atom properties consist of concentration-weighted properties of Ge

and Sn. The resulting potential is used to solve the eigenvalue problem described

by the Schrödinger equation. These theoretical findings gave reason to correct the

bandgaps of GeSn (and also SiGeSn) at the Γ- and L-points by introducing nonlinear

bowing terms bi,Γ/L using the elemental concentrations xi (∑

xi = 1), so they can be

7


calculated by:

Eg,Γ/L =EGe,Γ/L · xGe + ESi,Γ/L · xSi + ESn,Γ/L · xSn (2.1)

− bSiGe,Γ/L · xSi xGe − bGeSn,Γ/L · xGe xSn − bSiSn,Γ/L · xSi xSn.

Terms containing xSi are neglected for GeSn, but will be discussed and considered

in section 2.2. However, despite introducing nonlinearities in the bandgap behavior,

the virtual crystal approximation was not able to reproduce experimental findings

on bGeSn,Γ, which indicate a strong bowing ∼2 eV and therefore a transition below

20 at.%.23,51,54–59 Later on, the VCA method was found to be insufficient for deter-

mining the bandgap bowing parameter for GeSn, as it was addressed theoretically

in greater detail using more sophisticated approaches like the mixed atom super-

cell model.35,60–64 In this approach, Ge and Sn atoms are placed randomly onto

lattice sites of a supercell accounting for their concentration in the alloy. Since

there are different possibilities of arrangement, all configurations describing a ran-

domly distributed alloy are taken into account and the resulting band structures are

averaged.35 The discrepancy between this model and the VCA can be explained by

the strong perturbation caused by Sn atoms. As pointed out in Ref. [65], the pertur-

bation originates in the strong lattice mismatch and difference in electronegativity

between Ge and Sn. The bonding in such an alloy cannot be described anymore

by a perfect diamond bonding, which the VCA fails to consider. In Ref. [66] it was

shown that the distribution of Ge and Sn atoms in GeSn alloys is random and no

clustering of Sn atoms is preferred, which justifies the application of the mixed atom

supercell model with a random arrangement of atoms.

In this work, a bandgap bowing bGeSn,Γ at the Γ-point of 2.24 eV and a bowing tem-

perature dependence dGeSn,Γ of −4× 10−4 eV/K was used, which were derived in

Ref. [67] based on experimental results from our group. The bandgaps of the Γ and

L conduction bands for unstrained GeSn using these values are shown in Fig. 2.2a.

Within the scope of this work, the directness is defined as the difference between the

Γ and L band edge energies, denoted as ∆EL−Γ. It is 0 meV at the direct-indirect

semiconductor transition point, which occurs at an Sn concentration of ∼7 at.%,

and becomes positive with increasing Sn concentration, reaching values >200 meV

for 20 at.% Sn (Fig. 2.2b). With increasing directness, the fraction of injected charge

8


0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Eg (

eV

)

754

3

2

λ (µ

m)

0 4 8 12 16 20

-100

0

100

200

∆EL-Γ (

meV

)

Sn content (at.%)

(a)

(b)

Eg,L

Eg,Γ

Ninj

=5x1018cm-3

0

25

50

75

100

NΓ/

NG

es (%

)

Figure 2.2 – (a) Bandgap/wavelength and (b) directness and Γ-electron populationof unstrained GeSn for an injection carrier density of 5× 1018 cm−3.

carriers that reside in the Γ conduction band is also increased. When 5× 1018 cm−3

electrons are injected into unstrained GeSn, the population of electrons in the Γ

conduction band increases with Sn content, reaching almost unity for 20 at.% Sn

(Fig. 2.2). For unstrained direct bandgap GeSn alloys, a wide range of wavelengths

(2–6 µm) is accessible (Fig. 2.2a). Experimentally, this range is limited by the max-

imal Sn content that can be incorporated into Ge and strain caused due to hetero

epitaxial growth.68

2.1.2 Biaxial strain

The hetero epitaxial deposition of a layer with unstrained lattice constant a0 on

a substrate with lattice constant asub 6= a0 causes the unit cell of the top layer

to deform in- (||) and out-of-plane (⊥), changing the in-plane lattice constant a0

into a||. The relative deformation ε is called strain and the forces σ, causing the

strain, stress. Their relation can be described by Hook’s law using the deformation

potential tensor C:69

σ = Cε. (2.2)

9


-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Energ

y (

eV

)

ε|| (%)

0.0

0.2

0.4

0.6

0.8Γ

L

LH

HH

Ge0.93

Sn0.07

(b)

R = 0 % R = 80 %

R = 0 % R = 80 %On Ge

On Ge0.90

Sn0.10

(a)

0 4 8 12 16 20

-150

-100

-50

0

50

100

150

200

250

Sn content (at.%)

∆EL-Γ (

meV

)

ε ||= 1.54 %

ε ||= -1.48 %

ε ||= 0 %

ε ||= -2.97 %

Figure 2.3 – (a) Strain dependence of conduction and valence band energies ofGe0.93Sn0.07 with a schematic representation of a pseudomorphically strained heteroepitaxial layer on top of a substrate. (b) Directness of pseudomorphically grown andrelaxed GeSn on a Ge and Ge0.90Sn0.10 buffer for different Sn contents.

In the case of biaxially strained layers – which is the most common case in CVD

– the lattice exhibits a tetragonal distortion, so that the in-plane lattice constants

and strain components are the same (εxx = εyy = ε||), but differ from out-of-plane

(εzz = ε⊥, cf. section A.1). The in-plane strain is defined as:

ε|| =a|| − a0

a0

. (2.3)

Two cases can be distinguished: If the substrate lattice constant is smaller than the

unstrained lattice constant of the hetero epitaxial layer (a0 < asub), the top layer gets

contracted in-plane and stretched out-of-plane, which is called compressive strain

(left side of the inset in Fig. 2.3a). The case, in which a0 > asub, is referred to as

tensile strain (right side of the inset in Fig. 2.3a). If there is no relaxation of the

top layer (a|| = asub), the deposition is described as pseudomorph.

A displacement of atoms in the unit cell, as it is induced by strain, changes its volume

– and therefore the bonding length and electron density – and lowers the crystal sym-

metry. This has a strong impact on the band structure of a semiconductor. Fig. 2.3a

exemplarily shows the effect of strain on the band edge energies of Ge0.93Sn0.07. The

10


system of equations used for this calculations is described in section A.1. The strain

range considered in this work was chosen to be −1.5 % < ε|| < 1.5 %. This range cov-

ers the experimental results from Ref. [44] and results presented in subsection 2.1.5.

Since the indirect-direct bandgap transition for unstrained GeSn occurs at 7 at.%

Sn, the directness becomes 0 meV at ε|| = 0 %. The HH and LH valence band edges

are degenerate at the Γ-point for the unstrained case. Applying strain lifts this

degeneracy, shifting the HH band edge to the top for ε|| < 0 %, while for ε|| > 0 %

the top valence band is described by the LH band.

The lattice mismatch between Ge and Si is 4 % and increases when incorporat-

ing Sn (Si-Sn lattice mismatch of 16 %). As it is visible in Fig. 2.3a, compressive

strain (ε|| < 0 %) decreases the directness, but the strain can be reduced by fully

relaxed Ge virtual substrates (Ge-VS) or, additionally, partially relaxed GeSn buffer

layers.27,33,44,45,66 Moreover, above a critical thickness the top layer begins to relax

via formation of misfit dislocations, which reduces the compressive strain. Here,

relaxation degrees of up to 80 % on Ge can be achieved.44 The influence of different

buffer layers and relaxation degrees is shown in Fig. 2.3b. For pseudomorphically

grown GeSn on Ge (blue rectangles) the direct bandgap transition is shifted to Sn

concentrations above 20 at.%, while for a relaxation of 80 % the transition occurs

already around 9 at.% with directnesses up to 175 meV for a 20 at.% alloy (blue cir-

cles).

Replacing the Ge substrate by an unstrained Ge0.90Sn0.10 buffer releases the strain

strongly in the pseudomorphic case (−2.97 % ≤ ε||,max ≤ −1.48 %) and increases the

directness (orange rectangles). Here, only Sn contents above the buffer Sn content

are considered (>10 at.%). This can be justified by the fact that the Sn content is

strongly dependent on the growth temperature Tgrowth and increases with decreasing

Tgrowth.44 Temperatures above the growth temperature can cause Sn precipitation

and segregation at the surface.70 For the sake of completeness, however, it should

be mentioned that for CVD processes this is not a strict limit and the Sn content

can be tuned by a few at.% by adjusting the partial pressures of precursors.48 For

MBE processes, on the contrary, the Sn content can be even adjusted over a large

range at a constant growth temperature.71 MBE grown GeSn, however, suffers from

a poor crystal quality due to the need of low growth temperatures.

Additional relaxation of the top layer on a GeSn buffer reduces the strain even more

11


Figure 2.4 – Strain dependence of directness (a) and bandgap (b) for different Sncontents. The green and red regions mark the region where the the semiconductorbecomes negative and the bandgap becomes 0 eV at the Γ-point.

and leads to directnesses similar to unstrained GeSn (orange circles in Fig. 2.3b).

Strain relaxation and an ingenious utilization of buffer layers have to be taken into

account in order to benefit from direct bandgap GeSn.

From Fig. 2.3 it can also be seen that strain has a strong influence on bandgap and

directness. While for the directness it is obvious that it is reduced by compressive

strain and increased by tensile strain, it is more complicated for the bandgap. In

detail, this can be seen in Fig. 2.4, where ∆EL−Γ and Eg were calculated for the

whole range of Sn contents considered in this work. The green area in Fig. 2.4a

shows the region in which GeSn has the fundamental indirect bandgap and the cor-

responding strain, where the transition into a direct bandgap alloy occurs. For Sn

contents below 7 at.%, tensile strain is needed to achieve a direct bandgap, while for

alloys with higher Sn content a fundamental direct bandgap is already achieved at

compressive strain. Above an Sn content of 12 at.%, a direct bandgap is achieved

for the whole range of strain values considered here.

In the case of the effectively lowest bandgap, it has to be distinguished between the

indirect bandgap Eg,L and the direct bandgap Eg,Γ. In Fig. 2.4b, the lowest bandgap

is plotted in dependence of biaxial strain, where the green area again describes the

region of indirect bandgap. For low Sn content GeSn, depending on the strain,

the same lowest bandgap value can be achieved stemming either from the indirect

12


ε|| = -1.5 % ε

|| = 0.0 % ε

|| = 1.5 %

En

erg

y (e

V) HH

LH

(a) (c)(b)

-0.10 -0.05 0.00 0.05 0.10 -0.10 -0.05 0.00 0.05 0.10-0.10 -0.05 0.00 0.05 0.10-0.4

-0.2

0.0

0.2

kz (1/Å)

Figure 2.5 – Energy dispersion of HH and LH bands in the out-of-plane direction[001] around the Γ-point for (a) compressively strained, (b) unstrained and (c) tensilestrained Ge0.88Sn0.12.

bandgap Eg,L or from the direct bandgap Eg,Γ. In case of Ge, Eg,L remains the lowest

bandgap over the whole range of strain values. It is also remarkable that the range

of accessible emission wavelengths for direct bandgap GeSn is strongly expanded

into the long wavelength infrared region (LWIR, >8 µm) by applying tensile strain.

An extremum is reached at 1.5 % strain and 20 at.% Sn, where the bandgap becomes

negative (red area in Fig. 2.4b). This point is excluded in further calculations, since

for the calculation model used here no reasonable results can be expected.

2.1.3 Band dispersions and effective masses

While it is obviously important to have a semiconductor with a direct bandgap to

design efficient lasers, the band dispersion and, related to this, also the concept

of effective masses play also a crucial role. It has to be emphasized that the gain

calculations presented in subsection 2.1.5 can only be understood in the context of

the energy dispersion of conduction bands and, in particular, valence bands around

the Γ-point. Hence, in the following, the band dispersion of valence and conduction

bands shall be discussed in detail.

Wave vectors k with k = (0 0 kz) Å−1

The effective mass m∗ is a concept to describe the behavior of charge carriers in semi-

conductors similar to a free particle. It associates all disturbances and interactions

13


within the crystal and due to extrinsic fields to one parameter m∗ without losing

the simplicity of the free particle formalism. By definition it is inversely related to

the band dispersion curvature using the reduced Planck constant h:

1m∗

=1h2

∂2E

∂k2(2.4)

m∗ is a tensor and thus can be strongly anisotropic. The common use of the valence

band denotations "HH" and "LH" stems from the energy dispersion around the Γ-

point of the related bands of unstrained semiconductors. An example of the band

dispersion for small wave vectors (−0.1 Å−1 ≤ kz ≤ 0.1 Å

−1) in the [001] direction

is shown in Fig. 2.5b for unstrained bulk Ge0.88Sn0.12. At kz = 0 Å−1

HH and

LH are degenerate. Around that point (kz 6= 0 Å−1

), HH and LH show different

curvatures in their dispersion. The curvature is broader for the HH band (with

effective mass m∗⊥,HH) than for the LH band (m∗

⊥,LH), which with the help of Eq. 2.4

can be translated into:

m∗⊥,HH > m∗

⊥,LH for k = (0 0 kz) Å−1. (2.5)

This gives the valence bands their denotation and it is reasonable for all directions

of k, when there is no strain. Although the relation in Eq. 2.5 is also conserved in

kz direction, when compressive or tensile strain is applied to the layer (Fig. 2.5a,c),

the LH effective mass will be influenced. While for tensile strain m∗⊥,LH hardly

changes, it increases for compressive strain strongly because of band mixing with

the SO band. In case of tensile strain, it is remarkable that the LH band is only in

a small range above the HH band. For |kz| > 0.03 Å−1

it crosses the HH without

band mixing or anti-crossing effects and becomes the lower valence band. The

previously mentioned band splitting of HH and LH occurs due to the different

character of their wave functions in the 8-band k · p formalism.

Wave vectors k with k = (kx ky 0) Å−1

Since for the unstrained diamond lattice the in-plane directions kx and ky are equiv-

alent to kz, their associated effective masses m∗|| will be equal to m∗

⊥. This can be

14


HH

LH

ε|| = -1.5 % ε

|| = 0.0 % ε

|| = 1.5 %

(a)

(f)

(e)

(d)

(c)

(b)

Figure 2.6 – Energy dispersion of HH and LH band edges in in-plane directions [100]and [010] around the Γ-point for (a,b) compressively strained, (c,d) unstrained and(e,f) tensile strained Ge0.88Sn0.12.

seen in Fig. 2.6c,d, where the in-plane band dispersion in kx ([100]) and ky ([010])

directions of HH and LH for unstrained Ge0.88Sn0.12 is shown. Here, the strong

curvature of the LH band in contrast to the HH band means again a much smaller

m∗||,LH than m∗

||,HH.

But the situation changes significantly, when strain is applied to the crystal. The

effective mass of LH increases while for HH it decreases. Applying strong tensile

strain of 1.5 %, makes m||,HH much smaller than m||,LH, but since LH is above HH

there is no crossing or anti-crossing of them (Fig. 2.6e and f). Compressive strain of

−1.5 % shifts the HH band above the LH band and – similarly to the case of tensile

strain – decreases its effective mass close to the Γ-point, while for the LH band m||,LH

hardly changes. This would again lead to the crossing of the two valence bands. In

the in-plane direction this is forbidden, so that a strong anti-crossing effect occurs

spreading the HH band for |k||| > 0.03 Å−1

and causing a strong nonparabolicity

(Fig. 2.6a). A similar dispersion behavior can also be observed in Ref. [72] for SiGe

under compressive strain and it is in contrast to the notation of the bands, though

15


0.540

0.544

0.548

m* D

OS

,vb (

m0)

0.00

0.01

0.02

0.03

0.04

0.05

m* D

OS

,Γ (

m0)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

m* D

OS

,L (

m0)

ε|| (%)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

ε|| (%)

(a)

(b)

(c)

m*DOS,HH

m*DOS,LH

Sn content20 at.%16 at.%

12 at.%8 at.%

4 at.%0 at.%

0.02

0.04

0.06

0.27

0.28

0.29

Figure 2.7 – Strain dependence of the density of states effective mass m∗DOS for (a)

Γ, (b) L electrons and (c) HH (dashed lines) and LH holes.

in terms of the 8-band k · p model they keep their original wave functions. Usually,

the notation of the band is kept, but it is, strictly speaking, only valid for unstrained

crystals around the Γ-point.73

Density of states effective mass m∗DOS

To investigate the Sn dependent change in the conduction and valence band dis-

persion under strain, the effective masses of Γ, HH and LH bands were calculated

using the 8-band k · p model (details are given in subsection A.2.1). In order to

take into account the strong anisotropy of the valence band effective masses, as

described above, and to choose a representative value for the effective mass for an

individual band, the density of states effective mass m∗DOS will be discussed in the

following. m∗DOS is often used in calculations, where charge carriers from the whole

band, irrespectively of the anisotropic properties, are considered. This is for ex-

ample the case for analytical solutions of optical properties like gain and radiative

recombination.74 To calculate m∗DOS, the geometric mean of the longitudinal masses

m∗l and the transverse mass m∗

t of the regarded high symmetry point is taken:75

m∗DOS = (g2m∗

tm∗tm

∗l )

1/3. (2.6)

16


The degeneracy factor g accounts for the number of equivalent bands at high sym-

metry points in the Brillouin zone and is 1 for the bands at the Γ-point and 4 at the

L-point. For Γ-electrons, m∗DOS,Γ decreases strongly, when going from compressive

to tensile strain. This is depicted in Fig. 2.7a, where m∗DOS,Γ is plotted in units

of the free electron mass m0 in dependence on strain and Sn content. In the here

used strain range m∗DOS,Γ is reduced by 25 % for Ge. This reduction increases up

to 58 % for GeSn with an Sn content of 16 at.%. For electrons in the L conduction

band, however, the change of effective mass m∗DOS,L with strain is negligible and it

is somewhat reduced when increasing the Sn content (Fig. 2.7b).

Effective masses describing holes in valence bands of strained alloys are more com-

plex to describe. Fig. 2.7c plots the strain dependence of m∗DOS,HH and m∗

DOS,LH and,

at first, it is noticeable that their behavior becomes irregular around the unstrained

case. Starting from 0.29m0 for m∗DOS,HH and 0.024m0 for m∗

DOS,LH small perturba-

tions around ε|| = 0 % cause m∗DOS,HH/m∗

DOS,LH to significantly decrease/increase.

Especially for tensile strain below 0.2 %, peaks for LH and minima for HH seem to

appear. Since in this region the band mixing of HH and LH near the Γ-point is

very strong, these values should be treated with caution. In this region the bands

lose their parabolicity for small wave vectors, so that Eq. 2.4 gives spurious results.

For∣

∣

∣ε||

∣

∣

∣ > 0.2 %, the behavior of m∗DOS,HH and m∗

DOS,LH becomes smooth. Com-

pressive strain hardly changes either of the two effective masses, although there is

a strong dependence on the Sn content. The latter observation also holds true for

tensile strain and m∗DOS,HH. Its values remain constant over this particular range,

but m∗DOS,LH undergoes strong changes. For low Sn contents (<8 at.%), it increases

reaching values close to m∗DOS,HH, while at higher Sn contents it decreases again.

This complex behavior of effective masses for strained alloys will have a strong im-

pact on optical properties and from Fig. 2.7c it can be concluded that the unstrained

case should be considered separately.

2.1.4 Optical properties of GeSn bulk alloys

The injection of excess carriers into conduction and valence band of a semiconductor

causes radiative and non-radiative recombinations, the former process being prefer-

able for optical devices.74 Radiative processes can be again divided into spontaneous

17


and stimulated emission. In laser materials (light amplification by stimulated emis-

sion of radiation), emission of light is amplified by stimulated recombination. Lasing

is characterized by photon coherency concerning wave length and propagation direc-

tion, which makes laser materials interesting for many optoelectronic applications.

However, in order to achieve lasing, absorption losses have to be overcome by in-

jecting a sufficient number of charge carriers into the conduction and valence bands

at the Γ-point (optically or electrically). Theoretically this can be described by the

term inversion, which describes the state, in which the absorption α becomes nega-

tive. This condition is called gain g and can be calculated for photons with energy

hω (with ω being the angular frequency) using Eq. 9.2.127 from Ref. [76]:

α (hω) = −g (hω) =πω

nrcε0

2V

∑

kv

∑

kc

|e · µcv|2 δ (Ec − Ev − hω) (fv (k)− fc (k))

= α0 (hω) (fv (k)− fc (k)) , (2.7)

with the refractive index nr, the speed of light c, the vacuum permittivity ε0, the

crystal volume V , the transition matrix element |e · µcv|2 (describes how strong two

states are optically coupled) and kc,v and Ec,v being the conduction and valence band

wave vectors and energies, respectively. Under constant charge carrier injection, a

quasi-equilibrium is created and the absorption becomes negative for:

fv (k)− fc (k) < 0 (inversion condition), (2.8)

where the Fermi distributions of electrons in the valence and conduction band are

defined using the corresponding quasi-Fermi level EF,c and EF,v by:76

fv (k) =1

1 + e(Ev(k)−EF,v)/kBT, fc (k) =

1

1 + e(Ec(k)−EF,c)/kBT, (2.9)

with kB being the Boltzmann constant and T the absolute temperature. The above

condition can be transformed using the definitions in Eq. 2.9 to give the commonly

used lasing condition:

e(Ec(k)−EF,c)/kBT < e(Ev(k)−EF,v)/kBT , EF,c − EF,v > Ec − Ev = Eg. (2.10)

18


Figure 2.8 – Contribution of free carrier processes in unstrained Ge0.88Sn0.12 for dif-ferent electron (a) and (b) hole densities. (c) Sn dependence of free carrier processesfor unstrained GeSn at Ninj = 5× 1018 cm−3.

This condition describes the threshold for lasing and guarantees gain only for

photon energies satisfying Eg < hω < EF,c − EF,v. Above this energy absorption

becomes dominating, which is the reason why gain spectra exhibit a maximum.

Free carrier absorption

Based on Eq. 2.7 and the 8-band k · p model, calculations for Ge1−xSnSnxSn

were

performed to investigate the achievable material gain. In particular, the net gain

was calculated by subtracting free carrier absorption (FCA) from material gain. In

general, FCA describes the process of a charge carrier absorbing a photon and be-

ing excited to a higher energy state. Usually, this changes the momentum of the

particle, which is mediated by emission or absorption of phonons. The facilitation

of FCA by an intermediate state enables the utilization of a second order pertur-

bation approach within the quantum mechanical framework. Being a second order

perturbation process, FCA is usually smaller than first order processes like direct

bandgap transitions. In this work the analytical FCA expressions from Ref. [77]

were used and taken into account in net gain calculations. In this respect, acous-

19


tic phonon scattering of electrons, optical phonon deformation potential scattering

for L valleys, inter-valley scattering for the conduction band, ionized impurity scat-

tering and alloy disorder scattering were included. Also included is inter-valence

band absorption, where holes undergo transitions between different valence bands

by absorbing a photon. These are formally "interband transitions", because HH,

LH and SO are really different bands (with different character of wave functions)

within what is globally called "valence band". More details and information about

scattering parameters are given in section A.3 in the appendix.

These processes depend on material composition, strain, injection carrier density

and, therefore, also doping type and concentration and will be investigated in the

following. Fig. 2.8a and Fig. 2.8b show the absorption from each FCA process taken

into account for unstrained Ge0.88Sn0.12. The absorption values were determined at

the bandgap Eg or, in the case of achieved gain, at energies in the middle of the

gain region defined by Eq. 2.10, which is roughly at the gain maximum. Scatter-

ing processes from holes are indicated by circular symbols, processes including only

electron scattering are represented by rectangular symbols, while scattering from

holes and electrons is symbolized by triangles. When keeping the hole concentra-

tion constant at 1× 1017 cm−3, while increasing the electron concentration up to a

value of 1× 1020 cm−3, electron scattering processes, as expected, increase, while

hole scattering processes remain constant (Fig. 2.8a). In the case of increasing hole

concentration it is vice versa (Fig. 2.8b). Since ionized impurity scattering applies

to both hole and electron scattering, it increases in both cases (purple upright tri-

angles). However, when electrons are the majority charge carriers (n-type doping,

Fig. 2.8a), the total absorption (dashed black line) is completely dominated by intra-

conduction band scattering (red rectangles) and becomes very strong for high doping

values. In comparison, high p-type doping is needed to exceed intra-conduction band

scattering at low electron concentrations. In this region inter-valence band scatter-

ing and absorption from free holes play the dominant role (gray/light blue circles in

Fig. 2.8b).

These three processes (intra-c.b./-v.b and free hole scattering) are also the main

scattering processes for the Sn dependent FCA at equally high injection carrier

densities Ninj of electrons and holes of 5× 1018 cm−3 (Fig. 2.8c). Strikingly, the

intra-conduction band scattering has a maximum at Sn contents around 12 at.%,

20


before it decreases again strongly for higher Sn contents. This behavior can be ex-

plained by the intra-c.b. spectrum (not shown here) and the criterion which was

applied to determine the scattering value: The intra-c.b. spectrum shows a broad

peak at energies, which are dependent on the conduction band valley offsets and the

injection carrier density.77 The offset of Γ and L valleys increases with increasing

Sn content, shifting the intra-c.b. absorption peak to higher energies. The values

for FCA were determined at energies in the middle of the range given by the lasing

condition in Eq. 2.10. This energy can coincide with the peak energy of intra-c.b.

scattering (e.g. for 12 at.% Sn) or be located at energies far away from the absorp-

tion peak (e.g. for 20 at.% Sn). This explains the intra-c.b. behavior, but also the

minimum of inter-v.b. absorption at 20 at.% Sn in Fig. 2.8c, where the energy of

interest lies within a local minimum of the absorption spectrum. Furthermore, it

explains why intra-conduction band scattering has such a strong influence on FCA

results in Fig. 2.8a and b, so that it becomes maximal around 12 at.% Sn. Although

scattering stemming from perturbations in the alloy composition increase by several

orders of magnitude with the Sn content, their relative influence is very weak (yellow

rectangles).

Material gain

Introducing FCA into gain calculations results in the net material gain spectra of

unstrained GeSn, as shown for several Sn contents and injection carrier densities

Ninj in Fig. 2.9a. As described at the beginning of this section, gain can be only

achieved in a limited range of photon energies, which explains the appearance of

gain maxima. By lowering the bandgap (increasing the Sn content) the spectrum is

shifted to lower energies. On the other hand increasing Ninj causes a filling of the

lowest conduction and highest valence band states, shifting EF,c/v deeper into the

conduction and valence bands and the gain maximum to higher energies. Moreover,

the range where gain is achieved (Eg < hω < EF,c − EF,v) is broadened, so that

a higher number of charge carriers contribute to radiative processes increasing the

material gain. Additionally, at high temperatures a stronger inversion increases the

width of the gain spectrum.

Besides the Sn content, net gain strongly depends on the injection carrier density

(Fig. 2.9b). It increases strongly above the lasing threshold, while being lowered by

21


0.2 1.00.80.60.4

Energy (eV)

0.2

4.0

1.0

2.0

0.0

4.0

2.0

0.4

2.0

ne

t g

(x1

04 c

m-1)

0.1

0.3 4 at.% Sn

20 at.%

16 at.%

12 at.%

8 at.%

Ninj

(cm-3): 1x10205x10191x1019

(b)(a)

1018 1019 1020

0

1

2

3

4

5

net g

max (

x10

4 c

m-1)

Ninj

(cm-3)

ε|| = 0%

0 at.% Sn 4 at.% Sn 8 at.% Sn 12 at.% Sn

16 at.% Sn 20 at.% Sn

Figure 2.9 – (a) Net gain spectra of unstrained GeSn for different Sn contents andinjection carrier densities Ninj at 300 K. (b) Ninj dependent net gain maxima fordifferent Sn contents and no strain.

FCA processes (c.f. Fig. 2.8). For the unstrained case in Fig. 2.9b an unusual feature

is that for the vast majority of injection carrier densities the net gain of GeSn with

20 at.% Sn is below the net gain of Ge0.84Sn0.16, despite having a higher directness

∆EL−Γ and a lower bandgap Eg. The reason for this behavior is the change of the

character of the Γ conduction band wave function. As it is described in section A.2,

the conduction band wave function within the k · p formalism can be correlated to

s-like states |s ↑〉, |s ↓〉 with spin-up (↑) and spin-down (↓). This s-like character

can be extracted from the wave functions of the diagonalized Hamiltonian and

described by the expression:

|Ψi,↓|2 + |Ψi,↑|2 . (2.11)

It is unity for the Γ-electron wave function, if there is no mixing with other bands.

However, if the bandgap decreases and conduction and valence bands approach each

other, the s-like character decreases significantly, which in turn decreases the matrix

elements between these two states and therefore the "optical activity". In order to

demonstrate this effect, the Sn dependence of the maximum net gain was inves-

tigated for several strain values (Fig. 2.10a). Here, for GeSn under tensile strain

net gain maxima for z-polarized light were chosen, while for compressive strain the

22


0 2015105

Sn content (at.%)

0.0

1.2

1.0

0.8

0.6

0.4

0.2ne

t g

max (

x1

04 c

m-1)

Ninj

= 5x1018 cm-3

ε|| = 1.5 %

0.0 %

-1.5 %

(a) (b)

0 5 10 15 2080

85

90

95

100

avg. s-lik

e c

hara

cte

r (%

)

Sn content (at.%)

ε|| = 1.5 % 0.0 %

-1.5 %

|kavg

| < 0.2 Å-1

Γ conduction band

Figure 2.10 – (a) Sn dependent net gain maxima for different strain values andNinj = 5× 10−18 cm−3. (b) Corresponding k-space averaged s-like character of the Γ

conduction band for |kavg| < 0.02 Å−1

.

polarization of radiation is in-plane. This is in order to compare the maximal achiev-

able net gain, which will be explained in detail in the course of this section. When

biaxial strain exceeds 0 %, net gmax increases with Sn content, peaks and decreases

again. This peak occurs at lower Sn contents as the biaxial strain moves towards

high tensile strain (∼12 at.% for ε|| = 1.5 %). Fig. 2.10b depicts the corresponding

s-like character of the Γ wave function calculated and averaged for a small range of k

vectors and several strain values. The narrowing of the bandgap with increasing Sn

content is more pronounced at tensile strain, causing the s-like character to decrease

down to values below 85 % for Ge0.84Sn0.16 and ε|| = 1.5 %. The decrease of the

transition matrix element between conduction and valence bands with decreasing

bandgap can also be demonstrated using an analytical expression extracted from

the 8-band k · p model, as it is described in Eq. A8.14 in Ref. [78]. When investi-

gating the corresponding FCA and material gain separately (not shown here), the

same behavior can be found as in Fig. 2.10a, so that FCA can be excluded from

being responsible for this effect. Still, it is significantly decreasing the material gain.

The above results should be considered when designing optical devices with high

Sn contents, as this also influences the threshold current density Ninj,th needed to

achieve gain and will be demonstrated below.

In general, the amount of charge carriers needed to fulfill the lasing condition de-

23


0 5 10 15 201017

1018

1019

1020

1021

x,y-polarized z-polarized

0 5 10 15 20 0 5 10 15 20

Sn content (at.%)

ε|| = 1.5 %ε

|| = 0.0 %ε

|| = -1.5 %

Nin

j,th (

cm

-3)

(c)(b)(a)

Figure 2.11 – Sn dependence of the injection carrier threshold Ninj,th for compres-sively strained (a), unstrained (b) and tensile strained GeSn (c) and different polar-ization.

creases with decreasing bandgap and increasing directness. The former can be ex-

plained by a decreasing electron effective mass and, therefore, less charge carriers

needed to raise the difference between the quasi Fermi levels (EF,c − EF,v) above

the bandgap Eg, while the latter increases the number of charge carriers at quasi

equilibrium in the Γ conduction band. Accordingly, the injection carrier density

threshold Ninj,th is significantly decreased when increasing Sn content and strain

(Fig. 2.11). As mentioned in the above section, when the bandgap becomes small,

and conduction and valence band states mix, the "optical activity" decreases, so

that Ninj,th increases or stays constant (Fig. 2.11b and Fig. 2.11c). Ninj,th ranges

from 7× 1020 cm−3 for Ge (ε|| = −1.5 %) to 4× 1017 cm−3 for Ge0.92−0.84Sn0.08−0.16

(ε|| = 1.5 %).

As has been argued in subsection 2.1.2, strain has a strong influence on the band

structure of GeSn, which in turn influences the emission properties. The achievable

gain and Ninj,th differs for x,y-polarized and z-polarized radiation. For unstrained

semiconductors, the "nature" of HH and LH states, as it is described in section A.2,

depends on the k vector. The HH state character is |px〉 + |py〉 for k = (0, 0, kz)

showing a large transition matrix element only for x,y-polarized light, while for

k = (kx, 0, 0) they mix with LH states changing their character into |py〉 + |pz〉

24


5 µm2 µm

(a) (b)

GeSn

Ge

Si

Figure 2.12 – (a) Colored SEM image of a processed Ge0.94Sn0.06 microdisk with adiameter of 5 µm. (b) An exemplary microdisk with a diameter of 10 µm after SiNx

deposition. Derivative of Fig. 1 from Ref.[34], used under CC BY 4.0.1

states, which makes them solely optically active for y,z-polarized light. For k vec-

tors in between these cases, HH states are predominantly active for perpendicular

to k polarized light.

Inducing biaxial strain in the lattice, causes HH states to be predominantly active

for x,y-polarized radiation (|px〉 + |py〉 is the dominating character), although the

transition matrix element is non-zero for kx,y 6= 0 due to mixing with |pz〉 and |s〉states. LH states have |px〉 + |py〉 − 2|pz〉 character and have the strongest optical

activity for z-polarized light for strained GeSn. Based on this discussion the radi-

ation polarization dependence of Ninj,th for strained GeSn stems from the different

wave functions describing HH and LH states and depends on which of them is the

highest valence band.

2.1.5 Low Sn content GeSn under tensile strain

Every calculation presented so far discussed the possibilities and effects of band

structure engineering via strain and Sn content, without taking into account the

Sn dependence of the experimentally accessible strain values. In this context, there

is a difference between high and low Sn content GeSn. For compressively strained

GeSn, alloys with Sn contents up to 20 at.% Sn were experimentally demonstrated

by implementation of buffer layer relaxations above 80 %.44,79 For low Sn content

1https://creativecommons.org/licenses/by/4.0/legalcode

25


GeSn, however, using underetched microdisk designs, tensile strain of 1.5 % was

achieved using silicon nitride (SiNx) stressor layers.34 In the following subsection

the experimental results will be discussed and a theoretical framework for low Sn

content GeSn under tensile strain will be established.

For this purpose, GeSn layers with 6.3 at.% Sn and a residual strain of −0.32 % were

grown at 375 ◦C on top of Ge-VS80 by Dr. Nils von den Driesch from Forschungszen-

trum Jülich via reactive gas source epitaxy in an AIXTRON TRICENT reactor. A

detailed description of the CVD processes used to grow SiGeSn layers is given in

chapter 5. The Sn content and layer thickness for all samples in this thesis were

determined via Rutherford backscattering spectrometry (RBS), where the energy of

back-scattered He+ ions (original energy of 1.4 MeV) is measured. In-plane and out-

of-plane deformations were determined by X-Ray diffraction-reciprocal space maps

(XRD-RSM) around the asymmetric (224) reflection, employing a Bruker D8 high-

resolution diffractometer and the Kα line of Copper. The measurements were per-

formed by Dr. Gregor Mussler from Forschungszentrum Jülich.

The processing of microdisks out of these samples, the deposition of SiNx on top

of the disk and photoluminescence (PL) measurements were performed by Prof.

Moustafa El Kurdi and Dr. Anas Elbaz from the Université Paris Sud and are de-

scribed in Ref. [34]. Fig. 2.12a shows the processed bulk Ge0.94Sn0.06 layer, while

Fig. 2.12b shows an example of a microdisk with SiNx deposited on top. Here, a

bending of the rim becomes visible in the SiNx treated microdisk, causing strain

inhomogenities additional to inhomogenities stemming from growth imperfections

and the Ge pillar underneath the disk.

To extract the strain caused by deposition of the stressor layer and to investigate its

influence on the optical properties of the bulk layer, PL measurements at 15 K have

been performed using an Nd:YAG laser (E =1.17 eV) in continuous wave (CW)

mode and a cooled InGaAs photodiode detector with a cutoff energy of 0.51 eV

(Fig. 2.13a). In order to achieve an extended energy detection range (cutoff energy

of 0.26 eV), PL spectra were measured at 80 K using an LN2 cooled InSb detec-

tor (Fig. 2.13b). The optical output of the compressively strained bulk layer at a

pumping power of 30 mW is very poor and shows one distinct and one broad peak

at 0.66 eV and 0.62 eV (red graph in Fig. 2.13a), respectively. From calculations,

these peaks can be assigned to EΓ−HH and EL-HH recombinations, respectively.34

26


2.6 1.8 1.62.02.22.4

de

tectio

n c

uto

ff

strained microdisk

Inte

nsity (

a.u

.)

T = 15 K

P = 30 mW

InGaAs detector

as-grown

EΓ-HHEL-HH

λemission

(µm)

Energy (eV)

(b)(a)

0.5 0.6 0.80.7

pump

laser modes T = 80 K

P = 40 mW

InSb detector

exp. theor.

0.4 0.6 0.8

Inte

nsity (

a.u

.)

Energy (eV)

water

absorption

Figure 2.13 – (a) PL spectrum of bulk Ge0.94Sn0.06 and a processed microdisk withSiNx stressor layer on top. (b) Extended PL spectrum of the stressor strained mi-crodisk with calculated PL spectrum and indicated region showing water absorption.Derivative of Figs. 2 and 3 from Ref.[34], used under CC BY 4.0.1

After processing the thin films into 5 µm diameter microdisks and depositing SiNx

on top, PL changes drastically (blue graph in Fig. 2.13a). There is a strong redshift

of the PL spectrum, indicating a decreased bandgap with a concomitant increase

of intensity, giving strong evidence for an increased directness. There are also two

very sharp signals visible in the region, where PL of the strained microdisk becomes

maximal, which are caused by pump laser modes from the Nd:YAG laser.

The lowest peak energy of the microdisk lies below the detection cutoff of the detec-

tor, so that the measurement was repeated at a pumping power of 40 mW and 80 K

using an extended energy range, which makes the whole PL spectrum accessible

for detection (Fig. 2.13b). The red area indicates an energy range, where the PL

signal is decreased by water absorption. Using Eq. (8) and (12) from Ref. [81] and

band dispersions E(k) from 8-band k · p calculations, the PL signal could be fitted

to experimental results (orange graph). From these calculations, using an injection

carrier density of 5× 1017 cm−3, a strain value of 1.45 % could be extracted, which is

sufficient to create a direct bandgap semiconductor with a directness of 95 meV. The

fundamental direct bandgap is shifted from 410 meV to 495 meV, which is mainly

caused by band filling due to pumping rather than temperature effects. The valence

27


Figure 2.14 – (a) ∆EL−Γ dependence of net gain maxima for several Sn contents.(b) Corresponding range of strain values chosen for each Sn content according toexperimentally achievable strain (see text).

band splitting of HH and LH is 185 meV and guarantees that Γ-LH transitions are

dominating. To account for broadening effects, stemming from carrier scattering

and strain fluctuations or inhomogenities, the calculated PL spectra were convo-

luted with a Lorentzian function, where a homogeneous broadening of 25 meV led

to the best results. This significant broadening originates mostly from strain inho-

mogenities around the pillar and rim region82–86 and fluctuations in the out-of-plane

direction caused by an inhomogeneous deposition of SiNx. At higher pumping rates,

bands from these regions with larger bandgaps (lower strain) will be filled and con-

tribute to the optical output of the microdisk, which explains the strong peak at

higher energies in Fig. 2.13a. The achieved strain values are consistent with those

from other publications87,88 and promise an achievable tensile strain of 1.45 % for low

Sn contents. As will be shown in the following, it is not apparent that, in contrast

to low Sn content GeSn under tensile strain, compressively strained high Sn content

GeSn is favorable, when designing efficient light sources.

In order to exclude the directness as a parameter influencing the optical performance

– and therefore the number of charge carriers in the Γ valley –, net gain was calcu-

lated for high and low Sn content GeSn in dependence of ∆EL−Γ. The used strain

values are shown in Fig. 2.14b and were chosen the following way:

• For xSn ≤ 8 at.% strain ranges from values where ∆EL−Γ becomes 0 meV to

28


1.5 % (experimentally already demonstrated).

• For xSn > 8 at.% the strain minimum was chosen at the same condition as

above (∆EL−Γ = 0 meV) and went up to strain values where the relaxation

becomes 0 %. This describes an up to date experimentally reasonable range

for high Sn content GeSn.

Although the highest tensile strain values for GeSn alloys are achieved in microdisk

structures, which exhibit strain relaxation in the radial and out-of-plane direction,

for the sake of simplicity, biaxial strain was assumed in the here presented layers.

The influence of light polarization was included so that for alloys under compressive

strain the net gain maxima from x,y-polarized light were considered, while for tensile

strain only net gain from z-polarized radiation was taken into account. This gives

the possibility to investigate the influence of Γ-HH (x,y-polarization) and Γ-LH (z-

polarization) recombinations separately (c.f. discussion in subsection 2.1.4). An

injection carrier density of 1× 1018 cm−3 was assumed.

Comparing net gmax for low and high Sn content GeSn at the same directness reveals

that the achievable gain in low Sn content GeSn under tensile strain is several times

higher than for high Sn content GeSn (red dashed ellipse in Fig 2.14a). Another

remarkable observation is the predicted evolution of net gmax for high directnesses

and low Sn contents. Assuming a maximum tensile strain of 1.5 %, gives the highest

achieved material gain of ∼8200 cm−1 for Sn contents of 8 at.%. For high Sn content

GeSn, on the other side, above a certain directness the net gain maxima decrease

again.

In order to understand these findings, all results presented in this chapter have to

be taken into account. At high Sn contents and constant directness, gmax increases

up to 16 at.% Sn, before decreasing again at 20 at.% Sn. This can be explained in a

similar manner as in subsection 2.1.4, but here it is the decreasing bandgap instead

of the directness that increases gmax with increasing Sn content (0.435–0.270 eV).

Above 16 at.% Sn, band mixing effects cause a smaller gmax. Changing strain from

compressive to tensile at a fixed directness (by going from high to low Sn contents),

causes for the former case the HH band to be the highest valence band at the Γ-point,

while for the latter case it is described by the LH band. As shown in subsection 2.1.3,

for tensile strain mDOS,LH becomes very similar to mDOS,HH at low Sn contents, so

29


that already at small band splittings the majority of charge carriers will reside in

the LH band. Moreover the transition matrix elements of Γ-HH transitions close

to the Γ-point for x,y-polarized light are smaller than those of Γ-LH transitions for

z-polarized light. This explains why, at a constant directness, the gain of low Sn

content GeSn under tensile strain is higher than for compressively strained high Sn

content GeSn. In subsection 2.1.4 it was found that at high Sn contents and low

strain values the bandgap falls below a value where conduction and valence bands

mix significantly, which can lead to a decrease of the transition matrix element and

explains the decrease of net gmax at high directnesses. This is absent at low Sn

contents, since the influence of increasing strain on the bandgap is smaller than that

of increasing the Sn content. For 8 at.% Sn, Eg is 0.41 eV at ∆EL−Γ ≈ 100 meV,

which is above the bandgap of the corresponding high Sn content alloys.

2.2 SiGeSn as a barrier material

2.2.1 Band energies and directness

Si is an indirect bandgap semiconductor. The energy gaps between conduction and

valence band are significantly higher than for Ge and Sn and have a minimum of

1.13 eV between the valence band at the Γ-Point and the conduction band near the

X-point (c.f. Fig. 2.1). The incorporation of a small atom like Si into the GeSn lat-

tice, will decrease the resulting lattice constant, reversing the effect of Sn atoms on

the Ge lattice. A similar effect can be expected for the direct and indirect bandgaps.

Soon after the first theoretical and experimental investigations of GeSn had been

published, the interest for the ternary SiGeSn arouse.50 With a lattice mismatch

between Si and Ge of 4 %, it enables another degree of freedom to independently

engineer strain and bandgaps, as will be shown in this section. Similar as for GeSn,

first calculations and growth experiments aimed at finding an equation to interpo-

late the indirect and direct bandgaps of the ternary using the elemental bandgaps of

Si, Ge and Sn and corrective bowing terms bi. Since the bowing parameter for SiGe

was already intensively investigated61,89 and bGeSn became more and more accurate

with increasing layer quality and quantity,67 the only remaining missing parameter

was the bowing of SiSn at the Γ-point (c.f. Eq. 2.12).

30


First approaches tried to determine the bandgap behavior of SiSn binaries by ap-

plying theoretical models and growing SiSn layers on top of Si.90–92 The bowing

parameter results of these investigations contradict each other, deriving a constant

or Sn dependent bSiSn,Γ. Besides that, the quality of the layers appears to be poor.

At the same time, first SiGeSn layers were grown on strain relaxed GeSn or Ge buffer

layers.92–97 Using spectroscopic ellipsometry, the dependence of the direct and indi-

rect bandgaps on Sn content was investigated, and a wide spread of bSiSn,Γ values,

of 13.2 eV,92 17.5 eV96 or 5.75 eV97 were determined. As for GeSn, SiGeSn layers

were additionally investigated via photoluminescence98–102 and electroluminescence

measurements.103 Nevertheless, these investigations also deliver a spread of bSiSn,Γ

values, in which it is found to be similar as in Ref. [92, 96] or as high as 24 eV.101

The number of theoretical investigations of the SiGeSn band structure in literature

is rather scarce. Using empirical pseudopotential35,61,104 and tight binding105 meth-

ods, the band structure of unstrained and strained SiGeSn was calculated, where

from the empirical pseudopotential approach a bowing of 3.915 eV was determined.

A recent investigation of pseudomorphic SiGeSn layers grown on Ge buffer layers us-

ing MBE investigates the direct and indirect bandgaps by spectroscopic ellipsometry

for a wide range of Si and Sn contents (up to 46 at.% and 13.5 at.%, respectively).106

This investigation indicates a strong composition dependent bowing, which is sup-

ported by results from Ref. [30], where bSiSn,Γ extracted from PL measurements is

compared to values from other publications, indicating a linear Sn content depen-

dence of bSiSn,Γ. This behavior is similar to a giant composition dependent bowing

in GaAsN semiconductors. For this material system, the bowing parameter is the

sum of several contributions. It is strongly influenced by a small and constant band

like bowing and an impurity like bowing, causing strong deviations from the band

like bowing at low nitrogen concentrations.107–109

On an atomic scale, this could be explained by the distortion of the diamond bonds

by incorporating Si. In Ref. [110], for low Si contents, a distribution of Si deviating

from the random alloy distribution was found, causing Si to prefer other Si atoms

as next neighbor atoms. At high Si contents, which means samples grown at high

temperatures, a perfect random distribution of Si atoms was found, indicating a ki-

netically limited process. The non-random arrangement of Si atoms at lower growth

temperatures can cause locally strong perturbations in the lattice electron density

31


0 4 8 12 16 20Sn content (at.%)

0 4 8 12 16 20-400

-300

-200

-100

0

100

200

∆EL-Γ (

meV

)

Sn content (at.%)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

10 at.%8 at.%6 at.%4 at.%

Eg (

eV

)

Si content 2 at.%

65

4

3

2

λ (µ

m)

Indirect bandgap

(b)(a)

GeSn

GeS

n

Figure 2.15 – Bandgap/wavelength (a) and directness (b) of unstrained SiGeSn.Values for unstrained GeSn are depicted in dashed lines.

and, therefore, the band structure. This could induce localized conduction band

energy states and an impurity like bowing for small Si contents.92

Sophisticated investigations of the growth of SiGeSn have been published, recently,

achieving Si contents above 10 at.% at similar Sn contents and demonstrating

high material quality. This gives the possibility to investigate bSiSn,Γ over a wide

range of material compositions to extract an accurate bandgap behavior of SiGeSn

ternaries.30,46,111–113 The above evaluation of bSiSn,Γ underlines the need for a thor-

ough investigation of the bandgaps of SiGeSn over a large parameter space of Si

and Sn contents using PL measurements, which is not available up to date. Due to

this lack of reliable data, in the following, all band structure calculations on SiGeSn

were performed using a bowing of 3.915 eV as calculated in Ref. [61]. The range

of Si contents was chosen to be 10 at.% at most, which is in agreement with limits

given by low temperature CVD experiments.30,111,112

For SiGeSn alloys, Eq. 2.1 can be transformed, assuming a constant xSn and xGe,

into the following expression:

Eg,Γ/L = EGeSn,Γ/L (xGe, xSn) + xSi · (ESi,Γ/L − bSiGe,Γ/L xGe − bSiSn,Γ/L xSn). (2.12)

32


co

mp

ressiv

e

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.82 at.% Si

substrate Sn content 0 at.% 4 at.% 8 at.% 12 at.% 16 at.% 20 at.%

6 at.% Si 10 at.% Si

Eg (

me

V)

65

4

3

2

λ (µ

m)

0 4 8 12 16 200 4 8 12 16 200 4 8 12 16 20

Sn content (at.%)

tensile

(a) (b) (c)

Figure 2.16 – Bandgap/wavelength of pseudomorphic SiGeSn on several GeSn sub-strates and (a) 2 at.% (b) 6 at.% and (c) 10 at.% Si. The colored areas indicateregions of tensile strain for each GeSn substrate, respectively.

Since "bSiGe xGe − bSiSn xSn" will be, for a large range of Sn contents, smaller than

ESi (3.3 eV at the Γ-point), the incorporation of Si will increase the bandgap of

GeSn binaries. This is shown in Fig. 2.15a, where the effective bandgap is plotted

for several Sn and Si contents for unstrained SiGeSn. As a reference, the bandgap

of unstrained GeSn is shown in dashed lines. The increase of Eg with Si content is

more pronounced at high Sn contents (up to 280 meV at 10 at.% Si) than at low Sn

contents (110 meV at 10 at.% Si). As indicated in Eq. 2.12, the directness of SiGeSn

will be also influenced by the Si content, decreasing it below the directness of GeSn,

as shown in Fig. 2.15b. By increasing the Si content, higher Sn contents are needed

to leave the region of indirect bandgap alloys (green region in Fig. 2.15b). At an Si

content of 10 at.% the directness is decreased by around 200 meV.

Fig. 2.15 gives a good overview of achievable bandgaps and directnesses for cubic

SiGeSn. In experiments, this range is extended because substrate / buffer layer

lattice constants deviate from the lattice constant of cubic SiGeSn and, therefore,

introduce strain into SiGeSn. Moreover, as will be pointed out in the next chapter,

SiGeSn is a promising barrier material for GeSn/SiGeSn heterostructures. In this

regard, it is usually grown pseudomorphically on top of a GeSn substrate.31–33,71

33


Therefore, the influence of strain is exemplarily shown for the effective bandgap in

Fig. 2.16 for pseudomorphic SiGeSn with 2 at.%, 6 at.% and 10 at.% Si. The strain

inside the ternary is changed by using different substrate Sn contents. The colored

areas under each curve indicate the region, where the SiGeSn lattice becomes

tensile strained. In comparison to Fig. 2.15a, the range of bandgap energies can be

significantly extended by changing the substrate lattice constant. For an SiGeSn

ternary, e.g. with an Si content of 2 at.%, Eg can be tuned in a range from 0.68 eV

(Ge substrate) to 0.30 eV (GeSn substrate with 16 at.% Sn). When keeping the

substrate and ternary Sn content constant at 16 at.%, an increase of the Si content

from 2 at.% to 10 at.% increases the bandgap by 180 meV. Moreover, as described

by the colored areas, whenever the ternary’s Sn content is below the substrate’s

Sn content, SiGeSn will be tensile strained. At constant substrate composition,

the region of tensile strain increases with increasing Si content, which corresponds

to a decreasing lattice constant and an increasing bandgap. In CVD experiments,

the Sn content in the underlying substrates (or their lattice constants) is usually

similar or lower than the Sn content in SiGeSn, so that the colored areas describe

an experimentally hardly accessible region.33,114

The possibility to tune the bandgap is also reflected in the band offset between

Γ and L valley. This is shown in Fig. 2.17, where, similar to Fig. 2.16, ∆EL−Γ

was calculated for pseudomorphic SiGeSn with several Si contents on different

GeSn substrates. The directness can be increased by either an increased substrate

lattice constant or increased Sn content in SiGeSn, whereas with increasing Si

content ∆EL−Γ is lowered. This is reflected in the amount of data points shifted

into the green area, indicating indirect bandgap alloys, when going from 2 at.% Si

(Fig. 2.17a) to 10 at.% Si (Fig. 2.17c). The blue areas, which increase with higher Si

content, show the region of material parameters that cause tensile strain in SiGeSn,

similar to the colored regions in Fig. 2.16. Increasing the Si content from 2 to

10 at.% decreases the directness by around 130 meV. From above considerations it

becomes clear that by tuning both, Si content and strain, a wide range of bandgaps

and directnesses becomes accessible.

34


0 4 8 12 16 200 4 8 12 16 200 4 8 12 16 20

-300

-200

-100

0

100

200

-300

-200

-100

0

100

200

Sn content (at.%)

2 at.% Si

substrate Sn content 0 at.% 4 at.% 8 at.% 12 at.% 16 at.% 20 at.%

∆E

L-Γ

(m

eV

)

6 at.% Si 10 at.% Si

(c)(b)(a)co

mpr

essi

ve

tens

ile

Indirect bandgap

Figure 2.17 – Directness of pseudomorphic SiGeSn on several GeSn substrates and(a) 2 at.% (b) 6 at.% and (c) 10 at.% Si. The blue and green colored areas indicateregions of tensile strain and indirect bandgap ternaries, respectively.

2.2.2 Bandgap bowing at Γ

As described above, the reported experimental data on bΓ,SiSn scatter considerably for

varying material compositions and growth processes (CVD←→ MBE). In Ref. [30],

a linear Sn content dependence of the bandgap bowing at the Γ-point was indicated,

comparing the PL results of different publications. Of course, this does not describe

the actual behavior – bΓ,SiSn will be most probably a function of the Sn and Si

content – but it gives a possibility to roughly estimate the deviations that might

occur, when applying a constant bowing, as it has been done in this work.

In order to investigate the discrepancies of using different bΓ,SiSn, Γ band energies

were compared using bΓ,SiSn = 3.915 eV and a linear interpolation of bowing data

points collected in Ref. [30]. The band edge energies at Γ for different Sn and Si

contents of unstrained SiGeSn, using different bowings, are shown in Fig. 2.18a.

Depending on the Sn and Si content, substantial differences are noticeable. To

achieve a better overview of these deviations, the difference of these values is shown

in Fig. 2.18b. It should be pointed out that, assuming the same valence band

energies and no composition dependent bowing of the bandgap at the L-point, the

35


0.4

0.5

0.6

0.7

0.8

0.9

1.0

bSiSn,Γ = f(x

Sn)

Sn content (at.%)Sn content (at.%)

bSiSn,Γ = 3.915 eV

4 8 12 16 20 4 8 12 16 20-300

-200

-100

0

100

200

EΓ(

bS

iSn

,co

nst) -

EΓ,

(bS

iSn

,in

terp

ol)

(meV

)

EΓ

(eV

)

(a) (b)

10 at.%8 at.%6 at.%4 at.%Si content 2 at.%

Figure 2.18 – (a) Sn dependent Γ conduction band energy of cubic SiGeSn usingbSiSn,Γ = 3.915 eV and an Sn concentration dependent bowing as given in Ref. [30].(b) The corresponding difference of Γ conduction band energies.

absolute value of the conduction band difference ∆EΓ for two different bowings b1

and b2 describes the differences in bandgaps as well as directnesses:

∆Eg,Γ = EΓ (b1)− Evb − (EΓ (b2)− Evb) (2.13)

= EΓ (b1)− EΓ (b2) = ∆EΓ

∆EL−Γ (b1)−∆EL−Γ (b2) = EL − EΓ (b1)− (EL − EΓ (b2))

= EΓ (b2)− EΓ (b1) = −∆EΓ = −∆Eg,Γ.

In Fig. 2.18b it can be seen that Γ conduction band deviations are the strongest

for low Si and Sn contents, exceeding values of 200 meV. These differences are

substantial and will be considered in chapter 3 for band alignment calculations.

Band alignment calculations at low Si/Sn contents should be treated, therefore,

with caution, since they lack experimental backup.

2.3 Summary

In this chapter, the band structure of GeSn alloys with Sn contents ranging from

0–20 at.% in respect of designing laser devices was discussed in detail. The acces-

36

2.3 Summary

sible offsets between L and Γ valleys ∆EL−Γ, depending on Sn content and strain,

were calculated and investigated using the 8-band k · p model. These values exceed

200 meV, which guarantees that more than 98 % of charge carriers reside in the Γ

valley at an injection carrier density of 5× 1018 cm−3. Biaxial strain was investi-

gated in greater detail, especially concerning the influence on LH and HH valence

bands. Here, it was found that, depending on the wave vector direction, strain sig-

nificantly changes the magnitude of effective masses, especially for m∗LH at low Sn

contents and tensile strain, blurring the strict distinction implied by their names

(HH and LH). For the conduction bands, a strong decrease with increasing absolute

strain and Sn content was found only for the Γ valley, while there is only a weak Sn

dependence of the L valley effective mass. Based on these findings gain calculations

were performed. Here, the net gain contained material gain and absorption from

free charge carriers. To establish understanding of these losses, the influence of in-

dividual FCA processes was examined in dependence of doping concentrations and

Sn content. It was found that inter-valence band absorption, conduction band inter-

valley scattering induced FCA, and valence band FCA are the dominant sources of

losses. Moreover, it was found that at strains around 0 % and high Sn contents net

gain decreases while the threshold injection carrier densities Ninj,th increase. This

could be explained by band mixing at low bandgaps, which decreases the transition

matrix elements between conduction and valence band states near the Γ-point and,

therefore, the optical activity. Combined with findings for FCA, a trade-off between

low bandgaps/high directnesses and absorption losses has to be found in order to

design an efficient laser. Another elegant alternative to avoid these issues, at least

partially, is to use low Sn content GeSn under tensile strain. Experimentally, a ten-

sile strain of 1.45 % was demonstrated in underetched microdisks using SiNx stressor

layers. Subsequently, it was theoretically shown that low Sn content GeSn layers

(≤ 8 at.% Sn) under tensile strain could provide higher gain than unstrained high

Sn content alloys having the same directness. Here, maximal gain of 8200 cm−1 at

a directness of 140 meV was found. This describes a promising alternative to the

route of increasing the Sn content, in respect of designing efficient lasers.

By adding Si into the GeSn binary, another degree of freedom was introduced to

tune bandgap and directness. For unstrained SiGeSn, bandgap and directness can

be tuned up to 280/200 meV by tuning the material composition wisely. Growing

37


pseudomorphic SiGeSn ternaries on GeSn substrates deforms the SiGeSn lattice,

introducing strain. Here, the impact of strain and Si content can cause a bandgap

increase of almost 120 meV. In terms of possibilities using CVD processes a small

range of material compositions becomes available, where tensile strain in SiGeSn

can be achieved. The impact of strain on the directness of pseudomorphic ternaries

was also investigated, enabling the tuning of ∆EL−Γ up to 130 meV, when changing

the lattice constant and increasing the Si content in the range of accessible material

parameters. The possibility to extend the range of achievable bandgaps and direct-

nesses using SiGeSn, gives rise to the investigation of GeSn/SiGeSn heterostructures,

where the ternary would be the barrier material.

38

3 GeSn/SiGeSn Quantum Wells

Contents

3.1 Group IV heterostructures . . . . . . . . . . . . . . . . 40

3.2 Carrier confinement in GeSn/SiGeSn MQWs . . . . . . 41

3.2.1 Influence of strain and Si content . . . . . . . . . . . . 48

3.2.2 Strain balancing and critical thickness . . . . . . . . . 49

3.2.3 Material gain calculations . . . . . . . . . . . . . . . . 54

3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

This chapter discusses heterostructures using direct bandgap GeSn as active mate-

rial. Based on the results from chapter 2, material parameters will be extracted,

which enable good carrier confinement in the active region. SiGeSn is considered as a

potential barrier material, because it offers high bandgaps and, therefore, high band

offsets at conduction and valence bands. Moving from bulk material to structures

exhibiting quantum effects, GeSn multi quantum wells (MQWs) will be investigated,

arguing the benefits and disadvantages of utilizing quantized density of states. In

respect to designing efficient laser materials, calculations of the critical thickness

of strained layers and strain balancing in pseudomorphic heterostructures were per-

formed and evaluated concerning the optimal well thickness. One promising material

composition for GeSn/SiGeSn MQWs will be chosen to investigate material gain and

its dependence on doping. Parts of these results have been previously published in

Ref. [115].

39


3.1 Group IV heterostructures

The interest in using group IV heterostructures arose simultaneously with the inter-

est in the material system itself.116 This is due to the fact that substantial success

had already been achieved in implementing heterostructure designs to III-V alloys.117

Heterojunctions based on GeSn were proposed to achieve e.g. a direct bandgap in

Ge,116 to design quantum cascade lasers (QCLs)118 or tunnel field effect transistors

(TFETs).119–121

In optoelectronics, devices benefit from heterostructures, because they enhance the

probability that charge carriers recombine in the active layer, where emission and

gain is desired. Concomitant with that, the loss of charge carriers due to absorption

into trap-states or non-radiative processes can be reduced, when growing pseudo-

morphic designs on top of relaxed buffer layers and, therefore, separating the ac-

tive region from threading dislocations and defects in relaxed layers.31–33,98 This is

achieved by growing layers with different bandgaps and, i.e. different material com-

position. The lower bandgap semiconductor serves as the well for charge carriers,

which are confined in the active material by a potential barrier V . For both III-V

and group IV semiconductors, characteristics like the lasing threshold current could

be brought down by several orders of magnitude.32,117 This is not only owed to the

utilization of heterostructures, but also to the quantization of the band structure,

when the spatial dimensions fall below a certain size, as will be pointed out later in

this chapter.

Since the bandgap of group IV semiconductors can be tuned by composition and

strain, many different arrangements of heterostructures were proposed. Ge can be

found serving as the active material, with SiGeSn as the confining alloy,98,113,118,122

while, in other publications, GeSn is the well surrounded by Ge or GeSn with a

different Sn content.47,86,123–127 The advantage of using GeSn as active material is

the possibility to achieve a direct bandgap without strain engineering. Neverthe-

less, for all GeSn(well)/Ge(Sn)(barrier) heterojunctions, EL and PL measurements

showed no benefit to the optical performance in comparison to thick relaxed bulk

layers. In Ref. [127] it was theoretically shown that Ge is not suitable as a barrier

material for GeSn. Even if confinement of charge carriers in direct bandgap GeSn

is achieved, the band offsets for the Γ valley are very small (39 meV) in comparison

40

3.2 Carrier confinement in GeSn/SiGeSn MQWs

to the thermal energy of charge carriers at 300 K (26 meV).

Due to the possibility to independently tune bandgap and lattice constant, SiGeSn

became also a prominent candidate as a barrier material. Experimental data

are rather scarce, due to the difficulty of growing SiGeSn with a high mate-

rial quality.31–33,71,114,128 Nevertheless, a strong increase of the PL performance of

GeSn/SiGeSn multi quantum wells (MQWs) relative to GeSn/SiGeSn bulk het-

erostructures could be shown in recent publications.31–33 By growing MQWs with

different thicknesses, a shift of the PL peak due to quantization effects was demon-

strated with an up to date lowest lasing threshold.32 Unfortunately, this improve-

ment could only be demonstrated at low temperatures, while the benefit of MQW

heterostructures was lost at higher temperatures due to low band offsets.

Bandstructure calculations for particular laser designs using GeSn/SiGeSn hetero-

junctions predict efficient laser devices.123,129–132 Sophisticated band alignment cal-

culations cover a huge range of Sn and Si contents in order to design efficient laser

devices, but lack, so far, the consideration of experimental possibilities or the ex-

traction of a broad range of material compositions, where optimal band offsets can

be found.114,133 Therefore, this chapter focuses on determining experimentally ac-

cessible material compositions, which guarantee strong carrier confinement.


When two semiconductors with different band structures are brought into contact,

band discontinuity at the interface will occur with a potential difference Vi at con-

duction (i = c.b.) and valence bands (i = v.b.). If a conduction band valley of

lower energy is spatially surrounded by a valley of higher energy, a potential well

is created. This well possesses energetically allowed states for electrons. The sur-

rounding semiconductor is then called the barrier material. The same situation can

be defined for holes, but with the energy axis pointing in the opposite direction. In

general, different configurations of band alignment can occur and three types are

usually considered (Fig. 3.1a).134 If the well region for conduction and valence bands

is located in the same layer it is called type I alignment. If conduction and valence

band wells are spatially separated the alignment is of type II. If, additionally, con-

duction and valence bands of the two material overlap energetically, this is referred

41


type I type II type III

v

v

z

VΓ

VL

Vv.b.

∆EL-Γ,well

∆EL-Γ,barrier

mw

mw

dw

dw

dw

mw

mb

mb

mb

db

db

db

db

mb

∞

∞

(a)

(b)

(c)

Figure 3.1 – (a) Possible types of band alignment in heterostructures, as describedin Ref. [134] with colored areas indicating confined charge carriers. (b) Frameworkfor subband energy calculations of MQWs as used in this work (c) GeSn/SiGeSn QWwith denoted band offsets and directnesses at barrier and well. Derivative of Fig. 1from Ref. [115], used under CC BY 4.0.1

to as staggered or type III alignment. In this work, we will focus on heterojunctions

where the conduction and valence band alignment is of type I. The advantage of

this type of heterostructures is that it confines electrons and holes spatially in the

same layer, enhancing the spatial overlap of electron and hole wave functions and,

therefore, the probability to achieve gain.117 Apart from that, it enables separating

charge carriers in the active layer from defective interfaces, reducing optical losses.

The performance of optoelectronic devices based on heterojunctions can be further

improved by implementing quantum structures. When the well thickness decreases,

the number of atoms and available energy states decrease. For small enough thick-

nesses the quantization of energy states confined within the well (called subbands)

becomes noticeable. Materials with quantization in only one spatial dimension are

called quantum wells, while quantum wires and quantum dots show quantization of

energy states in two and three dimensions. The density of states of quantum wells


42


is reduced in comparison to bulk material:135

ρ3D(E) =1

2π2

(2m∗

h2

)

32

E12 (3D DOS) (3.1)

ρ2D(E) =m∗

πh2 (2D DOS)

Filling the available energy states with charge carriers will increase the Fermi en-

ergy for quantum wells faster than for bulk material, so that the population inversion

will be achieved earlier (c.f. Eq. 2.8). Because of that, the lasing threshold current

density in quantum structures is several orders of magnitude lower than for bulk

semiconductors.74,117

Theoretically, subbands in heterostructures or MQWs can be calculated using the

envelope function approximation, which uses the effective mass approximation (c.f.

subsection 2.1.3) and where the envelope function varies slowly on the scale of the

lattice constant. It takes into account the discontinuity of the effective mass and

band valley energies at interfaces (c.f. subsection A.2.2). The envelope function ap-

proximation works well in most cases, but not for very thin wells, since the potential

there does not vary slowly on the scale of the lattice constant.135

In order to calculate the band alignment in GeSn/SiGeSn MQWs, the design in

Fig. 3.1b was chosen. It consists of three GeSn wells with thickness dw and effective

mass m∗w surrounded by four SiGeSn barriers with thickness db and effective mass

m∗b. The compositions of well and barrier were kept constant, respectively. A barrier

thickness of 40 nm was chosen. Hereby, the overlap of wavefunctions from different

wells can be avoided, which would influence their energy states. The well thickness

was set to 30 nm, which will be justified in subsection 3.2.2. The Schrödinger equa-

tion is solved using the finite difference method including nonparabolicities.136 In the

codes used in this work, it is assumed that the outermost boundaries of the structure

are infinite potential barriers. In order to avoid the influence of these boundaries on

well subbands, an outer barrier thickness of 60 nm was found to be sufficient.

For the band alignment, in this work the model proposed by Ref. [137] was chosen,

which is explained in more detail in section A.1 of the appendix. In experiments,

band alignment may also be affected by effects like interface dipoles.138 However, as

a first approximation, they were neglected in the following calculations. In the case

43


of GeSn heterostructures, effective masses calculated using the 8-band k · p model,

and band discontinuities for Γ/L valleys and HH/LH valence bands were used. The

mixing of quantized HH and LH states was neglected for this first approach, but

can play an important role when calculating gain. A constant bowing parameter of

bSiSn,Γ = 3.915 eV for the conduction band at the Γ-point of SiGeSn was chosen. As

pointed out in chapter 2, bSiSn,Γ could be composition dependent. However, for high

Sn contents this value is similar to the value that can be derived from the linear

interpolation of bSiSn,Γ in Ref. [30].115

When designing efficient heterostructures for optoelectronic devices, certain require-

ments have to be satisfied to guarantee good carrier confinement. These will be

defined in the following:

• The optically active well should be a direct bandgap semiconductor with a

maximal directness ∆EL−Γ,well. Since in the previous chapter it has been

pointed out that GeSn is the most suitable group IV candidate, unstrained

GeSn will be used in the following discussion. By choosing a Sn content above

10 at.%, it is guaranteed that the well is a direct bandgap semiconductor.

• The band offsets Vi between barrier and well for the Γ conduction band and

the valence bands should be as high as possible and of type I. This will ensure

an efficient trapping of electrons and holes in the active region.

• The band discontinuity of the L valleys should be also of type I (VL > 0 meV).

As shown in chapter 2, a significant amount of injected electrons will reside

in the L valley. It is preferable to keep these electrons in the well layer, so

they can scatter into the Γ valley by fast Γ-L scattering processes after the

recombination of Γ-electrons to emit light. For type II alignment the L-valley

electrons would be in the barrier, remote from the well, making Γ-L scattering

processes slower.

• Another point to consider is the directness of the confining material

(∆EL−Γ,barrier). In Ref. [139] it is claimed that the thermionic current from

well to barrier can be strongly suppressed using an indirect bandgap barrier

material (with a direct bandgap well). Besides that, it would reduce the prob-

ability of radiative recombination in the barrier material. On the other hand,

44


10 12 14 16 18 2010 12 14 16 18 2010 12 14 16 18 20-20

-10

0

10

20

30

40

Sn content in barrier (at. %)

VΓ

(me

V)

VL (

me

V)

-40

0

40

80

120

160

∆E

L-Γ

,barr

ier (m

eV

)

Si content in barrier 2 at.% 4 at.% 6 at.% 8 at.% 10 at.%

type II

alignment 50

100

150

200

250

indirect bandgap

barrier

direct bandgap

barrier

Ge0.84

Sn0.16

(c)(b)(a)

Figure 3.2 – (a) Band offsets of the L valley, (b) barrier directness and (c) bandoffsets of the Γ valley for different barrier Sn and Si contents for a GeSn well withSn content of 16 at.%. The purple, red and blue areas indicate material compositionscausing type II alignment, a direct bandgap in the barrier and regions limited byexperimental possibilities of CVD, respectively. Derivative of Fig. 3 from Ref. [115],used under CC BY 4.0.1

recombination processes of charge carriers in the barrier will be very scarce,

if the mobility of charge carriers is very high. The majority of electrons and

holes will drift into the well, being confined. This has to be investigated ex-

perimentally, but will be, nevertheless, considered in the following discussion.

As a barrier material SiGeSn was chosen, due to the possibility to increase the

bandgap significantly in comparison to GeSn.

Fig. 3.1c depicts the sum of all these requirements with the denotations for band

offsets and directnesses. Beside these requirements, carrier confinement is also lim-

ited by the accessible material compositions in CVD experiments. The range of Sn

and Si contents is additionally limited by the fact that, when growing GeSn/SiGeSn

heterostructures, the Sn contents of barrier and well are usually similar. Therefore,

the barrier Sn content was chosen to deviate by at most 2 at.% from the well Sn

content.

Keeping in mind above considerations, band alignment calculations have been per-

formed for a range of Sn contents (10–20 at.%) in an unstrained well and a variety of

45


Sn and Si contents in a pseudormorphic barrier (10–20 at.% for Sn and 2–10 at.% for

Si). These are exemplarily shown in Fig. 3.2 for a Ge0.84Sn0.16 well. Here, the band

offsets for the L valley (Fig. 3.2a), the directness of the SiGeSn barrier (Fig. 3.2b)

and band discontinuities of the Γ valley (Fig. 3.2c) were calculated in dependence

of the Sn and Si content in the barrier. At Sn contents below <16 at.% and low Si

contents, the influence of tensile strain on the bandgap (decreases with increasing

strain) will be stronger than the influence of the Si content (increases with increasing

Si content). Therefore, the L band energy will be a few meV below EL of GeSn.

This causes a type II alignment (purple region in Fig. 3.2a), which can be overcome

by increasing the Sn or Si content. The former increases the lattice constant and

lowers the strain in the barrier.

As described in the previous chapter, the directness of SiGeSn can be decreased by

decreasing the Sn content and increasing the Si content. However, certain material

compositions cause a direct bandgap in the barrier (red area in Fig. 3.2b). Taking

into account the previously stated requirements enables the exclusion of data points

for VΓ. The resulting map in Fig. 3.2c gives an overview of achievable band offsets

for Γ valleys, that promise a good carrier confinement. VΓ is reduced with increasing

directness of barrier (increasing Sn content). Considering the experimental limit of

similar Sn contents in barrier and well (blue area in Fig. 3.2c), a maximum VΓ of

180 meV can be achieved for a Ge0.84Sn0.16/Si0.10Ge0.75Sn0.15 MQW. This composi-

tion describes a trade off between a maximal band offset in Γ and directness of the

well. Compared to the thermal energy of charge carriers at 300 K (26 meV), this re-

sult promises a band offset of ∼7kBT , which enables sufficient trapping of electrons

in the conduction band of the active binary.

Above described procedure can be performed more generally for the whole range

of Sn contents in the well. The optimal material composition of well and barrier,

therefore, is achieved for maximum achievable Si contents and barrier Sn contents of

∼1 at.% below the one of the well (Ge1−xSnSnxSn

/Si0.10Ge0.91−xSnSnxSn−0.01). Fig. 3.3a

shows the resulting directnesses of well/barrier and band discontinuities of conduc-

tion bands. While for the latter similar values can be achieved for any Sn content in

the well, the directness of the heterojunction alloys increases strongly with Sn con-

tent. The band offsets for HH and LH bands are for all well compositions 104 meV

and 41 meV, respectively. An increase of the VHH/LH with an increasing Sn content

46


10 12 14 16 18 20

-100

-50

0

50

100

150

200

250

Energ

y (

meV

)

Sn content in well (at.%)0 40 80 120 160 200 240

Energ

y (

meV

)

LH

z (nm)

Γ/L

HH

(a) (b)

∆EL-Γ,barrier

∆EL-Γ,well

VΓ

VL

0

100

200

500

600

Figure 3.3 – (a) Band alignment for Ge1−ySny/Si0.10Ge0.91−ySny−0.01 het-erostructures. (b) Band diagram of conduction and valence bands of aGe0.84Sn0.16/Si0.10Ge0.75Sn0.15 MQW. Derivative of Figs. 3 and 4 from Ref. [115],used under CC BY 4.0.1

in the well is counteracted by the increase of strain in SiGeSn (increase of EΓ,SiGeSn).

For an Sn content difference between barrier and well of 1 at.% these effects are

similar and cause the valence band offsets to stay constant. At a well Sn content of

16 at.%, the directness of the barrier will be ∼0 meV. Since it is unknown, whether

a direct or indirect bandgap barrier is favorable, the following calculations were per-

formed for a Ge0.84Sn0.16/Si0.10Ge0.75Sn0.15 MQW, where the directness of the barrier

is ∼0 meV. Although this will favor the electronic properties of indirect bandgap

GeSn, it will also show influences of charge carrier population in the Γ valley. Bulk

and subband energies of conduction and valence bands and the wave functions of

the first quantized states are shown in Fig. 3.3b. The requirements of high/low

band offsets for Γ/L valleys and strong/low directness in well and barrier are here

satisfied. Besides that, it can be seen that quantized energy states, close to the band

edge, in HH and LH bands show similar values. Since these states are also close to

each other in k-space, the character of these states will be a mixture of HH and LH

states. Stacking of wells was chosen to be in the z-direction. Since this MQW de-

sign contains three wells, each quantized state will split into three subbands, having

different probabilities of being located in each well and their nodes being located in

the barrier.

47


-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-100

0

100

200

300

Energ

y (

meV

)ε

|| in well (%)

2 4 6 8 10

0

50

100

150

200

Energ

y (

meV

)

Si content in barrier (at. %)

(a) (b)

∆EL-Γ,barrier

∆EL-Γ,well

VΓ

VLH

∆EL-Γ,barrier

VΓ

VL

400

-1.5 -0.5 0.5 1.5E

(m

eV

)ε

||,well (%)

VHH

VLH

20

40

60140

160

180

Figure 3.4 – (a) Strain dependence for Ge0.84Sn0.16/Si0.10Ge0.75Sn0.15 MQWs. (b)Influence of barrier Si content on band alignment in Ge0.84Sn0.16/SixSi

Ge0.85−xSiSn0.15

MQWs. Derivative of Fig. 5 from Ref. [115], used under CC BY 4.0.1

3.2.1 Influence of strain and Si content

In chapter 2 it was shown that experimentally a vast range of strain values can

be achieved in GeSn. This will, consequently, influence the here discussed band

alignment. Fig. 3.4a shows the strain dependence of the directness for coherent

Ge0.84Sn0.16/Si0.10Ge0.75Sn0.15 MQWs. On the one hand, the directness of barrier

and well are enhanced with increasing strain (∼80 meV %−1), which will also in-

crease the fraction of electrons in the Γ valley and benefit the gain. On the other

hand, the band discontinuities for Γ valley and LH band will slightly decrease, which

is critical for the latter (13 meV %−1), due to its low value of 41 meV for the cubic

case (inset of Fig. 3.4a). Compressive strain allows the tuning of VLH at the expense

of lower directnesses in barrier and well. The band offsets of L and HH bands do not

change significantly with strain. The results demonstrate that strain values close to

the cubic case should be aimed for.

In CVD experiments, it is difficult to simultaneously achieve high Si and Sn

contents.30,112 However, when designing efficient laser materials, the Si content

should be above 10 at.%, since, otherwise, it will decrease band discontinuities of

conduction and valence bands (Fig. 3.4b). Here, VΓ will be strongly shifted below

48


100 meV at 5.5 at.%. This is less pronounced for the valence band offsets and dis-

continuities of the indirect conduction band. The barrier directness increases and it

is, again, the task of future experiments to determine its applicability for efficient

carrier confinement. Therefore, taking into account these results, the Si content

should be >8 at.%.

3.2.2 Strain balancing and critical thickness

Hetero epitaxial growth, i.e. with varying lattice constants between the different

layers, causes strain in the top layer. The growth of this material will proceed

pseudomorphically, increasing the strain energy stored in the crystal with increasing

thickness. At a certain thickness, called the critical thickness hc, the strain energy

exceeds the energy required to break atomic bonds and generate dislocations, causing

a release of strain.73 These processes were theoretically described in Ref. [140] by

People and Bean, where the critical thickness is given by:

hc ≃(1− ν

1 + ν

)

(

1

16π√

2

)[

b2

alat

] [(

1f 2

)

ln

(

hc

b

)]

, (3.2)

with ν being Poisson’s ratio (ν = C12

C12+C11), alat the lattice constant, b the Burger’s

vector (here 4 Å) and f the interfacial strain. Fig. 3.5a compares experimentally

measured thicknesses of pseudomorphic and partially relaxed GeSn layers grown on

Ge, collected from several publications,43,141,142 and samples from the Forschungszen-

trum Jülich, to the predicted critical thickness derived from the model in Ref. [140]

(dashed green line). In Refs. [141, 142] it is claimed that the thickness of the pseu-

domorphic layers complies with the critical thickness (blue triangles, green circles).

This is in good agreement with the used model. The just relaxed layers from Ref. [43]

support the People-Bean model too (orange pentagons). However, for the samples

grown at the Forschungszentrum Jülich, only samples with high Sn contents seem to

accurately follow the model. At low Sn contents, high relaxation degrees (red rectan-

gles) are achieved close to the theoretical value of hc. Nevertheless, the People-Bean

model appears to be appropriate in roughly predicting critical thicknesses.

When utilizing high Sn content buffer layers, strain in the top layer can be reduced,

which, in turn, increases the critical thickness. This is shown in Fig. 3.5b, where

49


100

101

102

103

104

Sn content (at. %)

hc

(nm

)

xSn,sub

(at.%)

48

12

16

20

5.8315.7975.7625.7275.6935.658

hc,

Pe

op

le-B

ea

n (

nm

)

alat

(Å)

1%30%

fully strained Ref. 140 fully strained Ref. 141

partially relaxed Ref. 43

41%

61%

2%

pseudomorph relaxed People-Bean

100

101

102

103

104

Sn content in top layer (at. %)

tensilecompressive 0

0 4 8 12 16 200 4 8 12 16 20

Figure 3.5 – (a) Sn dependence of critical thickness with values from Ref. [141],Ref. [142] and Ref. [43], experimental results (green squares indicate pseudomorphiclayers, red squares relaxed layers), and calculated values from the Ref. [140] (dashedgreen line). (b) Calculated critical thicknesses depending on Sn content for severalGeSn substrates and their corresponding unstrained lattice constant.

the critical thickness was calculated for GeSn layers on top of GeSn buffer layers

with different lattice constants alat (different Sn contents). The colored dashed lines

indicate critical thicknesses, where the top layer Sn content is below the buffer Sn

content (regions of tensile strain). When buffer and top layer Sn content are equal,

the critical thickness becomes infinite. For a top layer Sn content of 16 at.% (dashed

black line), as it has been chosen above for the design of an optically efficient MQW,

increasing the buffer Sn content from 0 at.% to 12 at.% raises the critical thickness

from ∼13 nm to ∼450 nm (release of compressive strain). This enables the growth

of an MQW with a larger number of wells, before relaxation occurs.

However, a relaxation of the lattice would increase the directness in GeSn, but also

the dislocation density. The former will improve the optical performance, while the

latter will cause its deterioration. Consequently, an increasing relaxation will in-

crease the PL only to a certain degree.143 Apparently, pseudomorphic layers with

high directnesses would be beneficial. The here proposed MQW structure seems to

fulfill these requirements, having a low thickness (no relaxation) and high Sn con-

tents (high directness).

Still, even if the compressive strain in each well would be very small, the amount

of strain energy would increase with an increasing number of wells, threatening to

50


relax the lattice and diminish the advantage of confining charge carriers. This could

cause a severe degradation of the optical performance.32 The relaxation process can

be hindered by growing barrier layers with opposite strain compared to the well,

which compensates the average strain.73 As shown in chapter 2, there is a small

region of material parameters enabling the growth of tensile strained SiGeSn on top

of GeSn buffer layers. For a GeSn/SiGeSn MQW with 16 at.% Sn, this is especially

guaranteed for small strain in the well and high Si contents (c.f. Fig. 2.16c for a

Ge0.84Sn0.16 buffer).

The strain energy W per volume can be expressed using elastic stiffness constants

Cij, as:135

W =12

6∑

i=1

6∑

j=1

Cijεiεj. (3.3)

The balancing of barrier and well strain can be achieved by minimizing the strain

energy. For an MQW, the average strain energy W is the sum of strain energies Wk

for each layer with thickness dk divided by the total length. It is defined as:

W =

n∑

k=1Wkdk

n∑

k=1dk

. (3.4)

Based on this equation, a strain balancing formula can be derived for a structure

with nw/nb wells and barriers, which calculates the barrier thickness db using the

well thickness dw as an input:132,135

db = −nw

nb

· Aw(xSi, xSn)Ab(xSi, xSn)

· ab(xSi, xSn)aw(xSi, xSn)

· εw

εb

· dw, (3.5)

Ai = C(i)11 + C

(i)12 −

2C(i)212

2C(i)11

.

The lattice constants ai are interpolated using the parameters from Table A.1. When

calculating db in dependence of dw for Ge1−xSnSnxSn

/Si0.10Ge0.91−xSnSnxSn−0.01 MQWs

with different Sn contents and low compressive strain, there is hardly any Sn depen-

dence of the strain balance thicknesses. This originates in the pre-factors Aw

Aband

51


10 20 30 40 501

10

100

barr

ier

thic

kness (

nm

)

well thickness (nm)

-0.1

-0.2

-0.3

-0.4

-0.5

Ge1-xSn

SnxSn

/Si0.10

Ge0.91-xSn

SnxSn-0.01

0 20 40 60 80

Energ

y (

meV

)

well thickness (nm)

EΓ,1

EL,1

Ge0.84

Sn0.16

/Si0.10

Ge0.75

Sn0.15

0 20 40 60 80

∆EL-Γ (

meV

)

dw

(nm)

10 12 14 16

0

2

4

6

d2D

,crit (

nm

)

Sn content in well (at.%)

quadratic fit

80 120 160

∆EL-Γ,bulk

(meV)

ε|| (%)

(a) (c)(b)

300

400

500

600

0

40

80

120

160

Figure 3.6 – (a) Thickness of barrier and well under strain balance condition forseveral compressive strain values. Dashed lines indicate thicknesses used in the dis-cussed Ge0.84Sn0.16/Si0.10Ge0.75Sn0.15 MQW. (b) Conduction band energies of the firstquantized state of a well in a Ge0.84Sn0.16/Si0.10Ge0.75Sn0.15 MQW in dependence onwell thickness. The inset shows the corresponding directness. (c) Thickness at whichquantization causes direct bandgap well to become an indirect alloy in dependence onthe Sn content and bulk directness. (a) is a derivative of Fig. 6 from Ref. [115], usedunder CC BY 4.0.1

ab

awin Eq. 3.5 being both dependent on the material composition and canceling each

other out when xSn of barrier and well are very similar. Fig. 3.6a, therefore, shows

db averaged over the whole range of Sn contents. The calculated barrier thicknesses

deviate with the Sn content by 2 nm for 45 nm thick barriers, while for db = 220 nm,

there is a maximum deviation of 10 nm, when changing the Sn content in the here

investigated range.

At constant strain values, the barrier thickness necessary to compensate strain in

the well increases with increasing well thickness, which is concomitant with an in-

creasing strain energy. With an increasing compressive strain (green to red line), W

will increase too, demanding higher barrier thicknesses to achieve strain balancing.

For example, using a well thickness of 30 nm, as used above for the MQW design,

increasing the compressive strain in the well increases the necessary barrier thickness

from ∼5 nm (ε|| = −0.1 %) to ∼120 nm (ε|| = −0.5 %). For this well width a barrier

52


thickness of ∼45 nm at reasonable strain values of −0.4 % is needed to compensate

the strain, which is close to the above chosen value.

The conclusion that could be drawn from these calculations is that a small well

thickness would require only small barrier thicknesses to compensate the strain en-

ergy and enable efficient light emitters. This is only true for a limited range of well

thicknesses. GeSn represents a special case, in which the indirect and direct bandgap

energy are relatively close to each other, even at high Sn contents. Moreover, the L

valley effective mass is significantly larger than for the Γ valley. These will influence

the quantization energies to a different degree, which can be expressed as:135

EΓ/L,n ∝n2

m∗Γ/Ld

2w

. (3.6)

From Eq. 3.6 it becomes clear that the quantization energy, of e.g. the lowest state

E1, is shifted to higher energies with reduced well thickness or effective mass. The

consequence of this relation is shown in Fig. 3.6b, where EΓ/L,1 is calculated for a

Ge0.84Sn0.16/Si0.10Ge0.75Sn0.15 MQW in dependence of dw. Due to the lower effective

mass of Γ electrons, their energy increases faster with decreasing well thickness than

for electrons from the L valley. At a well thickness of ∼5 nm EΓ,1 will be above

EL,1, causing a transition back into an indirect bandgap semiconductor (inset of

Fig. 3.6b). For this reason, dw was chosen to be 30 nm in the previous calculations,

because EΓ,1 will be small, while still benefiting from the 2D DOS. Similar results

have been already shown in Ref. [144] for MQWs with lower Sn contents. A shift

of the PL peak of GeSn quantum structures due to different well thicknesses has

already been demonstrated in Refs. [33, 125, 144]. Although at a well thickness of

30 nm the energy of the lowest quantized state is close to the bulk energy, in the

structures investigated in this work the 2D DOS is still prominent, having only four

quantized states for electrons in the Γ valley in the z-direction (c.f. Fig. 3.4b).

Since directness is strongly influenced by Sn content, the thickness, at which the

transition back into an indirect bandgap semiconductor will occur, depends on Sn

content. In Fig. 3.6c the calculated critical quantization thickness d2D,crit is plotted

for unstrained Ge1−xSnSnxSn

/Si0.10Ge0.91−xSnSnxSn−0.01 MQWs. With increasing di-

rectness (increasing Sn content), d2D,crit decreases to values as low as 1 Å for 16 at.%

53


Sn (∆EL−Γ,bulk = 160 meV). Still, since ∆EL−Γ will be already strongly influenced

at smaller well thicknesses, at a dw of ∼30 nm the influence becomes almost negli-

gible, especially at high Sn contents. These results are supported by findings from

Ref. [32], where a strong decrease of PL was found when decreasing dw from 22 nm

to 12 nm. Finally, it should be mentioned that the increase of EΓ,1 with decreasing

well thickness will influence the band offsets VΓ by the same amount. This will

mitigate the electron confinement and therefore the efficiency of MQWs. Drawing

a conclusion from the above considerations, the here proposed MQW structure, us-

ing Ge0.84Sn0.16/Si0.10Ge0.75Sn0.15 quantum heterojunctions, promises efficient charge

carrier confinement. Hence, it will be used in the following to calculate the material

gain.

3.2.3 Material gain calculations

In chapter 2 it was demonstrated that higher gain values can be expected from

tensile strained GeSn. This will also hold true for the MQW. For a waveguide in

the x-direction, transverse magnetic (TM) and transverse electric (TE) modes can

be defined, in which the electric field oscillates in the z-direction (growth direction)

for the former and in the y-direction for the latter. In MQWs HH and LH states

are split by quantization, so that EHH,1 is the highest state in the valence band and,

therefore, it will be mostly populated with holes. Near the lasing threshold gain will

first appear on transitions from EΓ,1 to EHH,1, and since HH states are predominantly

optically active for in-plane polarized radiation, gain will stem from the TE mode.

However, for larger injection carrier densities both gTM and gTE can be positive,

and either one can be larger. Interband gain spectra were calculated using equation

9.4.14 from Ref. [76] with a carrier scattering induced linewidth broadening γ of

30 meV, which gives:

g(hω) =πe2

nrcε0m20ω

∑

n,m

|Ienhm|2

∞∫

0

ρ2Dr |e · µc.b.,v.b.|2

γ/π

[Eenhm + Et − hω]2 + γ2

× [fnc.b. (Et)− fm

v.b. (Et)] dEt. (3.7)

54


0.2 0.3 0.4 0.5 0.6 0.7

0

1

2

3

4

Energy (eV)0 2 4 6 8 10

-4

-2

0

2

4

6

gT

E,m

ax (

x10

2 c

m-1)

n-type doping (x1019 cm-³)

1

4

10

30

Ninj

(x1017 cm-3)

10 12 14 16 18 20Sn content in well (at.%)

0.2 0.4 0.6

5

10

15

20

gT

E (

x1

02

cm

-1)

E (eV)

-4

0

4

8

12

16

20

24

gT

E (

x10

2 c

m-1)

Ninj

= 5x1018 cm-3

Sn content (at.%)20

10

12

14

1618

gmax

net gmax

gT

E (

x10

3 c

m-1)

(a) (b) (c)

λ (µm)

0.06

0.1

0.5

1.00

10.00

bulk FCA at gmax

Ninj

(x1019 cm-3)

6 5 4 3 2

5.00

Figure 3.7 – (a) TE mode gain spectra (without FCA) of a Ge0.84Sn0.16 /Si0.10Ge0.75Sn0.15 MQW in dependence on the injection carrier density with the cor-responding bulk FCA values at the gain maximum (dashed lines). (b) gTE,max valuesin dependence on the n-type doping concentration in the well for several Ninj. (c) Sncontent dependent gTE,max and net gTE,max at Ninj = 5× 1018 cm−3. The inset showsthe corresponding spectra. Derivative of Fig. 4 from Ref. [115], used under CC BY4.0.1

Using the reduced effective mass m∗r =

m∗Γm∗

HH/LH

m∗Γ+m∗

HH/LHto calculate the density of states

ρ2Dr , the overlap integral Ien

hm of electron (e: φn) and hole (h: gm) wave functions

with quantum numbers n/m and Fermi distributions fn/mc.b./v.b. considering quantized

states (n/m):

ρ2Dr =

m∗r

πh2dw

, Ienhm =

∞∫

−∞

φn(z)gm(z)dz, (3.8)

fnc.b. =

[

1 + e

[(

Eg+Een+m

∗r

m∗e

Et−EF,c.b.

)

/kBT

]

]−1

, fmv.b. =

[

1 + e

[(

Ehm−m

∗r

m∗h

Et−EF,v.b.

)

/kBT

]

]−1

.

In order to account for losses from absorption processes, FCA was calculated for bulk

Ge0.84Sn0.16 (c.f. chapter 2), which is of the same order as for quantum structures122

and gives a rough estimate of the net material gain. Here, material gain can be

achieved up to injection carrier densities of 5× 1019 cm−3, before the increase of

55


FCA with Ninj is stronger than the material gain. This is shown in Fig. 3.7a,

where Ninj dependent gain spectra for a Ge0.84Sn0.16/Si0.10Ge0.75Sn0.15 MQW are

shown, with FCA values at gain maxima, indicated by dashed lines. The threshold

injection carrier density is ∼6× 1017 cm−3, lower than for bulk GeSn (c.f. chap-

ter 2) and lower than reported thresholds for GeSn/SiGeSn MQWs at low/high Sn

contents,129,131,132 which is due to the decreased density of states. At experimen-

tally reasonable injection carrier densities of 5× 1018 cm−3, a gmax of 1470 cm−1 is

achieved, corresponding to a net gain of 1070 cm−1. This is in agreement with other

theoretical gain maxima reported for GeSn heterostructures.122,129–132,145 Compared

to the calculations for bulk GeSn shown in subsection 2.1.4, the calculated gain

maxima are significantly lower for the MQW. As it has been pointed out in the

previous section, the directness is decreased by the quantization. Moreover, bulk

gain was completely calculated using the k · p model, while for MQWs the effective

masses calculated at the Γ-point from the k · p model were taken. For the latter, this

means that the HH and LH mixing was not taken into account in state dispersions

(though it is approximately accounted for in the transition matrix element µc.b.,v.b.

in Eq. 3.7), which can cause discrepancies when calculating gain.

For optoelectronic devices based on Ge one option to increase the efficiency is the

incorporation of n-type doping into the active material.20,146,147 This will increase

the number of electrons in the conduction bands and, therefore, in the Γ valley. For

GeSn heterojunction light emitters, the benefit of using n-type doping is limited to a

small range of doping concentrations. This is shown in Fig. 3.7b, where net gTE,max

was calculated for a range of well doping concentrations and injection carrier densi-

ties. At moderate doping concentrations of ∼1× 1018 cm−3, gain increases, lowering

the lasing threshold carrier density below 1× 1017 cm−3 (green graph in Fig. 3.7b).

By increasing the injection carrier density to 3× 1018 cm−3 (red graph), net gTE,max

of 480 cm−1 is achieved, corresponding to a material gain of 990 cm−1. Nevertheless,

when the n-type doping exceeds 1× 1018 cm−3, losses from FCA will decrease the

net gain. The strong increase of inter-valley absorption in the conduction band (c.f.

subsection 2.1.4), will substantially deteriorate the optical performance, leading to

a break down of gain for doping concentrations of ∼5× 1019 cm−3 at injection car-

rier densities above 3× 1018 cm−3. Therefore, the advantages of doping in GeSn are

limited to low injection carrier densities.

56


Finally, another important advantage of using quantum structures will be dis-

cussed. As already mentioned, the quantization of conduction and valence band

states influences the directness for the conduction band and the band discontinu-

ities for all bands. Due to this, the bandgap will also be increased. Fig. 3.7c

shows gmax (purple graph) and net gmax (green graph) of unstrained Ge1−xSnSnxSn

/

Si0.10Ge0.91−xSnSnxSn−0.01 MQWs for high Sn contents at an injection carrier density

of 5× 1018 cm−3. In the corresponding figure for bulk GeSn in subsection 2.1.4, a

decrease of net gain was observed at Sn contents above 16 at.%, originating from

band mixing of conduction and valence bands at low bandgaps. This effect would be

smaller for the same Sn contents and the here chosen MQW design, if energy states

were calculated by an 8-band k · p model, due to the increase of the bandgap caused

by quantization. This allows for the growth of high Sn content MQWs with gain

maxima up to 1780 cm−1. The change of the gain behavior at Sn contents >16 at.%

is caused by the appearance of another lasing mode, which competes with the first

one. This can be observed in the inset of Fig. 3.7c, which plots the corresponding

material gain spectra.

In real MQW designs, the achievable modal gain of lasing modes in a cavity is the

product of the number of wells, the material gain and the optical confinement fac-

tor. In Ref. [130] it was calculated that an optical confinement factor close to unity

can be achieved using more than 30 wells, while 10 wells are enough to approach

a saturation of the modal gain. For a smaller number of wells, optical confinement

factors around 6 % are found.122,132 Here, a trade-off between the number of wells

and carrier transport characteristics has to be found. Large numbers of wells guar-

antee modal gains close to the material gain, but can also cause the lasing threshold

current density to increase, because more charge carriers are needed to fill wells and

achieve transparency than for a smaller number of wells. A reevaluation of modal

gain using updated material parameters (e.g. the bandgap bowing of SiSn at the

Γ-point) should be performed in future work, but is not considered here.

It should also be mentioned that recombinations from Auger processes were not

considered in this work. Although, they do not influence gain directly, the car-

rier lifetime and, therefore, number of injected charge carriers will be significantly

reduced by these processes, especially at room temperature.130

57


3.3 Summary

In this chapter, GeSn/SiGeSn heterostructures were investigated using GeSn as the

active material and the ternary SiGeSn as a barrier material. By considering the

possibilities and limits given by CVD epitaxial growth, optimal Sn and Si contents

were found for efficient carrier confinement. Conduction band offsets of ∼200 meV

were found for Ge1−xSnSnxSn

/ Si0.10Ge0.91−xSnSnxSn−0.01 heterojunctions, while en-

suring high directnesses at the same time. Using a Ge0.84Sn0.16 / Si0.10Ge0.75Sn0.15

heterostructure, MQWs were investigated, where the quantization of energy states

occurs in growth direction. Here, it was demonstrated that strain values close to the

cubic case (±0.5 %) guarantee good carrier confinement, while values below 8 at.%

for the Si content in the barrier should be omitted.

A further aspect to be considered is the thickness of the well. For increasing well

thicknesses, strain energy in the layer increases, which can cause lattice relaxation

and dislocations to appear. For the here determined material composition of bar-

rier and well, thin wells are advantageous, in that the strain in the well can be

compensated by thin SiGeSn barriers. On the other hand, thin wells cause strong

quantization of electron states, which decrease band offsets and directness. Taking

both aspects into account, well/barrier thicknesses of 30/40 nm were found to be

suitable for Ge0.84Sn0.16 / Si0.10Ge0.75Sn0.15 MQWs to tackle these problems.

The last part of this chapter investigated the achievable material gain. gTE,max

values of 1470 cm−1 at carrier injection densities of 5× 1018 cm−3 were found for

Ge1−xSnSnxSn

/ Si0.10Ge0.91−xSnSnxSn−0.01 MQWs. The threshold injection carrier den-

sity was found to be 6× 1017 cm−3, being significantly lower than for bulk GeSn and

coming from the quantization effects on the density of states. By additional dop-

ing of the well, net gain values of 480 cm−1 were found at moderate n-type doping

concentrations of 1× 1018 cm−3 and Ninj = 3× 1018 cm−3. Increasing the doping

concentration causes a severe degradation of net gain, due to increasing inter-valley

losses in the conduction band. In contrast to unstrained bulk GeSn, the Sn depen-

dence of the material gain for Ge1−xSnSnxSn

/ Si0.10Ge0.91−xSnSnxSn−0.01 heterojunc-

tions showed a constant increase of gTE,max with Sn content. This was explained

by the quantization of conduction and valence band states, concomitant with an

increase of the effective bandgap decreasing band mixing effects.

58

4 GeSn Quantum Dots

Contents

4.1 Approaches to achieve GeSn QDs . . . . . . . . . . . . 60

4.2 GeSn QDs embedded in SiGeSn . . . . . . . . . . . . . 65

4.2.1 Hydrostatically strained QDs . . . . . . . . . . . . . . 65

4.2.2 Biaxially strained QDs . . . . . . . . . . . . . . . . . 68

4.2.3 High Sn content QDs . . . . . . . . . . . . . . . . . . 72

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

The following chapter investigates experimentally and theoretically GeSn quantum

dots (QDs). The first part of this chapter describes a method of achieving Sn-rich

crystals in GeSn single quantum wells (SQWs). The layers were grown by Dr. Nils

von den Driesch from the Forschungszentrum Jülich and subsequently annealed via

rapid thermal processing (RTP) by Patric Bernardy. In order to investigate the

applicability of these crystals for efficient laser devices, transmission electron mi-

croscopy (TEM) measurements with energy dispersive X-ray spectroscopy (EDX)

mappings were performed by Dr. Martina Luysberg and Lidia Kibkalo from the

Ernst Ruska Centre at the Forschungszentrum Jülich. Here, the Ge and Sn con-

tent in the precipitates were investigated qualitatively. A quantitative analysis was

performed via atom probe tomography (APT) by Dr. Ivan Povstugar from the Cen-

tral Institute for Engineering Electronics and Analytics at the Forschungszentrum

Jülich. Additional to experimental results, calculations on GeSn QDs, coherently

grown in an SiGeSn matrix, were performed. The Fortran codes were developed and

provided by Dr. Nenad Vukmirović from the Institute of Physics Belgrade at the

59

4 GeSn Quantum Dots

University of Belgrade and use the 8-band k · p model. Similar as in the previous

chapter, material parameters for ideal carrier confinement will be determined. Parts

of these results have been previously published in Refs. [115, 148].

4.1 Approaches to achieve GeSn QDs

In chapter 3 the advantages of heterostructures, especially heterojunctions benefit-

ing from quantum effects, were discussed. The quantization of energy states in one

spatial dimension, concomitant with a 2D density of states, caused a strong decrease

of the lasing threshold current density. By additionally reducing the geometry of

the active material in two more spatial dimensions, subbands and bands become

discrete energy states (called sublevels) and a QD is created. The bandstructure

becomes atom-like, with charge carrier transitions between single energy levels. The

zero-dimensional DOS guarantees extremely low lasing threshold current densities,

which show a high temperature stability.117 Additionally, the strong spatial local-

ization of charge carriers within the device geometry, reduces the probability for

non-radiative recombinations at defects and residual dislocations in the surround-

ing matrix.149 The interaction of charge carriers with phonons is also drastically

reduced, which is e.g. reflected in an increased photoconductivity.150

There are several approaches to obtain QDs, which are frequently studied in litera-

ture. The most prominent representatives are listed in the following.

• Colloidal quantum dots or nano crystals (NCs) are synthesized by

chemical reactions, where precursor molecules are injected into a solution and

forced to precipitate. Herewith small crystallites are obtained, where the dan-

gling bonds on the surface can be passivated by additional crystal layers or

ligands.151,152 NCs are often used to investigate the band structure of a mate-

rial system in a QD geometry and, during the last years, GeSn NCs covering

a wide range of Sn contents (up to 42 at.%) were synthesized.152–155

• QDs in a dielectric matrix can be obtained by e.g. dissolving precursor

molecules or implanting atoms in silicate or by sputtering each constituent to-

gether with SiO2.156,157 Each of these approaches are followed by an annealing

step, in which QDs are created. Similar to NCs, QDs in a dielectric matrix

60


are suitable to investigate the band structure by measuring their absorption

spectra. As a laser material, they show limited possibilities, because of their

embedding in an insulating matrix and the optical performance suffering from

surface defects.

• Heteroepitaxial QDs or self-assembled QDs are most commonly stud-

ied, since they allow to integrate QDs into the device structure during the

growth process. Physically, they are achieved by the heteroepitaxial growth

of materials with a large lattice mismatch. If the sum of the surface energy

of the deposited layer and the interface energy is below the surface energy of

the substrate, smooth layers are grown. This growth mode is called Frank-

van der Merve growth, and it prevails as long as the above requirement is

matched.117,158,159 An increasing thickness of the epitaxial layer, increases the

strain energy, so that either a plastic strain release (c.f. chapter 3) or strain re-

laxation via the growth of coherently strained, three dimensional islands will

occur. This growth mode is called Stranski-Krastanov growth and it serves

to decrease strain energy in the smooth wetting layer. In cases, where the

sum of surface and interface energies is larger than the substrate surface en-

ergy, Volmer-Weber growth is observed. Here, 3D-islands are directly grown

on the substrate without a wetting layer. The Stranski-Krastanov growth of

these islands has been substantially investigated for III-V semiconductors.160

Multi layers of QDs embedded in QWs show lasing at low threshold current

densities.161–164

• Annealing of metastable alloys causes phase separations inside the layer

and eventually precipitates to occur. For SiSn and GeSn this is observed

frequently.70,165–170 The dots are described by Sn-rich clusters,70,169 where it

was found for SiSn that these are created by vacancy-mediated diffusion of Sn

atoms.171 Thorough investigations show that the crystallites are either single

crystalline166 or show α- and β-Sn phases,165 have a cubic diamond lattice or

ordered zincblende structure,169 and a incoherent orientation in the lattice.165

However, diffraction measurements also indicate that lattice planes are ori-

ented parallel to the surrounding matrix.165

61

4 GeSn Quantum Dots

20 nm

GeSn SQW

5 nm

(a) (b)

Ge-VS

Ge capping

Figure 4.1 – (a) XTEM micrograph of an annealed GeSn SQW surrounded by Ge.(b) Detailed micrograph of a precipitate inside the GeSn layer.

Although the latter approach was carefully investigated, it lacks an exact determi-

nation of the achievable Sn content. Estimations from TEM measurements require

various assumptions, from which Sn contents with unknown uncertainties are de-

rived. In this regard, the determination of Sn content of precipitates in GeSn SQWs

will be discussed in the following. In order to reduce the complexity, GeSn SQWs

were grown in-between a Ge-VS and a Ge capping layer (instead of SiGeSn, which

would give a better band confinement, c.f. section 2.2) at 365 ◦C, as described in

subsection 2.1.5. The thickness and composition of SQW and capping layer were de-

termined via RBS to 17 nm and 23 nm, respectively, with an Sn content of ∼10 at.%

in the SQW. After growth, the samples were annealed using a temperature range

of 400–800 ◦C under Ar ambient for 60 s and 120 s (c.f. table in section A.5). The

structural properties of the annealed set of samples were investigated using a FEI

Tecnei F20 and FEI Titan 80-200. Each microscope was equipped with a Super

X EDX detector to analyze the local element distribution. Cross sectional speci-

mens were prepared by grinding and Ar ion milling. These measurements showed

no obvious influence of the temperature and ambient on the formation or density of

precipitates. Exemplarily, a cross sectional TEM (XTEM) micrograph of an SQW

annealed at 500 ◦C is shown in Fig. 4.1a. All samples exhibit clusters of several dots

with a low cluster density over the whole sample. The low density of dots hinders

the investigation of the influence of annealing parameters on dot density and mor-

phology. The precipitates are localized inside the original SQW region or at the

62


10 nm 10 nmGe Sn

(b)(a)

Figure 4.2 – (a) HAADF micrograph of a single precipitate. (b) CorrespondingEDX mapping of Ge and Sn.

interface between SQW and Ge capping. Moiré pattern detected on XTEM micro-

graphs are visible in every dot, proving a crystalline structure. A high resolution

XTEM micrograph, shown in Fig. 4.1b, additionally shows crystalline planes with

different orientations. Due to this, it can be concluded that the crystallites are not

coherently oriented in the surrounding matrix.

Besides the above described observations, high angle annular dark field micrographs

(HAADF) of many crystallites, where heavier elements cause brighter contrasts,

show dark regions at the edge of the dot (Fig. 4.2a). In order to extract informa-

tion about these dark regions and the local element distribution, EDX maps were

measured for the dot shown in Fig. 4.2a. Mappings of elemental Ge and Sn show a

noticeably higher Sn signal in the dot region (Fig. 4.2b). Although the crystallite

region also shows signals from Ge atoms, it cannot be excluded that these signals

stem from Ge atoms underneath the precipitate. Sophisticated measurements of the

specimen thickness are required in order to approximate the Ge and Sn content in

the dot, but bear unknown uncertainties. The Ge signal in the darker regions is

weaker than for SQW and Ge capping, which can be explained by the occurrence of

voids. These vacancy clusters support the finding of Sn precipitates in Si, where the

diffusion of Sn atoms is vacancy-mediated.171 In the SQW layer and at interfaces

these vacancies enable the diffusion and clustering of Sn atoms.

Elemental concentrations were measured using atom probe tomography. This elabo-

63

4 GeSn Quantum Dots

Ge

Sn

Ge

capping

100 nm

GeSn

Ge-VS

10 nm

-9 -6 -3 0 3 60

10

20

30

40

Sn

co

nte

nt (a

t.%

)

Distance (nm)

depletion

region

(a) (b)

(c)

GeSn dot-4 -2 0

2

4

6

x (nm)

xS

n (

at.%

)

Figure 4.3 – (a) SEM micrograph of a prepared sample tip, indicating a precipitateat the top. (b) Corresponding APT elemental map of Ge and Sn. The orange arrowdepicts the direction of the linescan, shown in (c) for Sn atoms.

rate technique allows to determine the spatial distribution of atoms and, herewith,

a quantitative, accurate estimation of the Ge and Sn content. An APT specimen of

the above described sample was prepared with an orientation parallel to the SQW,

as shown by a scanning electron microscopy (SEM) micrograph in Fig. 4.3a. The

specimen were prepared using a FEI Helios Nanolab 600i focused-ion-beam system

and analyzed by a LEAP 4000X HR Cameca Instruments atom probe tool (details

can be found in Ref. [67]). The parallel orientation increases the probability to find

a crystallite in the specimen. Subsequently, the elemental distribution of Ge and

Sn of the upper dot was measured (Fig. 4.3b). The composition of a cutout sphere

inside the center of the dot gives an Sn content of ∼30 at.%.

Hence, with a residual Sn content in the SQW of 3.5 at.%, the Sn content in the

SQW is locally three times higher than in the original GeSn layer. The decrease

of the Sn content in the SQW is caused by both diffusion and precipitation of Sn

atoms. From linescans of the SQW region (not shown here) a smooth decrease

of the Sn content towards the Ge layer was found, increasing the SQW thickness

and indicating a diffusion process. On the other hand, linescans at the interface

of dot and SQW (orange arrow in Fig. 4.3b) reveal a gradual decrease of the Sn

content towards the interface (Fig. 4.3c). Beyond this interface, on the SQW side,

a drop of the average Sn content from 3.5 at.% to 2 at.% was detected (inset in

64

4.2 GeSn QDs embedded in SiGeSn

Fig. 4.3c), fostering the observation of voids in XTEM measurements. Therefore, a

vacancy-mediated Sn atom diffusion can be assumed, in which voids cluster during

annealing and describe a sink for Sn atoms. This aggregation of Sn atoms inside

the layer causes Sn-rich crystals.

Taking all above results into account, it is difficult to consider Sn-rich GeSn crystal-

lites, achieved via RTP, as suitable laser material. Although the gradual decrease

of the Sn content from the center of the dot towards the matrix could substan-

tially lower Auger recombinations,172 it appears to be very difficult to control the

dot density and elemental composition. Additionally, high interface defect densities

between dot and SQW and grain boundaries will mitigate the achievable gain. Con-

sidering the achievements of III-V lasers based on QDs, an approach utilizing the

Stranski-Krastanov growth mode is preferable. In this regard, pyramidal QDs with

high crystal quality and uniformity were grown coherently on a matrix material.158


4.2.1 Hydrostatically strained QDs

Since there are, up to date, almost no publications on the heteroepitaxial growth

of GeSn QDs,173 the investigations are limited to theoretical considerations. Band

structure calculations have been presented using thight binding and k · p models

for Sn NCs174 and Sn/GeSn QDs in Si/Ge matrices.175,176 In these publications,

no direct bandgap in group IV QDs could be found for type I alignment. Hence,

based on the results in chapter 3, a reevaluation of GeSn QDs will be shown, using

SiGeSn as a matrix. Adapting the requirements for efficient carrier confinement

from the previous chapter, optimal material compositions will be determined.

The theoretical details are summarized in subsection A.2.2 of the appendix.

Energy states of cone shaped GeSn QDs were calculated within the 8-band k · pmodel using the wave expansion method. The cylindrical symmetry of the dots

enables solving the Schrödinger equation in cylindrical coordinates which is less

time-consuming. In this regard, the quantized electron (e) and hole (h) Eigenstates,

nemf and nhmf, are described by the quantum number n and the quantum number

of the quasi-total angular momentum mf (Hamiltonian with a discrete rotational

65

4 GeSn Quantum Dots

Lx

Ly

Lz

0 20 40 600

20

40

60

80

z (

nm

)

x (nm)

-1.40

-1.00

-0.60

-0.20

0.20

hydrostatic strain (%)100

80

(b)(a)

Figure 4.4 – (a) A cone shaped QD embedded in an SiGeSn matrix. (b) Strain fieldin the xz-plane for a Ge0.82Sn0.18 QD in an Si0.10Ge0.74Sn0.16 matrix. The dashed lineindicates the geometry of the dot.

symmetry). In order to evaluate strain in dot and matrix, a continuum mechanical

model was used. Here, the dots are placed in a cubic mesh, with dimensions Lx, Ly

and Lz, and the strain distribution is obtained by minimizing the elastic energy.

The QDs have a base diameter of 20 nm and a height of 30 nm, resembling pyrami-

dal shaped QDs (Fig. 4.4a), as they are often found for III-V semiconductors.162

However, usual QD dimensions lie in the range of a few nm, exhibiting a much

wider base diameter than height, but for thicknesses below 20 nm no direct bandgap

GeSn QDs with a type I alignment could be found in the investigated range of Sn

contents. Similar as for MQWs in chapter 3, for small dot sizes, the quantization

increases the value of the lowest energy state strongly. In the case of QDs this is

even more pronounced, due to the quantization in three spatial dimensions. On the

other hand, for the band offsets found in this work, larger dimensions would give a

large number of confined states in the dot with energies close to the bulk energy of

the matrix. The energy dispersion would become band like, causing a loss of the

advantage of a 0D DOS. The Sn and Si contents were chosen similarly as in the

discussions in chapter 3.

To get a general overview of the band offsets of GeSn QDs embedded in SiGeSn,

the approach of a matrix, unstrained far away from the the dot was chosen. This


66


15 16 17 18 19 20

-80

-40

0

40

80

120

Energ

y (

meV

)

Sn content in QD (at.%)

VΓ

VL

∆EL-Γ,matrix

∆EL-Γ,QD

Vv.b.

Si content in matrix 2 at.% 4 at.% 6 at.% 8 at.% 10 at.%

10 12 14 16 18 20-50

0

50

100

150

200

250

Sn content in matrix (at.%)

VΓ

(me

V)

direct bandgap

barrier

type II

alignment

Ge0.82

Sn0.18

QD

(a) (b)

Figure 4.5 – (a) Band discontinuities of the Γ valleys for a Ge0.82Sn0.18 QD for dif-ferent compositions of the SiGeSn matrix. The purple, red and blue areas indicatematerial compositions causing type II alignment, a direct bandgap in the matrix andregions limited by experimental possibilities of CVD for bulk materials, respectively.(b) Band alignment parameters for Ge1−ySny QDs in an Si0.10Ge0.92−ySny−0.02 ma-trix. Derivative of Fig. 7 from Ref. [115], used under CC BY 4.0.1

had the effect of an isotropic, hydrostatic strain deforming the dot lattice uniformly.

Fig. 4.4b shows exemplarily the strain distribution of a hydrostatically strained QD

with an Sn content of 18 at.% in an Si0.10Ge0.74Sn0.16 matrix, with a uniform strain

distribution and an average strain in the QD of −1.07 %.

In order to find the optimal material composition of matrix and strain concerning

carrier confinement, the same procedure as in chapter 3 was applied. The matrix

material composition dependence of VΓ are shown in Fig. 4.5a for a Ge0.82Sn0.18

QD. As in section 3.2 the purple, red and blue areas indicate material compositions

causing type II alignment between QD and matrix, a direct bandgap in SiGeSn

and CVD related material limits for bulk GeSn/SiGeSn heterostructures. Com-

paring the achievable values of VΓ of QDs to those achieved for MQWs, the band

discontinuities are significantly lower, due to the strong quantization in QDs. The

maximum achievable band offset is 130 meV.

For a Ge0.82Sn0.18 QD, the restraints for optimal carrier confinement, here defined by

the trade-off between maximal band discontinuities of Γ valleys and high directness

in GeSn, are satisfied for an Si0.10Ge0.74Sn0.16 matrix. It has to be pointed out that

67

4 GeSn Quantum Dots

the limits on the Sn content in confining and active material, given by CVD bulk

and QW heterojunctions, do not have to hold for the material composition in QD

heterstructures. Nevertheless, they will be taken in the following due to the lack of

experimental data.

Applying this procedure to the whole range of considered Sn contents, results in

the band alignment parameters shown in Fig. 4.5b. Similar to the previous chapter

but with a higher discrepancy between dot and matrix Sn content, the optimal

alignment is achieved for Ge1−xSnSnxSn

/Si0.10Ge0.92−xSnSnxSn−0.02 heterojunctions. A

type I alignment between matrix and active material is achieved with average band

offsets for the valence and conduction band of Vv.b. = 60 meV, VΓ = 110 meV and

VL = 25 meV, respectively. The reason why the band offsets do not change with the

QD Sn content can be argued by composition and strain. At a constant Si content,

if the Si0.10Ge0.92−xSnSnxSn−0.02 matrix is unstrained far from the Ge1−xSn

SnxSndot,

the average compressive strain in the QD and the Sn content difference between

matrix and dot are constant for all xSn. An increase of band offsets with increasing

xSn is, therefore, hindered. The average strain derived from a vertical line through

the center of the dot is −1.07 % for all QD Sn contents.

4.2.2 Biaxially strained QDs

Using the above model, the band offsets and directnesses are a good first estimate

but lack the experimentally more common case of a biaxially strained matrix, which

causes an anisotropic deformation of the QD lattice. Therefore, biaxial strain was

applied to the heterostructure by changing the Sn content in an underlying GeSn

buffer from 10 at.% to 20 at.%. In the following, the influence of biaxial strain will

be described for a Ge0.82Sn0.18 QD in an Si0.10Ge0.74Sn0.16 matrix. The strain distri-

bution using an unstrained Ge0.90Sn0.10 buffer is shown in Fig. 4.6a, where SiGeSn

adopts the strain imposed by the substrate far from the dot. The average strain in

the dot is −0.71 %. The strain field in the crystallite decreases towards the tip of

the dot, releasing the strain energy imposed by the biaxially strained matrix. The

fringes of the strain field around the dot from its geometry (dashed line) is due to

the low mesh density chosen to compute strain.

68


10 at. % Sn in substrate

0 20 40 600

20

40

60

80

z (

nm

)

x (nm)

100

80

(b)(a)-0.2

-1.0

-0.8

-0.6

-0.4

ε|| (%)

Energ

y (

eV

)

mf = 3/2m

f = 1/2m

f = -1/2m

f = -3/2

-0.3

-0.2

0.1

0.2

0.3

Γ

v.b.

bulk energy

Figure 4.6 – (a) Strain field in the xz-plane and (b) energy levels of Γ-electron and va-lence band hole states for different quasi-total angular momentum mf of a Ge0.82Sn0.18

QD in an Si0.10Ge0.74Sn0.16 matrix. The strain is induced by a Ge0.90Sn0.10 substrate.Dashed lines in (a) and (b) indicate the geometry of the dot and bulk energies,respectively. Derivative of Fig. 8 from Ref. [115], used under CC BY 4.0.1

The calculated conduction and valence band energies are denoted with the quanti-

zation number n and quantum number of the quasi-total angular momentumg mf,

which has half integer values. The confined Γ valley and valence band energies of

the Ge0.82Sn0.18 QD are shown in Fig. 4.6b for a few values of mf. The energies for

±mf are the same, and the lowest conduction band states are found for mf = ±1/2.

The optical activity will be, therefore, dominated by transitions with the initial/final

state of ne±1/2 (black arrows in Fig. 4.6b).

The confinement of electron states can be investigated in more detail by examin-

ing the spatial dependence of the wave function probability density |Ψ|2. This is

illustrated in Fig. 4.7, where |Ψ|2 is shown for the first three electron states with

mf = 1/2 in the xz-plane. States with odd quantum numbers are confined near the

base of the dot, while for even quantum numbers states are localized nearer to the

center.

As explicitly described in subsection A.2.2, the optical cross section gives a first in-

sight into the strength of the optical activity between two energy states, depending

on the polarization. In this context, only interband transitions were investigated.

If the radiation is z-polarized, only transitions fulfilling ∆mf = 0 are allowed, while

for in-plane polarization ∆mf = ±1 is required to allow for interband transitions.

69

4 GeSn Quantum Dots

x (nm)0 20 40 60 800 20 40 60 800 20 40 60 80

20

40

60

80

100

z (

nm

)

|Ψ|2 1e1/2

6x10-44x10-42x10-401x10-36x10-42x10-4 1x10-36x10-42x10-4 1.4x10-3

|Ψ|2 2e1/2

|Ψ|2 3e1/2(c)(b)(a)

Figure 4.7 – Wave function probability density of Γ-electrons with quantum number(a) n=1 (b) n=2 and (c) n=3 and quasi-total angular momentum mf for a Ge0.82Sn0.18

QD in an Si0.10Ge0.74Sn0.16 matrix. Derivative of Fig. 8 from Ref. [115], used underCC BY 4.0.1

Taking into account the considerations for the lowest energy states (c.f. Fig. 4.6b),

for z-polarized light, transitions from states with mf = 1/2 are the strongest, and

for in-plane polarized radiation transitions from mf = 1/2 to mf = 3/2 are coupled

the strongest.

The total optical cross section σεif for these two cases is plotted in Fig. 4.8 in de-

pendence of the substrate Sn content. While a decrease of σεif occurs for z-polarized

light with increasing Sn content (Fig. 4.8a), an increase for x-polarized radiation is

visible (Fig. 4.8b). This can be understood within the k · p formalism. In contrast

to quantized states in chapter 3, the valence and conduction band states of QDs

were calculated by the 8-band k · p model. Here, if the energies of LH and HH are

very near to each other in k-space close to the Γ-point, a strong mixing of these

states occurs. Therefore, it is rather more accurate to speak of valence band states

than HH or LH states, since quantized states contain both characters. When Sn

content in the substrate is increased, the strain in the dot increases from −0.71 %

to 0.81 %. This will change the contribution of LH and HH bands in the quantized

energy states. In contrast to bulk material, the contribution of the LH band de-

creases with increasing strain in the QD. For the case of z-polarized radiation the LH

contribution in hole energy states decreases from 74 % to 42 %, while for the case of

70


(a) (b)

σεif (1

0-1

8 m

2)

0.2 0.3 0.4 0.5 0.6 0.70.2 0.3 0.4 0.5 0.6 0.70.0

0.2

0.4

0.6

0.8

1.0

Energy (eV) Energy (eV)

1e1/2

0.0

0.2

0.4

0.6

0.8

1.0

1e1/2 → 3/2

substrate Sn content

avg. strain in QD

10 at.%

-0.71 %

12 at.%

-0.41 %

14 at.%

-0.10 %

16 at.%

0.20 %

18 at.%

0.51 %

20 at.%

0.81 %

ε=(0 0 1) ε=(1 0 0)

Figure 4.8 – Optical cross section spectra in dependence of the substrate Sn contentfor (a) z-polarized and ∆mf = 0 and (b) x-polarized radiation and ∆mf = 1 for aGe0.82Sn0.18 QD in an Si0.10Ge0.74Sn0.16 matrix. Derivative of Fig. 9 from Ref. [115],used under CC BY 4.0.1

x-polarization the HH contribution in hole states increases from 53 % to 82 %.115 As

described in subsection 2.1.3, since z-polarized light is mainly active for LH states

and in-plane radiation for HH states, this explains the decrease of the optical cross

section in Fig. 4.8a and the increase in Fig. 4.8b.

The influence of biaxial strain on band alignment parameters is depicted in Fig. 4.9.

Strikingly, there is a strong increase of the directnesses of matrix and QD induced

by the increasing substrate Sn content and strain. Contrary to this, there is hardly

any change of the band offsets for valence and conduction band with strain. This

can be explained by a similar shift of the Γ energy for SiGesn and GeSn, when strain

increases with Sn content.

Moderate Γ valley valence band discontinuities of ∼110 meV and ∼60 meV, respec-

tively, are found. QD directnesses of up to 150 meV are achieved, while the matrix

becomes a direct bandgap semiconductor at 0.14 % biaxial strain, before exhibiting

directnesses of up to 54 meV. A type I alignment for L valleys is achieved by only a

few meV. Integrating biaxial strain into GeSn QD calculations leads to similar results

as for QDs under hydrostatic pressure. Therefore, these results give an optimistic

outlook that good carrier confinement can be achieved in GeSn QDs surrounded by

an SiGeSn matrix and it is left for future experiments to verify them.

71

4 GeSn Quantum Dots

-80

-40

0

40

80

120

160

Sn content in substrate (at.%)10 12 14 16 18 20

ε||,QD

(%)

-0.8 -0.4 0.0 0.4 0.8

En

erg

y (

me

V) ∆E

L-Γ in QD

∆EL-Γ in matrix

VΓ

VL

Vv.b.

Figure 4.9 – Band alignment parameters for a Ge0.82Sn0.18 QD in anSi0.10Ge0.74Sn0.16 matrix for different Sn contents in the substrate (strain dependence).Derivative of Fig. 10 from Ref. [115], used under CC BY 4.0.1

4.2.3 High Sn content QDs

Although quantization lowers the directness and band offsets for conduction and

valence bands, it also shifts the region, where gain is decreased by band mixing,

to higher Sn contents, as it has been already indicated in subsection 3.2.3. QDs,

with their strong quantization in three dimensions, offer the possibility to achieve

gain at high directnesses and band offsets at Sn contents, where the bulk bandgap

would be zero or negative, similar to α-Sn.175,177 This is demonstrated in Fig. 4.10,

where the bandgap of a Ge0.66Sn0.34 QD in an SiGeSn matrix with 10 at.% Si and

different Sn contents is shown. The dimensions were kept the same as for QDs in the

previous discussion. By adjusting the Sn composition in the matrix, the strain in the

QD and, therefore, the bandgap changes. When the quantization is not considered

(empty squares), no positive bandgap can be achieved for matrix Sn contents close

to xSn of the QD. However, due to the strong quantization, the gap is opened, with

Eg = 88 meV for xSn,QD = xSn,matrix. In this case, a directness of 250 meV is achieved,

which can enable high gain values. By decreasing the thickness, both quantization

and bandgap can be increased, extending the range of Sn contents in QDs to higher

values. Of course, this extended range of Sn contents suitable for laser materials

faces the challenging task of experimental realization.

72

4.3 Summary

10 20 30 40-0.2

0.0

0.2

0.4

0.6

with quantization

without quantization

Eg (

eV

)

Sn content in matrix (at.%)

-6 -4 -2 0

ε||,QD

(%)

Ge0.66

Sn0.34

QD

Figure 4.10 – (a) Bandgap of a Ge0.66Sn0.34 QD in an Si0.10Ge0.90−xSnSnxSn

matrixfor different Sn contents in the matrix. Empty squares show values neglecting theeffect of quantization, while filled circles account for quantization in three dimensions.

4.3 Summary

This chapter described the experimental and theoretical investigation of GeSn QDs.

Annealed GeSn SQWs (10 at.% Sn), embedded in Ge layers, showed the occurrence

of high Sn content regions, as indicated by EDX mappings. TEM measurements

show multiple crystalline phases and an incoherent orientation in the matrix ma-

terial. An investigation using APT revealed an average Sn content of 30 at.% in

the crystallites with a gradual decrease towards the matrix (residual Sn content

of 3.5 at.%). Furthermore, voids were detected at the interface of matrix and dot,

supporting the hypothesis of vacancy-mediated diffusion of Sn atoms, eventually

causing the emergence of GeSn precipitates.

It is doubtful whether the annealing approach is suitable for a controlled gener-

ation of GeSn QDs. Therefore, the energy states of GeSn QDs embedded in an

SiGeSn matrix were calculated using an 8-band k · p model. At first, the hetero-

junctions were hydrostatically strained and investigated concerning their suitability

to confine charge carriers in QDs. Applying the same material limitations as in the

previous chapter maximal Γ valley offsets and directnesses of 110 meV were found,

for Ge1−xSnSnxSn

/Si0.10Ge0.92−xSnSnxSn−0.02 heterojunctions, which are lower than for

MQWs, due to the three-dimensional quantization.

73

4 GeSn Quantum Dots

The influence of biaxial strain was investigated on a Ge0.82Sn0.18 QD surrounded by

an Si0.10Ge0.74Sn0.16 matrix, where strain was applied using GeSn substrates with

varying Sn contents. Similar as for hydrostatically strained QDs, average band dis-

continuities for the Γ valley of 110 meV were found at QD directnesses of up to

150 meV.

In order to investigate the optical coupling strength of interband transitions, po-

larization dependent optical cross sections were calculated. It was found, that, by

increasing the strain in the QD, σεif decreased for linear-polarized light and states

satisfying the condition ∆mf = 0. On the other hand, an increase of σεif was found

for circular-polarized light and states with ∆mf = ±1. This could be explained

using the k · p formalism by the changing character of valence band states. There-

fore, when designing laser cavities proper strain engineering has to be performed to

increase the optical efficiency.

The strong quantization of energy states in QDs can be used to expand the range

of Sn contents where GeSn has a non-zero bandgap. As an example, it was shown

that the bandgap of a Ge0.66Sn0.34 QD, which has a negative bandgap in the bulk

material, could be opened due to the strong confinement of charge carriers. This

allows another possibility to extend the range of Sn contents and to achieve high

gain values at high temperatures. Summarizing the above findings, GeSn QDs con-

fined by SiGeSn should be considered for laser designs, although the experimental

possibilities still have to be explored.

74

5 Optimization of group IV photonic

devices

Contents

5.1 In-situ growth of graded contact layers . . . . . . . . . 76

5.2 Selective epitaxial growth of GeSn . . . . . . . . . . . . 78

5.3 CGeSn . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.3.1 CBr4 flow rate dependence . . . . . . . . . . . . . . . 84

5.3.2 Temperature dependence . . . . . . . . . . . . . . . . 88

5.3.3 Interpretation of CGeSn epitaxy . . . . . . . . . . . . 91

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

The following chapter summarizes experimental results, in which the optimization

of growth processes for laser applications is investigated. The first part describes

epitaxial growth of top and bottom contact layers, exhibiting a graded doping con-

centration towards the optically active material. The successful implementation

of contact layers is investigated using APT, performed and analyzed by Dr. Ivan

Povstugar. Subsequently, an alternative approach to deposit lasing cavities will

be presented, which is selective epitaxial growth (SEG). In this regard, GeSn lay-

ers were deposited at different temperatures and precursor configurations into SiO2

trenches on Si and Ge wafers. The structured wafers were provided by the IHP

Frankfurt/Oder.

A more fundamental concept to explore new possibilities concerning device optimiza-

tion is the extension of materials used. In this regard, carbon was epitaxially imple-

mented into GeSn. A basic investigation of the layer properties is shown concerning

75

5 Optimization of group IV photonic devices

the compositional range and impact on the background doping of GeSn. In this con-

text, measurements using RBS, electrochemical capacitance-voltage (ECV) profiling

and secondary ion mass spectrometry (SIMS) were performed. The SIMS spectra

were provided by Dr. Uwe Breuer from the Forschungszentrum Jülich. Strain in

the deposited CGeSn layers was determined via X-Ray diffraction by Dr. Gregor

Mussler and Dr. Alexander Shkurmanov from the Forschungszentrum Jülich.

5.1 In-situ growth of graded contact layers

So far, the main focus of previous chapters was the design of efficient laser materials

exhibiting high gain values. However, the goal of an electrically pumped laser also

requires a clever implementation of contact layers. These layers are usually made of

highly doped semiconductors with low resistances, which have been widely used for

group IV light emitting diodes (LEDs).126,178,179 The growth kinetics of boron and

phosphorous doped Si-Ge-Sn have been investigated in this regard.46,180–182 A vari-

ety of diodes using GeSn as an active material was experimentally demonstrated,

implementing bulk GeSn embedded in doped Ge/GeSn contact layers124,183,184 or

GeSn/SiGeSn MQWs with GeSn contacts.31 However, highly doped contact layers

can also be troublesome, causing a strong absorption of the lasing mode. This is

especially pronounced in laser designs, where the active material exhibits a small

thickness as in the case of MQWs. Here, the mode can be larger than the MQW

region, extending into the contact layers and suffering from free carrier absorption.

For high Sn content GeSn/SiGeSn MQWs with a total MQW thickness of 104 nm,

calculations show major modal losses stemming from p-type doped GeSn contact

layers.132 This problem is often circumvented by intrinsic spacer layers separating

the active region from contact layers.183,184 In the following approach an additional

measure will be proposed to tackle modal losses from highly doped layers.

A GeSn/SiGeSn MQW LED was grown via RPCVD using phosphine (PH3), di-

borane (B2H6), disilane (Si2H6), digermane (Ge2H6) and tin tetrachloride (SnCl4)

precursors. This approach introduces doped contact layers, where the doping con-

centration decreases towards the active layer. For this purpose, a thick boron doped

GeSn layer was grown on a Ge-VS at 365 ◦C. The high thickness of the bottom con-

tact caused a relaxation of the lattice, making GeSn:B also serve as a buffer layer.

76

5.1 In-situ growth of graded contact layers

GeSn:P

GeSn:B

GeSn / SiGeSn

MQW

Ge-VS

B

P

(a) (b)

0 100 200 300 400 5000

5

10

15

20

Ele

me

nta

l co

nc. (a

t.%

)

Distance (nm)

B

Sn

Si

P

1018 Do

pin

g c

on

c. (c

m-3)

1019

1020

(c)

40

nm

Sn

Si

Figure 5.1 – (a) Design of a GeSn/SiGeSn MQW LED with graded bottom and topcontacts. (b) Elemental APT mapping of Si, Sn, B and P. (c) Corresponding linescan perpendicular to the growth direction.

After growing a thick GeSn:B layer at a constant diborane flow rate QB2H6 , the flow

rate was gradually decreased to achieve a smooth grading towards the active layer.

After lowering the growth temperature to 350 ◦C, a GeSn/SiGeSn MQW was grown

with six wells. A small number of wells was chosen to prevent the active layer from

plastic relaxation, deteriorating its optical performance. For the first and the last

layer SiGeSn was chosen, serving not only as a potential barrier for conduction and

valence bands of the well but also as a spacer between well and contacts. Besides

that, it provides a spatial separation of GeSn from the dislocations in the relaxed

buffer layer. After depositing the last SiGeSn barrier, the flow rate of disilane was

gradually decreased, while the flow rate of PH3 was slowly increased in order to

grow a GeSn:P contact layer. The intention to create a smooth decrease of the Si

concentration was in order to avoid introducing a sharp potential barrier for charge

carriers. GeSn:P was chosen as a top contact layer instead of SiGeSn:P, due to the

lower surface roughness experienced from previous experiments.

Fig. 5.1a shows the design of the grown structure as intended. It is similar to

the structures that were investigated in Refs. [30, 31]. To verify the successful in-

tegration of the graded contact layer, APT measurements have been performed.

77


Fig. 5.1b depicts the elemental mappings of Si, Sn, B and P showing the clearly

distinguishable well and barrier layers. For B and P atom species, a smooth de-

crease of the doping towards the MQW can be conjectured. The verification can

be found in a line scan through the specimen perpendicular to the growth direction

(Fig. 5.1c). From these, bottom and top layer thicknesses of 180 nm and 116 nm can

be derived with a smooth B/P concentration grading of 3× 1016 cm−3 nm−1 and

1× 1017 cm−3 nm−1, respectively. The maximal boron and phosphorous concentra-

tions achieved are ∼3× 1018 cm−3 and ∼6× 1018 cm−3, respectively. While for the

top layer the Sn content in regions with graded and constant P flow rate remains

constant (13.2 at.%), the bottom layer exhibits, at first, an Sn content of 9.4 at.%,

before it linearly increases with the B concentration at a rate of 0.02 at.% nm−1.

Since the grading of boron concentration and Sn content happens at the same thick-

ness, they seem to be correlated, as it was also found in Ref. [46]. Another possibility

is the relaxation driven increase of the Sn content.68 For the MQW a well/barrier

thickness of 18 nm was found with average Sn contents of 13.4/14 at.% and a barrier

Si content of 3.8 at.%. The evaluation of the suitability of this structure lacks EL

measurements, which is left for future work. Still, on the epitaxial side the feasibility

could be demonstrated successfully.

5.2 Selective epitaxial growth of GeSn

An approach of paramount importance is the selective epitaxial growth (SEG) of

semiconductors. It enables the integration of different devices in separate growth

steps on the same micro chip. In the case of GeSn, photo detectors and waveguides

could be grown and subsequently processed. Thereafter, the sample is overgrown

with SiO2, in which trenches are etched, followed by the deposition of lasing cavities

inside these trenches. The design of each device could be chosen completely inde-

pendently.

Besides the utilization in optoelectronic devices, SEG can also be applied to the

growth of high mobility channel layers for FETs.185 By choosing a low aspect ratio

between trench width and height, a trapping of threading dislocations at the side-

walls of trenches can be achieved, enabling the growth of III-V semiconductors or Ge

on Si.186 Replacing trenches by pillars, where the tip is the exposed semiconductor

78


surface, a 3D elastic relaxation of the overgrown layer can be achieved exhibiting

high crystal quality.187,188

The latter design, using Si pillars, was also investigated for the SEG of GeSn via

MBE.189,190 In these publications it is suggested that a selectivity of GeSn deposi-

tion is achieved when desorption processes are stronger (lower energy needed) on

the oxide than on the pillar. The nucleation of adatoms on Si is therefore achieved

at high temperatures, causing small Sn contents in the layers. In contrast to MBE,

a key aspect of SEG via CVD is chemisorption rather than physisorption. Precur-

sor molecules diffuse to and adsorb on a surface and react with surface-atoms. If

a critical nucleus radius is bridged, growth is achieved. Thermodynamically this

nucleation process depends on the super-saturation of gas molecules and surface

energy of the solid.191 Therefore, if nucleation on an oxide is more unfavorable than

on the semiconductor substrate, selective growth can be achieved. Furthermore, the

selectivity can be increased by choosing oxides with a lower surface-site density and

lower mobility and bonding strength of adatoms.

Concerning the selective epitaxial growth of GeSn via CVD there are, up to date,

no publications. Therefore, the following section will summarize the experimental

findings of a first approach. GeSn was deposited on Si and Ge wafers with pat-

terned SiO2 on top. The trenches had widths of several µm with a depth of 30 nm

(on Si) and 40 nm (on Ge) after cleaning. The flow rates of Ge/Sn were kept con-

stant at 400 sccm/12 sccm and growth time was set to 3 min. The growth rate of

un-patterned wafers was around ∼20 nm min−1 at T = 375 ◦C. For the selectivity,

no influence of the SnCl4 flow rate was found and will, therefore, not be further

discussed.

The deposition of GeSn on structured Si at 375 ◦C shows rough layers with a thick-

ness similar to the trench height, while spherically shaped GeSn was deposited on the

oxide (Fig. 5.2a). The density of these particles varies along the sample, suggesting

an in-homogeneous deposition, and often pillow shaped structures are found only

in trenches (Fig. 5.2b). These pillows exhibit facets, which are (as the edges of the

trenches) oriented in crystallographic directions. Their growth might be initiated

by residual oxide particles on the Si surface and their shape can be explained by the

reduction of surface energy while growing on a crystal surface. This was intensively

studied in Ref. [192], where the density of overgrown oxide islands on the Si surface

79


800 nm

GeSn SiO2

Si

1 µm

(b)(a)

Figure 5.2 – (a) SEM micrograph of deposited GeSn (purple) on structured Si at375 ◦C with colored Si wafer (orange) and structured SiO2 (yellowish). (b) Top viewof the interface between trench and SiO2 from another region of the wafer.

was measured in dependence of the intentional exposure to oxygen. Particles, which

remain after wafer cleaning on SiO2, can also serve as nucleation points, impeding

the selectivity.

RBS measurements were performed on an 1 cm2 sized window in the middle of the

wafer (c.f. section A.4). The He+-ion beam was chosen to be randomly orientated to

the wafer surface and in a crystallographic direction. The ratio between the detected

Sn signals from the channeling and random direction is called χmin and indicates the

crystal quality of the layer. For the deposited GeSn an Sn content of 6.5 at.% and

χmin of ∼20 % was found, which is similar to values found for GeSn on unstructured

Si at 375 ◦C.67 Applying RBS measurements to sample regions covered completely

by oxide, amorphous GeSn was found. Therefore, except from the pronounced sur-

face roughness of GeSn in trenches, the layers exhibit a quality comparable to bulk

GeSn.

In order to achieve a higher selectivity, HCl was added into the reaction chamber

at different flow rates. HCl has an etching effect on the deposited GeSn. If the

growth rate of GeSn on Si is larger than the growth rate on SiO2, a suitable etching

rate controlled by QHCl could cause a deposition of GeSn exclusively in the trench.

Fig. 5.3 shows exemplarily SEM micrographs of samples, where GeSn was grown at

375 ◦C with QHCl = 10 sccm (Fig. 5.3a) and QHCl = 25 sccm (Fig. 5.3b). While for

80


1 µm

(b)(a) QHCl

= 25 sccmQHCl

= 10 sccm

2 µm

Figure 5.3 – SEM micrograph of the top view of trench and oxide after depositionof GeSn on Si with additional HCl precursor flow using flow rates of (a) 10 sccm and(b) 25 sccm.

lower HCl flow rates residual GeSn can be found on the oxide, a selective growth is

achieved at QHCl = 25 sccm. Unfortunately, only GeSn particles were deposited at

this flow rate. Assuming a decreased growth rate of GeSn due to HCl, the initial

stages of growth in trenches via particle formation can be assumed. Nevertheless,

by carefully adjusting QHCl and the growth time selective epitaxial growth could be

achievable.

Another parameter that can strongly influence the selectivity is the growth tempera-

ture. With decreasing temperatures, nucleation of adatoms becomes thermodynam-

ically less probable. If this effect is more pronounced at the oxide surface, SEG can

be achieved.191 In this regard, GeSn was deposited at lower temperatures. Fig. 5.4

compares the oxide-trench interface of two samples grown at 375 ◦C (Fig. 5.4a) and

365 ◦C (Fig. 5.4b). At 365 ◦C no GeSn was found on the oxide, while the trench

shows growth of GeSn particles predominantly at the oxide-trench interface. The

inset of Fig. 5.4b shows a detailed image of a GeSn island with different facets. In-

creasing the growth time from 3 min to 15 min results in a higher density of particles,

but no smooth coherent layer. Below 365 ◦C no growth of GeSn could be achieved

at all for both oxide and trench. This limitation is also found for unstructured Si

wafers and can be explained by the Ge precursor ceasing to dissociate on the ad-

sorbed semiconductor surface, as it was shown theoretically and experimentally in

81


1 µm

400 nm

1 µm

(b)(a) Tgrowth

= 375 °C Tgrowth

= 365 °C

Figure 5.4 – SEM micrograph showing the top view of trench-oxide interface of GeSndeposited on Si at temperatures of (a) 375 ◦C and (b) 365 ◦C. The inset in (b) showsa detailed micrograph of a deposited island.

Refs. [193–195]. This effect, of course, depends on the substrate material and should

be less pronounced for Ge substrates. It could be also met by increasing the reactor

pressure in the reaction chamber or a grading in the Sn content, but is left for future

work.

Structured Ge-VS were used for the growth of GeSn below 365 ◦C. During a growth

time of 3 min no GeSn was deposited. Increasing tgrowth to 10 min, however, showed

a partial coverage of the trenches with GeSn, while leaving no GeSn on the oxide.

Fig. 5.5 shows SEM micrographs of three trenches being located on a stripe of several

hundred µm in the middle of the wafer. Investigating the stripe from the left to the

right side demonstrates the different stages of epitaxial growth in the trenches. At

the beginning GeSn nuclei are created at the edge of the trench (Fig. 5.5a). Energet-

ically it is more favorable to adsorb and integrate atoms into the substrate layer on

kinks and edges, but taking into account the previous observations, the nucleation

could be catalyzed by residual oxide particles in the trench. After this initial step,

GeSn particles grow laterally (Fig. 5.5b) until a coherent and smooth layer is created

(Fig. 5.5c). The oxide-trench interface shows a certain roughness caused by oxide

fringes stemming from optical lithography. Although SEG was partially achieved,

a homogeneous growth of GeSn over the whole wafer is desired. For unstructured

Ge-VS the growth rate of GeSn is in the range of 15 nm min−1,67 which should be

82

5.3 CGeSn

1 µm 1 µm1 µm

400 nm

(c)(b)(a)

Figure 5.5 – (a,b,c) SEM micrographs of SiO2 trenches on Ge showing differentgrades of deposited GeSn on the same sample. The position of the trenches is indicatedby the structure design below the micrographs. The inset in (c) shows a detailed viewof the trench-oxide interface.

sufficient to fill all trenches of patterned Ge-VS (dtrench = 50 nm, tgrowth = 10 min).

Nevertheless, vast regions of the wafer show no deposition of GeSn. This can be

interpreted as an indication of a loading effect, which was extensively studied in

literature.196–198 The Ge-VS is mostly covered with SiO2, leaving only a small area

of Ge in trenches. The dissociative adsorption of precursor molecules is hindered at

lower growth temperatures. Besides that, the mobility of adsorbed atoms decreases,

impeding Ge and Sn atoms to reach the trench surface and nucleate. As mentioned

before, increasing the reactor pressure or implementing a wetting layer with graded

Sn content could tackle this obstacle.

5.3 CGeSn

Beside optimization of device geometry and contact design, there is a more

fundamental approach to tune laser performance, this is by the incorporation

of another element. Among the remaining group IV elements, carbon (C) was

additionally incorporated into the GeSn lattice. Group IV alloys with diluted

C atoms were vastly investigated and describe, similar to Si, another degree of

freedom to tune alloy properties.199 The main interest in using C is the reduction

83


of the lattice mismatch to Si or Ge200–202 (alat = 3.567 Å) and band engineering in

n-type MOS devices.203 Small C atoms (atomic radius of 0.91 Å) could also saturate

point defects in GeSn, which create non-radiative pathways decreasing the optical

performance. The incorporation of carbon into alloys is epitaxially challenging due

to the large lattice mismatch to Si (52 %) or Ge (59 %) and the estimated low solid

solubility of 1× 108 cm−3 in e.g. Ge.204 Still, non-equilibrium alloys were grown

with C contents of 2 at.% for CSi binaries203 and 3 at.% for CGe.205 Band structure

calculations of CSi show deep level carbon s-electron states strongly localized

around C atoms.202 They are caused by the large lattice mismatch and difference

of electronegativity between Si and C and show low coupling to Si valence band

states. In case of CGe, calculations show a splitting of the conduction band, which

decreases the bandgap at the Γ-point by 170 meV at.%−1C for xC < 1 at.%.206 A

carbon concentration of 0.78 at.% would be sufficient to turn cubic CGe into a

direct bandgap semiconductor.

In terms of efficient optoelectronic devices there are up to date no elaborate inves-

tigations on CGeSn or CSiGeSn. However, it could be shown that Sn segregation

and dislocation loops formation can be diminished by incorporating carbon.207,208

In the following a first evaluation of the growth of CGeSn will be discussed.

5.3.1 CBr4 flow rate dependence

CBr4 was used as a precursor for carbon atoms, which was delivered by a bubbler

at a temperature of 15 ◦C. In order to evaluate the influence of different amounts of

C on the growth of CGeSn, a range of 0–10 sccm was applied for the CBr4 flow rate

(QCBr4). The partial pressure ratio of Ge and Sn precursors was kept constant atpGe2H6

pSnCl4= 95, corresponding to a mass flow ratio of 250 sccm/7 sccm. Precursor gases

were introduced into the reaction chamber on a wafer kept at 375 ◦C using H2 as a

carrier gas. A 140 nm thick Ge layer was deposited at 450 ◦C as buffer layer. After

deposition of CGeSn, a ∼10 nm thick GeSn capping layer was grown on top. It

serves as a spacer between C, incorporated in CGeSn, and C surface contamination,

which can cause interference in SIMS measurements.

The growth rate and Sn content of all samples was measured by RBS and deter-

84

5.3 CGeSn

0 2 4 6 8 10

χ min (

%)

0 20 40 60 80 100

0.01

0.1

1

xC (

at.%

)

Depth (nm)

10

0.0

0.2

0.6

0.4

xC (

at.%

)0 2 4 6 8 10

QCBr4

(sccm)

QCBr4

(sccm)

QCBr4

(sccm) 0

(a)

(b)

(c)

(d)

10

20

30

40

50

70

80

90

100

S (

%) 1-χ

min,Sn

1-χmin,Ge

χmin,Sn

χmin,Ge

Figure 5.6 – χmin of Ge and Sn (a) and ratio of substitutional Sn atoms (b) of CGeSnlayers grown at 375 ◦C in dependence of the CBr4 flow rate. (c) Corresponding C con-centration profiles and average C concentration (d) derived from SIMS measurements.The blue area and dashed line indicate the thickness of the CGeSn and GeSn cappinglayers, respectively.

mined to be 19 nm min−1 (layer thickness of 55 nm) and 7.7 at.%, respectively. At a

CBr4 flow rate of 2 sccm, a χmin of 8 % is achieved, indicating a high crystal quality,

similar to the GeSn reference. Interestingly, with increasing QCBr4 the χmin of Ge

and Sn increases but at different rates (Fig. 5.6a). χmin,Ge and χmin,Sn show maximal

values of 28 % and 45 %, respectively, indicating a general decrease of the crystal

quality. The ratio S, given by 1−χmin,Sn

1−χmin,Ge, describes the amount of substitutional Sn

atoms on Ge lattice sites. It decreases to values of 76 % at QCBr4 = 10 sccm, vali-

dating the displacement of Sn atoms from lattice sites (Fig. 5.6b).

In order to extract information about the incorporated carbon concentration, SIMS

measurements have been performed. The SIMS profiles of carbon show a strong

increase of the C concentration for all CGeSn samples within the range of ∼10 nm

close to the Ge-CGeSn interface (depth of 60–70 nm), before it increases smoothly

(Fig. 5.6c). This behavior has also been observed for Si in SiGeSn and can be ex-

plained phenomenologically by different growth rates of GeSn and SiGeSn.46,144 At

an atomistic level, the rivaling processes of C incorporation and segregation might

cause this observation. While carbon atoms are incorporated into the Ge lattice with

85


0 20 40 60 80 100

1017

carr

ier

conc. (c

m-3)

Depth (nm)

1020

1019

1018

10

QCBr4

(sccm) 0

0 2 4 6 8 10Q

CBr4 (sccm)

1017

avg. carr

ier

conc. (c

m-3)1020

1019

1018

(a) (b)

Figure 5.7 – (a) Depth profile of background carrier concentration of CGeSn(Tgrowth = 375 ◦C) for different flow rates of CBr4. The blue area and dashed lineindicate the thickness of CGeSn and GeSn capping layer, respectively. (b) Corre-sponding average background carrier concentration.

increasing thickness, on the contrary, the concentration of C atoms on the surface

increases until it saturates. An equilibrium between both processes is established

and the C concentration remains constant. In this regard, the incorporation of C

would be governed by similar growth kinetics as Sn in GeSn.44,209

The capping layer shows only a slight decrease of the C concentration, which can

be explained by C segregation (Fig. 5.6c). This is supported by the increase of

the C concentration in the capping layer at elevated precursor flows. The carbon

signal of the reference is related to contamination in the SIMS measurement tool

and, therefore, describes a lower detection limit for C. Average C concentrations

of 0.04 at.% (5× 1019 cm−3) for QCBr4 = 2 sccm and 0.41 at.% (1.7× 1020 cm−3) for

QCBr4 = 10 sccm can be extracted (Fig. 5.6d).

Since the incorporation of C has a significant influence on the crystal quality, it is

reasonable to also assume an impact on the defect density. To address this parameter

electrochemical capacitance-voltage (ECV) profiling was performed. This technique

allows for the determination of the charge carrier density by CV measurements across

the Schottky barrier of a semiconductor-electrolyte interface.210 The electrolyte is

also used to etch well defined thicknesses of the layer, allowing the measurement of

a depth-dependent concentration profile. For ECV measurements of GeSn, however,

86

5.3 CGeSn

only qualitative conclusions can be drawn, since for low bandgap semiconductors an

early onset of the inversion region occurs,121 inhibiting a reliable determination of

quantitative values. The utilization of ECV for defect investigation of unintention-

ally doped GeSn layers is enabled by defects creating charge carriers. The impact of

defects in GeSn on electrical properties was extensively studied.211–215 Point defects

(e.g. vacancies) in the bulk of the layer and dislocations at the substrate interface

cause deep- and shallow-level states in the bandgap,211–213 which behave similarly to

acceptor background doping and increase the hole concentration.214,215 Measuring

the ECV profile of unintentionally doped GeSn enables a qualitative investigation

of these defects in GeSn, as has been demonstrated in Ref. [67].

Fig. 5.7a shows the measured profiles of CGeSn at different CBr4 flow rates. Starting

at the Ge-CGeSn interface (depth of ∼60 nm) a general gradual increase of the back-

ground carrier concentration becomes visible, reaching a maximum around 20 nm

below the surface before weakly decreasing in the capping layer for QCBr4 > 2 sccm.

Obviously, the incorporation of C into GeSn increases the carrier concentration.

Compared to the GeSn reference, an increase of the average background carrier con-

centration of more than one order of magnitude at QCBr4 = 10 sccm is measured

(Fig. 5.7b). This is in accordance with the increasing χmin measured by RBS. High

amounts of C displace Sn atoms from lattice sites, increasing the defect density and

decreasing the crystal quality of CGeSn. A saturation or termination of point de-

fects by carbon atoms, therefore, does not occur in the range of applied CBr4 flow

rates.

XRD measurements were also performed, investigating the lattice constants of

CGeSn. All layers show to be coherently grown on Ge, without a hint of strain

relaxation. Within the range of error, in-plane and out-of-plane lattice constants of

5.66 Å and 5.76 Å, respectively, were found for all samples. Θ − 2Θ measurements

of samples grown at QCBr4 = 2 sccm and QCBr4 = 10 sccm show no influence of C on

strain (Fig. 5.8a). Still, a broadening of the peak related to GeSn becomes visible for

samples grown at QCBr4 = 10 sccm, caused by a decreasing crystal quality. This is in

accordance with results from RBS measurements. In order to evaluate how much C

has to be incorporated to measure a strain releasing effect, strain calculations have

been performed of CGeSn on Ge for different C and Sn contents using Vergard’s law

(Fig. 5.8b). An increase of strain with increasing xC of 0.37 % at.%−1C is extracted,

87


62 64 66 68 70 72

Inte

nsity (

a.b

.)

2Θ (°)

(a)

0.0 0.2 0.4 0.6 0.8 1.0

-3

-2

-1

0

ε || (

%)

C content (at.%)

2 sccm

QCBr4

10 sccm12 at.%

8 at.%

4 at.% Sn(b)

16 at.%

20 at.%

GeSi

CGeSn

Figure 5.8 – (a) XRD Θ−2Θ scans of CGeSn with CBr4 flow rates of 2 sccm (orangegraph) and 10 sccm (blue graph). (b) Calculated strain of CGeSn on cubic Ge fordifferent C and Sn contents.

which causes a strain release of 0.04 % when xC increases from 0 at.% to 0.1 at.%.

Within this range of achievable C contents an advantage concerning strain release is

doubtful. Since the crystal quality decreases and background doping substantially

increases at CBr4 flow rates above 2 sccm, CGeSn layers grown at this flow rate will

be discussed in the following.

5.3.2 Temperature dependence

CVD growth kinetics is strongly temperature dependent. Hence, a deeper under-

standing is obtained when growing alloys at different temperatures. In this regard

CGeSn alloys were grown at temperatures in the range of 350–400 ◦C and a CBr4

flow rate of QCBr4 = 2 sccm. The layer structure was the same as for the flow series

above, using Ge buffers and GeSn capping layers. GeSn reference layers without the

introduction of CBr4 were grown at each temperature.

Fig. 5.9a juxtaposes the incorporated Sn content (red squares) and growth rate

(green squares) of CGeSn in dependence on growth temperature. Starting from a

growth rate of 22 nm min−1 and an Sn content of 5 at.% at 400 ◦C, the growth rate

decreases to 12 nm min−1, concomitant with an Sn content increase to 11 at.% at

350 ◦C. This observation is in accordance with results from Refs. [44, 46, 48], where

the weakening of the surfactant effect of Sn atoms and lower reactivity of Ge2H6

88

5.3 CGeSn

350 360 370 380 390 4000

5

10

χ min (

%)

T (°C)

4

6

8

10

12

xS

n (

at.%

)

10

15

20

25

gro

wth

rate

(nm

/min

)

0.01

0.1

1

xC (

at.%

) x

C (

at.%

)

0 20 40 60 80 100Depth (nm)

350 360 370 380 390 400

T (°C)

(a)

(b)

(c)

(d)

Ge

Sn

ca

pp

ing

T=400°C

T=350°C

0.04

0.08

0.12

Figure 5.9 – Sn content/growth rate (a) and χmin (b) of CGeSn grown at differenttemperatures. Corresponding SIMS profiles (c) and average C content (d).

with decreasing growth temperature is held responsible for the increase of Sn con-

tent. χmin values below 11 % are achieved for all samples with a substitutionality of

∼100 % reflecting a high crystal quality at the investigated temperature range and

C precursor flow (Fig. 5.9b). Within the range of error, the same values for the Sn

content, growth rate and crystal quality were found for reference samples, showing

no significant influence of CBr4 on growth.

As for the flow rate series, SIMS measurements were performed to determine the

C content. Fig. 5.9c shows the derived C concentration at different temperatures.

Similar to the profiles shown in Fig. 5.6c, a steep increase of the C concentration

occurs at the GeSn-Ge interface, before a smooth increase prevails. The increase at

the initial stage of growth is less pronounced at low temperatures and becomes im-

perceptible at a growth temperature of 350 ◦C. For a growth temperature of 400 ◦C,

however, the C content grading extends over a range of more than 30 nm, before

saturation occurs. As argued before, this can be understood by the competing pro-

cesses of C incorporation and segregation. At higher temperatures it takes longer to

saturate the surface C concentration, due to a higher growth rate. With decreasing

temperature/growth rate, a saturation is, therefore, achieved earlier. The temper-

ature behavior, additionally, indicates that, similar to Sn in Ge, carbon acts as an

89


350 360 370 380 390 400

T (°C)

1017

1020

1019

1018

0 20 40 60 80 100

carr

ier

conc. (c

m-3)

Depth (nm)

T=400°C

T=350°C

avg. carr

ier

conc. (c

m-3)(a) (b)

Ge

Sn

ca

pp

ing

GeSn

CGeSn

1017

1018

1019

Figure 5.10 – ECV depth profiles (a) and corresponding average background carrierconcentration (b) of CGeSn and GeSn grown at different temperatures.

surfactant for the incorporation of Ge surface atoms into the bulk layer.44 With

decreasing temperatures, the exchange of Ge surface atoms with bulk C atoms is

hindered, which increases the incorporation of C atoms.209

The carbon profile of the capping layer also shows a different behavior for high and

low temperatures. While for low temperatures a decrease of the C content is mea-

sured, this decrease is absent at high temperatures showing a continuous increase.

The residual C in GeSn cappings, grown at high temperatures, could stem from

segregation of C atoms from CGeSn layers.

Extracting the average C content from these profiles shows a weak increase of the

C concentration with decreasing growth temperature. The average carbon content

is 0.05 at.% at 400 ◦C and doubles to 0.1 at.% at 350 ◦C. In this work, a similar

temperature dependence of the Sn content in GeSn is found, and Ref. [203] shows

an increasing C content at lower temperatures, but using SiCH6 as a C precursor.

Calculations of the directness, using the C dependence of the direct and indirect

bandgap of CGe derived in Ref. [206], show an increase from−64 meV to 16 meV with

decreasing temperature. Therefore, potentially a direct bandgap can be achieved for

CGeSn at low temperatures, even for layers pseudomorphically grown on Ge. This is

in strong contrast to the results obtained for coherently grown GeSn, where 20 at.%

Sn is needed to achieve a direct bandgap (c.f. Fig. 2.3b in subsection 2.1.1).

In order to extract information about the temperature dependence of the defect

90

5.3 CGeSn

density, ECV profiles were measured. Fig. 5.10a shows the measured carrier con-

centration profiles, which show a similar behavior to profiles measured by SIMS.

Again, a lower background doping is found in the GeSn capping. Strikingly, the

average background doping reveals no obvious temperature dependence (squares in

Fig. 5.10b) within the range of errors. On the contrary, the GeSn reference samples

exhibit a significant increase of the carrier concentration with decreasing temper-

ature. But since this Sn related effect is several times smaller than for CGeSn,

the background carrier concentration is dominated by defects introduced by the

incorporation of C.

5.3.3 Interpretation of CGeSn epitaxy

The above presented investigation gives first insight into the growth of CGeSn. This

new ternary has to be investigated in more detail to extract reliable conclusions

about growth kinetics. Yet, there are some similarities to GeSn epitaxy. A recent

study of the growth kinetics of GeSn (using GeH4 as a Ge precursor) states that

the main processes influencing growth occur in the gas phase and on the surface but

of different relevance for each precursor.195 While the growth rate of Ge is mostly

determined by adsorption, diffusion and surface reactions, SnCl4 seems to undergo

important gas phase reactions (using hydrogen as an carrier gas), before reacting

with Ge radicals on the surface. Here, reactive intermediates containing Ge, Cl and

H are created, describing key elements for the incorporation of Sn.

Since in this work hydrogen was also used as an carrier gas, it is not far-fetched to

assume similar chemical processes between Ge2H6 and SnCl4 and Ge2H6 and CBr4,

with SnCl4 and CBr4 both containing constituents from group IV and group VII.

From the above results, a deterioration of the crystal quality and Sn substitutional-

ity at high CBr4 flow rates was found in CGeSn, suggesting competitive processes

between SnCl4 and CBr4. In the flow rate series, the partial pressure ratio of CBr4

and SnCl4 was varied from 0.44 to 2.18. Along with a bonding energy of 285 kJ mol−1

for C-Br and 323 kJ mol−1 for Sn-Cl,216 the amount of precursor molecules and re-

active potential of CBr4 is similar to SnCl4. Competing gas phase reactions of the

two precursors seem, nevertheless, rather unlikely, since for all CBr4 flows (and no

flow at all) the same Sn content was found in CGeSn. Therefore, it can be assumed

91


that the number of Sn containing molecules adsorbed on the surface and being in-

corporated in the layer seems to be constant.

Above QCBr4 = 2 sccm, the number of Sn atoms on non-substitutional lattice sites

increases. Along with an increase of incorporated C at elevated QCBr4, a clustering

of Sn atoms on non-substitutional lattice sites might be caused. Hence, competitive

surface reactions of C and Sn containing molecules (carbon acting as an surfactant)

impeding the incorporation on Ge lattice sites might be dominating at high CBr4

flow rates. This is also in agreement with ECV measurements showing an increase

of the background carrier concentration with increasing C precursor flows. A satu-

ration of C atoms in CSi on substitutional lattice sites at high precursor flows was

observed in Ref. [203]. Assuming a similar behavior for CGeSn at CBr4 flow rates

exceeding flow rates that cause a saturation of C in GeSn, could explain an increase

of the defect density with excess C atoms.

QCBr4 = 2 sccm describes an approximately maximal precursor flow rate (using the

above growth conditions), at which C and Sn atoms are still incorporated on lattice

sites. Therefore, no temperature dependence of the crystal quality at this flow rate

was found. What is noteworthy is the increase of the C content with decreasing tem-

perature. The doubling of both the C and Sn content could support the concept of

CBr4 behaving similarly to SnCl4 as an surfactant for the incorporation of Ge atoms.

The precipitation of C atoms to the capping layer is hindered by a lower thermal

energy. Growth at e.g. constant low temperatures and different Sn precursor flows

are needed to clarify the validity of these assumptions.

5.4 Summary

In this chapter, several approaches to optimize optical devices were investigated. At

first, an MQW design for electrically pumped lasers was introduced, where contact

layers show a smooth grading of B/P atoms towards the active layer. B and P

concentrations of, respectively, ∼3× 1018 cm−3 and ∼6× 1018 cm−3 are found with

a doping grading of 3× 1016 cm−3 nm−1 and 1× 1017 cm−3 nm−1. The aim of this

approach is to separate the active layer from highly doped regions, which degrade

the optical performance.

As a second approach the selective epitaxial growth of GeSn was achieved, which

92

5.4 Summary

could be utilized in sophisticated micro chip designs. In this regard, GeSn was de-

posited on structured Si and Ge substrates with SiO2 trenches. The growth on Si

at 375 ◦C shows no selectivity and an occurrence of pillow shaped GeSn structures

in trenches, probably stemming from residual oxide serving as nucleation points.

The Sn content, crystal quality and growth rate is found to be comparable to GeSn

deposited on blanket Si wafers (c.f. section A.4). If HCl is additionally added, the

selectivity increases due to an in-situ etching component, hindering the deposition

of GeSn on SiO2 and also on Si. Still, although no GeSn is found on the oxide

at QHCl = 25 sccm, only GeSn particles are grown in trenches. Therefore, a more

precise evaluation of the optimal HCl flow rate is needed. Another parameter highly

influencing growth conditions, is the growth temperature. When it decreases down

to 365 ◦C similar results as for increased HCl flows are found. While no GeSn is

deposited on the oxide, GeSn islands are found in trenches. Even for growth times

of 15 min the same results are achieved, showing strong evidence, that the cracking

of adsorbed Ge2H6 precursors is impeded. This can be met by the use of patterned

Ge-VS, which allows for SEG at lower temperatures. This approach enabled the de-

sired selectivity on small regions of the wafer, while huge regions show no deposition

of GeSn at all indicating the obstacle of an efficient surface wetting due to loading

effects. In principle, it could be shown that SEG of GeSn is possible.

A more fundamental approach to tune the device performance is the incorporation

of C into GeSn. Metastable CGeSn alloys were grown at 375 ◦C on Ge buffer layers

using the precursor CBr4 with C contents of 0.04 at.% to 0.41 at.% exceeding the

solid solubility of C in Ge. High crystal quality is achieved at flow rates of 2 sccm,

while for higher flow rates the crystal quality decreases, showing a decrease of the

substitutionality of Sn atoms on lattice sites down to 76 % at QCBr4 = 10 sccm.

The loss of high crystal quality with increasing C precursor flow is also reflected in

ECV measurements, where a substantial increase of the background carrier density,

associated with defects, is found for QCBr4 > 2 sccm. At sufficiently low flow rates

the corresponding C content will hardly cause a strain relaxation of GeSn layers,

as shown by strain calculations where the lattice constant was determined by Ver-

gard’s law. In order to investigate the temperature dependence of CGeSn growth,

samples were grown in the temperature range of 350–400 ◦C at QCBr4 = 2 sccm.

With decreasing temperature a doubling of Sn and C content from 5/0.05 at.% to

93


11/0.10 at.% is achieved. A decrease of the growth rate with temperature is found,

while maintaining a high crystal quality. First band structure calculations predict a

direct bandgap for coherently grown CGeSn on Ge at 350 ◦C, predicting a strong in-

fluence of C on the directness. From ECV measurements no influence of the growth

temperature on the background carrier concentration is found. A comparison with

GeSn reference samples reveals that the defect density of CGeSn is dominated by

the incorporation of carbon. These first experiments indicate that carbon acts as an

surfactant for the incorporation of Ge atoms. It, therefore, behaves similar to Sn,

and might hinder the incorporation of Sn. More detailed investigations are needed

for future work.

94

6 Conclusion and Outlook

Within the scope of this thesis, several paths were formulated to optimize optoelec-

tronic devices based on group IV semiconductors. By employing both theoretical

and experimental tools, the evaluation of several aspects of lasers was performed,

from different perspectives. Employing GeSn as active material, basic material prop-

erties were investigated starting from bulk layers, moving on to quantum structures

like GeSn/SiGeSn multi quantum wells (MQWs) and finally arriving at quantum

dots (QDs). Benefits and limitations due to quantization effects were studied. The

range of material properties can be extended by adding carbon into GeSn. In this

respect, epitaxial growth of the almost unexplored ternary CGeSn was investigated.

As a first step towards electrically pumped devices, contact layer designs were in-

troduced, exhibiting monolithically integrated contacts with graded doping profiles.

As an additional key factor for group IV optoelectronic circuits, selective epitaxial

growth (SEG) of GeSn cavities was studied. The main achievements will be sum-

marized in the following.

Band structure calculations for bulk GeSn (0–20 at.% Sn) were performed investi-

gating strain and composition dependence of bandgap, effective mass and the offsets

between L and Γ valleys ("directness"). Considering experimental constraints, high

directnesses (200 meV) and a large range of accessible wavelengths was found. By

applying strain to GeSn the effective masses undergo strong changes. Especially for

the valence band, high tensile strain at low Sn contents can cause a similar, large

density of states of HH and LH bands.

Lasing material properties were evaluated by gain calculations taking into account

losses from free carrier processes. Material gain maxima of up to 8200 cm−1 were

found, being predominantly limited by inter-valence band absorption and free car-

rier absorption coming from conduction band intervalley scattering and valence band

scattering. A decrease of the material gain was found for high Sn content GeSn with

95


small bandgaps, caused by band mixing of the conduction and valence band at the

Γ-point.

High directnesses, while avoiding band mixing effects, could be demonstrated from

low Sn content GeSn under tensile strain. GeSn layers with an Sn content of 6 at.%

were grown via CVD and processed into microdisks. Tensile Strain was applied by

an SiNx stressor, followed by Photoluminescence (PL) measurements. Compared to

unprocessed bulk layers, the PL signal shows a strong redshift and increase of inten-

sity. Modeling of the microdisk PL gives a tensile strain of 1.45 %, sufficient to turn

GeSn into a direct bandgap semiconductor. The experimental findings motivated a

theoretical investigation of the achievable gain in low Sn content GeSn. It was found

that at a constant directness higher gain values can be achieved for low Sn content

GeSn, due to its favorable band structure properties. With an increased thermal

budget concerning processing, and lower defect densities due to higher thermal sta-

bility, low Sn content GeSn under tensile strain is very interesting as a laser material.

Future experiments should, therefore, demonstrate lasing from these structures.

As an potential barrier material, SiGeSn ternaries with Si contents up to 10 at.%

were theoretically investigated. For coherently grown SiGeSn on GeSn buffers the

Si content induced increase of the bandgap and directness of 120 meV and 130 meV

was calculated. These findings, and experimental investigations of GeSn/SiGeSn

heterostructures, motivated an evaluation of material parameters to find optimal

carrier confinement. Here, Ge1−xSnSnxSn

/Si0.10Ge0.91−xSnSnxSn−0.01 MQWs were sug-

gested, promising high Γ valley offsets (∼200 meV) at high directnesses. For well

thicknesses below ∼30 nm, quantization effects cause a significant decrease of direct-

ness and valence band offsets. For optimized GeSn/SiGeSn MQWs high material

gain (1470 cm−1) was found at threshold injection carrier densities of 6× 1017 cm−3.

By including moderate n-type doping concentrations, an increase of gain (decrease

of threshold current density) is induced. However, for higher injection carrier den-

sities losses from inter-valley absorption threaten to severely degrade the gain. The

feasibility of the here proposed heterostructures remains to be demonstrated by ex-

periments.

Within quantum nano-structures, QDs were also investigated. Sn-rich GeSn crys-

tallites were found by annealing of GeSn single quantum wells (SQWs) embedded

in Ge. By investigating the morphology and material composition, an average Sn

96

content of 30 at.% was found. Strong evidence was given for clustering of point

defects and vacancy-mediated diffusion of Sn into defect clusters. Moreover, several

crystalline phases can be assumed in apparently incoherently embedded precipitates.

The controlled generation of GeSn QDs, using this approach, seems unlikely.

Therefore, calculations for pseudomorphically grown GeSn QDs in an SiGeSn

matrix were performed, delivering an achievable carrier confinement in direct

bandgap GeSn QDs. For hydrostatic and biaxial deformations of the QD lat-

tice and similar material composition constraints as for GeSn/SiGeSn MQWs,

Ge1−xSnSnxSn

/Si0.10Ge0.92−xSnSnxSn−0.02 heterojunctions were found to show maximal

carrier confinement. Γ valley offsets of up to 110 meV were calculated at high QD

directnesses. The strong quantization effect in QDs also allows for the implementa-

tion of high Sn content GeSn, where non-zero bandgaps can be achieved. In future

work, calculations for QDs with a pyramidal shape and an Sn gradient towards the

matrix could provide a more detailed understanding.

With the theoretical demonstration of carrier confinement in GeSn QDs the range

of laser designs of group IV materials can be widely extended. A common concept

is the implementation of QDs in MQWs and nano wires.217,218 This design can be

achieved by exploiting the Stranski-Krastanov growth mode. By stacking QDs in

higher bandgap wells or wires, serving as a barrier material, a high density of dots

can be achieved. The here presented calculations can give guidelines for further

experiments.

As the last point, an insight into several key aspects of optimized laser designs was

provided. GeSn/SiGeSn MQW light emitting diodes (LEDs) were epitaxially grown

using boron and phosphorous doped bottom and top contact layers. In order to

spatially separate the optically active MQW region from the highly doped regions,

a concentration gradient towards the MQW was implemented. This design could

significantly improve the optical performance of MQW lasers, which needs to be

verified experimentally.

The first GeSn SEG growth was presented for structured Si and Ge substrates. Thin

GeSn layers were grown at different temperatures and by adding HCl into the re-

action chamber. Inside the trenches pillow shaped structures were observed, which

could stem from residual oxide particles serving as nucleation points. An investiga-

tion using APT or SIMS, in order to verify this hypothesis, and an optimized wafer

97


cleaning process is, therefore, needed. At low temperatures no growth of GeSn on

structured Si substrates could be found due to ceasing of Ge growth. By replacing

Si substrates with Ge-VS, selective epitaxial growth is achieved. However, a large

part of the wafer seems to suffer from loading effects. In order to guarantee a ho-

mogeneous growth, an optimization of the growth parameters is needed by e.g. an

initial growth of a wetting layer, a grading of the Sn content and an increase of the

reactor pressure.

The difficulty to achieve smooth layers could also be exploited for the growth of GeSn

dots on patterned substrates.219 A thorough tuning of growth parameters and oxide

pattern could allow for the growth of GeSn islands at controlled densities across the

wafer. As a next step, SEG of doped GeSn and SiGeSn needs to be evaluated to

harness the full potential of this technique for photonic circuits.

As a last point of this thesis, the epitaxial growth of the hardly investigated ternary

CGeSn was discussed. C contents from 0.05 at.% to 0.10 at.% were achieved, while

maintaining high crystal quality. The growth kinetics of CGeSn was investigated at

different growth temperatures (350–400 ◦C) and flow rates of the carbon precursor

CBr4. For high flow rates, the substitutionality of Sn atoms is strongly decreased and

no strain relaxation effect was detected for the amount of C incorporated. With de-

creasing temperatures, a twofold increase of the C and Sn content was found, where

initial calculations of the bandgap predict a direct bandgap for structures grown

at low temperatures. The incorporation of carbon causes a strong increase of the

defect density in GeSn, indicating a competing incorporation of Sn and C atoms

(carbon acting as an surfactant). More experiments are needed to obtain detailed

information about growth kinetics. In this regard, lower CBr4 flow rates could lead

to a weaker impact on the defect density. Enabling APT measurements could re-

veal the distribution and possible clustering of C or Sn atoms. The growth of thick

CGeSn layers with subsequent PL measurements could provide information about

the influence on the optical performance and band structure. However, group IV

photonics could strongly benefit from CGeSn ternaries.

In summary, the investigated approaches promise an improved performance of GeSn

optoelectronic devices. A large range of wavelengths can be obtained with high ma-

terial gain suitable for use in e.g. sensor systems and biochemical applications. With

this foundation set, a path is opened for a variety of experiments and investigations.

98

A Appendix

A.1 Band alignment calculation of SiGeSn heterostructures

Every calculation result presented in this work is based on calculations of bulk band

energies using elemental band energies of Si, Ge and Sn, as described in section 2.1.

These have been used for band alignment optimization (chapter 3) and 8-band k · pcalculations as it is described in chapter A.2.

Band alignment calculations are strongly dependent on the reference energy, in this

work being the average valence band energy Ev,avg (Fig. A.1, dashed line). This

reference was calculated using the theoretical framework of Ref. [137], from which

Ev,avg for SixSiGe1−xSi−xSn

SnxSncan be extracted to:

Ev,avg = −0.48 eV · xSi + 0.69 eV · xSn. (A.1)

It should be pointed out that Ev,avg from Ref. [137] is derived using a very sim-

ple analytical expression containing the band gap, lattice constant and plasma fre-

quency. In contrast to this, there are publications using sophisticated ab-initio cal-

culations to derive expressions for Ev,avg.45,220 Nevertheless, the differences in band

energies and band discontinuities are insignificant, as shown in Fig. A.2. Chang-

ing the Sn content from 0 to 20 at.% in unstrained GeSn causes differences in the

band energies of maximally 35 meV (Fig. A.2a). To investigate the influence on

band discontinuities using different models for Ev,avg, band offsets for conduction

and valence bands were calculated and presented in Fig. A.2b. For that purpose a

Ge0.84Sn0.16/SixSiGe0.84−xSi

Sn0.16 double heterostructure with a constant barrier/well

Sn content of 16 at.% and Si contents from 1 to 10 at.% for barriers were used. The

barriers were assumed to be pseudomorphically grown on the unstrained wells. Here,

I

A Appendix

Γ

Eg,barrier

Eg,well

HH

LH

SO

Ev,avg

Ev,top

(unstr.)

Ev,top

(strained)

VΓ

Figure A.1 – Schematic representation showing the necessary parameters to deter-mine band alignment between SiGeSn heterostructures. A detailed description of eachstep to determine band discontinuities Vi can be found in the text.

0 2 4 6 8 10 12 14 16 18 20

0.0

0.2

0.4

0.6

0.8

Energ

y(e

V)

Sn content (at.%)

ε|| = 0 %

Ref. 45Ref. 136 Ref. 217

EL

EΓ

Ev

0 2 4 6 8 10

0

40

80

120

160

200

V (

meV

)

Si content (at.%)

Ge0.84

Sn0.16

/SixSi

Ge0.84-xSi

Sn0.16

VL

VΓ

VHH

VLH

VL VΓ

VHH

VLH

ε||,well

= 0 %

a|| = a

sub

(b)

Figure A.2 – (a) Sn content dependent band energies of unstrained GeSn and (b)band discontinuities for Ge0.84Sn0.16/SixSi

Ge0.84−xSiSn0.16 heterostructures using dif-

ferent valence band offset model from Ref. [137], Ref. [220], Ref. [45]

II

A.1 Band alignment calculation of SiGeSn heterostructures

differences in band discontinuities of around 10 meV are calculated. Due to the fact

that all models lack the support of experimental evidence and the influences on band

energies and discontinuities being negligible, in this work the model presented by

Ref. [137] was used.

Once the average valence band energy Ev,avg is calculated, the top valence band en-

ergy Ev,top for an unstrained alloy (yellow line in Fig. A.1) can be calculated using

the spin-orbit splitting ∆SO, with parameters listed in table A.2:

Ev,top = Ev,avg +∆SO

3, (A.2)

∆SO = ∆SO,Ge · xGe + ∆SO,Si · xSi + ∆SO,Sn · xSn.

In the absence of strain the HH- and LH band edges are equal to the valence band top

energy Ev,top, they are degenerate (right side of Fig. A.1). If the lattice constant a0

of a layer, wire or dot shaped crystal is different from the underlying or surrounding

lattice constant asub, strain is induced into the semiconductor. The displacement

u of atoms on lattice sites can be described by a second rank tensor ε with the

corresponding elements εij:135

ε =

εxx εxy εxz

εxy εyy εyz

εxz εyz εzz

, (A.3)

εij =12

(

δui

δxj

+δuj

δxi

)

.

In Eq. A.3 the x,y-directions ([100] and [010]) lie horizontally to the surface (here

the (001)-plane), while the [001]- or z-direction points perpendicular to the surface.

If there is no shear strain deforming the lattice and the substrate is oriented in the

[001] direction, the components where i 6= j are 0. The remaining tensor components

εxx, εyy and εzz stretch the lattice in the x-,y- and z directions respectively and can

III

A Appendix

be defined for the biaxial and uniaxial case using elastic constants C11 and C12 as:135

εxx =a|| − a0

a0

= εyy = ε||,

εzz = − (2C12/C11) εxx = ε⊥ (biaxial), (A.4)

εxx = −εzzC12

C11 + C12

(uniaxial),

where a|| is the strained lattice constant and a0 is interpolated using elemental lattice

constants and bowing parameters (table A.1):

a0 = a0,Ge ·xGe+a0,Si ·xSi+a0,Sn ·xSn+bSiGe ·xSi (1− xSi)+bGeSn ·xSn (1− xSn) . (A.5)

Applying tensile or biaxial strain lifts the degeneracy of HH- and LH bands edges at

the Γ-point. This causes a deviation of EHH/LH from Ev,top for the unstrained case,

so that a new valence band top can be defined (dashed yellow line in Fig. A.1). An

energy term δE is added to the conduction- and valence bands using the deformation

potentials given in table A.1:221–223

δEΓ = ac (2εxx + εzz) ,

δEL = aL (2εxx + εzz) ,

δEvb = av (2εxx + εzz) , (A.6)

δEHH = bv (2εxx − εzz) ,

δELH/SO = −δEHH −12

(

∆SO + δEHH ∓√

(∆SO + δEHH)2 + 8δE2HH

)

.

In the last equation the "-" sign is applied to ELH, while for ESO the expression in

the square root is added to the first terms. For strained SiGeSn the valence band

top is now described either by the HH or LH band edge. For ε|| < 0 (compressive

strain), the HH band edge is the top valence band, while for ε|| > 0 (tensile strain)

it is vice versa. Adding the bandgaps of Γ- and L bands (Eq. 2.1) to the valence

band top, gives the conduction band edge energies EΓ and EL, so that the band

IV

A.2 8-band k · p calculations

Table A.1 – Parameters used in this work to interpolate conduction and valence bandenergies.

Parameter Si Ge Sn SiGe GeSn SiSn

alat, blat [Å] 5.4307 a 5.6579 a 6.4890 a 0.026 b −0.041 c 0bΓ,0K [eV] 0.21 d 2.24 e 3.915 d

dΓ [eV/K] 0 −4× 10−4 e 0bL,0K [eV] 0.335 d 0.89 f 2.124 d

dL [eV/K] 0 −7× 10−4 f 0αVarshni,Γ [eV/K] −3.91× 10−4 g −5.82× 10−4 g 0βΓ [K] 125 g 296 g

αVarshni,L [eV/K] −4.774× 10−4 g −4.774× 10−4 g 0βL [K] 235 g 235 g

C11 [GPa] 165.77 h 128.53 h 69 h

C12 [GPa] 63.93 h 48.26 h 29.3 h

a Ref. [224] b Ref. [94] c Ref. [43] d Ref. [61] e Ref. [67] f Ref. [225] g Ref. [37]h Ref. [36]

discontinuities Vi of all bands of interest can be calculated (Inset in Fig. A.2):

VΓ = EΓ,barrier − EΓ,well,

VL = EL,barrier − EL,well, (A.7)

VHH = EHH,well − EHH,barrier,

VLH = ELH,well − ELH,barrier.

The temperature dependence of bandgaps was calculated using Varshni’s equation.

The Varshni parameters of Sn could not be found in the literature and were set to

0 eV K−1. For the range of Sn contents used here, the error should be small.


A.2.1 Bulk semiconductors

The effective masses presented and used in this work were calculated using the

8-band k · p method. This perturbation method was originally developed by Lut-

tinger and Kohn226 and extended to eight bands by Pidgeon and Brown.227 Bahder

V

A Appendix

applied its framework to zinc blende and diamond crystal lattices,228,229 which will

be briefly described in the following section. The state of a single charge carrier in

a semiconductor can be described by the time-independent Schrödinger equation:

HΨ = EΨ, (A.8)

where Ψ describes a wave function corresponding to the Eigenenergy E. The Hamil-

tonian H of an unstrained crystal228 is defined, using the free-electron mass m0, the

speed of ligth c and the reduced Planck constant h =h

2π, as:

H =p2

2m0

+ V (x) +h

4m20c

2(∇V (x))× p · σ. (A.9)

The first two terms describe the kinetic energy with the momentum operator p and

the periodic potential energy V (x), while the last term represents the spin-orbit

interaction with the Pauli matrices σ:

σx =

0 1

1 0

, σy =

0 −ii 0

, σz =

1 0

0 −1

. (A.10)

Since the k · p method describes the state of a single particle, all particle-particle

interactions are expressed in the effective potential V (x). The state of e.g. an

electron with wave vector k in a periodic potential can be described using Bloch’s

theorem, in which unk (x) is called the periodic Bloch function:

Ψ = unk (x) eikx (A.11)

The periodicity is defined by the crystal lattice constant. Inserting Eq. A.11 into

Eq. A.8 and rearranging terms, gives the following Hamiltonian with the k · p term

giving this method its name:

H = H0 +Hk +Hk·p +Hs.o. +H ′s.o., (A.12)

VI


with each term being:

H0 =p2

2m0

+ V (x) ,

Hk =h2k2

2m0

,

Hk·p =h

m0

k · p, (A.13)

Hs.o. =h

4m20c

2(∇V (x))× p · σ,

H ′s.o. =

h2

4m20c

2(∇V (x))× k · σ.

With the above Hamiltonian, the band structure can be calculated over the whole

Brillouin zone using an infinite or sufficient high number of bands. For the majority

of semiconductors, the valence band top is at the center of the Brillouin zone (Γ-

point), while the conduction band bottom may be at Γ-, L-, or close to X-points.

The strongest optical activity (especially in direct bandgap materials) comes from

electron transitions ("vertical transitions" in the k space, with absorption or emission

of a single photon) between the valence and conduction band, taking place between

states with small wave vectors, around Γ. In such cases the band dispersion can

be sufficiently accurately calculated using the perturbation approach around the

Γ-point, k = 0 Å−1

. According to the Löwdin second order perturbation theory,

the normalized interaction matrix Umn can be defined to achieve an Eigenvalue

problem:230

Umn = Hmn +B∑

α

HmαHαn

E − Eα

. (A.14)

The first term considers only the set of relevant states (class A states), which can be

attributed to a certain degree to s-like orbitals (Γ-electron states) and p-like orbitals

(x,y,z for HH-, LH- and SO-holes), while the second term describes the influence of

remote bands (class B states) on class A states. In summary, using the notation

chosen in Ref. [231] this gives, considering spin-up (↑) and spin-down (↓), a set of 8

Bloch states:

|s ↑〉, |x ↑〉, |y ↑〉, |z ↑〉, |s ↓〉, |x ↓〉, |y ↓〉, |z ↓〉 (A.15)

VII

A Appendix

To diagonalize the Hamiltonian Umn at k = 0 Å−1

, it is common to use the basis of

the total angular momentum, employing the Td point group irreducible representa-

tion where Γ6 describes the conduction band, Γ7 the SO bands and Γ8 the LH and

HH bands.228 The basis states are:159

|1〉 = |12,−1

2〉 = |s ↓〉,

|2〉 = |12,12〉 = |s ↑〉,

|3〉 = |32,12〉 = − i√

6(|x ↓〉+ i|y ↓〉) + i

√

23|z ↑〉,

|4〉 = |32,32〉 =

i√2

(|x ↑〉+ i|y ↑〉) , (A.16)

|5〉 = |32,−3

2〉 = − i√

2(|x ↓〉 − i|y ↓〉) ,

|6〉 = |32,−1

2〉 =

i√6

(|x ↑〉 − i|y ↑〉) + i

√

23|z ↓〉,

|7〉 = |12,−1

2〉 = − i√

3(|x ↑〉 − i|y ↑〉) +

i√3|z ↓〉,

|8〉 = |12,12〉 = − i√

3(|x ↓〉+ i|y ↓〉)− i√

3|z ↑〉.

States |1〉 and |2〉 denote the electron Bloch functions, while states |3〉 and |6〉correspond to LH-, |4〉 and |5〉 to HH- and |7〉 and |8〉 to SO bands. Using this basis

of wave functions, neglecting the k-dependent spin-orbit interaction due its small

value in comparison to the k-independent spin-orbit interaction231 and replacing E

VIII


with Ec and E ′v, leads to the following Hamiltonian Umn for diamond crystals:228

Umn = (A.17)

A 0 V ∗ 0√

3V −√

2U −U√

2V ∗

0 A −√

2U −√

3V ∗ 0 −V√

2V U

V −√

2U −P +Q −S∗ R 0

√

32S −

√2Q

0 −√

3V −S −P −Q 0 R −√

2R

√

12S

√3V ∗ 0 R∗ 0 −P −Q S∗

√

12S∗

√2R∗

−√

2U −V ∗ 0 R∗ S −P +Q√

2Q

√

32S∗

−U√

2V ∗

√

32S∗ −

√2R∗

√

12S

√2Q Z 0

√2V U −

√2Q

√

12S∗

√2R

√

32S 0 Z

with the parameters:

A = Ec +

(

A′ +h2

2m0

)

(

k2x + k2

y + k2z

)

, U =1√3P0kz, (A.18)

V =1√6P0 (kx − iky) , P = −Ev +

12γ1h2

m0

(

k2x + k2

y + k2z

)

,

Q =12γ2h2

m0

(

k2x + k2

y − 2k2z

)

, R = −√

32h2

m0

[γ2

(

k2x − k2

y

)

− 2iγ3kxky],

S =√

3h2

m0

γ3kz (kx − iky) , Z = −P −∆SO.

The transition matrix element P0 describes the mixing of conduction- and valence

bands (Ec, E′v) and ∆SO/3 the spin-orbit interaction operator:

P0 = −i hm0

〈s|px|x〉, A′ =h2

m20

∑

nj

|〈s|px|nΓ5j〉|2Ec − En,Γ5

, (A.19)

Ev = E ′v +

∆SO

3,

∆SO

3= −i h

4m20c

2〈x| (∇V0 × p)y |z〉.

IX

A Appendix

A′ describes the influence of remote bands on states 1 to 8 and is chosen here to be

zero, since remote bands for SiGeSn are far away from bands at the Γ point.159

γ1, γ2 and γ3 are modified Luttinger parameters, which can be defined using the

experimentally measurable bandgap Eg = Ec−Ev, parameters γL1 , γ

L2 and γL

3 intro-

duced by Luttinger and the Kane matrix element EP = 2m0

h2 P 20 as:232

γ1 = γL1 −

EP

3Eg + ∆SO

,

γ2 = γL2 −

12

EP

3Eg + ∆SO

, (A.20)

γ3 = γL3 −

12

EP

3Eg + ∆SO

.

The spatially uniform displacement of atoms from their lattice sites is called strain

and has a strong influence on the band energies of semiconductors. In group-IV semi-

conductors the degeneracy of HH- and LH energies is lifted, which has to be taken

into account when designing lasers with a high material gain.16 Introducing strain

into the crystal lattice (x,p −→ x′,p′) extends the Hamiltonian for the component

D, which changes the Schrödinger equation to:

(H (x′, p′) +D (x′, p′))unk (x′) = E (k)unk (x′) . (A.21)

Applying the same procedure as for the unstrained Hamiltonian, using the basis of

the total angular momentum and neglecting again the spin-orbit interaction term,

X


results in the following components for the strain Hamiltonian Umn,s:

Umn,s = (A.22)

a′e 0 −v∗ 0 −√

3v√

2u u −√

2v∗

0 a′e√

2u√

3v∗ 0 v −√

2v −u

−v√

2u −p+ q −s∗ r 0

√

32s −

√2q

0√

3v −s −p− q 0 r −√

2r

√

12s

−√

3v∗ 0 r∗ 0 −p− q s∗

√

12s∗

√2r∗

√2u v∗ 0 r∗ s −p+ q

√2q

√

32s∗

u −√

2v∗

√

32s∗ −

√2r∗

√

12s

√2q −ae 0

−√

2v −u −√

2q

√

12s∗

√2r

√

32s 0 −ae

with the set of parameters:

a′ = 〈s|Dxx|s〉, p = a (exx + eyy + ezz) , (A.23)

q = b[ezz −12

(exx + eyy)], u =1√3P0

∑

j

ezjkj,

r =

√3

2b (exx − eyy)− idexy, v =

1√6P0

∑

j

(exj − ieyj) kj,

s = −d (exz − ieyz) , e = exx + eyy + ezz,

and the state interaction terms:

a = −13

(l + 2m) , l = 〈x|Dxx|x〉,

b =13

(l −m) , m = 〈y|Dxx|y〉, (A.24)

d =1√3n, n = 2〈x|Dxz|z〉.

XI

A Appendix

The strain Hamiltionian Umn,s is added to the Hamiltionian Umn for the unstrained

case in the Schrödinger equation, describing the resulting Eigenvalue problem to be

solved. The calculations performed in this thesis use the above described method

including the strain Hamiltonian.

All k · p parameters used in this work can be found in table A.2. For L-band

energies it was assumed that the interaction of the L-band with the 4 bands at the

Γ-point is negligible, so that the most simple case of the k ·p perturbation approach

- also called effective mass method - was applied. Within this approximation, the

constant-energy surfaces are rotational ellipsoids with the main axis along the [111]-

direction in the Brillouin zone. The effective mass in the [111]-direction is called

longitudinal mass m∗l , with the corresponding wave vector kl. If the wave vector

changes in any direction normal to the [111]-direction, the effective mass describing

the change of energy, in respect to the L valley bottom, is called the transverse

effective mass m∗t with corresponding wave vector kt. Moreover, kt has two compo-

nents (kt1 and kt2), so that the energy dispersion around the L-point is calculated by:

EL(k) =h2

2

(

k2l

ml

+k2

t1 + k2t2

mt

)

. (A.25)

A.2.2 Heterostructures

In order to calculate quantized conduction- and valence band states, the effective

mass method for quantum wells and the k · p model for quantum dots was applied.

Due to the lack of periodicity of the lattice, Bloch’s theorem is not valid anymore and

the wave function Ψ (x) is expressed by a set of orthonormal wave functions ui (x)

describing the lattice periodicity and a slowly varying envelope function ψi (x):159

Ψ (x) =∑

i

ψi (x)ui (x) . (A.26)

The Hamiltonian of Schrödinger’s equation is usually derived in a heuristic way,

which means that the k vector is replaced by the momentum operator p. In order

to keep the Hamiltonian hermitian, a reordering of operators is performed with

several approaches to choose.

XII


Table A.2 – 8-band k · p parameters used in thiswork

Parameter Si Ge Sn

γL1 4.285 a 13.38 a −12 b

γL2 0.339 a 4.24 a −8.45 b

γL3 1.446 a 5.69 a −6.84 b

Eg,Γ [eV] 4.185 a 0.898 a −0.408 a

Eg,L [eV] 2.176 c 0.744 d 0.1202 e

EP [eV] 21.6 a 26.3 a 23.8 f

ac [eV] −10.06 g −8.24 h −6 g

av [eV] 2.46 h 1.24 h 1.58 b

bv [eV] −2.1 h −2.9 h −2.7 c

d [eV] −4.8 a −5.3 a −4.1 i

aL [eV] −0.66 h −1.54 h −2.14 b

∆SO [eV] 0.044 j 0.297 k 0.80 l

a Ref. [36] b Ref. [41] c Ref. [233]d Ref. [37] e Ref. [133] f Ref. [234]g Ref. [224] h Ref. [235] i Ref. [236]j Ref. [237] k Ref. [238] l Ref. [239]

XIII

A Appendix

Multi quantum wells

For a quantum well with quantization in the z-direction and different effective masses

and bandgaps in barrier and well, the Schrödinger equation transforms into:135

− h2

2∂

∂z

1m∗(z)

∂

∂zψ(z) + V (z)ψ(z) = Eψ(z) (A.27)

To calculate quantized states a finite difference method was applied to quantum

wells.136 This model uses an effective mass approximation with included non-

parabolicities to calculate quantized energy states. The used bulk energies and

effective masses were calculated using the k · p model. For the latter, effective

masses in the [001]-direction were calculated and applied, since this describes the

direction of quantum confinement. The projection of the L-valley effective mass

from the [111]-direction into the [001]-direction (z-direction) is given by:240

m∗z = 3m∗

lm∗t/(2m

∗l +m∗

t ). (A.28)

Quantum dots

In this work, energy states of QDs were calculated using the 8-band k · p method,

as described in Ref. [159]. Here, a symmetrical rearrangement of operators in the

Hamiltonian was used, which transforms operators in the following manner:

f (x) kikj −→12

(kif (x) kj + kjf (x) ki) , (A.29)

f (x) ki −→12

(kif (x) + f (x) ki) .

The k ·p method may deliver spurious solutions, which may appear for large values

of k-vectors. This can be avoided using the model described in Ref. [241].

The energy states were determined using the wave expansion method, which de-

scribes the envelope functions as a linear combination of orthonormal basis functions

al:

ψj(r) =∑

l

Ajlal(r). (A.30)

By inserting this expression into the Schrödinger equation, the expansion coefficients

XIV


Ajl can be determined. The here used dots had a cylindrical shape, which offers the

possibility to express the Schrödinger equation in cylindrical coordinates. In this

basis, the energy states can be described by a radial, vertical and angle-dependent

part. The dot is embedded in a cylinder of radius Rt and height Ht. Within the

wave expansion method, the envelope function is given by:159,242

ψj(r) =∑

nl

Ajnlfnm(j)(r)gl(z)Φm(ϕ) (n ∈ {1, ..., nmax}, l ∈ {−lmax, ..., lmax}),

(A.31)

where radial (fnm), z-direction (gl) and angle-dependent (Φm) functions are given

by:

fnm(j)(r) =

√2

Rt

Jm(knmr)∣

∣

∣J|m|+1

∣

∣

∣ (knmRt),

gl(z) =1√Ht

ei 2πlz

Ht , (A.32)

Φm(ϕ) =1√2πeimϕ.

Here, Jm is the Bessel function of m-th order and its n-th zero at knmRt. m contains

the quantum numbers of the envelope function’s z-component of the total angular

momentum mf and the orbital angular momentummj(j) of the Bloch function. Since

the Hamiltonian commutes with the total quasi-angular momentum, mf (describing

a good quantum number) was chosen to represent the wave functions, denoting

electron Eigenstates as nemf and hole state as nhmf. This mathematical framework

gives a transition matrix element of:

Mεif =

∑

jnl

∑

j′n′l′Ai∗

jnlAfj′n′l′

1A

∫

V

b∗nm(j)lH

′b∗n′m(j′)l′ , (A.33)

where b describes the basis functions, ε indicates that the transition matrix element

is polarization dependent, H ′ = H (x′, p′) and the indices i and f denote the initial

and final states to be considered. From the matrix element the selection rules for

XV

A Appendix

z-polarized and in-plane-polarized radiation can be deduced:

∆mf = 0 (z-polarization), (A.34)

|∆mf| = 1 (in-plane-polarization).

The strain distribution in the QD and surrounding matrix was calculated using a

continuum mechanical model. In this regard, the strain energy W of a cubical mesh,

with dimensions Lx, Ly and Lz and number of nodes Nx, Ny and Nz, was minimized

numerically using a finite element method.159 A list of calculation parameters that

lead to the conversion of Eigenenergies is given in Table A.3.

When semiconductors interact with electromagnetic radiation this perturbation can

be described by Fermi’s golden rule, which gives the transition probability between

an initial and final state. The optical cross section σεif takes this probability and the

flux of incident radiation into account, describing the optical activity of two states

by:

σεif(ω) =

2πnrε0cω

|Mεif|2

1

σ√

2πe

(Ef−Ei∓hω)2

2σ . (A.35)

σ is a broadening factor of the Gaussian distribution function, accounting for inho-

mogenities in a QD ensemble. Due to the lack of peak broadening data for GeSn

QDs, σ was set to be 10 % of the transition energy difference, as it is used for III-V

semiconductor QDs.242,243

A.3 Free carrier absorption

To account for absorption processes from electrons and holes scattered by phonons,

the free carrier absorption (FCA) model from Ref. [77] was used for gain calculations

in section 2.1. This model contains inter- and intra-valley scattering. The former

included conduction band deformation potential scattering, while for the latter de-

formation potential scattering from L-valleys, acoustic phonon, ionized impurity and

alloy scattering in the conduction bands were taken into account.

Deformation potential scattering stems from the interaction of atoms with phonons.

This interaction causes a displacement of atoms on lattice sites, which in turn causes

perturbations in the band structure. These perturbations describe scattering centers

XVI

A.3 Free carrier absorption

Table A.3 – Calculation parameter for GeSnQDs in an SiGeSn matrix, ensuring a conver-gence of energies.

Parameter Value

Geometrical parameters of QD and matrix

NQD 1hQD, dQD [nm] 45, 30

Mesh dimensions and node numberfor strain calculations

Nx 80Ny 80Nz 120

Lx, Ly, Lz [nm] 80Dimensions of cylinder surrounding QD and

basis function parametersfor Eigenstate calculations

mf ±52,±3

2,±1

2

nmax, lmax 10, 20nr, nz, nϕ 100, 500, 20Rt, Ht [nm] 60, 80

XVII

A Appendix

Table A.4 – FCA parameters used in this work

Intra conduction band LO-phonon scatteringdeformation potentials [eV/Å] and phonon energies [meV]

DIV,Γ−L DIV,Γ−X DIV, L-X DIV, L-L DIV, X-X

4.0 a 2.5 a 4.1 b 0.8 a 5.0 c,d

hωΓ−L hωΓ−X hωL-X hωL-L hωX-X

27 d 27 d 27 d 27 d 37 d

Intra band LO-phonon scattering in L-valleysdeformation potential [eV/Å] and phonon energy [meV]

DLO hωLO

3.6 f 37 f

Acoustic phonon scatteringdeformation potentials [eV], velocity of sound [m/s]

and relative permittivity

ΞAC,Γ ΞAC, L ΞAC, X vAC ǫs

5.3 f 11.5 f 9.5 b 3810 16

a Ref. [244] b Ref. [245] c Ref. [246] d Ref. [247]f Ref. [248]

for electrons. The parameters used here are summarized in table A.4.

In an alloy atoms are randomly distributed on crystal lattice sites. Due to this

random distribution, there are regions in the alloy with a higher concentration of

one constituent in comparison to the average element concentrations causing fluctua-

tions in the band energies. These fluctuations serve, similar to phonons, as scattering

centers for charge carriers. Therefore, expressions for alloy disorder scattering were

derived by Zoran Ikonić from the University of Leeds using Refs. [249, 250]. These

expressions are similar to the FCA equations in Ref. [77], but the transition matrix

XVIII

A.4 Selective epitaxial growth

element |Malloy|2 is replaced by:

|Malloy|2 =14a3

latU2alloy

Ualloy = xSi (1− xSi) (USi − UGe)2 + xSn (1− xSn) (USn − UGe)

2

− 2xSixSn (USn − UGe) (USi − UGe) (A.36)

USi − UGe = −0.48eV + Eg,Si − Eg,Ge

USn − UGe = 0.69eV + Eg,Sn − Eg,Ge.

Ui describes the atomic crystal potential of an charge carrier on lattice sites and

Uj − Ui the scattering potential. USi − UGe and USn − UGe become for holes

−0.48 eV/0.69 eV. Additionally, losses due to inter-valence band absorption were

calculated from transition matrix elements and band dispersions derived from the

8-band k · p model.

For free-hole scattering a parameterized equation from Ref. [251] was used, where

an expression for hole scattering in Ge was derived from experiments. In this work

this expression was chosen as a first approximation to hole scattering in SiGeSn

alloys. For all FCA processes, strain dependence of the parameters was neglected.

The temperature dependence is given by the sum of logarithmic terms in Ref. [77]

or by the transition matrix elements.

A.4 Selective epitaxial growth

Fig. A.3a shows the random (black line) and channeling RBS spectra (light blue

line) of GeSn grown at 375 ◦C on patterned Si, as described in section 5.2. Although

the ion beam was directed at an 1 cm2 SiO2 window in the middle of the wafer,

an oxide signal was detected for random measurements. This can be explained by

both the difficulty to accurately align the ion beam and the angle of 7° used for

random measurements, decreasing the effective region of interest. By comparing

the Sn signals for random and channeling measurements a χmin of 20 % was found.

The thickness and Sn content of the GeSn layer were determined by fitting the

random signal (purple line), giving values of 110 nm and 6.5 at.%, respectively. For

measurements of the oxide region (Fig. A.3b) no channeling could be found. The

XIX

A Appendix

0.2 0.4 0.6 0.8 1.0 1.2

Energy (MeV)

0.2 0.4 0.6 0.8 1.0 1.2

0

2

4

6

8

Sig

nal (a

.u.)

Energy (MeV)

Ge

Si

O

Sn

randomchannelingfitted

open oxide

windowoxide region

(a) (b)

Figure A.3 – RBS spectra of GeSn grown at 375 ◦C on structured Si with an randomalignment of sample and ion beam (black line) and in channeling direction (light blueline). The ion beam was directed at (a) an open SiO2 window and (b) on oxide. Theelement signals of Sn, Ge, Si and O are indicated by red, green, orange and dark blueregions, respectively. The fitted spectrum is represented by the purple line.

GeSn deposited on the oxide is, therefore, poly-crystalline or amorphous.

A.5 Annealing of GeSn SQWs

The following table summarizes the parameters used for annealing of GeSn SQWs

embedded in Ge. As described in chapter 4, the parameters showed no obvious

influence on the density or morphology of dots, when analyzed via XTEM.

XX

A.5 Annealing of GeSn SQWs

Table A.5 – Annealing parameters used for GeSn SQWs surrounded by Ge

Sample name Ambient Temperature (◦C) Annealing time (s)20150805b_RTP_01 Ar 400 6020150805b_RTP_02 Ar 450 6020150805b_RTP_03 Ar 500 6020150805b_RTP_04 Ar 400 12020150805b_RTP_05 Ar 450 12020150805b_RTP_06 Ar 500 12020150805b_RTP_07 Ar 600 12020150805b_RTP_08 Ar 700 12020150805b_RTP_09 Ar 800 120

XXI

Bibliography

[1] Cisco. Cisco Visual Networking Index: Forecast and Trends, 2017–2022 White

Paper. 2019.

[2] L. Vivien. “Silicon chips lighten up”. In: Nature 528 (2015), pp. 483–484. doi:

10.1038/528483a.

[3] D. Miller. “Device Requirements for Optical Interconnects to Silicon Chips”.

In: Proceedings of the IEEE 97.7 (July 2009), pp. 1166–1185. doi: 10.1109/

JPROC.2009.2014298.

[4] C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S.

Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar,

F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen,

K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović. “Single-chip

microprocessor that communicates directly using light”. In: Nature 528.7583

(2015), pp. 534–538. doi: 10.1038/nature16454.

[5] T. Hu, B. Dong, X. Luo, T.-Y. Liow, J. Song, C. Lee, and G.-Q. Lo. “Sili-

con photonic platforms for mid-infrared applications [Invited]”. In: Photonics

Research 5.5 (Oct. 2017), p. 417. doi: 10.1364/PRJ.5.000417.

[6] V. M. Lavchiev and B. Jakoby. “Photonics in the Mid-Infrared: Challenges

in Single-Chip Integration and Absorption Sensing”. In: IEEE Journal of

Selected Topics in Quantum Electronics 23.2 (Mar. 2017), pp. 452–463. doi:

10.1109/JSTQE.2016.2619330.

[7] R. Shankar and M. Lončar. “Silicon photonic devices for mid-infrared appli-

cations”. In: Nanophotonics 3.4-5 (Jan. 2014). doi: 10.1515/nanoph-2013-

0027.

XXIII

Bibliography

[8] S. Bogdanov, M. Y. Shalaginov, A. Boltasseva, and V. M. Shalaev. “Material

platforms for integrated quantum photonics”. In: Optical Materials Express

7.1 (Jan. 2017), p. 111. doi: 10.1364/OME.7.000111. arXiv: 1609.02851.

[9] L. Schares, J. Kash, F. Doany, C. Schow, C. Schuster, D. Kuchta, P. Pe-

peljugoski, J. Trewhella, C. Baks, R. John, L. Shan, Y. Kwark, R. Budd, P.

Chiniwalla, F. Libsch, J. Rosner, C. Tsang, C. Patel, J. Schaub, R. Dangel,

F. Horst, B. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal,

C.-K. Lin, A. Tandon, G. Trott, M. Nystrom, D. Bour, M. Tan, and D. Dolfi.

“Terabus: Terabit/Second-Class Card-Level Optical Interconnect Technolo-

gies”. In: IEEE Journal of Selected Topics in Quantum Electronics 12.5 (Sept.

2006), pp. 1032–1044. doi: 10.1109/JSTQE.2006.881906.

[10] J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho.

“Quantum Cascade Laser”. In: Science 264.5158 (Apr. 1994), pp. 553–556.

doi: 10.1126/science.264.5158.553.

[11] R. Q. Yang. Infrared laser based on intersubband transitions in quantum wells.

1995. doi: 10.1006/spmi.1995.1017.

[12] I. J. Luxmoore, R. Toro, O. D. Pozo-Zamudio, N. A. Wasley, E. A.

Chekhovich, A. M. Sanchez, R. Beanland, A. M. Fox, M. S. Skolnick, H. Y.

Liu, and A. I. Tartakovskii. “III–V quantum light source and cavity-QED

on Silicon”. In: Scientific Reports 3.1 (Dec. 2013), p. 1239. doi: 10.1038/

srep01239.

[13] M. E. Groenert, A. J. Pitera, R. J. Ram, and E. A. Fitzgerald.

“Improved room-temperature continuous wave GaAs/AlGaAs and In-

GaAs/GaAs/AlGaAs lasers fabricated on Si substrates via relaxed graded

GexSi1-x buffer layers”. In: Journal of Vacuum Science & Technology B: Mi-

croelectronics and Nanometer Structures 21.3 (2003), p. 1064. doi: 10.1116/

1.1576397.

[14] Z. Wang, B. Tian, M. Pantouvaki, W. Guo, P. Absil, J. Van Campenhout,

C. Merckling, and D. Van Thourhout. “Room-temperature InP distributed

feedback laser array directly grown on silicon”. In: Nature Photonics 9.12

(Dec. 2015), pp. 837–842. doi: 10.1038/nphoton.2015.199.

XXIV

[15] S. Wirths, B. F. Mayer, H. Schmid, M. Sousa, J. Gooth, H. Riel, and K. E.

Moselund. “Room-Temperature Lasing from Monolithically Integrated GaAs

Microdisks on Silicon”. In: ACS Nano 12.3 (Mar. 2018), pp. 2169–2175. doi:

10.1021/acsnano.7b07911.

[16] D. S. Sukhdeo, Y. Kim, S. Gupta, K. C. Saraswat, B. R. Dutt, and D.

Nam. “Anomalous threshold reduction from <100> uniaxial strain for a low-

threshold Ge laser”. In: Optics Communications 379 (Nov. 2016), pp. 32–35.

doi: 10.1016/j.optcom.2016.05.030.

[17] M. Bollani, D. Chrastina, L. Gagliano, L. Rossetto, D. Scopece, M. Barget, V.

Mondiali, J. Frigerio, M. Lodari, F. Pezzoli, F. Montalenti, and E. Bonera.

“Local uniaxial tensile strain in germanium of up to 4% induced by SiGe

epitaxial nanostructures”. In: Applied Physics Letters 107.8 (2015), p. 083101.

doi: 10.1063/1.4928981.

[18] K. Guilloy, N. Pauc, A. Gassenq, Y. M. Niquet, J. M. Escalante, I. Duchemin,

S. Tardif, G. Osvaldo Dias, D. Rouchon, J. Widiez, J. M. Hartmann, R.

Geiger, T. Zabel, H. Sigg, J. Faist, A. Chelnokov, V. Reboud, and V. Calvo.

“Germanium under High Tensile Stress: Nonlinear Dependence of Direct

Band Gap vs Strain”. In: ACS Photonics 3.10 (2016), pp. 1907–1911. doi:

10.1021/acsphotonics.6b00429. arXiv: 1606.01668.

[19] R. E. Camacho-Aguilera, Y. Cai, N. Patel, J. T. Bessette, M. Romagnoli,

L. C. Kimerling, and J. Michel. “An electrically pumped germanium laser”.

In: Optics Express 20.10 (2012), p. 11316. doi: 10.1364/OE.20.011316.

[20] R. Koerner, M. Oehme, M. Gollhofer, M. Schmid, K. Kostecki, S. Bechler,

D. Widmann, E. Kasper, and J. Schulze. “Electrically pumped lasing from

Ge Fabry-Perot resonators on Si”. In: Optics Express 23.11 (2015), p. 14815.

doi: 10.1364/OE.23.014815.

[21] M. El Kurdi, M. Prost, A. Ghrib, A. Elbaz, S. Sauvage, X. Checoury, G.

Beaudoin, I. Sagnes, G. Picardi, R. Ossikovski, F. Boeuf, and P. Boucaud.

“Tensile-strained germanium microdisks with circular Bragg reflectors”. In:

Applied Physics Letters 108.9 (2016), p. 091103. doi: 10.1063/1.4942891.

XXV

Bibliography

[22] S. Bao, D. Kim, C. Onwukaeme, S. Gupta, K. Saraswat, K. H. Lee, Y. Kim,

D. Min, Y. Jung, H. Qiu, H. Wang, E. A. Fitzgerald, C. S. Tan, and D.

Nam. “Low-threshold optically pumped lasing in highly strained germanium

nanowires”. In: Nature Communications 8.1 (2017), pp. 1–7. doi: 10.1038/

s41467-017-02026-w. arXiv: 1708.04568.

[23] T. R. Harris, M.-y. Ryu, Y. K. Yeo, B. Wang, C. L. Senaratne, and J. Kouve-

takis. “Direct bandgap cross-over point of Ge1-ySny grown on Si estimated

through temperature-dependent photoluminescence studies”. In: Journal of

Applied Physics 120.8 (Aug. 2016), p. 085706. doi: 10.1063/1.4961464.

[24] S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl, Z.

Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D. Buca,

and D. Grützmacher. “Lasing in direct-bandgap GeSn alloy grown on Si”. In:

Nature Photonics 9.2 (2015), pp. 88–92. doi: 10.1038/nphoton.2014.321.

[25] S. Wirths, R. Geiger, N. von den Driesch, G. Mussler, T. Stoica, S. Mantl,

Z. Ikonic, M. Luysberg, S. Chiussi, J. M. Hartmann, H. Sigg, J. Faist, D.

Buca, and D. Grützmacher. “Lasing in direct-bandgap GeSn alloy grown on

Si - Supplementary Information”. In: Nature Photonics 9.2 (2015), pp. 88–92.

doi: 10.1038/nphoton.2014.321.

[26] S. Al-kabi, S. A. Ghetmiri, J. Margetis, T. Pham, Y. Zhou, W. Dou, B.

Collier, W. Du, A. Mosleh, J. Liu, G. Sun, R. A. Soref, J. Tolle, B. Li, H. A.

Naseem, S.-q. Yu, S. Al-kabi, S. A. Ghetmiri, J. Margetis, T. Pham, Y. Zhou,

W. Dou, B. Collier, R. Quinde, W. Du, A. Mosleh, J. Liu, H. A. Naseem, and

S.-q. Yu. “An optically pumped 2.5 µm GeSn laser on Si operating at 110 K”.

In: Applied Physics Letters 109.171105 (2016). doi: 10.1063/1.4966141.

[27] J. Margetis, S. Al-Kabi, W. Du, W. Dou, Y. Zhou, T. Pham, P. Grant, S.

Ghetmiri, A. Mosleh, B. Li, J. Liu, G. Sun, R. Soref, J. Tolle, M. Mortazavi,

and S.-Q. Yu. “Si-Based GeSn Lasers with Wavelength Coverage of 2–3 µm

and Operating Temperatures up to 180 K”. In: ACS Photonics 5 (2017),

pp. 827–833. doi: 10.1021/acsphotonics.7b00938. arXiv: 1708.05927.

[28] V. Reboud, A. Gassenq, N. Pauc, J. Aubin, L. Milord, Q. M. Thai, M.

Bertrand, K. Guilloy, D. Rouchon, J. Rothman, T. Zabel, F. Armand Pilon,

XXVI

H. Sigg, A. Chelnokov, J. M. Hartmann, and V. Calvo. “Optically pumped

GeSn micro-disks with 16% Sn lasing at 3.1 µm up to 180 K”. In: Applied

Physics Letters 111.9 (2017). doi: 10.1063/1.5000353. arXiv: 1704.06436.

[29] W. Dou, Y. Zhou, J. Margetis, S. A. Ghetmiri, S. Al-Kabi, W. Du, J. Liu,

G. Sun, R. A. Soref, J. Tolle, B. Li, M. Mortazavi, and S.-Q. Yu. “Optically

pumped lasing at 3 µm from compositionally graded GeSn with tin up to

22.3%”. In: Optics Letters 43.19 (Oct. 2018), p. 4558. doi: 10.1364/OL.43.

004558.

[30] N. von den Driesch, D. Stange, S. Wirths, D. Rainko, I. Povstugar, A.

Savenko, U. Breuer, R. Geiger, H. Sigg, Z. Ikonic, J. M. Hartmann, D.

Grützmacher, S. Mantl, and D. Buca. “SiGeSn Ternaries for Efficient Group

IV Heterostructure Light Emitters”. In: Small 13.16 (2017), pp. 1–9. doi:

10.1002/smll.201603321.

[31] D. Stange, N. von den Driesch, D. Rainko, S. Roesgaard, I. Povstugar, J.-M.

Hartmann, T. Stoica, Z. Ikonic, S. Mantl, D. Grützmacher, and D. Buca.

“Short-wave infrared LEDs from GeSn/SiGeSn multiple quantum wells”. In:

Optica 4.2 (Feb. 2017), p. 185. doi: 10.1364/OPTICA.4.000185.

[32] D. Stange, N. von den Driesch, T. Zabel, F. Armand-Pilon, D. Rainko, B.

Marzban, P. Zaumseil, J.-M. Hartmann, Z. Ikonic, G. Capellini, S. Mantl, H.

Sigg, J. Witzens, D. Grützmacher, and D. Buca. “GeSn/SiGeSn Heterostruc-

ture and Multi Quantum Well Lasers”. In: ACS Photonics 5.11 (Nov. 2018),

pp. 4628–4636. doi: 10.1021/acsphotonics.8b01116.

[33] N. von den Driesch, D. Stange, D. Rainko, I. Povstugar, P. Zaumseil, G.

Capellini, T. Schröder, T. Denneulin, Z. Ikonic, J.-M. Hartmann, H. Sigg, S.

Mantl, D. Grützmacher, and D. Buca. “Advanced GeSn/SiGeSn Group IV

Heterostructure Lasers”. In: Advanced Science 5.6 (June 2018), p. 1700955.

doi: 10.1002/advs.201700955.

[34] D. Rainko, Z. Ikonic, A. Elbaz, N. von den Driesch, D. Stange, E. Herth,

P. Boucaud, M. El Kurdi, D. Grützmacher, and D. Buca. “Impact of tensile

strain on low Sn content GeSn lasing”. In: Scientific Reports 9.1 (Jan. 2019),

p. 259. doi: 10.1038/s41598-018-36837-8.

XXVII

Bibliography

[35] P. Moontragoon, Z. Ikonić, and P. Harrison. “Band structure calculations

of Si-Ge-Sn alloys: achieving direct band gap materials”. In: Semiconductor

Science and Technology 22.7 (July 2007), pp. 742–748. doi: 10.1088/0268-

1242/22/7/012.

[36] O. Madelung, M. Schultz, and H. Weiss. Semiconductors, Physics of Group

IV Elements and III-V Compounds. Ed. by O. Madelung, M. Schultz, H.

Weiss, and Landolt-Börnstein. 17a. New York: Springer-Verlag, 1982.

[37] M. E. Levinshten, S. L. Rumyantsev, and M. Shur. Handbook Series on Semi-

conductor Parameters. Ed. by M. Levinshtein, S. Rumyantsev, and M. Shur.

Vol. 1. 0. Singapore: World Scientific, 1996. doi: 10.1142/9789812832078_

0008.

[38] R. Braunstein, A. R. Moore, and F. Herman. “Intrinsic optical absorption

in germanium-silicon alloys”. In: Physical Review 109.3 (1958), pp. 695–710.

doi: 10.1103/PhysRev.109.695.

[39] R. W. Olesinski and G. J. Abbaschian. “The Ge-Sn (Germanium-Tin) sys-

tem”. In: Bulletin of Alloy Phase Diagrams 5.3 (June 1984), pp. 265–271.

doi: 10.1007/BF02868550.

[40] S. Groves and W. Paul. “Electronic band structure of gray tin”. In: Physical

Review Letters 11.5 (1963), pp. 194–196. doi: 10.1103/PhysRev.132.2047.

[41] T. Brudevoll, D. S. Citrin, M. Cardona, and N. E. Christensen. “Electronic

structure of α-Sn and its dependence on hydrostatic strain”. In: Physical

Review B 48.12 (1993), pp. 8629–8635. doi: 10.1103/PhysRevB.48.8629.

[42] R. A. Carrasco, C. M. Zamarripa, S. Zollner, J. Menéndez, S. A. Chastang, J.

Duan, G. J. Grzybowski, B. B. Claflin, and A. M. Kiefer. “The direct bandgap

of gray α-tin investigated by infrared ellipsometry”. In: Applied Physics Let-

ters 113.23 (Dec. 2018), p. 232104. doi: 10.1063/1.5053884.

[43] F. Gencarelli, B. Vincent, J. Demeulemeester, A. Vantomme, A. Moussa, A.

Franquet, A. Kumar, H. Bender, J. Meersschaut, W. Vandervorst, R. Loo,

M. Caymax, K. Temst, and M. Heyns. “Crystalline Properties and Strain

Relaxation Mechanism of CVD Grown GeSn”. In: ECS Journal of Solid State

Science and Technology 2.4 (2013), P134–P137. doi: 10.1149/2.011304jss.

XXVIII

[44] N. von den Driesch, D. Stange, S. Wirths, G. Mussler, B. Holländer, Z. Ikonic,

J. M. Hartmann, T. Stoica, S. Mantl, D. Grützmacher, and D. Buca. “Direct

Bandgap Group IV Epitaxy on Si for Laser Applications”. In: Chemistry of

Materials 27 (2015), pp. 4693–4702. doi: 10.1021/acs.chemmater.5b01327.

[45] C. L. Senaratne, P. M. Wallace, J. D. Gallagher, P. E. Sims, J. Kouvetakis,

and J. Menéndez. “Direct gap Ge1-ySny alloys: Fabrication and design of mid-

IR photodiodes”. In: Journal of Applied Physics 120.2 (July 2016), p. 025701.

doi: 10.1063/1.4956439.

[46] J. Margetis, A. Mosleh, S. A. Ghetmiri, S. Al-Kabi, W. Dou, W. Du, N.

Bhargava, S.-Q. Yu, H. Profijt, D. Kohen, R. Loo, A. Vohra, and J. Tolle.

“Fundamentals of Ge1-xSnx and SiyGe1-x-ySnx RPCVD epitaxy”. In: Ma-

terials Science in Semiconductor Processing 70 (Nov. 2017), pp. 38–43. doi:

10.1016/j.mssp.2016.12.024.

[47] M. Fukuda, D. Rainko, M. Sakashita, M. Kurosawa, D. Buca, O. Nakat-

suka, and S. Zaima. “Optoelectronic properties of high-Si-content-Ge1-x-

ySixSny/Ge1-xSnx/Ge1-x-ySixSny double heterostructure”. In: Semiconduc-

tor Science and Technology 33.12 (Dec. 2018), p. 124018. doi: 10.1088/

1361-6641/aaebb5.

[48] J. Aubin and J. Hartmann. “GeSn growth kinetics in reduced pressure chem-

ical vapor deposition from Ge2H6 and SnCl4”. In: Journal of Crystal Growth

482 (Jan. 2018), pp. 30–35. doi: 10.1016/j.jcrysgro.2017.10.030.

[49] Y. Li. “New semiempirical construction ofthe Slater-Koster parameters for

group-IV semiconductors”. In: Physical Review B 27.6 (1983), pp. 3465–3470.

[50] R. A. Soref and C. H. Perry. “Predicted band gap of the new semiconductor

SiGeSn”. In: Journal of Applied Physics 69.1 (1991), pp. 539–541. doi: 10.

1063/1.347704.

[51] V. R. D’Costa, C. S. Cook, A. G. Birdwell, C. L. Littler, M. Canonico, S.

Zollner, J. Kouvetakis, and J. Menéndez. “Optical critical points of thin-

film Ge1-ySny alloys: A comparative Ge1-ySny/Ge1-xSix study”. In: Physical

Review B 73.12 (Mar. 2006), p. 125207. doi: 10.1103/PhysRevB.73.125207.

XXIX

Bibliography

[52] D. W. Jenkins and J. D. Dow. “Electronic properties of metastable GexSn1-x

alloys”. In: Physical Review B 36.15 (Nov. 1987), pp. 7994–8000. doi: 10.

1103/PhysRevB.36.7994.

[53] K. Mäder, A. Baldereschi, and H. von Känel. “Band structure and instabil-

ity of Ge1-xSnx alloys”. In: Solid State Communications 69.12 (Mar. 1989),

pp. 1123–1126. doi: 10.1016/0038-1098(89)91046-6.

[54] G. He and H. A. Atwater. “Interband Transitions in SnxGe1-x Alloys”. In:

Physical Review Letters 79.10 (Sept. 1997), pp. 1937–1940. doi: 10.1103/

PhysRevLett.79.1937.

[55] H. Pérez Ladrón de Guevara, A. G. Rodríguez, H. Navarro-Contreras, and

M. A. Vidal. “Nonlinear behavior of the energy gap in Ge1-xSnx alloys at

4K”. In: Applied Physics Letters 91.16 (Oct. 2007), p. 161909. doi: 10.1063/

1.2800296.

[56] R. Chen, H. Lin, Y. Huo, C. Hitzman, T. I. Kamins, and J. S. Harris. “In-

creased photoluminescence of strain-reduced, high-Sn composition Ge1-xSnx

alloys grown by molecular beam epitaxy”. In: Applied Physics Letters 99.18

(2011). doi: 10.1063/1.3658632.

[57] A. A. Tonkikh, C. Eisenschmidt, V. G. Talalaev, N. D. Zakharov, J. Schilling,

G. Schmidt, and P. Werner. “Pseudomorphic GeSn/Ge(001) quantum wells:

Examining indirect band gap bowing”. In: Applied Physics Letters 103.3 (July

2013), p. 032106. doi: 10.1063/1.4813913.

[58] S. A. Ghetmiri, W. Du, J. Margetis, A. Mosleh, L. Cousar, B. R. Conley, L.

Domulevicz, A. Nazzal, G. Sun, R. A. Soref, J. Tolle, B. Li, H. A. Naseem,

and S.-Q. Yu. “Direct-bandgap GeSn grown on silicon with 2230 nm pho-

toluminescence”. In: Applied Physics Letters 105.15 (Oct. 2014), p. 151109.

doi: 10.1063/1.4898597.

[59] S. Al-Kabi, S. A. Ghetmiri, J. Margetis, W. Du, A. Mosleh, M. Alher, W. Dou,

J. M. Grant, G. Sun, R. A. Soref, J. Tolle, B. Li, M. Mortazavi, H. A. Naseem,

and S.-Q. Yu. “Optical Characterization of Si-Based Ge1-xSnx Alloys with

Sn Compositions up to 12%”. In: Journal of Electronic Materials 45.4 (Apr.

2016), pp. 2133–2141. doi: 10.1007/s11664-015-4283-6.

XXX

[60] Y. Chibane, B. Bouhafs, and M. Ferhat. “Unusual structural and electronic

properties of SnxGe1-x alloys”. In: Physica Status Solidi (B) Basic Research

240.1 (2003), pp. 116–119. doi: 10.1002/pssb.200301857.

[61] P. Moontragoon, R. A. Soref, and Z. Ikonic. “The direct and indirect

bandgaps of unstrained SixGe1-x-ySny and their photonic device applica-

tions”. In: Journal of Applied Physics 112.7 (2012), p. 073106. doi: 10 .

1063/1.4757414.

[62] K. Lu Low, Y. Yang, G. Han, W. Fan, and Y.-C. Yeo. “Electronic band

structure and effective mass parameters of Ge1-xSnx alloys”. In: Journal of

Applied Physics 112.10 (Nov. 2012), p. 103715. doi: 10.1063/1.4767381.

[63] S. Gupta, B. Magyari-Köpe, Y. Nishi, and K. C. Saraswat. “Achieving di-

rect band gap in germanium through integration of Sn alloying and external

strain”. In: Journal of Applied Physics 113.7 (Feb. 2013), p. 073707. doi:

10.1063/1.4792649.

[64] J. D. Gallagher, C. L. Senaratne, J. Kouvetakis, and J. Menéndez. “Com-

positional dependence of the bowing parameter for the direct and indirect

band gaps in Ge1-ySny alloys”. In: Applied Physics Letters 105.14 (2014),

p. 142102. doi: 10.1063/1.4897272.

[65] W.-J. Yin, X.-G. Gong, and S.-H. Wei. “Origin of the unusually large band-

gap bowing and the breakdown of the band-edge distribution rule in the

SnxGe1-x alloys”. In: Physical Review B 78.16 (Oct. 2008), p. 161203. doi:

10.1103/PhysRevB.78.161203.

[66] S. Assali, J. Nicolas, S. Mukherjee, A. Dijkstra, and O. Moutanabbir.

“Atomically uniform Sn-rich GeSn semiconductors with 3.0–3.5 µ m room-

temperature optical emission”. In: Applied Physics Letters 112.25 (June

2018), p. 251903. doi: 10.1063/1.5038644.

[67] N. von den Driesch. “Epitaxy of group IV Si-Ge-Sn alloys for advanced het-

erostructure light emitters”. PhD thesis. RWTH Aachen University, 2018.

[68] S. Assali, J. Nicolas, and O. Moutanabbir. “Enhanced Sn incorporation in

GeSn epitaxial semiconductors via strain relaxation”. In: Journal of Applied

Physics 125.2 (Jan. 2019), p. 025304. doi: 10.1063/1.5050273.

XXXI

Bibliography

[69] R. Hook. Lectures de Potentia Restitutiva, Or of Spring Explaining the Power

of Springing Bodies. London, 1678, p. 56.

[70] P. Zaumseil, Y. Hou, M. A. Schubert, N. von den Driesch, D. Stange, D.

Rainko, M. Virgilio, D. Buca, and G. Capellini. “The thermal stability of

epitaxial GeSn layers”. In: APL Materials 6.7 (July 2018), p. 076108. doi:

10.1063/1.5036728.

[71] I. A. Fischer, T. Wendav, L. Augel, S. Jitpakdeebodin, F. Oliveira, A.

Benedetti, S. Stefanov, S. Chiussi, G. Capellini, K. Busch, and J. Schulze.

“Growth and characterization of SiGeSn quantum well photodiodes”. In: Op-

tics Express 23.19 (Sept. 2015), p. 25048. doi: 10.1364/OE.23.025048.

[72] Y. Kim, M. Takenaka, T. Osada, M. Hata, and S. Takagi. “Strain-induced

enhancement of plasma dispersion effect and free-carrier absorption in SiGe

optical modulators”. In: Scientific Reports 4.1 (May 2015), p. 4683. doi:

10.1038/srep04683.

[73] S. J. Sweeney, T. D. Eales, and A. R. Adams. “The impact of strained layers

on current and emerging semiconductor laser systems”. In: Journal of Applied

Physics 125.8 (Feb. 2019), p. 082538. doi: 10.1063/1.5063710.

[74] G. Agrawal and N. Dutta. Semiconductor Lasers. 2nd ed. New York: Kluwer

Academic Publishers, 1993.

[75] J. Singh. Physics of Semiconductors and Their Heterostructures. New York,

1993, p. 851.

[76] S. L. Chuang. Physics of Photonic Devices. Ed. by G. Boreman. 2nd ed.

Wiley, 2009.

[77] Chin-Yi Tsai, Chin-Yao Tsai, Chih-Hsiung Chen, Tien-Li Sung, Tsu-Yin

Wu, and Fang-Ping Shih. “Theoretical model for intravalley and intervalley

free-carrier absorption in semiconductor lasers: beyond the classical Drude

model”. In: IEEE Journal of Quantum Electronics 34.3 (Mar. 1998), pp. 552–

559. doi: 10.1109/3.661466.

[78] L. Coldren, S. Corzine, and M. Masanovic. Diode Lasers and Photonic Inte-

grated Circuits. Ed. by K. Chang. 2nd. Wiley, 2012, p. 614.

XXXII

[79] J. Aubin, J. M. Hartmann, A. Gassenq, J. L. Rouviere, E. Robin, V. De-

laye, D. Cooper, N. Mollard, V. Reboud, and V. Calvo. “Growth and struc-

tural properties of step-graded, high Sn content GeSn layers on Ge”. In:

Semiconductor Science and Technology 32.9 (2017). doi: 10.1088/1361-

6641/aa8084.

[80] J. M. Hartmann, A. Abbadie, N. Cherkashin, H. Grampeix, and L. Clavelier.

“Epitaxial growth of Ge thick layers on nominal and 6° off Si(001); Ge surface

passivation by Si”. In: Semiconductor Science and Technology 24.5 (May

2009), p. 055002. doi: 10.1088/0268-1242/24/5/055002.

[81] M. Virgilio, C. L. Manganelli, G. Grosso, G. Pizzi, and G. Capellini. “Ra-

diative recombination and optical gain spectra in biaxially strained n-type

germanium”. In: Physical Review B 87.23 (2013), p. 235313. doi: 10.1103/

PhysRevB.87.235313.

[82] A. Ghrib, M. El Kurdi, M. De Kersauson, M. Prost, S. Sauvage, X. Checoury,

G. Beaudoin, I. Sagnes, and P. Boucaud. “Tensile-strained germanium mi-

crodisks”. In: Applied Physics Letters 102.22 (2013), p. 221112. doi: 10 .

1063/1.4809832.

[83] A. Ghrib, M. El Kurdi, M. Prost, S. Sauvage, X. Checoury, G. Beaudoin,

M. Chaigneau, R. Ossikovski, I. Sagnes, and P. Boucaud. “All-Around SiN

Stressor for High and Homogeneous Tensile Strain in Germanium Microdisk

Cavities”. In: Advanced Optical Materials 3.3 (2015), pp. 353–358. doi: 10.

1002/adom.201400369.

[84] D. Stange, S. Wirths, R. Geiger, C. Schulte-Braucks, B. Marzban, N. von den

Driesch, G. Mussler, T. Zabel, T. Stoica, J.-m. Hartmann, S. Mantl, Z. Ikonic,

D. Grützmacher, H. Sigg, J. Witzens, and D. Buca. “Optically Pumped GeSn

Microdisk Lasers on Si”. In: ACS Photonics 3.7 (July 2016), pp. 1279–1285.

doi: 10.1021/acsphotonics.6b00258.

[85] R. Millar, K. Gallacher, J. Frigerio, A. Ballabio, A. Bashir, I. MacLaren, G.

Isella, and D. J. Paul. “Analysis of Ge micro-cavities with in-plane tensile

strains above 2 %”. In: Optics Express 24.5 (2016), p. 4365. doi: 10.1364/

OE.24.004365.

XXXIII

Bibliography

[86] C. S. Fenrich, X. Chen, R. Chen, Y.-C. Huang, H. Chung, M.-Y. Kao, Y. Huo,

T. I. Kamins, and J. S. Harris. “Strained Pseudomorphic Ge1– x Snx Multiple

Quantum Well Microdisk Using SiNy Stressor Layer”. In: ACS Photonics 3.12

(Dec. 2016), pp. 2231–2236. doi: 10.1021/acsphotonics.6b00562.

[87] S. Wirths, D. Stange, M.-A. Pampillón, A. T. Tiedemann, G. Mussler, A.

Fox, U. Breuer, B. Baert, E. San Andrés, N. D. Nguyen, J.-M. Hartmann, Z.

Ikonic, S. Mantl, and D. Buca. “High-k Gate Stacks on Low Bandgap Tensile

Strained Ge and GeSn Alloys for Field-Effect Transistors”. In: ACS Applied

Materials & Interfaces 7.1 (2015), pp. 62–67. doi: 10.1021/am5075248.

[88] R. W. Millar, D. C. S. Dumas, K. F. Gallacher, P. Jahandar, C. MacGregor,

M. Myronov, and D. J. Paul. “Mid-infrared light emission > 3 µm wavelength

from tensile strained GeSn microdisks”. In: Optics Express 25.21 (2017),

p. 25374. doi: 10.1364/OE.25.025374.

[89] J. H. Bahng, K. J. Kim, S. H. Ihm, J. Y. Kim, and H. L. Park. “Evolution of

optical constants and electronic structure of disordered Si1-xGex alloys”. In:

Journal of Physics: Condensed Matter 13.4 (Jan. 2001), pp. 777–786. doi:

10.1088/0953-8984/13/4/323.

[90] K. A. Johnson and N. W. Ashcroft. “Electronic structure of ordered sili-

con alloys: Direct-gap systems”. In: Physical Review B 54.20 (Nov. 1996),

pp. 14480–14486. doi: 10.1103/PhysRevB.54.14480.

[91] J. Tolle, A. V. G. Chizmeshya, Y. Y. Fang, J. Kouvetakis, V. R. D’Costa,

C. W. Hu, J. Menéndez, and I. S. T. Tsong. “Low temperature chemi-

cal vapor deposition of Si-based compounds via SiH3SiH2SiH3: Metastable

SiSn/GeSn/Si(100) heteroepitaxial structures”. In: Applied Physics Letters

89.23 (2006), pp. 2004–2007. doi: 10.1063/1.2403903.

[92] V. R. D’Costa, Y. Y. Fang, J. Tolle, J. Kouvetakis, and J. Menéndez. “Tun-

able Optical Gap at a Fixed Lattice Constant in Group-IV Semiconduc-

tor Alloys”. In: Physical Review Letters 102.10 (Mar. 2009), p. 107403. doi:

10.1103/PhysRevLett.102.107403.

XXXIV

[93] M. Bauer, C. Ritter, P. A. Crozier, J. Ren, J. Menendez, G. Wolf, and

J. Kouvetakis. “Synthesis of ternary SiGeSn semiconductors on Si(100) via

SnxGe1-x buffer layers”. In: Applied Physics Letters 83.11 (2003), p. 2163.

doi: 10.1063/1.1606104.

[94] P. Aella, C. Cook, J. Tolle, S. Zollner, A. V. G. Chizmeshya, and J. Kouve-

takis. “Optical and structural properties of SixSnyGe1-x-y alloys”. In: Applied

Physics Letters 84.6 (2004), pp. 888–890. doi: 10.1063/1.1645324.

[95] V. R. D’Costa, C. S. Cook, J. Menéndez, J. Tolle, J. Kouvetakis, and S.

Zollner. “Transferability of optical bowing parameters between binary and

ternary group-IV alloys”. In: Solid State Communications 138.6 (May 2006),

pp. 309–313. doi: 10.1016/j.ssc.2006.02.023.

[96] V. R. D’Costa, Y. Y. Fang, J. Tolle, J. Kouvetakis, J. Menéndez, M. Caldas,

and N. Studart. “Direct absorption edge in GeSiSn alloys”. In: AIP Confer-

ence Proceedings. Vol. 1199. January 2010. 2010, pp. 39–40. doi: 10.1063/

1.3295471.

[97] C. Xu, C. L. Senaratne, J. Kouvetakis, and J. Menéndez. “Compositional

dependence of optical interband transition energies in GeSn and GeSiSn al-

loys”. In: Solid-State Electronics 110 (Aug. 2015), pp. 76–82. doi: 10.1016/

j.sse.2015.01.015.

[98] R. Soref, J. Kouvetakis, J. Tolle, J. Menendez, and V. D’Costa. “Advances

in SiGeSn technology”. In: Journal of Materials Research 22.12 (2007),

pp. 3281–3291. doi: 10.1557/JMR.2007.0415.

[99] J. D. Gallagher, C. Xu, L. Jiang, J. Kouvetakis, and J. Menéndez. “Funda-

mental band gap and direct-indirect crossover in Ge1-x-ySixSny alloys”. In:


[100] L. Jiang, C. Xu, J. D. Gallagher, R. Favaro, T. Aoki, J. Menéndez, and J.

Kouvetakis. “Development of Light Emitting Group IV Ternary Alloys on Si

Platforms for Long Wavelength Optoelectronic Applications”. In: Chemistry

of Materials 26.8 (Apr. 2014), pp. 2522–2531. doi: 10.1021/cm403801b.

XXXV

Bibliography

[101] T. Wendav, I. A. Fischer, M. Montanari, M. H. Zoellner, W. Klesse, G.

Capellini, N. von den Driesch, M. Oehme, D. Buca, K. Busch, and J. Schulze.

“Compositional dependence of the band-gap of Ge1-x-ySixSny alloys”. In:

Applied Physics Letters 108.24 (June 2016), p. 242104. doi: 10.1063/1.

4953784.

[102] B. Alharthi, J. Margetis, H. Tran, S. Al-kabi, W. Dou, S. A. Ghetmiri, A.

Mosleh, J. Tolle, W. Du, M. Mortazavi, B. Li, H. Naseem, and S.-Q. Yu.

“Study of material and optical properties of SixGe1-x-ySny alloys for Si-

based optoelectronic device applications”. In: Optical Materials Express 7.10

(Oct. 2017), p. 3517. doi: 10.1364/OME.7.003517.

[103] J. D. Gallagher, C. Xu, C. L. Senaratne, T. Aoki, P. M. Wallace, J. Kouve-

takis, and J. Menéndez. “Ge1-x-ySixSny light emitting diodes on silicon for

mid-infrared photonic applications”. In: Journal of Applied Physics 118.13

(2015), p. 135701. doi: 10.1063/1.4931770.

[104] P. Moontragoon, P. Pengpit, T. Burinprakhon, S. Maensiri, N. Vukmirovic, Z.

Ikonic, and P. Harrison. “Electronic properties calculation of Ge1-x-ySixSny

ternary alloy and nanostructure”. In: Journal of Non-Crystalline Solids

358.17 (2012), pp. 2096–2098. doi: 10.1016/j.jnoncrysol.2012.01.025.

[105] A. Attiaoui and O. Moutanabbir. “Indirect-to-direct band gap transition in

relaxed and strained Ge1-x-ySixSny ternary alloys”. In: Journal of Applied

Physics 116.6 (Aug. 2014), p. 063712. doi: 10.1063/1.4889926.

[106] I. A. Fischer, A. Berrier, F. Hornung, M. Oehme, P. Zaumseil, G. Capellini,

N. von den Driesch, Dan Buca, and J. Schulze. “Optical critical points of

SixGe1-x-ySny alloys with high Si content”. In: Semiconductor Science and

Technology 32.12 (Dec. 2017), p. 124004. doi: 10.1088/1361-6641/aa95d3.

[107] S. H. Wei and A. Zunger. “Giant and composition-dependent optical bowing

coefficient in GaAsN alloys”. In: Physical Review Letters 76.4 (1996), pp. 664–

667. doi: 10.1103/PhysRevLett.76.664.

[108] T. Mattila, S.-H. Wei, and A. Zunger. “Localization and anticrossing of elec-

tron levels in GaAs1-xNx alloys”. In: Physical Review B 60.16 (Oct. 1999),

R11245–R11248. doi: 10.1103/PhysRevB.60.R11245.

XXXVI

[109] U. Tisch, E. Finkman, and J. Salzman. “The anomalous bandgap bowing

in GaAsN”. In: Applied Physics Letters 81.3 (July 2002), pp. 463–465. doi:

10.1063/1.1494469.

[110] S. Mukherjee, N. Kodali, D. Isheim, S. Wirths, J. M. Hartmann, D. Buca,

D. N. Seidman, and O. Moutanabbir. “Short-range atomic ordering in

nonequilibrium silicon-germanium-tin semiconductors”. In: Physical Review

B 95.16 (Apr. 2017), p. 161402. doi: 10.1103/PhysRevB.95.161402.

[111] S. Wirths, D. Buca, Z. Ikonić, P. Harrison, A. T. Tiedemann, B. Holländer,

T. Stoica, G. Mussler, U. Breuer, J.-M. Hartmann, D. Grützmacher, and

S. Mantl. “SiGeSn growth studies using reduced pressure chemical vapor

deposition towards optoelectronic applications”. In: Thin Solid Films 557

(2014), pp. 183–187. doi: 10.1016/j.tsf.2013.10.078.

[112] R. Khazaka, E. Nolot, J. Aubin, and J.-M. Hartmann. “Growth and charac-

terization of SiGeSn pseudomorphic layers on 200 mm Ge virtual substrates”.

In: Semiconductor Science and Technology 33.12 (Dec. 2018), p. 124011. doi:

10.1088/1361-6641/aaea32.

[113] A. Attiaoui, S. Wirth, A.-P. Blanchard-Dionne, M. Meunier, J. M. Hartmann,

D. Buca, and O. Moutanabbir. “Extreme IR absorption in group IV-SiGeSn

core-shell nanowires”. In: Journal of Applied Physics 123.22 (June 2018),

p. 223102. doi: 10.1063/1.5021393. arXiv: 1702.00682.

[114] S. A. Ghetmiri, Y. Zhou, J. Margetis, S. Al-Kabi, W. Dou, A. Mosleh, W.

Du, A. Kuchuk, J. Liu, G. Sun, R. A. Soref, J. Tolle, H. A. Naseem, B.

Li, M. Mortazavi, and S.-Q. Yu. “Study of a SiGeSn/GeSn/SiGeSn structure

toward direct bandgap type-I quantum well for all group-IV optoelectronics”.

In: Optics Letters 42.3 (2017), p. 387. doi: 10.1364/OL.42.000387.

[115] D. Rainko, Z. Ikonic, N. Vukmirović, D. Stange, N. von den Driesch, D.

Grützmacher, and D. Buca. “Investigation of carrier confinement in direct

bandgap GeSn/SiGeSn 2D and 0D heterostructures”. In: Scientific Reports

8.1 (Dec. 2018), p. 15557. doi: 10.1038/s41598-018-33820-1.

[116] R. A. Soref. “Direct-gap Ge/GeSn/Si and GeSn/Ge/Si heterostructures”. In:

Superlattices and Microstructures 14.2/3 (1994), pp. 189–193.

XXXVII

Bibliography

[117] Z. Alferov. “Double heterostructure lasers: Early days and future perspec-

tives”. In: IEEE Journal on Selected Topics in Quantum Electronics 6.6

(2000), pp. 832–840. doi: 10.1109/2944.902131.

[118] G. Sun, H. H. Cheng, J. Menéndez, J. B. Khurgin, and R. A. Soref. “Strain-

free Ge/GeSiSn quantum cascade lasers based on L-valley intersubband tran-

sitions”. In: Applied Physics Letters 90.25 (June 2007), p. 251105. doi: 10.

1063/1.2749844.

[119] S. Wirths, A. T. Tiedemann, Z. Ikonic, P. Harrison, B. Holländer, T. Stoica,

G. Mussler, M. Myronov, J. M. Hartmann, D. Grützmacher, D. Buca, and

S. Mantl. “Band engineering and growth of tensile strained Ge/(Si)GeSn

heterostructures for tunnel field effect transistors”. In: Applied Physics Letters

102.19 (2013), p. 192103. doi: 10.1063/1.4805034.

[120] H. Wang, G. Han, Y. Liu, S. Hu, and C. Zhang. “Theoretical Investigation

of Performance Enhancement in GeSn / SiGeSn Type-II Staggered Hetero-

junction Tunneling FET”. In: 63.1 (2016), pp. 303–310. doi: 10.1109/TED.

2015.2503385.

[121] C. Schulte-Braucks, R. Pandey, R. N. Sajjad, M. Barth, R. K. Ghosh, B.

Grisafe, P. Sharma, N. von den Driesch, A. Vohra, G. B. Rayner, R. Loo, S.

Mantl, D. Buca, C.-c. Yeh, C.-h. Wu, W. Tsai, D. A. Antoniadis, and S. Datta.

“Fabrication, Characterization, and Analysis of Ge/GeSn Heterojunction p-

Type Tunnel Transistors”. In: IEEE Transactions on Electron Devices 64.10

(Oct. 2017), pp. 4354–4362. doi: 10.1109/TED.2017.2742957.

[122] G.-E. Chang, S.-W. Chang, and S. L. Chuang. “Theory for n-type doped,

tensile-strained Ge-SixGeySn1-x-y quantum-well lasers at telecom wave-

length”. In: Optics Express 17.14 (July 2009), p. 11246. doi: 10.1364/OE.

17.011246.

[123] R. Chen, S. Gupta, Y. C. Huang, Y. Huo, C. W. Rudy, E. Sanchez, Y.

Kim, T. I. Kamins, K. C. Saraswat, and J. S. Harris. “Demonstration of

a Ge/GeSn/Ge quantum-well microdisk resonator on silicon: Enabling high-

quality Ge(Sn) materials for micro-and nanophotonics”. In: Nano Letters 14.1

(2014), pp. 37–43. doi: 10.1021/nl402815v.

XXXVIII

[124] J. D. Gallagher, C. L. Senaratne, C. Xu, P. Sims, T. Aoki, D. J. Smith,

J. Menéndez, and J. Kouvetakis. “Non-radiative recombination in Ge1-ySny

light emitting diodes: The role of strain relaxation in tuned heterostructure

designs”. In: Journal of Applied Physics 117.24 (2015), p. 245704. doi: 10.

1063/1.4923060.

[125] B. Schwartz, M. Oehme, K. Kostecki, D. Widmann, M. Gollhofer, R. Koerner,

S. Bechler, I. A. Fischer, T. Wendav, E. Kasper, J. Schulze, and M. Kittler.

“Electroluminescence of GeSn/Ge MQW LEDs on Si substrate”. In: Opt.

Lett. 40.13 (2015), pp. 3209–3212. doi: 10.1364/OL.40.003209.

[126] Y. Zhou, W. Dou, W. Du, T. Pham, S. A. Ghetmiri, S. Al-Kabi, A. Mosleh,

M. Alher, J. Margetis, J. Tolle, G. Sun, R. Soref, B. Li, M. Mortazavi,

H. Naseem, and S.-q. Yu. “Systematic study of GeSn heterostructure-based

light-emitting diodes towards mid-infrared applications”. In: Journal of Ap-

plied Physics 120.2 (July 2016), p. 023102. doi: 10.1063/1.4958337.

[127] D. Stange, N. von den Driesch, D. Rainko, C. Schulte-Braucks, S. Wirths, G.

Mussler, A. T. Tiedemann, T. Stoica, J. M. Hartmann, Z. Ikonic, S. Mantl, D.

Grützmacher, and D. Buca. “Study of GeSn based heterostructures: towards

optimized group IV MQW LEDs”. In: Optics Express 24.2 (2016), p. 1358.

doi: 10.1364/OE.24.001358.

[128] J. Zheng, S. Wang, H. Cong, C. S. Fenrich, Z. Liu, C. Xue, C. Li, Y.

Zuo, B. Cheng, J. S. Harris, and Q. Wang. “Characterization of a Ge1-x-

ySiySnx/Ge1-xSnx multiple quantum well structure grown by sputtering epi-

taxy”. In: Optics Letters 42.8 (2017), pp. 1608–1611. doi: 10.1364/OL.42.

001608.

[129] Y.-H. Zhu, Q. Xu, W.-J. Fan, and J.-W. Wang. “Theoretical gain of strained

GeSn0.02/Ge1-x-ySixSny quantum well laser”. In: Journal of Applied Physics

107.7 (Apr. 2010), p. 073108. doi: 10.1063/1.3329424.

[130] G. Sun, R. A. Soref, and H. H. Cheng. “Design of a Si-based lattice-

matched room-temperature GeSn/GeSiSn multi-quantum-well mid-infrared

laser diode.” In: Optics express 18.19 (2010), pp. 19957–19965. doi: 10.1364/

OE.18.019957.

XXXIX

Bibliography

[131] G. Sun, R. A. Soref, and H. H. Cheng. “Design of an electrically pumped

SiGeSn/GeSn/SiGeSn double-heterostructure midinfrared laser”. In: Journal

of Applied Physics 108.3 (Aug. 2010), p. 033107. doi: 10.1063/1.3467766.

arXiv: 1608.03629.

[132] G.-E. Chang, S.-W. Chang, and S. L. Chuang. “Strain-Balanced GezSn1-z

SixGeySn1-x-y Multiple-Quantum-Well Lasers”. In: IEEE Journal of Quan-

tum Electronics 46.12 (2010), pp. 1813–1820.

[133] P. Moontragoon, R. A. Soref, and Z. Ikonic. “The direct and indirect

bandgaps of unstrained SixGe1-x-ySny and their photonic device applica-

tions”. In: Journal of Applied Physics 112.7 (Oct. 2012), p. 073106. doi:

10.1063/1.4757414.

[134] T. Ihn. Semiconductor Nanostructures Quantum States and Electronic Trans-

port. Oxford University Press, 2010.

[135] P. Harrison and A. Valavanis. Quantum Wells, Wires and Dots. 2nd ed. Leeds:

John Wiley & Sons, Ltd, 2005.

[136] F. Alharbi. “An explicit FDM calculation of nonparabolicity effects in energy

states of quantum wells”. In: Optical and Quantum Electronics 40.8 (2008),

pp. 551–559. doi: 10.1007/s11082-008-9241-6.

[137] M. Jaros. “Simple analytic model for heterojunction band offsets”. In: Physi-

cal Review B 37.12 (1988), pp. 7112–7114. doi: 10.1103/PhysRevB.37.7112.

arXiv: arXiv:1011.1669v3.

[138] F. Capasso and G. Margaritondo. heterojunction band discontinuities -

physics and device application. Elsevier Science Publishers B.V., 1987.

[139] D. Tammaro, K. Hess, and F. Capasso. “Γ-X phonon-assisted thermionic

currents in the GaAs/AlxGa1-xAs interface system”. In: Journal of Applied

Physics 73.12 (1993), pp. 8536–8543. doi: 10.1063/1.353383.

[140] R. People and J. C. Bean. “Calculation of critical layer thickness versus lattice

mismatch for GexSi1-x/Si strained- layer heterostructures”. In: Appl. Phys.

Lett. 47.1985 (1985), p. 322. doi: 10.1063/1.96206.

XL

[141] W. Wang, Q. Zhou, Y. Dong, E. S. Tok, and Y.-C. Yeo. “Critical thickness for

strain relaxation of Ge1-xSnx (x < 0.17) grown by molecular beam epitaxy

on Ge(001)”. In: Applied Physics Letters 106.23 (2015), p. 232106. doi: 10.

1063/1.4922529.

[142] N. Bhargava, M. Coppinger, J. Prakash Gupta, L. Wielunski, and J.

Kolodzey. “Lattice constant and substitutional composition of GeSn alloys

grown by molecular beam epitaxy”. In: Applied Physics Letters 103.4 (2013),

p. 041908. doi: 10.1063/1.4816660.

[143] D. Stange, S. Wirths, N. von den Driesch, G. Mussler, T. Stoica, Z. Ikonic,

J. M. Hartmann, S. Mantl, D. Grützmacher, and D. Buca. “Optical Transi-

tions in Direct-Bandgap Ge1-xSnx Alloys”. In: ACS Photonics 2.11 (2015),


[144] D. Stange, N. von den Driesch, D. Rainko, T. Zabel, B. Marzban, Z. Ikonic,

P. Zaumseil, G. Capellini, and S. Mantl. “Quantum Confinement Effects in

GeSn/SiGeSn Heterostructure Lasers”. In: IEEE International Electron De-

vices Meeting (IEDM). San Francisco, 2017, pp. 589–592.

[145] H. S. Maczko, R. Kudrawiec, and M. Gladysiewicz. “Material gain engineer-

ing in GeSn/Ge quantum wells integrated with an Si platform”. In: Scientific

Reports 6.1 (Dec. 2016), p. 34082. doi: 10.1038/srep34082.

[146] R. Camacho-Aguilera, Z. Han, Y. Cai, L. C. Kimerling, and J. Michel. “Direct

band gap narrowing in highly doped Ge”. In: Applied Physics Letters 102.15

(2013), p. 152106. doi: 10.1063/1.4802199.

[147] S. Saito, A. Z. Al-Attili, K. Oda, and Y. Ishikawa. “Towards monolithic

integration of germanium light sources on silicon chips”. In: Semiconductor

Science and Technology 31.4 (Apr. 2016), p. 043002. doi: 10.1088/0268-

1242/31/4/043002.

[148] D. Rainko, D. Stange, N. von den Driesch, C. Schulte-braucks, G. Mussler,

Z. Ikonić, J. M. Hartmann, M. Luysberg, S. Mantl, D. Grützmacher, and

D. Buca. “(Si)GeSn nanostructures for light emitters”. In: SPIE. Ed. by L.

Vivien, L. Pavesi, and S. Pelli. Vol. 9891. Brussels, May 2016, 98910W. doi:

10.1117/12.2227573.

XLI

Bibliography

[149] A. Y. Liu, S. Srinivasan, J. Norman, A. C. Gossard, and J. E. Bowers. “Quan-

tum dot lasers for silicon photonics [Invited]”. In: Photonics Research 3.5

(Oct. 2015), B1. doi: 10.1364/PRJ.3.0000B1.

[150] A. I. Yakimov, V. V. Kirienko, V. A. Armbrister, A. A. Bloshkin, and A. V.

Dvurechenskii. “Phonon bottleneck in p-type Ge/Si quantum dots”. In: Ap-

plied Physics Letters 107.21 (2015). doi: 10.1063/1.4936340.

[151] A. Alivisatos. “Semiconductor Clusters, Nanocrystals, and Quantum Dots”.

In: Science 271.5251 (1996), pp. 933–937.

[152] B. W. Boote, L. Men, H. P. Andaraarachchi, U. Bhattacharjee, J. W. Petrich,

J. Vela, and E. A. Smith. “Germanium-Tin/Cadmium Sulfide Core/Shell

Nanocrystals with Enhanced Near-Infrared Photoluminescence”. In: Chem-

istry of Materials 29.14 (2017), pp. 6012–6021. doi: 10 . 1021 / acs .

chemmater.7b01815.

[153] K. Ramasamy, P. G. Kotula, A. F. Fidler, M. T. Brumbach, J. M. Pietryga,

and S. a. Ivanov. “SnxGe1-x Alloy Nanocrystals: A First Step Toward

Solution-Processed Group IV Photovoltaics”. In: Chemistry of Materials

JUNE (2015), p. 150616121704000. doi: 10.1021/acs.chemmater.5b01041.

[154] V. Tallapally, T. A. Nakagawara, D. O. Demchenko, Ü. Özgür, and I. U.

Arachchige. “Ge1-xSnx alloy quantum dots with composition-tunable en-

ergy gaps and near-infrared photoluminescence”. In: Nanoscale 10.43 (2018),

pp. 20296–20305. doi: 10.1039/C8NR04399J.

[155] Q. Yang, X. Zhao, X. Wu, M. Li, Q. Di, X. Fan, J. Zhu, X. Song, Q. Li, and

Z. Quan. “Facile Synthesis of Uniform Sn1-xGex Alloy Nanocrystals with

Tunable Bandgap”. In: Chemistry of Materials (Mar. 2019). doi: 10.1021/

acs.chemmater.8b04153.

[156] A. Ekimov, A. Efros, and A. Onushchenko. “Quantum size effect in semicon-

ductor microcrystals”. In: Solid State Communications 56.11 (Dec. 1985),

pp. 921–924. doi: 10.1016/S0038-1098(85)80025-9. arXiv: NIHMS150003.

XLII

[157] S. J. Shin, J. Guzman, C.-W. Yuan, C. Y. Liao, C. N. Boswell-Koller, P. R.

Stone, O. D. Dubon, a. M. Minor, M. Watanabe, J. W. Beeman, K. M. Yu,

J. W. Ager, D. C. Chrzan, and E. E. Haller. “Embedded Binary Eutectic

Alloy Nanostructures: A New Class of Phase Change Materials”. In: Nano

Letters 10.8 (2010), pp. 2794–2798. doi: 10.1021/nl100670r.

[158] D. Leonard, M. Krishnamurthy, C. M. Reaves, S. P. Denbaars, and P. M.

Petroff. “Direct formation of quantum-sized dots from uniform coherent is-

lands of InGaAs on GaAs surfaces”. In: Applied Physics Letters 63.23 (1993),

pp. 3203–3205. doi: 10.1063/1.110199.

[159] N. Vukmirović. “Physics of intraband quantum dot optoelectronic devices”.

PhD thesis. University of Leeds, 2007.

[160] L. Goldstein, F. Glas, J. Y. Marzin, M. N. Charasse, and G. Le Roux.

“Growth by molecular beam epitaxy and characterization of InAs/GaAs

strained-layer superlattices”. In: Applied Physics Letters 47.10 (Nov. 1985),

pp. 1099–1101. doi: 10.1063/1.96342.

[161] Y. Kim, K. Y. Ban, C. Zhang, and C. B. Honsberg. “Material and device

characteristics of InAs/GaAsSb sub-monolayer quantum dot solar cells”. In:

Applied Physics Letters 107.15 (2015). doi: 10.1063/1.4933272.

[162] D. Tang, Y. Kim, N. Faleev, C. B. Honsberg, and D. J. Smith. “Investiga-

tion of single-layer/multilayer self-assembled InAs quantum dots on GaAs1-

xSbx/GaAs composite substrates”. In: Journal of Applied Physics 118.9

(2015), p. 094303. doi: 10.1063/1.4929639.

[163] Y. Wan, Q. Li, A. Y. Liu, W. W. Chow, A. C. Gossard, J. E. Bowers, E. L.

Hu, and K. M. Lau. “Sub-wavelength InAs quantum dot micro-disk lasers

epitaxially grown on exact Si (001) substrates”. In: Applied Physics Letters

108.22 (May 2016), p. 221101. doi: 10.1063/1.4952600.

[164] Y. Zhou, J. Zhang, Y. Ning, Y. Zeng, J. Zhang, X. Zhang, L. Qin, C. Tong,

Y. Liu, and L. Wang. “High-power dual-wavelength lasing in bimodal- sized

InGaAs / GaAs quantum dots”. In: Optics Express 24.25 (2016), p. 29321.

XLIII

Bibliography

[165] M. F. Fyhn, J. Chevallier, A. N. Larsen, R. Feidenhans’l, and M. Seibt.

“alpha-Sn and beta-Sn precipitates in annealed epitaxial Si0.95Sn0.05”.

In: Physical Review B 60.8 (Aug. 1999), pp. 5770–5777. doi: 10 . 1103 /

PhysRevB.60.5770.

[166] R. Ragan and H. A. Atwater. “Diamond cubic Sn-rich nanocrystals: Synthe-

sis, microstructure and optical properties”. In: Applied Physics A: Materials

Science and Processing 80.6 (2005), pp. 1335–1338. doi: 10.1007/s00339-

004-3163-3.

[167] S. Takeuchi, A. Sakai, O. Nakatsuka, M. Ogawa, and S. Zaima. “Tensile

strained Ge layers on strain-relaxed Ge1-xSnx/virtual Ge substrates”. In:

Thin Solid Films 517.1 (Nov. 2008), pp. 159–162. doi: 10.1016/j.tsf.

2008.08.068.

[168] H. Li, Y. X. Cui, K. Y. Wu, W. K. Tseng, H. H. Cheng, and H. Chen. “Strain

relaxation and Sn segregation in GeSn epilayers under thermal treatment”.

In: Applied Physics Letters 102.25 (June 2013), p. 251907. doi: 10.1063/1.

4812490.

[169] A. Tonkikh, N. D. Zakharov, A. Suvorova, C. Eisenschmidt, J. Schilling,

and P. Werner. “Cubic phase Sn-rich GeSn nanocrystals in a Ge matrix”.

In: Crystal Growth and Design 14.4 (2014), pp. 1617–1622. doi: 10.1021/

cg401652f.

[170] S. Roesgaard, J. Chevallier, P. I. Gaiduk, J. L. Hansen, P. B. Jensen, A. N.

Larsen, A. Svane, P. Balling, and B. Julsgaard. “Light emission from silicon

with tin-containing nanocrystals”. In: AIP Advances 5.7 (2015). doi: 10.

1063/1.4926596. arXiv: 1504.07759.

[171] P. Kringhøj and A. N. Larsen. “Anomalous diffusion of tin in silicon”.

In: Physical Review B 56.11 (Sept. 1997), pp. 6396–6399. doi: 10.1103/

PhysRevB.56.6396.

[172] A. L. Efros and D. J. Nesbitt. “Origin and control of blinking in quantum

dots”. In: Nature Nanotechnology 11.8 (Aug. 2016), pp. 661–671. doi: 10.

1038/nnano.2016.140.

XLIV

[173] F. Oliveira, I. A. Fischer, A. Benedetti, M. F. Cerqueira, M. I. Vasilevskiy,

S. Stefanov, S. Chiussi, and J. Schulze. “Multi-stacks of epitaxial GeSn self-

assembled dots in Si: Structural analysis”. In: Journal of Applied Physics

117.12 (Mar. 2015), p. 125706. doi: 10.1063/1.4915939.

[174] R. V. S. Jensen, T. Garm Pedersen, and K. Pedersen. “Optical properties

and size/shape dependence of alpha-Sn nanocrystals by tight binding”. In:

Physica Status Solidi (C) Current Topics in Solid State Physics 8.3 (2011),

pp. 1002–1005. doi: 10.1002/pssc.201000397.

[175] P. Moontragoon, N. Vukmirović, Z. Ikonić, and P. Harrison. “Electronic struc-

ture and optical properties of Sn and SnGe quantum dots”. In: Journal of

Applied Physics 103.10 (May 2008), p. 103712. doi: 10.1063/1.2932169.

[176] B. Ilahi. “Design of direct band gap type I GeSn/Ge quantum dots for mid-

IR light emitters on Si substrate”. In: Physica Status Solidi - Rapid Research

Letters 11.5 (2017), pp. 1–5. doi: 10.1002/pssr.201700047.

[177] H.-S. Lan, S. T. Chang, and C. W. Liu. “Semiconductor, topological

semimetal, indirect semimetal, and topological Dirac semimetal phases of

Ge1-xSnx alloys”. In: Physical Review B 95.20 (May 2017), p. 201201. doi:

10.1103/PhysRevB.95.201201. arXiv: 1612.00159.

[178] J. D. Gallagher, C. L. Senaratne, P. M. Wallace, J. Menéndez, and J. Kou-

vetakis. “Electroluminescence from Ge1 - y Sn y diodes with degenerate pn

junctions Electroluminescence from Ge 1 2 y Sn y diodes with degenerate

pn junctions”. In: Applied Physics A: Materials Science and Processing 107

(2015), p. 123507. doi: 10.1063/1.4931707.

[179] R. Koerner, D. Schwaiz, I. A. Fischer, L. Augel, S. Bechler, L. Haenel,

M. Kern, M. Oehme, E. Rolseth, B. Schwartz, D. Weisshaupt, W. Zhang,

and J. Schulze. “The Zener-Emitter: A novel superluminescent Ge optical

waveguide-amplifier with 4.7 dB gain at 92 mA based on free-carrier modula-

tion by direct Zener tunneling monolithically integrated on Si”. In: Technical

Digest - International Electron Devices Meeting, IEDM (2017), pp. 22.5.1–

22.5.4. doi: 10.1109/IEDM.2016.7838474.

XLV

Bibliography

[180] B. Vincent, F. Gencarelli, H. Bender, C. Merckling, B. Douhard, D. H. Pe-

tersen, O. Hansen, H. H. Henrichsen, J. Meersschaut, W. Vandervorst, M.

Heyns, R. Loo, and M. Caymax. “Undoped and in-situ B doped GeSn epi-

taxial growth on Ge by atmospheric pressure-chemical vapor deposition”. In:

Applied Physics Letters 99.15 (2011), pp. 1–4. doi: 10.1063/1.3645620.

[181] S. Wirths, Z. Ikonic, N. von den Driesch, G. Mussler, U. Breuer, A. Tiede-

mann, P. Bernardy, B. Hollander, T. Stoica, J.-M. Hartmann, D. Grutz-

macher, S. Mantl, and D. Buca. “Growth Studies of Doped SiGeSn/Strained

Ge(Sn) Heterostructures”. In: ECS Transactions 64.6 (Aug. 2014), pp. 689–

696. doi: 10.1149/06406.0689ecst.

[182] J. Aubin, J.-M. Hartmann, J.-P. Barnes, J.-B. Pin, and M. Bauer. “Very

Low Temperature Epitaxy of Heavily In-situ Phosphorous Doped Ge Layers

and High Sn Content GeSn Layers”. In: ECS Transactions 75.8 (Sept. 2016),

pp. 387–398. doi: 10.1149/07508.0387ecst.

[183] M. Oehme, J. Werner, M. Gollhofer, M. Schmid, M. Kaschel, E. Kasper,

and J. Schulze. “Room Temperature Electroluminescence from GeSn Light

Emitting pin Diodes on Si”. In: IEEE Photonics Technology Letters 23.23

(2011), pp. 1751–1753. doi: 10.1109/LPT.2011.2169052.

[184] H. H. Tseng, H. Li, V. Mashanov, Y. J. Yang, H. H. Cheng, G. E. Chang,

R. A. Soref, and G. Sun. “GeSn-based p-i-n photodiodes with strained active

layer on a Si wafer”. In: Applied Physics Letters 103.23 (Dec. 2013), p. 231907.

doi: 10.1063/1.4840135.

[185] C. Merckling, S. Jiang, Z. Liu, N. Waldron, G. Boccardi, R. Rooyackers, Z.

Wang, B. Tian, M. Pantouvaki, N. Collaert, J. Van Campenhout, M. Heyns,

D. Van Thourhout, W. Vandervorst, and A. Thean. “(Invited) Monolithic

Integration of III-V Semiconductors by Selective Area Growth on Si(001)

Substrate: Epitaxy Challenges & Applications”. In: ECS Transactions 66.4

(May 2015), pp. 107–116. doi: 10.1149/06604.0107ecst.

[186] J.-S. Park, J. Bai, M. Curtin, B. Adekore, M. Carroll, and a. Lochtefeld. “De-

fect reduction of selective Ge epitaxy in trenches on Si(001) substrates using

XLVI

aspect ratio trapping”. In: Applied Physics Letters 90.5 (2007), p. 052113.

doi: 10.1063/1.2435603.

[187] C. V. Falub, H. von Känel, F. Isa, R. Bergamaschini, A. Marzegalli, D.

Chrastina, G. Isella, E. Müller, P. Niedermann, and L. Miglio. “Scaling

Hetero-Epitaxy from Layers to Three-Dimensional Crystals”. In: Science

335.6074 (2012), pp. 1330–1334. doi: 10.1126/science.1217666.

[188] M. Salvalaglio, R. Bergamaschini, F. Isa, A. Scaccabarozzi, G. Isella, R. Back-

ofen, A. Voigt, F. Montalenti, G. Capellini, T. Schroeder, H. von Känel, and

L. Miglio. “Engineered Coalescence by Annealing 3D Ge Microstructures into

High-Quality Suspended Layers on Si”. In: ACS Applied Materials & Inter-

faces 7.34 (2015), pp. 19219–19225. doi: 10.1021/acsami.5b05054.

[189] V. Schlykow, W. M. Klesse, G. Niu, N. Taoka, Y. Yamamoto, O. Skibitzki,

M. R. Barget, P. Zaumseil, H. von Känel, M. A. Schubert, G. Capellini,

and T. Schroeder. “Selective growth of fully relaxed GeSn nano-islands by

nanoheteroepitaxy on patterned Si(001)”. In: Applied Physics Letters 109.20

(Nov. 2016), p. 202102. doi: 10.1063/1.4967500.

[190] V. Schlykow, P. Zaumseil, M. A. Schubert, O. Skibitzki, Y. Yamamoto, W. M.

Klesse, Y. Hou, M. Virgilio, M. De Seta, L. Di Gaspare, T. Schroeder, and G.

Capellini. “Photoluminescence from GeSn nano-heterostructures”. In: Nan-

otechnology 29.41 (Oct. 2018), p. 415702. doi: 10.1088/1361-6528/aad626.

[191] J. Holleman. “Selective Chemical Vapor Deposition”. In: Chemical Physics

of Thin Film Deposition Processes for Micro- and Nano-Technologies. Dor-

drecht: Springer Netherlands, 2002, pp. 171–198. doi: 10.1007/978- 94-

010-0353-7_8.

[192] T. O. Sedgwick, P. Agnello, and A. D. Grützmacher. “Effects of Trace Sur-

face Oxidation in Low Temperature Epitaxy Grown from Dichlorosilane”.

In: Journal of The Electrochemical Society 140.12 (1993), p. 3684. doi: 10.

1149/1.2221150.

[193] M. Hierlemann and C. Werner. “Modeling of SiGe deposition using quan-

tum chemistry techniques for detailed kinetic analysis”. In: Materials Science

XLVII

Bibliography

in Semiconductor Processing 3.1-2 (Mar. 2000), pp. 31–39. doi: 10.1016/

S1369-8001(00)00007-X.

[194] S. Wirths, D. Buca, A. T. Tiedemann, B. Hollander, P. Bernardy, T. Stoica,

D. Grutzmacher, and S. Mantl. “Epitaxial Growth of Ge1-xSnx by Reduced

Pressure CVD Using SnCl4 and Ge2H6”. In: ECS Transactions 50.9 (Mar.

2013), pp. 885–893. doi: 10.1149/05009.0885ecst.

[195] J. Margetis, S.-Q. Yu, B. Li, and J. Tolle. “Chemistry and kinetics governing

hydride/chloride chemical vapor deposition of epitaxial Ge1-xSnx”. In: Jour-

nal of Vacuum Science & Technology A 37.2 (Mar. 2019), p. 021508. doi:

10.1116/1.5055620.

[196] R. Loo and M. Caymax. “Avoiding loading effects and facet growth: Key

parameters for a successful implementation of selective epitaxial SiGe depo-

sition for HBT-BiCMOS and high-mobility hetero-channel pMOS devices”.

In: Applied Surface Science 224.1-4 (2004), pp. 24–30. doi: 10.1016/j.

apsusc.2003.08.024.

[197] J. Hållstedt, E. Suvar, C. Menon, P. E. Hellström, M. Östling, and H. H.

Radamson. “Methods to reduce the loading effect in selective and non-

selective epitaxial growth of sigec layers”. In: Materials Science and Engi-

neering B: Solid-State Materials for Advanced Technology 109.1-3 (2004),

pp. 122–126. doi: 10.1016/j.mseb.2003.10.062.

[198] J. P. Liu, H. G. Chew, A. See, M. S. Zhou, and L. C. Hsia. “Loading Effect of

Selective Epitaxial Growth of Silicon Germanium in Submicrometer-Scale Sil-

icon (001) Windows”. In: Electrochemical and Solid-State Letters 12.3 (2009),

H58. doi: 10.1149/1.3049895.

[199] R. A. Soref. “Optical band gap of the ternary semiconductor Si1-x-yGexCy”.

In: Journal of Applied Physics 70.4 (Aug. 1991), pp. 2470–2472. doi: 10.

1063/1.349403.

[200] H. J. Osten, E. Bugiel, and P. Zaumseil. “Growth of an inverse tetragonal dis-

torted SiGe layer on Si(001) by adding small amounts of carbon”. In: Applied

Physics Letters 64.25 (1994), pp. 3440–3442. doi: 10.1063/1.111235.

XLVIII

[201] K. Eberl, S. S. Iyer, S. Zollner, J. C. Tsang, and F. K. Legoues. “Growth

and strain compensation effects in the ternary Si1-x-yGexCy alloy system”.

In: Applied Physics Letters 60.24 (1992), pp. 3033–3035. doi: 10.1063/1.

106774.

[202] W. Windl, O. Sankey, and J. Menéndez. “Theory of strain and electronic

structure of Si1-yCy and Si1-x-yGexCy alloys”. In: Physical Review B 57.4

(1998), pp. 2431–2442. doi: 10.1103/PhysRevB.57.2431.

[203] J. M. Hartmann, T. Ernst, F. Ducroquet, G. Rolland, D. Lafond, A.-M. Pa-

pon, R. Truche, P. Holliger, F. Laugier, M. N. Séméria, and S. Deleonibus.

“High C content Si/Si1-yCy heterostructures for n-type metal oxide semicon-

ductor transistors”. In: Semiconductor Science and Technology 19.5 (2004),

pp. 593–601. doi: 10.1088/0268-1242/19/5/007.

[204] R. I. Scace and G. A. Slack. “Solubility of Carbon in Silicon and Germanium”.

In: The Journal of Chemical Physics 30.6 (June 1959), pp. 1551–1555. doi:

10.1063/1.1730236.

[205] J. Kolodzey, P. A. O’Neil, S. Zhang, B. A. Orner, K. Roe, K. M. Unruh,

C. P. Swann, M. M. Waite, and S. I. Shah. “Growth of germanium-carbon

alloys on silicon substrates by molecular beam epitaxy”. In: Applied Physics

Letters 67.1995 (1995), p. 1865. doi: 10.1063/1.114358.

[206] C. A. Stephenson, W. A. O’Brien, M. W. Penninger, W. F. Schneider, M.

Gillett-Kunnath, J. Zajicek, K. M. Yu, R. Kudrawiec, R. A. Stillwell, and

M. A. Wistey. “Band structure of germanium carbides for direct bandgap sil-

icon photonics”. In: Journal of Applied Physics 120.5 (Aug. 2016), p. 053102.

doi: 10.1063/1.4959255.

[207] A. Jamshidi, M. Noroozi, M. Moeen, A. Hallén, B. Hamawandi, J. Lu, L.

Hultman, M. Östling, and H. Radamson. “Growth of GeSnSiC layers for

photonic applications”. In: Surface and Coatings Technology 230 (Sept. 2013),

pp. 106–110. doi: 10.1016/j.surfcoat.2013.06.074.

[208] P. I. Gaiduk, J. Lundsgaard Hansen, A. Nylandsted Larsen, F. L. Bregolin,

and W. Skorupa. “Suppression of tin precipitation in SiSn alloy layers by

XLIX

Bibliography

implanted carbon”. In: Applied Physics Letters 104.23 (2014), pp. 0–5. doi:

10.1063/1.4882175.

[209] E. Kasper, J. Werner, M. Oehme, S. Escoubas, N. Burle, and J. Schulze.

“Growth of silicon based germanium tin alloys”. In: Thin Solid Films 520.8

(Feb. 2012), pp. 3195–3200. doi: 10.1016/j.tsf.2011.10.114.

[210] P. Blood. “Capacitance-voltage profiling and the characterisation of III-V

semiconductors using electrolyte barriers”. In: Semiconductor Science and

Technology 1.1 (July 1986), pp. 7–27. doi: 10.1088/0268-1242/1/1/002.

[211] V. P. Markevich, A. R. Peaker, B. Hamilton, V. V. Litvinov, Y. M. Pokotilo,

S. B. Lastovskii, J. Coutinho, A. Carvalho, M. J. Rayson, and P. R. Briddon.

“Tin-vacancy complex in germanium”. In: Journal of Applied Physics 109.8

(Apr. 2011), p. 083705. doi: 10.1063/1.3574405.

[212] S. Gupta, E. Simoen, H. Vrielinck, C. Merckling, B. Vincent, F. Gencarelli,

R. Loo, and M. Heyns. “Identification of Deep Levels Associated with Ex-

tended and Point Defects in GeSn Epitaxial Layers Using DLTs”. In: ECS

Transactions 53.1 (May 2013), pp. 251–258. doi: 10.1149/05301.0251ecst.

[213] W. Takeuchi, T. Asano, Y. Inuzuka, M. Sakashita, O. Nakatsuka, and S.

Zaima. “Characterization of Shallow- and Deep-Level Defects in Undoped

Ge1-xSnx Epitaxial Layers by Electrical Measurements”. In: ECS Journal

of Solid State Science and Technology 5.4 (Dec. 2016), P3082–P3086. doi:

10.1149/2.0151604jss.

[214] O. Nakatsuka, Y. Shimura, W. Takeuchi, N. Taoka, and S. Zaima. “Devel-

opment of epitaxial growth technology for Ge1-xSnx alloy and study of its

properties for Ge nanoelectronics”. In: Solid-State Electronics 83 (May 2013),

pp. 82–86. doi: 10.1016/j.sse.2013.01.040.

[215] T. Asano, N. Taoka, K. Hozaki, W. Takeuchi, M. Sakashita, O. Nakat-

suka, and S. Zaima. “Impact of hydrogen surfactant on crystallinity of Ge1-

xSnx epitaxial layers”. In: Japanese Journal of Applied Physics 54.5 (2015),

p. 059202. doi: 10.7567/jjap.54.059202.

[216] J. E. Huheey, E. A. Keiter, and R. L. Keiter. Inorganic Chemistry. Ed. by

J. Piro. 4th ed. New York: Harper Collins, 1993.

L

[217] Z. Alferov. “Double heterostructure lasers: early days and future perspec-

tives”. In: IEEE Journal of Selected Topics in Quantum Electronics 6.6 (Nov.

2000), pp. 832–840. doi: 10.1109/2944.902131.

[218] J. Tatebayashi, S. Kako, J. Ho, Y. Ota, S. Iwamoto, and Y. Arakawa. “Room-

temperature lasing in a single nanowire with quantum dots”. In: Nature Pho-

tonics 9.8 (2015), pp. 501–505. doi: 10.1038/nphoton.2015.111.

[219] E. S. Kim, N. Usami, and Y. Shiraki. “Control of Ge dots in dimension

and position by selective epitaxial growth and their optical properties”. In:


[220] Y. H. Li, A. Walsh, S. Chen, W. J. Yin, J. H. Yang, J. Li, J. L. Da Silva, X. G.

Gong, and S. H. Wei. “Revised ab initio natural band offsets of all group IV,

II-VI, and III-V semiconductors”. In: Applied Physics Letters 94.21 (2009),

pp. 1–4. doi: 10.1063/1.3143626.

[221] J. Bardeen and W. Shockley. “Deformation Potentials and Mobilities in Non-

Polar Crystals”. In: Physical Review 80.1 (Oct. 1950), pp. 72–80. doi: 10.

1103/PhysRev.80.72.

[222] F. H. Pollak and M. Cardona. “Piezo-Electroreflectance in Ge, GaAs, and

Si”. In: Physical Review 172.3 (Aug. 1968). Ed. by Intergovernmental Panel

on Climate Change, pp. 816–837. doi: 10.1103/PhysRev.172.816.

[223] G. L. Bir and G. E. Pikus. Symmetry and strain-induced effects in semicon-

ductors. New York: Wiley, 1974.

[224] Y. H. Li, X. G. Gong, and S. H. Wei. “Ab initio all-electron calculation of

absolute volume deformation potentials of IV-IV, III-V, and II-VI semicon-

ductors: The chemical trends”. In: Physical Review B - Condensed Matter

and Materials Physics 73.24 (2006), pp. 1–5. doi: 10.1103/PhysRevB.73.

245206.

[225] M.-Y. Ryu, T. R. Harris, Y. K. Yeo, R. T. Beeler, and J. Kouvetakis.

“Temperature-dependent photoluminescence of Ge/Si and Ge1-ySny/Si, in-

dicating possible indirect-to-direct bandgap transition at lower Sn content”.

In: Applied Physics Letters 102.17 (Apr. 2013), p. 171908. doi: 10.1063/1.

4803927.

LI

Bibliography

[226] J. M. Luttinger and W. Kohn. “Motion of Electrons and Holes in Perturbed

Periodic Fields”. In: Physical Review 97.4 (1955), pp. 869–883. doi: 10.1103/

PhysRev.97.869.

[227] C. R. Pidgeon and R. N. Brown. “Interband magneto-absorption and faraday

rotation in InSb”. In: Physical Review 146.2 (1966), pp. 575–583. doi: 10.

1103/PhysRev.146.575.

[228] T. B. Bahder. “Eight-band kp model of strained zinc-blende crystals”. In:

Physical Review B 41.17 (1990), pp. 11992–12001. doi: 10.1103/PhysRevB.

41.11992.

[229] T. B. Bahder. “Eight-band k.p model of strained zinc-blende crystals - erra-

tum”. In: Physical Review B 46.15 (1992), p. 9913.

[230] P. O. Löwdin. “A note on the quantum-mechanical perturbation theory”.

In: The Journal of Chemical Physics 19.11 (1951), pp. 1396–1401. doi: 10.

1063/1.1748067.

[231] E. O. Kane. “Band structure of indium antimonide”. In: Journal of Physics

and Chemistry of Solids 1.4 (1957), pp. 249–261. doi: 10 . 1016 / 0022 -

3697(57)90013-6.

[232] J. M. Luttinger. “Quantum Theory of Cyclotron Resonance in Semiconduc-

tors: General Theory”. In: 102.4 (1956).

[233] S. Krishnamurthy, A. Sher, and A. Chen. “Generalized Brooks’ formula and

the electron mobility in SixGe1-x alloys”. In: Applied Physics Letters 47

(1985), pp. 160–162. doi: doi.org/10.1063/1.96248View.

[234] P. Lawaetz. “Valence-band parameters in cubic semiconductors”. In: Physical

Review B 4.10 (1971), pp. 3460–3467. doi: 10.1103/PhysRevB.4.3460.

[235] C. G. Van De Walle and R. M. Martin. “Theoretical calculations of hetero-

junction discontinuities in the Si/Ge system”. In: Physical Review B 34.8

(1986), pp. 5621–5634. doi: 10.1103/PhysRevB.34.5621.

[236] B. J. Roman and A. W. Ewald. “Stress-Induced Band Gap and Related

Phenomena in Gray Tin”. In: Physical Review B 5.10 (1972).

LII

[237] D. E. Aspnes and A. A. Studna. “Direct observation of the E0 and E0 + ∆0

transitions in silicon”. In: Solid State Communications 11 (1972), pp. 1375–

1378. doi: 10.1016/0038-1098(72)90546-7.

[238] D. E. Aspnes. “Schottky-barrier electroreflectance of Ge: Nondegenerate and

orbitally degenerate critical points”. In: Physical Review B 12.6 (1975),

pp. 2297–2310. doi: 10.1103/PhysRevB.12.2297.

[239] S. H. Groves, C. R. Pidgeon, A. W. Ewald, and R. J. Wagner. “Interband

magnetoreflection of α-Sn”. In: Journal of Physics and Chemistry of Solids

31.9 (1970), pp. 2031–2049. doi: 10.1016/0022-3697(70)90006-5.

[240] A. Rahman, M. S. Lundstrom, and A. W. Ghosh. “Generalized effective-

mass approach for n-type metal-oxide-semiconductor field-effect transistors

on arbitrarily oriented wafers”. In: Journal of Applied Physics 97.5 (Mar.

2005), p. 053702. doi: 10.1063/1.1845586.

[241] B. A. Foreman. “Effective-mass Hamiltonian and boundary conditions for

the valence bands of semiconductor microstructures”. In: Physical Review B

48.7 (Aug. 1993), pp. 4964–4967. doi: 10.1103/PhysRevB.48.4964.

[242] N. Vukmirović, Ž. Gačević, Z. Ikonić, D. Indjin, P. Harrison, and V. Mi-

lanović. “Intraband absorption in InAs/GaAs quantum dot infrared photode-

tectors—effective mass versus kxp modelling”. In: Semiconductor Science and

Technology 21.8 (2006), pp. 1098–1104. doi: 10.1088/0268-1242/21/8/021.

[243] N. Vukmirovic, Z. Ikonic, V. Jovanovic, D. Indjin, and P. Harrison. “Optically

pumped intersublevel MidInfrared lasers based on InAs-GaAs quantum dots”.

In: IEEE Journal of Quantum Electronics 41.11 (Nov. 2005), pp. 1361–1368.

doi: 10.1109/JQE.2005.856077.

[244] J. Sjakste, N. Vast, H. Jani, S. Obukhov, and V. Tyuterev. “Ab initio study of

the effects of pressure and strain on electron-phonon coupling in IV and III-V

semiconductors”. In: physica status solidi (b) 250.4 (Apr. 2013), pp. 716–720.

doi: 10.1002/pssb.201200526.

LIII

Bibliography

[245] C. Jacoboni and L. Reggiani. “The Monte Carlo method for the solution of

charge transport in semiconductors with applications to covalent materials”.

In: Reviews of Modern Physics 55.3 (July 1983), pp. 645–705. doi: 10.1103/

RevModPhys.55.645.

[246] S. Smirnov. “Physical Modeling of Electron Transport in Strained Silicon and

Silicon-Germanium”. PhD thesis. Technische Universität Wien, 2003.

[247] M. Fischetti. “Monte Carlo simulation of transport in technologically signif-

icant semiconductors of the diamond and zinc-blende structures. I. Homo-

geneous transport”. In: IEEE Transactions on Electron Devices 38.3 (Mar.

1991), pp. 634–649. doi: 10.1109/16.75176.

[248] F. Murphy-Armando and S. Fahy. “Giant enhancement of n-type carrier mo-

bility in highly strained germanium nanostructures”. In: Journal of Applied

Physics 109.11 (2011). doi: 10.1063/1.3590334.

[249] D. L. Rode and P. A. Fedders. “Electron scattering in semiconductor alloys”.

In: Journal of Applied Physics 54 (1983), p. 6425. doi: 10.1063/1.331921.

[250] P. K. Basu and K. Bhattacharya. “Alloy scattering limited mobility of two-

dimensional electron gas in quaternary alloy semiconductors”. In: Journal of

Applied Physics 59.3 (Feb. 1986), pp. 992–994. doi: 10.1063/1.336584.

[251] J. Liu, X. Sun, D. Pan, X. Wang, L. C. Kimerling, T. L. Koch, and J. Michel.

“Tensile-strained, n-type Ge as a gain medium for monolithic laser integration

on Si.” In: Optics express 15.18 (2007), pp. 11272–11277. doi: 10.1364/OE.

15.011272.

LIV

Eidesstattliche Erklärung

Ich, Denis Rainko, erkläre hiermit, dass diese Dissertation und die darin dargelegten

Inhalte die eigenen sind und selbstständig als Ergebnis der eigenen originären

Forschung generiert wurden.

Hiermit erkläre ich an Eides statt

1. Diese Arbeit wurde vollständig oder größtenteils in der Phase als Doktorand

dieser Fakultät und Universität angefertigt;

2. Sofern irgendein Bestandteil dieser Dissertation zuvor für einen akademischen

Abschluss oder eine andere Qualifikation an dieser oder einer anderen Institu-

tion verwendet wurde, wurde dies klar angezeigt;

3. Wenn immer andere eigene- oder Veröffentlichungen Dritter herangezogen wur-

den, wurden diese klar benannt;

4. Wenn aus anderen eigenen- oder Veröffentlichungen Dritter zitiert wurde,

wurde stets die Quelle hierfür angegeben. Diese Dissertation ist vollständig

meine eigene Arbeit, mit der Ausnahme solcher Zitate;

5. Alle wesentlichen Quellen von Unterstützung wurden benannt;

6. Wenn immer ein Teil dieser Dissertation auf der Zusammenarbeit mit anderen

basiert, wurde von mir klar gekennzeichnet, was von anderen und was von mir

selbst erarbeitet wurde;

7. Teile dieser Arbeit wurden zuvor veröffentlicht in: [34, 115, 148]

Acknowledgments

I would like to fill some pages to express my gratitude to all the people who inspired

me and supported this work by meeting me with patience and care. The recent

years were very important to me and I am grateful to the people that I met at the

Forschungszentrum Jülich.

First of all, I would like to thank my doctoral supervisors Prof. Detlev Grützmacher

and Prof. Siegfried Mantl, who enabled me to do my thesis at the institute and were

always open-minded for interesting and inspiring discussions. I am thankful to Prof.

Jeremy Witzens for willingness to do the second review of my thesis and giving me

advice for my work.

I am really grateful for my supervisor Dr. Dan Buca. He never gave up supporting

me and my work, allowed me to visit beautiful places and encouraged me to face my

fears and doubts. I enjoyed the lively conversations with him and wish him and his

family all the best. Besides him, I am in great debt to Dr. Zoran Ikonić, who, since

I visited him at the University of Leeds, supported all theoretical investigations pre-

sented in this work. He was outstandingly kind and patient with me and answered

hundreds of questions with care. I admire his humble and decent character and I am

very happy to have met him. I would also like to thank Prof. Nenad Vukmirović,

who invited me to his institute at the University of Belgrade and enabled me to

use his codes for QD calculations. I really enjoyed his hospitality and the time in

Belgrade. I want to thank Prof. Osamu Nakatsuka for the fruitful collaboration and

giving me the opportunity to visit Japan, one of the most beautiful countries I have

ever been to.

Sometimes, life appears to me like a play in a theater, with people playing minor

and major roles and appearing at the right time at the right spot. In the last years

three major characters appeared in my life, which deserve all of my gratitude. Dr.

Nils von den Driesch is a never ending spring of knowledge. I enjoyed his lessons on

LVII

Bibliography

differentiated thinking and I thank him for never being tired of taking the time to

tame my sometimes bewildered mind. Dr. Daniela Stange is a beacon of optimism.

Her positive aura is contagious and, once encountered, slowly infiltrates your heart

without being able to resist. I enjoyed all the conversations we had and I want to

thank both of you for expanding my horizons. I was really lucky to meet Carlos

Rosário. This pure-hearted soul always managed to bring me down to earth, when

things seemed to fall apart. I am happy that there are people like him and Maria

and things would have been a lot less colorful without them.

I was also lucky to end up with a bunch of funny PhD students, to whom I would like

to express my gratitude. I will miss the unannounced evening visits of Dr. Thomas

Carl Ulrich Tromm that we spend with Ciara, beer and sausages. Thanks for shift-

ing my mind into another direction. I want to thank Konstantin Mertens for playing

the "Nine Inch Nails"-DVD at the end of a party while serving us wonderful goat

cheese. I enjoyed the recaps of the latest John Oliver episode with Dr. Stefan Glaß

and the fun we had when talking about funny presidents and the wild west. Dr.

Christian Schulte-Braucks embodies to me a real "Ruhrpott-Junge", which helped

me to feel at home in our group. Besides excellent scientists, I was lucky to meet

Dr. Gia Vinh Luong, one of the best Pokémon trainer I ever encountered and who

never hesitated to support me and my Pokémon trainer career. In an internation-

ally positioned group I was fortunate to meet Mingshan Liu, with whom I could

philosophize about Taijiquan, Qigong and the nature of Dào.

All the work presented was supported by many scientists of the Forschungszentrum

Jülich and other institutes. I am in great debt of the Waldschlösschen team. They

never hesitated to support my work and helped and taught me in many interest-

ing conversations and lessons how to work with and sometimes dismount a CVD

reactor. Therefore, thanks to Andreas Tiedemann, Patric Bernardy and Karl-Heinz

Deussen. Thanks to Lidia Kibkalo, Dr. Martina Luysberg, Christian Scholtysik,

Andre Dahmen, Dr. Jürgen Schubert, Katja Palmen, Dr. Uwe Breuer, Dr. Ivan

Povstugar, Dr. Gregor Mussler and Dr. Alexander Shkurmanov for spending a lot

of time with me discussing results and possibilities to move on. I was also lucky

to have much external support. Therefore, I would like to thank Prof. Giovanni

Capellini, Dr. Yuji Yamamoto and Dr. Michael Andreas Schubert from the IHP,

and from the Université Paris Sud my gratitude goes to Prof. Moustafa El Kurdi

LVIII

and Dr. Anas Elbaz.

Ich bin sehr dankbar für all die Hilfe, die ich durch meine Eltern erhalten habe. Die

letzten drei Jahre wären mir deutlich schwieriger gefallen, hätten sie mich und meine

Tochter nicht so viel unterstützt. Und als letztes gilt mein Dank natürlich meiner

Tochter Sophia. Du gibst mir Kraft, du gibst mir Zuversicht und einen Grund hier

zu sein. Ich bin froh, dass es dich gibt und in meinem Herzen wird immer ein Platz

für dich sein.

LIX

List Of Publications

First Authored Publications

• D. Rainko, Z. Ikonic, A. Elbaz, N. von den Driesch, D. Stange, E. Herth, P.

Boucaud, M. El Kurdi, D. Grützmacher, and D. Buca. “Impact of tensile strain

on low Sn content GeSn lasing”. In: Scientific Reports 9.1 (Jan. 2019), p. 259.

doi: 10.1038/s41598-018-36837-8.

• D. Rainko, Z. Ikonic, N. Vukmirović, D. Stange, N. von den Driesch, D. Grütz-

macher, and D. Buca. “Investigation of carrier confinement in direct bandgap

GeSn/SiGeSn 2D and 0D heterostructures”. In: Scientific Reports 8.1 (Dec.

2018), p. 15557. doi: 10.1038/s41598-018-33820-1.

Contributed Publications

• N. von den Driesch, D. Stange, D. Rainko, U. Breuer, G. Capellini, J.-m.

Hartmann, H. Sigg, S. Mantl, D. Grützmacher, and D. Buca. “Epitaxy of

Si-Ge-Sn-based heterostructures for CMOS-integratable light emitters”. In:

Solid-State Electronics (Mar. 2019). doi: 10.1016/j.sse.2019.03.013.

• M. Fukuda, D. Rainko, M. Sakashita, M. Kurosawa, D. Buca, O. Nakat-

suka, and S. Zaima. “Optoelectronic properties of high-Si-content-Ge1-x-

ySixSny/Ge1-xSnx/Ge1-x-ySixSny double heterostructure”. In: Semiconduc-

tor Science and Technology 33.12 (Dec. 2018), p. 124018. doi: 10.1088/1361-

6641/aaebb5.

LXI

Bibliography

• D. Stange, N. von den Driesch, T. Zabel, F. Armand-Pilon, D. Rainko, B.

Marzban, P. Zaumseil, J.-M. Hartmann, Z. Ikonic, G. Capellini, S. Mantl, H.

Sigg, J. Witzens, D. Grützmacher, and D. Buca. “GeSn/SiGeSn Heterostruc-

ture and Multi Quantum Well Lasers”. In: ACS Photonics 5.11 (Nov. 2018),


• P. Zaumseil, Y. Hou, M. A. Schubert, N. von den Driesch, D. Stange, D.

Rainko, M. Virgilio, D. Buca, and G. Capellini. “The thermal stability of

epitaxial GeSn layers”. In: APL Materials 6.7 (July 2018), p. 076108. doi:

10.1063/1.5036728.

• N. von den Driesch, D. Stange, D. Rainko, I. Povstugar, P. Zaumseil, G.

Capellini, T. Schröder, T. Denneulin, Z. Ikonic, J.-M. Hartmann, H. Sigg,

S. Mantl, D. Grützmacher, and D. Buca. “Advanced GeSn/SiGeSn Group IV

Heterostructure Lasers”. In: Advanced Science 5.6 (June 2018), p. 1700955.

doi: 10.1002/advs.201700955.

• D. Stange, N. von den Driesch, D. Rainko, S. Roesgaard, I. Povstugar, J.-M.

Hartmann, T. Stoica, Z. Ikonic, S. Mantl, D. Grützmacher, and D. Buca.

“Short-wave infrared LEDs from GeSn/SiGeSn multiple quantum wells”. In:

Optica 4.2 (Feb. 2017), p. 185. doi: 10.1364/OPTICA.4.000185.

• N. von den Driesch, D. Stange, S. Wirths, D. Rainko, I. Povstugar, A. Savenko,

U. Breuer, R. Geiger, H. Sigg, Z. Ikonic, J. M. Hartmann, D. Grützmacher,

S. Mantl, and D. Buca. “SiGeSn Ternaries for Efficient Group IV Heterostruc-

ture Light Emitters”. In: Small 13.16 (2017), pp. 1–9. doi: 10.1002/smll.

201603321.

• D. Stange, N. von den Driesch, D. Rainko, T. Zabel, B. Marzban, Z. Ikonic,

P. Zaumseil, G. Capellini, and S. Mantl. “Quantum Confinement Effects in

GeSn/SiGeSn Heterostructure Lasers”. In: IEEE International Electron De-

vices Meeting (IEDM). San Francisco, 2017, pp. 589–592.

LXII

First Authored Conference Contributions

• D. Stange, N. von den Driesch, D. Rainko, C. Schulte-Braucks, S. Wirths, G.

Mussler, A. T. Tiedemann, T. Stoica, J. M. Hartmann, Z. Ikonic, S. Mantl, D.

Grützmacher, and D. Buca. “Study of GeSn based heterostructures: towards

optimized group IV MQW LEDs”. In: Optics Express 24.2 (2016), p. 1358.

doi: 10.1364/OE.24.001358.

First Authored Conference Contributions

• D. Rainko, D. Stange, N. von den Driesch, C. Schulte-braucks, G. Mussler,

Z. Ikonić, J. M. Hartmann, M. Luysberg, S. Mantl, D. Grützmacher, and

D. Buca. “(Si)GeSn nanostructures for light emitters”. In: SPIE. Ed. by L.

Vivien, L. Pavesi, and S. Pelli. Vol. 9891. Brussels, May 2016, 98910W. doi:

10.1117/12.2227573.

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Design and Growth of Group IV Laser Structures

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