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Doctoral Thesis
Molecular beam epitaxial growth of high-quality Sb-based III/V
semiconductor heterostructures
Author(s):
Charpentier, Christophe
Publication Date:
2014
Permanent Link:
https://doi.org/10.3929/ethz-a-010384191
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ETH Library
Diss. ETH No. 21998
Molecular beam epitaxial
growth of high-quality Sb-based
III/V semiconductor
heterostructures
A dissertation submitted to
ETH ZURICH
for the degree of
DOCTOR OF SCIENCES
presented by
CHRISTOPHE CHARPENTIER
Master of Science in Physics (ETH Zurich)
born 6 March 1985
citizen of Luxembourg
accepted on the recommendation of
Prof. Dr. Werner Wegscheider, examiner
Prof. Dr. Klaus Ensslin, co-examiner
2014
ii
iii
Abstract
Einzigartige Eigenschaften wie schmale Bandlücken in InAs und InSb, hohe
instrinsische Elektronenbeweglichkeiten bei Raumtemperatur, hohe g-Faktoren oder ungewöhnliche Bandkantenverläufe haben Sb-basierte HalbleiterHeterostrukturen zur Grundlage vieler neuartiger Bauelemente und physikalischer Erkenntnisse werden lassen. Die kürzliche Vorhersage topologisch
geschützer Randkanäle in InAs/GaSb/AlSb-Quantentöpfen und deren mögliche Verwendung zur Erzeugung von Majorana-Fermionen haben das Interesse an Quantentopfstrukturen hoher Qualität noch einmal verstärkt.
Für diese Arbeit haben wir ein Molekularstrahlenepitaxiesystem zur Herstellung von Sb-basierten Heterstrukturen hoher Qualität aufgebaut. Molekulahrstrahlenepitaxie ist eine physikalische Beschichtungstechnik, bei der Einkristalle im Ultrahochvakuum und bei geringen Wachstumsraten hergestellt
werden. Dadurch erreicht man einen möglichst geringen Einbau an Verunreinigungen in die Proben und eine möglichst geringe Dichte an Kristalldefekten, zudem können die Schichtdicken atomlagengenau kontrolliert werden.
Zunächst werden wir einen Einblick in die physikalischen Grundlagen zweidimensionaler Elektronensysteme und die speziellen Eigenschaften Sb-basierter
Heterostrukturen geben. Danach werden wir einige Grundlagen des Kristallwachstums einführen und einen Überblick über den experimentellen Aufbau
geben.
Die erfolgreiche Herstellung von InAs/AlSb-Quantentöpfen hoher Qualität
hängt von der Optimierung einer grossen Anzahl von Wachstumsparametern
ab, dazu gehören unter anderem Wachstumstemperaturen, Pufferschichtfolgen oder Partialdruckverhältnisse. Wir waren in der Lage, InAs/AlSb-Quantentöpfe mit ausserordentlich hohen Elektronenbeweglichkeiten und geringen Oberflächenrauigkeiten reproduzierbar herzustellen. Die Proben wurden
charakterisiert durch die Messung des elektrischen Widerstands entlang und
quer zur Stromrichtung in Magnetfeldern bis zu 6 T, diese elektronischen Eigenschaften können mit der Qualität des Kristalls, der das zweidimensionale
Elektronensystem umgibt, in Verbindung gesetzt werden. Oberflächenrauigkeiten wurden mittels Rasterkraftmikroskopie ermittelt.
Der eindeutige Nachweis der speziellen Randkanäle in InAs/GaSb/AlSbQuantentöpfen konnte noch nicht erbracht werden, obwohl die potentiellen topologischen Eigenschaften dieser Strukturen ein grosses Interesse geweckt haben. Die Eliminierung von Streukanälen durch die Minimierung der
Leitfähigkeit des Volumenteils einer solchen Probe wäre ein vielversprechender Schritt zur Sichtbarmachung von topologisch geschützten Randkanälen
iv
und zur Messung der genauen Quantisierung der Leitfähigkeit, die damit
einhergeht. Wir konnten zeigen, dass der kontrollierte Einbau einer moderaten Konzentration ungeladener Fremdatome diese Volumenleitfähigkeit um
mehrere Grössenordnungen absenkt, ohne die Kristallqualität zu stark zu
beschränken.
Zuletzt zeigen wir erste Experimente zum Wachstum von weiteren Sb-basierten Heterostrukturen wie InSb/AlInSb-Quantentöpfen, GaSb/AlSb-Quantentöpfen sowie InAs/InAlAs-Töpfen mit gestuften Bufferschichten.
v
Abstract
Because of their unique physical properties that include very small band
gaps in InAs and InSb, high intrinsic electron mobilities at room temperature, high g-factors or unusual band line-ups, Sb-based III/V semiconductor
heterostructures have been at the origin for many new devices and physical insights for more than three decades. Recently, the prediction of novel
topologically protected helical edge states in InAs/GaSb/AlSb composite
quantum wells and their potential use for the creation of Majorana fermions
has reinforced the interest in quantum well structures of high quality and
tunability.
We set up a molecular beam epitaxy system customized for the fabrication of
high-quality Sb-based heterostructures. Molecular beam epitaxy is a physical
deposition technique where single crystals can be fabricated in ultra high
vacuum at low growth rates to simultaneously minimize the incorporation
of impurities and the creation of crystal defects and to allow for atomically
precise layer thickness control. We first give an insight into the physical
background of two-dimensional electron systems and the special properties
of Sb-based heterostructures. We then introduce fundamental notions of
crystal growth and give a detailed view of the experimental setup.
The successful fabrication of high quality InAs/AlSb quantum wells is achieved
by optimizing a large number of growth parameters such as substrate temperature, buffer layer sequences or partial pressure ratios. We were able to
reproducibly grow InAs/AlSb quantum wells showing very high electron mobilities as well as low surface roughnesses. The samples were characterized
by measuring the sheet resistivities parallel and transversal to the current
flow in magnetic fields up to 6 T and relating these electronic properties to
the quality of the crystal surrounding the two-dimensional electron system
unter investigation. Surface roughnesses were measured by atomic force microscopy.
The unequivocal identification of the helical edge states in InAs/GaSb/AlSb
composite quantum wells is still eluding the scientific community excited by
their prospective topological properties. Lowering the residual conductivity
in the bulk of these samples and thus eliminating scattering channels would
be a step towards the observation of topologically protected helical edge
states and the exact quantization of the conductivity associated with these
edge channels. We could show that a step towards the suppression of bulk
conductivity without compromising the crystal quality can be a controlled
addition of a moderate level of electrically neutral impurities.
vi
We also show preliminary experiments on other Sb-based heterostructures
such as InSb/AlInSb or GaSb/AlSb quantum wells as well as on InAs/InAlAs
graded buffer wells.
Contents
1 Introduction
1
2 Theory
2.1 Single Quantum Wells . . . . . . . . . . . . . . . .
2.1.1 Magnetotransport . . . . . . . . . . . . . . .
2.2 The 6.1 Å family of III/V semiconductors . . . . . .
2.2.1 InAs/AlSb QWs . . . . . . . . . . . . . . .
2.2.2 GaSb/InAs/AlSb Composite Quantum Wells
2.3 Principles of crystal growth . . . . . . . . . . . . .
2.3.1 Growth Modes . . . . . . . . . . . . . . . .
2.3.2 Crystal Defects . . . . . . . . . . . . . . . .
2.3.3 Critical layer thickness . . . . . . . . . . . .
2.3.4 RHEED . . . . . . . . . . . . . . . . . . . .
2.3.5 Temperature measurements . . . . . . . . .
3 Experimental setup
3.1 MBE system . . . . . . . . . . . . . . . . . . . .
3.1.1 Gauges and Mass Spectroscopy . . . . .
3.1.2 Cells . . . . . . . . . . . . . . . . . . . .
3.1.3 Pumps . . . . . . . . . . . . . . . . . . .
3.2 Transport characterization . . . . . . . . . . . .
3.2.1 Magnetotransport . . . . . . . . . . . . .
3.2.2 Sample preparation . . . . . . . . . . . .
3.2.3 Measurement setup . . . . . . . . . . . .
3.3 Optical characterization . . . . . . . . . . . . .
3.3.1 Photoluminescence . . . . . . . . . . . .
3.3.2 Fourier Transform Infrared Spectroscopy
3.4 Structural characterization . . . . . . . . . . . .
3.4.1 Atomic Force Microscopy . . . . . . . . .
3.4.2 Transmission Electron Microscopy . . . .
vii
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29
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46
viii
4 Experimental results
4.1 InAs/AlSb quantum wells . . . . . . . . .
4.1.1 Buffer layers . . . . . . . . . . . . .
4.1.2 Channel thickness . . . . . . . . . .
4.1.3 Capping layer and barriers . . . . .
4.1.4 Growth temperatures . . . . . . . .
4.1.5 Interfaces . . . . . . . . . . . . . .
4.1.6 Substrates . . . . . . . . . . . . . .
4.1.7 Growth rates and partial pressures
4.1.8 Antimony oligomers . . . . . . . .
4.1.9 Doping schemes . . . . . . . . . . .
4.1.10 FTIR measurements . . . . . . . .
4.2 Surface roughness . . . . . . . . . . . . . .
4.2.1 III/V ratio . . . . . . . . . . . . . .
4.2.2 Optimized transitions . . . . . . . .
4.3 InAs/GaSb/AlSb CQWs . . . . . . . . . .
4.3.1 Suppression of bulk conductivity .
4.4 InSb/AlInSb QWs . . . . . . . . . . . . .
4.5 InAs/InAlAs QWs . . . . . . . . . . . . .
4.6 GaSb/AlSb QWs . . . . . . . . . . . . . .
CONTENTS
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47
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75
80
81
5 Conclusions & Outlook
85
List of Symbols and Acronyms
93
List of Figures
95
List of Tables
99
Acknowledgements
101
Collaborations
103
Curriculum vitae
105
Chapter 1
Introduction
The development of molecular beam expitaxy (MBE) in the late 1960s and
early 1970s by Cho et al.[1, 2] made the fabrication of atomically precise
semiconductor heterostructures of high purity possible and was one the most
important steps toward the fabrication of sophisticated electronic and optoelectronic devices. Ever ince, this technique has continuously been optimized
by the addition of features such as sample loadlocks, liquid nitrogen shields
and better ultra high vacuum pumps which led to even higher sample purities, devices of higher performance but also to the discovery of completely
new physical effects such as the fractional quantum hall effect[3] or twodimensional topological insulators[4].
The main goal of this thesis is the setup of a MBE system for the growth
of Sb-based semiconductor heterostructures. Technical prerequisites for the
high quality of the samples we aim to fabricate are a careful assembly of the
system, advanced pumping techniques and source materials of best available
purity. A large number of structural and growth parameters will then have
to be optimized.
From the special band lineup and unique properties of Sb-based semiconductor heterostructures arises a myriad of fascinating physical effects and
potential electronic devices. InAs and InSb have the smallest bandgaps, the
highest intrinsic electron mobilities and the highest g-factors of all III/V semiconductors which makes them interesting for present and future applications
such as infrared detectors, thermal imaging sensors, high electron mobility
transistors with switching frequencies in the terahertz range or spintronics.
Further excitement was created when a topologically non-trivial phase was
predicted in InAs/GaSb/AlSb composite quantum wells (CQWs) due to the
1
2
CHAPTER 1. INTRODUCTION
band inversion stemming from the unique broken gap band line up in these
structures[5]. While this band inversion and the hybridization gap it engenders have been known for many years, the prospect of new physical insight as
e.g. by the creation of Majorana fermions in combination with superconducting electrodes[6] led many groups to renew their interest in these structures
and triggered the need for high-purity samples.
While Sb-based structures were among the early materials grown by MBE
precisely because of their promising properties[7], most groups focussed primarily on device fabrication and less on the growth of high-purity samples
for fundamental research. The pioneers were the group of Prof. Kroemer
at the University of California in Santa Barbara who developed most of the
techniques still in use today[8, 9, 10]. However, the special needs of today’s
research focus as e.g. superconducting electrodes, low bulk conductivities in
InAs/GaSb/AlSb CQWs or the fabrication of sub-micron structures makes
further optimization of these growth techniques necessary, this is what we
want to aim for in this work.
Chapter 2
Theory
2.1
Single Quantum Wells
Electrons in a potential well or quantum wells are one of the standard textbook examples in quantum mechanics due to their relatively simple mathematical description. Here quantum wells denote one-dimensional confinement and consequently free electron movement along two orthogonal directions. Despite their apparent simplicity, when such systems became available
experimentally with the advent of advances semiconductor fabrication techniques (such as e.g. molecular beam epitaxy), narrow quantum wells allowed
for a great manifold of new devices and truly genuine new effects due to
the quasi two-dimensional nature of the conducting layer in these wells. A
notable example for such an effect is the Quantum Hall Effect, the quantization of the transversal resistivity in a high magnetic field, which opened up
a whole new field of physics.
The energy of the electrons in a quantum well with infinite barriers is given
by
2
h̄2 kxy
.
(2.1)
E = En +
2m∗QW
where
2
h̄2 kxy
2m∗QW
is an expression for the energy of the motion in the xy- or QW-
plane with m∗QW being the effective mass of the quantum well (QW) material,
taking into account the parabolic dispersion. En is the energy of the n-th
subband n and is given by
En =
h̄2 nπ 2
( ),
2m∗QW L
3
(2.2)
4
CHAPTER 2. THEORY
Figure 2.1: Landau levels in dependence of B-field, from [11]. Note the
stepwise change of the Fermi energy EF as the Landau levels are depopulated.
where L is the width of the quantum well. By measuring the energies at
which the interband absorptions for different quantum well widths occur,
the effective mass m∗QW can be determined.
2.1.1
Magnetotransport
In high magnetic fields, electrons in a two-dimensional electron system (2DES)
or 2DEG (frequently also denoted by two-dimensional electron gas (2DEG))
will take quantized energy levels, called Landau levels (LLs), given by
1
En = h̄ωc n +
(2.3)
2
where ωc = eBz /m? is the cyclotron frequency with m? the effective electron
mass in the host material of the 2DEG and the LLs are counted by the
number n (see Figure 2.1). The degeneracy of each LL is given as
nL =
eBz
h
(2.4)
thus, as the magnetic field is increased, more states become available in each
LL. Each time the filling factor ν = nnLS (indicating how many LL are occupied in the 2DEG, nS is the electronic density in the 2DEG) is integer, one
LL is depopulated, leading to minima in the longitudinal magnetoresistance
(Shubnikov-de Haas (SdH) effect, see Figure 2.4).
For high magnetic fields, the electron spin has to be taken into account,
leading to the Zeeman splitting of each LL:
1
1
±
En = h̄ωc n +
± g ? µB Bz ,
(2.5)
2
2
2.1. SINGLE QUANTUM WELLS
5
120
100
⇢xx [⌦]
80
60
40
20
0
0
1
2
3
4
B-field [T]
5
6
Figure 2.2: Longitudinal resistivity of an InAs/AlSb QW showing Shubnikovde Haas oscillations in function of a perpendicular magnetic field.
where g ? is the effective g-factor. This explains why, at low B-fields we will
only observe minima at even ν, whereas odd values of ν can be observed for
higher magnetic fields, depending on g ? of the material.
Our previous explanations suggest a density of states (DOS) that is a sum of
delta functions, whereas in real systems, the degeneracy of the LLs is partly
lifted due to scattering and the LLs are broadened. More elaborate calculations show that only the states in a narrow range around the peaks are
extended and can contribute to transport, all other states are localized, as
shown in Figure 2.3. We can derive an analytical expression for the oscillations of the longitudinal resistivity ρxx
ρxx
EF
m?
2π 2 kT /(h̄ωc )
−π/(ωc τq )
cos 2π
= 2
1 + 4e
,
ne τ0
sinh 2π 2 kT /(h̄ωc )
h̄ωc
(2.6)
where 1/τ0 is the zero-magnetic field scattering rate, τq the life time of sin2
n the Fermi energy[11]. This expression
gle particle states and EF = πh̄
m? S
suggests that we can obtain a large number of informations from the measurement of the SdH-oscillations: on one hand, the temperature dependence
of the envelope function gives a value for τq which allows us to gain information about scattering processes and limiting energy scales in our mesoscopic
structures. More importantly, the SdH-effect allows us to deduce the electron density from the position in B-field of the SdH-minima. Indeed, we can
6
CHAPTER 2. THEORY
Figure 2.3: Scattering-broadened Landau levels from [11]. States close to the
center of the LL are extended, states in the tails of the LL are localized.
observe a minimum if the following condition is met:
EF
n
=
=i
h̄ωc
2eB/h
(2.7)
which allows us to extract the electronic density n from plotting the measured
values of 1/Bi against the index i and calculating the slope of the linear fit:
1
2e 1
=
i
Bi
hn
(2.8)
Comparing the densities obtained from the SdH oscillations and from the
low B-field slope of the Hall curve can provide additional information on the
conduction channels.
Klaus von Klitzing discovered in 1980[12] that the transversal or Hall resistance showed plateaus at values of ρ corresponding to integer filling factors
ν such as seen in Figure 2.4:
ρxy =
h1
e2 ν
(2.9)
In a simple picture, we can imagine that the electrons cannot complete their
cyclotron orbits along the sample edges but are reflected. This provides them
a non zero kinetic energy which bends the LL at the sample edges above the
Fermi energy. These edge channels contribute to transport in one single direction while the electrons in the centre of the sample are localized at impurities.
Backscattering is therefore completely suppressed, which yields σxx = 0 and,
after tensor inversion with finite ρxy , ρxx = 0. This vanishing longitudinal
2.2. THE 6.1 Å FAMILY OF III/V SEMICONDUCTORS
7
4
⇢xy [k⌦]
3
2
1
0
0
1
2
3
4
B-field [T]
5
6
Figure 2.4: Transverse resistivity of an InAs/AlSb QW showing Quantum
Hall plateaus in function of a perpendicular magnetic field.
resistivity explains the SdH oscillations in the edge-channel picture. The
plateaus in the Hall resistance occur because, at the same time where the
longitudinal resistance is zero, there is no connection between channels at
opposite edges. Each one-dimensional edge channel contributes σxy = e2 /h
to the transverse conductivity if opposite edges are at a potential difference.
Accordingly, the filling factor thus counts the populated edge channels. For
an illustration see Figure 2.5. If one LL is at the Fermi energy and thus not
completely filled, both edges are connected and our argument breaks down,
we then see the transition region between the plateaus (Hall) or minima
(SdH) in transversal and longitudinal resistance, respectively.
2.2
The 6.1 Å family of III/V semiconductors
InAs, GaSb and AlSb are three approximately lattice-matched semiconductor
materials with lattice constants of approximately 6.1 Å and very interesting
properties due to their band alignments[10] which are shown in Figure 2.6.
With band gaps of 1.61 eV in AlSb, 0.78 eV in GaSb and 0.36 eV in InAs and
conduction band offsets as large as 1.35 eV (between InAs and AlSb, 0.41 eV
between AlSb and GaSb), a wide range of different band lineups and quantum
wells with different properties can be realized. Of special interest for us are
InAs QWs inside AlSb barriers and InAs/GaSb composite quantum wells
8
CHAPTER 2. THEORY
Figure 2.5: Hall bar with edge channels. States in the center are localized
for integer filling factors and cannot contribute to electronic transport, thus
completely decoupling opposite edge channels. A four-terminal measurement
setup is also shown in the figure. From [11].
between AlSb barriers, these will be studied in more detail in the following
paragraphs and in the result section of this thesis.
2.2.1
InAs/AlSb QWs
InAs has a very small band gap of 0.36 eV which leads to a very small effective
electron mass m? of only 0.03 me , where me is the free electron mass. The
relation between m? and the band gap Eg is given by k·p theory[11]
2 me P 2
1
1
=
1+ 2
,
(2.10)
m?
me
h̄ Eg
where P is the expectation value of the momentum in the vicinity of the
Γ-point. From a more intuitive point of view, it means that level repulsion
causes bands to curve as the band gap is reduced, leading to a lower effective
mass.
In combination with the very high AlSb barriers (1.35 eV band offset), we can
obtain deep QWs with very high electron concentrations (up to 1013 cm−2 )
and high electron mobilities (up to 106 cm2 /Vs). Together with the large
effective g-factor of g ∗ = −16, these QWs have very interesting properties for
spintronics, high electron mobility transistors or for their excellent interface
to superconductors.
2.2. THE 6.1 Å FAMILY OF III/V SEMICONDUCTORS
9
Figure 2.6: Relative band lineup and band gaps of the InA/GaSb/AlSb material system, from [10].
InAs QWs do not need to be doped - indeed their high electron concentration
comes entirely from its intrinsic properties. A high density of surface states
in the GaSb capping layer 0.85 eV below the conduction band edge of AlSb
pins the Fermi level approximately 150 meV above the InAs conduction band
edge, high enough to cause a strong population of the QW[13], as illustrated
in Figure 2.7. A further source for electrons are deep donors in the AlSb wells,
i.e. excess electrons from Sb atoms on Al sites that can drain into the very
deep QW. Experimental findings indicate that the two mentioned sources
do not account for the entire electron density in a given sample[14, 15, 16].
Speculations on the source of the remaining electrons include delocalized
states at the InSb-like interface between the InAs channel and the AlSb
barriers[16].
Doping is made difficult by the fact that silicon, which is readily available
in most III-V MBE systems, is an amphoteric element for AlSb and GaSb:
depending on temperature and other growth parameters, it can be p-type or
n-type. The alternative n-dopant - tellurium[9] - introduces strong memory
effects into the growth chamber due to its very high vapour pressure. Nevertheless, controlled and reliable n-doping using Si is possible using highly
n-doped InAs layers close to the InAs QW[17]. A band diagram[18] of such
a structure is shown in Figure 2.8.
10
CHAPTER 2. THEORY
Figure 2.7: Conduction band alignment for an InAs/AlSb QW sample from
[13]. The Fermi energy is pinned at the surface, ES = 850 meV below the
AlSb conduction band edge.
Figure 2.8: Conduction band alignment and energy levels of a Si-doped
InAs/AlSb QW structure with an InAlAs capping layer, from [18]. Ψ0 and
Ψ1 are the electron wave functions of the first two subbands.
2.2. THE 6.1 Å FAMILY OF III/V SEMICONDUCTORS
11
The strong spin-orbit coupling due to the high g ? should lead to beating
patterns in the oscillations of the longitudinal resistance but these could not
be seen in our samples, confirming previous experiments[19]. The reason for
the absence of the beating pattern is still open for debate. It is interesting
to note that such beating patterns can apparently be seen in InAs/GaSb
composite quantum wells in the electron transport regime[20].
An interesting feature of InAs/AlSb QWs is the negative photoconductivity
effect. Photoconductivity is well known from GaAs/AlGaAs heterostructures where deep donors such as DX centers are energetically activated by
illumination at cryogenic temperatures thus increasing the electron density
in the 2DEG. In general, the InAs/AlSb QWs are not intentionally doped,
but the AlSb barriers can provide deep donors and acceptors from AlSb and
SbAl antisite defects respectively. Indeed, experiments where InAs/AlSb
QWs are illuminated at low temperatures show a strong negative persistent photoconductivity[8] where the electron density can be lowered by up
do one order of magnitude[21].
2.2.2
GaSb/InAs/AlSb Composite Quantum Wells
As can be seen in Figure 2.6, InAs and GaSb feature a unique band line
up where the bottom of the conduction band of InAs lies 150 meV below
the top of the valence band of GaSb[10], usually called Type II band lineup.
This band line up gives rise to many special properties, as electrons can
directly drain from the GaSb layer into the InAs layer or, if the InAs layer
is sufficiently narrow compared to the GaSb layer, the order of the energy
levels will reverse (see Figure 2.9(a)). Such semimetallic, semiconductor or
inverted structures have been investigated for a long time[7, 22, 23, 24],
we will concentrate here on the inverted band structure with the highest
hole energy level being higher than the lowest electron level and study its
consequences on a composite quantum well of GaSb and InAs between AlSb
barriers.
Let us consider the lowest electron level E1 and the highest hole level H1
as depicted in Figure 2.9(b). We assume that all other subbands are well
spaced in energy so that we do not need to include them in this reasoning.
In not too narrow wells, E1 will be lower in energy than H1 and electrons and
holes will coexist in their respective quantum wells. As the electron levels
disperse upwards and the hole levels disperse downwards, we can predict that
a crossing of the bands must occur when in-plane momenta and carrier energies become equal. As the respective wave functions of electrons and holes
12
CHAPTER 2. THEORY
(a) Inverted type-II alignment in an
InAs/AlSb/GaSb CQW structure. The
lowest electron and highest hole levels (b) Band structure of an inverted type-II
are denoted by E1 and H1 respectively. structure with hybridization gap Eg .
Figure 2.9: Inverted type-II structure with hybridization gap Eg , from [5].
will extend into the neighboring well, their bands will be coupled quantum
mechanically which lifts the degeneracy at the band crossing and leads to a
hybridization gap, following the same reasoning than e.g. for bonding and
anti-bonding states.
The band alignment cannot only be influenced by the relative thicknesses of
the quantum wells but also by external electric fields[25]. Figure 2.10 shows
the different situations that can be obtained by applying a gate voltage which
shifts the position in energy of E1 and H1 in opposite directions. In addition,
we can tune the Fermi energy and hence charge or discharge the quantum
wells. The charge in a quantum well can be modeled by a simple plate
capacitor model and we find the charge to follow ∆n = ed ∆V where is
the dielectric constant, d the distance between the metallic gate and the well
and ∆V the applied voltage. To tune the Fermi energy separately from the
relative position of the electron and hole bands, we need two different metallic
gates. This has been verified experimentally by applying a gate voltage to an
InAs/GaSb CQW, tuning the Fermi energy into the hybridization gap and
measuring the conductance of the sample which is expected to drop down to
zero[26].
The occurrence of edge states at the sample edge of such an inverted type-II
structure can be qualitatively understood in a very simple picture: as the
conduction states are lower in energy than the valence states inside the sample but have to be higher in energy outside the sample (in vacuum), energy
states inside and outside the sample can only be connected smoothly if the
gap closes at the sample edge (see Fig. 2.11). This state is called the Quantum Spin Hall (QSH) state and is topologically protected[5]. Historically,
2.2. THE 6.1 Å FAMILY OF III/V SEMICONDUCTORS
13
Figure 2.10: Band structure of an inverted type-II structure under different
external electrical fields, from [25].
14
CHAPTER 2. THEORY
Figure 2.11: Dispersion relation for InAs/GaSb/AlSb CQWs with different
relative layer thicknesses. There are no band inversion and no edge states
for the situation on the left, we have a normal insulator. The QSH sample
on the right shows band inversion and we see the occurrence of edge states
in the center of the hybridization gap [5].
the QSH state was first predicted for HgTe/CdTe QWs[27] and soon after
these theoretical works, signs for helical edge channels were measured[4]. The
QSHE arises in HgTe because of its intrinsic band inversion which is similar
to the band inversion in InAs/GaSb CQWs with the important difference
that the absence of spatial separation between the electron and hole states
makes it impossible to control the band inversion and thus the hybridization
by an external electric field. In addition to this fundamental advantage of
InAs/GaSb/AlSb CQWs, these structures are of considerably more ease to
fabricate and handle.
2.3
Principles of crystal growth
The following sections follow closely the representation of Herman and Sitter[28].
2.3.1
Growth Modes
The growth of epitaxial layers depends on a large number of parameters such
as substrate material, substrate temperature, background pressure, deposited
materials, source material fluxes etc. These parameters influence the mobility
of the atoms on the surface and the binding energies to other atoms of the
molecular beams or the substrate. Schematic representations of all growth
modes can be found in Figure 2.12.
2.3. PRINCIPLES OF CRYSTAL GROWTH
15
Figure 2.12: Growth modes for different epitaxial layer thicknesses Θ:
(a) Frank-van der Merve or layer-by-layer growth. (b) Step-flow growth.
(c) Vollmer-Weber or island growth. (d) Stransky-Krastanow growth. (e)
Columnar growth. From [28].
If the surface mobility is high and the binding energy to the substrate higher
than the binding energy to the other atoms of the molecular beam, the
atoms form a complete monolayer (ML) on the substrate surface. The atoms
condensate in layers on the surface and the binding energy decreases to attain
the binding energy of the bulk crystal. This growth mode is called layer-bylayer growth or Frank-van der Merve (FM) mode and is the mode growth
parameters are usually optimized for in semiconductor epitaxy.
If the wafer is not perfectly cut along a specific crystal direction, the surface
of the wafer is divided in terraces of monoatomic thickness and of a certain
length depending on the crystallographic misorientation. FM growth will
start at each of these terraces, leading to the so called step-flow-growth
(SF), occurring in almost all semiconductor growth processes. SF growth can
be subdivided in a nucleation-driven growth on the terraces which occurs at
low surface mobilities of the adatoms and growth by advancing the steps when
the adatoms can migrate freely on the substrate surface and be incorporated
directly into the step edges.
The complementary growth mode to FM, where the atoms are bound more
strongly to each other than to the substrate (and where usually surface mobility is low) is called island growth mode or Volmer-Weber (VW) mode.
The atoms from the molecular beam condensate in small clusters on the surface which eventually grow into larger islands which merge and cover the
entire substrate surface. This is often observed when the lattice mismatch
between the substrate and the bulk crystal of the deposited material is too
16
CHAPTER 2. THEORY
large. The quality of the finally obtained film depends on all the growth
parameters mentioned above and can vary from single crystal growth after a
VW transition to completely amorphous layers.
The growth mode observed e.g. for InAs grown on a GaAs substrate is
characterized by a wetting layer of 1-2 monolayers of the deposited material
followed by island growth. This can be due to a high surface energy which
enables layer-by-layer growth in the beginning in combination with a high
strain, which then leads to island growth. This growth mode is usually
called the Stransky-Krastanow (SK) mode and is used in a controlled
way to fabricate self-assembled quantum dots e.g. in the aforementioned
InAs/GaAs materials system.
For very low surface mobilities of adatoms on highly lattice mismatched substrates, the deposited material can grow in an array of whisker-like nanocrystals which will not merge during the growth process. This more exotic growth
mode is called columnar growth (CG) mode and is not relevant for III-V
semiconductor growth.
2.3.2
Crystal Defects
Even carefully grown epitaxial layers are limited in quality by crystal defects,
a good understanding of the possible types of defects and the parameters
driving their occurrence is therefore necessary to optimize the structures to
be fabricated.
Crystal defects that can be enclosed in an imaginary sphere are called point
defects. Examples for point defects include missing host atoms (vacancies),
atoms squeezed inside the crystal lattice (interstitials), atoms different from
the host atoms (impurities, called doping if intentional) or atoms of a compound on the wrong lattice place (antisite defects). They can be due to a
wide range of reasons, impurities can stem e.g. from residual gases or contaminated source materials, antisite defects can be caused by non-stoichiometric
growth, vacancies or interstitials can be due to unsuitable growth temperatures. Careful analysis of optical or electronic properties of the defective
crystal is necessary to identify the nature of the point defect.
Line defects generated by displacing atoms from the perfect crystal lattice
are called dislocations. These dislocations strongly distort the crystal lattice and thus introduce a strong strain field into the crystal which can be
detected e.g. by transmission electron microscopy as it will affect electron
2.3. PRINCIPLES OF CRYSTAL GROWTH
17
Figure 2.13: Schematic illustration of microtwins in an InSb lattice (left)
and a TEM image of an InSb/Al0.09 In0.91 Sb QW grown on a GaAs substrate
(right), from [29].
diffraction around the dislocation. This causes the typical Moiré fringes in
electron microscopy pictures of thin crystal layers by which dislocations can
be readily identified. The main reasons for the occurrence of dislocations are
strained layers, dislocations already present in the substrate, displacements
between agglomerating islands, the aggregation of point defects or physical
deformation of the crystal lattice during growth or cooling after growth.
Stacking faults are planar defects across which the crystal has been displaced (by a vector which is not a lattice translation vector), due to misfit
accommodation between coalescing island or aggregation of point defects.
Similarly to dislocations, stacking faults can be detected by transmission
electron microscopy.
It can occur that the resulting epitaxial crystal is not a sequence of identical unit cells but that two neighboring unit cells are mirrored with respect
to each other. The defect created by this reflection of atomic positions is
called a twin (or microtwin), the plane accross which this reflection occurred is called twinning plane. In III-V semiconductors that crystallize in
zincblende structures, this twinning plane is always the (111)-plane. As microtwins fundamentally alter the crystal orientation and cause considerable
misfit, electron mobilities are highly affected by these defects. They are
a common problem in the growth of InSb-based heterostructures on GaAs
substrates if growth temperatures are not ideal[29]. Figure 2.13 shows an
electron micrograph of microtwins in an InSb/AlInSb heterostructure.
Misfit dislocations occur at virtually all lattice mismatched heterointerfaces - as for example between GaAs and AlSb - where they are a way of
accommodating misfit across the interface (see Fig. 2.14). Misfit dislocations
are always accompanied by two threading dislocations at the ends of the
misfit which must thread to a surface or form a loop so that the two ends
18
CHAPTER 2. THEORY
Figure 2.14: Misfit dislocation at the interface between the substrate S and
the epitaxial layer O, with aO < aS , taken from [28].
of the dislocation can join. The effect of misfit dislocations on crystal quality respectively the way they propagate through the crystal depends on the
direction of the misfit dislocation. By a careful adjustment of the growth
parameters, it is possible to force the misfit dislocations to only propagate
along the interface plane and not through the crystal, this technique is often
called interfacial misfit growth (IMF)[30, 31] and is also used in this thesis
to improve surface roughnesses in InAs/AlSb quantum wells.
2.3.3
Critical layer thickness
Lattice mismatch is a source of many problems encountered in heteroexpitaxy
as it is accommodated by structural defects in the layer or strain altering the
potential energy of the structures. For sufficiently small misfits between the
substrate and the growing layer, the first deposited atomic layers will be
strained to match the substrates. This type of coherent epilayer deposition
is also known as pseudomorphic growth[32]. With growing layer thickness
however, the strain energy, which depends on both the mismatch and the
layer thickness, will increase and a thickness will be reached where it is
favorable to introduce misfit dislocations. This thickness is called critical
layer thickness. The two cases are shown in Figure 2.15. Independently
from other assumptions on the exact crystal configuration, all calculations to
derive an expression for the critical layer thickness start from the assumption
that the interfacial energy per unit area EI must be minimal with respect to
2.3. PRINCIPLES OF CRYSTAL GROWTH
19
the in-plane strain e
∂EI
= 0.
∂|e|
(2.11)
Here the interfacial energy EI = EH + ED is the sum of the homogeneous
strain energy EH and the areal energy density of the dislocation ED . Following [33], we obtain an implicit expression for the critical layer thickness that
only depends on the details of the dislocations and the misfit
b(1 − ν cos2 β)
ln
tc =
8π|f0 |(1 + ν) sin β cos γ
ρtc
b
,
(2.12)
with f0 the natural misfit, b the magnitude of the Burger’s vector characterizing the dislocation, ν the interfacial Poisson’s ratio, β and γ the angles
between the Burger’s vector and the dislocation line and between the glide
plane of the dislocation and the interface, respectively.
2.3.4
RHEED
Reflection high-energy electron diffraction (RHEED) is a very powerful tool
for in-situ characterization of epitaxial growth and heavily used in molecular
beam epitaxy. It allows to obtain detailed information about the surface
of the deposited material as for example the measurement of growth rates,
temperatures, growth modes and crystal quality.
The setup consists of an electron gun where electrons are accelerated by
high voltages (up to 35 kV for our setup which is usually operated at 15 kV),
the epitaxial sample under scrutiny and a phosphorescent screen where the
diffraction patterns can be detected. Our setup is completed by a camera
which captures the diffraction patterns and, in combination with a computer
program, allows for a time resolved analysis and thereby the calculation of
growth rates.
For a reflection diffraction pattern, the electron beam from the electron gun
has to strike the surface of the sample at a very small angle as shown in
Figure 2.16. In a typical RHEED-pattern (see Fig. 2.17), we can observe
different features arising from different diffraction mechanisms. The vertical
lines, bright spots and rings (Laue circles) arise from electron waves elastically
diffracted by the atoms at the sample surface and interfering constructively at
the screen. The fanlike lines (Kikuchi lines) are due to electrons undergoing
multiple inelastic scattering events.
20
CHAPTER 2. THEORY
Figure 2.15: (a) Strained or pseudomorphic epilayer, (b) Relaxed epilayer of
a lattice mismatched heterostructure (c) strained and relaxed unit cells.[28].
2.3. PRINCIPLES OF CRYSTAL GROWTH
21
Figure 2.16: Schematic illustration of the RHEED setup with a visualization
of the Ewald sphere and the reciprocal lattice rods[34].
#![110]
[11̄0]
Figure 2.17: Typical RHEED-pattern with direct spot (top) and specular
image (bottom). The Laue circle and Kikuchi lines are well developed.
22
CHAPTER 2. THEORY
The basic mechanism of the elastic diffraction can be understood from kinematic theory, a geometrical analysis in reciprocal space. We consider on one
hand the reciprocal lattice of the analyzed sample surface which is degenerate
to a set of parallel rods in reciprocal space due to the small angle of incidence
of the electron beam which ensures that electrons are only reflected by the
2D-sample surface. On the other hand, the incident electrons are represented
where λ is the
in reciprocal space by the Ewald sphere with radius k0 = 2π
λ
wavelength of the electrons. Diffraction is possible at the points in reciprocal
space where the Ewald sphere intersects the reciprocal lattice of the sample
surface and the Laue condition is met, i.e.
~k0 − k~i = G,
~
(2.13)
where ~ki is the electron wave vector at the intersection of the Ewald sphere
~ is a reciprocal lattice
and the reciprocal lattice rods of the surface, and G
vector.
In the layer-by-layer growth mode, the intensity of the bright spots oscillates,
the period being exactly the time for the growth of a complete monolayer.
After the growth of a complete monolayer, the surface becomes less perfect
and the intensity of the spots decrease as more electrons are scattered to
higher order reflexes. This effect allows to calibrate the growth rate of the
different materials which is one of the most important uses of RHEED in
MBE (Figure 2.18).
Another important use of RHEED takes advantage of the different surface
reconstructions depending on the ambient conditions in the growth chamber.
The shape of the streaky features in the RHEED signal is linked to the periodicity of the rearrangement of the surface atoms due to the termination
of the crystal: the spacing of the brighter streaks is related to the lattice
constant of the material, the number of streaks between the bright features
corresponds to the periodicity index of the surface reconstruction in the observed crystal direction. In practice, as the periodicity indexes of the surface
reconstruction in semiconductors are generally relative to perpendicular directions, these reconstructions can be identified by counting the stripes in
two directions separated by 90◦ as shown in Figure 2.19. Most semiconductor materials have rich surface reconstruction phase diagrams, usually
analyzed in function on group-V beam equivalent pressure (BEP) and substrate temperature, which allow the transitions of surface reconstructions to
be used for temperature calibrations given a fixed group-V BEP.
2.3. PRINCIPLES OF CRYSTAL GROWTH
23
(a) Illustration of the mechanism for RHEED spot intensity oscillations during the
growth of a monolayer [35].
Intensity [a.u.]
Intensity [a.u.]
Shutter opened
#
3.2
6.4
Time [a.u.]
9.6
12.8
16
Time [s]
(b) RHEED spot intensity oscillations recorded during the growth of InAs and
used to calibrate the growth rates.
Figure 2.18: RHEED oscillations.
24
CHAPTER 2. THEORY
Figure 2.19: Images on the RHEED screen with the electron beam pointed
along the [011] (2 × ) and [011̄] (4 × ) directions on an As-terminated GaAs
surface at 600 ◦ C.
2.3.5
Temperature measurements
For the growth of epitaxial layers, a very precise temperature control is crucial as most thermodynamic and molecular processes are heavily temperature
dependent. The most important goal for every day laboratory work is reproducibility, the exact temperature value only being of interest for quantitative analyses or the comparison between different MBE systems. Important
tools for temperature control are thermocouples, pyrometers and band edge
thermometers, completed by surface reconstruction transitions observed by
RHEED.
Thermocouple
All cells as well as the substrate manipulator are equipped with type C thermocouples for temperature monitoring. The temperature is measured by
measuring the temperature dependent voltage between the two wires of the
thermocouple. For type C thermocouples, the wires are made of 95%Tungsten/5% Rhenium and 74% Tungsten/26% Rhenium respectively, and their
temperature range extends from 0 ◦ C to 2300 ◦ C[36]. This makes them the
type of choice for the temperature ranges relevant in MBE growth, i.e. between 100 ◦ C and 1200 ◦ C for effusion cells, substrate temperatures have to
be measured reliably between 200 ◦ C for low-temperature III/V growth and
650 ◦ C for the growth of ultrahigh quality GaAs/AlGaAs heterostructures.
2.3. PRINCIPLES OF CRYSTAL GROWTH
25
Figure 2.20: Position of the thermocouple relative to the substrate heater
(coils) on the substrate manipulator.
Even though type C thermocouples can measure these temperatures with
a good degree of precision, the physical realization of the manipulator and
the substrate heating (see Figure 2.20) seriously limits the usability of the
temperature measurement for growth temperature control. Indeed, the thermocouple does not directly measure the temperature of the substrate but
is located in a hollow space between the substrate block and the substrate
heater. The temperature in this enclosure can be different by as much as
250 ◦ C from the actual substrate temperature, depending on the absorption
and emission properties of the tantalum block, the substrate and the deposited epitaxial film. Although there is no univocal relation between the
thermocouple reading and the temperature measured by other methods because of the not perfectly reproducible thermal coupling of the substrate
to the heater radiation, thermocouple measurements can still give a useful
feedback for temperature changes during sample growth. However, it is indispensable to have a method that measures the substrate temperature directly
and quantitatively.
Pyrometry
A pyrometer measures the thermal radiation intensity of the target in a certain range of wavelengths determined by the temperature range of interest.
The radiation spectrum is then fitted to Planck’s black body radiation formula to extract the temperature.
ρ(ν, T )dν = α(ν)
1
8πhν
dν,
3
hν/kT
c e
−1
(2.14)
26
CHAPTER 2. THEORY
where α(ν) is the emissivity specific to the material. Although pyrometry
allows for quantitative temperature readings, there are several drawbacks.
On one hand, the measured emission spectrum from the substrate does not
only depend on the substrate temperature but also on the substrate material,
the deposited film and the transmissivity of the window of the view port the
pyrometer is connected to. By thorough calibration using band edge thermometry and RHEED thermometry, this drawbacks can be reduced, but the
quantitative results of pyrometry should always be read with the necessary
caution. The second drawback is the limited wavelength range at which the
emission spectrum is sampled. The pyrometer mainly used for the sample
growth presented in this thesis was a Modline 3 pyrometer by the manufacturer Ircon. This device measures infrared signals in the range from 0.91 µm
to 0.97 µm. As can be seen in Figure 2.21(a), the temperature sensitivity
below 400 ◦ C is negligible and useful measurements can only be obtained at
much higher temperatures. For the growth of GaAs-based samples, this temperature range is well-suited, but not for InAs growth at around 450 ◦ C and
even more so for InSb-based samples, where temperatures below 400 ◦ C have
to be measured reliably. For this usage, a second pyrometer was tested, an
Impac IP 120 measuring at wavelengths between 2 µm and 2.8 µm, i.e. much
further in the infrared range. At these wavelengths, the resolution below
400 ◦ C is much higher but the windows are close to a cutoff in transmission
(Fig. 2.21(b)) and, in addition, the GaAs substrates are transparent so that
we measure the temperature of the Ga used to fix the substrates to the blocks
and the temperature of the blocks themselves. If the layers of small band gap
materials such as InAs or InSb are sufficiently thick, it is possible to directly
measure the temperature of the wafer.
Band edge thermometry
As the band gap of a semiconductor is temperature dependent, its influence on the absorption of semiconductor wafers can be used to measure the
temperature of the wafer. This technique is called band edge thermometry or, more commonly, diffusive reflection spectroscopy (DRS). A typical
setup consists of a halogen lamp whose light is reflected by the unpolished
backside of the wafer and measured by an infrared detector[39], see also
Figure 2.22(a). Typical spectra for GaAs wafers at different temperatures
are shown in Figure 2.22(b), the temperature is extracted by fitting these
spectra to determine the position of the band edge in energy and comparing
to semi-empirical curves describing the exact substrate used. This method
is very reliable for lower temperatures but not for lower band gap materi-
2.3. PRINCIPLES OF CRYSTAL GROWTH
(a) Relative detector signal vs.
target temperature for two Ircon
pyrometer models [37].
27
(b) Typical transmission spectrum of borosilicate glass as used for the pyrometer viewport (1 mm thickness)[38].
Figure 2.21
als, because of the wavelength range of the detector limiting the accessible
temperature range. Tests on our setup, a kSA BandiT with a detector covering wavelengths up to 1.3 µm, showed, that from a GaSb layer thickness
of 1 µm, the band edge is above the detection limit of the detector. A possible solution would be to change the detector of the setup for a far-infrared
detector. However, there are no affordable detectors for InSb (band gaps
around 7.3 µm) and the materials used in this work cover such a large band
gap range that several detectors would have to combined for an efficient use
of DRS for temperature monitoring during growth.
Temperature measurements using RHEED
None of the aforementioned techniques can give reliable and quantitative
temperature measurements for GaAs substrates covered by thick low band
gap material layers such as InSb. Surface reconstruction transitions can be
used to measure temperatures, phase diagrams for all materials used in this
work are available in literature[40, 41]. The drawback of this technique is
that growth has to be interrupted and the temperature be ramped in at least
a modest range which prevents the use during growth and can potentially
damage the crystal structure. For temperatures below 400 ◦ C and small band
gap materials such as InSb, however, it is the only reliable method available
in our setup. It should be stressed that a very precise calibration of the group
V BEP is necessary for comparisons with phase diagrams from literature and
thus for quantitative temperature measurements.
28
CHAPTER 2. THEORY
(a) Setup of the MBE chamber and the band edge
thermometer.
(b) Spectra taken using the band edge thermometer
setup for different temperatures.
Figure 2.22: Band edge thermometer setup (a) and spectra of a 500 µm GaAs
wafer (b), from [39].
Chapter 3
Experimental setup
3.1
MBE system
The work covered in this thesis consisted to a large part in setting up a
molecular beam epitaxy system for high purity Sb-based III/V semiconductor
heterostructures. We chose this system to be a customized Veeco Gen-II
MBE system similar to one (in the meantime two) other systems installed
in the same laboratory, thus giving a great advantage in synergy for spare
parts, control programs and maintenance routines.
A photograph of the MBE system in our laboratory can be seen in Figure 3.1(a). The core part of the system is the main growth chamber, which
is schematically shown in Figure 3.1(b). The chamber is pumped by a 400mm cryopump (for details on the working mechanisms of all pumps, see
section 3.1.3) connected to the chamber by a polymer-sealed (Viton) gate
valve. We opted against the use of an all-metal valve (as in the other MBE
systems operated in our facilities) because of the lower costs of a Viton-sealed
valve and because we did not expect inferior vacuum quality due to the very
low outgassing rate of Viton and the valve only being used to seal the chamber from the cryopump where the vacuum conditions excellent are in general.
The entire chamber is doubled by a hollow stainless-steel cylinder where the
inner part is constantly flushed by liquid nitrogen and used as a cryoshroud.
One side of the chamber is connected to the cell flange which has 8 openings to accommodate 8 effusion cells and is also flushed by liquid nitrogen
to pump all evaporating molecules not directed towards the growing wafer.
Our system is equipped with two cells for gallium and one each for arsenic,
antimony, indium, aluminum, silicon and carbon. The gallium, indium and
29
30
CHAPTER 3. EXPERIMENTAL SETUP
aluminum cells are of Knudsen type, arsenic and antimony are evaporated
from cracker cells and the cells for the dopants silicon and carbon consist
of a filament of the corresponding material being heated by a large current
(up to 14 A for Si and over 50 A for C). All cells are installed such that the
molecular beams originating from the crucibles or filaments are directed directly towards the sample. The central part of the growth chamber is the
substrate manipulator. It consists of a sample heater which can rotate the
sample around an axis perpendicular to the wafer surface during growth, a
setup for flipping the sample from the growth position (facing the cell flange)
to the transfer position (facing the transfer rod) and a beam flux gauge. The
sample is glued using liquid Ga to a tantalum block (Fig. 3.2(a)) which is
then mounted onto the substrate heater using a transfer rod. The Ta-block
is designed to allow for optimal heat conduction and distribution.
The substrates are inserted into the growth chamber via two auxiliary chamber to prevent degradation of the ultrahigh vacuum which is in the low
10−11 mbar range in standby. The first chamber, called “load lock” is the
only part of the system regularly exposed to air. Up to five wafers on tantalum blocks can be loaded onto the trolley shown in Fig. 3.2(b). After baking
out the load lock chamber for at least two hours at 200 ◦ C, the pressure is
below 10−7 mbar and the valve to the so called buffer chamber is opened. The
load-lock trolley is moved on its rail to the buffer chamber where the wafers
are loaded onto the buffer-chamber trolley with the help of a transfer rod.
Before loading the wafer into the growth chamber, it has to be baked out
on the buffer-chamber heating station for at least two hours at temperatures
above 400 ◦ C so that the pressure in the buffer chamber will be in the low
10−10 mbar range. The transfer into the growth chamber is also carried out
using a transfer rod.
3.1.1
Gauges and Mass Spectroscopy
Prior to and during operation of the MBE system, it is crucial to know the
quality of the vacuum inside the growth and auxiliary chambers. Several
types of gauges are used to measure the pressure inside the chambers and
in the roughening system depending on the vacuum level. For low vacuum
measurements, we use convection tubes which measure the heat conduction
of the remaining gas in the vacuum chamber. This also means that they are
sensitive to the gas being pumped which in our case can be air, nitrogen or
argon and that the pressure reading has to be recalculated accordingly. At
lower pressures, convection gauges cannot be used as the number of atoms
3.1. MBE SYSTEM
(a) The E-chamber in our MBE laboratory at ETH Zürich, shortly
after the first samples were grown in summer 2011.
(b) Schematic of the main growth chamber, very similar to our
setup.
Figure 3.1: Overview of the MBE system.
31
32
CHAPTER 3. EXPERIMENTAL SETUP
(a)
(b)
Figure 3.2: A GaAs wafer being glued to a Ta block covered in Ga (a) and
MBE trolley with 5 sample positions outside the load lock (b).
in the vacuum chamber is not high enough for a measurable molecular heat
conduction. Pressures in high and ultra high vacuum are usually measured
using ion or hot cathode gauges that measure the ion current produced by
impacts of electrons emitted from a hot tungsten filament with molecules of
the residual gas. This ion current is proportional to the density of the gas
and pressures as low as 10−12 mbar can be measured. Ion gauges are also
used as beam flux monitors, especially to monitor the beam fluxes of group
V elements.
Only measuring pressure is not sufficient for a full assessment of the vacuum
quality as nocuous gases like oxygen (O2 ) can deteriorate the sample quality
or even damage the system by e.g. oxidizing filaments already at very low
partial pressures. The molecular composition of the residual gas is measured
using a quadrupole mass spectrometer (see Figure 3.3). It consists of 4 rods
connected together in pairs where a high DC voltage is applied between the
pairs and overlaid with a low amplitude radio-frequency AC voltage. For
every given AC/DC voltage ratio, a particular mass-to-charge ratio of the
previously ionized gas molecules will have a stable trajectory through the
setup and arrive at the detector. The partial pressure is then calculated in
function of the measured ion current. For our pressure ranges, an electron
multiplier is necessary where the ions induce emission of several electrons
by secondary emission at the impact on an emissive material. Sample mass
spectra for different situations are shown in Figure 3.4.
3.1. MBE SYSTEM
33
Figure 3.3: Quadrupole mass analyzer: (1) and (2) inlet and exit slits of
analyzer, (3) trajectory of ions, (4) high-frequency voltage generator, from
[42].
3.1.2
Cells
Knudsen cells consist of conical or cylindrical pyrolytic boron nitride (PBN)
crucibles heated by tungsten filaments, the material is typically evaporated
from the liquid phase. Pyrolytic boron nitride is an amorphous, ceramic form
of boron nitrite with excellent mechanical, chemical, thermal and outgassing
properties up to 3000 ◦ C which make it the material of choice for crucibles
and other parts in MBE systems such as insulating parts for wirings. A
detailed view of the construction of a typical Knudsen cell is depicted in
Figure 3.5(a). The crucibles in these cells are optimized for a homogeneous
molecular beam profile with the two shapes most used being conical crucibles
and the so called “sumo” crucibles, which are cylindrical crucibles with small
openings, see Figure 3.5(b).
For materials such as As or Sb that evaporate in tetramers (Al4 and Sb4 ), a
cracking cell is used to split these molecules in smaller parts, either dimers
or single atoms by heating them to high temperature. The cracking zone can
be heated to temperatures up to 1200 ◦ C, independently from the bulk temperature. The growth properties for the different kind of group-V molecules
are very different, the possibility of cracking the molecules thus gives a much
better control of the growth dynamics. The arsenic cell installed in our system is a Veeco 500cc valved cracker cell with a bulk crucible accommodating
a 2.5 kg arsenic block, for a detailed sketch, see Figure 3.6.
34
CHAPTER 3. EXPERIMENTAL SETUP
10
7
10
8
Partial Pressure [torr]
H+
2
10
9
H2 O +
10
HO+
O+
10
As+
N+
2
He+
10
11
10
12
1
10
20
30
40
50
60
Mass/Charge
70
80
90
100
(a)
10
7
10
8
H+
2 H O+
2
Partial Pressure [torr]
HO+
As+
N+
2
10
Ar+
As++
He+O+
Ar++
9
AsO+
10
10
10
11
10
12
1
10
20
30
40
50
60
Mass/Charge
70
80
90
100
(b)
Figure 3.4: Two different mass spectra recorded in the growth chamber of
our MBE setup, peaks are labeled with the name of the detected molecule.
(a) After baking out the chamber at 200 ◦ C and subsequent long standby at
room temperature. The only visible peaks are hydrogen H+
2 and the fraction
series of water at Mass/Charge = 16, 17, 18 (b) Immediately after bake-out of
an effusion cell (In4). Prominent peaks are N+
2 from the PBN crucibles, the
As-series from the arsenic deposited on the chamber walls and He+ liberated
by the heat radiation into the cryopump.
3.1. MBE SYSTEM
(a) A standard Veeco effusion cell with
a conical PBN crucible.
35
(b) A Veeco effusion cell with a “sumo”
PBN crucible.
Figure 3.5: Knudsen-type effusion cells with conical (a) and “sumo”-type (b)
crucibles. Drawings from Veeco.
The antimony cracker cell is a Veeco 200cc Mark V valved cracker cell for
corrosive materials which is filled with 3-5 51 g Sb-rods. As we operate the
cell in a down-looking position, great care is necessary to prevent the rods
from sliding down and blocking the valve mechanism. The use of this special
valved cracker cell in the Veeco Gen-II MBE system gave rise to unexpected
problems due to the distance of the valve opening and the cell port opening in
the shroud. A large amount of Sb condensated on the cryocooled walls inside
the cell port between the valve an the shutter and completely blocked the
opening of the cell. Heating the cracker and front bulk heaters to very high
temperature around 1200 ◦ C helped to evaporate part of the material, but
corrosion of the heating wires due to Sb deposition and possibly oxidation
after an air-leak eventually prevented us to reach these temperatures and
forced us to dismount and repair the cell and mechanically clean the cell
port. To prevent the port from being blocked again, we extended the valved
cracker tip to the edge of the cell port using a PBN tube, the construction
can be seen in Figure 3.7.
3.1.3
Pumps
For the growth of high purity semiconductor samples, it is crucial not to
introduce any contaminants into the MBE system. Possible sources for impurities are, among others, vacuums seals and pump oils. It is therefore
important to only use pumps that are completely oil free and only use all
metal seals and gaskets, the only exception being the aforementioned Viton
seal between the cryopump of the growth chamber and the growth chamber
itself.
Under operating conditions, the MBE system is only pumped by cryogenic
pumps. This kind of pumps consists of a large stainless-steel recipient cooled
36
CHAPTER 3. EXPERIMENTAL SETUP
Corrosive
Series
Valved Cracker
200cc Mark V Corrosive Series Valved Cracker
d all-PBN
and valve
ism with more
5 in the field
lved antimony
with proven
a nozzle for
nt flux
ity and
d material
Description
The patented Veeco Corrosive Series Valved Cracker is the only proven all-PBN
valved source available on the market today. This innovative technology offers
valved flux control for reactive high-vapor pressure materials (such as antimony
and tellurium) not compatible with the metal crucibles and valves of traditional
valved sources. The source design utilizes an entire valve assembly, crucible, and
conductance tube constructed exclusively of pyrolytic boron nitride (PBN) to protect
(a) A Veeco valved cracker as used in our systhem from corrosion.
tem for As sublimation. The As block is inThe valve assembly
is removable,
allowingvisible
easy loading
theseclarge capacity
side
the PBN crucible
throughofthe
crucible through the
conductance
tube.
The
crucible
is
heated
to
generate a beam
tion.
flux. Gas flow is regulated through the PBN valve, providing rapid flux
stabilization, quick shut-off, and excellent reproducibility. In the cracking zone, a
molecular flux may be thermally cracked to smaller molecular or atomic species.
The source can also be operated in uncracked mode, if desired.
eproducible
ical flux
harge capacity
operation in
or uncracked
ible with Sb,
CdTe, Zn and
Principle of operation for the Corrosive Series Valved Cracker. Source material is loaded into the
(b) Schematic of the Veeco valved cracker cell used for Sb.
PBN crucible through the conductance tube and heated. An all-PBN valve regulates the gas flow
into the growth chamber. The valve must be controlled with a Veeco SMC-II Automated Valve
Heating ofcracker
the conductance
keepsin
theour
valve setup.
clear and provides
thermalfrom
crackingVeeco.
FigurePositioner.
3.6: Valved
cellszone
used
Drawings
of polyatomic species. An integrated nozzle optimizes the flux uniformity across the substrate while
minimizing material waste.
3.1. MBE SYSTEM
37
Figure 3.7: Custom made extension of the valve lip supposed to prevent
blocking of the cell opening. The extension fits completely into the cell port,
but can also potentially be operated outside of the cell port.
to below 10 K by compressed helium expanding from 20 bar to 13 bar, controlled by a displacer. Baffles covered in activated charcoal enlarge the cold
surface and allow for a much higher pumping capacity. Cryopumps are the
pumps with highest pumping speeds for the gases pumped, up to 10 m3 /s
for argon and the opening diameter of 400 mm used in our setup[43], but
saturate very quickly in bad vacuum conditions such that they can only be
used at low pressures (we operate the pumps below 10−4 mbar) and regular regeneration at room temperature to allow for outgassing of the pumped
gases is necessary. It should be pointed out that cryopumps do not effectively
pump helium and hydrogen as these do not condensate on the cold surfaces.
However, helium can be cryotrapped in the recipient as remaining helium
atoms in the apparatus will ballistically move into the cryopump recipient
where they will be slowed down by each impact with the cold surfaces as their
kinetic energy is reduced due to the low temperatures. At some point, the
velocity of the atoms will be so low, that they cannot escape the cryopump
recipient and will be trapped as long as the cold temperature is maintained.
In order to reach acceptable vacuum conditions for the use of the cryopumps,
we use roughening pumps such as special all metal scroll pumps, sorption
pumps and membrane pumps. Scroll pumps consist of two scroll spirals
where one of the spirals is fixed and the second spiral orbits eccentrically,
without rotating, around the first. The volume of gas enclosed between the
spirals will thus be pumped from one recipient to the other. The special type
of scroll pumps used in our systems was developed for the nuclear industry
to pump radioactive gases and does not have any rubber seals (contrarily
to normal scroll pumps which have at least a polymer tip seal to tighten
the front spiral from atmosphere). This pump is used on a daily basis to
38
CHAPTER 3. EXPERIMENTAL SETUP
achieve rough vacuum after loading new samples into the load lock because
it is easy to use and does not need cooling by liquid nitrogen. If larger gas
volumes have to be pumped, the roughening pumps of choice are sorption
pumps. These pumps are very simple stainless-steel containers filled with
zeolite or activated coal that are cooled by liquid nitrogen. The large surface
at 77 K pumps effectively all gases with condensation temperatures above
77 K and even pumps a large part of other gases (as helium or hydrogen) by
the molecular drag of the condensating gases.
A membrane pump is used as backing pump to the scroll pump described
above to decrease the minimal pressure that can be attained to 10−4 mbar.
Membrane pumps are very simple pumps, the eponymous membrane, with
suitable valves on either side, displacing a volume of gas from one container to
the other, thereby reducing the pressure in the fist container. It is important
to regularly control the membrane as it will eventually disintegrate and could
cause a large reflux of particles into the vacuum chamber.
During bake out of the chamber, the partial pressure of hydrogen gas is
reduced by a titanium sublimation pump. A very large current (above 40 A)
is passed for a very short time (a few seconds) through Ti rods with Ti atoms
evaporating from the rods and being deposited on the cold surface of the
chamber shroud cooled by liquid nitrogen. The clean Ti surface effectively
getters all kinds of gases, including hydrogen.
The hollow cylinder inside the growth chamber which we call “cryoshroud”
is also used for pumping purposes, supporting the main 400 mm cryopump.
It is cooled by liquid nitrogen and its 77 K cold surface pumps different gases
and molecules evaporating from the effusion cells.
3.2
3.2.1
Transport characterization
Magnetotransport
The most important benchmark for the quality of our samples is the carrier
mobility µ of the charge carriers in a two-dimensional electron or hole system.
This quantity is defined as the the constant of proportionality between the
drift velocity of the carriers and the electric field applied and is given in the
Drude model of electrical conduction as
µ=
eτ
,
m?
(3.1)
3.2. TRANSPORT CHARACTERIZATION
39
where τ is the mean scattering time of the electrons and m? the effective
electron mass. The mobility resp. τ includes all scattering events such as
crystal defects, interface roughness, ionized donors, phonons etc and as such
is a good overall indicator for sample quality even though more detailed
studies have to be undertaken to identify the factors that limit the mobility.
Another important quantity for the assessment of the samples is the carrier density in the two-dimensional electron (or hole) system in our samples.
It gives feedback on the carrier sources and the reproducibility of the samples. In addition, the relation between the electron density and the electron
mobility can give an indication on the nature of the scattering processes.
In our laboratory, we measure both quantities by carrying out transport
measurements in magnetic fields, i.e. by driving a current through the twodimensional carrier system and measuring the longitudinal and transverse
voltages. The resistivities are then given by
ρxy =
UH
I
(3.2)
for the transverse resistance, where UH is the transverse or Hall voltage and
ρxx =
UW
I L
(3.3)
for the longitudinal resistivity, where W is the width of the sample and L
the distance between the contacts at which the longitudinal voltage drop is
measured.
These simple relations are only valid for long and narrow samples with perfectly aligned contacts. Most samples measured for this thesis were of rectangular shape so that the expressions for the resistivities have to be adapted
following the work of van der Pauw[44] to read:
RP Q,RS
π RP Q,RS + RQR,SP
ρxx =
f
(3.4)
ln 2
2
RQR,SP
ρxy (B) =
RP R,QS (B) − RP R,QS (0) + RQS,RP (B) − RQS,RP (0)
2
(3.5)
RP Q,RS indicates that the current flows from P to Q and the voltage is
measured between R and S, see Figure 3.8. Four-point measurements are
commonly used to prevent measuring the resistance of the contacts in series
40
CHAPTER 3. EXPERIMENTAL SETUP
(a)
(b)
Figure 3.8: (a) Contact arrangement and (b) geometry factor for the calculation of resistivities after van-der-Pauw. Taken from [11].
with the resistance of the 2DEG. The geometry factor f (x) is implicitly given
by
f
1
ln 2
x−1
=
a cosh
exp
.
(3.6)
x+1
ln 2
2
f
The electron density can be calculated by measuring the slope of the linear Hall voltage curve in function of magnetic field for small B-fields or by
plotting the positions of the Quantum Hall plateaus or the Shubnikov-deHaas minima of ρxx in 1/B and calculating the slope of the linear fit for
larger B-fields:
2e 1
1
=
i
Bi
hn
(3.7)
µ can be determined using the (classical) Hall effect:
µ=
dρxy /dB|B=0
ρxx (B = 0)
(3.8)
Further informations about sample quality and properties can be extracted
from the longitudinal and transversal resistivities in function of the magnetic
field. Beatings in ρxx usually indicate different occupied subbands and a
parabolic shape in ρxx at low fields is usually an indicator for the existence
of a parallel conductive layer.
3.2. TRANSPORT CHARACTERIZATION
41
Figure 3.9: A van-der-Pauw sample with hand-soldered indium contacts,
connected to the chip carrier using gold wires.
3.2.2
Sample preparation
The rectangular pieces were contacted using hand-soldered indium contacts
on all four corners and on the middle of each side. As there is no Schottky
barrier between InAs and metals, no complicated annealing sequences are
necessary to obtain Ohmic contacts, we only heated the sample for 20 minutes at 200 ◦ C to ensure homogeneous repartition of the contact metal. The
sample was then glued onto and contacted using gold wire to a simple chip
carrier as shown in Figure 3.9.
3.2.3
Measurement setup
Most measurements were carried out in a 4 He dewar using a special measurement rod with a superconducting magnet which can be completely inserted
into the dewar. We use four-point measurements by driving an AC current
through one pair of contacts and reading out the voltage drop between two
different contacts using standard lock-in measurement techniques. Typical
values are currents of 1 µA and driving and read-out frequencies of 13.6 Hz.
For magnetotransport measurements, a superconducting magnet that can
produce fields up to 6.2 T is included in the setup. A computer connected
to the system controls all outputs, measures all relevant quantities and automatically calculates the desired values as e.g. electron mobility or density
and records measurement traces for sweeps of the magnetic field.
The measurements of the InAs/GaSb/AlSb CQWs presented in section 4.3
were performed in a 3 He/4 He dilution refrigerator where a mixture of 3 He
and 4 He can undergo a phase transition below 0.86K between two relative
concentrations, thereby absorbing heat from the sample space. Temperatures as low as 1 mK can be obtained with this technique - in our case, the
measurements were carried out at 20 mK in magnetic fields up to 14 T.
42
CHAPTER 3. EXPERIMENTAL SETUP
Figure 3.10: Illustration of the basic mechanisms of photoluminescence.
3.3
3.3.1
Optical characterization
Photoluminescence
Photoluminescence (PL) is a powerful tool for characterizing energy states in
semiconductors. Photons originating from an excitation laser are absorbed
by the system and an electron-hole pair is created. This pair usually relaxes
into its ground state by inelastic scattering and will eventually recombine,
emitting a photon in the process (Fig. 3.10). The wavelength of this photon
will give informations on the energetic landscape of the analyzed material
which can be influenced by effects such as confinement, donor-like impurities,
strain, bound electron-hole states (excitons), etc. The identification of the
origin of the peak positions in a PL spectrum will either rely on theoretical
models or on careful phenomenological analysis.
3.3.2
Fourier Transform Infrared Spectroscopy
For the optical characterization of samples in the infrared wavelength range,
Fourier transform infrared spectroscopy (FTIR) spectroscopy is the method
of choice. Instead of scanning through a wavelength range, a FTIR spectrometer measures all wavelengths simultaneously, for different optical paths
through the setup using a movable mirror (Fig. 3.11). The spectra are then
calculated by computing the Fourier transform of the interferograms in function of the mirror position. FTIR spectrometers have several advantages
over traditional dispersive spectrometers such as better signal to noise ratio,
higher throughput of light and high spectral resolution. For more information
see Ref. [45].
3.3. OPTICAL CHARACTERIZATION
43
Figure 3.11: Schematic diagram a FTIR setup.
To avoid Fabry-Pérot oscillations from reflections at the boundary between
materials with different refractive indices (as e.g. GaAs and GaSb) and to
be able to measure intersubband transitions, the samples were prepared for
attenuated total reflectance (ATR) measurements: two opposite faces of the
samples have to be wedged at an angle of 45◦ relative to the surface as shown
in Figure 3.12(a). The light enters the sample through one of these faces and
is reflected several times inside the sample by the surfaces before leaving the
sample though the opposite sample face.
The spectrometer used for all measurements was a Bruker Vertex 80v. It featured an evacuable internal sample compartment, a KBr beamsplitter and
KBr and CaF2 windows, which are transparent in the mid-infrared spectral
range. The detectors used are shown in Table 3.1. For the ATR measurements an additional external setup was used (Fig. 3.12(b)).
44
CHAPTER 3. EXPERIMENTAL SETUP
(a) Schematic diagram of the ATR setup with polarized light entering the sample normal to the
tilted edges [46].
(b) Schematic of the setup for the ATR
measurements.
Figure 3.12: Details on ATR measurements.
Range [cm−1 ]
Range [meV]
DLaTGS
350 - 12500
43 - 1550
Normal incidence measurements
PbSe
1920 - 6670
240 - 825
Normal incidence measurements
MCT
400 - 11700
50 - 1450
ATR for intersubband measurements
Name
Use
Table 3.1: Detectors used for FTIR measurements.
3.4. STRUCTURAL CHARACTERIZATION
45
Figure 3.13: Schematic setup of an atomic force microscope in contact
mode[47].
3.4
3.4.1
Structural characterization
Atomic Force Microscopy
Atomic force microscopy (AFM) is a type of scanning probe microscopy
that allows to obtain lateral resolutions as small as 1 Å for standard setups (Fig. 3.13). The probe, which is a sharp tip attached at the end of a
cantilever, is scanned over a surface and deflected by the forces between the
tip and the surface atoms - these forces can be mechanical contact forces,
van-der-Waals forces, chemical bonding etc. In contact mode, the intensity of
the reflection of a laser spot from the top of the cantilever is used to measure
the cantilever deflection, where typically this intensity (and thus the force
on the cantilever) is kept constant by varying the distance between the tip
and the surface. This avoids potential damages due to collisions between the
tip and the sample surface. The position of the tip is controlled by piezoelectric elements for all three spatial directions. In our case, the AFM was
operated in the so called tapping mode where the cantilever is vibrated near
the resonance frequency and the surface height is measured by keeping the
amplitude of the vibration constant as the interaction force with the surface
will shift the resonance frequency. This operation mode allows to reduce the
forces exerted on the tip and the surface even further.
We used a Veeco Nanoscope IV AFM setup with Au-coated silicon cantilevers
and 10 nm-sized tips in tapping mode for the AFM measurements shown in
the later chapters.
46
CHAPTER 3. EXPERIMENTAL SETUP
source
C1
condenser system
C2
condenser aperture
sample holder
sample
objective lens
objective aperture
projector system
imaging
Figure 3.14: Schematic of a transmission electron microscope, from [48].
3.4.2
Transmission Electron Microscopy
In transmission electron microscopy (TEM), a beam of electrons (usually
emitted from a tungsten filament) is transmitted through a thin layer of
material. The electrons interact with the sample matter and thus create an
image of the sample which is magnified and focussed onto a phosphorescent
screen or a CCD camera. Because of the small de-Broglie wavelength of
the accelerated electrons, which can be as small as a few picometers, TEM
has a much higher resolution than light microscopes. It is possible to image
structures at the near-atomic level as for example the material interfaces
in our heterostructures or crystal defects. Electromagnetic lenses are used
to focus the electron beam, most setups use three lenses to form an electron
beam (condensator lens), focus the beam onto the sample (objective lens) and
to expand the beam onto the phosphorescent screen or the CCD sensor. For
a schematic view of this setup, see Figure 3.14. To allow for the high voltages
and to avoid unwanted collision of the electrons with the ambient gases in the
setup, TEMs are usually operated under high vacuum conditions of 10−6 mbar
or lower. The main disadvantage of TEM is the laborious preparation of
the samples which have to be thinned to thicknesses below 100 nm - 1 µm.
Semiconductor samples are usually prepared using a combination of chemical
etching, mechanical milling and ion etching.
Chapter 4
Experimental results
4.1
InAs/AlSb quantum wells
In this section we will first describe a typical growth routine of a representative InAs/AlSb Quantum Well sample before giving a detailed analysis of the
influence of the different growth parameters. A simplified model structure
is shown in Figure 4.1. If not mentioned otherwise, all magnetotransport
data were measured at 4K. Measurements of samples used to illustrate the
dependence of sample properties on growth parameters are always chosen, if
possible, to be from the same growth campaign as source materials, heater
efficiency etc. differed between openings of the growth chamber.
Lattice-matched semi-insulating substrate materials are not available for the
6.1 Å family, consisting of InAs, AlSb and GaSb, due to its members’ small
band gaps. For this reason all samples presented in this work were grown
on (001)-GaAs substrate wafers. These wafers are heated above 580 ◦ C to
remove the oxide layer on the surface, successful desorption is subsequently
controlled by checking the RHEED pattern changing from being completely
blurry due to the random diffraction of the electron by the amorphous oxide
layer to showing clear spots typical for bulk single crystals.
The substrate surface is initially planarized by a layer of GaAs grown at
640 ◦ C before the substrate is cooled down to around 540 ◦ C to deposit the
AlSb nucleation layer. AlSb shows 2D growth on GaAs already after only
around 40 monolayers (MLs) due to its limited surface migration length[49]
and is thus the material of choice for the lattice mismatched transition from
the substrate to the 6.1 Å materials[9], although a high density of thread47
48
CHAPTER 4. EXPERIMENTAL RESULTS
Figure 4.1: Typical layer sequence for an InAs/AlSb QW sample
ing dislocations is introduced. Thick buffer structures of around 1-3 µm are
subsequently grown at the same temperature of 540 ◦ C to allow for the dislocations to bend towards the sample edges. The active region consists of an
InAs channel inserted between two Al(Ga)Sb barriers, capped by a layer of
GaSb to prevent oxidization of the Al-containing barriers.
4.1.1
Buffer layers
Because of the large lattice mismatch and the resulting high dislocation density, a careful choice of appropriate buffer layer sequences is crucial to ensure
a high crystal quality in the active region and thus to achieve high electron mobilities. The prevalent type of dislocations due to the nucleation on
the lattice-mismatched substrate is the threading type with densities up to
50 µm−2 [50] in GaSb, as measured on the sample surface by AFM or scanning tunneling microscopy (STM). Using thicker layers, we can reduce the
dislocation densities by more than an order of magnitude as they annihilate
each other or reach the sample edge. As observed empirically[51], AlSb is
not as well suited as a buffer material as it does not considerably reduce
the dislocation density, instead, it preserves the roughness pattern created at
the nucleation interface. We used 5 different buffer structures for this thesis,
they are shown schematically in Figure 4.2. From the electron mobility val-
4.1. INAS/ALSB QUANTUM WELLS
A"
49
C"
B"
D"
E"
Figure 4.2: The five buffer layer schemes tested in this thesis. SL denotes a
10 period AlSb/GaSb superlattice of 2.5 nm layer thickness for each material.
ues in Table 4.1, we see that the buffer structure A gives the best results, this
structure was also used for the majority of samples fabricated. All samples
shown are identical except for the buffer layers, these are followed by 200 nm
AlSb, the 15 nm InAs channel, a 20 nm top barrier and 5 nm GaSb as capping layer. The addition of 30% alumnium in some of the buffer layers was
chosen to minimize the parasitic conduction from the naturally p-type GaSb
layers without degrading the crystal structure. It is interesting to notice that
the omission of the 50 nm GaSb layer between the otherwise identical buffer
structures A and D leads to a sharp and reproducible drop in electron mobility, confirming again the important role of GaSb in the reduction of the
dislocation density.
4.1.2
Channel thickness
As the electron wave function of our quantum well structure will reside inside the InAs layer, great care has to be used for the choice of thickness of
that layer. For thin layers, the effective barrier height is reduced by confinement, and, more importantly, mobility is reduced due to interface roughness
scattering. On the other hand, if the channel layers are thicker than the
critical layer thickness, the layers will relax and misfit dislocations occur. In
addition, intersubband scattering is increasingly probable in wider wells.
50
CHAPTER 4. EXPERIMENTAL RESULTS
Buffer scheme
Peak mobility [cm2 /Vs]
Density [1011 cm−2 ]
A
400,000
9.13
B
320,000
9.69
C
310,000
9.13
D
210,000
8.63
E
250,000
8.5
Table 4.1: Samples with different buffer schemes.
It is interesting to note that, following the theoretical approach by MatthewsBlakeslee[33], the critical layer thickness for InAs on AlSb is expected to be
as low as100 Å resp. 200 Å on GaSb. However, as investigated by Bennett
et al.[52], substantially thicker InAs layers (3000 Å) can be grown on GaSb
substrates before the strain is relaxed. For InAs layers on GaSb buffers grown
on GaAs substrates, the epilayer strain is very close to the fully strained case
for InAs layer thicknesses up to 1000 Å if the buffers are sufficiently thick.
Indeed, the driving factor for epilayer relaxation is the appearance of misfit
dislocations which are nucleated mainly on threading dislocations from the
nucleation process on the substrate surface. This is another strong hint that
thicker buffers improve the sample quality. From these results, we deduce
that the InAs layers in the InAs/AlSb QW samples are almost fully strained
and that the mobility is not significantly decreased by misfit dislocations for
the layer thicknesses we investigated and which range between 100 − 200 Å.
Although no rigorous study of the dependence of the electron mobility in
InAs QWs on the channel thickness was conducted in this thesis, our results
are in qualitative agreement with the work of Bolognesi et al.[53] which led
us to using a thickness of 150 Å for almost all InAs channels grown by our
group. Mobilities and densities for samples with different layer thicknesses
are listed in Table 4.2. The density in the thicker layer is increased as the
electron states are lower in energy relative to the barriers and the surface
states due to the weaker confinement in the well.
4.1.3
Capping layer and barriers
Since the barriers of the quantum well contain aluminum which oxidizes
quickly if exposed to air, the active region has to be capped by a material less
4.1. INAS/ALSB QUANTUM WELLS
51
Channel thickness
Density [1011 cm−2 ]
Mobility [cm2 /Vs]
E121122B
150 Å
8.64
230,000
E121128A
200 Å
9.67
140,000
Sample
Table 4.2: Samples with different channel thicknesses.
Cap material
Density [1011 cm−2 ]
Mobility [cm2 /Vs]
E120906A
GaSb
7.49
320,000
E120925C
InAs
1.91
70,000
Sample
Table 4.3: Samples with different capping layer materials.
prone to oxidization. Both InAs and GaSb can potentially be used. However,
the discussion in section 2.2.1 showed the crucial influence of the choice of
capping layer material on the electron density and mobility in InAs/AlSb
QWs. This is confirmed by our experiments as shown in Table 4.3 which are
similar to the work of Nguyen et al.[15]. Indeed, the high energy at which
the Fermi level is pinned at the GaSb surface allows for an electron density
of 7.49 × 1011 cm−2 in the sample shown. For the InAs cap, the Fermi energy
is much lower in energy which is reflected by the much lower electron density
of 1.91 × 1011 cm−2 . The thickness of the capping layer does not have a large
influence on these basic properties, it only contributes to the overall distance
between the quantum well and the surface.
This distance is the second central parameter in influencing the electron
density in our quantum well[14]. In Table 4.4 we show a number of samples
with different top barrier thicknesses. Indeed, we see that an increase in
top barrier thickness leads to a decrease in electron density in the QW, as
expected from the simple plate capacitor model described in section 2.2.1.
Figure 4.3 shows the linear dependence of the electron density in the 2DEG
on the upper barrier thickness of the samples. As expected, the density has
a lower limit given by the carrier contribution from the barrier material.
The mobility has a maximum of 560,000 cm2 /Vs at a density of 7.64 ×
1011 cm−2 which corresponds to a top barrier thickness of 200 Å where the
screening effect of an increased electron density starts to be compensated by
the quantum well being moved too close to the surface. Doped structures
52
CHAPTER 4. EXPERIMENTAL RESULTS
n2DEG [1011 cm−2 ]
10
8
6
100
200
300
400
tupper barrier [Å]
Figure 4.3: Electron densities in the InAs channel in function of the upper
barrier thickness for the samples listed in Table 4.4.
have been used to achieve even higher mobilities while keeping sufficiently
large top barriers as shown by Nguyen et al.[9].
The barrier material is of high importance as the residual barrier height
is strongly reduced with increasing Ga-fraction in Alx Ga1−x Sb as the band
alignment of InAs and the barrier evolves from Type I using AlSb to the
broken gap alignment of GaSb and InAs. On the other hand, the electron
mobility is increased for samples with high Ga-fractions following the arguments about buffer layers in the paragraphs above. For a Ga-fraction of
23 %, the valence band of GaSb is at the same energy as the conduction band
of InAs, leading to carrier transfer at higher fractions. This effect leads to
parallel conductance or leakage problems with gated structures. The influence of lower barrier composition is shown in Figure 4.4 where we display
magnetotransport data for two samples using different lower barrier materials. Fig. 4.4(a) shows a sample with a lower Al0.3 Ga0.7 Sb barrier where we
see strong signs of parallel conductance, i.e. the minima in the longitudinal resistance are not at zero for higher magnetic fields, indicating residual
conductivity in the sample. The right panel of Fig. 4.4(c) shows the same
longitudinal magnetoresistance measurement for an identical structure with
a lower AlSb barrier. Here, all minima at higher fields are at zero resistance,
no signs for parallel conductance are observed.
It was only in samples with pure AlSb barrier (top and bottom) that we
could successfully gate the samples and operate the gate in a large voltage
range.
4.1. INAS/ALSB QUANTUM WELLS
53
500
n = 7.5 ⇥ 1011 cm
300
400
4
2
⇢xx [⌦]
200
⇢xy [k⌦]
100
2
4
300
200
2
100
0
0
0
1
2
3
4
B-field [T]
5
0
(a) Lower Al0.3 Ga0.7 Sb barrier.
120
100
0
0
6
1
3
4
B-field [T]
5
6
(b) Upper and lower Al0.3 Ga0.7 Sb barriers.
n = 9.1 ⇥ 1011 cm
2
4
3
80
⇢xx [⌦]
2
60
2
40
⇢xy [k⌦]
⇢xx [⌦]
n = 7.4 ⇥ 1011 cm
2
⇢xy [k⌦]
400
1
20
0
0
0
1
2
3
4
B-field [T]
5
6
(c) Lower AlSb barrier
Figure 4.4: Three identical samples only differing by the aluminum concentration in the barriers. The density is a function of the lower barrier height.
54
CHAPTER 4. EXPERIMENTAL RESULTS
Upper barrier thickness
Density [1011 cm−2 ]
Mobility [cm2 /Vs]
E111014B
125 Å
9.77
490,000
E111019A
150 Å
9.11
430,000
E111213B
200 Å
7.64
560,000
E111025A
300 Å
5.77
370,000
E120919B
450 Å
4.54
70,000*
Sample
Table 4.4: Samples with different upper barrier thicknesses. The mobility
of the last sample cannot be compared with the other samples as the source
material was contaminated at that moment. The densities of samples with
200 Å-barriers using that source material were within 10% of the density of
sample E111213B.
The parallel conduction effect induced by the material choice of the upper
barrier is even more pronounced as seen in Figure 4.4(b) where we show
magnetotransport data for a sample identical to the samples in Table 4.4
except for a 200 Å Al0.3 Ga0.7 Sb upper barrier.
4.1.4
Growth temperatures
The congruent sublimation temperatures of the materials used in InAs/AlSb
QW structures range from 390 ◦ C for InAs to 600 ◦ C for AlSb. This large disparity means that optimized growth temperature profiles have to be found to
ensure high crystal qualities. In addition, the surface mobility of the atoms,
the exact details of the adsorption and desorption processes and the incorporation of the atoms into the crystal all depend critically on temperature.
In our work, we did not carry out rigorous studies on temperature profiles
and their microscopic effects on the different layers, but our experiments with
large ranges of temperatures confirmed the values found in literature and we
chose the temperatures which resulted in optimal electronic mobilities for
our setup. These were as mentioned above, around 540 ◦ C for AlSb and
GaSb and 450 ◦ C for InAs respectively. We did not see any negative effect
of lowering the temperature from 540 ◦ C to 450 ◦ C during the growth of the
lower QW barrier compared to pausing growth and lower the temperature
just before growing InAs. We also did not observe any difference in electron
mobility for the growth of the upper barrier and capping layers at 450 ◦ C or
4.1. INAS/ALSB QUANTUM WELLS
55
540 ◦ C. The different growth temperature profiles for low surface roughnesses
are presented in section 4.2.
4.1.5
Interfaces
For the transition between InAs and AlSb, the group III element and the
group V element are both changed and the interface bond can be either of
InSb (where the AlSb layer is terminated by Sb and the InAs layer starts with
In) or AlAs (where the AlSb layer is terminated by Al and the InAs layer
starts with As) type. One of the first important results in the investigation of
InAs/AlSb was that the interface between the lower barrier and the quantum
well has to be of InSb-type to ensure high electron mobilities[54]. This is due
to AlAs antisite defects which form on the Al-rich AlSb surface and serve as
scattering centers for the electrons in the QW if ionized. This explanation
is confirmed by the fact that the interface type of the upper interface, where
this type of defects cannot form, does not have any effect on the electron
mobility. We thus have to use a shutter sequence that assures an InSb-type
interface for the lower transition. This can be realized by exposing the AlSb
to an Sb-flux after pausing the growth, closing the Sb shutter and then grow
1 ML In onto the Sb-rich AlSb surface before the start of InAs growth. A
schematic of that sequence is shown in Figure 4.5. Sigmund et al. proposed
a further refinement of this shutter sequence with additional As-exposure of
the InSb-interface.[55]. This was supposed to prevent Sb segregation into
the InAs well and thus improve the structural and electronic properties of
the sample. Our electron mobility measurements could not confirm these
findings (although no structural investigation like TEM was carried out) so
that either we are limited in structural quality by different effects or that this
additional As soaking time helped reduce the effect of a source of problems
in the setup of Sigmund et al.
The effect of interface bonds in the transition between the 5.85 Å materials
and the 6.1 Å materials is not relevant since the transition yielding the best
samples is the transition using AlAs and AlSb[9].
4.1.6
Substrates
All samples grown for this thesis were grown on 2”, semi-insulating GaAs
substrates with a (001) oriented surface. Lattice matched substrates exist
and especially GaSb substrates are regularly used in semiconductor indus-
56
CHAPTER 4. EXPERIMENTAL RESULTS
Figure 4.5: To avoid the negative effect of the AlAs interface bonds, we grow
InSb interface bonds using the shutter sequence proposed by Tuttle et al.[54]
try, but also InAs wafers are available. However, these substrates are much
more expensive (by more than a factor of 5) and, above all, they cannot be
produced to be semi-insulating due to their small band gap which prevents
the creation of electron states compensating the p-type conductivity inherent
to these wafers due to GaSb antisite defects which cannot be avoided during the production process. The use of conductive substrates would make a
whole series of processing steps necessary to contact the 2DEG in our samples without shorting it through the substrate. A further advantage of GaAs
substrates is their oxide desorption temperature which is much lower than
their melting point. This is not the case for InAs, where the oxide desorbs
at only around 5 ◦ C below the melting point of the substrate and thermal
desorption of the oxide becomes difficult. An atomic hydrogen cell would be
necessary to expose the unoxidized InAs surface at lower temperatures.
Even though lattice-mismatched substrates definitely limit the structural
quality of the samples due to the dislocations introduced at the transition between the different lattice-constant materials, literature suggests that there
are no improvements to be expected from growing on GaSb substrates, at
least not in the mobility regime currently accessible. Indeed, similar surface
roughness on the order of the Fermi wavelength was observed for homoepitaxial growth of GaSb on GaSb substrates[56]. Our group still plans experiments
4.1. INAS/ALSB QUANTUM WELLS
57
using GaSb substrates in the near future as we expect a higher surface treatment quality during the production process compared to the substrates used
in the 20-year-old study [56].
4.1.7
Growth rates and partial pressures
With only a few exceptions, all samples were grown using growth rates of
1 ML/s for the GaSb and AlSb layers and 0.5 ML/s for the InAs channel. In
general, lower growth rates lead to better structural properties of the sample
while introducting a higher impurity densitiy as these impurities have more
time to be incorporated into the crystal. However, no significant dependence
of the electron mobility on the growth rates could be found for the range we
tested, i.e. 0.4 ML/s - 1.3 ML/s for AlGaSb and 0.25 ML/s - 0.8 ML/s for
InAs.
We usually grow our samples under group V overpressure so that the effective growth rate is determined by the group III element. To prevent
non-stoichiometric growth, the group V partial pressure, as measured using a beam flux gauge, is lowered until the sample shows the well-known
signs of group-V deficiency, i.e. a non-mirrorlike surface due to Ga droplets.
Subsequent samples are then grown using the lowest partial pressure giving
mirror-like surfaces. For the As partial pressure, no important effect on the
electron mobility could be measured in the tested range of 6 × 10−6 torr to
1.2 × 10−5 torr. The effect of the Sb partial pressure in all other layers on
the surface roughness was studies in more detail, the results are shown in
section 4.2.
The lack of dependence of the electron mobility on the growth rates and As
partial pressure (at least in a reasonable range) suggests that these are not
the limiting factors for the electron mobility and thus the electron scattering.
4.1.8
Antimony oligomers
Similar to As4 , the Sb tetramer Sb4 has the lowest sublimation temperature
of all Sb-oligomers and the molecular beam produced at the sublimation
temperatures of 450 ◦ C used in our experiments is mainly composed of Sb4 .
A heated zone at the tip of the cell can be used to thermally crack the Sb
tetramers into dimers or even monomers. A diagram showing the composition
of the molecular beam for different temperatures of the cracking zone (of the
EPI (former name of Veeco) setup used for that experiment[57]) is shown
58
CHAPTER 4. EXPERIMENTAL RESULTS
Figure 4.6: Calculated Sb dimer/tetramer flux versus the temperature of the
cracking zone, from [57].
Sample
E121009A
Mobility [cm2 /Vs]
Sb cracker temp.
600 ◦ C
◦
15% Sb2 /85% Sb4
25,000
E130128C
700 C
50% Sb2 /50% Sb4
299,000
E121122B
850 ◦ C
95% Sb2 /5% Sb1
230,000
Table 4.5: Samples grown using different Sb cracker temperatures.
in Figure 4.6. Although this cell is not identical to the cell used in our
setup, we expect to have a similar concentration dependence on temperature
because the cracking zone is a cylinder of a rather small diameter in both cells
and thus should have a homogeneous temperature close to the thermocouple
reading plotted in Figure 4.6 resp. measured by us to determine the Sb
oligomer. We did a number of tests with different cracker temperatures
which are shown in Table 4.5 which led us to conclude that the best results
as assessed by electron mobilities was obtained using a temperature of 700 ◦ C
corresponding to a 50%-each mixture of Sb4 and Sb2 . Our relatively high
growth temperatures of around 540 ◦ C for the Sb-containing layers allow us
to use lower cracker temperatures as the tetrameric part of the molecular
beam will be cracked on the sample surface, thus limiting the Sb aggregation
due to the low surface mobility of Sb4 . Higher cracker temperatures would
increase the evaporation of impurities from the cell and the cell shroud.
4.1. INAS/ALSB QUANTUM WELLS
59
It is interesting to note that, according to Rouillard et al.[57], As deposited on
the opening of the Sb cell degrades the structural properties of the samples by
replacing Sb atoms in the crystal. Operating the Sb cracker at a temperature
well above the sublimation temperature of As (as is the case for our samples)
helps to prevent the unwanted deposition of As on the cell shroud and the
Sb shutter.
4.1.9
Doping schemes
For a versatile use of InAs/AlSb heterostructures in fundamental research
as well as device applications, a good control of the electron density in the
InAs channel is necessary. As seen before, one way of changing this electron
density is to vary the thickness of the upper AlSb barrier. However, this
method is only of limited use as the electron mobility depends on the distance
between the channel and the surface and methods for selective doping of such
structures are necessary.
Tellurium has been successfully used as a remote n-dopant in the AlSb barriers of InAs/AlSb QWs[9] to produce samples showing very high mobilities.
It is however of great interest to find alternatives to Te as this material is
difficult to handle and gives rise to a memory effect in the MBE system. Silicon, which is used for n-type doping in GaAs/AlGaAs heterostructures, is of
amphoteric nature in III/V semiconductors and leads to p-type conductivity
in AlSb and GaSb and to n-type conductivity in InAs. This inspired Malik
et al. [58] with a new doping scheme for GaSb layers where the remote Si
doping layer is replaced by a strongly Si-doped and very thin InAs QW. This
scheme was then adapted to remotely dope InAs/AlSb QWs by inserting a
second, strongly Si-doped InAs channel into the AlSb barrier to successfully
produce high-quality HEMTs [17, 59]. Due to confinement effects, the electron states in the extremely narrow doping wells lie considerably above the
states in the main InAs channel and can thus transfer electrons into this
well. Our results using different numbers of InAs doping wells are displayed
in Table ??. The main difficulty to effectively dope the InAs layers and thus
allow for electron transfer into the main well is a precise control of the growth
temperature in the doping wells to prevent segregation of the Si atoms. In
our case, the temperature had to be lowered to 430 ◦ C before the doping was
effective.
60
CHAPTER 4. EXPERIMENTAL RESULTS
Sample
# of QWs
QW width
Properties
E110830B
1
15 nm
high mobility
E120829B
1
15 nm
moderate mobility
E120925A
20
8 nm
E120925B
20
10 nm
E121114C
20
12 nm
Table 4.6: Samples measured using FTIR spectroscopy.
4.1.10
FTIR measurements
To assess the quality of the interfaces in our QWs, we wanted to correlate
the Fourier Transform Infrared (FTIR) spectra of InAs/AlSb single quantum well (SQW) and multiple quantum well (MQW) samples with the MBE
growth processes, the samples used are listed in Table 4.6. In a first attempt,
normal incidence measurements were carried out to test the usability of the
experimental setup for our type of samples, these measurements are shown in
Figure 4.7(a). The y-axis in all measurement plots show the absorbance which
is defined as − ln(Ts (p)/Tref (p)), where Ts and Tref are the transmittance of
the sample and the reference transmittance of the GaAs substrate.
The Fabry-Pérot oscillations seen in these spectra are due to multiple reflections of the incident light at interfaces with different refractive indices. Their
period can be used to calculate the thicknesses of the corresponding layers
which are also in good agreement with the theoretically calculated values.
Figure 4.7(b) shows the absorption edges due to interband transitions of the
MQW samples which shift in wavelength in good quantitative accordance
with our simulations[45]. They were measured in ATR geometry to prevent
the Fabry-Pérot oscillations.
The most interesting measurements for our project were the intersubband
transitions shown in Figure 4.8 also taken in ATR geometry. The width of
the absorption features is expected to only depend on interface roughness
and we could see a clear difference in the absorption spectra between a very
high quality sample and a sample of identical structure but lower electron
mobility due to imperfect growth temperatures and possibly contaminated
source materials. In addition, our measurements show that the width of
the features does not depend on temperature which can be understood by
the limited number of phonons that can scatter the intersubband resonance
4.1. INAS/ALSB QUANTUM WELLS
(a) Normal incidence measurements on SQW samples
with Fabry-Pérot oscillations.
(b) Interband absorption for MQW samples of different QW thicknesses in ATR geometry.
Figure 4.7: FTIR measurements in SQW and MQW samples.
61
62
CHAPTER 4. EXPERIMENTAL RESULTS
Figure 4.8: Intersubband transitions in SQW samples of high (red) and moderate (black) moblities.
plasmon respecting its dispersion relations. Straightforward measurements at
room temperature are therefore possible. These first results are a promising
step toward a quick optical feedback on the growth quality of the samples.
Further experiments using more refined measurement techniques and larger
number of samples should be carried out to find a reproducible dependence
of the shape of the intersubband absorption line on the different growth
parameters.
4.2. SURFACE ROUGHNESS
63
Figure 4.9: 3D AFM view of a standard InAs/AlSb QW sample.
4.2
Surface roughness
The successful fabrication of nanoscale structures is not possible without a
surface that is flat on the scale of the structures to be patterned. In addition,
a surface roughness on the order of the Fermi wavelength λF = (2π/n)1/2 will
lead to enhanced scattering and reduced electron mobility as only the electrons close to the Fermi energy contribute to charge transport. The Fermi
wavelength is on the order 10 nm for most of our samples, the length scale of
the structures to be patterned is 1 µm.
As mentioned in the previous chapters, the 7% lattice mismatch between
the GaAs substrate and the 6.1 Å materials leads to large islands on the surface with sizes between 1 µm and 10 nm. A three-dimensional AFM picture
of the sample surface of a typical InAs/AlSb QW is shown in Figure 4.9. We
can observe mounds of one to several µm lateral dimension and a height of a
few nm. To reduce the surface roughness, two main parameters were studied
in more detail: growth temperature, especially the substrate temperature at
the transition between AlAs and AlSb and the Sb partial pressure.
64
CHAPTER 4. EXPERIMENTAL RESULTS
Sample
III/V ratio
Surface roughness [nm]
E131128A
1:4
1.54
E131129A
1:5
1.38
E131128B
1:6
1.44
E131205A
1:8
1.26
E131211A
1:10
1.27
E131211B
1:12
1.23
Table 4.7: RMS surface roughness measured by AFM for samples with different III/V ratios.
4.2.1
III/V ratio
Adatom mobility is not only important at the material interface but also during the growth of the buffer layers that are supposed to reduce the number of
threading dislocations. An important parameter that has to be analyzed is
therefore the ratio between the group-III and group-V elements, i.e. Al or Ga
and Sb. A series of samples with different III/V ratios achieved by changing
the Sb partial pressure for the growth of the buffer layers and the root mean
square (RMS) surface roughnesses measured by AFM is shown in Table 4.7.
The buffer layer, grown at a substrate temperature of 540 ◦ C, consists of
a 32 nm nucleation layer followed by 1100 nm Al0.3 Ga0.7 , 500 nm GaSb, a
10-period 2.5 nm GaSb/2.5 nm AlSb superlattice and a 5 nm GaSb cap to
prevent oxidation. While the roughness tends to decrease with decreasing
III/V ratio for the ratios measured, this effect is very weak and contrary to
our intuition which suggests a decrease in roughness with lower Sb overpressure (i.e. higher III/V ratio). This suggests that these samples were grown
under conditions where the limiting factor for the surface roughness is not
the III/V ratio.
4.2.2
Optimized transitions
A large number of threading dislocations forms at the AlSb nucleation layer
and will only partially be diluted by the thick buffer structures grown on top
of this nucleation layer. Successful strategies for a reduced surface roughness
would therefore focus on optimizing this transition between AlAs and AlSb.
4.2. SURFACE ROUGHNESS
Sample
65
Transition
Surface roughness [nm]
E130123B*
A
1.03
E140128B
B
1.07
E140213C
C
0.86
Table 4.8: Samples with different transitions, RMS surface roughness measured by AFM. E130123B is a complete InAs/AlSb QW sample.
AlSb is chosen as nucleation material as the aluminum adatoms have a reduced surface mobility that will favor the growth of subsequently coalescing
islands. The surface mobility of the Al atoms can be further reduced by
lowering the temperature of the substrate during the growth of the nucleation layer. For the growth of the buffer layers, the temperature was raised
again to the normal temperature of 540 ◦ C to allow for an attenuation of the
threading dislocations introduced at the nucleation layer. This scheme was
tested with a transition or nucleation temperature of 390 ◦ C. The material
transition was controlled by RHEED and 2D growth could be observed after
only a few MLs, even quicker than for the standard nucleation temperature of
540 ◦ C. The surface roughness was dramatically decreased - from an average
RMS surface roughness of 2 nm for the standard nucleation temperature to
only 1.03 nm with this improved temperature profile A as shown in table 4.8.
To fully appreciate the reduction in surface roughness, it is important to
note that sample E130123B is not a special sample for AFM measurements
as all other samples presented in this section, but a complete InAs/AlSb QW
sample.
A different strategy for optimizing the AlGaAs/AlGaSb transition would be
to create growth conditions that favor the creation of 90◦ misfit dislocations
instead of the 60◦ dislocations that cause threading dislocations in the subsequent layers, thus relieving the strain at the interface between the substrate
and the 6.1 Å materials[60, 61, 30]. This interfacial misfit (IMF) technique
involves a careful balancing of the strain energy and adatom migration via
control of the substrate temperature and the Sb-overpressure. The samples
consisted of a GaAs substrate, 300 nm GaAs grown at 560 ◦ C followed by
two different transition schemes as shown in Table 4.9. For scheme B, sample growth was paused at 560 ◦ C under As overpressure. The As valve was
then closed and the surface changed from As-rich to Ga-rich as confirmed
by the transition in RHEED surface reconstruction from (2 × 4) to (4 × 2).
4 ML AlSb were grown as nucleation layer, followed by 500 nm GaSb, a 10-
66
CHAPTER 4. EXPERIMENTAL RESULTS
period 2.5 nm AlSb/2.5 nm GaSb superlattice and a 5 nm GaSb cap. Scheme
C differs by the growth pause being under Sb-flux which changes the surface
reconstructions from (2 × 4) to (2 × 8) and a subsequent lowering in temperature to 510 ◦ C before resuming growth[62]. During growth of the epilayers,
all schemes showed the standard (1 × 3) surface reconstruction.
The surface roughness values in Table 4.8 suggest that the most promising
transition scheme is C. While the exact distribution and direction of misfit
dislocations can only be reliably analyzed using TEM which we have only
access to via a collaboration with the Universität Bremen, we can still evaluate the surface roughness, which is our main goal, using AFM scans of the
sample surface. In addition to the RMS roughness measurements already
presented, AFM scans for the different samples are shown in Figure 4.10.
The further strategy will be to investigate transition schemes A and C using
TEM and to further improve surface roughness. We would like to also note
that we managed to reduce the lateral size of the mounds on the surface
(which is related to the size of the islands formed during nucleation) by a
factor of around 5 with IMF transition C. A full InAs/AlSb QW structure
will have to be grown on top of such a buffer structure to analyze the influence on electron transport as the lateral dimensions of the mounds are only
one order of magnitude larger than the Fermi wavelength which could lead
to enhances scattering.
Transition
Description
A
Cool down to 390 ◦ C before nucleation start, 32 nm AlSb at 540 ◦ C
B
Transition at 560 ◦ C, pause under As flux, grow 4 ML AlSb
C
Pause under Sb flux at 560 ◦ C, transition at 510 ◦ C, 4 ML AlSb
Table 4.9: Overview of the different transitions mentioned in Table 4.8.
4.2. SURFACE ROUGHNESS
67
15#nm#
0#
30#µm#
(a) AFM scan of sample E140128B.
15#nm#
0#
30#µm#
(b) AFM scan of sample E140213C.
Figure 4.10: AFM scans of two samples with different types of IMF transitions.
68
CHAPTER 4. EXPERIMENTAL RESULTS
12.4 12.8 13.2 13.6
14
14 14.4 14.8 15.2 15.6 16
16 16.4 16.8 17.2 17.6 18
18
5 meV
44
5
4.4
4.8
5.2
6.4
d_InAs @nmD
dInAs [nm]
5.6
66
6.8
7.2
7.6
88
8.4
8.8
9.2
9.6
1010
37
10.4
10
d_GaSb @nmD
-6
-4
-20246
dGaSb [nm]
Figure 4.11: Hybridization gaps for different InAs and GaSb layer thicknesses
calculated from band simulations using Nextnano.
4.3
InAs/GaSb/AlSb CQWs
The unusual band setup in InAs/GaSb/AlSb CQWs gives rise a large number
of interesting effects[63, 64, 26, 65]. Recently, the prediction of the Quantum
Spin Hall Effect[5] renewed the interest in this material system that had
been out of the focus of fundamental research for almost a decade. The main
interest of our group was the fabrication of CQW samples of the highest
achievable quality to allow the observation of the QSHE.
The technical growth details and challenges of the CQWs are identical to
those of InAs/AlSb, analyzed in great detail in the previous sections. Specific
to these structures is the relative thickness of the InAs and GaSb layers which
influences the overlap and thus the hybridization of the bands. Using the
Schrödinger-Poisson solver Nextnano, we calculated the hybridization gap
for different relative layer thicknesses, obtaining a qualitative phase diagram
of the possible regimes in an InAs/GaSb/AlSb CQW (Figure 4.11). The
values obtained are in good agreement with the simulations by Liu et al.[5]
and our own experimental results[66].
The InAs/GaSb/AlSb CQW samples measured below were grown on n-doped
200 GaAs substrates insulated from the active region by a 200 nm low temperature GaAs layer grown at 300 ◦ C. The active region consists of the 8 nm
GaSb and 15 nm InAs QW sandwiched between two 50 nm AlSb barriers. All
4.3. INAS/GASB/ALSB CQWS
69
other growth details are identical to the standard growth routine presented in
section 4.1. On both samples, identical 50 µm × 25 µm Hall bars were etched
by conventional photolithography and plasma etching. The devices were then
covered by a 200 nm Si3 N4 layer deposited by plasma enhanced chemical vapor deposition followed by a metallic top gate to tune the electron and hole
densities.
Electronic transport experiments were performed in a pumped bath cryostat
at a temperature of 1.3 K at magnetic fields up to 7 T and in a 3 He/4 He dilution refrigerator at 20 mK at magnetic fields up to 12 T. Sample preparation
and all measurements shown in this section were carried out in collaboration
with the group of Prof. Dr. Ensslin at ETH Zürich.
Clear Shubnikov-de Haas oscillations in longitudinal resistance as shown in
Figure 4.12 allow to extract electron (left) and hole (right) densities and
show the excellent sample quality. Electron mobilities up to 300,000 cm2 /Vs
and hole mobilities up to 10.000 cm2 /Vs could be achieved, depending on
the transport regime (i.e. top gate voltage). A complete fan diagram of the
longitudinal resistance in dependence of magnetic field and top gate voltage
measured at T = 100 mK is shown in Figure 4.13. The resistance resonance
at the charge neutrality point (CNP) where the electron density and the hole
density are equal (n ≈ p) confirms the existence of the hybridization gap.
This resistance plateau is not quantized at the value of h/2e2 as expected for
helical edge channels[4, 67] which is due to the macroscopic size of our sample.
Indeed, the edge channels are only protected against elastic scattering so that
a quantized value of the CNP resistance can only be expected for samples of
a size below the inelastic scattering length. Du et al. estimated this length
to be on the order of 4 µm[68] for wafers of similar quality to ours.
4.3.1
Suppression of bulk conductivity
In all studies on the Quantum Spin Hall Phase in InAs/GaSb/AlSb CQWs,
the principal issue is the residual conductivity from the bulk which is attributed to sample disorder and obscures the visibility of the dissipationless
edge channel transport. If the disorder in the sample cannot be reduced sufficiently to observe pure edge channel transport, an alternative approach would
be to adjust the disorder in the sample to such a degree that the mobility of
the charge carriers in the bulk is so low that they no longer provide scattering channels between the edge states. Schemes consisting of Si doping at the
interface between InAs and GaSb[68] or of p-doping of the Al(Ga)Sb barriers
surrounding the CQWs[69] have been employed. However, these approaches
70
CHAPTER 4. EXPERIMENTAL RESULTS
Figure 4.12: Longitudinal resistance oscillations of a CQW sample with top
gate in the electron (left) and hole (right) transport regime.
Figure 4.13: (a) Longitudinal resistance for different top gate voltages and
magnetic fields of an InAs/GaSb/AlSb CQW. Numbers indicate resistance
minima for electrons (positive) and holes (negative). (b) Longitudinal and
transverse resistance resp. conductivity at B = 11 T (along dashed line of
(a))[66].
AlSb InAs GaSb AlSb
50 nm 15 nm 8 nm 50 nm
E1
H1
4.3. INAS/GASB/ALSB CQWS
(b)
Top gate
Back gate
(a)
71
(c)
Figure 4.14: Magnetotransport data of an InAs/GaSb/AlSb CQW in the
electron regime (at a top gate voltage of 4 V, i.e. an electron density of
2.5 × 1012 cm−2 ). Red: longitudinal resistance, black: transverse resistance.
provide strong scatterers and are thus also prone to strongly influence edge
channel transport. This work studies a further strategy of obtaining an
insulating sample bulk material by creating a smooth disorder potential using gallium source material with an adequate impurity concentration[70] and
thus confirming that the topological insulator (TI) phase can be made visible
by sufficiently reducing the charge carrier mobility in the bulk.
All samples used for this study were using the two different gallium effusion
cells present in our system. The two cells were filled with materials from two
different manufacturers, both nominally of highest purity MBE grade. As
only metallic impurities are measured to indicate the nominal purity of the
material, the quality of the source materials can still vary widely due to nonmetallic impurities (as e.g. by their carbon, nitrogen or oxygen content).
The electron mobility of remotely doped 2D-electron systems is a direct
measure for the quality of the source materials as impurities contained in
these source materials will be incorporated in the samples and thus lead to
additional scattering. The AlGaAs/GaAs double-sided doped QW structures
used for quality assessment are known to show mobilities over 35×106 cm2 /Vs
if grown in a MBE system optimized for the growth of ultra high mobility
AlGaAs/GaAs samples[73, 74]. In our system also used for the growth of
antimony based samples, employing such a structure, we could reproducibly
achieve low-temperature (T ≈ 1 K) mobilities of 14×106 cm2 /Vs at a density
of 3.1 × 1011 cm−2 for one charge of gallium source material, which we will
subsequently refer to as high mobility (HM) gallium. In contrast, if using
the second gallium source material (referred to below as low mobility (LM)
72
CHAPTER 4. EXPERIMENTAL RESULTS
excitons bound
LM Ga PL intensity
PL intensity (counts)
to neutral donors
810
HM Ga PL intensity
T = 4.2 K
excitons bound to
neutral acceptor-like
point defects
free exciton
820
830
Wavelength (nm)
Figure 4.15: Near-band-edge PL spectra of GaAs structures grown using both
gallium sources. Blue: low mobility gallium, red: high mobility gallium. The
peaks are labeled according to references [71, 72].
gallium), we did not reach mobilities higher than 1.5×106 cm2 /Vs at a density
of 2.7 × 1011 cm−2 . This demonstrates that the LM gallium is of inferior
quality in terms of impurity concentrations compared to the HM gallium but
still allows to grow samples with reasonably high mobilities. This finding is
confirmed by comparing the PL spectra (Figure 4.15, taken at 4.2 K using a
HeNe laser as an excitation source at a wavelength of 633 nm), where the off
band gap peaks linked to impurity assisted absorption are higher by a factor
of 8 for the LM gallium compared to the HM gallium. We want to point out
that we were able to grow AlGaAs/GaAs samples showing electron mobilities
in excess of 107 cm2 /Vs after the growth of antimony based samples. This
proves that the presence of Sb in the system does not influence the quality
of high-purity arsenide based structures at this level.
Figure 4.14 shows magneto-transport data of the device fabricated using HM
gallium in the electron regime (at a top gate voltage of +4 V, corresponding
to a density of 2.5 × 1012 cm−2 ). The clear hall plateaus and Shubnikov-de
Haas oscillations together with a high electron mobility of 300,000 cm2 /Vs
at a density of 8 × 1011 cm−2 demonstrate the high CQW quality. Samples
grown using LM gallium only show a mobility of 8,000 cm2 /Vs at a density of
8.1 × 1011 cm−2 , i.e. lower by more than an order of magnitude, similar to the
AlGaAs/GaAs reference samples. The sharp drop in electron mobility in the
electron transport regime exclusively due to a higher impurity concentration
in the GaSb layer indicates that the electron wave function must extend
4.3. INAS/GASB/ALSB CQWS
73
considerably into the GaSb part of the CQW. For comparison, using LM Ga,
electron mobilities as high as 140,000 cm2 /Vs at densities of 9.7 × 1011 cm−2
could be achieved in conventional InAs/AlSb QWs where the electron wave
function does not reside in a Ga-containing layer.
We now focus on the effect of the gallium purity on the transport properties of InAs/GaSb CQWs at the charge neutrality point (CNP) where the
electron and hole densities are equal and the hybridization gap opens (see
Figure 4.16). The sample grown using HM gallium shows a resistance two
orders of magnitude higher than the lowest resistance in the high electron
density regime at positive top gate voltages. However, the resistivity never
rises above 2 kΩ even at the CNP. The sample fabricated using the LM gallium shows a far higher increase in resistance, over more than 4 orders of
magnitude to 1.5 MΩ at the CNP, indicating a truly insulating bulk. In
agreement with our previous findings, we observe a qualitatively different
transport behavior for the two samples when a perpendicular magnetic field
is applied. As shown in the inset of Figure 4.16 where we display the longitudinal resistance at the CNP RCNP of both samples for different magnetic
fields, for the HM gallium sample, RCNP increases by a factor of 30 when
the magnetic field strength is swept from 0 to 7 T whereas the LM gallium
sample shows hardly any dependence of RCNP on the magnetic field. This
can be understood as a result of the strong localization at impurities in the
LM gallium samples which is much stronger than the localization effect of
the B-field. In contrast to other schemes tested so far, our method should
not significantly alter the edge channel transport properties of the CQW.
Another way to implement this strategy would be the controlled addition of
isoelectric impurities, e.g. a very small fraction on the order of 1% of Al to
the GaSb CQW layer.
74
CHAPTER 4. EXPERIMENTAL RESULTS
(k
1000
CNP
B = 0 T
T = 1.3 K
R
1M
)
10M
100k
10
1
)
(
xx
100
0
2
4
6
B (T)
10k
1k
100
10
-12
-6
0
V
6
12
(V)
TG
Figure 4.16: Longitudinal resistance of HM Ga (red) and LM Ga (blue)
InAs/GaSb/AlSb CQW samples in function of top gate voltage at zero perpendicular magnetic field. The dashed lines indicate the position of the CNP
at which RCNP was determined. Inset: RCNP for different B-fields from 0 to
7 T.
4.4. INSB/ALINSB QWS
4.4
75
InSb/AlInSb QWs
InSb, with a lattice constant of 6.49 Å, has the smallest band gap (Eg =
0.17 eV), the smallest effective electron mass (m? = 0.014me ) and highest
effective g-factor (g ? = −51) of all III/V-semiconductors. This would make
it a very interesting material for infrared detectors, high electron mobility
transistors (HEMTs) or spintronics. The very high g ? also makes the existence of Majorana fermions in combination with superconducting electrons
probable if the 2DEG can be brought close enough to the surface. However,
a number of important challenges make the fabrication of InSb-based heterostructures a difficult task and has so far prohibited the industrial use of
this type of structures except for detectors.
The main difficulty is the lack of a lattice-matched III/V barrier material.
The first InSb heterostructures were InSb/CdTe structures, CdTe having
a lattice constant of 6.48 Å and a bandgap of 1.44 eV[75, 76]. The interface between the III/V and the II/VI materials is very difficult to optimize
so that the mobilities at 4 K were limited to less than 25,000 cm2 /Vs[76].
A different way of solving this problem is the use of Alx In1−x Sb as barrier material, following the work of the Santos group from the University of
Oklahoma[77]. Even though there is a trade-off between large barrier height
and low lattice-mismatch, the interfaces of the heterostructures were dramatically enhanced. Alx In1−x Sb barriers with x between 9 − 20% and Si
δ-doping led to electron mobilities of almost 300,000 cm2 /Vs, which could be
improved to values around 400,000 cm2 /Vs with the use of Te-based doping
schemes by the QinetiQ group[78].
The samples fabricated for this project were grown on semi-insulating GaAs
substrates which have a lattice mismatch of 14.6% to InSb, as, in analogy to the 6.1 Å materials, no semi-insulating InSb substrates are available.
The lattice mismatch is accommodated in two steps: first, 1 µm AlSb is
grown onto the GaAs substrate at 540 ◦ C, followed by 1 µm of Alx In1−x Sb at
approximately 400 ◦ C. The transition is relatively smooth, two-dimensional
Alx In1−x Sb growth can be observed in the RHEED pattern after around
100 MLs. The growth temperature of 400 ◦ C is the lower temperature limit
of our pyrometer so that the temperature reading is not very reliable. A
solution to this problem would be the temperature calibration by observing
the transition between the (2 × 4) and c(4 × 4) surface reconstructions which
takes place at 390 ◦ C for a III/V ratio of 1.3[79]. The first Alx In1−x Sb layer is
followed by a strained-layer superlattice consisting of 10 periods of InSb and
Alx In1−x Sb layers with thicknesses of 2.5 nm each and a second Alx In1−x Sb
76
CHAPTER 4. EXPERIMENTAL RESULTS
layer of 2 µm. As the intrinsic background doping in InSb layers is p-type,
InSb wells have to be doped to obtain n-type conduction. For the growth of
the Si δ-doping layers, the temperature has to be lowered by around 30 ◦ C
to avoid migration of the Si atoms.
The sample shown in Figure 4.17(a) has an Al content of x = 0.1 and two Silayers near the well to provide electrons to the QW and one Si-layer near the
surface to compensate the surface states. The thickness of the fully strained
InSb QW is 20 nm, well below the critical thickness[33]. They were deposited
by opening the Si and Sb shutters 50 s at currents of 7.5 A which corresponds
to a doping density of 6.5 × 1011 cm−2 for the layers around the QW and 50 s
at 9 A for the doping layer below the surface. The spacers had a thickness
of 50 nm on both sides of the QW and 10 nm below the surface. The sample
was capped with a 10 nm InSb layer.
Magnetotransport data for this sample are shown Figure 4.17(b) and a parallel conductance channel is clearly visible even though the electron mobility
is 130,000 cm2 /Vs at an electron density of 2.5 × 1011 cm−2 . Subsequent efforts to eliminate this parallel conductance by reducing the doping densities
or the spacer thickness were unsuccessful because of the low reproducibility
rate of the samples, indicating that the growth parameters described above
were not optimal. The first measure to take for the optimization process
will have to be the reduction of complexity by only using a single doping
layer. The other problem is temperature control as we are on the limit of
our temperature measurement devices. Solutions include the use of a longer
wavelength pyrometer and better control over the surface reconstructions to
improve temperature calibration.
The problem with the InSb/Alx In1−x Sb QW structures do not only originate
from the growth kinetics of InSb but also from the large lattice mismatch to
the substrate material. In analogy to studies on InSb bulk samples[80], we
tried a scheme using InAs quantum dots (QDs) self-assembled on the GaAs
substrate that serve as nuclei for subsequent InSb or Alx In1−x Sb growth.
After a 100 nm GaAs buffer grown at 580 ◦ C, the substrate temperature
is lowered to 480 ◦ C and 3 monolayers of InAs are deposited which, leading Stranski-Krastanov growth, followed by an annealing for 1 min. The
RHEED pattern changed from (2 × 4) to spots due to the QDs when opening the In cell, as expected. The substrate is cooled down to 400 ◦ C and
the rest of the sample is grown as described above. Due to its efficient nucleation mechanism, this technique is expected to reduce surface roughness
and material consumption as thinner buffer layers can be used. First results
were promising: 2D growth was reached after only around 40 ML as observed
4.4. INSB/ALINSB QWS
77
(a) Schematic layer sequence, the dashed
lines correspond to the Si doping layers.
4,000
10
2,000
5
⇢xy [k⌦]
⇢xx [⌦]
3,000
1,000
0
0
0
1
2
3
4
B-field [T]
5
6
(b) Magnetotransport measurements at 4K: clear
signs for a high-mobility 2DEG and a strong parallel conduction channel.
Figure 4.17: Structure and magnetotransport measurements of an
InSb/Al0.1 In0.9 Sb QW with a two-step accommodation of the lattice mismatch to the GaAs substrate.
78
CHAPTER 4. EXPERIMENTAL RESULTS
by RHEED and the RMS surface roughness indeed decreased from 28 nm to
9.5 nm but the electronic properties were far from improved with mobilities
never exceeding 10,000 cm2 /Vs. This is confirmed by the TEM images shown
in Figure 4.18 which show a large density of threading dislocations extending into the QW. The two-step lattice mismatch accommodation however
shows a QW with a much lower dislocation density. We will have to further
investigate the QD transition and adapt the QD density an size on the surface as well as the buffer layer thicknesses to be able to exploit the possible
advantages of this technique.
4.4. INSB/ALINSB QWS
(a) Two-step transition.
79
(b) InAs-QD transition.
Figure 4.18: TEM images for the two types of lattice mismatch accommodation. The QW is the fairer line annotated with QW. We see that the
dislocations in the QD sample (b) extend to the sample surface and cross the
QW whereas the QW in the two-step sample (a) is almost free of dislocations.
80
CHAPTER 4. EXPERIMENTAL RESULTS
Type
# of steps
QW channel
Comment
Reference
A
15
In0.75 Ga0.25 As/InAs
-
[86]
B
10
In0.75 Ga0.25 As/InAs
-
[83]
C
10
In0.75 Ga0.25 As
undoped
[85]
Table 4.10: Different graded Inx Al1−x As buffer sample types.
4.5
InAs/InAlAs QWs
There has been an ongoing effort to realize InAs or Inx Ga1−x As quantum
wells on GaAs substrates without the need for an antimony cell in the MBE
system[81, 82, 83, 84]. In these structures, the large lattice mismatch between
the GaAs substrate and the InAs channel is accommodated by a special
buffer structure in which the In-content of an Inx Al1−x As layer is gradually
increased from 10% to 75% and the InAs channel, if present, is subsequently
inserted between two In0.75 Ga0.25 As layers. While most schemes shown in
litterature rely on remote doping as source of the electrons in the QW[81], it
is also possible to fabricate undoped samples, only taking advantage of the
unique band alignment of the materials[85]. For our needs, these structures
can be very useful to assess source material quality as it is possible to separate
the influence of In and Sb and to compare the mobilities of similar structures
grown in different MBE systems.
We grew three different categories of samples, the structures and corresponding electron densities and mobilities are presented in Table 4.10 (missing).
In Figure 4.19, we show magnetotransport measurements for samples A and
B. Sample A shows clear beating pattern which can be related to the population of two electronic subbands. A Fourier transform of the longitudinal
resistance in function of the inverse magnetic field 1/B shows the corresponding electron densities of the two subbands: n1 = 3.5 × 1011 cm−2 and n2 =
4.8 × 1011 cm−2 . Intersubband scattering limits the mobilities of these samples so it is worth noting that this sample shows a very high electron mobility
of µ = 250,000 cm2 /Vs. We can thus certainly claim that our growth procedures and buffer structures can compete with the state-of-the-art samples by
Richter et al.[83] or Capotondi et al.[87]. Sample B was grown after the airleak and thus has a lower mobility of only µ = 100,000 cm2 /Vs at a density
of 1.2 × 1012 cm−2 , which is similar to the InAs/AlSb quantum wells grown at
that time. Nevertheless, the structural properties are of sufficient quality to
4.6. GASB/ALSB QWS
81
1,000
8
200
6
150
200
0
0
1
2
3
4
B-field [T]
5
100
2
50
0
0
1
0
0
6
⇢xy [k⌦]
4
400
⇢xx [⌦]
⇢xx [⌦]
600
⇢xy [k⌦]
2
800
1
2
3
B-field [T]
4
5
(a) Magnetotransport data of an over- (b) Magnetotransport data of a InAs
doped InAs QW in InAlAs/InGaAs QW in InAlAs/InGaAs barriers on a
barriers on a graded buffer (Sample graded buffer (Sample B).
A).
Figure 4.19
use the magnetotransport data of that sample for illustrative purposes. We
could only obtain useful Shubnikov-de-Haas oscillation allowing to extract
electron densities after illuminating the samples using a 700 nm LED.
We also tried to grow InAs/AlSb on relaxed buffers, albeit without success,
the samples were not measurable at low temperatures.
As a conclusion of this short adventure into relaxed buffer structures, we
can claim that the indium source material of the first growth campaign was
of outstanding purity, a fact which is unfortunately not true for the indium
source material of the second growth campaign after the air-leak. This also
gives a hint on the reason for the sharp dip in mobility of the InAs/AlSb
QWs of later growth campaigns. The skills acquired in the growth of this
type of structures can serve to measure the quality of the current indium
charge or compare it to samples grown in other chambers in our laboratory.
4.6
GaSb/AlSb QWs
To the best of our knowledge, no group has ever successfully measured 2Dmagnetotransport in single GaSb/AlSb quantum wells or heterointerfaces.
The only work known to us that measures any electrical properties of similar
structures is based on Te-doped multiple (30x) AlSb/Al0.4 Ga0.6 Sb quantum
wells of rather poor quality (µ ≈ 90, 000 cm2 /Vs at high electron densities
82
CHAPTER 4. EXPERIMENTAL RESULTS
1 .8
1 .2
E (e V )
A lS b
G a S b
A lS b
0 .6
0 .0
-0 .6
9 5 0
1 0 0 0
1 0 5 0
z (A )
Figure 4.20: Band diagram relative to EF of a GaSb/AlSb QW as calculated
by Nextnano.
of n ≈ 1.5 × 1012 cm−2 [88]). and does not show any magnetotransport data.
This lack of previous experiments motivated us to try to fill this gap.
The band structure of a typical undoped GaSb/Al(Ga)Sb structure calculated using Nextnano is shown in Figure 4.20, it is very similar to band
structures in GaAs/AlGaAs QWs. Undoped structures are p-type as expected from experiments on bulk GaSb or AlSb and n-type doping is made
difficult by the fact that our MBE system does not have a suitable material
for this type of doping in GaSb or AlSb, Si and C both giving rise to p-type
doping. First tries to incorporate 2, 4 or 30 layers of strongly Si-doped InAs
layers similar to the doping strategy that successfully allows to increase the
electron density in InAs/AlSb QWs were unsuccessful, the samples were not
measurable at low temperatures. We changed our strategy and grew Si-doped
structures expected to show p-type conduction for this first series of experiments, a table with some of the samples fabricated is displayed in Table 4.11.
There is no reason to believe that the structural properties and growth issues due to the lattice mismatch to the GaAs substrate material should be
different from the problems encountered in InAs/AlSb QWs but the higher
effective hole mass in GaSb (0.05 me (light holes) and 0.5 me (heavy holes))
compared 0.023 me for electrons in InAs lets us expect lower mobilities if we
succeed to induce 2DHGs in our QWs. All growth parameters used for the
samples studied in this chapter are identical to the growth parameters used
for the growth of the buffers of the InAs/AlSb QWs. The samples consisted
of a 1.1 µm Al0.3 Ga0.7 Sb lower buffer layer followed by a 50 nm GaSb layer
4.6. GASB/ALSB QWS
Sample
Doping
E120905A
bulk upper barrier,
12
E121026B
83
Density [1011 cm−2 ]
Mobility [cm2 /Vs]
5.50
32,000
12.0
2,500
−2
8 × 10 cm
δ-doping,
7 × 1012 cm−2
Table 4.11: GaSb/AlSb QW samples with different doping schemes.
and a 200 nm AlSb upper barrier, capped by a 5 nm GaSb layer. The growth
temperature for all Sb-containing layers was 540 ◦ C and lowered to 450 ◦ C
for the growth of doped layers to prevent segregation of the Si atoms. Our
samples are effectively single heterointerfaces.
It is not clear whether hand-soldered In contact as used for all other samples
in this thesis are also suitable for hole gases in GaSb. However, as hole
transport can be measured in InAs/GaSb/AlSb CQWs and GaSb and AlSb
bulk samples using In contacts, it is reasonable to expect working In contacts
in GaSb/AlSb samples. The investigation of different contacting schemes
should however be part of the further work on GaSb/AlSb structures.
The different doping schemes that were used consisted of (A) bulk doping
of the entire upper barrier starting 100 Å above the GaSb/AlSb interface, at
different Si cell currents and (B) delta doping at different Si cell currents and
different spacers. The samples using a delta doping scheme showed very high
p-type densities around 1 - 3×1012 cm−2 and low mobilities of under 3000
cm2 /Vs. The bulk-doped samples showed a more interesting behavior with
moderate densities of 5 to 9×1011 cm−2 and mobilities of up to 31000 cm2 /Vs.
These mobilities are higher than the mobilities of bulk p-doped GaSb or AlSb
which hints at the formation of a two-dimensional hole gas (2DHG). However,
we cannot clearly answer this question using magnetotransport data (see
Figure 4.21) as there is some visible structure in the longitudinal resistance
trace but no clear oscillations.
This small side project will have to be continued and different structures
with different barrier heights, doping schemes and contacts will have to be
investigated. In the meantime, a collaboration with the group of G. Salis
at IBM Research has been started for photoluminescence measurements on
GaSb/AlSb QWs.
84
CHAPTER 4. EXPERIMENTAL RESULTS
1,550
⇢xx [⌦]
1,450
2
1,400
0
0
2
4
B-field [T]
⇢xy [k⌦]
4
1,500
6
Figure 4.21: Magnetotransport measurement of a bulk doped GaSb/AlSb
single interface.
Chapter 5
Conclusions & Outlook
We successfully set up a MBE laboratory and managed to grow high quality
Sb-based III/V semiconductor heterostructures.
By analyzing and optimizing a large number of growth parameters and
buffer schemes, we achieved electron mobilities in excess of 560,000 cm2 /Vs
in InAs/AlSb QWs which are second only to samples grown in the no longer
operational University of California, Santa Barbara group. We also successfully reduced the surface roughness of the InAs/AlSb QWs by more than a
factor of two by the use of new transition temperature and flux profiles.
The main physical interest was the fabrication of InAs/GaSb/AlSb CQWs
which have a unique broken-gap alignment and that were predicted to show
a topologically non-trivial phase manifested by helical edge channels. CQW
samples of high quality were grown and investigated in collaboration with
the group of Prof. Dr. Klaus Ensslin. Although the helical edge channels
could not be probed directly due to a large conductivity in the sample bulk,
experiments by the Ensslin group found a large non-local resistance at high
perpendicular magnetic fields that can be interpreted in terms of a model of
counter propagating helical Quantum Hall edge states. By using Ga source
material with a moderate neutral impurity concentration, we could lower the
bulk conductivity at the CNP by more than 3 orders of magnitude without
significally altering the edge channel transport properties of the sample. This
might be a route to enhance the visibility of the helical edge channels.
We also tested the growth of different other Sb-based heterostructures. InAs
channels in Inx Al1−x As graded buffers of high structural quality successfully
served as indicators for the purity of the In source material. GaSb/AlSb
and InSb/Alx In1−x Sb QWs will have to be further optimized before they can
85
86
CHAPTER 5. CONCLUSIONS & OUTLOOK
compete with the GaAs/AlGaAs material system regarding sample quality. This would allow a large number of future experiments. However,
first InSb/Alx In1−x Sb QWs with mobilities in excess of 130,000 cm2 /Vs were
grown, albeit with only limited reproducibility.
Further work on InAs QWs will include optimization of the surface roughness
to allow for the fabrication of nanometer-sized structures. If the physical and
chemical properties of the GaSb surface and the InAs channel are suitable,
the flat surface could even make the fabrication of mesoscopic structures
using local anodic oxidation possible.
The irrevocable identification of the helical edge states in InAs/GaSb/AlSb
CQWs and the measurement of exact quantization of the resistance at the
CNP are still missing to confirm the existence of the QSHE in these structures. We can contribute to this search by lowering the bulk conductance
without compromising the carrier mobility in the samples and by making the
patterning of nanometer-sized structures possible by flat surfaces.
InSb/Alx In1−x Sb heterostructures are very promising materials for a large
range of optical an electronic devices but the fabrication of such structures
still poses a large number of problems. In more fundamental research, the
prediction of Majorana fermions in such structures in combination with superconducting electrodes is a fascinating outlook. Our group will focus on
solving the issues in temperature control and doping schemes that so far limit
the quality and reproducibility of such samples. Further steps would include
the reduction of surface roughness to allow for smaller lateral structure dimensions.
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List of Symbols and Acronyms
Symbol
Definition
B-field
magnetic field
EF
Fermi energy
Eg
hybridization gap
g
?
effective g-factor
λF
Fermi wavelength
m?
effective electron mass
µ
carrier mobility
n
electron density
p
hole density
ρxx
longitudinal resistivity
ρxy
transversal resistivity
τ
scattering time
93
94
Acronym
Definition
2DEG
two-dimensional electron gas
2DES
two-dimensional electron system
2DHG
two-dimensional hole gas
AFM
atomic force microscopy
ATR
attenuated total reflectance
BEP
beam equivalent pressure
CNP
charge neutrality point
CQW
composite quantum well
DOS
density of states
FTIR
Fourier transform infrared spectroscopy
HEMT
high electron mobility transistor
HM
high mobility
IMF
interfacial misfit growth
LL
Landau level
LM
low mobility
MBE
molecular beam expitaxy
ML
monolayer
MQW
multiple quantum wells
PBN
pyrolytic boron nitride
PL
photoluminescence
QD
quantum dot
QSH
Quantum Spin Hall
QW
quantum well
RHEED
reflection high-energy electron diffraction
RMS
root mean square
SdH
Shubnikov-de Haas
SQW
single quantum well
STM
scanning tunneling microscopy
TEM
transmission electron microscopy
TI
topological insulator
List of Figures
2.1
Landau levels in dependence of B-field, from [11]. Note the
stepwise change of the Fermi energy EF as the Landau levels
are depopulated. . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Longitudinal resistivity of an InAs/AlSb QW showing Shubnikovde Haas oscillations in function of a perpendicular magnetic
field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Scattering-broadened Landau levels from [11]. States close to
the center of the LL are extended, states in the tails of the LL
are localized. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Transverse resistivity of an InAs/AlSb QW showing Quantum
Hall plateaus in function of a perpendicular magnetic field. . . 7
2.5 Hall bar with edge channels. States in the center are localized
for integer filling factors and cannot contribute to electronic
transport, thus completely decoupling opposite edge channels.
A four-terminal measurement setup is also shown in the figure.
From [11]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.6 Relative band lineup and band gaps of the InA/GaSb/AlSb
material system, from [10]. . . . . . . . . . . . . . . . . . . . . 9
2.7 Conduction band alignment for an InAs/AlSb QW sample
from [13]. The Fermi energy is pinned at the surface, ES =
850 meV below the AlSb conduction band edge. . . . . . . . . 10
2.8 Conduction band alignment and energy levels of a Si-doped
InAs/AlSb QW structure with an InAlAs capping layer, from
[18]. Ψ0 and Ψ1 are the electron wave functions of the first
two subbands. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.9 Inverted type-II structure with hybridization gap Eg , from [5]. 12
2.10 Band structure of an inverted type-II structure under different
external electrical fields, from [25]. . . . . . . . . . . . . . . . . 13
95
96
LIST OF FIGURES
2.11 Dispersion relation for InAs/GaSb/AlSb CQWs with different
relative layer thicknesses. There are no band inversion and no
edge states for the situation on the left, we have a normal
insulator. The QSH sample on the right shows band inversion
and we see the occurrence of edge states in the center of the
hybridization gap [5]. . . . . . . . . . . . . . . . . . . . . . .
2.12 Growth modes for different epitaxial layer thicknesses Θ: (a)
Frank-van der Merve or layer-by-layer growth. (b) Step-flow
growth. (c) Vollmer-Weber or island growth. (d) StranskyKrastanow growth. (e) Columnar growth. From [28]. . . . .
2.13 Schematic illustration of microtwins in an InSb lattice (left)
and a TEM image of an InSb/Al0.09 In0.91 Sb QW grown on a
GaAs substrate (right), from [29]. . . . . . . . . . . . . . . .
2.14 Misfit dislocation at the interface between the substrate S and
the epitaxial layer O, with aO < aS , taken from [28]. . . . . .
2.15 (a) Strained or pseudomorphic epilayer, (b) Relaxed epilayer of
a lattice mismatched heterostructure (c) strained and relaxed
unit cells.[28]. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 Schematic illustration of the RHEED setup with a visualization of the Ewald sphere and the reciprocal lattice rods[34]. .
2.17 Typical RHEED-pattern with direct spot (top) and specular
image (bottom). The Laue circle and Kikuchi lines are well
developed. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.18 RHEED oscillations. . . . . . . . . . . . . . . . . . . . . . .
2.19 Images on the RHEED screen with the electron beam pointed
along the [011] (2 × ) and [011̄] (4 × ) directions on an Asterminated GaAs surface at 600 ◦ C. . . . . . . . . . . . . . .
2.20 Position of the thermocouple relative to the substrate heater
(coils) on the substrate manipulator. . . . . . . . . . . . . .
2.21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.22 Band edge thermometer setup (a) and spectra of a 500 µm
GaAs wafer (b), from [39]. . . . . . . . . . . . . . . . . . . .
3.1
3.2
3.3
. 14
. 15
. 17
. 18
. 20
. 21
. 21
. 23
. 24
. 25
. 27
. 28
Overview of the MBE system. . . . . . . . . . . . . . . . . . . 31
A GaAs wafer being glued to a Ta block covered in Ga (a) and
MBE trolley with 5 sample positions outside the load lock (b). 32
Quadrupole mass analyzer: (1) and (2) inlet and exit slits
of analyzer, (3) trajectory of ions, (4) high-frequency voltage
generator, from [42]. . . . . . . . . . . . . . . . . . . . . . . . 33
LIST OF FIGURES
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
4.1
4.2
4.3
4.4
4.5
4.6
97
Two different mass spectra recorded in the growth chamber
of our MBE setup, peaks are labeled with the name of the
detected molecule. (a) After baking out the chamber at 200 ◦ C
and subsequent long standby at room temperature. The only
visible peaks are hydrogen H+
2 and the fraction series of water
at Mass/Charge = 16, 17, 18 (b) Immediately after bake-out
of an effusion cell (In4). Prominent peaks are N+
2 from the
PBN crucibles, the As-series from the arsenic deposited on
the chamber walls and He+ liberated by the heat radiation
into the cryopump. . . . . . . . . . . . . . . . . . . . . . . . . 34
Knudsen-type effusion cells with conical (a) and “sumo”-type
(b) crucibles. Drawings from Veeco. . . . . . . . . . . . . . . . 35
Valved cracker cells used in our setup. Drawings from Veeco. . 36
Custom made extension of the valve lip supposed to prevent
blocking of the cell opening. The extension fits completely
into the cell port, but can also potentially be operated outside
of the cell port. . . . . . . . . . . . . . . . . . . . . . . . . . . 37
(a) Contact arrangement and (b) geometry factor for the calculation of resistivities after van-der-Pauw. Taken from [11]. . 40
A van-der-Pauw sample with hand-soldered indium contacts,
connected to the chip carrier using gold wires. . . . . . . . . . 41
Illustration of the basic mechanisms of photoluminescence. . . 42
Schematic diagram a FTIR setup. . . . . . . . . . . . . . . . . 43
Details on ATR measurements. . . . . . . . . . . . . . . . . . 44
Schematic setup of an atomic force microscope in contact mode[47]. 45
Schematic of a transmission electron microscope, from [48]. . . 46
Typical layer sequence for an InAs/AlSb QW sample . . . .
The five buffer layer schemes tested in this thesis. SL denotes
a 10 period AlSb/GaSb superlattice of 2.5 nm layer thickness
for each material. . . . . . . . . . . . . . . . . . . . . . . . .
Electron densities in the InAs channel in function of the upper
barrier thickness for the samples listed in Table 4.4. . . . . .
Three identical samples only differing by the aluminum concentration in the barriers. The density is a function of the
lower barrier height. . . . . . . . . . . . . . . . . . . . . . .
To avoid the negative effect of the AlAs interface bonds, we
grow InSb interface bonds using the shutter sequence proposed
by Tuttle et al.[54] . . . . . . . . . . . . . . . . . . . . . . .
Calculated Sb dimer/tetramer flux versus the temperature of
the cracking zone, from [57]. . . . . . . . . . . . . . . . . . .
. 48
. 49
. 52
. 53
. 56
. 58
98
LIST OF FIGURES
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
FTIR measurements in SQW and MQW samples. . . . . . . . 61
Intersubband transitions in SQW samples of high (red) and
moderate (black) moblities. . . . . . . . . . . . . . . . . . . . 62
3D AFM view of a standard InAs/AlSb QW sample. . . . . . 63
AFM scans of two samples with different types of IMF transitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Hybridization gaps for different InAs and GaSb layer thicknesses calculated from band simulations using Nextnano. . . . 68
Longitudinal resistance oscillations of a CQW sample with top
gate in the electron (left) and hole (right) transport regime. . 70
(a) Longitudinal resistance for different top gate voltages and
magnetic fields of an InAs/GaSb/AlSb CQW. Numbers indicate resistance minima for electrons (positive) and holes (negative). (b) Longitudinal and transverse resistance resp. conductivity at B = 11 T (along dashed line of (a))[66]. . . . . . . 70
Magnetotransport data of an InAs/GaSb/AlSb CQW in the
electron regime (at a top gate voltage of 4 V, i.e. an electron
density of 2.5 × 1012 cm−2 ). Red: longitudinal resistance,
black: transverse resistance. . . . . . . . . . . . . . . . . . . . 71
Near-band-edge PL spectra of GaAs structures grown using
both gallium sources. Blue: low mobility gallium, red: high
mobility gallium. The peaks are labeled according to references [71, 72]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Longitudinal resistance of HM Ga (red) and LM Ga (blue)
InAs/GaSb/AlSb CQW samples in function of top gate voltage at zero perpendicular magnetic field. The dashed lines
indicate the position of the CNP at which RCNP was determined. Inset: RCNP for different B-fields from 0 to 7 T. . . . . 74
Structure and magnetotransport measurements of an InSb/Al0.1 In0.9 Sb
QW with a two-step accommodation of the lattice mismatch
to the GaAs substrate. . . . . . . . . . . . . . . . . . . . . . . 77
TEM images for the two types of lattice mismatch accommodation. The QW is the fairer line annotated with QW. We see
that the dislocations in the QD sample (b) extend to the sample surface and cross the QW whereas the QW in the two-step
sample (a) is almost free of dislocations. . . . . . . . . . . . . 79
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Band diagram relative to EF of a GaSb/AlSb QW as calculated by Nextnano. . . . . . . . . . . . . . . . . . . . . . . . . 82
Magnetotransport measurement of a bulk doped GaSb/AlSb
single interface. . . . . . . . . . . . . . . . . . . . . . . . . . . 84
List of Tables
3.1
Detectors used for FTIR measurements. . . . . . . . . . . . . 44
4.1
4.2
4.3
4.4
. 50
. 51
. 51
Samples with different buffer schemes. . . . . . . . . . . . .
Samples with different channel thicknesses. . . . . . . . . . .
Samples with different capping layer materials. . . . . . . . .
Samples with different upper barrier thicknesses. The mobility
of the last sample cannot be compared with the other samples
as the source material was contaminated at that moment. The
densities of samples with 200 Å-barriers using that source material were within 10% of the density of sample E111213B. .
4.5 Samples grown using different Sb cracker temperatures. . . .
4.6 Samples measured using FTIR spectroscopy. . . . . . . . . .
4.7 RMS surface roughness measured by AFM for samples with
different III/V ratios. . . . . . . . . . . . . . . . . . . . . . .
4.8 Samples with different transitions, RMS surface roughness
measured by AFM. E130123B is a complete InAs/AlSb QW
sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9 Overview of the different transitions mentioned in Table 4.8.
4.10 Different graded Inx Al1−x As buffer sample types. . . . . . .
4.11 GaSb/AlSb QW samples with different doping schemes. . . .
99
. 54
. 58
. 60
. 64
.
.
.
.
65
66
80
83
100
LIST OF TABLES
Acknowledgements
First of all, I want to thank my supervisor Prof. Dr. Werner Wegscheider
for all his support and patience during my time in his group. His enthusiasm
for the subject and the technical part of the setup were of great motivation
to me and I am very grateful for everything I could learn in the past almost
five years. The setup of our new MBE facilities was only possible because of
his experience and help.
Many thanks to Prof. Dr. Klaus Ensslin who did not only take his time to
serve as a co-examiner in the exam committee and to carefully read my thesis
but also was at the origin of the very fruitful collaboration which led to many
of the results shown in this work. Fabrizio Nichele, Dr. Atin Pal and Patrick
Pietsch from his research group were great to work with, I particularly want
to thank for the sample processing routines they developed, the interesting
discussions we had and their valuable feedback.
I am greatly indebted to Christian Reichl, Sigi Heider and Dr. Stefan Fält
for their help setting up the technical facilities in our laboratories and making it fun to work in the MBE lab. It was a great time! Many thanks to
Jessica Gmür for her valuable support for the daily routines in the MBE and
magnetotransport laboratories.
I further want to thank Prof. Dr. Keita Ohani who introduced me to the
secrets of the MBE growth InAs/AlSb structures and Dr. Elisabeth MüllerGubler for the TEM micrographs.
Many thanks to Thomas Tschirky who will take over this project and contributed the FTIR results from his master’s thesis and Nextnano simulations
to this work. It was very pleasant to work with him.
Thank you Wolf, Sebastian, Stefan R., Thomas F., Marcel, Adrian, Lars,
Wolfgang and everyone else in our group who made my PhD a special time.
101
102
ACKNOWLEDGEMENTS
Good luck to Thomas T. and Christian L. with the continuation of the project
and may they take good care of the E-chamber!
Financial support from the Swiss National Science Foundation and the National Competence Centre in Research - Quantum Science and Information
Technology was highly appreciated.
Collaborations
InAs/AlSb QWs
• Ultrastrong light-matter coupling between superconducting complementary THz metasurfaces and Landau levels in semiconductors, Prof.
Dr. J. Faist, ETH Zürich.
• Spin galvanic effects in InAs QWs, Prof. Dr. S. Ganychev, Universität
Regensburg
• Spintronics, Prof. Dr. D. Weiss, Universität Regensburg
• TEM investigation of interfaces in InAs/AlSb QW structures, Prof. Dr.
A. Rosenauer, Universität Bremen
InAs/GaSb/AlSb CQWs
• Superconductor/topological insulator hybrid structures, Prof. Dr. L.
Kouwenhoven, TU Delft
• InAs/GaSb superlattices for thermoelectronics, Prof. Dr. M. Grayson,
Northwestern University
GaSb/AlSb QWs
• Dr. G. Salis, IBM Research Zürich
InSb/AlInSb QWs
• TEM investigation of interfaces in InSb/AlInSb QW structures, Prof.
Dr. A. Rosenauer, Universität Bremen
103
104
COLLABORATIONS
Curriculum vitae
Personal data
Name
Christophe Charpentier
Date of birth 6 March 1985
Place of birth Luxembourg-City
Citizenship
Luxembourg
Education
2009
2007
2004
1997
-
2014
2009
2007
2004
Doctoral student, Laboratory of Solid State Physics (Dr. Sc. ETH)
Master of Science ETH in Physics (MSc ETH)
Bachelor of Science ETH in Physics (BSc ETH)
Diplôme de fin d’études secondaires, section B (mathematics)
105