JOONAS HILSKA
NOVEL METHOD FOR ARSENIC FLUX DETERMINATION IN MOLECULAR BEAM EPITAXY
Bachelor of Science Thesis
Examiner: Tomi Leinonen
i
ABSTRACT
TAMPERE UNIVERSITY OF TECHNOLOGY
Bachelor’s Degree
HILSKA, JOONAS: Novel method for arsenic flux determination in molecular
beam epitaxy
Bachelor of Science Thesis, 35 pages
November 2015
Major: Teknillinen Fysiikka
Examiner: Tomi Leinonen
Keywords: molecular beam epitaxy, gallium arsenide, arsenic flux
In this thesis, a novel method for the determination of arsenic flux in molecular beam
epitaxy is presented. The method is based on the growth and ex-situ characterization of
a GaAs layer grown at a low temperature and under arsenic limited conditions. Growth
under these conditions results in excess gallium accumulation on the surface, which is
proportional to the supplied arsenic flux during growth. Using ab initio calculations, a
dependency between the arsenic flux and the amount of accumulated surface gallium is
derived, from which the arsenic flux is determined. The amount of accumulated gallium
is determined from scanning electron microscope images, using a geometric model
based on atomic force microscope measurements. A proof of concept is offered by
comparing results with the already established high resolution X-ray diffraction technique. Additionally, an example calculation of the spatial arsenic flux distribution is
presented.
ii
CONTENTS
1.
INTRODUCTION ................................................................................................ 1
1.1 Molecular beam epitaxy .............................................................................. 1
1.2 The aim of this work ................................................................................... 1
2. BACKGROUND .................................................................................................. 2
2.1 Basic description of MBE ........................................................................... 2
2.2 Gallium arsenide ......................................................................................... 2
2.3 MBE growth of GaAs ................................................................................. 3
2.4 Low temperature and arsenic limited growth of GaAs ................................. 3
3. EXPERIMENTAL SETUP AND CHARACTERIZATION METHODS............... 6
3.1 MBE-system ............................................................................................... 6
3.2 MBE operation and sample growth ............................................................. 8
3.2.1
Flux measurement ......................................................................... 8
3.2.2
Sample growth ............................................................................ 10
3.3 Characterization methods .......................................................................... 11
3.3.1
Scanning electron microscopy ..................................................... 11
3.3.2
High resolution X-ray diffraction ................................................ 11
3.3.3
Atomic force microscopy ............................................................ 13
4. CALCULATION OF ARSENIC FLUX FROM ARSENIC LIMITED AND LOW
TEMPERATURE GROWN GALLIUM ARSENIDE ................................................. 15
5. RESULTS ........................................................................................................... 18
5.1 Gallium droplet geometry ......................................................................... 18
5.2 Proof of concept ....................................................................................... 21
5.3 Spatial arsenic flux distribution ................................................................. 24
5.3.1
Applying the results .................................................................... 28
6. DISCUSSION AND CONCLUSION .................................................................. 29
7. REFERENCES ................................................................................................... 30
iii
LIST OF ABBREVIATIONS AND SYMBOLS
AFM
AlAs
BAG
BEP
BSE
FEL
GaAs
GaAsBi
HRXRD
LT-GaAs
MBE
RADS
SE
SEM
VLS
XRD
Atomic force microscopy
Aluminum arsenide
Bayard-Alpert ionization gauge
Beam equivalent pressure
Back-scattered electron
Fast entry lock
Gallium arsenide
Gallium arsenide bismide
High resolution X-ray diffraction
Low temperature gallium arsenide
Molecular beam epitaxy
Rocking curve analysis by dynamical simulation
Secondary electron
Scanning electron microscopy
Vapor-liquid-solid method
X-ray diffraction
N
A
NA
BEP
ρ
D
F
h
γ
η
M
T
z
V
Number of atoms
Area
Avogadro’s constant
Beam equivalent pressure
Density
Diameter
Atomic flux
Height
Height to diameter ratio
Ionization efficiency
Molar weight
Temperature
Thickness
Volume
1
1. INTRODUCTION
1.1
Molecular beam epitaxy
Molecular beam epitaxy (MBE) is an epitaxial growth technique where materials are
deposited on a substrate in a vacuum. MBE enables the growth of various epitaxial
structures with a wide range of available deposition materials, such as metals, semiconductors, oxides and even organic materials. In particular, the growth of semiconductor
devices, such as lasers, solar cells or transistors, is the predominant use for MBE in industry as well as research. A key attribute of MBE that allows for the production of
these devices is the precision in controllability of the material composition and doping
during growth. With MBE it is possible to grow (i) materials with low defect concentrations, (ii) structures with abrupt interfaces and doping profiles, and (iii) quantum structures. Owing to these properties, MBE has led major advances in the electronics industry as well as in material research. [1, 2]
1.2
The aim of this work
Enabling the successful MBE growth of the aforementioned semiconductor device
structures it is required that the critical growth parameters, namely the growth temperature and molecular fluxes, are precisely known and controlled. In this work, the focus is
on gallium arsenide (GaAs) growth and, in particular, the accurate determination of the
arsenic molecular flux. The growth of high quality GaAs films is usually achieved with
high growth temperatures (~600 ºC) and with high arsenic overpressures [1]. As long as
sufficient arsenic overpressure is achieved, the quality of the GaAs film is essentially
independent of the arsenic molecular flux. Therefore, accurate control of the arsenic
molecular flux is often neglected. However, beyond this typical GaAs growth, the arsenic molecular flux often becomes deciding factor in material properties. Importance of
arsenic flux control is evident in the growth of GaAs based alloys (e.g. GaAs1-xBix) [2],
low temperature GaAs [3] and GaAs nanostructures (e.g. quantum rings) [4]. For these
cases, the precision in the control of arsenic flux is often insufficient, due to the poor
accuracy of arsenic flux measurements. For example, an accuracy of ~10 % is achieved
in ion-gauge measurements of the arsenic flux [1]. The aim of this work is to establish a
novel method for determining the arsenic flux based on growth and ex-situ characterization of a calibration sample, in conjunction with ab initio calculation. Furthermore, a
few results gained by this method are also presented and discussed.
2
2. BACKGROUND
2.1
Basic description of MBE
The basic technique of MBE was developed in the late 60s at Bell Laboratories by Alfred Y. Cho and John R. Arthur. Although MBE technology has improved vastly from
the early designs, the simple working principle of MBE remains the same. A source
material is heated in a crucible in ultrahigh vacuum conditions, causing the source material to evaporate. The evaporated material forms a beam as it passes through the crucible
orifice. The beam is then directed towards a substrate material where some of the evaporated atoms or molecules are adsorbed to the surface of the substrate. The vacuum ensures that the source species travel to the substrate uninterrupted by other source or residual gas particles. The species traverse in free molecular flow as opposed to a viscous
one, because the vacuum is low enough for the mean free path of the species to be larger
than the dimensions of the chamber. Adsorption to the substrate is dependent on growth
conditions, such as substrate material, other incident source material fluxes and substrate temperature (in this work referred to as growth temperature). In addition to the
uninterrupted molecular flow of the source species, the vacuum environment ensures
that the amount of impurity species in the chamber is minimized, which might be harmful to the properties of the grown layer if adsorbed during growth. To this end, the
source materials and substrates must be of high-purity. [1, 2]
The growth of typical semiconductor device structures, where different alloys are grown
on top of each other with well-defined interfaces and layer thicknesses, requires the accurate control of numerous different material fluxes simultaneously. To achieve this,
MBE systems have several independently heated sources which, in turn, have individual
mechanical shutters to block the molecular beams from the source when necessary.
Layer thicknesses can be controlled with a precision of a single monolayer, due to the
rate of closing and opening the shutters being faster than the time it takes to grow a single monolayer at typical growth rates. [1, 2]
2.2
Gallium arsenide
Gallium arsenide (GaAs) is a compound semiconductor used in a wide range of applications that are manufactured with MBE. As many other semiconductor compounds,
GaAs forms a zinc blende crystalline structure as a solid, which is analogous to diamond with the exception that the two face centered-cubic lattices have different atoms,
in this case gallium and arsenic. Due to its high intrinsic electron mobility, GaAs enables the production of high-performance transistors with higher functioning frequency
3
than typical silicon based transistors. GaAs is also an intrinsically resistive material because of its relatively wide band gap of 1.424 eV (at room temperature) [5]. The width
of the band gap also results in good temperature tolerance for GaAs based devices.
However, these intrinsic electrical properties can be controlled by introducing doping
materials or alloying GaAs with other elements. Another important material property of
GaAs is that the band gap is direct, which allows for efficient light absorption and emission. This property makes GaAs ideal for optoelectronic devices. [5]
2.3
MBE growth of GaAs
The production of high quality films of GaAs with MBE is typically done by using high
growth temperatures and high As/Ga material flux ratios. Although optimal growth
conditions can vary for each MBE system, due to their individual geometry and components, growth temperatures of ~600 ºC and As/Ga flux ratios of over ~2 are typically
used to grow GaAs with excellent optical, structural and electrical properties together
with smooth surface morphology. These properties are influenced by the incorporation
of lattice defects, impurities and deep levels, which, in turn, are controlled by the
growth temperature. Moreover, growth temperature also controls surface morphology,
and therefore interface roughness, since adatom diffusion, adsorption and desorption are
all temperature dependent. [1]
The role of the As/Ga flux ratio on the GaAs crystal quality has similar effects as the
growth temperature. Growth kinetics at the surface are controlled by the ratio of the As
and Ga surface vacancies and the relative population of chemisorbed As and Ga precursors, which, in turn, are controlled by the As/Ga flux ratio. As a result, the As/Ga flux
ratio influences impurity sticking and incorporation coefficients, thereby influencing
lattice defect, impurity and deep level concentrations. Similarly, surface morphology,
dopant surface segregation and diffusion are also influenced by the As/Ga flux ratio. [1]
The growth rate of GaAs under typical growth conditions is controlled by the gallium
flux due to its unity sticking coefficient and negligible desorption from the surface for
temperatures below ~620 ºC [1]. Arsenic, however, is a more volatile species and its
sticking coefficient is highly dependent on the available group V site concentration on
the surface. At typical growth temperatures, all excess arsenic will desorb from the surface, allowing the growth of stoichiometric crystalline GaAs [1, 6, 7].
2.4
Low temperature and arsenic limited growth of GaAs
GaAs grown at low temperatures, referred to as LT-GaAs, has been studied extensively
due to its unique properties, which allow for the manufacture of highly resistive material. At low growth temperatures of below ~400 ºC and above unity As/Ga flux ratios,
excess arsenic can incorporate into the GaAs lattice forming arsenic anti-sites, As Ga, and
gallium vacancies, VGa [8]. Furthermore, thermally annealing such defects results in
4
AsGa diffusion in the bulk to form arsenic clusters, making the crystalline structure highly resistive. This, in conjunction with high carrier mobility and fast recombination lifetime, allows for subpicosecond photoconductive device applications [9].
Concentration of the aforementioned point defects is a function of both temperature and
the As/Ga flux ratio. The concentration rises quickly when increasing the As/Ga flux
ratio above stoichiometric conditions and eventually saturates to a constant value [3].
On the other hand, under these arsenic rich conditions the concentration decreases linearly when increasing the growth temperature [8]. An excess of roughly 1% arsenic can
be achieved using high As/Ga ratios and low temperatures [3, 8]. In this work, however,
the focus is on growth conditions where an excess of Ga is supplied at low temperatures.
In the growth regime where the As/Ga flux ratio is below unity, the arsenic (As2) sticking coefficient has been found to be practically unity, due to the excess amount of group
V sites available at the surface [6, 7]. During growth, however, excess gallium nucleates
on the surface forming liquid droplets [1]. The droplets are essentially pure gallium, as
arsenic solubility in the liquid gallium at these low temperatures is negligible [4, 10,
11]. As growth proceeds at these conditions, the gallium droplets grow larger as excess
amounts of gallium accumulates. Formation of the droplets changes the fundamental
growth process of GaAs over and around the gallium droplets. On one hand, the gallium
droplets act as gallium reservoirs, which supply the surrounding areas with gallium adatoms, enabling the nucleation of GaAs with the incident arsenic [7]. On the other hand,
the arsenic that is incident directly on top of the droplets gets trapped on the droplet
surface from where it migrates to the edges of the droplet where GaAs nucleation is
energetically preferable [4]. It should be noted that arsenic diffusion through the droplets or vapor-liquid-solid (VLS) type growth mediated by the gallium droplets is negligible, due to the previously mentioned low solubility of arsenic into the liquid gallium.
As the growth proceeds, the liquid droplets can freely move on top of the surface, which
eliminates the chances of droplets being buried. This, together with the high surface
diffusion rate of gallium on gallium rich surfaces [1], creates relatively smooth GaAs
surfaces on the perimeters of the droplets.
The LT-GaAs layers grown under arsenic limited conditions are stoichiometric, as the
GaAs phase diagram at these growth temperatures only indicates a stoichiometric GaAs
phase and a liquid phase of practically pure gallium. This is supported by observations
of no strain between the LT-GaAs layer and the GaAs substrate in high resolution X-ray
diffraction (HRXRD) measurements. The point defects formed during growth under
these conditions are not known, however, due to limited research conducted in this
growth regime. Nonetheless, some things can be deduced from proposed incorporation
effects. The AsGa anti-site defects are the main cause of compressive strain in As-rich
LT-GaAs [8] and as the As-limited LT-GaAs shows no strain, it can be deduced that the
incorporation of this particular defect is rare (concentration below ~10 19 cm-3) in this
5
growth regime. Furthermore, if the V Ga defect is incorporated as a part of a defect complex with the AsGa anti-site, it is likely that this point defect is rare as well.
6
3. EXPERIMENTAL SETUP AND CHARACTERIZATION METHODS
3.1
MBE-system
The MBE-system used in this work is the VG V80H, which is a model often used for
research purposes. This specific system has been configured for III-V epitaxy and has
sources for aluminum, gallium and indium as well as nitrogen, arsenic and bismuth for
the group III and V species, respectively. Additionally, silicon and beryllium are provided for n- and p-type doping, respectively. The group III and dopant sources, along
with bismuth, are traditional Knudsen effusion cells (K-cell). These cells are simple
thermal evaporators where the source material melt is in a heated crucible and the material flux is controlled by careful temperature regulation. All the K-cells are fitted with
individual mechanical shutters. As for the remaining group V cells, there are specially
designed sources.
b)
a)
Throughput
connectors
Thermocouple
Back flange
Power and thermocouple
connectors
Crucible
Water
circulation
Power and thermocouple
connectors
Mounting flange
Crucible
Crackin zone
Needle valve
positioner
Heating filaments
Mounting flange
Fig. 3.1 a) Schematic of a K-cell. b) Schematic of a valved cracker cell.
For arsenic, a valved cracker cell is fitted. This cell comprises two segments: a bulk
stage where solid arsenic is heated to produce As4 and a cracker stage where the As4
molecules can be dissociated to create As2. Generally speaking, the arsenic source has
two operation modes. One where the cracker stage is heated to a lower temperature to
let As4 molecules pass without dissociation and one where the cracker stage is heated to
a high temperature to generate As2. In this work, the latter mode is used. The arsenic
flux is controlled by a needle valve positioned between the bulk stage and the cracker.
For nitrogen, a plasma source is fitted to the reactor in conjunction with a mass flow
controller providing atomic nitrogen. However, as it is not used in this work, the specifications for this source are omitted here.
7
Fig. 3.2 Schematic cross-section of the MBE system used in this work.
The MBE vacuum chamber is divided into three segments: a growth chamber, a preparation chamber and a fast entry lock (FEL) chamber (see Fig. 3.2). The chambers are
separated with vacuum valves and have individual pumping systems. The loading of
substrates and samples between atmospheric conditions and the MBE-system takes
place via the FEL chamber. During loading, this chamber is filled with pure nitrogen
while the FEL vacuum pumps are turned off. After reaching an atmospheric pressure in
the FEL chamber, substrates and samples wafers can be loaded in or out of the system
together with wafer holding blocks. The blocks are made of molybdenum due to their
excellent thermal stability and inertness. The FEL chamber is then pumped down by a
turbomolecular pump in conjunction with a diaphragm backing pump. After the FEL
chamber has been pumped down to ~10-7 mbar vacuum level, the substrates can be
moved with their blocks to the preparation chamber using a wobble stick and a mechanical trolley transfer mechanism. The wobble sticks are used in both the preparation and
the growth chamber to maneuver the blocks. They consist of a magnetically actuating
arm, to mimic movements made on the handle outside the chamber, with a spatula that
can hold the blocks via an upright facing pin.
In the preparation chamber, the substrates are heat treated to promote desorption of impurities, such as water and atmospheric particles, from the substrate surface. The preparation chamber is pumped by an ionization pump and its vacuum level is typically ~10 -8
mbar. After the substrate has been heat treated sufficiently, i.e. the preparation chamber
pressures are stable and have reached a reference pressure level, it can be moved into
the growth chamber. The growth chamber has the best pumping capability and pressures
of ~10-10 mbar can be reached when cells are at their idle temperatures. This chamber is
pumped by a diffusion pump together with liquid nitrogen-filled cryopanel surrounding
the chamber. The diffusion pump is backed by two rotary vane pumps. The growth
chamber is also fitted with an additional ionization pump and a titanium sublimation
pump.
8
3.2
MBE operation and sample growth
The day-to-day MBE operation involves flux measurement and sample growth. In the
following chapters, the specifics of these procedures are explained for the measurements
and growths relevant to this work.
3.2.1 Flux measurement
The flux measurement of the sources, as well as chamber pressure monitoring, is done
with nude Bayard-Alpert ionization gauges (BAG). In this particular system, the flux
measurement BAG is mounted on to the backside of the manipulator arm which can be
rotated so that it is in the path of the molecular beams (see Fig. 3.2). An ion gauge consists of three components: a filament (cathode), a grid (anode) and an ion collector
(ground). A schematic drawing of an ion gauge is provided in Fig. 3.3.
Fig. 3.3 Schematic drawing of a nude Bayard-Alpert ionization gauge
The ion gauge working principle is simple. By driving current through the filament, it
heats up and begins to emit electrons. These electrons are accelerated towards the positively charged grid. The electrons travelling towards the grid can pass into the space
enclosed by the grid. In this space, they can collide with gas molecules and ionize them,
producing positively charged ions. These positively charged ions are then collected efficiently by the grounded ion collector which is connected to an electrometer. The current
generated at the ion collector, referred to as beam equivalent pressure (BEP) by convention, is proportional to the amount of gas molecules inside the grid and thereby proportional to the molecular flux.
9
Measurement of group III BEPs is straightforward, due to their tendency to adsorb to
surfaces present in the chamber. This means that when the beam is directed towards the
ion gauge, all the beam species pass the ion gauge grid only once and stick to the manipulator arm and chamber walls behind the ion gauge. Therefore, when opening the
shutter, the ion collector current quickly rises to a stable value, as seen in Fig. 3.4.
Group III BEPs can be typically measured and reproduced to within about 0.5 % [1].
This, however, is often not the case with group V species. The more volatile group V
species, such as As2 and As4, can reflect off the surfaces behind the ion gauge and make
a second pass through the ion gauge grid. This results in the increase of BEP over time
and, since the sticking coefficient of the group V species to different surfaces in the
chamber is essentially unknown, renders the measurement useless. However, this problem can be circumvented by depositing a layer of Ga, Al or In on the surfaces behind
the ion gauge before measuring the group V BEP, because group V species tend to have
unity sticking coefficient on these clean group III surfaces. This way, the group V species initially stick with unity coefficient to the group III coating and subsequently start
saturating the available group V sites, resulting in reflection and BEP rise. Due to the
transient unity sticking coefficient and saturation of the coating with group V species,
the accuracy in group V BEP measurements is poor. For example, when using typical
As4/Ga ratios and a 60 s gallium pre-deposition, an accuracy of 10% is achieved in
measuring the As4 BEP [1]. Furthermore, it should be noted that the group V BEP stability over time is much more variable than the typical group III BEP, making the flux
reproducibility even worse [12].
Absolute BEP values are dependent on many factors, of which the most crucial ones are
ion gauge sensitivity, geometry of the grid and ionization efficiency of the molecular
species. Therefore, flux ratios are related to BEP values by equation 3.1.
=
/
3.1
In equation 3.1, the ionization efficiency , absolute source temperature and molecular weight are denoted for species X and Y, with respective sub-indices.
80
70
60
50
40
30
20
10
0
1000
(iii)
800
(ii)
600
Ga
Al
As
(i)
5
10
15
20
25
10
Time (s)
20
30
40
400
BEP (nA)
BEP (nA)
10
200
0
50
Fig. 3.4 Typical BEP measurements for Ga, Al and As (approximate BEP values
shown by double-headed arrows). In the right hand graph, the (i) valve jog start, (ii)
arsenic unity sticking coefficient transient and (iii) increasing BEP due to arsenic
reflection are indicated. The initial decrease in the Al BEP is believed to be due to a
shutter transient, caused by thermal instability of the cell after opening the shutter.
BEP measurements in this work were measured in the following way. First, Al was
measured for 3 min and after closing the shutter the background BEP was measured for
1 min and subtracted from the averaged Al BEP. Second, Ga was measured three times
for 30 s and 15 s for Ga BEP and background, respectively. Finally, As was measured at
different valve openings (by gradually jogging the needle valve to a set value) with each
measurement being preceded by an Al deposition of 2 min and BEP was tracked for 1
min. Typical BEP measurement results are depicted in Fig. 3.4.
3.2.2 Sample growth
Sample growth is preceded by a standard cleaning process by heating the substrate in a
specialized outgassing stage situated in the preparation chamber at a temperature of
roughly 300 ºC. This heat treatment is done for two to three hours, depending on the
wafer holding block and substrate cleanliness, until a reference pressure of 2×10 -8 mbar
is achieved in the preparation chamber. After this, the sample is moved to the growth
chamber and placed in the manipulator arm, which is kept at ~315 ºC.
Growth is initiated by starting manipulator rotation and a heating sequence of the sample to ~620 ºC to remove the native oxide layer and any remaining impurities. An arsenic overpressure is required during this heat treatment to prevent arsenic desorption
from the substrate, which would result in surface degradation. After 10 minutes of the
heat treatment, the sample temperature is lowered to ~580 ºC while arsenic overpressure
is maintained to grow a high quality buffer layer. A buffer layer of 150 nm thickness is
grown to ensure a smooth and clean surface on top of which the actual sample structure
is grown. For this work, few different structures were grown; including a gallium deposition sample, three LT-GaAs samples, two AlAs/GaAs heterostructures and a single
11
GaAs1-xBix alloy sample. The details of each sample are presented in the results and
discussion chapter.
3.3
Characterization methods
3.3.1 Scanning electron microscopy
Scanning electron microscopy (SEM) works by tracing a focused beam of electrons in a
raster pattern across a sample surface and then producing an image by detecting the signals that change in response to electron bombardment. SEM can provide information on
surface topology and composition for up to nanometer resolution. In this work, imaging
is done by two detection modes, each of which provide unique information. Firstly, a
secondary-electron (SE) detector is used. The secondary-electrons are low energy electrons (typically under 100 eV) that are ejected from the first few atomic layers of the
specimen, due to inelastic scattering interactions with the incident beam. This detector
provides good insight into the topology of the surface, due to its high depth of field.
Secondly, a back-scattered electron (BSE) detector is used. The back-scattered electrons
are incident electrons that have elastically scattered from the specimen surface and
therefore have the same energy as the incident electrons, typically in the order of 100 to
10 000 eV. The back-scattered electron imaging mode provides information on the surface composition, as the scattering efficiency is proportional to atomic number. [13]
In this work, the specific SEM system used is the Zeiss Ultra 55. All subsequent mentions of the imaging detectors are denoted by SE and BSE for secondary-electron and
back-scattered electron detectors, respectively.
3.3.2 High resolution X-ray diffraction
HRXRD is a versatile characterization method to determine material properties of crystalline structures. Accurate information on thin film thickness, composition, as well as
crystal and interface quality can be achieved non-destructively. This, in conjunction
with little to no sample preparation, makes it an ideal method for thin film research.
In X-ray diffraction (XRD), a collimated beam of X-ray radiation is incident on a crystalline structure and, due to its wavelength being comparable to interatomic distances in
the crystal structure, it can diffract and constructively interfere to specific angles. These
angles are determined by Bragg’s law and are depend on many factors, of which incident angle with respect to the crystal planes and lattice plane separation are the most
crucial ones. Moreover, in HRXRD the diffraction angles around a single diffraction
maximum (corresponding to a single lattice plane group) is measured with high angular
resolution. In HRXRD, the aim of the measurement is to detect slight deviations from
the ideal crystal structure, which form an intensity distribution around the ideal structure
12
diffraction maximum, due to slightly different lattice plane separation in the different
parts of the crystal structure. For the case of thin films, this is particularly useful, as the
lattice plane separation is proportional to the film’s composition. In addition to composition determination, with HRXRD it is possible to determine thin film thicknesses, as
the film’s thickness causes additional interference fringes (Pendellösung fringes) around
the thin film peak which can be analyzed. A detailed analysis of the thin film parameters, such as composition and film thickness, is gained by fitting a model to the experimental data. In this work, this is done by Bede RADS (rocking curve analysis by dynamical simulation) software, which uses a dynamical theory of X-ray diffraction formulated by Takagi-Taupin. In Fig. 3.5 there are two measurements and their corresponding simulation using the RADS software of two typical structures grown in this
study. [14]
1000000
1E7
Measurement
Simulation
1000000
10000
10000
Intensity (a.u.)
Intensity (a.u.)
100000
1000
100
1000
100
10
10
1
1
0.1
-1000
Measurement
Simulation
100000
-500
0
w-2q (arcseconds)
500
1000
0.1
-1000
-500
0
500
1000
w-2q (arcseconds)
Fig. 3.5 Examples of HRXRD measurements and simulations for structures grown in
this work. On the left, an AlAs/GaAs heterostructure and, on the right, a LT-GaAs
layer grown under slightly arsenic rich conditions.
In this work, the XRD measurements are carried out with a Phillips X’Pert XRD system. In this specific system, the X-rays are Cu K-alpha (0.154056 nm) radiation which
are generated in a high power ceramic X-ray tube. The X-rays are then directed towards
an X-ray mirror that focuses the beam towards a four crystal Ge(022) monochromator.
Past the monochromator, a triple-axis goniometer holds the sample in front of the focused X-ray beam. The goniometer can be positioned in such a way that the diffracted
intensity from specific lattice planes is directed towards the detector. The detector is
fitted with an analyzer, which provides a narrow angular detection range. [15]
In this work the scans are so called ω-2θ triple-axis coupled scans, where both the sample (i.e. goniometer) and detector are moved simultaneously (although with different
velocities). The ω and θ angles refer to the incidence and diffraction angles, respectively, which are measured with respect to the lattice plane being measured. The GaAs
(004) lattice planes are measured owing to their high structure factor, which governs the
diffraction maximum intensity.
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3.3.3 Atomic force microscopy
Atomic force microscopy (AFM) is a method for measuring surface geometry threedimensionally with nanometer resolution. AFM works by probing the specimen surface
with an atomically sharp tip which is connected to a cantilever. When moving the tip
closer to the surface (in order of multiple nanometers) with a piezoelectric actuator, attractive forces, such as van der Waals, electrostatic and magnetic forces, are formed
between the surface and the tip, which deflects the cantilever according to Hooke’s law.
However, as the tip gets closer to the sample surface (sample-tip distance fractions of
nm) repulsive chemical forces deflect the cantilever in the opposite way. Adjusting the
sample-tip distance while measuring the cantilever deflection by tracking laser light
reflection off the top of the flat cantilever head with a photodetector, yields information
of the interacting forces between the tip and the sample. Furthermore, raster-scanning
over the sample surface while keeping, for example, the interaction force or tip height
constant allows for accurate determination of the surface geometry. Depending on what
parameter is kept constant during the raster-scan, AFM can be divided into three imaging modes: contact, non-contact and tapping. In this work, the measurements are performed using the tapping mode. [16, 17]
In the tapping mode (also referred to as amplitude-modulation AFM), the cantilever is
oscillated perpendicularly with respect to the sample surface near its resonance frequency by a piezo element mounted in the cantilever holder. When lowering the oscillating
tip closer to the surface, the oscillation amplitude of the cantilever is decreased, due to
the interacting forces between the tip and the sample surface. Surface height is determined by keeping the oscillation amplitude constant over the raster-scan by moving the
cantilever up or down. The tapping mode has several advantages over the other imaging
modes of AFM for semiconductor research, for example no sample preparation is needed and sample surfaces are rarely damaged.
14
a)
b)
Fig. 3.6 a) Diagram of AFM components. b) Artifact formation due to a dull probing
tip. Adapted from reference [18].
However, compared to other microscopy techniques, AFM has some disadvantages. As
a microscopy technique it is considered to be slow, when compared to SEM, for example. When raster-scanning across the sample, the tip velocities are typically in the order
of µm/s, resulting in slow scan times over large areas. The resolution of AFM is limited
by tip geometry and imaging artifacts are possible, due to poor tip quality or steep sample topography, as depicted in Fig. 3.6.
The AFM system used in this study was the Veeco Dimension D3100 with the Nanoscope IV control unit. Further analysis on the data was done by Veeco V613r1 and
Matlab 2014a/2015a software.
15
4. CALCULATION OF ARSENIC FLUX FROM
ARSENIC LIMITED AND LOW TEMPERATURE
GROWN GALLIUM ARSENIDE
In this chapter the method of calculating the arsenic flux based on the calibration structure is presented. Additionally, the chosen growth parameters for the calibration structure are explained. A motivation behind the derived analysis method is also discussed
briefly, which arises from the similarity of the structure and the substrate.
To calculate the arsenic molecular beam flux, a low temperature GaAs (~220 ºC) sample is grown with below unity As/Ga flux ratio. The rationale for the low temperature is
to prevent any desorption of the deposited As and Ga species. In the case of Ga, this is
clear, as the desorption of Ga is negligible for even up to ~620 ºC [1]. In the case of As,
it is bound to the excess amounts of Ga available forming GaAs, which is thermally
stable for temperatures up to ~590 ºC [19]. The arsenic-limited growth mode on the
other hand ensures that the sticking coefficient of the As2 species used is unity [6, 7].
Based on these assumptions, a calculation of the arsenic molecular flux is possible from
the thickness of the LT-GaAs layer grown, as it is directly proportional to the supplied
arsenic.
Measuring the grown LT-GaAs layer thickness directly is difficult, as its structure is
virtually the same as the buffer layer grown before it and therefore an accurate interface
location between the two is hard to determine. One way of circumventing this issue, is
to grow a marker layer before the growth of the LT-GaAs layer from which the interface location between the marker and the LT-GaAs can be determined by various techniques. In this work, an AlAs marker layer is used for three reasons. First, its lattice
mismatch with respect to GaAs is low enough to enable relaxation free interfaces, but
high enough to enable HRXRD analysis. Second, the elemental composition difference
enables the measurement of the interfaces directly by cross-sectional SEM measurements, for example. Third, growth of the structure is straight forward, as only group III
species need to be controlled precisely. However, circumventing the problem of measuring the LT-GaAs thickness directly can be done without any marker layers by a detailed analysis on the amount of accumulated gallium at the surface.
Let us assume that a LT-GaAs layer is grown with a known As/Ga flux ratio, denoted
by
/ , which is below unity with all incident species sticking to the substrate. As
discussed previously, some of the gallium is incorporated in the bulk LT-GaAs layer,
denoted by
, while the excess gallium is accumulated on the surface as pure
,
16
gallium droplets, denoted by
. Arsenic, however, is only incorporated in the
,
bulk, denoted by
. Since fluxes are proportional to amount of atoms deposited,
,
the following relation can be written
=
+
,
,
,
Applying the knowledge that stoichiometry in pure GaAs is 1:1, i.e.
the previous equation can simplified to
=
Expressions for the quantities
,
1+
,
and
,
=
1
,
,
4.1
,
=
,
,
4.2
are achieved by a simple density
and geometry calculation. In the following equations, the densities, , and molar masses, , are used for the atomic species . Avogadro’s constant is denoted by . For the
gallium on the surface, individual gallium droplet volumes are summed over a sample
area giving some total volume of gallium in this area. The determination of droplet volumes by their shape is discussed in detail in the results chapter. Total mass of gallium in
these droplets is obtained by multiplying the total volume with density. Moreover, the
number of gallium atoms is then achieved by multiplying with Avogadro’s constant and
dividing by the molar mass of gallium.
4.3
In equation 4.3, the summation of individual droplet volumes is done of droplets indexed up to that are located in some sample area, subsequently referred to as . For
the bulk gallium, the number of atoms is proportional to the volume of the grown bulk
layer in the sample area, denoted by . By a similar density and amount of substance
calculation, it follows that
=
,
4.4
+
From equations 4.3 and 4.4, the fraction in the denominator of equation 4.2 is given by
,
,
=
(
+
)
4.5
17
If now, postulating an imaginary scenario where an excess of As was supplied instead
(assuming a formation of stoichiometric GaAs without any point defects), the Ga flux
would be proportional to this imaginary (nominal) layer thickness, denoted by . Based
on this proportionality and, on the other hand, the proportionality between the As flux
and , it follows that
=
=
1
+
(
1+
)
4.6
∑
Since the Ga flux is well-known and reproducible with accuracy [1], the quantity
can
be easily determined. Furthermore, if an accurate calculation on the volumes of the gallium droplets over a measurable sample area is made, the only unknown in the above
equation is . The latter equation in 4.6 can be solved analytically, with the fair assumption that ≠ 0 (i.e. some LT-GaAs is grown).
=
−
(
+
)
4.7
So in conclusion from equation 4.7, obtaining the real thickness of the arsenic-limited
LT-GaAs sample is possible if the gallium volume in the accumulated droplets is obtained and the nominal amount of gallium supplied is known. Moreover, from this calculated thickness it is possible to determine the arsenic flux from the following equation.
=
In this work, investigation into the validity of this method is performed.
4.8
18
5. RESULTS
In this chapter, the results of this work are presented and discussed. First, the geometry
of gallium droplets is investigated, as the method’s accuracy depends crucially on being
able to determine the volume of the droplets. Second, a proof of concept is offered by
comparing results between the method presented here and HRXRD analysis. Finally, an
example is presented, in which the arsenic flux profile over the substrate during growth
is determined.
5.1
Gallium droplet geometry
The analysis method presented in this work relies on accurate evaluation of the accumulated surface gallium during arsenic limited growth, as seen from equation 4.7. To this
end, the geometry of the droplets was determined from AFM measurements performed
on (i) a gallium deposition sample and (ii) an arsenic limited LT-GaAs sample.
The gallium deposition sample was grown by depositing pure gallium on top of the
GaAs buffer layer for ~30 s at growth rate which was equivalent to ~0.35 µm/h of
GaAs. The deposition was performed at a growth temperature of ~220 ºC to prevent
gallium desorption. This resulted in droplet sizes of around 100 nm diameter. Furthermore, the substrate rotation was stopped at the start of the gallium deposition, which
resulted in a variation in the total deposited gallium across the wafer surface due to the
intrinsic non-uniformity of the flux, which will be presented in detail later.
The arsenic limited LT-GaAs sample had a nominal thickness of 250 nm and was
grown at a growth rate of ~0.32 µm/h at a temperature of ~220 ºC. The estimated As/Ga
flux ratio based on flux measurements was 0.55. However, as in the gallium deposition
sample, the substrate rotation was stopped during the LT-GaAs growth and a gradient in
the As/Ga ratio over the wafer was formed. Generally speaking, one side of the wafer
had As-limited conditions whereas the opposite side had As-rich conditions and between these two sides a smooth gradient was formed.
The samples were chosen for analysis based on the sizes of the droplets, namely the
gallium deposition sample had relatively small droplets compared to the LT-GaAs sample, which had bigger droplets. Simultaneously, an effect of surface roughness on the
geometry was investigated, as the LT-GaAs sample had a somewhat rougher surface,
which can influence the contact angle, for example.
19
Fig. 5.1 A planefitted AFM measurement of the gallium deposition sample.
To determine the geometry of gallium droplets, AFM images were measured from the
samples and a simple data analysis was conducted. Fig. 5.1 depicts a typical AFM
measurement. The data was analyzed in the following way. First, the raw AFM data was
planefitted with a 3rd order xy-plane to level the background, because typically the AFM
tip is not normal to the specimen surface, resulting in a tilted raw image. Second, an
appropriate cut-off height level was chosen to separate the background from the droplets. This cut-off was chosen to be slightly above to the background height value, so any
height data above this value was likely to be measured from the droplets. Then, the
droplets were individually analyzed by height and area. Moreover, from the height and
area data of the droplet, the droplet volume and diameter were determined. The droplet
volume was approximated by the total sum of the height data for a single droplet multiplied by the data resolution (i.e. a three dimensional Riemann integral). The diameter
was approximated based on an assumption that the droplet had a round base. This assumption was made based on SEM observations on the droplet shape, seen in Fig. 5.2.
Fig. 5.2 SEM images of the gallium deposition sample. On the left hand side, a SE
detector image. On the right hand side, a BSE detector image.
The first geometrical relation shown here is between the gallium droplet height and diameter. The height follows the diameter linearly, i.e. the height to diameter ratio is con-
20
stant, of about ~0.17, seen in Fig. 5.3. Similar relation has been observed for smaller
and less dense gallium droplets on GaAs [20].
Gallium deposition (A)
Gallium deposition (B)
Arsenic limited LT-GaAs
Linear fit
Gallium droplet height (nm)
80
60
40
20
0
0
100
200
300
400
Gallium droplet diameter (nm)
500
600
Fig. 5.3 Gallium droplet height versus diameter calculated from AFM measurements.
The deposition sample was measured from two locations (A and B) whereas the Aslimited LT-GaAs was measured from one location.
Based on observations of droplet shapes from the SEM and AFM measurements, the
droplet shape follows the geometry of a spherical cap, i.e. a portion of a sphere cut off
by a plane. Again, this conclusion has been made for smaller and less dense gallium
droplets on GaAs [20]. Volume of a spherical cap, , can be determined from the diameter of the base, , and the height of the droplet, ℎ [21]. Furthermore, if the height to
diameter ratio, = ℎ/ , is constant, as shown previously, the spherical cap volume can
be simplified to be dependent on only the droplet area, .
=
ℎ 3
6 4
+ℎ
=
3√
(3 + 4
)
/
5.1
In equation 5.1 on the right hand side, the power dependency of volume with respect to
the area of a spherical cap is seen, which is typical for other three dimensional geometrical objects on surfaces. The pre-factor is dependent only on the height to diameter
ratio, which is a constant, making the analysis on droplet volumes simple, as only the
areas of the droplets are needed.
21
7
3
Gallium droplet volume (nm )
10
Ga deposition (A)
Ga deposition (B)
Arsenic limited LT-GaAs
Spherical Cap (h/D=0.17)
6
10
5
10
4
10
3
10
10
3
10
4
5
10
2
Gallium droplet area (nm )
Fig. 5.4 Gallium droplet volume versus area based on AFM measurements. Measurements here correspond to the measurements in Fig. 5.3.
Fig. 5.4 shows the comparison between the data calculated from AFM measurements
and the analytical formula from equation 5.1. For large droplets the agreement is good.
However, for smaller droplets, of around ~1000 nm2 area, there is some deviation. Here,
this deviation is ascribed to the AFM measurement having two likely causes of error for
the case of the smaller droplets. Firstly, the data resolution of the AFM measurements
was in the order of ~2nm/px, resulting in smaller droplets being represented by fewer
data points. Secondly, the AFM tip geometry can be a factor in misrepresenting smaller
droplets accurately, as discussed in chapter 3.3.3. Nonetheless, this discrepancy can be
neglected in cases where droplet volumes are relatively large, as is the case for samples
presented in this work where the method is applied. Furthermore, even if smaller droplets coexist together with big droplets, the majority of the total droplet volume can be
ascribed to large droplets, as seen in Fig. 5.2 from the relative population of larger droplets.
5.2
Proof of concept
To verify that the analysis method presented here is valid, a comparison between the
method in question and the already established HRXRD analysis was conducted. A
sample with an As-limited LT-GaAs layer on top of an AlAs marker layer was grown.
From this sample, the thickness of the formed LT-GaAs would be analyzed and compared between the two methods. The As/Ga flux ratio based on flux measurements was
estimated to be 0.66 for the LT-GaAs layer, which grown at a temperature of ~220 ºC.
The AlAs layer thickness was ~50 nm (confirmed by HRXRD) and grown under typical
AlAs growth conditions, i.e. high temperature and high As/Al flux ratio. The LT-GaAs
layer thickness nominal value was estimated to be ~232 nm, based on HRXRD meas-
22
urement and simulation from a previously grown dilute GaAs1-xBix alloy sample, grown
with the same gallium cell temperature. No major variation in the film thickness over
the wafer was observed (confirmed by HRXRD) for samples rotated during growth, so
this nominal value was used for the analysis over the wafer.
The droplet volumes, from which the thickness of the LT-GaAs layer would be calculated using equation 4.7, were determined by an analysis on SEM images. The analysis
was done on BSE detector images with ImageJ software and conducted as follows.
First, the image pixel size was set to correspond with the SEM image scale, so that
measurements from the image would be in nm. Second, the grayscale BSE image was
converted to a binary image using an automatically applied threshold value. Third, noise
of the binary image was reduced by applying an outlier removal filter of typically 5 pixel radius. The outlier removal replaces pixel values based on the median value of the
surrounding pixels inside a given radius. This was done for both white and black pixels
consecutively, to reduce noise existing in the background and droplet areas, respectively. Fourth, as the outlier removal left edges of the droplets still noisy, a median filter of
3 pixel radius was applied. Finally, a watershed function was applied, which separated
droplets that were connected to each other. Optionally, some touch-ups, such as covering white pixels left inside droplets, were manually performed. The image from this
analysis, i.e. a binary mask of the droplets, was then analyzed by ImageJ’s particle analyzer function, which counted the droplets areas individually. A typical measurement
and a result of the analysis are provided in Fig. 5.5. From the droplet area data provided
by the image analysis, the droplet volumes were calculated and summed using the
spherical cap model formulated in the previous chapter. This together with the
knowledge of the sample area (SEM image area) enabled the calculation of the LTGaAs layer thickness from equation 4.7.
23
a)
c)
b)
Fig. 5.5 Droplet analysis conducted on a SEM BSE image. a) A raw BSE image from
which the droplets were analyzed, b) a binary mask based on the BSE picture and c)
droplet outlines (numbered in red) overlaid on top of a SE image taken from the same
location.
An important thing to note from Fig. 5.5 is that some of the droplets which lay at the
edges of the image are cut-off. This causes some error in the droplet volume calculation,
as the volume of a cut-off droplet is calculated as a droplet with a smaller base area.
However, this error can be significantly reduced by choosing an appropriate SEM image
magnification, so that the number of droplets cut-off by the image edges is outnumbered
by the total amount of droplets in the picture, as is the case in Fig. 5.5.
The small deviation in lattice constants between the AlAs and GaAs layer enabled the
HRXRD analysis of the sample, an example measurement and simulation is provided in
the left hand side of Fig. 3.5. The sample was measured and analyzed by both of the
methods over the wafer at 5 mm intervals to compare their agreement, seen in Fig. 5.6.
24
210
LT-GaAs thickness (nm)
Droplet analysis
HRXRD
208
206
204
0
5
10
15
Distance from wafer center (mm)
20
Fig. 5.6 Comparison between LT-GaAs layer thickness over the wafer from droplet
analysis and HRXRD simulation.
In Fig. 5.6, the agreement between the methods is good. Surprisingly, even the absolute
values agree well, with absolute relative error average of ~0.3 %. However, it should be
noted that even the HRXRD analysis has error, which is dependent on the structure being analyzed, so here the main point is that the analysis method gives consistent results
and is within reasonable bounds when compared to HRXRD. Additionally, the As/Ga
flux ratio calculated by the method averages to about 0.89, which is considerably different from the estimated flux ratio of 0.66. This discrepancy will be discussed in chapter
6.
5.3
Spatial arsenic flux distribution
To investigate the arsenic flux distribution during growth, two LT-GaAs samples were
grown with As-limited conditions without rotation. The samples were grown with
As/Ga flux ratios of 0.7 and 0.55 for the first and second sample, respectively. These
flux ratios were estimated from flux measurements. However, due to the non-uniformity
of the fluxes and not rotating the sample during growth, an As/Ga flux gradient formed
over the wafer. This previously mentioned gradient is depicted schematically in Fig.
5.7.
25
Sample #2
Sample #1
+
(ii)
As
(ii)
0 mm
Ga
-
As
0 mm
(i)
(i)
Ga
+
-
Fig. 5.7 Top view of the flux gradient for samples #1 and #2. Two surface phases are
indicated by color: (i) an area with As-limited conditions forming droplets and (ii) an
area with As-rich conditions forming smooth surfaces. The labelled boxes represent
the molecular source positions with respect to the wafer orientation during growth
(estimated from manipulator position) and the arrow represents the measurement
axis. The schematics are drawn based on optical microscope, SEM and diffuse light
scattering observations.
Fig. 5.7 shows, that the directionality for the As/Ga flux gradient is well defined and
reproducible. The interface between below unity and above unity As/Ga flux ratio is
perpendicular to the gradient, indicating that flux variation is only significant along the
axis depicted in Fig. 5.7. A rough illustration of how the As/Ga flux behaves is depicted
in Fig. 5.8, where the droplet size decreases going towards the positive side of the axis.
a)
b)
c)
Fig. 5.8 SEM images taken from sample #1 with the SE detector along the flux gradient axis. The positions along the axis are: a) -15 mm, b) -5 mm and c) +5 mm.
Analyzing the arsenic flux based on equations 4.7 and 4.8 required the accurate value of
the nominal thickness (i.e. the gallium flux) along the same axis. Therefore a reference
sample was grown where a typical high temperature (~580 ºC) and high As/Ga flux
ratio (~5) GaAs layer was grown without rotation on top of an AlAs marker layer. From
this sample, the grown GaAs layer thickness, which is proportional to the gallium flux,
was determined along the flux gradient axis by HRXRD.
320
As/Ga < 1
300
As/Ga > 1
200
180
280
260
160
240
Measured
Linear fit
220
200
-20
-10
0
Nominal
Measured
10
20
-20
-10
0
Distance from wafer center (mm)
140
10
20
120
LT-GaAs thickness (nm)
GaAs thickness (nm)
26
Fig. 5.9 On the left, the measured thicknesses along the flux gradient axis of the
AlAs/GaAs reference sample and a linear fit. On the right, the nominal thickness calculated for sample #1 based on the reference sample with a few measured thicknesses
from the As-rich side where HRXRD analysis was possible. The red dashed line indicates the location of the interface between the two surface phases.
In Fig. 5.9, the measured GaAs thicknesses for the reference sample show a clear linear
relationship across the wafer, indicating that the change in the gallium flux across the
wafer is linear, too. The nominal thicknesses for samples #1 and #2 were calculated
using the proportionality of thickness and gallium BEP, i.e. the ratio between the LTGaAs nominal thickness and the reference sample GaAs thickness was equal to the ratio
of the gallium BEPs used in the growths. The right hand side of Fig. 5.9 shows the nominal thickness of the LT-GaAs based on the reference sample in comparison with the
measured thickness by HRXRD. The thicknesses from the As-rich side of the wafer
could be determined by HRXRD due to the compressive strain induced by the point
defects incorporated in As-rich growth. An example HRXRD measurement and simulation from sample #1’s As-rich side is shown in the right hand side of Fig. 3.5.
SEM measurements were made across the flux gradient axis with 5 mm intervals and
the droplet volumes were analyzed from the images as described in the previous chapter. From the droplet volumes and the nominal thicknesses, the real thickness of the Aslimited LT-GaAs layer was determined using equation 4.7. Furthermore, the gallium
flux was calculated from the nominal thickness and using equation 4.8 the arsenic flux
was calculated. The flux distributions obtained are depicted in Fig. 5.10. Furthermore,
using the arsenic and gallium flux distributions, the As/Ga flux ratio was determined,
depicted in Fig. 5.11.
27
14
2.6x10
Ga flux:
Sample #1
Sample #2
As flux:
Sample #1
Sample #2
-2 -1
Atomic flux (atoms cm s )
14
2.4x10
14
2.2x10
14
2.0x10
14
1.8x10
14
1.6x10
-20
-10
0
10
Distance from wafer center (mm)
20
Fig. 5.10 Calculated gallium and arsenic fluxes across the flux gradient axis.
As/Ga flux ratio (dimensionless)
1.00
Sample #1
Sample #2
0.95
0.90
0.85
0.80
0.75
-20
-10
0
10
Distance from wafer center (mm)
20
Fig. 5.11 Calculated As/Ga flux ratios across the flux gradient axis along with linear
fits.
In Fig. 5.10 it is shown that the arsenic flux is almost constant throughout both the samples. The arsenic flux has an average slope of −4 × 10 atoms cm-2 s-1/mm whereas the
gallium slope of −3 × 10 atoms cm-2s-1/mm is an order of magnitude higher. This
results in gallium being the controlling factor in the total As/Ga flux distribution, which
can be seen in Fig. 5.11. Consequently, as the gallium flux was shown to be linear
across the wafer, the As/Ga flux ratio distribution is linear, too. The slope of the As/Ga
flux ratio from the linear fit is approximately the same for both samples and has an average value of ~0.0057 mm-1.
28
5.3.1 Applying the results
To further examine if the calculated As/Ga flux ratio gradient agreed with observations
published in the literature, a few different samples where As/Ga was a deciding factor in
material properties were grown and analyzed. The growths of the layers analyzed were
conducted without rotation in order to form a flux gradient. The flux gradient was observed to be orientated in the same direction as those of Fig. 5.7, albeit with some variation in the absolute interface position due to the different nominal As/Ga flux ratio used
for each growth.
3.5
3.0
4
2.5
2.0
3
1.5
1.0
0.5
0.0
2
Bi fraction (%)
19
-3
AsGa concentration (10 cm )
The first dependency examined here, is the AsGa point defect concentration in As-rich
grown LT-GaAs, which can be seen in the left hand side of Fig. 5.12. The AsGa concentration was determined from the linear dependency on compressive strain that the defect
induces in the lattice [8], which was determined by HRXRD. The relationship agrees
qualitatively with that found in the literature [3].
1
0.95 1.00 1.05 1.10 1.15 1.20 0.90 0.95 1.00 1.05 1.10 1.15
As/Ga flux ratio (dimensionless)
Fig. 5.12 The AsGa concentration and GaAs1-xBix alloy bismuth fraction as a function
of As/Ga flux ratio in left and right hand side, respectively.
The second dependency examined here, is the bismuth incorporation into GaAs, forming the GaAs1-xBix alloy. Generally speaking, to incorporate bismuth into the GaAs lattice, low growth temperatures and near stoichiometric As/Ga flux ratios are required [2].
On the right hand side of Fig. 5.12, the dependency on As/Ga shows the critical nature
of arsenic flux control in GaAs1-xBix growth.
29
6. DISCUSSION AND CONCLUSION
In summary of the results shown here: (i) the gallium droplet geometry has been resolved, (ii) a proof of concept test for the method has been carried out and (iii) the
method has been applied to gain information on arsenic flux distribution. The results
have shown good consistency with HRXRD and agreement with results published in the
literature. However, one discrepancy has been observed between As/Ga flux ratio values given by the method and flux measurements. In fact, during the early testing of this
method, a motivation was to show that As/Ga values determined from the two methods
had at least a linear dependence. However, the flux measurements consistently gave
lower As/Ga estimates and a linear trend was not evident.
The discrepancy for As/Ga values can arise from multiple factors. As discussed in chapter 3.2.1, there is a lot of uncertainty in the As flux measurement which complicates
finding a linear trend, especially from the small sample size (4) used in the early testing.
An important factor is also brought up by the volatile nature of the As species. During
the growth process, an excess As pressure is used before growing the LT-GaAs layer.
This results in a background As pressure in the growth chamber and can affect the real
flux value being higher than intended from flux measurements. This residual pressure is
also present after growth and might consume some amount of the gallium droplets,
again resulting in a higher As/Ga estimate when compared to flux measurements. However, to investigate this discrepancy further, a more systematic study with a bigger sample size would be needed to establish a relationship between the method presented here
and flux measurements.
There is some room for future development in the analysis process. Automating the
image analysis and calculation processes would enable a faster analysis, although the
sample growth and measurement processes would still be the dominating components in
terms of time consumption. Some minor improvements, such as accounting for cut-off
droplets correctly and confirming the spherical cap model for small gallium droplets,
would result in a more accurate analysis.
In conclusion, a novel method has been presented for analyzing the arsenic flux from
ex-situ measurement and calculation of a grown calibration sample. Results show good
agreement with established methods and literature.
30
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