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Process design issues in hydride vapor phase epitay of indium gallium arsenide phosphide

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Process design issues in hydride vapor phase epitay of indium gallium arsenide phosphide
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Hsieh, Julian Juu-Chuan, 1959-
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English
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viii, 250 leaves : ill. ; 28 cm.

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Atoms ( jstor )
Chemical equilibrium ( jstor )
Chemicals ( jstor )
Chlorides ( jstor )
Conceptual lattices ( jstor )
Gallium ( jstor )
Hydrides ( jstor )
Indium ( jstor )
Reaction kinetics ( jstor )
Trajectory control ( jstor )
Chemical Engineering thesis Ph. D
Dissertations, Academic -- Chemical Engineering -- UF
Epitaxy ( lcsh )
Indium gallium arsenide phosphide ( lcsh )
Thin films ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
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Typescript.
General Note:
Vita.
Statement of Responsibility:
by Julian Juu-Chuan Hsieh

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PROCESS DESIGN ISSUES
IN HYDRIDE VAPOR PHASE EPITAXY OF
INDIUM GALLIUM ARSENIDE PHOSPHIDE
By
JULIAN JUU-CHUAN ¡HSIEH
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1988


To my parents,
Mih and Sheue-Mei Ding Ksieh


ACKNOWLEDGEMENTS
The author wishes to express his sincere gratitude to
his graduate advisor, Dr. Tim Anderson. Without his
guidance, encouragement, trust and support, it would have
been a much less enjoyable experience. He is also grateful
to the other members of the advisory committee: Dr. Lewis
Johns, Dr. Ranga Narayanan, Dr. Hong Lee and Dr. Sheng Li for
their valuable time and many helpful discussions of this
work.
The author also wishes to thank the members of his
research group for creating a stimulating research
environment. Special thanks are due to Francoise Defoort for
her assistance in the design and execution of normal pressure
experiments. Jim Edgar provided unequivocal assistance in
the construction of the gas delivery system for low pressure
experiments. Stuart Hoekje helped in atomic absorption
spectrometry measurement.
Love and moral support provided by the author's family
members, Juu-Jeng, Juurong, Rudolf and Iris, were essential
to the completion of this work.
iii


TAELE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
ABSTRACT vii-viii
CHAPTERS
1 INTRODUCTION 1
2 III-V COMPOUND SEMICONDUCTORS 4
2.1 Physical and Electrical Properties 4
2.2 Material & Device Perspective 8
2.3 Binary, Ternary and Quaternary InGaAsP
Compound 11
2.3.1 Applications 11
2.3.2 Epitaxy 13
3 HYDRIDE VAPOR PHASE EPITAXY OF INDIUM GALLIUM
ARSENIDE PHOSPHIDE 16
3.1 Process Chemistry 17
3.2 Literature Review 23
3.3 Process Design Issues 31
3.3.1 Process Thermodynamics 32
3.3.2 Nonequilibrium Mechanisms 3 6
3.3.3 Process Design Considerations 39
4 COMPLEX CHEMICAL EQUILIBRIUM ANALYSIS
IN In/Ga/As/P/H/Cl SYSTEM 44
4.1 Formulation and Method of Calculation... 44
4.1.1 Chemical Species and Reactions.... 44
4.1.2 Complex Chemical Equilibrium
Equations and Equilibrium
Parameters 53
4.1.3 Process Parameters 65
4.1.4 Calculational Procedures 76
4.1.4.1 Equilibrium Constants 76
4.1.4.2 Complex Chemical
Equilibrium Calculation... 77
4.2 Solution Thermodynamics of InGaAsP 86
4.2.1Solution Thermodynamics 86
IV


4.2.2Solid Solution Models 89
4.2.2.1 Ideal Solution Model 94
4.2.2.2 Strictly Regular Solution
Model 9 6
4.2.2.3 Delta Lattice Parameter
Model 100
4.2.2.4 First Order Quasi-Chemical
Model 10 4
5 PROCESS CONTROLLABILITY & OPTIMUM OPERATION
CONDITION 112
5.1 Interdependence of Process Parameters
in Hydride VPE of InGaAsP 117
5.2 Compositional Sensitivity 120
5.3 Parameter Value Fluctuation 121
5.4 Process Controllability Evaluation 124
5.5 Process Controllability Study 125
5.5.1 InGaAs Lattice-Matched to InP 125
5.5.2 InGaAsP Lattice-Matched to InP.... 130
5.6 Process Sensitivity Analysis 133
5.6.1 Relative Sensitivities in Hydride
VPE of InGaAs 136
5.6.2 Relative Sensitivities in Hydride
VPE of InGaAsP 142
6 MODELING OF GALLIUM AND INDIUM SOURCE
REACTORS 15 5
6.1 Thermodynamic Model 158
6.2 Nonequilibrium Mechanisms 160
6.2.1 Chemical Reaction Kinetics 160
6.2.2 Transport Phenomena 164
6.2.2.1 Hydrodynamic and Thermal
Entrance Region Effects... 165
6.2.2.2 Mass Transport in the
Reaction Zone 169
6.3 Transport Models 171
6.3.1 2-D Convective Diffusion Model.... 171
6.3.2 Axial Dispersion Model 179
7 EXPERIMENTAL STUDY OF GALLIUM AND INDIUM
SOURCE TRANSPORT AT NORMAL PRESSURE 18 6
7.1 Literature Review 186
7.2 Experimental Method 187
7.3 Data Analysis 193
7.4 Results and Discussion 194
7.4.1 Gallium Source Transport 194
7.4.2 Indium Source Transport 203
8 EXPERIMENTAL STUDY OF GALLIUM AND INDIUM
SOURCE REACTIONS AT LOW PRESSURE 214
V


8.1 Equilibrium Calculations 214
8.2 Experimental Method 218
8.3 Data Analysis 223
8.4 Results and Discussion 223
8.4.1 Gallium Source Reaction 223
8.4.2 Indium Source Reaction 228
9 CONCLUSIONS AND RECOMMENDED FUTURE WORK 234
9.1 Conclusions 234
9.2 Discussions and Suggested Future Work... 241
REFERENCES 245
BIOGRAPHICAL SKETCH 250
vi


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PROCESS DESIGN ISSUES
IN HYDRIDE VAPOR PHASE EPITAXY OF
INDIUM GALLIUM ARSENIDE PHOSPHIDE
By
JULIAN JUU-CHUAN HSIEH
April 1988
Chairman: Dr. Timothy J. Anderson
Major Department: Chemical Engineering
Hydride vapor phase epitaxy (VPE) has been used to
prepare indium gallium arsenide phosphide thin film devices
in the industry. One objective of process design for hydride
VPE of In]__xGaxASyP2__y is to achieve composition control of
deposited epitaxial films. The resolution of this process
design issue involves investigating the dependence of solid
solution composition on various process parameters.
Complex chemical equilibrium analysis of the
In/Ga/As/P/Cl/H system is constructed with the required
thermochemical data and calculation procedures to evaluate
the dependence of solid solution composition on process
parameters at equilibrium conditions. Simulation of
composition controllability at different parameter settings
was also investigated for the growth of two technologically
vii


important compositions, In.53Ga.47As and In.74Ga.26As.56P.44
The results indicate the range of parameter settings for best
control of composition.
Transport and reaction kinetic limitations were found to
exist in gallium and indium source reactors in hydride VPE.
The nonequilibrium mechanisms slow down the reaction of
hydrogen chloride with gallium and indium. Experimental
characterization of source reactors was carried out at normal
pressure in the temperature range 943-1131 K. The reaction
products, group III metal chlorides, were collected in cold
traps and the group III transport rate was measured by atomic
absorption spectrometry. Group III monochloride was found to
be the dominant reaction product. With the application of a
two-dimensional convective diffusion model, first-order
heterogeneous rate constants were determined for both gallium
and indium source reactions. In order to study the reaction
kinetics of HC1 with liquid Ga and In at dif f us ion 1 e s s
conditions, low pressure (< 1 Torr) experiments were carried
out in the temperature range 973-1223 K. The HCl consumption
was measured by mass spectrometry and an axial dispersion
model was developed to reduce the data. First order rate
constants determined at low pressure were quite different
than determined from the normal pressure results. It is
suggested that quite different surface conditions or reaction
mechanisms exist at different pressures.
viii


CHAPTER 1
INTRODUCTION
Vapor phase epitaxy (VPE) of group III-V compound
semiconductors by the hydride process has proved to be a
successful method for producing device quality films,
particularly for growth of In]__xGaxAsvP]__y solutions [1]. In
this process the source species are gaseous group V hydrides
and volatile group III chlorides generated by reacting HC1
with liquid group III metal at elevated temperature.
Control of the solid solution composition is the primary
concern in process design of hydride VPE for thin film
deposition of In.]__xGaxASyP]__y solutions. The large number of
process parameters and the incomplete understanding of how
these parameters influence composition control, however, have
complicated process design issues and discouraged potential
users.
In this dissertation work, a unified approach to the
process design issues was attempted. The process design
considerations were taken to identify the important process
design issues. The relationships between the process
parameters and the process controlling mechanisms,
thermodynamics, transport phenomena and reaction kinetics,
were established. Composition controllability and source
1


2
zone reaction kinetics were two areas of particular interest
in the process design of hydride VPE of Ini_xGaxASyP]__y.
These two topics form the central theme of this dissertation.
Chapter 2 presents a survey of some physical and
electrical properties of III-V compound semiconductors and
the practical importance of the quaternary semiconductor
material Ini_xGaxASyP]__y. Most device applications of III-V
compound semiconductors require successful growth of
epitaxial film.
In chapter 3, hydride VPE is introduced and reviewed.
Both process thermodynamics and nonequilibrium mechanisms,
transport and kinetics, are important for process design
considerations. This chapter is concluded with an outline of
the important process design issues in hydride VPE of
I ril XGaxASyP J^_y .
A complex chemical equilibrium analysis is performed to
determine the equilibrium composition of the system under
specified conditions. Formulation and calculation procedures
for complex chemical equilibrium analysis in the
In/Ga/As/P/H/Cl system are detailed in chapter 4. Process
controllability, specif-ical ly the solid solution composition
controllability, can also be evaluated through the aid of
complex chemical equilibrium analysis. Controllability
studies for two technologically important Ini_xGaxAsvPi_v
compound compositions are reported in chapter 5.


3
A thermodynamic model and transport models are presented
in chapter 6. These models were developed to assist
definition of experimental operating conditions and reactor
geometry and to interpret the experimental data.
Experimental studies of the performance of gallium and
indium source reactors at both atmospheric and reduced
pressure are presented in chapter 7 and chapter 8,
respectively. The data were analyzed by the application of
the appropriate transport model. Rate expressions are
deduced and reported.
Conclusions on composition controllability study and
source zone transport reactions are given in chapter 9. The
results of the experimental studies are compared and
discussed. Finally, areas for future investigation of
process design issues in hydride VPE of In]__xGaxAsvP^_v
suggested.
are


CHAPTER 2
III-V COMPOUND SEMICONDUCTORS
2.1 Physical and Electrical Properties
Table 2-1 lists the band gap energy, lattice parameter,
refractive index, dielectric constant, conduction band
effective mass and valence band effective mass of the nine
binary III-V compounds made from group III atoms(Al, Ga or
In) and group V atoms(P, As or Sb) Five of the nine
compounds(InP, GaAs, InAs, GaSb and InSb) have a direct
energy gap. In general, increasing the atomic weight of the
group III or group V element decreases the band gap energy,
increases the refractive index, and the lattice parameter
increases with the exception of Ga-Al pairs. The In and Ga
binary III-V compound are available as substrate materials.
Ternary -and quaternary mixtures usually have properties
intermediate between the end components. Most device
applications include heteroepitaxial growth of multicomponent
solutions that are lattice-matched to the available binary
substrates. These structures permit variation of the band
gap energy, which provides physical and electrical properties
and device applications beyond the range possible with
elemental semiconductors.
4


5
Table 2-1. Lattice parameter, band gap energy, refractive
index, electron effective mass and hole effective
mass of III-V binary compounds.
III-V
binary
compound
Lattice
parameter
(nm)
Band gap
energy
(eV)
Refractive
index
Electron
effective
mass
Hole
ef f ectiV'
mass
A1P
.54625
2.45(1)
3.027

0.70mQ
AlAs
.56611
2.16(1)
3.178
0.15 mg
0.79mo
AlSb
.61355
1.58(1)
3.400
0.12 mg
0.9 8mQ
GaP
.54495
2.261(1)
3.452
0.0 82mQ
0.6 OmQ
GaAs
.56419
1.42(D)
3.655
0.067mo
0.4 8mo
GaSb
.60940
0.81(D)
3.820
0.042mo
0.44mo
InP
.58687
1.35(D)
3.450
0.0 77mQ
0.64mQ
InAs
.60584
0.36(D)
3.520
0.0 23mo
0.40mo
InSb
.64788
0.236(D)
4.000
0.0145mo
0.40mo
(I): indirect band gap
(D): direct band gap


6
When more than one element from group III or group V is
distributed on group III or group V lattice sites,
11IXI111_XV or IIIVyV]__y ternary alloys can be achieved.
There are 18 possible ternary systems among the group III
elements(Al, Ga, In) and group V elements(P, As, Sb).
The band gap energy Eg(x) or Eg(y) of a ternary compound
can be represented as a quadratic function of composition.
For example,
Eg(x) = Eg/0 + ax x + a2 X2 (2-1)
where Egfo is the band gap energy of the binary compound at
x = 0. The bowing parameter a2 has been determined
theoretically by Van Vetchen and Bergstresser [2]. Their
theory may be used to estimate a2 when experimental data are
unavailable. The lattice parameter of a ternary compound is
generally well represented as a linear function of the alloy
composition. This is called the Vegard's law, which is
obeyed quite well in III-V ternary alloys. The composition
dependence of the direct energy gap in the III-V ternary
solid solutions at 300 K can be found in the literature [3].
Two kinds of quaternary compounds exist. The first kind
is of the type AyBzC]__y_zD, where A, B and C are group III
elements, or the type AByCzDi_y_z, where B, C and D are group
V elements. This kind of quaternary compound can be
considered as composed of three binary compounds. The


7
calculation of lattice constant for this kind of quaternary
compounds obeys Vegard1s law. The second kind is of the type
Ai_xBxCi_yDy, where A and B are group III elements, and C and
D are group V elements. This kind of quaternary compound can
be considered as composed of two ternary compounds (1-x mole
fraction of ACyD]__y and x mole fraction of BCyD]__y, or 1-y
mole fraction of A]__XBXC and y mole fraction of A^_XBXD) or
of four binary compounds (AC, BC, AD and BD) of indeterminate
molar percentages. Ilegem and Panish [4] calculated the
phase diagrams for the second kind with the quaternary alloy
decomposed into ternary alloys. Jordan and Ilegems [5]
obtained equivalent formulations by treating the solid as a
mixture of binary alloys: (l-x)y AD, (1-x)(1-y) AC, x(l-y) BC
and xy BD. The lattice parameter of the quaternary alloy
Al _xBxC]__yDy is assumed to depend linearly on the composition
of its ternary components. Since the lattice parameter of a
ternary compound can be determined by Vegard' s law, so the
lattice parameter ag of the alloy A]__xBxC]__yDv is given by
a0 = (1-x)y aAD + xy aBD + x(l-y) aBC
+ (1-x)(1-y) aAC (2-2)
The band gap energy determination is more complicated. The
bowing parameters, however, are found to be small and can be
neglected and the band gap energy may be approximated from
the band gap of the binaries as follows


8
Eg = (l-x)y Eg AD + xy Eg BD + x(l-y) Eg BC
+ (1-X) (1-y) EgrAC. (2-3)
Figure 2-1 [6] illustrates schematically the variation
of the band gap energy and the lattice parameter with respect
to composition for the second type quaternary compound
InGaAsP. Also shown in figure 2-1 are the composition planes
of two compounds of the first kind, AlGalnAs and AlGalnP.
Each compositional plane of the first kind is surrounded by
three ternary compositional lines, with a total of three
binary endpoints, and thus triangular. The quaternary
compositional plane of the second kind, enclosed by four
ternary lines and four binary points, is always square.
Constant lattice parameter and constant direct band gap
energy are shown in the compositional plane of InGaAsP in
figure 2-1 by solid lines and broken lines, respectively.
The boldface lines indicate the ternary and quaternary
compositions lattice-matched to binary compounds, with the
solid line for GaAs lattice matching compositions and the
broken line for InP.
2.2 Material and Device Perspectives
The existence of a direct energy gap in compound
semiconductors (e.g., InSb, InAs, InP, GaSb and GaAs) is in
contrast to the indirect band gap of Si and Ge. In general,
direct band gap materials also have a high electron mobility.
These properties offer the potential for high efficiency


9
Al As
Figure 2-1. The compositional plane for In^_xGaxAsvPi_y at
300K [6]. The boldface solid line represents the
GaAs-lattice matching composition. The boldface
broken line represents the InP-lattice matching
composition. The solid lines are for constant
lattice parameters. The broken lines are for
constant direct bandgap energy values. The
shaded area at the lower left corner is the
indirect band gap region.


10
light emitting, light sensing, and high speed switching
devices. With the band gap energy of these compounds ranging
from 0.17 eV (InSb) to 2.2 eV (GaP), these compounds provide
an ideal basis for the preparation of semiconductor materials
with the desired energy gap over a continuous spectrum of
energies.
Because of the difficulties related to the preparation
of single crystals of III-V compounds, all of the available
single crystal substrate materials are binary compounds.
Although all of the Ga and In binary compound are available,
only GaAs and InP are produced in large quantity with good
quality at the present time. In order to access the full
range of property values offered by ternary and quaternary
compounds, it is necessary to grow layers of the desired
composition of the ternary or quaternary compound on a binary
substrate by the technique called "epitaxy." Epitaxy has
been used successfully in forming heterojunctions of III-V
compounds. A heterojunction is a junction in a single
crystal between two compositionally different semiconductors.
Due to the band gap differences across heterojunctions, the
effects of carrier and optical confinement are provided and
applications in optoelectronics and high-speed switching
devices are realized. Heterojuction devices, however,
require a low interfacial state density which demands good
lattice matching to reduce tension between the different
materials. Except for (Ga, Al)-containing ternary systems,


11
the IIIV semiconductor ternary alloys suffer from severe
problems associated with lattice mismatch when grown on
binary substrates. The addition of a fourth component to the
alloy system gives a quaternary compound and allows the band
gap to be changed while maintaining a lattice parameter
matched to a particular binary substrate. Therefore, the
interest in quaternary alloys has centered on their use in
conjunction with binary and ternary compounds to form
lattice-matched heterojunction structures with different band
gaps. The Ini_xGaxASyP]__y/InP hetero junction with 2.12x=y is
one example of a lattice-matched system.
2.3 Binary, Ternary and Quaternary InGaAsP Compound
2.3.1 Applications
In terms of present device applications, InGaAsP is the
most important III-V quaternary compound semiconductor.
Figure 2-1 indicates the lattice parameter and the band gap
energy for any given InGaAsP composition. To maintain a
given lattice constant for the quaternary system a
simultaneous variation of the Ga/In and As/P ratio is
required. Both InP and GaAs are useful substrate materials
for lattice-matched heterojunctions. The InP-based system
covers the band gap energy range 0.75 to 1.35 eV (wavelength
range 1.65 to 0.92 micrometer) while GaAs-based system ranges
from 1.42 to 1.9 eV (0.87 to 0.65 micrometer). InGaAsP


12
matched to InP covers a longer wavelength region and as a
result the material has aroused great interest for sources in
optical fiber communications systems operating at 1.3
micrometer and 1.55 micrometer where high-quality fused
silica fibers exhibit minimum transmission loss (less than 1
dB/km) and minimum material dispersion. The ternary endpoint
of this InGaAsP system, In.53Ga.47As lattice-matched to InP
has been developed as light detectors to complement the 1.3
to 1.6 micrometer light sources. InGaAsP matched to GaAs
with shorter wavelength is also of interest in the
applications of visible lasers and light-emitting diodes.
The interest in InGaAsP lattice-matched to InP has been
expanded to microwave device applications ever since superior
mobilities and velocity-field characteristics were predicted
from theoretical calculations [7] on both GaAs and InP.
Later experimental observations, however, did not agree with
the calculated curves of low-field mobility across the
composition range, except for the ternary end-point,
In 53Ga.47As Consequently, attention has been focused on
this ternary. Room temperature mobilities of 11,000 to
13,800 cm^/v-sec have been recorded [8-10] and these are the
highest mobilities of any III-V semiconductor suitable for
room temperature operation. With high peak velocity and low
threshold field [11, 12], transferred electron oscillation
devices with improvements over GaAs and InP are possible.
Computer calculations [13] also showed that In.53Ga.47As


13
(lattice-matched to InP) offers superior dynamic properties
to InP or GaAs. Since the high frequency operation makes use
of transient properties of the material rather than steady-
state properties, the ternary material would appear to be a
very useful candidate in microwave and millimeter-wave
applications.
Future devices that are likely to achieve considerable
attention are integrated circuits involving both optical and
high-speed logic devices. Integrated optical circuits will
contain sources (laser or light-emitting diode), passive
waveguides, modulators, couplers, switches and detectors all
on one chip. This is possible due to the versatile
properties of the InGaAsP alloy range lattice-matched to InP.
High-speed integrated logic devices could combine the
sensitive current control and short delay time of Gunn
devices with stable on-off operation of MESFET devices, all
made of InGaAsP lattice-matched to InP.
2.3.2 Epitaxy
Figure 2-2 shows the simplified diagrams of two typical
InGaAsP/InP heterojunetion devices, a InGaAsP double
heterostructure (DH) semiconductor laser and a InGaAs
photodetector. For both of these heterojuction devices, it
is required to grow layers of semiconductor materials of
different compositions on top of the substrate. Such
controlled growth of crystal, termed "epitaxial growth," has


14
a
b
Figure 2-2. Simplified diagrams for typical InGaAsP/InP
hterojunction devices. a. InGaAs/InP diode
photodetector. b. double heterostructure
semiconductor laser.


15
been accomplished by a number of techniques, including
hydride vapor phase epitaxy(hydride VPE), trichloride vapor
phase epitaxy(chloride VPE), metalorganic chemical vapor
deposition (MOCVD) liquid phase epitaxy (LPE) and molecular
beam epitaxy (MBE). Excellent reviews are in the literature
which discuss the general aspects of these techniques (e. g.
hydride VPE [14], trichloride VPE [15], MOCVD [16], LPE [17],
and MBE [18]) .


CHAPTER 3
HYDRIDE VAPOR PHASE EPITAXY OF
INDIUM GALLIUM ARSENIDE PHOSPHIDE
Hydride vapor phase epitaxy is a member of the set of
processes termed vapor phase epitaxy(VPE). VPE processes
adopt a halide transport chemistry, in which the group III
elements are transported to the deposition reaction region in
the form of group III halides. For chloride representing the
halide species, the monochloride e.g., GaCl or InCl is the
dominant species at elevated temperature. Depending upon how
the group V species is introduced into the reactor, two
techniques exist in VPE: the "hydride" technique [19] and the
"trichloride" or simply "chloride" technique [20]. The main
attraction of the chloride technique is its ability to
produce epitaxial materials with extremely low background
impurity levels. One drawback of the chloride process is
that gaseous group V trichloride is introduced by evaporation
of a liquid, and therefore its transport rate varies
exponentially with temperature. The major drawback, however,
is that the transport rate of group III chlorides is
determined by the input flowrate of group V trichloride,
therefore independent control of III/V ratio is not possible
with the chloride technique. The gas phase III/V ratio above
the growing film determines the point defect structure of the
16


17
grown film and therefore the electrical properties. The
hydride system, on the other hand, has the advantage that all
input reactants to the system are gaseous and can be
independently controlled in a linear manner. The drawbacks
of the hydride process include less purity of the starting
materials (i.e. group V hydrides) and increased safety
concern in handling hydrides. In spite of the disadvantages,
hydride VPE is widely accepted in the industry, especially
for the preparation of ternary and quaternary alloys of In
and Ga.
3.1 Process Chemistry
The chemistry of the hydride vapor phase epitaxy
technique can be illustrated by describing the reactions
involved in the growth of gallium arsenide. A representative
schematic diagram of a hydride VPE reactor used for the
preparation of GaAs is shown as in figure 3-la. The reactor
is usually heated by a multi-zone resistance furnace. The
most upstream temperature zone, operated in temperature range
1000-1150 K, is termed the source zone. In this zone, HC1 is
introduced into the reactor in a carrier gas, usually H2, to
react with pure gallium liquid to form principally gallium
monochloride
Ga(1) + HC1 < > GaCl + 1/2 H2.
(3-1)


18
Source
Zone
Mixing Deposition
Zone Zone
1 050-1 150K 11 00-1 200K 950-1050K
a
b
Figure 3-1. Schematic diagrams of hydride VPE processes.
a. growth of GaAs. b. growth of In^_xGaxASyP1_y


19
Arsine, diluted by the carrier gas, is introduced in the
second temperature zone (the mixing zone) which is operated
at temperature equal to or slightly above the source zone.
In the mixing zone part of arsine thermally decomposes
forming molecular arsenic species and hydrogen. The main
reactions are
ASH3 < > 1/2 As2 + 3/2 H2
(3-2)
As2 < > 1/2 As4
(3-3)
The decomposition of arsine is pyrolytic with arsenic dimer,
As2, and tetramer, As4, being the major products. Depending
upon the reactor design and the operating condition of the
mixing zone, the dominant arsenic species can be unreacted
ASH3, As2 or As4. Gallium monochloride, unreacted HC1 and
arsenic-containing species are then mixed in the mixing zone
and transported to the deposition zone. Gas-solid reactions
occur in the deposition zone in the temperature range 9 5 0-
1050 K. The major reactions are
GaCl + 1/2 As2 + 1/2 H2 < > GaAs(s) + HC1 (3-4)
GaCl + 1/4 As4 + 1/2 H2 <
\
/
GaAS(S) + HC1
(3-5)
GaCl + ASH3 < > GaAs(s) + KC1 + H2
(3-6)


20
Each of the above reactions are thought to contribute to the
overall deposition rate. The presence of all of these
species in the deposition zone have been confirmed by Ban in
by mass spectrometric sampling [21] The total growth rate
and the relative importance of a particular reaction path
depend upon the gas phase makeup in the deposition zone. The
double arrow (< >) sign in equations (3-1) to (3-6)
indicates that these reactions are reversible.
Similar chemistry exists for the growth of indium
phosphide if gallium is replaced by indium, and arsine by
phosphine. Ternary and quaternary alloys of the gerneral
chemical formula Inj__xGaxASyP]__y can also be grown by this
technique. Figure 3-lb shows the schematic diagram of a
reactor used for growing In]__xGaxASyP]__y quaternary alloy.
In this reactor design, two separate HC1 flows are admitted
to the source zone to independently transport indium and
gallium. Arsine and phosphine are introduced into the mixing
zone through the same gasline, and partially decompose to
group V molecular species. In addition to the formation of
the dimers and tetramers of the group V elements, molecules
composed of both arsenic and phosphorous atoms are also
possible. For example,
As2 + P2 < > 2 AsP (3-7)
n As4 + (4-n) P4 < > 4 AsnP4_n
n
1,2,3
(3-8)


21
The deposition process for the growth of InGaAsP, involving
all the chemical species generated and transported before
deposition zone, is very complicated and can not be
represented by a simple equation. However, the net equations
of the deposition reactions can be written as follows
r1: GaCl + 1/4 As4 + 1/2 H2 < > GaAs(s) + HC1 (3-9)
r2: GaCl + 1/4 P4 + 1/2 H2 < > GaP(s) + HC1 (3-10)
r3: InCl + 1/4 P4 + 1/2 H2 < > InP(s) + HC1 (3-11)
r4: InCl + 1/4 As4 + 1/2 H2 < > InAS(s) + HC1 (3-12)
Clearly, the overall deposition rate should be the sum of the
deposition rate for each binary compound. Thus the overall
deposition rate, r(-, is equal to r ]_ + r 2 + r 3 + r 4 The
composition of the quaternary solid solution can also be
determined by the binary deposition rates through the
following mole balance equations
x = (r1+r2)/rt = Xi + X2 (3-13)
1x = (r3+r4)/rt = X3 + X4 (3-14)
1-y = (r2+r3)/rt = X2 + X3
(3-16)


22
y = (ri + r4) /rt = X]_+ X4
(3-17)
where
Xi = r/rt/ i=l,2,3 & 4 (3-18)
(X4, X2, X3, X4) is defined as the nearest neighbor pair
distribution. There values can be considered as the mole
fractions of the four binary compounds in the quaternary
alloy Ini_xGaxASyPi_y. The crystal is constructed at the
atomic scale by filling the crystal lattice with binary
pairs. For each nearest neighbor pair distribution, there is
only one corresponding solid composition (x, y). Since there
are infinite number of ways to fill the crystal lattice with
four binary pairs, the number of nearest neighbor pair
distribution for a fixed composition (x, y) is infinity.
This is a unique feature of the III-V quaternary compound of
the second kind.
The deposition reactions, equations (3-9) to (3-12), are
exthothermic, therefore deposition extent increases with
lower temperature. For this reason, resistance heated
reactors with hot walls are usually employed and the mixing
zone temperature is usually raised higher than both the
source zone and the deposition zone to prevent oversaturation
and extraneous deposition. The high temperature of the
mixing zone also enhances the decomposition of the group V


23
hydrides. Ideal epitaxial growth in the deposition zone
requires a well-controlled gas phase supersaturation over the
substrate. This condition is obtained by careful design of
the process apparatus and complete understanding of the
process behavior.
3.2 Literature Review
The epitaxial growth of GaAs by direct synthesis from
evaporated solid arsenic and gallium chloride was reported by
Amick [22]. Tietjen and Amick [19] redesigned Amick's
apparatus to permit the introduction of arsenic in the form
of its arsenic hydride, ASH3, and reported the preparation of
homogeneous solid solutions of gallium arsenide-gallium
phosphide, GaASyP]__y, by the addition of arsine and phosphine
in the reactor at the same time. The objective was to
develop a process which permitted independent control of the
partial pressures of group V and III species. Before the
adoption of this technique, liquid or solid arsenic and
phosphorus were sometimes provided as the group V sources,
which results in exponential dependence of the vapor
pressures on the temperature of the source reservoirs. This
dependence, although not critical for binary compound growth,
is extremely important for the preparation of homogeneous
ternaries and quaternaries. Hydride gas sources can also be
diluted in hydrogen to any desired concentration, and metered
into the apparatus through electronic mass flow controllers,


2 4
allowing the introduction rate to be held constant and
measured with precision. The independent control of arsine
and phosphine flowrates provided the possibility of gradual
or rapid changes in the composition of the growing layer.
Also, because of the separation of the introduction of group
III and group V species, variation of V/III ratio is
achievable. Doping of both n-type and p-type over a wide
range of resistivity can be obtained with different V/III
ratios. Because of its success in preparing homogeneous
GaASyP^-y alloys for a wide range of doping concentrations
and its versatility to grow multi-layer structure, hydride
VP E was adopted industrially in the mass production of
GaASyPi_y light emitting diodes.
The vapor growth of InGaAsP lattice-matched to GaAs was
first reported by Olsen and Ettenberg [23], Sugiyama et. al.
[24] and Enda [25]. Hydride VPE of InGaAsP lattice-matched
to InP has been described by Olsen et. al. [26], Beuchet et.
al. [27], Hyder et. al. [28], Mizutani [29] and Yanase et.
al. [30]. The hydride VPE of InGaAs lattice-matched to InP
has been reported by Susa et. al. [31], Olsen et. al. [32]
and Zinkiewicz et. al. [33].
A single-barrel hydride VPE reactor for the growth of
I n i_xGaxASyP]__y is exemplified as in figure 3-lb. The
associated chemistry has been introduced in section 3.1. It
is cumbersome to prepare multi-heterojunction layers in the
single-barrel reactors because the substrate has to be slid


25
out of the deposition zone during reactant changeover and the
subsequent transient period. During this period the surface
quality is not always preserved. In recent years multi
barrel hydride VPE reactors have been reported by a number of
researchers [27, 29, 34]. The concept involves the use of
more than one conventional VPE systems placed in parallel and
feeding into a single growth chamber. With multi-barrel
reactors, different gas mixtures can be run through different
source tubes, so that multiple heterojunction devices can be
prepared by simply switching the substrate from one tube to
the other, thus removing the need for preheat cycles. Growth
time is reduced and reactant chemicals are conserved in this
manner. In addition, surface defect states, induced by
preheating, are also minimized, improving the quality of the
heterojunction interface.
The process parameters that affect the growth rate and
the solid solution composition have been found to be the
reactant and carrier gas flowrates and the zone temperatures.
Since the Gibbs energy of formation for Ga arsenides and
phosphides are more negative than for the corresponding In
compounds, a higher HCl flowrate over the In source is
required than over the Ga source. Similarly, higher PH3
flowrate than ASH3 flowrate is required since phosphorus
compounds have higher vapor pressure at equilibrium than
arsenic compounds. For ternary compounds, increasing the
temperature will tend to increase the composition of the


26
binary component whose Gibbs energy of formation decreases
most with temperature. Thus, by increasing the deposition
temperature while holding other parameters constant, more Ga
and As tend to be incorporated in the solid solution.
Increasing the carrier gas flowrate results in a decrease of
reactant gas partial pressures and brings the same effect as
increasing deposition temperature. Growth rate, gas phase
transport and temperature uniformity in the deposition zone
are important factors to achieve film thickness uniformity
and compositional uniformity across the wafer.
Similar to other epitaxial processes, there has been an
ongoing effort to improve the purity of hydride VPE films.
Early studies [35, 36] reported that the purity of the HC1
and ASH3 was crucial to the material quality. But, later
published results on the chloride VPE system [37] showed that
in addition to certain fundamental parameters such as
reactant purity and general system cleanliness, impurity
incorporation in the epitaxial film is significantly
influenced by process parameters(e.g. input ASCI3 mole
fraction, substrate orientation and substrate temperature).
It was proposed- by DiLorenzo and Moore [38] that silicon is
the major residual donor and the carrier concentration in
undoped (100) GaAs, prepared by chloride VPE, is determined
by the silicon activity in the vapor phase above the
substrate. This unintentional silicon doping is brought
about by the decomposition of chlorosilanes, which are formed


27
from the reduction of the silica reactor by hydrogen carrier
gas and hydrogen chloride. This doping reaction can be
described as follows
STEP 1: chloro-silane formation at reactor wall
n HC1 + Si02 + (4-n) H2 < > SiClnH4_n + 2 H20 (3-19)
STEP 2: silicon incorporation at substrate
(n2) H2 + SiClnH4_n < > Si + n HC1 (3-20)
where n=0,1...4. At elevated temperature, equilibrium of the
above reaction steps is quickly attained. From equation (3-
20) it is clear that the unintentional doping level of
silicon in the growing GaAs epitaxial layer should decrease
with an increase of HC1 in the vapor phase. This theory
successfully explained the decrease of carrier concentration
and the increase in electron mobility in the preparation of
GaAs in trichloride method by increasing the partial pressure
of ASCI3. In light of this finding, Kennedy et. al. [35]
studied the effect of the hydrogen carrier gas flow rate on
the electrical properties of epitaxial GaAs prepared in a
hydride system. By reducing the hydrogen carrier gas flow
rate while holding the flowrates of HC1 and ASH3 constant,
thus raising the mole fraction of HC1 in the vapor phase,
improvement of epitaxial film quality, including a decreasing
total impurity level, decreasing carrier concentration and


28
increasing electron mobility were obtained. This result
seemed to agree with Dilorenzo's explanation of silicon
incorporation in chloride VPE. When additional HC1 was
introduced downstream of the reactor source zone, however,
further improvement, anomalous results were observed. The
anomalous doping behavior could not be explained by the
Dilorenzo model or by impurities contained in the reactant
gases. Pogge and Kemlage [39] studied the effect of arsine
on impurity incorporation and proposed a surface kinetic
model. The decrease of residual silicon concentration with a
higher ASCI3 mole fraction in the trichloride system,
observed by DiLorenzo [40], was explained by Pogge's model as
a result of blocking of impurity atoms from the surface sites
by the adsorption of As 4. Since surface sites can be
occupied by the adsorption of both arsenic and gallium
chloride, the unintentional doping level should decrease with
an increase in the total concentration of arsenic and gallium
chlorides in the vapor phase. The findings of Kennedy et.
al. [35] could also be explained by this model. In fact, by
using Pogge's model and considering that the total
concentration of group V molecules and group III chlorides in
hydride VPE has been traditionally lower than chloride VPE,
one could perceive why the resulted epitaxial film prepared
by hydride VPE has had higher residual impurity and inferior
carrier mobility than what has been achieved by chloride VPE.
Abrokwah et. al. [41], using a commercial hydride VPE,


29
achieved undoped epitaxial GaAs of high purity comparable to
the best chloride VPE results. The effects of the flowrates
of HC1 over Ga source and arsine were studied and showed
qualitative agreement with Pogge's theoretical model. When
the arsine flowrate or the HC1 flowrate over gallium was
increased a higher purity in the epitaxial film was achieved.
When a secondary HCl flow was introduced at the downstream of
the gallium boat, the film purity was decreased and the
epitaxial layer was more compensated as a result of increased
acceptor incorporation. The secondary HCl probably does
react with SO2 introducing some amount of silicon to the
growing layer; however, the incorporation mechanism might be
kinetic and cannot be compared with DiLorenzo's equilibrium
model. It was realized also in Abrokwah's study that a clean
gallium surface can gather metallic contaminants in the HCl
flow, thus reducing acceptor incorporation and compensation.
An aging effect of the HCl tank was also observed to create
high level of metallic chloride contaminants, affecting
epitaxial layer quality and should be carefully taken into
account. Because of the contamination problems related to
the HCl tank, the studies on the influence of HCl
concentration on silicon donor level by a secondary HCl flow
have so far failed to give interpretable results on the
incorporation mechanism of this residual donor. By far-
infrared photoconductivity and low temperature
photoluminescence measurements, Abrokwah et. al [41] also


30
found sulfur to be the dominant residual donor, and carbon
and zinc to be the major acceptors in their undoped GaAs
prepared by the hydride VPE technique. By cooling the HC1
liquid source to 198 K, Enstrom and Appert [42] reported
consistently improved mobility and impurity incorporation in
hydride VPE of GaAs and InGaAsP. Improved results were
obtained even after extended use of the HC1 at room
temperature after initial cooling. It was argued that when
liquid HC1 is cooled, impurities are forced out of the HC1
phase and can then be swept out of the tank during a short
purge conducted prior to use for vapor growth. From these
studies, it is clear that in order to obtain ultra-pure
undoped GaAs by hydride VPE, one has to (i) maintain the HC1
tank at high purity, (ii) avoid secondary HC1, (iii) maximize
arsine flowrate to block residual donors (e.g. Si, S)
incorporation, (iv) minimize HC1 flowrate to reduce residual
acceptors (Cu, Zn) contamination levels, (v) prevent
contaminants (C, O, S) from leaks and (vi) maintain the
overall cleanliness of the apparatus. Hydride VPE generally
produces InGaAsP crystals with background impurity
concentrations around 5-20 x 1015 per cubic centimeter. This
unintentional doping level is low enough to produce good
laser and light-emitting-diode structures.
P-type doping can be accomplished by heating a bucket of
zinc in a hydrogen atmosphere in order to obtain elemental
zinc vapor or by introduction of gaseous diethyl-zinc (DEZ).


31
N-type doping is accomplished by adding hydrogen sulfide to
the hydride line.
Surface defects(pits and hillocks) are the major
problems in the attainment of good surface morphology.
Kennedy and Potter [43] studied the effect of various growth
parameters on the formation of pits and hillocks on the
surface of epitaxial GaAs layers by hydride VPE and found
that the appearance of pits with a paucity of GaCl in the
vapor phase at the deposition zone and the appearance of
hillocks with an excess of GaCl in the vapor phase at the
deposition zone.
The advantage of hydride vapor phase epitaxy is the
finely controlled gas composition, which allows easy control
of alloy composition, doping and surface morphology. Hydride
VPE also has the potential of easy scale-up for large
quantity device manufacture. Hydride VPE has proved its
suitability for fabricating epitaxial Inj__xGaxASyP]__v
quaternary compound with high crystalline quality, planar and
uniform layers and reproducible properties. Thickness
uniformities of +5%, composition uniformities of +0.1%, and
interfacial transient width of 3.5 nm have all been reported
in the literature.
3.3 Process Design Issues
Process design involves both the appropriate design of
process equipment and the optimum choice of process operation


32
conditions. The ultimate goal is an efficient and effective
process, which can be judged by its performance in process
controllability, process reproducibility, and product
quality. Prediction of optimum process operation conditions
with a specific process equipment design requires a complete
understanding of how the process and the product quality
respond to the changes of process parameter settings.
Prediction of optimum operation conditions for hydride
VPE of In]__xGaxASyP]__y is difficult because of the complexity
of this reaction system. Whereas liquid phase epitaxy can be
considered to take place under near equilibrium and
deposition from metalorganic chemical vapor deposition
(MOCVD) is a typical nonequilibrium process, both hydride VPE
and chloride VPE are intermediate techniques. In general,
equilibrium is not achieved in hydride VPE and the effect of
reaction kinetics and mass transfer can further shift the
reactor performance from the thermodynamic values. A
meaningful description of the hydride VPE process requires
considerations of both the equilibrium (thermodynamics) and
the nonequilibrium (reaction kinetics, mass transfer) aspects
of the process.
3.3.1 Process Thermodynamics
A thermodynamic treatment of a hydride VPE process
requires knowledge of the chemical species present in the
process and the appropriate thermodynamic data of these


33
species. In addition, for growth of a ternary or a
quaternary alloy, a solid solution model that describes the
activities of each binary constituents in the alloy has to be
chosen.
A detailed thermodynamic treatment of hydride VPE of
Ini_xGaxASyPi_y will be discussed in Chapter 4. Here, a
simplified treatment for hydride VPE of GaAs is given as
follows. The objective of this treatment is to demonstrate
how the maximum attainable deposition rate is determined by
equilibrium considerations only and why the real deposition
rate can be different from the thermodynamically predicted
values.
From the calculation of Hurle and Mullin [44] it can be
assumed that H2 HC1, GaCl and A s 4 are the only
quantitatively important species during hydride VPE of GaAs
when Cl/H, the ratio of the number of input chlorine atoms
over the number of input hydrogen atoms, and As/H, the number
of input arsenic atoms over the number of input hydrogen
atoms, are equal and less than 0.01. Therefore, it is
sufficient to consider the equilibrium between these chemical
species for the calculation of the equilibrium growth rate.
In the source zone, HC1 reacts with Ga to form GaCl at
source temperature Ts according to equation (3-1). If
equilibrium is reached and the hydrogen partial pressure is
close to 1 atm, the partial pressures of HC1 and GaCl have
the relationship,


34
pGaCl = K1 PHC1' (3-21)
in which is the equilibrium constant for reaction equation
(3-1). The chlorine balance equation is
p0HCl = PHC1 + pGaCl (3-22)
where P^HCl Is the HC1 partial pressure in the input flow.
From equations (3-21) and (3-22) PcaCl and PHC1 can be
solved.
PHC1 = 1/(1+Ki) PHC1 (3-23)
pGaCl = Ki/d + Ki) Phc1 (3-24)
Assuming complete decomposition of arsine in the mixing zone,
then
pAs = 1/4 PAsH (3-25)
4 3
The equilibrium deposition rate of reaction equation (3-
5) is dependent on the partial pressures of the reactants,
equations (3-23) to (3-25) and the deposition zone
temperature T. Clearly, if equilibrium is reached in the
deposition zone, then


35
Kd(Td)=-
HC1
(PHd + ss)
0.25
PS PS
GaCl As4
4
0.25
(3-26)
where is the equilibrium constant for equation (3-5), Pef
is the partial pressure of gas species i at equilibrium, and
ss is defined as the amount of super satura tion in the
deposition zone. Also assumed in equation (3-26) is that
carrier gas hydrogen is in excess with partial pressure close
to 1 atm. The equilibrium maximum attainable growth rate
(Rg) is proportional to the amount of supersaturation
available for deposition. Therefore, after solving equation
(3-26) for ss, Rg can be obtained from the following
equation.
R
g
SS Vf Vm
R T As
(3-27)
In the above equation, Vf represents the total volumetric
flowrate, R is the gas constant, Vm is the molar volume of
the solid compound, and As is the substrate surface area.
The actual deposition rate is always less than the rate
calculated above. When equilibrium is not reached in the
source zone and mixing zone, the supersaturation ss can be
very different from that calculated from equation (3-26).
Eesides, the actual deposition rate is influenced by mass
transfer, chemical kinetics and residence time in the


36
deposition zone. These nonequilibrium mechanisms drive the
deposition reaction away from the equilibrium growth
condition.
3.3.2 Nonequilibrium Mechanisms
In vapor phase epitaxy with open flow systems, the
reactive species are transported through the reactor tube
with a carrier gas and undergo chemical reactions along the
transport axis leading to a change in gas phase composition.
A sequence of steps is followed for these reactions to take
place.
STEP 1: Mass transport of chemical vapor reactants
(into the reaction zone)
STEP 2: Mass transfer of reactants to condensed
surfaces
(source zone: melt metallic III surface)
(mixing zone: quartz reactor wall)
(deposition zone: substrate surface)
STEP 3: Surface processes: adsorption, surface diffusion
STEP 4: Chemical reaction at the surface
STEP 5: Surface processes: diffusion, desorption


37
STEP 6: Mass transfer of gaseous reaction products away
from the surface
STEP 7: Mass transport of reaction products and
unreacted reactants
(away from the reaction zone)
Steps 2 and 6 represent mass transfer of species between the
main gas stream and the condensed surfaces. This transfer
occurs through physical mechanisms such as intermolecular
diffusion and convective diffusion. Reaction rates that are
limited by these steps are said to be controlled by mass
transfer or, in general, diffusion-limited. Steps 3,4 and 5,
involving adsorption, surface reaction, surface diffusion,
and desorption, are complicated. Although the separate
effect of each step is very difficult to determine, the
combined effect of these surface steps can be distinguished
from the physical mechanisms of diffusion and convection.
Reaction rates that are limited by surface mechanisms are
usually called kinetica1ly-1imited No matter how the
reaction rates are controlled, equilibrium results when the
main gas stream allows sufficient residence time, step 1 and
7, for the physical and chemical mechanisms, steps 2 to 6, to
achieve complete equilibration. In this case, the gas phase
composition at the outlet of the reaction zone (step 7) can
be determined by the gas phase composition of step 1


38
bypassing the consideration of the nonequilibrium mechanisms.
Thermodynamic equilibrium of hydride VPE system has been
briefly discussed in the last section.
When the process is controlled by nonequilibrium
mechanisms, process parameters, temperature, flowrates,
pressure, etc., influence the process behavior according to
the actual controlling step. For example, reaction rates for
kinetically-limited processes usually have very strong
temperature dependence, expressed as
r = r0 exp (-Ea/RT),
(3-28)
where r is the actual reaction rate, rg is the preexponential
constant, R is the gas constant, T is the reactor temperature
in Kelvin, and Ea is the activation energy for the surface
reaction or kinetic process. On the other hand, for a
diffus ion-1imited process, the temperature dependence is
relatively small. Gas phase diffusion coefficients for
molecular species are proportional to Tm, with m varying from
1.5 to 2. Another example is the dependence of process
behavior on gas phase hydrodynamics, which directly results
from the reactor design and flowrate settings. Diffusion-
limited processes are very sensitive to hydrodynamic effects,
while kinetically-limited processes are not influenced by
these parameters. Kinetica1ly-1imited processes are also
affected by the surface properties of the condensed phase


39
e.g., crystal orientation, surface cleanliness, surface
defects.
The slowest step of steps 2 to 6 determines the local
reaction rate. The rate-limiting step, however, can change
from point to point in a reaction zone causing the problem of
non-uniformity. As discussed above, the overall reaction
rate is determined partly by the local reaction rate and
partly by residence time. Since the local reaction rate is
different for different reactor design and operating
conditions, the required residence time for reaching
equilibrium (reaction completeness) varies from one system to
another. It is important to understand that the local
nonequilibrium mechanisms always exist regardless of the
length of residence time and the degree of reaction
completeness.
3.3.3 Process Design Considerations
Figure 3-2 outlines the process design considerations
for hydride vapor phase epitaxy of binary, ternary and
quaternary Ini_xGaxASyPi_y. The primary objectives, as
indicated in figure 3-2 by the shaded boxes, are to control
the epitaxial layer composition and thickness. The process
designer's choices, including the parameter settings and the
design of the three reaction zones, are represented in figure
3-2 by the bold-lined boxes. The solid-lined boxes in figure
3-2 connect "the process designer's choices" with "the


40
Figure 3-2. Outline of process design considerations for
hydride vapor phase epitaxy of InGaAsP.


41
primary objectives" and contain the thermodynamic, physical
and chemical events in the process. These events have been
discussed in sections 3.3.1 and 3.3.2.
Because thermodynamic information is already available
and the convective diffusion process can be mathematically
simulated, mass transport in the source zone can be
calculated for known source zone design and operating
parameter settings if reaction kinetics in the source zone is
also known. It has been a common assumption that the
transport reaction in the source zone is rapidly attained,
therefore careful studies on source reaction kinetics have
been scarce and quantitative rate expressions, most desirable
for process design, are still missing in the literature. A
similar situation occurs for design of mixing zone. Mass
transport in the mixing zone for a specific design and a set
of parameter settings can be simulated if the reaction
kinetics in the mixing zone are known. The pyrolytic
decomposition reaction of arsine and phosphine in the mixing
zone has been studied and the rate expressions for these
reactions are available, see for example [45]. With results
of mass transport from the source zone and the mixing zone, a
thermodynamic analysis of the deposition process can be
performed. This analysis is called a complex chemical
equilibrium analysis and the epitaxial layer composition,
along with the maximum attainable growth rate, can be
predicted. Realistically, a complex chemical equilibrium


42
analysis does not accurately predict both the composition and
the growth rate, because nonequilibrium mechanisms are
usually dominant in the deposition zone. It provides,
however, process designers with valuable insight into
compositional controllability. Based on the result of the
complex chemical equilibrium analysis alone, the optimum
operation conditions for composition control can be
predicted. Reaction kinetics in the deposition zone is
another process design issue that needs to be resolved. Not
only the macroscopic events, growth rate and epitaxial layer
composition, are affected by the kinetics, but microscopic
events (e.g. doping and interphase quality) are also greatly
influenced.
From the discussion presented in this chapter, three
issues are identified as left to be resolved in the process
design of hydride VPE of In]__xGaxASyP]__v. These issues are
(1) the reaction kinetics in the source zone, (2) the optimum
operating condition for compositional controllability, and
(3) the reaction kinetics in the deposition zone. The rest
of this dissertation reports the resolution of the first and
the second issues. Since information relevant to the third
issue is not available, process fine-tuning still needs to be
pursued by observing the physical and electrical properties
of the resulting epitaxial film; composition, surface
morphology, minority carrier lifetime, photoluminescence
intensity, and PL halfwidth. With the results presented in


43
the remaining chapters, however, the amount of fine-tuning
can be greatly reduced.


CHAPTER 4
COMPLEX CHEMICAL EQUILIBRIUM ANALYSIS
IN In/Ga/As/P/H/Cl SYSTEM
4.1 Formulation and Method of Calculation
4.1.1 Chemical Species and Reactions
To consider the complex chemical equilibrium in hydride
VPE of InGaAsP, the chemical species involved in the system
have to be identified first. In hydride VPE systems, three
reaction zones with different sets of chemical species are
encountered. Therefore, a complete complex chemical
equilibrium calculation includes the calculations of complex
chemical equilibrium in each and every one of the three
temperature zones.
In the source zone, where HC1 in H2 carrier gas reacts
with group III metal, three atomic species III/H/C1 are
involved. Specifically for hydride VPE of Ini_xGaxASyPi_y,
the source region is composed of two source zones the
gallium source zone and the indium source zone, and two
complex chemical equilibrium systems, Ga/H/Cl and In/H/Cl,
should be considered separately.
In the mixing zone group V hydrides, also carried by
hydrogen gas, are introduced into the reactor and mixed with
44


45
the product flow from the group III source region. Since the
product flow from the source zone is composed of group III
chlorides, it is possible that the group III chlorides and
the group V hydrides can react in mixing zone to form solid
deposits before the gas mixture reaches the deposition zone.
Therefore, the mixing zone should always be operated at
conditions to prevent parasitic reactions between group Ill-
containing and group V-containing species and avoid
extraneous deposition and loss of group III and group V
nutrients. On account of this process constraint, two
independent complex chemical equilibrium systems are
considered in the mixing zone, namely, Ga/In/H/Cl and
As/P/H/Cl.
In the deposition zone, group III chlorides and group V
species react, and chemical equilibrium of Ga/In/As/P/H/Cl is
considered.
Table 4-1 lists the chemical species chosen for the
In/Ga/As/P/H/Cl system. Near one atmosphere pressure and in
the temperature range of interest to VPE, 900-1200 K, some of
the chemical species are fairly unstable, thus insignificant
in quantity. Mole fractions of gallium hydrides, indium
hydrides, arsenic chlorides and phosphorous chlorides are
typically less than lO-1^' hence they are excluded from
consideration. The binary compound vapor species of GaAs,
GaP, InAs and InP are also insignificant and do not have a
great impact on the overall chemical equilibrium. Group III


46
Table 4-1. Possible chemical species in In/Ga/As/P/H/Cl
system*.
Name
Symbol
Gallium
Ga Ga (3 j
Indium
In, In(i)
Gallium Chlorides
GaC 1 / GaCl2 r GaCl3 ,
Ga2c^2' Ga2Cl4, Ga2Clg
Indium Chlorides
InCl, InCl2> InCl3,
In2Cl2r In2Cl4, In2Clg
Arsenic
As, AS2, AS3, AS4
Phosphorous
P, P2, P3, P4
Arsenic Hydrides
ASH, AsH2, ASH3
Phosphorous
Hydrides
PH, PH2, PH3
Hydrogen/Chiorine
H2, H, HC1, Cl, Cl2
Gallium Arsenide
GaAs(s)
Indium Arsenide
InAs(s)
Gallium Phosphide
GaP(s)
Indium Phosphide
InP(s)
* Unless indicated
phase.
otherwise all species are in the gas
(1): 1iquid phase
(s): solid phase


47
chlorides and Group V molecules are the dominant species in
the In/Ga/As/P/H/Cl system. Kinetic studies on the growth of
GaAs have proven that gallium monochloride and arsenic
molecules are responsible for the epitaxial reaction in a
hydrogen-rich ambient, and in addition, gallium trichloride
plays a certain role in a hydrogen-deficient atmosphere.
Although some of the chlorides are less important than the
others, it is of strategic value to take them all into
account because their influence on the kinetics might not
have been revealed. For similar reasons, the group V
molecules composed of different number of atoms should be
considered. Group V hydrides, possibly competing with Group
V molecules in the growth reaction, are used as group V
element carriers. The inclusion of all possible V-hydrides
species is thus meaningful. Molecules formed by both arsenic
and phosphorous atoms have not been adequately studied, and
their reported thermochemical properties, at present, are
missing or inconclusive. Therefore, these chemical species
are discarded in the complex chemical equilibrium
calculation. The thermochemical properties of the resulting
39 chemical species are reviewed and gathered. Table 4-2 &
4-3 provide the compilation with references to the selected
values.
System reactions are determined after the chemical
species are chosen. Every system reaction describes the
relationship of one added chemical species to the existing


Table 4-2. Selected values of standard state heat capacity,
Cp (cal/mole- K) = Cq
+ C3T +
c2t2 + C3T
3 + C4T2 +
C5lnT
(T : K)
c0
C1*103
c2*io6
C3*109
C4*10-6
C5
ref.
Ga
30.138
2.09
0.
0.
-0.2662
-3.812
46
Ga(l)
6.65
0.
0.
0.
0.
0.
47
In
3.575
4.426
0.
-1.689
0.
0.
46
In(l)
7.10
0.
0.
0.
0.
0.
47
GaCl
8.84749
23.287
-0.04918
0.
-0.039674
0.
48
GaCl 2
13.7942
13.33964
-0.04050
0.
-0.083318
0.
48
GaCl 3
19.463
0.566884
-0.21157
0.
-0.151843
0.
48
Ga2C12
19.5208
0.547979
-0.23262
0.
-0.153321
0.
48
Gel 2C1 4
(298K-
600K)
17.9843
26.683
-15.7484
0.
-0.151084
0.
48
(600K-
12 00 K)
28.1419
4.0013
-1.27179
0.
-0.784768
0.
48
Ga2Gl6
43.0051
0.989928
-0.37017
0.
-0.340547
0.
48
InCl
8.93
0.
0.
0.
-0.209
0.
49


(continued)
Cp (cal/mole- K) =
C0 + C]T
+ C2T2 +
c3T3 + C4T-2
+ C5lnT
(T : K)
c0
Cj/103
C2*106
C3*109
C4*106
c5
ref.
InCl2
13.84
0.0515
0.
0.
0.08644
0.
50
InCl 3
18.00
1.7
0.
0.
0.
0.
49
In2Cl4
26.93
1.7
0.
0.
-0.209
0.
51
In2Cle
40.
3.4
0.
0.
0.
0.
45
As
4.968
0.
0.
0.
0.
0.
46
As2
8.772
0.2571
-0.121
0.
-0.04241
0.
52,53
As3
13.836
-0.1365
0.
0.
-0.05889
0.172
46
As 4
19.696
0.2834
-0.1252
0.
-0.168
0.
52,53
P
4.968
0.
0.
0.
0.
0.
54
P2
8.236
8.6618
0.
0.
0.06036
0.
54,55
P4
19.2
0.5744
0.
0.
-0.02974
0.
54,55
AsH
6.4
1.432
0.
0.
0.0108
0.
54
AsH3
10.07
5.42
0.
0.
-0.220
0.
56
PH
6.4
1.432
0.
0.
0.0108
0.
54


(continued)
Cp (cal/mole- K) =
C0 + Cj_T
+ c2t2 +
C3T3 + C4T-2
+ C5InT
(T : K)
-
c0
C3 *103
c2*io6
C3*109
C4*10~6
C5
ref.
ph2
6.524
6.237
0.
-1.506
0.
0.
54
ph3
4.77
14.97
-0.4388
0.
0.
0.
54
GaAs(s)
10.8
1.46
0.
0.
0.
0.
52,57
InAs(S)
10.6
2.0
0.
0.
0.
0.
52,57
Gap(S)
11.85
0.68
0.
0.
-0.14
0.
55,58
(298K-
12.27
0.
0.
0.
-0.114
0.
55,58
91 OK)
(910K-
5.89
6.4
0.
0.
0.
0.
55,58
1500K)
2
15.256
2.12
0.
0.
-0.05906
-1.462
54
H
4.968
0.
0.
0.
0.
0.
59
HC1
6.224
1 .29
0.
0.
0.03251
0.
54
Cl
5.779
-0.4083
0.
0.
-0.0387
0.
60
ci2
8.8
0.208
0.
0.
-0.067
0.
48


51
Table 4-
-3. Selected values of standard state enthalpy of
formation and absolute entropy at 298 K,
A Hf (298K) (kcal/mole) S(298K) (cal/mole- K)
AHf(298K)
ref
0
s(298K)
ref
Ga
65.0
46
40.375
46
Gad)
1.3
47
14.2
47
In
57.3
46
41.507
46
In(l)
0.8
47
15.53
47
GaCl
- 17.1
48
57.236
48
GaCl 2
- 39.0
48
71.668
48
GaCl 3
-102.4
48
77.515
48
Ga2c^2
- 56.1
48
83.681
48
Ga 2C14
-148.5
48
103.031
48
Ga2G^ 6
-228.9
48
116.9
48
InCl
- 16.7
49
59.3
49
InCl2
- 58.4
45
73.4
45
InCl 3
- 90.0
56
82.3
56
In2cl4
-140.84
61
110.6
61
In2Cl6
-208.5
45
129.7
45
As
68.7
46
41.611
46
As2
45.58
53
57.546
46
AS3
52.2
46
74.121
46
AS4
36.725
53
78.232
46


52
(continued)
AHf(298K)
ref
s (298K)
ref
p
75.62
46
38.98
46
p2
34.34
46
52.11
54
p4
12.58
45
66.89
46
AsH
58.
45
51.
45
AsH3
16.
61
53.22
62
PH
56.2
54
46.9
54
ph2
25.9
54
50.8
54
ph3
1.3
63
50.24
54
GaAs(s)
-19.54
52
16.05
52
InAs (S)
-14.29
52
17.84
52
GaP(s)
-23.93
55
10.96
55
InP(s)
-14.73
55
14.18
55
h2
0.
31.207
64
H
52.103
64
27.391
64
HC1
-22.063
64
44.643
64
Cl
28.992
64
39.454
64
Cl2
0.
53.29
64


53
ones. This also implicitly means that the system reactions
are independent. Although the number of system reactions is
fixed when the chemical species are chosen, the reaction
formulae can be written in various forms as long as the
requirement of independence is met. The system reactions of
the chosen chemical species (as listed in Table 4-1) are
tabulated in Table 4-4.
4.1.2 Complex Chemical Equilibrium Equations and Equilibrium
Parameters
Gallium Source Zone The system reactions involved in
gallium source zone are listed in table 4-4. The equilibrium
equations for these system reactions are written as follows
Kg (T)
K10(T)
k14(T)
p
GaCl3
?H2
p
GaCl
PHC1
PGa_Cl .
2 4
p
GaCl3
P
GaCl
p
GaCl 2
P *5
H2
P
GaCl
PHC1
PGa2cl6
PGaCl3
(4-1)
(4-2)
(4-3)
k16(T)
(4-4)


54
Table 4-4. Chemical reactions in hydride VPE of InGaAsP
applicable*
number reaction temperature
zone
1 GaCl + 1/4 As4 + 1/2 H2 < > GaAs(SS>)# + HC1 d
2 InCl + 1/4 As4 + 1/2 H2 < > InAs(s>s>)# + HC1 d
3 GaCl + 1/4 P4 + 1/2 H2 < > GaP(s.s>)# + HC1 d
4 InCl + 1/4 P4 + 1/2 H2 < > InP(S#s.)# + HC1 d
5 2 As2 < > As4 m, d
6 AsH3 < > 1/2 As2 + 3/2 H2 m, d
7 2 P2 < > P4 m, d
8 PH3 < > 1/2 P2 + 3/2 H2 m, d
9 GaCl + 2 HC1 < > GaCl3 + H2 s(Ga),
m, d
10 GaCl + GaCl3 Ga2Cl4 s(Ga) t
m, d
11 InCl + 2 HC1 < > InCl3 + H2 s(In),
m, d
12 InCl + InCl3 < > In2Cl4 s(In),
m, d
13 InCl + HC1 < > InCl2 + 1/2 H2 s(In),
m, d
14 GaCl + HC1 < > GaCl2 + 1/2 H2 s(Ga),
m, d
15 2 InCl3 < > In2Clg s(In),
m, d
16 2 GaCl3 < > Ga2C1g s(Ga),
m, d
17 2 InCl < > In2Cl2 s(In),
m, d
(Cont'd)


55
applicable*
number reaction temperature
zone
18
2 GaCl < > Ga2Cl2
s(Ga),
m, d
19
AsH3 < > AsH2 + 1/2 H2
m, d
20
AsH3 < > AsH + H2
m, d
21
PH3 < > PH2 + 1/2 H2
m, d
22
PH3 < > PH + H2
m, d
23
As2 < > 2 As
m, d
24
AS4 + As2 < > 2 As3
m, d
25
P2 < > 2P
m, d
26
p4 + P2 < > 2 P3
m, d
27
H2 < > 2H
s(Ga) ,
s (In) ,
m, d
28
HC1 < > H + Cl
s(Ga) ,
s(In),
m, d
29
2C1 < > Cl2
s(Ga) ,
s(In) ,
m, d
30
GaCl ^ y Ga + Cl
s(Ga) ,
m, d
31
InCl < > In + Cl
s (In) ,
m, d
32
Ga(1) + HC1 < > GaCl + 1/2 H2
s (Ga)
33
In(1) + HC1 < > InCl + 1/2 H2
s (In)
* s(Ga): Ga source zone
s(In): In source zone
m: mixing zone
b: deposition zone
^ (s.s.): InGaAsP solid solution


56
K18(T) =
Ga2C12
GaCl
K27 =
4
H.
k28(t) =
^C1
PHC1
Cl.
K29(T) =
Cl
K30(T) =
P P
Ga Cl
P
GaCl
K32(T) =
P P0-5
GaCl H2
P
HC1
(4-5)
(4-6)
(4-7)
(4-8)
(4-9)
(4-10)
In the equations above, Kj_(T) is the equilibrium constant of
reaction i which is a function of temperature T, and Pj is
the partial pressure of chemical species j in the vapor
phase. In all zones, the number of chlorine atoms and
hydrogen atoms in the vapor phase is constant. It is thus
convenient to define the parameter As(Ga) that represents the
ratio of chlorine atoms to hydrogen atoms in the gas phase.


57
PGaCl + 2(PGaCl2+ PGa2Cl2 + PC12> + 3PGaCl3
Ac(Ga) = (Cl/H) =
+ 4PGa2Cl4 + 6P
+ P + P
Ga2Cl6 ^HCl *C1
2P + p + P
*2 fhci
(4-11)
The summation of the vapor pressure of the twelve vapor
species is equal to the total pressure, Ptot' i-e*
P = P + P
tot GaCl GaCl
+ PGa + PH.
2
+ P
+ P +P +P +P
GaCl-. Ga_Cl~ Ga_Cl. Ga_Clc
3 2 2 2 4 2 6
+ P + P + P
KC1 H Cl Cl.
(4-12)
Complex chemical equilibrium in the gallium source zone is
completely defined by equations (4-1) to (4-12). When values
of the gallium source zone temperature, Ts(Ga), total system
pressure, Ptot' an<^ As(Ga) are specified, equations (4-1) to
(4-12) can be solved simultaneously to resolve the
equilibrium partial pressure of the twelve vapor species.
Indium source zone Similar equilibrium equations exist
for the indium source zone. There are twelve equilibrium
equations with three system parameters; indium source zone
temperature, Ts (In) total system pressure, Ptot' an<^
chlorine to hydrogen ratio, As(In). The twelve equilibrium
equations are written as follows.


58
K11(T)
K
12
(T)
K13(T)
ki5(T)
K
17
(T)
k27(T)
K28(T)
k29(T)
K31(T)
K
33
(T)
p
InCl3
?H2
P
InCl
PHC1
Pln2C14
PInClj
PInCl
P
I nC 12
P -5
H2
P
InCl
PHC1
P
In2C16
P 2
I nC 13
In2Cl2
p 2
InCl
PH
?H2
P P
H *C1
p
HC1
P2
pc?
PT p
In
Cl
P
InCl
P
InCl
P -5
p
HC1
(4-13)
(4-14)
(4-15)
(4-16)
(4-17)
(4-18)
(4-19)
(4-20)
(4-21)
(4-22)


59
PInCl + 2(PInCl2+ PIn2Cl2 + PC12) + 3PInCl3
As(In) = (Cl/H) =
+ 4Pt + 6P
In_Cl.
2 4
+ F + P
In2Cl6 KC1 Cl
2PH2 + PHC1 + PH
(4-23)
P = P + P
tot InCl InCl
+ P
+ PT + P
In H.
2
+ P
InCl.
+ P + P + P
In_Cl_ In.Cl. In-Cl,
2 2 2 4 2 6
+ P + P + P
HC1 E Cl Cl.
(4-24)
Mixing zone There are 33 chemical species in the vapor
phase of the mixing zone; GaCl, GaCl2> GaCl3, Ga2Cl2> Ga2Cl4,
Ga2Clg, Ga, InCl, InCl2r InC13, In2Cl2/ In2Cl4, In2Clg, In,
ASH3, ASH2, AsH, As, AS2, AS3, AS4, PH3, PH2, PH, P, P2, P3,
P4, H2, HC1, H, Cl and CI2. A total of 27 reactions are
involved with the 33 chemical species, as discussed in
section 4.1.1. The equilibrium equations can be written
similar to those given for the source zone. Fifteen of the
27 equilibrium equations have been presented in the last
section, the other twelve equilibrium equations are written
as follows.
As
k5 (T) =
AS.
k6 (T) -
0.5 1.5
As2 H2
PASH
(4-25)
(4-26)


60
k7 (T)
K8 (T) =
pO-5 pl.5
P2 H2
PPH
k19(t) =
PAsH2 PH2
PAsH,
K20(T)
P P
AsH H.
ASH.
K21(T) =
P P 5
PH2 H2
PPH.
K22(T)
P P
PH H.
PH.
K23(T) =
As
As.
k24(t)
As.
P P
As- As.
2 4
K25(T)
(4-27)
(4-28)
(4-29)
(4-30)
(4-31)
(4-32)
(4-33)
(4-34)
(4-35)


61
K26(T) =
(4-36)
Define B1 as the gallium to hydrogen ratio, B2 the
indium to hydrogen ratio, Cl the arsenic to hydrogen ratio,
and C2 the phosphorus to hydrogen ratio. Denoting the
parameters in mixing zone by subscript m, then Am, Blm, B2m,
Clm, and C2m can be written as follows.
A = (Cl/H)
m m
PHCl+PCl+PGaCl+PInCl+z(PGaCl2+PInCl2+PGa2Cl2+
PIn2Cl2+PCl2) +3(PGaCl3+PInCl3)
4 (PGa Cl +PIn Cl.1 +6 (PGa Cl/PIn Cl 1
2 4 2 4 2 6 2 6
2P +P +P ,+3P +3P +2(P +2P +P +P )
H2 H HC1 AsH-, PH3 1 PH2 AsH2 PH AsH;
B1m = (Ga/H)m =
PGa + PGaCl+PGaCl + PGaCl7 + 2PGa Cl +2PGa Cl .+2PGa Cl,
2 3 2 2 2 4 2 6
P +P + P ,+3P +3P +2P +2P +P +P
H2 H HC1 AsH3 PH3 AsH2 PH2 AsH PH
B2 = (In/H)
m m
p +p +p +p +?P +2P +PP
In InCl InCl_ InCl, In_Cl. InCl. In.Cl,
2 3 2 2 2 4 2 6
P +P +P .+3P +3P +2P +2P +P +P
H2 H HC1 AsH3 PH3 AsH2 PH2 AsH PH
(4-37)
(4-38)
(4-39)


62
Cl = (As/H)
m m
P. +P, +P, +P- + 2P, +3P + 4P
AsH AsH0 AsH-, As As_ As., As.
2 3 2 3 4
p + p +p +3p +3p +2p +2P +P +P
H2 H HC1 AsH3 PH3 AsH2 PH2 AsH PH
(4-40:
C2 = (P /H)
m m
PPH +PPH2 +PPH3 +PP +2PP2 +3Pp3 +4Pp4
ph2+ph+phci+3pash3+3pph3+zPash2+2pph2+pash+pph
(4-41)
The summation of partial pressure of the 33 vapor
species equals to the total pressure, Ptot-
) = p +p +p +p + p +P +P +P
tot *H2 ^HCl *H rCl Cl2 ^GaCl GaCl2 *GaCl3
+ P +P +P +P +P +P
Ga2Cl2 Ga2Cl4 Ga2Clg Ga InCl InCl2
+ P *fP +P +P +P +P
InCl, In-Cl- In-Cl. In_Clc In AsH-.
3222426 3
+ P +P +P + P + P +P +P +P
AsH~ AsH As As0 As. As- PH- PHn
2 2 3 4 3 2
+ PPH+VPP, + PP 'V
2 3 4
(4-42)
The complex chemical equilibrium in mixing zone is
completely defined by equations (4-1) to (4-9), (4-11) to (4-
15), (4-19) (4-25) to (4-36) and equations (4-37) to (4-41) .
When mixing zone temperature, Tm, and the values of the
parameters, Am, Blm, B2m, Clm, C2m, and system pressure,
ptot' are given, the complex chemical equilibrium in mixing
zone can be calculated by solving the simultaneous
equilibrium equations.


63
Deposition zone All of the gaseous chemical species
listed in table 4-1 are included for the discussion of
complex chemical equilibrium in deposition zone. The
condensed phase is the solid solution In^_xGaxASyPi_y. In
addition to the 27 homogeneous system reactions for the 33
gaseous chemical species, as explained in the last section,
four heterogeneous system reactions also exist in deposition
zone. The equilibrium equations for these four reactions are
Kx (T)
K2 (T)
K3 (T)
k4 (T)
aGaAs
P
HC1
P
GaCl
0.25
As4
0.5
H2
aInAs
P
HC1
P
0.25
P0-5
InCl
As .
4
H2
aGaP
P
HC1
P
GaCl
0.25
P4
P.5
H2
aInP
PHC1
P
InCl
0.25
P4
P0-5
H2
(4-43)
(4-44)
(4-45)
(4-46)
where a is the activity of binary component i in solid
solution Inj__xGaxASyP]__y. The a' s are dependent upon the
solid solution composition (x, y) and temperature T. The
solution thermodynamics of solid In^_xGaxASyP]__y ,which
elucidates the dependence of a' s on (x, y) and T, will be


64
discussed later in this chapter. Define D as the ratio of
the difference between the number of group III atoms and
group V atoms to the total number of hydrogen atoms in the
vapor phase, so that
D =
P +P +P +P +2P +2P +2P +
*Ga GaCl *GaCl, ^GaCl, Ga,Cl, ^Ga,Cl. ZiGa,Cl,
2 3 22 24 6
p +p +p +p +2P +2P +2P
in ^InCl InCl2 InCl3 In2Cl2 In2Cl4 In2Cl6
-P, -P, -P* -P -2P. -3P -4P
AsH. AsH- AsH As As As, As.
3 2 2 3 4
_p _p _p _p -op -3p -4p
PH, PH, PH P P, P, P.
3 2 2 3 4
2P +P +P +3P +3P +2P +2P +P +P
H2 H HC1 AsH3 PH3 AsH2 PH2 AsH PH
(4-47)
When values of the deposition zone temperature, T, system
pressure Ptot, parameters D and Aj (chlorine to hydrogen
ratio in the deposition zone), and solid solution composition
(x, y) are given, the partial pressure of the 33 gaseous
chemical species can be obtained by solving equations (4-1 to
4-9, 4-11 to 4-15, 4-19, 4-25 to 4-36), equation (4-37),
equation (4-42), equations (4-43 to 4-46), and equation (4-
47) simultaneously.
Define Y as the ratio of the number of gallium atoms to
the total number of group III atoms in the vapor phase, and Z
the ratio of arsenic atoms to group V atoms in the vapor
phase. Then after the partial pressures have been
calculated, Y and Z can be readily evaluated as follows.


65
Y
PGa+PGaCl+PGaCl2+PGaCl3+2PGa2Cl2+2PGa2Cl4+2PGa2Cl6
P GaP GaCP GaCl2P GaCl*21* Ga2Cl22P Ga2Cl42P Ga2Cl*
PIn+PInCl+PInCl2+PInCl3+2PIn2Cl2+2PIn2Cl4+2PIn2Cl6
(4-48)
P +P +P + P +2P +3P + 4P,
AsH3 AsH2 AsH As As2 As3 As4
~p +p +p +p +2F + 3 p +4P ~
AsH, AsH, AsH As As As, As.
3 2 2 3 4
P +P +P +P +2P +3P +4P
ph3 ph2 ph p p2 p3 p4
(4-49
Therefore, complex chemical equilibrium can also be
defined by a set of chosen values of T, Ptot' Ad' D' anc^
Z. In this case, equations (4-1 to 4-9, 4-11 to 4-15, 4-
19, 4-25 to 4-37, 4-42 to 4-49) are solved together for the
partial pressure of the 33 vapor species and the solid
solution composition (x, y).
4.1.3 Process Parameters
The parameters that have been discussed in the last
section are called "equilibrium parameters", since
specification of the values of these parameters defines
equilibrium condition. Table 4-5 lists the equilibrium
parameters and their shorthand definitions.
In open VPE reactor systems, equilibrium parameters can
not be directly controlled. Rather, process performance is
controlled by changing various "process parameters", the
flowrates, temperature settings and pressure setting.


66
Table 4-5. Equilibrium Parameters
Zone
Equilibrium Parameters
Symbol
Definition
gallium source zone
As(Ga)
Cl /H
Ts(Ga)
temperature
^tot
pressure
indium source zone
As(In)
Cl /H
Ts(In)
temperature
^tot
pressure
mixing zone
Am
Cl /H
Blm
Ga/H
B2m
In/H
dm
As/H
C2m
P/H
Tra
temperature
ptot
pressure
deposition zone
Ad
Cl /H
D
(III-V)/H
Y
Ga/III
Z
As/V
Td
temperature
^tot
pressure


67
In addition, the three temperature zones are connected in
series, the product gasflow of upstream zone is transported
into the downstream zone and becomes the input gasflow of
that region. Specification of equilibrium of equilibrium
parameters in the mixing zone is directly connected to the
values of the source zone output, and similarly equilibrium
parameters in the deposition zone are dependent upon the
mixing zone condition. Therefore, it is of practical value
to investigate the relationship between the equilibrium
parameters from one temperature zone to the other, and the
relationship between the equilibrium parameters and the
process parameters.
Gallium source zone Denoting the input flowrates of HCl
and H2 into gallium source zone by FHC1(Ga) and FH2(Ga), then
the transport rate of hydrogen atoms FH(Ga) and the transport
rate of chlorine atoms FC1(Ga) are simply
FH(Ga) = 2FH2(Ga) + FHC1(Ga) (4-50)
FC1(Ga) = FHC1(Ga) (4-51)
Using the above equations, equilibrium parameter As(Ga) can
be related to process parameters FHCl(Ga) and FH2(Ga) as
follows.
As(Ga)
FC1(Ga) / FH(Ga)
(4-52)


68
When the process parameters FHCl(Ga), FH2(Ga), Ts(Ga) and
ptot are specified, the equilibrium parameters, As(Ga),
Ts(Ga) ,and Ptot' are also specified, and complex chemical
equilibrium calculation can be carried out as discussed in
section 4.1.2.
The result of gallium source reactions is transport of
gallium atoms in the vapor phase. Two different transport
rates of gallium should be differentiated, namely the
equilibrium transport rate of gallium F*Ga(Ga) and the
process transport rate of gallium FGa(Ga). The equilibrium
transport rate of gallium is the calculated gallium transport
rate from complex chemical equilibrium, therefore F*Ga(Ga)
can be written as
F*Ga(Ga) = FH(Ga)
P +p +p +p +
Ga GaCl GaCl2 GaCl3
2P +2P +2P
Ga_Cl_ Ga_Cl. Ga0Cl,
2 2 2 4 2 6
2P + p +P
ZyH2 iHCl H
(4-53)
while the process transport rate of gallium is the physically
obtained gallium transport in the process. Clearly, the
process transport rate of gallium, which is always less than
or equal to the equilibrium transport rate of gallium, is
dependent upon source zone design and process operating
conditions. For convenience, define e(Ga) as the gallium
transport factor as follows


69
e (Ga)
FGa(Ga) / FC1(Ga)
(4-54)
The value of e(Ga) at equilibrium equals F*Ga(Ga) / FC1(Ga)
and is denoted e*(Ga). The value of e(Ga) equals zero at the
inlet of gallium source zone, increases in the direction of
gasflow, and, given sufficient residence time, is saturated
at the source zone outlet. e(Ga) serves as an important
process parameter for the mixing zone, as will be explained
later in this section.
Indium source zone Similar to gallium source zone, four
process parameters exist in indium source zone, namely, HC1
input flowrate, FHC1(Ga), H2 input flowrate, FH2(In), indium
source zone temperature, Ts(In), and total pressure, Ptot.
The hydrogen transport rate, FH(In), and chlorine transport
rate, FCl(In), are given by
FH(In) = 2FH2(In) + FHCl(In)
(4-55)
FC1(In) = FHC1(In)
(4-56)
The equilibrium parameter, As(In), is determined by FH(In)
and FC1(In),
As(In) = FC1(In) / FH(In)
(4-57)


70
The equilibrium transport rate of indium F*In(In) is
calculated from equilibrium partial pressures accordinq to
P +p +p +p +
In InCl InCl2 InCl3
2P +2P +2P
* ^In Cl ztln Cl. ^In Cl,
F In (In) = FH(In) TT1 (4-58)
H2 HC1 H
The indium transport e(In) is defined by
e(In) = Fin(In) / FCl(In) (4-59)
where Fin(In) is the process transport rate of indium.
Mixing zone Denote the input flowrates of H2, ASH3 and
PH3 by FH2(m), FASH3 and FPH3, then the total transport rate
of hydrogen in the mixing zone, FH(m), is given by
FH(m) = FH(Ga) + FH(In) + 2FH2(m) + 3(FAsH3 + FPH3) (4-60)
The connective nature between source zone and mixing zone is
evident from the first two terms in the RHS of equation (4-
60). The transport rates of chlorine, gallium, indium,
arsenic and phosphorous in mixing zone are as follows.
FCl(m) = FCl(Ga) + FCl(In) (4-61)
FGa(m)
FGa(Ga) = e(Ga) FC1(Ga)
(4-62)


71
Fin(m) = Fin(In) = e(In) FCl(In) (4-63)
FAs(m) = FAsH3 (4-64)
FP(m) = FPH3 (4-65)
The equilibrium parameters Am, Blm, B2m, Clm and C2m are
related the transport rates and can be written as follows.
Am = FC1(m) / FH(m) (4-66)
Blm = FGa(m) / FH(m) (4-67)
B2m = Fin(m) / FH(m) (4-68)
Clm = FAs(m) / FH(m) (4-69)
C2m = FP(m) / FH(m) (4-70)
From the equations presented above, it is clear that there
are seven process parameters in the mixing zone; FH2 F AsH 3 FPH3, Tm, Ptot' e(Ga) and e(In). When values of
FH(Ga), FCl(Ga), FH(In) ,FCl(In), and the process parameters
are specified, the seven equilibrium parameters, Am, Blm,
B2m, Clm, C2m, Tm and Ptot can evaluated and the complex
%
chemical equilibrium in mixing zone is completely defined.


72
Since the overall reaction rate can be affected by mass
transfer and kinetic effects in the process, chemical
equilibrium might not be reached in mixing zone. If the
mixing zone is operated under the correct criteria
prohibiting formation of any condensable reaction products,
then, irrespective of if equilibrium is reached, the process
transport rates of all six atomic species, equations (4-60 to
4-65), will not change. Therefore, the transport rates
derived for mixing can be directly used in deposition zone.
Deposition zone Equilibrium parameters Ad, D, Y and Z
at the inlet of deposition zone are determined by transport
rates FH(m), FC1(m), FGa(m), Fln(m), FAs(m) and FP(m).
Ad = FC1(m) / FH(m) (4-71)
D = (FGa(m) + Fln(m) FAs(m) FP(m)) / FH(m) (4-72)
Y = FGa(m) / (FGa(m) + Fln(m)) (4-73)
Z = FAs(m) / (FAs(m) + FP(m)) (4-74)
The reactant gas is supersaturated and deposition reaction
occurs in the deposition zone. In the course of the
deposition process, group III atoms (In, Ga) and group V
atoms (As, P) leave the vapor phase, therefore the values of
Y and Z begin to change along the flow direction. Define


73
supersaturation, S, to be the total number of group III atoms
(or equivalently the total number of group V atoms) that
leave the vapor phase before complete equilibrium is reached.
Then, at equilibrium, the equilibrium parameters Y and Z are
Y = (FGa(m) x S) / (FGa(m) + Fln(m) S) (4-75)
Z = (FAs(m) y S) / (FAs(m) + FP(m) S) (4-76)
where x and y are mole fractions in the deposited compound
Ini_xGaxASyPi_y. Note that stoichiometry is usually assumed
for the deposition III-V compound, therefore, in writing
equations (4-75 & 4-76) the number of deposited group III
atoms has been assumed to be equal to the number of deposited
group V atoms. On account of this assumption, it is clear
that the value of equilibrium parameter D is not affected by
the deposition process. Since the amount of hydrogen and
chlorine atoms incorporated in the deposited compound is very
small compared with the total transport rate, the value of
equilibrium parameter A also remains unchanged throughout
the deposition zone.
The deposition zone temperature, T, and the system
total pressure, Ptotr are the only process parameters in the
deposition zone. With specified Tj, Ptot' and values of the
transport rates at the deposition zone inlet, FH(m), FC1(m),
FGa(m), Fln(m), FAs(m), and FP(m), equilibrium parameters T


74
ptot' Ad' Y and z can be evaluated directly or indirectly
by equations (4-71, 4-72, 4-75 & 4-76). With the complex
chemical equilibrium defined, composition (x, y) and
supersaturation S can be obtained.
Summary Equilibrium parameters that are used to
initiate complex chemical equilibrium calculation are quite
different from the realistic process parameters used in
process control. But, in order to study the effects of
equilibrium on realistic processes, equilibrium parameters
have to be used to bridge between process parameters and
complex chemical equilibrium calculation. Table 4-6 gives a
complete listing of the process parameters discussed in this
section. There are basically two types of process
parameters. Type 1 is the "process control" parameters.
Most of the process parameters, e.g. flowrate, temperature,
and pressure, belong to this group. The second type, the
"process design parameters", can not be easily tuned during
process runs. For example, transport factors e(Ga) and e(In)
are determined primarily as a result of source zone design.
Note that there are totally 14 process parameters in hydride
YPE of Inx-xGaxASyPi-y ; FH2 (Ga ) FHC1 (Ga) Ts (Ga) e(Ga),
FH2(In) FHCl(In), Ts(In), e(In), FH2(m) FAsH3, FPH3, Tm,
Td, and Ptot-


75
Table 4-6. Process parameters
Zone
Process
Parameters
Symbol
Definition
gallium source zone
FH2(Ga)
FHCl(Ga)
Ts(Ga)
^tot
H2 input flowrate
HC1 input flowrate
temperature
pressure
indium source zone
FH2(In)
H2 input flowrate
FHCl(In)
HC1 input flowrate
Ts(In)
temperature
ptot
pressure
mixing zone
s (Gel)
Ga transport factor
e (In)
In transport factor
FH2(m)
H2 input flowrate
FASH3
AsH3 input flowrate
fph3
PH3 input flowrate
Tm
temperature
^tot
pressure
deposition zone
Td
temperature
^tot
pressure


76
4.1.4 Calculational Procedures
4.1.4.1 Equilibrium Constants
The reaction equilibrium constant Ka is given by its
definition as
n n A o
Ka = n ai = exp ( Z u- y? ) = exp ( ) (4-77)
i=l i=1
where a is the activity of chemical species i, ui is the
stoichiometric constant of i in the reaction, y is the
standard Gibbs free energy of i, and n equals the total
number of chemical species involved in the reaction. The
o
standard Gibbs free energy of the reaction, Ay at
temperature T can be evaluated from the standard enthalpy of
o
formation at 298 K, AHf(298K)' absolute entropy at 298 K,
S298K)' and high temperature heat capacity, Cp(T), of the
involved chemical species.
n
o
Ay ~ E
i = 1
Using equations (4-77 & 4-78) and the selected
thermochemical data of table 4-2 & 4-3, equilibrium constants
of the 33 reactions listed in table 4-4 can be calculated.
/ H TQ +
i1 nf(298K) (298K)
r
298K
P/i
dT
- T
/T
298K
dT
P/i
(4-78)


77
4.1.4.2 Complex Chemical Equilibrium Calculation
Gallium source zone Assuming that qj_ = PH2'^ and q2 =
PHC1 PH2-0*5/ then the partial pressure of each chemical
species in gallium source zone can be rewritten in terms of
q^, q2i and temperature dependent equilibrium constants.
*0
ro
ii
*1
(4-79)
HCl
*1*2
(4-80)
PH =
0.5
K27 ql
(4-81)
PC1 =
K K_^^ a
28 27 42
(4-82)
PC12 =
K29K28K27 *2
(4-83)
P
GaCl
K32 q2
(4-84)
PGa2Cl2
K18K32 q2
(4-85)
P
GaCl 2
= K14K32 q2
(4-86)
PGa2cl4
= K10K9K32q2
(4-87)
P
GaCl 3
= K9K32 q2
(4-88)
PGa2cl6
= K16Kg K32 q2
(4-89)
PGa
K30K32K28 K27
(4-90)


78
Substituting equations (4-79 to 4-90) in equations (4-11 & 4-
12) ,
A (Ga)
s
(ql+K32+K28K27 )q2 + K9K32q2
+(K29K28K27+K18K32+K14K32^ q2
+K10K9K32q2 +K16K9K32q2
(q2+K275) ql + ql
(4-91)
tot
q?+K-5 q1+(K
ll
(K
+ K K ^ ^ )
32 28 27 1
29K28K27 +K18K32+K14K32)
q2 +
2
^ +
K9K32m2
q0 +kioK9K32 q2 + qlq2+
K16K9K32q2 +K30K32K^K275
(4-92)
The nonlinear algebraic equations, equations (4-91 & 4-92),
can be solved together numerically for q^ and q2. Newton-
Raphson method was chosen and has been found adequate for the
numerical solution of this problem.
Indium source zone The same procedure for gallium
source zone calculation is used for indium source zone
calculation.
PInCl K33 q2
(4-93)
In~Cl~
2 2
K17K32 q2
(4-94)


79
P
InC12
Pln2cl4
P
I nC 13
Pln2C16
K13K33 q2
K12K11K33 q2
KllK33q2
K15K11K33 4
K31K33K28 K275
(4-95)
(4-96)
(4-97)
(4-98)
(4-99)
Substitution of equations (4-79 to 4-83 & 4-93 to 4-99) into
equations (4-23 & 4-24) and rewriting equations (4-23 & 4-
24) gives,
As(In) =
(ql+K33+K28K27 )q2 +KllK33q2
+(K29K28K¡7+K17K32+K13K33) q2
+K12KllK33q2+K15KllK33q2
.0.5
(q2 + K27 ) 'tot = ql+K27 ql+(K33+K28K27 ] q2
(K29K28K27 +K17K33+K13K33) q2
KllK33q2 +K12KllK33q2 + qlq2+
K15KIlK33q2 +K
K V ^ v ^
31*33*28*27
(4-100)
(4-101)
Solution of equations (4-100 & 4-101) by the Newton-Raphson
method gives the values of qj_ and q2, from which values of


80
the partial pressure of chemical species in indium source
zone at equilibrium can be calculated.
Mixing zone Assuming that = Pas *2^, q4 = pp 0.25f
4 4
q5 = pGaCl anc^ <36 = pInCl' then the partial pressure of the
chemical species in mixing zone can be written in terms of
*51/ q2 r <33/ q4f qs and qg as follows.
GaCl
q5
(4-102)
Ga2C12
K18q5
(4-103)
GaCl2
= K14 q5 q2
(4-104)
Ga2C14
K10K9 q5q2
(4-105)
GaCl3
= k9 q5 <*l
(4-106)
Ga2C16
= K16K9 q5 q2
(4-107)
Ga
K30K28K27 q5 q2
(4-108)
InCl
q6
(4-109)
^n2G^2
= K17 q6
(4-110)
InCl
Z
= K13 q6 q2
(4-111)
In2Cl4
K12K11 q6 q2
(4-112)


81
PInCI3
= KX1 q6^2 (4-113)
Pln2C16
- K16K11 q6 q2 (4-114)
PIn
K31K28K275 41 a-6 (4-115)
PAs4 =
q4 (4-116)
?As3 =
0.5 -0.25 3
K24 K5 q3 (4-117)
PAs2 =
-0 5 2
K5U*3 q3 (4-118)
PAs =
K235 K¡-25 q3 (4-119)
PAsH3
-1 -0.2 5 3 .
= K6 K5 q3 q (4-120)
PAsH
-1 -0 25 2
= K19K6X K5U,3 q3 (4-121)
PAsH
K20K61k¡'25 q3ql ,4-1221
\ *
q4 (4-123)
Pp3 *
0.5 -0.25 3 .........
K26 K7 ^4 (4-124)
K)
II
-0 5 2
Ky q4 (4-125)
PP =
K3 5 q4 (4 126)
PPH
*5
-l -0.25 3
Kg k7 q4 (4-127)


82
P
PH
2
K21K^
K
-0.25
7
q4
(4-128)
PH
= K22K¡1K;0-25 qaq
4H1
(4-129)
Substituting equations (4-79 to 4-83 & 4-102 to 4-129) in
equations (4-37 to 4-42) yields six nonlinear algebraic
equations of q^, q2r q3, qj, qs, and qg, which are solved
simultaneously by the Newton-Raphson method. The complex
chemical equilibrium partial pressure can be readily
calculated.
Deposition zone The partial pressure of the vapor phase
species can be represented by the definition of q q2, and
q3 presented in the last two sections,
PGaCl = K1 aGaAs q2 q3
P.-, -2 2 2 -2
Ga2C12 K18 K1 aGaAs q2 q3
P -12-1
GaC12 K14 K1 aGaAs q2 q3
Ga2C14 = K10K9K1 aGaAs q2 q3
PGaCl3 K9 K-1 aGaAs q2 q¡2
P_ v2 -2 2 6 -2
Ga_Cl, = K-,Ka K.. q_ q_
26 16 9 1 GaAs^2 ^3
(4-130)
(4-131)
(4-132)
(4-133)
(4-134)
(4-135)


83
Gel
K K K ^ a a~^
K30K28K27 K1 GaAs q3
InCl
K2 ainAs q2 q3
In2C12
= K17 K¡2 alnAs q2 q¡2
InC12 K13 K2 aInAs q2 q3
In_Cl.
2 4
-2 2 4-2
K12K11K2 ainAs q2 q3
InCl3 K1 K2 aInAs *32 ^3
In2C16
v2 -2 2 6-2
K15K11 K2 ainAsq2 q3
In
K K ^ a a
K31K28K27 K2 InAs q3
-4 v\ 4 -4 4
K, K.. a a q.,
3 1 GaP GaAs 3
0.5 -0.25 -3 t-3 3 -3 3
Kor K-, K, K. a a q-,
26 7 31 GaP GaAs n3
-0.5 -2 v2 2 -2 2
K7 K3 K1 aGaP aGaAs q3
^0.5 -0.25 -1 -1
K_c K-, K, K. a a q,
25 7 31 GaP GaAs ^3
PH.
-l -0.25 -1 -1 3
K8 K7 K3 KlaGaPaGaAs q3 ql
PH.
*21*? K7'25 KilKlaGaPaGaAs *3 4
PH
- K22K81k7'25 ¡S^aP^As ^3
(4-136)
(4-137)
(4-138)
(4-139)
(4-140)
(4-141)
(4-142)
(4-143)
(4-144)
(4-145)
(4-146)
(4-147)
(4-148)
(4-149)
(4-150)


84
Substituting equations (4-79 to 4-83, 4-116 to 4-122 & 4-130
to 4-150) into equations (4-37, 4-42 & 4-47) gives three
nonlinear algebraic equation of qj_, q2, and q3. When aGaAs,
aGaP r ajnAs (and ajnp) are specified, the equations can be
solved for q^, q2, and q3. The complex chemical equilibrium
of deposition zone is calculated by an iterative algorithm,
which is succinctly explained in figure 4-1.


85
START
*
Read Process parameters: T, Ptot
& Mixing Zone Transport Rates:
FC1(m), FGa(m), FIn(m), FAS(m), FP(m)
$
Calculate Equilibrium Parameters: Aj, D
Initial Guess: x, y
2
Calculate Activities: aGaAs, aInAs, aGaP, aInP
(by Solid Solution Model)
2
Solve qp, q2 r q3
(by Newton-Raphson method)
.
Calculate Partial Pressure: P-¡_'s
2
Calculate Equilibrium Parameters: Y, Z
^
Calculate Supersaturation: S
& Composition of Deposited Solid: xcaTC, yca]_c
(by eqs.(75 & 76))
y
xcalc x ?
NO
Ad ju
Ycalc Y
x, y
YES
,
PRINT OUT
i
STOP
Figure 4-1. Algorithm for complex chemical equilibrium
calculation in the deposition zone


86
4.2 Solution Thermodynamics of InGaAsP
4.2.1 Solution Thermodynamics
Let Xj_ denote the mole fraction of component i in a
homogeneous solution of C components, then
X1 + x2 + x3 + + xc = 1 (4-151)
Let W denote an extensive property of the mixture, then the
intensive property w-j_ of component i can be derived from the
basic thermodynamic relationship,
W-i
= (
3W
3Ni
i T, P, Nj (jjti) ,
(4-152)
where T is temperature, P is pressure and is the amount of
component in the mixture. If Nj_ has the unit moles, then w-^
is called a partial molar property. Therefore the partial
molar Gibbs free energy, g, or chemical potential, y -¡_, is
simply
u = gi
)
3NT, P, Nj (j^i) ,
(4-153)
The partial molar entropy, s-¡_, the partial molar enthalpy,
hj_, the partial molar volume, v and the partial molar heat


87
capacity, Cp^, are derived from the chemical potential by
classical thermodynamics.
si = "hi/ T (4-154)
hi = hi T( pi/ T) (4-155)
Vi = hi/ P (4-156)
Cpi = T( Si/ T) = -T(hi/ T2) (4-157)
Besides its use of conveniently evaluating other partial
properties, the chemical potential is useful in formulating
phase equilibrium. Consider two homogeneous mixtures A1 and
A2 of C components at equilibrium, the system of phase
equilibrium equations can be written as follows.
Tai = ta2 (4-158)
PAl = ?A2 (4-159)
Ui,Al = Ui,A2' i = 1 2, 3, C (4-160)
In the consideration of a homogeneous mixture, we are
also concerned with the comparison of partial properties of
the components in the mixture with those properties in pure


88
components. Let yOj_ denote the chemical potential of pure
component i at temperature T and pressure P of interest, then
relative activity a of component i in the mixture is defined
by the relationship,
ai = exp (( J*i- yi)/RT) (4-161)
Clearly, a is a direct measure of the chemical potential
difference of component i between the mixture and the pure
component i. This quantity can be directly used in the
description of phase equilibrium between two solutions. M
can be rewritten in terms of y^ and a,
yi = yi + RT ln(ai) (4-162)
Substituting equation (4-162) in equation (4-160) and
cancelling u0-¡_ on both sides of the equality sign results in
another form of phase equilibrium equations.
ai,Al ai,A2 (4-163)
From the review above, it is clear that if extensive
Gibbs free energy G (T, P, N]_, N2, ...., Nq) is known, all of
the partial molar properties can be readily derived.
Furthermore, if the standard chemical potential yO^(T, P) is
known, relative activity a is obtained.


89
4.2.2 Solid Solution Models
The solid solution models used for type A]__XBXCj__yDy
III-V quaternary compound system are reviewed in this
section. The objective is to develop a mathematical
representation of the extensive Gibbs free energy G in terms
of the variables, T, P, n^c, nB^, nAD, and nBD. A solid
solution model is usually constructed on an atomic or a
statistical viewpoint and its compatibility with the solution
system is tested by its capability to describe the system's
experimental behavior. However, when the experimental
characterization of the solution is difficult, solid solution
models are also employed to interpolate and extrapolate sytem
behavior from the limited amount available information.
The A]__xBxC]__yDv type of III-V quaternary solid solution
has often been treated as a pseudoquaternary mixture of
binary components AC, AD, BC, and BD. The characteristic
feature of this type of solution is that the distribution of
the nearest neighbor pairs is not uniquely determined by the
apparent composition (x, y) of the quaternary compound. Let
nAC nAD' nBC > an<^ nBD represent the number of nearest
neighbor pairs AC, AD, BC, and BD, respectively. These
numbers are related to the number of constituent atoms, ,
Nb, Nq, and Nb, as follows.
nAC + nAD = Z1 nA
(4-164)


90
nBC + nBD = Z1 nB
(4-165)
nAC + nBC = Z1 NC
(4-166)
nAD + nBD = Z1 nD
(4-167)
, where z^ (= 4) is the number of nearest neighbors for each
atom in the zinc-blende lattice structure. The number of
constituent atoms; NA, Ng, Nq and Np, is related to the
apparent composition (x, y) and the total number of group III
or group V sites, N.
Na = (1-x) N (4-168)
Nb = x N (4-169)
Nc = (1-Y) N (4-170)
nd = y N (4-171)
By observing equations (4-164 to 4-171), it can be seen that
equations (4-164 to 4-167) are a set of dependent equations
and one of the four equations can be eliminated. The
resulting set of three independent equations, after
substitution of NA, Ng, Nq, and Np by equations (4-168 to 4-
171) into equations (4-164 to 4-167), is written as follows.


91
nAD = (1-x)(Z! N) nAC
(4-172)
nBC = (1-y) (4-173)
nBD = (x+y-1)(zi N) + nAC
(4-174)
It is obvious from equations (4-172 to 4-174) that nAc, nAB,
nBC, and nBB are not uniquely determined with specified x, y,
and N. This feature is characteristic for III-V compound
systems with mixing on both sublattices. However, if nA(B,
nAD/ nBc, and nBB are specified, x, y, and N can be readily
calculated by
x = (nBC + nBD)/(nAC + nAD + nBC + nBD) (4-175)
y = (nAD + nBD)/(nAC + nAD + nBC + nBD) (4-176)
N = (nAC + nAD + nBC + nBD)/zl (4-177)
If a completely random distribution is assumed, the number of
nearest pairs is given as follows.
nAc = (i-x) d-y) zi N
(4-178)
nAD = (1-x) y ZX N
(4-179)


Full Text

PROCESS DESIGN ISSUES
IN HYDRIDE VAPOR PHASE EPITAXY OF
INDIUM GALLIUM ARSENIDE PHOSPHIDE
By
JULIAN JUU-CHUAN,HSIEH
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1988

To my parents,
Mih and Sheue-Mei Ding Ksieh

ACKNOWLEDGEMENTS
The author wishes to express his sincere gratitude to
his graduate advisor, Dr. Tim Anderson. Without his
guidance, encouragement, trust and support, it would have
been a much less enjoyable experience. He is also grateful
to the other members of the advisory committee: Dr. Lewis
Johns, Dr. Ranga Narayanan, Dr. Hong Lee and Dr. Sheng Li for
their valuable time and many helpful discussions of this
work.
The author also wishes to thank the members of his
research group for creating a stimulating research
environment. Special thanks are due to Francoise Defoort for
her assistance in the design and execution of normal pressure
experiments. Jim Edgar provided unequivocal assistance in
the construction of the gas delivery system for low pressure
experiments. Stuart Hoekje helped in atomic absorption
spectrometry measurement.
Love and moral support provided by the author's family
members, Juu-Jeng, Juurong, Rudolf and Iris, were essential
to the completion of this work.
iii

TAELE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
ABSTRACT vii-viii
CHAPTERS
1 INTRODUCTION 1
2 III-V COMPOUND SEMICONDUCTORS 4
2.1 Physical and Electrical Properties 4
2.2 Material & Device Perspective 8
2.3 Binary, Ternary and Quaternary InGaAsP
Compound 11
2.3.1 Applications 11
2.3.2 Epitaxy 13
3 HYDRIDE VAPOR PHASE EPITAXY OF INDIUM GALLIUM
ARSENIDE PHOSPHIDE 16
3.1 Process Chemistry 17
3.2 Literature Review 23
3.3 Process Design Issues 31
3.3.1 Process Thermodynamics 32
3.3.2 Nonequilibrium Mechanisms 3 6
3.3.3 Process Design Considerations 39
4 COMPLEX CHEMICAL EQUILIBRIUM ANALYSIS
IN In/Ga/As/P/H/Cl SYSTEM 44
4.1 Formulation and Method of Calculation... 44
4.1.1 Chemical Species and Reactions.... 44
4.1.2 Complex Chemical Equilibrium
Equations and Equilibrium
Parameters 53
4.1.3 Process Parameters 65
4.1.4 Calculational Procedures 76
4.1.4.1 Equilibrium Constants 76
4.1.4.2 Complex Chemical
Equilibrium Calculation... 77
4.2 Solution Thermodynamics of InGaAsP 86
4.2.1Solution Thermodynamics 86
IV

4.2.2Solid Solution Models 89
4.2.2.1 Ideal Solution Model 94
4.2.2.2 Strictly Regular Solution
Model 9 6
4.2.2.3 Delta Lattice Parameter
Model 100
4.2.2.4 First Order Quasi-Chemical
Model 10 4
5 PROCESS CONTROLLABILITY & OPTIMUM OPERATION
CONDITION 112
5.1 Interdependence of Process Parameters
in Hydride VPE of InGaAsP 117
5.2 Compositional Sensitivity 120
5.3 Parameter Value Fluctuation 121
5.4 Process Controllability Evaluation 124
5.5 Process Controllability Study 125
5.5.1 InGaAs Lattice-Matched to InP 125
5.5.2 InGaAsP Lattice-Matched to InP.... 130
5.6 Process Sensitivity Analysis 133
5.6.1 Relative Sensitivities in Hydride
VPE of InGaAs 136
5.6.2 Relative Sensitivities in Hydride
VPE of InGaAsP 142
6 MODELING OF GALLIUM AND INDIUM SOURCE
REACTORS 15 5
6.1 Thermodynamic Model 158
6.2 Nonequilibrium Mechanisms 160
6.2.1 Chemical Reaction Kinetics 160
6.2.2 Transport Phenomena 164
6.2.2.1 Hydrodynamic and Thermal
Entrance Region Effects... 165
6.2.2.2 Mass Transport in the
Reaction Zone 169
6.3 Transport Models 171
6.3.1 2-D Convective Diffusion Model.... 171
6.3.2 Axial Dispersion Model 179
7 EXPERIMENTAL STUDY OF GALLIUM AND INDIUM
SOURCE TRANSPORT AT NORMAL PRESSURE 18 6
7.1 Literature Review 186
7.2 Experimental Method 187
7.3 Data Analysis 193
7.4 Results and Discussion 194
7.4.1 Gallium Source Transport 194
7.4.2 Indium Source Transport 203
8 EXPERIMENTAL STUDY OF GALLIUM AND INDIUM
SOURCE REACTIONS AT LOW PRESSURE 214
V

8.1 Equilibrium Calculations 214
8.2 Experimental Method 218
8.3 Data Analysis 223
8.4 Results and Discussion 223
8.4.1 Gallium Source Reaction 223
8.4.2 Indium Source Reaction 228
9 CONCLUSIONS AND RECOMMENDED FUTURE WORK 234
9.1 Conclusions 234
9.2 Discussions and Suggested Future Work... 241
REFERENCES 245
BIOGRAPHICAL SKETCH 250
vi

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PROCESS DESIGN ISSUES
IN HYDRIDE VAPOR PHASE EPITAXY OF
INDIUM GALLIUM ARSENIDE PHOSPHIDE
By
JULIAN JUU-CHUAN HSIEH
April 1988
Chairman: Dr. Timothy J. Anderson
Major Department: Chemical Engineering
Hydride vapor phase epitaxy (VPE) has been used to
prepare indium gallium arsenide phosphide thin film devices
in the industry. One objective of process design for hydride
VPE of In]__xGaxASyP2__y is to achieve composition control of
deposited epitaxial films. The resolution of this process
design issue involves investigating the dependence of solid
solution composition on various process parameters.
Complex chemical equilibrium analysis of the
In/Ga/As/P/Cl/H system is constructed with the required
thermochemical data and calculation procedures to evaluate
the dependence of solid solution composition on process
parameters at equilibrium conditions. Simulation of
composition controllability at different parameter settings
was also investigated for the growth of two technologically
vii

important compositions, In.53Ga.47As and In.74Ga.26As.56P.44•
The results indicate the range of parameter settings for best
control of composition.
Transport and reaction kinetic limitations were found to
exist in gallium and indium source reactors in hydride VPE.
The nonequilibrium mechanisms slow down the reaction of
hydrogen chloride with gallium and indium. Experimental
characterization of source reactors was carried out at normal
pressure in the temperature range 943-1131 K. The reaction
products, group III metal chlorides, were collected in cold
traps and the group III transport rate was measured by atomic
absorption spectrometry. Group III monochloride was found to
be the dominant reaction product. With the application of a
two-dimensional convective diffusion model, first-order
heterogeneous rate constants were determined for both gallium
and indium source reactions. In order to study the reaction
kinetics of HC1 with liquid Ga and In at dif f us ion 1 e s s
conditions, low pressure (< 1 Torr) experiments were carried
out in the temperature range 973-1223 K. The HCl consumption
was measured by mass spectrometry and an axial dispersion
model was developed to reduce the data. First order rate
constants determined at low pressure were quite different
than determined from the normal pressure results. It is
suggested that quite different surface conditions or reaction
mechanisms exist at different pressures.
viii

CHAPTER 1
INTRODUCTION
Vapor phase epitaxy (VPE) of group III-V compound
semiconductors by the hydride process has proved to be a
successful method for producing device quality films,
particularly for growth of In]__xGaxAsvP]__y solutions [1]. In
this process the source species are gaseous group V hydrides
and volatile group III chlorides generated by reacting HC1
with liquid group III metal at elevated temperature.
Control of the solid solution composition is the primary
concern in process design of hydride VPE for thin film
deposition of In.]__xGaxASyP]__y solutions. The large number of
process parameters and the incomplete understanding of how
these parameters influence composition control, however, have
complicated process design issues and discouraged potential
users.
In this dissertation work, a unified approach to the
process design issues was attempted. The process design
considerations were taken to identify the important process
design issues. The relationships between the process
parameters and the process controlling mechanisms,
thermodynamics, transport phenomena and reaction kinetics,
were established. Composition controllability and source
1

2
zone reaction kinetics were two areas of particular interest
in the process design of hydride VPE of Ini_xGaxASyP]__y.
These two topics form the central theme of this dissertation.
Chapter 2 presents a survey of some physical and
electrical properties of III-V compound semiconductors and
the practical importance of the quaternary semiconductor
material Ini_xGaxASyP]__y. Most device applications of III-V
compound semiconductors require successful growth of
epitaxial film.
In chapter 3, hydride VPE is introduced and reviewed.
Both process thermodynamics and nonequilibrium mechanisms,
transport and kinetics, are important for process design
considerations. This chapter is concluded with an outline of
the important process design issues in hydride VPE of
I ril —XGaxASyP J^_y .
A complex chemical equilibrium analysis is performed to
determine the equilibrium composition of the system under
specified conditions. Formulation and calculation procedures
for complex chemical equilibrium analysis in the
In/Ga/As/P/H/Cl system are detailed in chapter 4. Process
controllability, specif-ical ly the solid solution composition
controllability, can also be evaluated through the aid of
complex chemical equilibrium analysis. Controllability
studies for two technologically important Ini_xGaxAsvPi_v
compound compositions are reported in chapter 5.

3
A thermodynamic model and transport models are presented
in chapter 6. These models were developed to assist
definition of experimental operating conditions and reactor
geometry and to interpret the experimental data.
Experimental studies of the performance of gallium and
indium source reactors at both atmospheric and reduced
pressure are presented in chapter 7 and chapter 8,
respectively. The data were analyzed by the application of
the appropriate transport model. Rate expressions are
deduced and reported.
Conclusions on composition controllability study and
source zone transport reactions are given in chapter 9. The
results of the experimental studies are compared and
discussed. Finally, areas for future investigation of
process design issues in hydride VPE of In]__xGaxAsvP^_v
suggested.
are

CHAPTER 2
III-V COMPOUND SEMICONDUCTORS
2.1 Physical and Electrical Properties
Table 2-1 lists the band gap energy, lattice parameter,
refractive index, dielectric constant, conduction band
effective mass and valence band effective mass of the nine
binary III-V compounds made from group III atoms(Al, Ga or
In) and group V atoms(P, As or Sb) . Five of the nine
compounds(InP, GaAs, InAs, GaSb and InSb) have a direct
energy gap. In general, increasing the atomic weight of the
group III or group V element decreases the band gap energy,
increases the refractive index, and the lattice parameter
increases with the exception of Ga-Al pairs. The In and Ga
binary III-V compound are available as substrate materials.
Ternary -and quaternary mixtures usually have properties
intermediate between the end components. Most device
applications include heteroepitaxial growth of multicomponent
solutions that are lattice-matched to the available binary
substrates. These structures permit variation of the band
gap energy, which provides physical and electrical properties
and device applications beyond the range possible with
elemental semiconductors.
4

5
Table 2-1. Lattice parameter, band gap energy, refractive
index, electron effective mass and hole effective
mass of III-V binary compounds.
III-V
binary
compound
Lattice
parameter
(nm)
Band gap
energy
(eV)
Refractive
index
Electron
effective
mass
Hole
effectiv
mass
A1P
.54625
2.45(1)
3.027
—
0.70mo
AlAs
.56611
2.16(1)
3.178
0.15 mg
0.79mo
AlSb
.61355
1.58(1)
3.400
0.12 mg
0.9 8mQ
GaP
.54495
2.261(1)
3.452
0.0 82mQ
0.6 OmQ
GaAs
.56419
1.42(D)
3.655
0.067mo
0.4 8mo
GaSb
.60940
0.81(D)
3.820
0.042mo
0.44mo
InP
.58687
1.35(D)
3.450
0.0 77mQ
0.64mQ
InAs
.60584
0.36(D)
3.520
0.0 23mo
0.40mo
InSb
.64788
0.236(D)
4.000
0.0145mo
0.40mo
(I): indirect band gap
(D): direct band gap

6
When more than one element from group III or group V is
distributed on group III or group V lattice sites,
111 x 111 ]_ -XV or IIIVyV]__y ternary alloys can be achieved.
There are 18 possible ternary systems among the group III
elements(Al, Ga, In) and group V elements(P, As, Sb).
The band gap energy Eg(x) or Eg(y) of a ternary compound
can be represented as a quadratic function of composition.
For example,
Eg(x) = Eg/0 + ax x + a2 x2 (2-1)
where Egfo is the band gap energy of the binary compound at
x = 0. The bowing parameter a2 has been determined
theoretically by Van Vetchen and Bergstresser [2]. Their
theory may be used to estimate a2 when experimental data are
unavailable. The lattice parameter of a ternary compound is
generally well represented as a linear function of the alloy
composition. This is called the Vegard's law, which is
obeyed quite well in III-V ternary alloys. The composition
dependence of the direct energy gap in the III-V ternary
solid solutions at 300 K can be found in the literature [3].
Two kinds of quaternary compounds exist. The first kind
is of the type AyBzC]__y_zD, where A, B and C are group III
elements, or the type AByCzDi_y_z, where B, C and D are group
V elements. This kind of quaternary compound can be
considered as composed of three binary compounds. The

7
calculation of lattice constant for this kind of quaternary
compounds obeys Vegard's law. The second kind is of the type
Al-xBxcl-yDy' where A and B are group III elements, and C and
D are group V elements. This kind of quaternary compound can
be considered as composed of two ternary compounds (1-x mole
fraction of ACyD]__y and x mole fraction of BCyD]__y, or 1-y
mole fraction of A]__XBXC and y mole fraction of A^_XBXD) or
of four binary compounds (AC, BC, AD and BD) of indeterminate
molar percentages. Ilegem and Panish [4] calculated the
phase diagrams for the second kind with the quaternary alloy
decomposed into ternary alloys. Jordan and Ilegems [5]
obtained equivalent formulations by treating the solid as a
mixture of binary alloys: (l-x)y AD, (1-x)(1-y) AC, x(l-y) BC
and xy BD. The lattice parameter of the quaternary alloy
A1 _xBxC]__yDy is assumed to depend linearly on the composition
of its ternary components. Since the lattice parameter of a
ternary compound can be determined by Vegard's law, so the
lattice parameter ag of the alloy A]__xBxC]__yDv is given by
a0 = (1-x)y aAD + xy aBD + x(l-y) aBC
+ (1-x)(1-y) aAC (2-2)
The band gap energy determination is more complicated. The
bowing parameters, however, are found to be small and can be
neglected and the band gap energy may be approximated from
the band gap of the binaries as follows

8
Eg = (l-x)y Eg AD + xy Eg BD + x(l-y) Eg BC
+ (1-x) (1-y) EgfAC. (2-3)
Figure 2-1 [6] illustrates schematically the variation
of the band gap energy and the lattice parameter with respect
to composition for the second type quaternary compound
InGaAsP. Also shown in figure 2-1 are the composition planes
of two compounds of the first kind, AlGalnAs and AlGalnP.
Each compositional plane of the first kind is surrounded by
three ternary compositional lines, with a total of three
binary endpoints, and thus triangular. The quaternary
compositional plane of the second kind, enclosed by four
ternary lines and four binary points, is always square.
Constant lattice parameter and constant direct band gap
energy are shown in the compositional plane of InGaAsP in
figure 2-1 by solid lines and broken lines, respectively.
The boldface lines indicate the ternary and quaternary
compositions lattice-matched to binary compounds, with the
solid line for GaAs lattice matching compositions and the
broken line for InP.
2.2 Material and Device Perspectives
The existence of a direct energy gap in compound
semiconductors (e.g., InSb, InAs, InP, GaSb and GaAs) is in
contrast to the indirect band gap of Si and Ge. In general,
direct band gap materials also have a high electron mobility.
These properties offer the potential for high efficiency

9
Al As
Figure 2-1. The compositional plane for In;j__xGaxAsvP-L_v at
300K [6]. The boldface solid line represents the
GaAs-lattice matching composition. The boldface
broken line represents the InP-lattice matching
composition. The solid lines are for constant
lattice parameters. The broken lines are for
constant direct bandgap energy values. The
shaded area at the lower left corner is the
indirect band gap region.

10
light emitting, light sensing, and high speed switching
devices. With the band gap energy of these compounds ranging
from 0.17 eV (InSb) to 2.2 eV (GaP), these compounds provide
an ideal basis for the preparation of semiconductor materials
with the desired energy gap over a continuous spectrum of
energies.
Because of the difficulties related to the preparation
of single crystals of III-V compounds, all of the available
single crystal substrate materials are binary compounds.
Although all of the Ga and In binary compound are available,
only GaAs and InP are produced in large quantity with good
quality at the present time. In order to access the full
range of property values offered by ternary and quaternary
compounds, it is necessary to grow layers of the desired
composition of the ternary or quaternary compound on a binary
substrate by the technique called "epitaxy." Epitaxy has
been used successfully in forming heterojunctions of III-V
compounds. A heterojunction is a junction in a single
crystal between two compositionally different semiconductors.
Due to the band gap differences across heterojunctions, the
effects of carrier and optical confinement are provided and
applications in optoelectronics and high-speed switching
devices are realized. Heterojuction devices, however,
require a low interfacial state density which demands good
lattice matching to reduce tension between the different
materials. Except for (Ga, Al)-containing ternary systems,

11
the III—V semiconductor ternary alloys suffer from severe
problems associated with lattice mismatch when grown on
binary substrates. The addition of a fourth component to the
alloy system gives a quaternary compound and allows the band
gap to be changed while maintaining a lattice parameter
matched to a particular binary substrate. Therefore, the
interest in quaternary alloys has centered on their use in
conjunction with binary and ternary compounds to form
lattice-matched heterojunction structures with different band
gaps. The Ini_xGaxASyP]__y/InP hetero junction with 2.12x=y is
one example of a lattice-matched system.
2.3 Binary, Ternary and Quaternary InGaAsP Compound
2.3.1 Applications
In terms of present device applications, InGaAsP is the
most important III-V quaternary compound semiconductor.
Figure 2-1 indicates the lattice parameter and the band gap
energy for any given InGaAsP composition. To maintain a
given lattice constant for the quaternary system a
simultaneous variation of the Ga/In and As/P ratio is
required. Both InP and GaAs are useful substrate materials
for lattice-matched heterojunctions. The InP-based system
covers the band gap energy range 0.75 to 1.35 eV (wavelength
range 1.65 to 0.92 micrometer) while GaAs-based system ranges
from 1.42 to 1.9 eV (0.87 to 0.65 micrometer). InGaAsP

12
matched to InP covers a longer wavelength region and as a
result the material has aroused great interest for sources in
optical fiber communications systems operating at 1.3
micrometer and 1.55 micrometer where high-quality fused
silica fibers exhibit minimum transmission loss (less than 1
dB/km) and minimum material dispersion. The ternary endpoint
of this InGaAsP system, In.53Ga.47As lattice-matched to InP
has been developed as light detectors to complement the 1.3
to 1.6 micrometer light sources. InGaAsP matched to GaAs
with shorter wavelength is also of interest in the
applications of visible lasers and light-emitting diodes.
The interest in InGaAsP lattice-matched to InP has been
expanded to microwave device applications ever since superior
mobilities and velocity-field characteristics were predicted
from theoretical calculations [7] on both GaAs and InP.
Later experimental observations, however, did not agree with
the calculated curves of low-field mobility across the
composition range, except for the ternary end-point,
In . 53Ga.47As . Consequently, attention has been focused on
this ternary. Room temperature mobilities of 11,000 to
13,800 cm^/v-sec have been recorded [8-10] and these are the
highest mobilities of any III-V semiconductor suitable for
room temperature operation. With high peak velocity and low
threshold field [11, 12], transferred electron oscillation
devices with improvements over GaAs and InP are possible.
Computer calculations [13] also showed that In.53Ga.47As

13
(lattice-matched to InP) offers superior dynamic properties
to InP or GaAs. Since the high frequency operation makes use
of transient properties of the material rather than steady-
state properties, the ternary material would appear to be a
very useful candidate in microwave and millimeter-wave
applications.
Future devices that are likely to achieve considerable
attention are integrated circuits involving both optical and
high-speed logic devices. Integrated optical circuits will
contain sources (laser or light-emitting diode), passive
waveguides, modulators, couplers, switches and detectors all
on one chip. This is possible due to the versatile
properties of the InGaAsP alloy range lattice-matched to InP.
High-speed integrated logic devices could combine the
sensitive current control and short delay time of Gunn
devices with stable on-off operation of MESFET devices, all
made of InGaAsP lattice-matched to InP.
2.3.2 Epitaxy
Figure 2-2 shows the simplified diagrams of two typical
InGaAsP/InP heterojunetion devices, a InGaAsP double
heterostructure (DH) semiconductor laser and a InGaAs
photodetector. For both of these heterojuction devices, it
is required to grow layers of semiconductor materials of
different compositions on top of the substrate. Such
controlled growth of crystal, termed "epitaxial growth," has

14
a
b
Figure 2-2. Simplified diagrams for typical InGaAsP/InP
hterojunction devices. a. InGaAs/InP diode
photodetector. b. double heterostructure
semiconductor laser.

15
been accomplished by a number of techniques, including
hydride vapor phase epitaxy(hydride VPE), trichloride vapor
phase epitaxy(chloride VPE), metalorganic chemical vapor
deposition (MOCVD) , liquid phase epitaxy (LPE) and molecular
beam epitaxy (MBE). Excellent reviews are in the literature
which discuss the general aspects of these techniques (e. g.
hydride VPE [14], trichloride VPE [15], MOCVD [16], LPE [17],
and MBE [18]) .

CHAPTER 3
HYDRIDE VAPOR PHASE EPITAXY OF
INDIUM GALLIUM ARSENIDE PHOSPHIDE
Hydride vapor phase epitaxy is a member of the set of
processes termed vapor phase epitaxy(VPE). VPE processes
adopt a halide transport chemistry, in which the group III
elements are transported to the deposition reaction region in
the form of group III halides. For chloride representing the
halide species, the monochloride e.g., GaCl or InCl is the
dominant species at elevated temperature. Depending upon how
the group V species is introduced into the reactor, two
techniques exist in VPE: the "hydride" technique [19] and the
"trichloride" or simply "chloride" technique [20]. The main
attraction of the chloride technique is its ability to
produce epitaxial materials with extremely low background
impurity levels. One drawback of the chloride process is
that gaseous group V trichloride is introduced by evaporation
of a liquid, and therefore its transport rate varies
exponentially with temperature. The major drawback, however,
is that the transport rate of group III chlorides is
determined by the input flowrate of group V trichloride,
therefore independent control of III/V ratio is not possible
with the chloride technique. The gas phase III/V ratio above
the growing film determines the point defect structure of the
16

17
grown film and therefore the electrical properties. The
hydride system, on the other hand, has the advantage that all
input reactants to the system are gaseous and can be
independently controlled in a linear manner. The drawbacks
of the hydride process include less purity of the starting
materials (i.e. group V hydrides) and increased safety
concern in handling hydrides. In spite of the disadvantages,
hydride VPE is widely accepted in the industry, especially
for the preparation of ternary and quaternary alloys of In
and Ga.
3.1 Process Chemistry
The chemistry of the hydride vapor phase epitaxy
technique can be illustrated by describing the reactions
involved in the growth of gallium arsenide. A representative
schematic diagram of a hydride VPE reactor used for the
preparation of GaAs is shown as in figure 3-la. The reactor
is usually heated by a multi-zone resistance furnace. The
most upstream temperature zone, operated in temperature range
1000-1150 K, is termed the source zone. In this zone, HC1 is
introduced into the reactor in a carrier gas, usually H2, to
react with pure gallium liquid to form principally gallium
monochloride
Ga(1) + HC1 < > GaCl + 1/2 H2.
(3-1)

18
Source
Zone
Mixing Deposition
Zone Zone
1 050-1 150K 11 00-1 200K 950-1050K
a
b
Figure 3-1. Schematic diagrams of hydride VPE processes.
a. growth of GaAs. b. growth of Ini_xGaxAsyPi_y

19
Arsine, diluted by the carrier gas, is introduced in the
second temperature zone (the mixing zone) which is operated
at temperature equal to or slightly above the source zone.
In the mixing zone part of arsine thermally decomposes
forming molecular arsenic species and hydrogen. The main
reactions are
ASH3 < > 1/2 As2 + 3/2 H2
(3-2)
As2 < > 1/2 As4
(3-3)
The decomposition of arsine is pyrolytic with arsenic dimer,
As2, and tetramer, As4, being the major products. Depending
upon the reactor design and the operating condition of the
mixing zone, the dominant arsenic species can be unreacted
ASH3, As2 or As4. Gallium monochloride, unreacted HC1 and
arsenic-containing species are then mixed in the mixing zone
and transported to the deposition zone. Gas-solid reactions
occur in the deposition zone in the temperature range 9 5 0-
1050 K. The major reactions are
GaCl + 1/2 As2 + 1/2 H2 < > GaAs(s) + HC1 (3-4)
GaCl + 1/4 As4 + 1/2 H2 < —
\
/
GaAS(S) + HC1
(3-5)
GaCl + ASH3 < > GaAs(s) + KC1 + H2
(3-6)

20
Each of the above reactions are thought to contribute to the
overall deposition rate. The presence of all of these
species in the deposition zone have been confirmed by Ban in
by mass spectrometric sampling [21] . The total growth rate
and the relative importance of a particular reaction path
depend upon the gas phase makeup in the deposition zone. The
double arrow (< >) sign in equations (3-1) to (3-6)
indicates that these reactions are reversible.
Similar chemistry exists for the growth of indium
phosphide if gallium is replaced by indium, and arsine by
phosphine. Ternary and quaternary alloys of the gerneral
chemical formula Inj__xGaxASyP]__y can also be grown by this
technique. Figure 3-lb shows the schematic diagram of a
reactor used for growing In]__xGaxASyP]__y quaternary alloy.
In this reactor design, two separate HC1 flows are admitted
to the source zone to independently transport indium and
gallium. Arsine and phosphine are introduced into the mixing
zone through the same gasline, and partially decompose to
group V molecular species. In addition to the formation of
the dimers and tetramers of the group V elements, molecules
composed of both arsenic and phosphorous atoms are also
possible. For example,
As2 + P2 < > 2 AsP (3-7)
n As4 + (4-n) P4 < > 4 AsnP4_n
n
1,2,3
(3-8)

21
The deposition process for the growth of InGaAsP, involving
all the chemical species generated and transported before
deposition zone, is very complicated and can not be
represented by a simple equation. However, the net equations
of the deposition reactions can be written as follows
r1: GaCl + 1/4 As4 + 1/2 H2 < > GaAs(s) + HC1 (3-9)
r2: GaCl + 1/4 P4 + 1/2 H2 < > GaP(s) + HC1 (3-10)
r3: InCl + 1/4 P4 + 1/2 H2 < > InP(s) + HC1 (3-11)
r4: InCl + 1/4 As4 + 1/2 H2 < > InAs(s) + HC1 (3-12)
Clearly, the overall deposition rate should be the sum of the
deposition rate for each binary compound. Thus the overall
deposition rate, r^-, is equal to r ]_ + r 2 + r 3 + r 4 . The
composition of the quaternary solid solution can also be
determined by the binary deposition rates through the
following mole balance equations
x = (r1 + r2)/rt = Y-i + X2 (3-13)
1—x = (r3+r4)/rt = X3 + X4 (3-14)
1-y = (r2+r3)/rt = X2 + X3
(3-16)

22
y = (r1+r4)/rt = X;]_ + X4
(3-17)
where
Xi = r±/rt, i=l,2,3 & 4 (3-18)
(X4, X21 X3, X4) is defined as the nearest neighbor pair
distribution. There values can be considered as the mole
fractions of the four binary compounds in the quaternary
alloy Ini_xGaxASyPi_y. The crystal is constructed at the
atomic scale by filling the crystal lattice with binary
pairs. For each nearest neighbor pair distribution, there is
only one corresponding solid composition (x, y). Since there
are infinite number of ways to fill the crystal lattice with
four binary pairs, the number of nearest neighbor pair
distribution for a fixed composition (x, y) is infinity.
This is a unique feature of the III-V quaternary compound of
the second kind.
The deposition reactions, equations (3-9) to (3-12), are
exthothermic, therefore deposition extent increases with
lower temperature. For this reason, resistance heated
reactors with hot walls are usually employed and the mixing
zone temperature is usually raised higher than both the
source zone and the deposition zone to prevent oversaturation
and extraneous deposition. The high temperature of the
mixing zone also enhances the decomposition of the group V

23
hydrides. Ideal epitaxial growth in the deposition zone
requires a well-controlled gas phase supersaturation over the
substrate. This condition is obtained by careful design of
the process apparatus and complete understanding of the
process behavior.
3.2 Literature Review
The epitaxial growth of GaAs by direct synthesis from
evaporated solid arsenic and gallium chloride was reported by
Amick [22]. Tietjen and Amick [19] redesigned Amick's
apparatus to permit the introduction of arsenic in the form
of its arsenic hydride, ASH3, and reported the preparation of
homogeneous solid solutions of gallium arsenide-gallium
phosphide, GaASyP]__y, by the addition of arsine and phosphine
in the reactor at the same time. The objective was to
develop a process which permitted independent control of the
partial pressures of group V and III species. Before the
adoption of this technique, liquid or solid arsenic and
phosphorus were sometimes provided as the group V sources,
which results in exponential dependence of the vapor
pressures on the temperature of the source reservoirs. This
dependence, although not critical for binary compound growth,
is extremely important for the preparation of homogeneous
ternaries and quaternaries. Hydride gas sources can also be
diluted in hydrogen to any desired concentration, and metered
into the apparatus through electronic mass flow controllers,

2 4
allowing the introduction rate to be held constant and
measured with precision. The independent control of arsine
and phosphine flowrates provided the possibility of gradual
or rapid changes in the composition of the growing layer.
Also, because of the separation of the introduction of group
III and group V species, variation of V/III ratio is
achievable. Doping of both n-type and p-type over a wide
range of resistivity can be obtained with different V/III
ratios. Because of its success in preparing homogeneous
GaASyP^-y alloys for a wide range of doping concentrations
and its versatility to grow multi-layer structure, hydride
VP E was adopted industrially in the mass production of
GaASyPi_y light emitting diodes.
The vapor growth of InGaAsP lattice-matched to GaAs was
first reported by Olsen and Ettenberg [23], Sugiyama et. al.
[24] and Enda [25]. Hydride VPE of InGaAsP lattice-matched
to InP has been described by Olsen et. al. [26], Beuchet et.
al. [27], Hyder et. al. [28], Mizutani [29] and Yanase et.
al. [30]. The hydride VPE of InGaAs lattice-matched to InP
has been reported by Susa et. al. [31], Olsen et. al. [32]
and Zinkiewicz et. al. [33].
A single-barrel hydride VPE reactor for the growth of
I n i_xGaxASyP^_y is exemplified as in figure 3-lb. The
associated chemistry has been introduced in section 3.1. It
is cumbersome to prepare multi-heterojunction layers in the
single-barrel reactors because the substrate has to be slid

25
out of the deposition zone during reactant changeover and the
subsequent transient period. During this period the surface
quality is not always preserved. In recent years multi-
barrel hydride VPE reactors have been reported by a number of
researchers [27, 29, 34]. The concept involves the use of
more than one conventional VPE systems placed in parallel and
feeding into a single growth chamber. With multi-barrel
reactors, different gas mixtures can be run through different
source tubes, so that multiple heterojunction devices can be
prepared by simply switching the substrate from one tube to
the other, thus removing the need for preheat cycles. Growth
time is reduced and reactant chemicals are conserved in this
manner. In addition, surface defect states, induced by
preheating, are also minimized, improving the quality of the
heterojunction interface.
The process parameters that affect the growth rate and
the solid solution composition have been found to be the
reactant and carrier gas flowrates and the zone temperatures.
Since the Gibbs energy of formation for Ga arsenides and
phosphides are more negative than for the corresponding In
compounds, a higher HCl flowrate over the In source is
required than over the Ga source. Similarly, higher PH3
flowrate than ASH3 flowrate is required since phosphorus
compounds have higher vapor pressure at equilibrium than
arsenic compounds. For ternary compounds, increasing the
temperature will tend to increase the composition of the

26
binary component whose Gibbs energy of formation decreases
most with temperature. Thus, by increasing the deposition
temperature while holding other parameters constant, more Ga
and As tend to be incorporated in the solid solution.
Increasing the carrier gas flowrate results in a decrease of
reactant gas partial pressures and brings the same effect as
increasing deposition temperature. Growth rate, gas phase
transport and temperature uniformity in the deposition zone
are important factors to achieve film thickness uniformity
and compositional uniformity across the wafer.
Similar to other epitaxial processes, there has been an
ongoing effort to improve the purity of hydride VPE films.
Early studies [35, 36] reported that the purity of the HC1
and ASH3 was crucial to the material quality. But, later
published results on the chloride VPE system [37] showed that
in addition to certain fundamental parameters such as
reactant purity and general system cleanliness, impurity
incorporation in the epitaxial film is significantly
influenced by process parameters(e.g. , input ASCI3 mole
fraction, substrate orientation and substrate temperature).
It was proposed- by DiLorenzo and Moore [38] that silicon is
the major residual donor and the carrier concentration in
undoped (100) GaAs, prepared by chloride VPE, is determined
by the silicon activity in the vapor phase above the
substrate. This unintentional silicon doping is brought
about by the decomposition of chlorosilanes, which are formed

27
from the reduction of the silica reactor by hydrogen carrier
gas and hydrogen chloride. This doping reaction can be
described as follows
STEP 1: chloro-silane formation at reactor wall
n HC1 + Si02 + (4-n) H2 < > SiClnH4_n + 2 H20 (3-19)
STEP 2: silicon incorporation at substrate
(n—2) H2 + SiClnH4_n < > Si + n HC1 (3-20)
where n=0,1...4. At elevated temperature, equilibrium of the
above reaction steps is quickly attained. From equation (3-
20) , it is clear that the unintentional doping level of
silicon in the growing GaAs epitaxial layer should decrease
with an increase of HC1 in the vapor phase. This theory
successfully explained the decrease of carrier concentration
and the increase in electron mobility in the preparation of
GaAs in trichloride method by increasing the partial pressure
of ASCI3. In light of this finding, Kennedy et. al. [35]
studied the effect of the hydrogen carrier gas flow rate on
the electrical properties of epitaxial GaAs prepared in a
hydride system. By reducing the hydrogen carrier gas flow
rate while holding the flowrates of HC1 and ASH3 constant,
thus raising the mole fraction of HC1 in the vapor phase,
improvement of epitaxial film quality, including a decreasing
total impurity level, decreasing carrier concentration and

28
increasing electron mobility were obtained. This result
seemed to agree with Dilorenzo's explanation of silicon
incorporation in chloride VPE. When additional HC1 was
introduced downstream of the reactor source zone, however,
further improvement, anomalous results were observed. The
anomalous doping behavior could not be explained by the
Dilorenzo model or by impurities contained in the reactant
gases. Pogge and Kemlage [39] studied the effect of arsine
on impurity incorporation and proposed a surface kinetic
model. The decrease of residual silicon concentration with a
higher ASCI3 mole fraction in the trichloride system,
observed by DiLorenzo [40], was explained by Pogge's model as
a result of blocking of impurity atoms from the surface sites
by the adsorption of As 4. Since surface sites can be
occupied by the adsorption of both arsenic and gallium
chloride, the unintentional doping level should decrease with
an increase in the total concentration of arsenic and gallium
chlorides in the vapor phase. The findings of Kennedy et.
al. [35] could also be explained by this model. In fact, by
using Pogge's model and considering that the total
concentration of group V molecules and group III chlorides in
hydride VPE has been traditionally lower than chloride VPE,
one could perceive why the resulted epitaxial film prepared
by hydride VPE has had higher residual impurity and inferior
carrier mobility than what has been achieved by chloride VPE.
Abrokwah et. al. [41], using a commercial hydride VPE,

29
achieved undoped epitaxial GaAs of high purity comparable to
the best chloride VPE results. The effects of the flowrates
of HC1 over Ga source and arsine were studied and showed
qualitative agreement with Pogge's theoretical model. When
the arsine flowrate or the HC1 flowrate over gallium was
increased a higher purity in the epitaxial film was achieved.
When a secondary HCl flow was introduced at the downstream of
the gallium boat, the film purity was decreased and the
epitaxial layer was more compensated as a result of increased
acceptor incorporation. The secondary HCl probably does
react with SÍO2 introducing some amount of silicon to the
growing layer; however, the incorporation mechanism might be
kinetic and cannot be compared with DiLorenzo's equilibrium
model. It was realized also in Abrokwah's study that a clean
gallium surface can gather metallic contaminants in the HCl
flow, thus reducing acceptor incorporation and compensation.
An aging effect of the HCl tank was also observed to create
high level of metallic chloride contaminants, affecting
epitaxial layer quality and should be carefully taken into
account. Because of the contamination problems related to
the HCl tank, the studies on the influence of HCl
concentration on silicon donor level by a secondary HCl flow
have so far failed to give interpretable results on the
incorporation mechanism of this residual donor. By far-
infrared photoconductivity and low temperature
photoluminescence measurements, Abrokwah et. al . [41] also

30
found sulfur to be the dominant residual donor, and carbon
and zinc to be the major acceptors in their undoped GaAs
prepared by the hydride VPE technique. By cooling the HC1
liquid source to 198 K, Enstrom and Appert [42] reported
consistently improved mobility and impurity incorporation in
hydride VPE of GaAs and InGaAsP. Improved results were
obtained even after extended use of the HC1 at room
temperature after initial cooling. It was argued that when
liquid HC1 is cooled, impurities are forced out of the HC1
phase and can then be swept out of the tank during a short
purge conducted prior to use for vapor growth. From these
studies, it is clear that in order to obtain ultra-pure
undoped GaAs by hydride VPE, one has to (i) maintain the HC1
tank at high purity, (ii) avoid secondary HC1, (iii) maximize
arsine flowrate to block residual donors (e.g. Si, S)
incorporation, (iv) minimize HC1 flowrate to reduce residual
acceptors (Cu, Zn) contamination levels, (v) prevent
contaminants (C, O, S) from leaks and (vi) maintain the
overall cleanliness of the apparatus. Hydride VPE generally
produces InGaAsP crystals with background impurity
concentrations around 5-20 x 1015 per cubic centimeter. This
unintentional doping level is low enough to produce good
laser and light-emitting-diode structures.
P-type doping can be accomplished by heating a bucket of
zinc in a hydrogen atmosphere in order to obtain elemental
zinc vapor or by introduction of gaseous diethyl-zinc (DEZ).

31
N-type doping is accomplished by adding hydrogen sulfide to
the hydride line.
Surface defects(pits and hillocks) are the major
problems in the attainment of good surface morphology.
Kennedy and Potter [43] studied the effect of various growth
parameters on the formation of pits and hillocks on the
surface of epitaxial GaAs layers by hydride VPE and found
that the appearance of pits with a paucity of GaCl in the
vapor phase at the deposition zone and the appearance of
hillocks with an excess of GaCl in the vapor phase at the
deposition zone.
The advantage of hydride vapor phase epitaxy is the
finely controlled gas composition, which allows easy control
of alloy composition, doping and surface morphology. Hydride
VPE also has the potential of easy scale-up for large
quantity device manufacture. Hydride VPE has proved its
suitability for fabricating epitaxial In^_xGaxASyP]__v
quaternary compound with high crystalline quality, planar and
uniform layers and reproducible properties. Thickness
uniformities of +5%, composition uniformities of +0.1%, and
interfacial transient width of 3.5 nm have all been reported
in the literature.
3.3 Process Design Issues
Process design involves both the appropriate design of
process equipment and the optimum choice of process operation

32
conditions. The ultimate goal is an efficient and effective
process, which can be judged by its performance in process
controllability, process reproducibility, and product
quality. Prediction of optimum process operation conditions
with a specific process equipment design requires a complete
understanding of how the process and the product quality
respond to the changes of process parameter settings.
Prediction of optimum operation conditions for hydride
VPE of In]__xGaxASyP]__y is difficult because of the complexity
of this reaction system. Whereas liquid phase epitaxy can be
considered to take place under near equilibrium and
deposition from metalorganic chemical vapor deposition
(MOCVD) is a typical nonequilibrium process, both hydride VPE
and chloride VPE are intermediate techniques. In general,
equilibrium is not achieved in hydride VPE and the effect of
reaction kinetics and mass transfer can further shift the
reactor performance from the thermodynamic values. A
meaningful description of the hydride VPE process requires
considerations of both the equilibrium (thermodynamics) and
the nonequilibrium (reaction kinetics, mass transfer) aspects
of the process.
3.3.1 Process Thermodynamics
A thermodynamic treatment of a hydride VPE process
requires knowledge of the chemical species present in the
process and the appropriate thermodynamic data of these

33
species. In addition, for growth of a ternary or a
quaternary alloy, a solid solution model that describes the
activities of each binary constituents in the alloy has to be
chosen.
A detailed thermodynamic treatment of hydride VPE of
Ini_xGaxASyPi_y will be discussed in Chapter 4. Here, a
simplified treatment for hydride VPE of GaAs is given as
follows. The objective of this treatment is to demonstrate
how the maximum attainable deposition rate is determined by
equilibrium considerations only and why the real deposition
rate can be different from the thermodynamically predicted
values.
From the calculation of Hurle and Mullin [44] , it can be
assumed that ü 2 ' HC1, GaCl and A s 4 are the only
quantitatively important species during hydride VPE of GaAs
when Cl/H, the ratio of the number of input chlorine atoms
over the number of input hydrogen atoms, and As/H, the number
of input arsenic atoms over the number of input hydrogen
atoms, are equal and less than 0.01. Therefore, it is
sufficient to consider the equilibrium between these chemical
species for the calculation of the equilibrium growth rate.
In the source zone, HC1 reacts with Ga to form GaCl at
source temperature Ts according to equation (3-1). If
equilibrium is reached and the hydrogen partial pressure is
close to 1 atm, the partial pressures of HC1 and GaCl have
the relationship,

34
pGaCl = K1 PHC1' (3-21)
in which is the equilibrium constant for reaction equation
(3-1). The chlorine balance equation is
p0HCl = PHC1 + pGaCl• (3-22)
where P^HCl is the HC1 partial pressure in the input flow.
From equations (3-21) and (3-22) , PcaCl and PHC1 can be
solved.
PHC1 = 1/(1+Ki) P°HC1 (3-23)
pGaCl = Kp/d + Ki) P°hc1 (3-24)
Assuming complete decomposition of arsine in the mixing zone,
then
pAs “ p/4 pAsH (3-25)
4 3
The equilibrium deposition rate of reaction equation (3-
5) is dependent on the partial pressures of the reactants,
equations (3-23) to (3-25) , and the deposition zone
temperature T¿. Clearly, if equilibrium is reached in the
deposition zone, then

35
Kd(Td)=-
HC1
(PHd + ss)
0.25
PS PS
GaCl As4
4
0.25
(3-26)
where is the equilibrium constant for equation (3-5), Pej_
is the partial pressure of gas species i at equilibrium, and
ss is defined as the amount of super satura tion in the
deposition zone. Also assumed in equation (3-26) is that
carrier gas hydrogen is in excess with partial pressure close
to 1 atm. The equilibrium maximum attainable growth rate
(Rg) is proportional to the amount of supersaturation
available for deposition. Therefore, after solving equation
(3-26) for ss, Rg can be obtained from the following
equation.
R
g
SS Vf Vm
R T¿ As
(3-27)
In the above equation, Vf represents the total volumetric
flowrate, R is the gas constant, Vm is the molar volume of
the solid compound, and As is the substrate surface area.
The actual deposition rate is always less than the rate
calculated above. When equilibrium is not reached in the
source zone and mixing zone, the supersaturation ss can be
very different from that calculated from equation (3-26).
Eesides, the actual deposition rate is influenced by mass
transfer, chemical kinetics and residence time in the

36
deposition zone. These nonequilibrium mechanisms drive the
deposition reaction away from the equilibrium growth
condition.
3.3.2 Nonequilibrium Mechanisms
In vapor phase epitaxy with open flow systems, the
reactive species are transported through the reactor tube
with a carrier gas and undergo chemical reactions along the
transport axis leading to a change in gas phase composition.
A sequence of steps is followed for these reactions to take
place.
STEP 1: Mass transport of chemical vapor reactants
(into the reaction zone)
STEP 2: Mass transfer of reactants to condensed
surfaces
(source zone: melt metallic III surface)
(mixing zone: quartz reactor wall)
(deposition zone: substrate surface)
STEP 3: Surface processes: adsorption, surface diffusion
STEP 4: Chemical reaction at the surface
STEP 5: Surface processes: diffusion, desorption

37
STEP 6: Mass transfer of gaseous reaction products away
from the surface
STEP 7: Mass transport of reaction products and
unreacted reactants
(away from the reaction zone)
Steps 2 and 6 represent mass transfer of species between the
main gas stream and the condensed surfaces. This transfer
occurs through physical mechanisms such as intermolecular
diffusion and convective diffusion. Reaction rates that are
limited by these steps are said to be controlled by mass
transfer or, in general, diffusion-limited. Steps 3,4 and 5,
involving adsorption, surface reaction, surface diffusion,
and desorption, are complicated. Although the separate
effect of each step is very difficult to determine, the
combined effect of these surface steps can be distinguished
from the physical mechanisms of diffusion and convection.
Reaction rates that are limited by surface mechanisms are
usually called kinetica1ly-1imited . No matter how the
reaction rates are controlled, equilibrium results when the
main gas stream allows sufficient residence time, step 1 and
7, for the physical and chemical mechanisms, steps 2 to 6, to
achieve complete equilibration. In this case, the gas phase
composition at the outlet of the reaction zone (step 7) can
be determined by the gas phase composition of step 1

38
bypassing the consideration of the nonequilibrium mechanisms.
Thermodynamic equilibrium of hydride VPE system has been
briefly discussed in the last section.
When the process is controlled by nonequilibrium
mechanisms, process parameters, temperature, flowrates,
pressure, etc., influence the process behavior according to
the actual controlling step. For example, reaction rates for
kinetically-limited processes usually have very strong
temperature dependence, expressed as
r = r0 exp (-Ea/RT),
(3-28)
where r is the actual reaction rate, rg is the preexponential
constant, R is the gas constant, T is the reactor temperature
in Kelvin, and Ea is the activation energy for the surface
reaction or kinetic process. On the other hand, for a
diffus ion-1imited process, the temperature dependence is
relatively small. Gas phase diffusion coefficients for
molecular species are proportional to Tm, with m varying from
1.5 to 2. Another example is the dependence of process
behavior on gas phase hydrodynamics, which directly results
from the reactor design and flowrate settings. Diffusion-
limited processes are very sensitive to hydrodynamic effects,
while kinetically-limited processes are not influenced by
these parameters. Kinetica1ly-1imited processes are also
affected by the surface properties of the condensed phase

39
e.g., crystal orientation, surface cleanliness, surface
defects.
The slowest step of steps 2 to 6 determines the local
reaction rate. The rate-limiting step, however, can change
from point to point in a reaction zone causing the problem of
non-uniformity. As discussed above, the overall reaction
rate is determined partly by the local reaction rate and
partly by residence time. Since the local reaction rate is
different for different reactor design and operating
conditions, the required residence time for reaching
equilibrium (reaction completeness) varies from one system to
another. It is important to understand that the local
nonequilibrium mechanisms always exist regardless of the
length of residence time and the degree of reaction
completeness.
3.3.3 Process Design Considerations
Figure 3-2 outlines the process design considerations
for hydride vapor phase epitaxy of binary, ternary and
quaternary Ini_xGaxASyPi_y. The primary objectives, as
indicated in figure 3-2 by the shaded boxes, are to control
the epitaxial layer composition and thickness. The process
designer's choices, including the parameter settings and the
design of the three reaction zones, are represented in figure
3-2 by the bold-lined boxes. The solid-lined boxes in figure
3-2 connect "the process designer's choices" with "the

40
(Deposition Zone)
Equilibrium
Parameters
Complex
Chemical
Equilibrium
Source Zone
Process
Parameters
Source Zone
Design
Source Zone
Reaction Kinetics
Source Zone
Mass Transport
Mixing Zone
Process
Parameters
i
! Mixing
Zone
Design
Mixing Zone
Reaction Kinetics
Mixing Zone
Mass Transport ¡
Deposition Zone
Process
Parameters
Deposition Zone
Design
-â– 5H
Deposition Zone
Mass Trans or
Deposition Zone j_
Reaction Kinetics ;
Supersaturation
f
Composition
Controllability
¿i
&
•• S»; fí ...
Growth Rate
Reproducibility
Figure 3-2. Outline of process design considerations for
hydride vapor phase epitaxy of InGaAsP.

41
primary objectives" and contain the thermodynamic, physical
and chemical events in the process. These events have been
discussed in sections 3.3.1 and 3.3.2.
Because thermodynamic information is already available
and the convective diffusion process can be mathematically
simulated, mass transport in the source zone can be
calculated for known source zone design and operating
parameter settings if reaction kinetics in the source zone is
also known. It has been a common assumption that the
transport reaction in the source zone is rapidly attained,
therefore careful studies on source reaction kinetics have
been scarce and quantitative rate expressions, most desirable
for process design, are still missing in the literature. A
similar situation occurs for design of mixing zone. Mass
transport in the mixing zone for a specific design and a set
of parameter settings can be simulated if the reaction
kinetics in the mixing zone are known. The pyrolytic
decomposition reaction of arsine and phosphine in the mixing
zone has been studied and the rate expressions for these
reactions are available, see for example [45]. With results
of mass transport from the source zone and the mixing zone, a
thermodynamic analysis of the deposition process can be
performed. This analysis is called a complex chemical
equilibrium analysis and the epitaxial layer composition,
along with the maximum attainable growth rate, can be
predicted. Realistically, a complex chemical equilibrium

42
analysis does not accurately predict both the composition and
the growth rate, because nonequilibrium mechanisms are
usually dominant in the deposition zone. It provides,
however, process designers with valuable insight into
compositional controllability. Based on the result of the
complex chemical equilibrium analysis alone, the optimum
operation conditions for composition control can be
predicted. Reaction kinetics in the deposition zone is
another process design issue that needs to be resolved. Not
only the macroscopic events, growth rate and epitaxial layer
composition, are affected by the kinetics, but microscopic
events (e.g. doping and interphase quality) are also greatly
influenced.
From the discussion presented in this chapter, three
issues are identified as left to be resolved in the process
design of hydride VPE of In]__xGaxASyP]__v. These issues are
(1) the reaction kinetics in the source zone, (2) the optimum
operating condition for compositional controllability, and
(3) the reaction kinetics in the deposition zone. The rest
of this dissertation reports the resolution of the first and
the second issues. Since information relevant to the third
issue is not available, process fine-tuning still needs to be
pursued by observing the physical and electrical properties
of the resulting epitaxial film; composition, surface
morphology, minority carrier lifetime, photoluminescence
intensity, and PL halfwidth. With the results presented in

43
the remaining chapters, however, the amount of fine-tuning
can be greatly reduced.

CHAPTER 4
COMPLEX CHEMICAL EQUILIBRIUM ANALYSIS
IN In/Ga/As/P/H/Cl SYSTEM
4.1 Formulation and Method of Calculation
4.1.1 Chemical Species and Reactions
To consider the complex chemical equilibrium in hydride
VPE of InGaAsP, the chemical species involved in the system
have to be identified first. In hydride VPE systems, three
reaction zones with different sets of chemical species are
encountered. Therefore, a complete complex chemical
equilibrium calculation includes the calculations of complex
chemical equilibrium in each and every one of the three
temperature zones.
In the source zone, where HC1 in H2 carrier gas reacts
with group III metal, three atomic species III/H/C1 are
involved. Specifically for hydride VPE of Ini_xGaxASyPi_y,
the source region is composed of two source zones , the
gallium source zone and the indium source zone, and two
complex chemical equilibrium systems, Ga/H/Cl and In/H/Cl,
should be considered separately.
In the mixing zone group V hydrides, also carried by
hydrogen gas, are introduced into the reactor and mixed with
44

45
the product flow from the group III source region. Since the
product flow from the source zone is composed of group III
chlorides, it is possible that the group III chlorides and
the group V hydrides can react in mixing zone to form solid
deposits before the gas mixture reaches the deposition zone.
Therefore, the mixing zone should always be operated at
conditions to prevent parasitic reactions between group Ill-
containing and group V-containing species and avoid
extraneous deposition and loss of group III and group V
nutrients. On account of this process constraint, two
independent complex chemical equilibrium systems are
considered in the mixing zone, namely, Ga/In/H/Cl and
As/P/H/Cl.
In the deposition zone, group III chlorides and group V
species react, and chemical equilibrium of Ga/In/As/P/H/Cl is
considered.
Table 4-1 lists the chemical species chosen for the
In/Ga/As/P/H/Cl system. Near one atmosphere pressure and in
the temperature range of interest to VPE, 900-1200 K, some of
the chemical species are fairly unstable, thus insignificant
in quantity. Mole fractions of gallium hydrides, indium
hydrides, arsenic chlorides and phosphorous chlorides are
typically less than lO-1^' hence they are excluded from
consideration. The binary compound vapor species of GaAs,
GaP, InAs and InP are also insignificant and do not have a
great impact on the overall chemical equilibrium. Group III

46
Table 4-1. Possible chemical species in In/Ga/As/P/H/Cl
system*.
Name
Symbol
Gallium
Ga , Ga (]_ j
Indium
In, In(i)
Gallium Chlorides
GaCl, GaCl2/ GaCl3,
Ga2c^2' Ga2Cl4, Ga2Clg
Indium Chlorides
InCl, InCl2^ InCl3,
In2Cl2r In2Cl4, In2Clg
Arsenic
As, AS2, AS3, AS4
Phosphorous
P, P2, P3, P4
Arsenic Hydrides
ASH, AsH2, ASH3
Phosphorous
Hydrides
PH, PH2, PH3
Hydrogen/Chiorine
H2, H, HC1, Cl, Cl2
Gallium Arsenide
GaAs(s)
Indium Arsenide
InAs(s)
Gallium Phosphide
GaP(s)
Indium Phosphide
InP(s)
* Unless indicated
phase.
otherwise all species are in the gas
(1): 1iquid phase
(s): solid phase

47
chlorides and Group V molecules are the dominant species in
the In/Ga/As/P/H/Cl system. Kinetic studies on the growth of
GaAs have proven that gallium monochloride and arsenic
molecules are responsible for the epitaxial reaction in a
hydrogen-rich ambient, and in addition, gallium trichloride
plays a certain role in a hydrogen-deficient atmosphere.
Although some of the chlorides are less important than the
others, it is of strategic value to take them all into
account because their influence on the kinetics might not
have been revealed. For similar reasons, the group V
molecules composed of different number of atoms should be
considered. Group V hydrides, possibly competing with Group
V molecules in the growth reaction, are used as group V
element carriers. The inclusion of all possible V-hydrides
species is thus meaningful. Molecules formed by both arsenic
and phosphorous atoms have not been adequately studied, and
their reported thermochemical properties, at present, are
missing or inconclusive. Therefore, these chemical species
are discarded in the complex chemical equilibrium
calculation. The thermochemical properties of the resulting
39 chemical species are reviewed and gathered. Table 4-2 &
4-3 provide the compilation with references to the selected
values.
System reactions are determined after the chemical
species are chosen. Every system reaction describes the
relationship of one added chemical species to the existing

Table 4-2. Selected values of standard state heat capacity,
Cp (cal/mole- K) = Cq
+ C3T +
c2t2 + C3T
3 + C4T“2 +
C5lnT
(T : K)
c0
Cj‘103
c2*io6
C3*109
C4*10-6
C5
ref.
Ga
30.138
2.09
0.
0.
-0.2662
-3.812
46
Ga(l)
6.65
0.
0.
0.
0.
0.
47
In
3.575
4.426
0.
-1.689
0.
0.
46
In(l)
7.10
0.
0.
0.
0.
0.
47
GaCl
8.84749
23.287
-0.04918
0.
-0.039674
0.
48
GaCl 2
13.7942
13.33964
-0.04050
0.
-0.083318
0.
48
GaCl 3
19.463
0.566884
-0.21157
0.
-0.151843
0.
48
Ga2C12
19.5208
0.547979
-0.23262
0.
-0.153321
0.
48
Ga 2C14
(298K-
17.9843
26.683
-15.7484
0.
-0.151084
0.
48
600K)
(600K-
12 00 K)
28.1419
4.0013
-1.27179
0.
-0.784768
0.
48
Ga2Gl6
43.0051
0.989928
-0.37017
0.
-0.340547
0.
48
InCl
8.93
0.
0.
0.
-0.209
0.
49

(continued)
Cp (cal/mole- K) =
C0 + C]T
+ C2T2 +
c3T3 + C4T-2
+ C5lnT
(T : K)
c0
Cj/103
C2*106
C3*109
C4*10“6
c5
ref.
InCl2
13.84
0.0515
0.
0.
0.08644
0.
50
InCl 3
18.00
1.7
0.
0.
0.
0.
49
In2Cl4
26.93
1.7
0.
0.
-0.209
0.
51
In2Cle
40.
3.4
0.
0.
0.
0.
45
As
4.968
0.
0.
0.
0.
0.
46
As2
8.772
0.2571
-0.121
0.
-0.04241
0.
52,53
As3
13.836
-0.1365
0.
0.
-0.05889
0.172
46
As 4
19.696
0.2834
-0.1252
0.
-0.168
0.
52,53
P
4.968
0.
0.
0.
0.
0.
54
P2
8.236
8.6618
0.
0.
0.06036
0.
54,55
P4
19.2
0.5744
0.
0.
-0.02974
0.
54,55
ASH
6.4
1.432
0.
0.
0.0108
0.
54
AsH3
10.07
5.42
0.
0.
-0.220
0.
56
PH
6.4
1.432
0.
0.
0.0108
0.
54

(continued)
Cp (cal/mole- K) =
C0 + CXT
+ C2T2 +
c3t3 + C4T-2
+ C5InT
(T : K)
-
c0
C3 *103
c2*io6
C3*109
C4*10~6
c5
ref.
ph2
6.524
6.237
0.
-1.506
0.
0.
54
ph3
4.77
14.97
-0.4388
0.
0.
0.
54
GaAS(S)
10.8
1.46
0.
0.
0.
0.
52,57
InAs(S)
10.6
2.0
0.
0.
0.
0.
52,57
GaP(S)
11.85
0.68
0.
0.
-0.14
0.
55,58
InPisi
(298K-
12.27
0.
0.
0.
-0.114
0.
55,58
9 1 OK)
(910K-
5.89
6.4
0.
0.
0.
0.
55,58
1500K)
«2
15.256
2.12
0.
0.
-0.05906
-1.462
54
H
4.968
0.
0.
0.
0.
0.
59
HC1
6.224
1 .29
0.
0.
0.03251
0.
54
Cl
5.779
-0.4083
0.
0.
-0.0387
0.
60
ci2
8.8
0.208
0.
0.
-0.067
0.
48

51
Table 4-
-3. Selected values of standard state enthalpy of
formation and absolute entropy at 298 K,
A Hf (298K) (kcal/mole) S(°298K) (cal/mole- K)
AHf°(298K)
ref
0
s(298K)
ref
Ga
65.0
46
40.375
46
Gad)
1.3
47
14.2
47
In
57.3
46
41.507
46
In(l)
0.8
47
15.53
47
GaCl
- 17.1
48
57.236
48
GaCl 2
- 39.0
48
71.668
48
GaCl 3
-102.4
48
77.515
48
Ga2c^2
- 56.1
48
83.681
48
Ga 2C14
-148.5
48
103.031
48
Ga2G^6
-228.9
48
116.9
48
InCl
- 16.7
49
59.3
49
InCl2
- 58.4
45
73.4
45
InCl 3
- 90.0
56
82.3
56
In2cl4
-140.84
61
110.6
61
In2Cl6
-208.5
45
129.7
45
As
68.7
46
41.611
46
As2
45.58
53
57.546
46
AS3
52.2
46
74.121
46
AS4
36.725
53
78.232
46

52
(continued)
AHf°(298K)
ref
s (298K)
ref
p
75.62
46
38.98
46
p2
34.34
46
52.11
54
p4
12.58
45
66.89
46
AsH
58.
45
51.
45
AsH3
16.
61
53.22
62
PH
56.2
54
46.9
54
ph2
25.9
54
50.8
54
ph3
1.3
63
50.24
54
GaAs(s)
-19.54
52
16.05
52
InAs(s)
-14.29
52
17.84
52
GaP(s)
-23.93
55
10.96
55
InP(s)
-14.73
55
14.18
55
h2
0.
31.207
64
H
52.103
64
27.391
64
HC1
-22.063
64
44.643
64
Cl
28.992
64
39.454
64
Cl2
0.
53.29
64

53
ones. This also implicitly means that the system reactions
are independent. Although the number of system reactions is
fixed when the chemical species are chosen, the reaction
formulae can be written in various forms as long as the
requirement of independence is met. The system reactions of
the chosen chemical species (as listed in Table 4-1) are
tabulated in Table 4-4.
4.1.2 Complex Chemical Equilibrium Equations and Equilibrium
Parameters
Gallium Source Zone The system reactions involved in
gallium source zone are listed in table 4-4. The equilibrium
equations for these system reactions are written as follows
Kg (T)
K10(T)
k14(T)
p
GaCl3
?H2
p
GaCl
PHC1
PGa_Cl .
2 4
p
GaCl3
P
GaCl
p
GaCl 2
P °*5
H2
P
GaCl
PHC1
PGa2cl6
PGaCl3
(4-1)
(4-2)
(4-3)
k16(T)
(4-4)

54
Table 4-4. Chemical reactions in hydride VPE of InGaAsP
number
reaction
applicable*
temperature
zone
1
GaCl + 1/4 As4 + 1/2 H2 < > GaAs(S-S>)#
+ HC1
2
InCl + 1/4 As4 + 1/2 H2 < > InAs(s.s.)#
+ HC1
3
GaCl + 1/4 P4 + 1/2 H2 < > GaP(s.s.)# +
HC1
4
InCl + 1/4 P4 + 1/2 H2 < > InP(S#s#)# +
HC1
5
2 As2 < > As4
6
AsH3 < > 1/2 As2 + 3/2 H2
7
2 P2 < —> P4
8
PH3 < > 1/2 P2 + 3/2 H2
9
GaCl + 2 HC1 < > GaCl3 + H2
10
GaCl + GaCl3 Ga2Cl4
11
InCl + 2 HC1 < > InCl3 + H2
12
InCl + InCl3 < > In2Cl4
13
InCl + HC1 < > InCl2 + 1/2 H2
14
GaCl + HC1 < > GaCl2 + 1/2 H2
15
2 InCl3 < > In2Clg
16
2 GaCl3 < > Ga2Cl6
17
2 InCl < > In2Cl2
(Cont'd)
d
d
d
d
m, d
m, d
m, d
m, d
s(Ga) ,
m, d
s(Ga) ,
m, d
s(In) ,
m, d
s(In) ,
m, d
s(In) ,
m, d
s(Ga) ,
m, d
s(In) ,
m, d
s(Ga) ,
m, d
s(In) ,
m, d

55
applicable*
number reaction temperature
zone
18
2 GaCl < > Ga2Cl2
s(Ga),
m, d
19
AsH3 < > AsH2 + 1/2 H2
m, d
20
AsH3 < > AsH + H2
m, d
21
PH3 < > PH2 + 1/2 H2
m, d
22
PH3 < > PH + H2
m, d
23
As2 < > 2 As
m, d
24
AS4 + As2 < > 2 As3
m, d
25
P2 < > 2P
m, d
26
p4 + P2 < > 2 P3
m, d
27
H2 < > 2H
s(Ga) ,
s (In) ,
m, d
28
HC1 < > H + Cl
s(Ga) ,
s(In),
m, d
29
2C1 < > Cl2
s(Ga) ,
s(In) ,
m, d
30
GaCl ^ y Ga + Cl
s(Ga) ,
m, d
31
InCl < > In + Cl
s (In) ,
m, d
32
Ga(1) + HC1 < > GaCl + 1/2 H2
s (Ga)
33
In(1) + HC1 < > InCl + 1/2 H2
s (In)
* s(Ga): Ga source zone
s(In): In source zone
m: mixing zone
b: deposition zone
^ (s.s.): InGaAsP solid solution

56
K18(T) =
Ga2C12
GaCl
K27(T) =
4
h.
K28(T) =
^ci
PHC1
Cl.
K29(T) =
Cl
K30(T) =
P P
Ga Cl
P
GaCl
K32(T) =
P P0-5
GaCl H2
P
HC1
(4-5)
(4-6)
(4-7)
(4-8)
(4-9)
(4-10)
In the equations above, Kj_(T) is the equilibrium constant of
reaction i which is a function of temperature T, and Pj is
the partial pressure of chemical species j in the vapor
phase. In all zones, the number of chlorine atoms and
hydrogen atoms in the vapor phase is constant. It is thus
convenient to define the parameter As(Ga) that represents the
ratio of chlorine atoms to hydrogen atoms in the gas phase.

57
PGaCl + 2(PGaCl2+ PGa2Cl2 + PC12> + 3PGaCl3
Ac(Ga) = (Cl/H) =
+ 4PGa2Cl4 + 6P
+ P + P
Ga2Clg ^HCl *C1
2P + p + P
fhci
(4-11)
The summation of the vapor pressure of the twelve vapor
species is equal to the total pressure, Ptot' i-e*
P = P + P
tot GaCl GaCl
+ PGa + PH.
2
+ P
+ P +P +P +P
GaCl, Ga_Cl~ Ga_Cl. Ga_Clc
3 2 2 2 4 2 6
+ P + P + P
KC1 H Cl Cl.
(4-12)
Complex chemical equilibrium in the gallium source zone is
completely defined by equations (4-1) to (4-12). When values
of the gallium source zone temperature, Ts(Ga), total system
pressure, Ptot' and As(Ga) are specified, equations (4-1) to
(4-12) can be solved simultaneously to resolve the
equilibrium partial pressure of the twelve vapor species.
Indium source zone Similar equilibrium equations exist
for the indium source zone. There are twelve equilibrium
equations with three system parameters; indium source zone
temperature, Ts(In) , total system pressure, Ptot' and
chlorine to hydrogen ratio, As(In). The twelve equilibrium
equations are written as follows.

58
K11(T)
K
12
(T)
K13(T)
ki5(T)
K
17
(T)
k27(T)
K28(T)
k29(t)
K31(T)
K
33
(T)
p
I nC 13
Pfi2
p
InCl
PHC1
Pln2C14
PInClj
PInCl
P
I nC 12
P °-5
H2
P
InCl
PHC1
P
In2C16
P 2
I nC 13
In2Cl2
p 2
InCl
PH
?H2
P P
H *C1
p
HC1
P«2
pc?
PT p
In
Cl
P
InCl
P
InCl
P °-5
p
HC1
(4-13)
(4-14)
(4-15)
(4-16)
(4-17)
(4-18)
(4-19)
(4-20)
(4-21)
(4-22)

59
PInCl + 2(PInCl2+ PIn2Cl2 + PC12) + 3PInCl3
As(In) = (Cl/H) =
+ 4Pt + 6P
In_Cl.
2 4
+ F + P
In2Cl6 KC1 Cl
2PH2 + PHC1 + PH
(4-23)
P = P + P
tot InCl InCl
+ P
+ PT + P„
In H,
2
+ P
InCl.
+ p + P + P
In_Cl_ In.Cl. In_Clc
2 2 2 4 2 6
+ P + P + P
HC1 K FC1 Cl.
(4-24)
Mixing zone There are 33 chemical species in the vapor
phase of the mixing zone; GaCl, GaCl2> GaCl3, Ga2Cl2> Ga2Cl4,
Ga2Clg, Ga, InCl, InCl2f InC13, In2Cl2/ In2Cl4, In2Clg, In,
ASH3, ASH2, AsH, As, AS2, AS3, AS4, PH3, PH2, PH, P, P2, P3,
P4, H2, HC1, H, Cl and CI2. A total of 27 reactions are
involved with the 33 chemical species, as discussed in
section 4.1.1. The equilibrium equations can be written
similar to those given for the source zone. Fifteen of the
27 equilibrium equations have been presented in the last
section, the other twelve equilibrium equations are written
as follows.
As
k5 (T) =
AS.
k6 (T) =
0.5 1.5
As2 H2
PASH„
(4-25)
(4-26)

60
Kv (T) =
K8 (T) =
pO-5 pi-5
P2 H2
PPH.
k19(t) =
PAsH2 PH2
PAsH,
K20(T) =
P P
AsH H.
ASH.
K21(T) =
P P° ' 5
PH2 H2
PPH.
K22(T) =
P P
PH H.
PH.
K23(T) =
As
As.
As.
k24(t) =
P P
As_ As.
2 4
K25(T) =
(4-27)
(4-28)
(4-29)
(4-30)
(4-31)
(4-32)
(4-33)
(4-34)
(4-35)

61
K26(T) =
(4-36)
Define B1 as the gallium to hydrogen ratio, B2 the
indium to hydrogen ratio, Cl the arsenic to hydrogen ratio,
and C2 the phosphorus to hydrogen ratio. Denoting the
parameters in mixing zone by subscript m, then Am, Blm, B2m,
Clm, and C2m can be written as follows.
A = (Cl/H)
m m
PHCl+PCl+PGaCl+PInCl+¿(PGaCl2+PInCl2+PGa2Cl2+
PIn2Cl2+PCl2) +3(PGaCl3+PInCl3)
4 (PGa Cl +PIn Cl.1 +6 ,PGa Cl/PIn Cl 1
2 4 2 4 2 6 2 6
2P +P +P ,+3P +3P +2(P +2P +P +P )
H2 H HC1 AsH-, PH3 ' PH2 AsH2 PH AsH;
E1m * (Ga/H)m *
PGa+PGaCl'>PGaCl +PGaCl,'>'2PGa,Cl,*'2PGa,Cl . *2PGa,Cl,
2 3 2 2 2 4 2 6
P + P + P ,+3P +3P +2P +2P +P +P
H2 H HC1 AsH3 PH3 AsH2 PH2 AsH PH
B2 = (In/H)
m m
p +p +p +p +?P +2P +PP
In inCl InCl_ InCl, In-Cl- In„Cl. In_Cl,
2 3 2 2 2 4 2 6
P +P +P .+3P +3P +2P +2P +P +P
H2 H HC1 AsH3 PH3 AsH2 PH2 AsH PH
(4-37)
(4-38)
(4-39)

62
Cl = (As/H)
m m
P. „+P, „ +P, „ +P- + 2P, +3P„ + 4P
AsH AsH0 AsH-, As As_ As., As.
2 3 2 3 4
p + p +p +3p +3p +2p +2P +P +P
H2 H HC1 AsH3 PH3 AsH2 PH2 AsH PH
(4-40)
C2 = (P /H)
m m
PPH +PPH2 +PPH3 +PP +2PP2 +3Pp3 +4Pp4
ph2+ph+phci+3pash3+3pph3+zFash2+2pph2+pash+pph
(4-41)
The summation of partial pressure of the 33 vapor
species equals to the total pressure, Ptot-
’tot " PH2+PHCl+PH+PCl+PCl2+PGaCl+PGaCl2+PGaCl3
+PGa2Cl2+PGa2Cl4+PGa2Cl6+PGa+PInCl+PInCl2
+ P + P + P 4* P + P + P
I nC 1In0Cl_ In-Cl. In_Clc In AsH-.
3222426 3
+ P +P +P +P + P + P +P +P
AsH~ AsH As As0 As^ As. PH-, PHn
2 2 3 4 3 2
+ PPH+PP*PP, + PP
2 3 4
(4-42)
The complex chemical equilibrium in mixing zone is
completely defined by equations (4-1) to (4-9), (4-11) to (4-
15), (4-19) , (4-25) to (4-36) and equations (4-37) to (4-41) .
When mixing zone temperature, Tm, and the values of the
parameters, Am, Blm, B2m, Clm, C2m, and system pressure,
ptot» are Given, the complex chemical equilibrium in mixing
zone can be calculated by solving the simultaneous
equilibrium equations.

63
Deposition zone All of the gaseous chemical species
listed in table 4-1 are included for the discussion of
complex chemical equilibrium in deposition zone. The
condensed phase is the solid solution Ini_xGaxASyPi_y. In
addition to the 27 homogeneous system reactions for the 33
gaseous chemical species, as explained in the last section,
four heterogeneous system reactions also exist in deposition
zone. The equilibrium equations for these four reactions are
Kx (T)
K2 (T)
K3 (T)
k4 (T)
aGaAs
P
HC1
P
GaCl
0.25
As4
0.5
H2
aInAs
p
HC1
P
0.25
P0*5
InCl
As .
4
H2
aGaP
p
HC1
P
GaCl
0.25
P4
P0-5
H2
aInP
PHC1
P
InCl
0.25
P4
P0-5
H2
(4-43)
(4-44)
(4-45)
(4-46)
where a¿ is the activity of binary component i in solid
solution Ini_xGaxASyP]__y. The a¿' s are dependent upon the
solid solution composition (x, y) , and temperature T. The
solution thermodynamics of solid Ini_xGaxASyPi_y ,which
elucidates the dependence of a-j_' s on (x, y) and T, will be

64
discussed later in this chapter. Define D as the ratio of
the difference between the number of group III atoms and
group V atoms to the total number of hydrogen atoms in the
vapor phase, so that
D =
p +p + p +p +2P +2P +2P +
*Ga GaCl *GaCl, ^GaCl, ¿ Ga,Cl, ^Ga,Cl. ZiGa,Cl,
2 3 22 24 ¿6
p +p + p +p +2P +2P +2P
in ^InCl InCl2 InCl3 In2Cl2 In2Cl4 In2Cl6
-P, „ -P, „ -P* -P„ -2P. -3P„ -4P
AsH. AsH- AsH As As» As, As.
3 2 2 3 4
_p _p _p _p -op -3p -4p
PH, PH, PH P P, P, P.
3 2 2 3 4
2P +P +P +3P +3P +2P +2P +P +P
H2 H HC1 AsH3 PH3 AsH2 PH2 AsH PH
(4-47)
When values of the deposition zone temperature, T¿¡, system
pressure Ptot, parameters D and A¿j (chlorine to hydrogen
ratio in the deposition zone), and solid solution composition
(x, y) are given, the partial pressure of the 33 gaseous
chemical species can be obtained by solving equations (4-1 to
4-9, 4-11 to 4-15, 4-19, 4-25 to 4-36), equation (4-37),
equation (4-42), equations (4-43 to 4-46), and equation (4-
47) simultaneously.
Define Y as the ratio of the number of gallium atoms to
the total number of group III atoms in the vapor phase, and Z
the ratio of arsenic atoms to group V atoms in the vapor
phase. Then after the partial pressures have been
calculated, Y and Z can be readily evaluated as follows.

65
Y
PGa+PGaCl+PGaCl2+PGaCl3+2PGa2Cl2+2PGa2Cl4+2PGa2Cl6
P GaP GaCÍP GaCl2P GaCl*21* Ga2Cl22P Ga2Cl42P Ga2Cl*
PIn+PInCl+PInCl2+PInCl3+2PIn2Cl2+2PIn2Cl4+2PIn2Cl6
(4-48)
P +P +P + P +2P +3P + 4P,
AsH3 AsH2 AsH As As2 As3 As4
~p +p +p +p +2F + 3 p + 4 p —
AsH, AsH, AsH As As» As, As.
3 2 2 3 4
P +P +P +P +2P +3P +4P
ph3 ph2 ph p p2 p3 p4
(4-49
Therefore, complex chemical equilibrium can also be
defined by a set of chosen values of T¿¡, Ptot' Ad' D' anc^
Z. In this case, equations (4-1 to 4-9, 4-11 to 4-15, 4-
19, 4-25 to 4-37, 4-42 to 4-49) are solved together for the
partial pressure of the 33 vapor species and the solid
solution composition (x, y).
4.1.3 Process Parameters
The parameters that have been discussed in the last
section are called "equilibrium parameters", since
specification of the values of these parameters defines
equilibrium condition. Table 4-5 lists the equilibrium
parameters and their shorthand definitions.
In open VPE reactor systems, equilibrium parameters can
not be directly controlled. Rather, process performance is
controlled by changing various "process parameters", the
flowrates, temperature settings and pressure setting.

66
Table 4-5. Equilibrium Parameters
Zone
Equilibrium Parameters
Symbol
Definition
gallium source zone
As(Ga)
Cl /H
Ts(Ga)
temperature
^tot
pressure
indium source zone
As(In)
Cl /H
Ts(In)
temperature
^tot
pressure
mixing zone
Am
Cl /H
Blm
Ga/H
B2m
In/H
dm
As/H
C2m
P/H
Tm
temperature
ptot
pressure
deposition zone
Ad
Cl /H
D
(III-V)/H
Y
Ga/III
Z
As/V
Td
temperature
^tot
pressure

67
In addition, the three temperature zones are connected in
series, the product gasflow of upstream zone is transported
into the downstream zone and becomes the input gasflow of
that region. Specification of equilibrium of equilibrium
parameters in the mixing zone is directly connected to the
values of the source zone output, and similarly equilibrium
parameters in the deposition zone are dependent upon the
mixing zone condition. Therefore, it is of practical value
to investigate the relationship between the equilibrium
parameters from one temperature zone to the other, and the
relationship between the equilibrium parameters and the
process parameters.
Gallium source zone Denoting the input flowrates of HCl
and H2 into gallium source zone by FHC1(Ga) and FH2(Ga), then
the transport rate of hydrogen atoms FH(Ga) and the transport
rate of chlorine atoms FC1(Ga) are simply
FH(Ga) = 2FH2(Ga) + FHC1(Ga) (4-50)
FC1(Ga) = FHC1(Ga) (4-51)
Using the above equations, equilibrium parameter As(Ga) can
be related to process parameters FHCl(Ga) and FH2(Ga) as
follows.
As(Ga)
FC1(Ga) / FH(Ga)
(4-52)

68
When the process parameters FHCl(Ga), FH2(Ga), Ts(Ga) and
ptot are specified, the equilibrium parameters, As(Ga),
Ts(Ga) ,and Ptot' are also specified, and complex chemical
equilibrium calculation can be carried out as discussed in
section 4.1.2.
The result of gallium source reactions is transport of
gallium atoms in the vapor phase. Two different transport
rates of gallium should be differentiated, namely the
equilibrium transport rate of gallium F*Ga(Ga) , and the
process transport rate of gallium FGa(Ga). The equilibrium
transport rate of gallium is the calculated gallium transport
rate from complex chemical equilibrium, therefore F*Ga(Ga)
can be written as
F*Ga(Ga) = FH(Ga)
P +p +p +p +
Ga GaCl GaCl2 GaCl3
2P +2P +2P
Ga_Cl_ Ga_Cl. Ga0Cl,
2 2 2 4 2 6
2P + p +P
/yH2 iHCl H
(4-53)
while the process transport rate of gallium is the physically
obtained gallium transport in the process. Clearly, the
process transport rate of gallium, which is always less than
or equal to the equilibrium transport rate of gallium, is
dependent upon source zone design and process operating
conditions. For convenience, define e(Ga) as the gallium
transport factor as follows

69
e (Ga)
FGa(Ga) / FC1(Ga)
(4-54)
The value of e(Ga) at equilibrium equals F*Ga(Ga) / FC1(Ga)
and is denoted e*(Ga). The value of e(Ga) equals zero at the
inlet of gallium source zone, increases in the direction of
gasflow, and, given sufficient residence time, is saturated
at the source zone outlet. e(Ga) serves as an important
process parameter for the mixing zone, as will be explained
later in this section.
Indium source zone Similar to gallium source zone, four
process parameters exist in indium source zone, namely, HC1
input flowrate, FHC1(Ga), H2 input flowrate, FH2(In), indium
source zone temperature, Ts(In), and total pressure, Ptot.
The hydrogen transport rate, FH(In), and chlorine transport
rate, FCl(In), are given by
FH(In) = 2FH2(In) + FHCl(In)
(4-55)
FC1(In) = FHC1(In)
(4-56)
The equilibrium parameter, As(In), is determined by FH(In)
and FC1(In),
As(In) = FC1(In) / FH(In)
(4-57)

70
The equilibrium transport rate of indium F*In(In) is
calculated from equilibrium partial pressures accordinq to
P +p +p +p +
In InCl InCl2 InCl3
2P +2P +2P
* ztIn_Cl_ z*In Cl. ^In Cl,
F In (In) = FH(In) Tp"2 — (4-58)
¿ h2 fhci
The indium transport e(In) is defined by
e(In) = Fin(In) / FCl(In) (4-59)
where Fin(In) is the process transport rate of indium.
Mixing zone Denote the input flowrates of H2, ASH3 and
PH3 by FH2(m), FASH3 and FPH3, then the total transport rate
of hydrogen in the mixing zone, FH(m), is given by
FH(m) = FH(Ga) + FH(In) + 2FH2(m) + 3(FAsH3 + FPH3) (4-60)
The connective nature between source zone and mixing zone is
evident from the first two terms in the RHS of equation (4-
60). The transport rates of chlorine, gallium, indium,
arsenic and phosphorous in mixing zone are as follows.
FCl(m) = FCl(Ga) + FCl(In) (4-61)
FGa(m)
FGa(Ga) = e(Ga) FC1(Ga)
(4-62)

71
Fin(m) = Fin(In) = e(In) FCl(In) (4-63)
FAs(m) = FAsH3 (4-64)
FP(m) = FPH3 (4-65)
The equilibrium parameters Am, Blm, B2m, Clm and C2m are
related the transport rates and can be written as follows.
Am = FC1(m) / FH(m) (4-66)
Blm = FGa(m) / FH(m) (4-67)
B2m = Fin(m) / FH(m) (4-68)
Clm = FAs(m) / FH(m) (4-69)
C2m = FP(m) / FH(m) (4-70)
From the equations presented above, it is clear that there
are seven process parameters in the mixing zone; FH2 F AsH 3 , FPH3, Tm, Ptot' e(Ga) and e(In). When values of
FH(Ga), FCl(Ga), FH(In) ,FCl(In), and the process parameters
are specified, the seven equilibrium parameters, Am, Blm,
B2m, Clm, C2m, Tm and Ptot can evaluated and the complex
*
chemical equilibrium in mixing zone is completely defined.

72
Since the overall reaction rate can be affected by mass
transfer and kinetic effects in the process, chemical
equilibrium might not be reached in mixing zone. If the
mixing zone is operated under the correct criteria
prohibiting formation of any condensable reaction products,
then, irrespective of if equilibrium is reached, the process
transport rates of all six atomic species, equations (4-60 to
4-65), will not change. Therefore, the transport rates
derived for mixing can be directly used in deposition zone.
Deposition zone Equilibrium parameters Ad, D, Y and Z
at the inlet of deposition zone are determined by transport
rates FH(m), FC1(m), FGa(m), Fln(m), FAs(m) and FP(m).
Ad = FC1(m) / FH(m) (4-71)
D = (FGa(m) + Fln(m) - FAs(m) - FP(m)) / FH(m) (4-72)
Y = FGa(m) / (FGa(m) + Fln(m)) (4-73)
Z = FAs(m) / (FAs(m) + FP(m)) (4-74)
The reactant gas is supersaturated and deposition reaction
occurs in the deposition zone. In the course of the
deposition process, group III atoms (In, Ga) and group V
atoms (As, P) leave the vapor phase, therefore the values of
Y and Z begin to change along the flow direction. Define

73
supersaturation, S, to be the total number of group III atoms
(or equivalently the total number of group V atoms) that
leave the vapor phase before complete equilibrium is reached.
Then, at equilibrium, the equilibrium parameters Y and Z are
Y = (FGa(m) - x S) / (FGa(m) + Fln(m) - S) (4-75)
Z = (FAs(m) - y S) / (FAs(m) + FP(m) - S) (4-76)
where x and y are mole fractions in the deposited compound
Ini_xGaxASyPi_y. Note that stoichiometry is usually assumed
for the deposition III-V compound, therefore, in writing
equations (4-75 & 4-76) the number of deposited group III
atoms has been assumed to be equal to the number of deposited
group V atoms. On account of this assumption, it is clear
that the value of equilibrium parameter D is not affected by
the deposition process. Since the amount of hydrogen and
chlorine atoms incorporated in the deposited compound is very
small compared with the total transport rate, the value of
equilibrium parameter A¿ also remains unchanged throughout
the deposition zone.
The deposition zone temperature, T¿, and the system
total pressure, Ptotr are the only process parameters in the
deposition zone. With specified T¿j, Ptot' and values of the
transport rates at the deposition zone inlet, FH(m), FC1(m),
FGa(m), Fln(m), FAs(m), and FP(m), equilibrium parameters T¿

74
ptot' Ad' Y and z can be evaluated directly or indirectly
by equations (4-71, 4-72, 4-75 & 4-76). With the complex
chemical equilibrium defined, composition (x, y) and
supersaturation S can be obtained.
Summary Equilibrium parameters that are used to
initiate complex chemical equilibrium calculation are quite
different from the realistic process parameters used in
process control. But, in order to study the effects of
equilibrium on realistic processes, equilibrium parameters
have to be used to bridge between process parameters and
complex chemical equilibrium calculation. Table 4-6 gives a
complete listing of the process parameters discussed in this
section. There are basically two types of process
parameters. Type 1 is the "process control" parameters.
Most of the process parameters, e.g. flowrate, temperature,
and pressure, belong to this group. The second type, the
"process design parameters", can not be easily tuned during
process runs. For example, transport factors e(Ga) and e(In)
are determined primarily as a result of source zone design.
Note that there are totally 14 process parameters in hydride
YPE of Inx-xGaxASyPi-y ; FH2 (Ga ) , FHC1 (Ga) , Ts (Ga) , e(Ga),
FH2(In) , FHCl(In), Ts(In), e(In), FH2(m) , FAsH3, FPH3, Tm,
Td, and Ptot.

75
Table 4-6. Process parameters
Zone
Process
Parameters
Symbol
Definition
gallium source zone
FH2(Ga)
FHCl(Ga)
Ts(Ga)
^tot
H2 input flowrate
HC1 input flowrate
temperature
pressure
indium source zone
FH2(In)
H2 input flowrate
FHCl(In)
HC1 input flowrate
Ts(In)
temperature
ptot
pressure
mixing zone
0 (Gel)
Ga transport factor
e (In)
In transport factor
FH2(m)
H2 input flowrate
FASH3
AsH3 input flowrate
fph3
PH3 input flowrate
Tm
temperature
^tot
pressure
deposition zone
Td
temperature
^tot
pressure

76
4.1.4 Calculational Procedures
4.1.4.1 Equilibrium Constants
The reaction equilibrium constant Ka is given by its
definition as
n , n _ A o
Ka = n ai = exp ( — Z Ui y? ) = exp ( ) (4-77)
i=l i=1
where a-j_ is the activity of chemical species i, ui is the
stoichiometric constant of i in the reaction, y£ is the
standard Gibbs free energy of i, and n equals the total
number of chemical species involved in the reaction. The
o
standard Gibbs free energy of the reaction, Ay , at
temperature T can be evaluated from the standard enthalpy of
o
formation at 298 K, AHf(298K)' absolute entropy at 298 K,
S°298K)' and high temperature heat capacity, Cp(T), of the
involved chemical species.
n
o
Ay ~ Z
i = 1
Using equations (4-77 & 4-78) and the selected
thermochemical data of table 4-2 & 4-3, equilibrium constants
of the 33 reactions listed in table 4-4 can be calculated.
/ ah° - TG° +
i1 ü nf(298K) (298K)
r
298K
P/i
dT
- T
/T
298K
dT
P/i
(4-78)

77
4.1.4.2 Complex Chemical Equilibrium Calculation
Gallium source zone Assuming that qj_ = PH2®'^ and q2 =
PHC1 PH2-0*5/ then the partial pressure of each chemical
species in gallium source zone can be rewritten in terms of
q^, q2i and temperature dependent equilibrium constants.
K
ro
ii
4
(4-79)
HCl
qlq2
(4-80)
PH =
^0.5
K27 ql
(4-81)
PC1 =
K K_^’^ a
28 27 42
(4-82)
PC12 =
K29K28K27 q2
(4-83)
P
GaCl
K32 q2
(4-84)
PGa2C12
K18K32 q2
(4-85)
P
GaCl 2
= K14K32 q2
(4-86)
PGa2cl4
= K10K9K32q2
(4-87)
P
GaCl 3
= K9K32 q2
(4-88)
PGa2cl6
= K16Kg K32 q2
(4-89)
PGa
K30K32K28 K27
(4-90)

78
Substituting equations (4-79 to 4-90) in equations (4-11 & 4-
12) ,
(4-91)
A (Ga)
s
tot
P
(4-92)
The nonlinear algebraic equations, equations (4-91 & 4-92),
can be solved together numerically for q^ and q2. Newton-
Raphson method was chosen and has been found adequate for the
numerical solution of this problem.
Indium source zone The same procedure for gallium
source zone calculation is used for indium source zone
calculation.
PInCl K33 q2
(4-93)
P
In-Cl
K17K32 q2
(4-94)

79
P
InC12
Pln2cl4
P
I nC 13
Pln2C16
K13K33 q2
K12K11K33 q2
KllK33q2
K15K11K33 4
K31K33K28 K2°75
(4-95)
(4-96)
(4-97)
(4-98)
(4-99)
Substitution of equations (4-79 to 4-83 & 4-93 to 4-99) into
equations (4-23 & 4-24) and rewriting equations (4-23 & 4-
24) gives,
As(In) =
(ql + K33 + K28K27 ><32 +KllK33q2
+(K29K28K¡7+K17K32+K13K33) q2
+K12KllK33q2+K15KllK33q2
.0.5
(q2 + K27 ) 'tot ql+K27 ql+(K33+K28K27 } q2 +
(K29K28K27 +K17K33+K13K33) q2
K11K33m2
q'1 +K12KllK33q2 + qlq2 +
Í5K11K3392 *K
K K ^ Y ® ^
31*33*28*27
(4-100)
(4-101)
Solution of equations (4-100 & 4-101) by the Newton-Raphson
method gives the values of q]_ and q2, from which values of

80
the partial pressure of chemical species in indium source
zone at equilibrium can be calculated.
Mixing zone Assuming that = P^.q °*2^, q4 = pp 0.25 f
4 4
35 = pGaCl and 36 = pInCl' then the partial pressure of the
chemical species in mixing zone can be written in terms of
31/ 32' 33' 34' 35 and 36 as follows.
GaCl
q5
(4-102)
Ga2C12
K18q5
(4-103)
GaCl2
= K14 q5 q2
(4-104)
Ga2C14
K10K9 q5q2
(4-105)
GaCl3
= k9 q5 ^2
(4-106)
Ga2C16
= K16K^ q2 q4
(4-107)
Ga
K30K28K27 q5 q2
(4-108)
InCl
q6
(4-109)
^n2G^2
= K17 q6
(4-110)
InCl „
Z
= K13 q6 q2
(4-111)
In2Cl4
K12K11 q6 q2
(4-112)

81
PInCI3
= Kn q6ql (4-113)
Pln2C16
- K16K11 q6 q2 (4-114)
PIn
K31K28K275 41 a-6 (4-115)
PAs4 =
q4 (4-116)
?As3 =
„0.5 „-0.25 3 i a i i -i\
K24 K5 q3 (4-117)
PAs2 =
-0 5 2
Kg3 q3 (4-118)
PAs =
K235 K¡°-25 q3 (4-119)
PAsH3
= K6 K5 q3 q± (4-120)
PAsH„
-1 -0 25 2
= K19K6X K5U-¿3 q3 (4-121)
PAsH
K20K61k¡°'25 q3ql ,4-1221
\ *
q4 (4-123)
Pp3 -
0.5 -0.253 . _
K26 K7 ^4 (4-124)
K)
II
-0 5 2
Ky q4 (4-125)
PP =
K3 5 q4 (4 — 126)
PPH
*5
—-
„-l „-0.25 3
Kg k7 q4 (4-127)

82
P
PH
2
K21K^
K
-0.25
7
q4
(4-128)
PH
= K^K^K;0-25 qaq
4H1
(4-129)
Substituting equations (4-79 to 4-83 & 4-102 to 4-129) in
equations (4-37 to 4-42) yields six nonlinear algebraic
equations of q^, q2, q3, q4, q5, and qg, which are solved
simultaneously by the Newton-Raphson method. The complex
chemical equilibrium partial pressure can be readily
calculated.
Deposition zone The partial pressure of the vapor phase
species can be represented by the definition of q^, q2, and
q3 presented in the last two sections,
PGaCl = K1 aGaAs q2 q3
P.-, „ -2 2 2 -2
Ga2C12 “ K18 K1 aGaAs q2 q3
P -12-1
GaC12 ■ K14 K1 aGaAs <¡2 q3
Ga2C14 = K10K9K1 aGaAs q2 q3
PGaCl3 - K9 K-1 aGaAs q2 q¡2
P_ i -2 2 6 -2
Ga_Cl, = K-,Kfl K.. , q- q_
26 16 9 1 GaAs^2 ^3
(4-130)
(4-131)
(4-132)
(4-133)
(4-134)
(4-135)

83
Gel
K K K ^ a a~^
K30K28K27 K1 GaAs q3
PInCl K2 ainAs q2 q3
In2C12
= K17 K¡2 alnAs q2 q¡2
InCl.
„ -1 2 -1
K13 K2 aInAs q2 q3
In_Cl .
2 4
„ „ „-2 2 4-2
K12K11K2 ainAs q2 q3
InCl3 K±1 K2 aInAs ^2 q3
In2C16
„ v2 -2 2 6-2
K15K11 K2 ainAsq2 q3
In
K K ^ a a q
K31K28K27 K2 InAs q3
-4 v\ 4 -4 4
K, K.. a„ _ a„ , q,
3 1 GaP GaAs 3
„0.5 -0.25 -3 „3 3 -3 3
Kor K-, K, K. a„ _ a„ , q,
26 7 31 GaP GaAs n3
„-0.5 -2 „2 2 -2 2
K7 K3 K1 aGaP aGaAs q3
,,0.5 -0.25 -1 „ -1
K_c K-, K, K- a„ _ a„ „ q,
25 7 31 GaP GaAs ^3
PH.
„-l „-0.25 -1„ -1 3
K8 K7 K3 KlaGaPaGaAs q3 ql
PH.
*21*? K7°'25 KilKlaGaPaGaAs *3 4
PH
- K22K81k7°'25 SX^aP^aAs ^3
(4-136)
(4-137)
(4-138)
(4-139)
(4-140)
(4-141)
(4-142)
(4-143)
(4-144)
(4-145)
(4-146)
(4-147)
(4-148)
(4-149)
(4-150)

84
Substituting equations (4-79 to 4-83, 4-116 to 4-122 & 4-130
to 4-150) into equations (4-37, 4-42 & 4-47) gives three
nonlinear algebraic equation of qj_, q2, and q3. When aGaAs,
aGaP r 3-inAs (and ajnp) are specified, the equations can be
solved for q^, q2, and q3. The complex chemical equilibrium
of deposition zone is calculated by an iterative algorithm,
which is succinctly explained in figure 4-1.

85
START
*
Read Process parameters: T¿, Ptot
& Mixing Zone Transport Rates:
FC1(m), FGa(m), FIn(m), FAS(m), FP(m)
S
Calculate Equilibrium Parameters: A¿j, D
Initial Guess: x, y
2
Calculate Activities: aGaAs, aInAs, aGaP, aInP
(by Solid Solution Model)
2
Solve qp, q2 r q3
(by Newton-Raphson method)
. —
Calculate Partial Pressure: P-¡_'s
2
Calculate Equilibrium Parameters: Y, Z
^
Calculate Supersaturation: S
& Composition of Deposited Solid: xcaTC, yca]_c
(bv eqs.(75 & 76))
xcalc - x ?
NO
V
Ad ju
Ycalc " Y •
x, y
YES
—,
PRINT OUT
i
STOP
Figure 4-1. Algorithm for complex chemical equilibrium
calculation in the deposition zone

86
4.2 Solution Thermodynamics of InGaAsP
4.2.1 Solution Thermodynamics
Let Xj_ denote the mole fraction of component i in a
homogeneous solution of C components, then
X1 + x2 + x3 + + xc = 1 (4-151)
Let W denote an extensive property of the mixture, then the
intensive property w-j_ of component i can be derived from the
basic thermodynamic relationship,
w-i
= (
3W
3Ni
i T, P, Nj (jjti) ,
(4-152)
where T is temperature, P is pressure and is the amount of
component in the mixture. If Nj_ has the unit moles, then w-^
is called a partial molar property. Therefore the partial
molar Gibbs free energy, g¿, or chemical potential, Ui, is
simply
ui = gi
)
3N¿ T, P,
(4-153)
The partial molar entropy, s-¡_, the partial molar enthalpy,
h, the partial molar volume, v¿ and the partial molar heat

87
capacity, Cp¿, are derived from the chemical potential ¿ by
classical thermodynamics.
si = "hi/ T (4-154)
hi = hi " T( yi/ T) (4-155)
Vi = hi/ P (4-156)
Cpi = T( Si/ T) = -T(hi/ T2) (4-157)
Besides its use of conveniently evaluating other partial
properties, the chemical potential is useful in formulating
phase equilibrium. Consider two homogeneous mixtures A1 and
A2 of C components at equilibrium, the system of phase
equilibrium equations can be written as follows.
Tai = ta2 (4-158)
PAl = ?A2 (4-159)
Ui,Al = Ui,A2' i = 1» 2, 3, C (4-160)
In the consideration of a homogeneous mixture, we are
also concerned with the comparison of partial properties of
the components in the mixture with those properties in pure

88
components. Let denote the chemical potential of pure
component i at temperature T and pressure P of interest, then
relative activity a¿ of component i in the mixture is defined
by the relationship,
ai = exp (( J*i- y°j_) /RT) (4-161)
Clearly, a¿ is a direct measure of the chemical potential
difference of component i between the mixture and the pure
component i. This quantity can be directly used in the
description of phase equilibrium between two solutions. y
can be rewritten in terms of yO-j_ and a¿,
yi = y°i + RT lnfa^) (4-162)
Substituting equation (4-162) in equation (4-160) and
cancelling u0-¡_ on both sides of the equality sign results in
another form of phase equilibrium equations.
ai,Al = ai,A2 (4-163)
From the review above, it is clear that if extensive
Gibbs free energy G (T, P, Nj_, N2, ...., N^;) is known, all of
the partial molar properties can be readily derived.
Furthermore, if the standard chemical potential yO^(T, P) is
known, relative activity a± is obtained.

89
4.2.2 Solid Solution Models
The solid solution models used for type A]__XBXC]__yDy
III-V quaternary compound system are reviewed in this
section. The objective is to develop a mathematical
representation of the extensive Gibbs free energy G in terms
of the variables, T, P, n^c, nB^, nAD, and nBD. A solid
solution model is usually constructed on an atomic or a
statistical viewpoint and its compatibility with the solution
system is tested by its capability to describe the system's
experimental behavior. However, when the experimental
characterization of the solution is difficult, solid solution
models are also employed to interpolate and extrapolate sytem
behavior from the limited amount available information.
The Ai_xBxC]__yDv type of III-V quaternary solid solution
has often been treated as a pseudoquaternary mixture of
binary components AC, AD, BC, and BD. The characteristic
feature of this type of solution is that the distribution of
the nearest neighbor pairs is not uniquely determined by the
apparent composition (x, y) of the quaternary compound. Let
nAC • nAD' nBC > an<^ nBD represent the number of nearest
neighbor pairs AC, AD, BC, and BD, respectively. These
numbers are related to the number of constituent atoms, ,
Nb, Nq, and Nd, as follows.
nAC + nAD = Z1 nA
(4-164)

90
nBC + nBD = Z1 nB
(4-165)
nAC + nBC = Z1 NC
(4-166)
nAD + nBD = Z1 nD
(4-167)
, where z^ (= 4) is the number of nearest neighbors for each
atom in the zinc-blende lattice structure. The number of
constituent atomsf NA, Ng, Nq, and NB, is related to the
apparent composition (x, y) and the total number of group III
or group V sites, N.
Na = (1—x) N (4-168)
Nb = x N (4-169)
Nc = (1-y) N (4-170)
nd = y N (4-171)
By observing equations (4-164 to 4-171), it can be seen that
equations (4-164 to 4-167) are a set of dependent equations
and one of the four equations can be eliminated. The
resulting set of three independent equations, after
substitution of NA, Ng, Nq, and Np by equations (4-168 to 4-
171) into equations (4-164 to 4-167), is written as follows.

91
nAD = (1-x)(2! N) - nAC
(4-172)
nBC = (1-y) (Zl N) - nAC
(4-173)
nBD = (x+y-1) (Z]_ N) + nAC
(4-174)
It is obvious from equations (4-172 to 4-174) that nAc, nAB,
nBC, and nBB are not uniquely determined with specified x, y,
and N. This feature is characteristic for III-V compound
systems with mixing on both sublattices. However, if nA^,
nAD/ nBc, and nBB are specified, x, y, and N can be readily
calculated by
x = (nBC + nBD)/(nAC + nAB + nBC + nBD) (4-175)
y = (nAD + nBD)/(nAC + nAD + nBC + nBD) (4-176)
N = (nAC + nAD + nBC + nBD)/zl (4-177)
If a completely random distribution is assumed, the number of
nearest pairs is given as follows.
nAc = (i-x) d-y) zi N
(4-178)
nAD = U-x) y Zl N
(4-179)

92
nBC = x (1-y) z± N
(4-180)
nBD = x y z1 N
(4-181)
The molar ratio of the binary components X-¡_j (i=A,B; j=C,D)
is defined by
^*ij = (r*ij/z^) / N
(4-182)
In the case of random mixing, X-^j's are evaluated as
XAC = (1-x)(1-y)
(4-183)
xad = (i-x) Y
(4-184)
XBC = x (1-y)
(4-185)
Xbd = x y
(4-186)
The extensive Gibbs free energy G of the solid solution
Ai_xBxCi_yDy is given as a function of n^Q, nAB, ngc r nBB,
and T. From equations (4-172 to 4-174), it is obvious that G
can also be written as a function of n^, N, x, y, and T.
When completely random distribution is assumed, G is a
function of N, x, y, and T only, as evidenced by equations
(4-179 to 4-181).

93
In addition to equations (4-172 to 4-174), the
distribution of nearest neighbor pairs is dictated by the
minimization of Gibbs free energy in the system. The total
differential of G, dG, is written from its functional
dependence as
dG=-SdT
+ ( MACdnAC+ l-1ADdnAD + ViBCdnBC+ V1 BDdnBD^ /Z1 (4-187)
Gibbs free energy minimizes when dG equals to zero.
Therefore, with constant temperature (dT=0) at thermodynamic
equilibrium, equation (4-187) becomes
0 = ^AC dnAC + ’¿AD dnAD + ¿BC dnBC + ¿BD dnBD (4-188)
From equations (4-172 to 4-174), the relationship between the
total differential of the number of nearest neighbor pairs is
obtained as
dnBD “ -dnBC = -dnAD = dnAC (4-189)
Combing equation (4-188) and equation (4-189), we obtain
UAC + UBD = yAD + yEC (4-190)
Equations (4-172 to 4-174) and equation (4-190) together
define the distribution of nearest neighbor pairs.

94
Four models will be presented in the following for type
Ai_xBxCi_yDy III-V solid solution, namely, the ideal solution
model, the strictly regular solution model, the delta lattice
parameter (DLP) model and the first-order quasi-chemical
model.
4.2.2.1 Ideal Solution Model
Ideal solution model assumes random mixing on both
sublattices and zero enthalpy of mixing, i.e.
Asmix=-NR(xlnx+(1-x)In(1-x)+ylny+(l-y)ln(l-y)) (4-191)
AHmix=0 (4-192)
Therefore,
A^mix “ AHm;j_x-T ASmix
=NRT(xlnx+(1-x)In(1-x)+ylny+(l-y)ln(l-y)) (4-193)
The extensive Gibbs free energy can be derived from the
definition of ¿Gmix.
¿G
mix
= G-(nAC
U°AC + nAD 0
y AD+nBC pOBC+RBDyoBD)/Zl (4-194)

95
Therefore,
G = (nACy°AC +nADu°AD +nBCy°BC +nBB |PBD) /Z]_
+NRT(xlnx+(1-x)In(1-x)+ylny+(l-y)ln(l-y)) (4-195)
The chemical potential of the binary compound components can
be derived by substituting equation (4-195) in equation (4-
153) .
hij = y°ij + RT In (NiNj/N2) (4-196)
Therefore,
hAC = ^°AC + RT ln((1-x)(1-y)) (4-197)
hBC = ^°BC + RT In(x(1-y)) (4-198)
Had = h°ad + RT ln((l-x)y) (4-199)
V>BD = h°BD + RT ln(xy) (4-200)
With equations (4-197 to 4-200), the activity of the binary
compound components can be derived by its definition of
equation (4-161).
aij = (NiNj/N2)
(4-201)

96
aAC = U-x) (l-y)
(4-202)
aBC = x(l-y)
(4-203)
aAD = d-x)y
(4-204)
aBD = xy
(4-205)
4.2.2.2 Strictly Regular Solution Model
The definition of a strictly regular solution model is
best described in the case of a binary mixture. Suppose the
binary mixture comprises component 1 and 2, with x being the
molar fraction of component 1. The strictly regular solution
model assumes random mixing of the two constituent components
and interaction between the neighboring unlike molecules
only. Suppose the volume of mixing is also negligible, then
the entropy and enthalpy of mixing of N moles of the binary
mixture can be expressed as follows.
Asmix = - NR (xlnx + (1-x)In(1-x))
(4-206)
AKmix = ft i2 N x(l-x)
(4-207)
where ^ ±2 is the interaction parameter between component 1
and 2. The interaction parameter can be a function of
temperature (an assumption used in the simple solution model)

97
or a function of composition (an assumption used in the
generalized regular solution model), the strictly regular
solution model dictates that the interaction prameter is
assumed to be a constant value and the mixture properis
symmetrical.
Jordan [65] derived the activity coefficients for
strictly regular multicomponent solutions in a convenient
form for Gibbs energy of mixing, and also reported detailed
expressions of activity coefficients in quaternary mixtures.
But, it was Ilegems and Panish [4] who used the concept of
regular solution for the application in type A^_xBxCi_yDv
solid solution.
If treated as a strictly regular solution, the
quaternary solid A^_XBXCy_yDy can be considered as a
pseudobinary mixture of its ternary components, ACy-yDy and
BCy-yDy, or A^_XBXC and A]__XBXD. In terms of ACy_vDy and
BC]_ _yDy ,
G = N (
NRT ( xlnx + (l-x)ln(l-x) )
(4-208)
Or, in terms of Ay.^c and A]__xbxD,

98
G = N (
(l-y)
0 + V
HA- B C y
0
^A. B C
1-x X
1-x X
N (
y(l-y)
^ A, B C-A.
B D * +
1-x x 1-
-X X
NRT
( ylny
+ (l-y)In(1-
-y) )
(4-209)
The four ternary components can be considered again as
pseudobinary mixtures of their binary components, and the
chemical potential can be derived by strictly regular
solution approach as follows.
0
^JAC1
D
-y y
(1-y) mac + Y had + Y(1 y) ^ac-ad
+ RT ( ylny + (l-y)ln(l-y) )
(4-210)
0
^JBC1
D
-y y
d-y) yBC + y yBD + y d-y) -BC_BD
+ RT ( ylny + (l-y)ln(l-y) )
(4-211)
0
^A
i B C
1 —x x
^ l1 AC + X ^BC + x(1-x) ft AC-BC
+ RT ( xlnx + (l-x)ln(l-x) )
(4-212)
Al-xBxD
(1-x) u°D * * uBD + xd-x) aAD.BD
+ RT ( xlnx + (l-x)ln(l-x) )
(4-213)
If the interation parameters between ternary components are
assumed to obey the linear relationship,
-AC. D -BC. D
i-y y i-y y
AC-BC
y n
AD-BD
(4-214)

99
'A, B C-A, B D
1-x X 1-x X
(1-x) ft
AC-AD
+ x ft
BC-BD
(4-215)
Then, substitution of equations (4-210 & 4-211) in equation
(4-208) and substitution of equations (4-212 & 4-213) in
equation (4-209) result in the same equation.
G = N ( (1-x) (1-y) ^PAC + (1-x) y y°AD +x(l-y) y°BC +xy y °BD
+ ^Ac-AD d-x) d-y)y
+ ^bc-bd xd-y)y
+ ^AD-BD x(l-x)(1-y) (4-216)
+ ^AC-BC x(l-x)(1-y)
RT (xlnx + (l-x)ln(l-x) + ylny + (1-y)In(1-y)))
Chemical
equation
^ AC
potential of binary components can be derived from
(4-153) by applying equation (4-216).
= P°AC + xy Ay° + RT In((1-x)(1-y))
+ ftAC-AD Y(x+y-2xy)
+ ^AC-BC x(x+y-2xy)
+ ^ BC-BD xy(2y-l)
+ ftAD-BD xy(2x-l) (4-217)
yAD
M° AD
+
+
+
+
x(1-y)
ftAC-AD
nAC-BC
nBC-BD
ft
AyO + RT In((1-x)y)
(1-y)(l-x-y+2xy)
x(l-y)(2x-l)
x(1-y)(l-2y)
AD-BD
x (l-x-y+2xy)
(4-218)

100
^BC = U°BC “
+
+
+
+
(l-x)y Ay0 + RT In(x(1-y))
Í2 AC-AD (1-x) y (2y-l)
íí AC-BC (1-x) (l-x-y+2xy)
nBC-BD y(l-x-y+2xy)
ftAD-BD (1-x)y(l-2x)
(4-219)
yBD = y°BD +
+
+
+
+
(1-x) (1-y) ^0 + RT ln(xy)
ft AC-AD (1-x)(1-y)(l-2y)
ft AC-BC (1-X)(1-y)(l-2x)
ftBC-BD (1-y)(x+y-2xy)
ftAD-BD (1-x)(x+y-2xy)
(4-220)
where
U°AD + y°EC “ y °AC “ y°BD
(4-221)
Activity of the binary components can be readily derived from
equations (4-217 to 4-220) straightforwardly and will not be
elaborated here.
4.2.2.3 Delta Lattice Parameter Model
The Gibbs free energy is considered to be equal to the
Helmholtz free energy, F, for condensed phases. The
extensive Helmholtz free energy can be derived from
statistical thermodynamics by the partition function Z.

101
G = F = - kT InZ (4-222)
where the partition function Z is given as
Z = £ qi exp (-Ej_/kT) (4-223)
i
where q-j_ is the number of distinguishable configurations with
the same potential energy Ej_.
Consider N moles of quaternary A]__xBxCp_yDy mixture with
lattice molecules of a single potential energy Es, then
F = - kT In qs + Es = - T Sc + Es (4-224)
where Sc is the configurational entropy. From the equation
above, clearly Sc is equal to k In qs.
For the quaternary solid solution with random
distributed anions and cations on their sublattices,
(N N0) ! (N Nq) !
Sc in ( (N Nqx)! (N Nq(1-x))! (N NQy)! (N NQ(1-y))! 1
(4-225)
where Nq is the Avogadro ' s number. Using Stirling's
approximation, equation (4-225) becomes
Sc = - NR (xlnx+(1-x)ln(l-x)+ylny+(1-y)In(1-y)) (4-226)

102
Since the bonding energy in semiconductors is linearly
dependent on the bandgap energy and the work of Philips and
Van Vetchen [66] suggested that the average bandgap energy
varies with lattice parameter ag in III-V semiconductors
according to the relationship,
Eg (bandgap energy) = ag-2*^ (4-227)
Therefore, Stringfellow [67] proposed that the enthalpy of
atomization Hat (and the bonding energy) can be approximated
by
Hat = K ag-2.5
(4-228)
K, in the above equation, is a proportionality constant.
Furthermore, if the infinitely distant atoms represent the
zero potential energy state, the potential energy Es of the
crystal lattice is simply -Hat' or
Es = 0 - Hat
(4-229)
The lattice parameter of a quaternary III-V compound has
usually been assumed to obey Vegard's law, therefore
ag = aAC(1-x)(1-y)+aAD(1-x)y+aBCx(1-y)+aBDxy (4-230)

103
Substituting equation (4-230) for ag in equation (4-229) and
combining equations (4-229 & 4-226) with equation (4-224)
results in the expression for the extensive free energy-
function, F
F=— K (aAC(1-x)(1-y)+aAD(1-x)y+aBCx(1-y)+aBDxy)~2•5
+ NRT (xlnx+(1-x)In(1-x)+ylny+(1-y)In(1-y)). (4-231)
Chemical potential of the binary components is derived from
its definition.
'-‘AC = - K ao 2 *-* + 2.5 K ag-3*5 (-x AaB -y AaB +2xy a^)
+ RT In((1-x)(1-y)) (4-232)
0Ad =_ K a0-2*5 +2-5 K a0 3,5 (-x AaB + (1-y) AaD +x(2y-l) Aa)
+ RT In((1-x)y) (4-233)
yBC = “ K a0 2,5 +2-5 K a0~3*5 ( (1-x) AaB +y AaD +y(2x-l) Aa)
+ RT In(x(1-y)) (4-234)
yBD=-K a0-2*5 +2.5K a0 3,5 ((1-x) AaB+(l-y) JaD+(2xy-x-y) Aa)
+ RT ln(xy) (4-235)
where
AaB - aBC - aAC (4-236)
AaD = aAD ~ aAC
(4-237)

104
Aa = aAD + aBC -aAC -aBD (4-238)
To derive the activity of the binary component, the standard
chemical potential of pure component ij is required,
li^ij can be derived as special cases of equation (4-231) by
assigning the quaternary composition (x, y) to be those in
the binary compound e.g.,
U°AC = “ K aAC-2*5 (4-239)
The activity aBB is derived as
K(a¡C'5_a02•5)*2.SKa¡3•5(2xy¿a-xiaB-yaaD)
aAC = (1-x) (1-y) exp ( ^ )
(4-240)
The DLP model has been found to be successful in
predicting the magnitude of interation parameters in III-V
ternary (pseudobinary) compound systems and has also been
used extensively in complex chemical equilibrium calculation
of III-V quaternary compound systems.
4.2.2.4 First Order Quasi-Chemical Model
The ideal solution model, the strictly regular solution
model and the DLP model all assumed random distribution of
constituent atoms on both sublattices. That is, the

105
arrangement of group III atoms on group-III sublattice sites
is independent with that of group V atoms on group-V
sublattice sites. The quasi-chemical models discard the
random distribution assumption by taking into account the
preferrential occupation of lattice sites by short range
clustering of like-atoms. The short range clustering occurs
because it reduces the number of neighboring unlike atom
pairs and results in decreased enthalpy of mixing and lowered
total free energy. As pointed out in equations (4-172 to 4-
174) , the distribution of the number of nearest neighbor
pairs is not uniquely determined by the apparent solid
solution composition (x, y), but also affected by the
minimization of free energy (equation (4-188) or equation (4-
190)) due to short range clustering.
Onabe [68] described the second nearest neighbor pair
distribution as a function of the (first) nearest neighbor
pair distribution on the basis of a Bethe lattice model,
neglecting the quasi-chemical nature of the second nearest
neighbor pair distribution, and developed the first-order
quasi-chemical model for quaternary III-V compound systems of
the A]__xBxC^_yDy type.
The number of second nearest neighbor pairs of like
atoms is
n
iji
z
2
2
N .
3
(i=A,B & j=C,D; or i=C,D & j =A,B) ,
(4-241)

106
where Z2 (=12) is the number of second nearest neighbor pairs
for an atom in the zinc-blende lattice structure. And the
number of second nearest neighbor pairs of unlike atoms is
n. .,
ljk
(i?k)
z_ n, . n.
2 ki n
n
ACA
n
ACB
2
N .
Z1
D
imple,
2
Z2
nAC
_ 2
N_
2 z^
C
Z2
nBC nAC
2
N_,
Z1
C
(i=A,B & j=C,D;
or i = C,D S. j=A,B)
(4-242)
(4-243)
(4-244)
Denoting the interaction energy of (first) nearest neighbor
pairs AC, AD, BC and BD by v^q, and vgg, and the
interaction energy of second nearest neighbor pairs ACA, ACB,
etc. by vACA, vAqB, etc., the potential energy of the
quaternary solid solution can be derived as
Es = VAC nAC + VAD nAD + VBC nBC + VBD nBD +
VACA nACA + VADA nADA + VBCB nBCB + VBDB nBDB +
VACB nACB + VADB nADB + vCAC nCAC + vCBC nCBC +
vDAg nDAg + vDBg nDBg + vCAq nCAg + VCBg nCBg
(4-245)

107
Since the potential energy of (nj_j/Z]_) moles of binary ij
compound (i=A,B & j=C,D) is
E j_ j = Vij ^ij + ^^iji + v j i j ) ( Z2/2zj_) nij (4 — 246)
The interaction parameter in the ternary (pseudobinary) solid
solutions can be considered as the difference between unlike
atoms and like atoms, therefore
•" AB-AC = N0 Z2 " AD-BD = N0 Z2 (VADB“(VADA+VBDB)(4-248)
^AC-AD = N0 Z2 (VcaD-(VCAC+VDAD)/2) (4-249)
^BC-BD = N0 Z2 (vCBD-(vCBC+vDBD)/2) (4-250)
Rearranging equation (4-245) with the use of equations (4-
246 to 4-250) results in
E
s
EACnAC + E;
r‘AC-BC
“AD-BD
n
AC-AD
n
BC-BD
nAD +
EBCnBC + E
1
nACnBC
Z1N0
nAC+nBC
1
nADnBD
ziNo
nAD+nBD
1
nACnAD
Z1N0
nAC+nAD
1
nBCnBD
z N
TO
nBC + r'BD
BDnBD
)
)
)
(
(4-251)

108
The configurational entropy Sc takes the following form,
- k In q
- k ( In
- In
n * n i n i n
AC AD BC BD*
0 , 0 , 0 , 0 .
nAC'nAD‘nBC'nBD‘
In
m I n 1
0 *
N i N i N i N l
A B C D*
(ZiNqH
(4-252)
where q is the degeneracy factor and n^-^j's represent nj_j at
completely random distribution.
n.
ID
N.N .
= z 1 3.
1 N0
(4-253)
With the potential energy, Es, in equation (4-251) and the
configurational entropy, Sc, in equation (4-252), the
Helmholtz free energy can be readily obtained. The chemical
potential of the binary components can, then, be derived from
its definition in equation (4-151).
X
AC
AC
yAc + RT In ( (1-x) (1-y) ) + ZlRT In ( (1_x) j T-VT
+ ^AC-BC
WBC
(l-y)
+ ^ ar-
AD
AC-AD
4-254!
(1-x)

109
mad = m°d * RT ln(u-x)y) * z^T ln(
+ ft
BD
AD-BD
+ Í2
AC
AC-AD
(1-x)
(4-255)
BC
BC MBC
+ RT In (X (1-y) ) + Z1RT In ( —--y—■;
+ n
AC
AC-BC
(l-y)
+ «
BD
BC-BD
x
(4-256)
‘BD
y + RT ln(xy) + Z..RT In
JdU i.
BD
+ Í2 an-
AD
AD-BD
+ n
xy
x2
BC
BC-BD
(4-257)
And the activity of the binary components is again readily
derivable form equations (4-254 to 4-257) and the definition
of activity in equation (4-161). For example,
BD
xy
BD
xy
z1 exp(
-AD-BD XAD +
RT yz
BC-BD XBC ,
2
RT x
(4-258)
To calculate the activity of the binary components requires
knowledge of the nearest neighbor pair distribution X^g,
XSq and Xg£). This can be done by solving equations (4-172 to

110
4-174 & 4-190) simultaneously. Plugging equations (4-254 to
4-257) into equation (4-190) results in
z^RT ln(
y y
AC BD
XAD XBC
= Í2
n
2 2
XAC-XBC
AC-BC .. ,2
(l-y)
XBD-XBC
BC-BD 2
+ n
+ n
AC-AD
AD-BD
Ay
2 2
XAC~XAD
(1-x)2
XBD-XAD
2
y
(4-259)
0 in the equation (4-259) has been defined in equation (4-
221). Equations of mass conservation are obtained by
applying equation (4-182) in equations (4-172 to 4-174).
Xad + ^AC = 1~X (4—260)
XBC + XAC = 1-Y (4-261)
XBD “ XAC = x+y-1 (4-262)
The distribution of the nearest neighbor pairs is determined
by equations (4-259 to 4-262).
When the apparent solid solution composition (x, y) of a
type Ax-xBxCx -ycy 111 -V quaternery compound is specified, the
activity of the binary components can be calculated by
firstly solving for (XAq, X^p,, XBc, XBB) , followed by the

Ill
direct calculation through the use of equations (4-254 to 4-
257) and equation (4-161).

CHAPTER 5
PROCESS CONTROLLABILITY & OPTIMUM OPERATION CONDITION
The growth of quaternary Ini_xGaxAsvP^_y by hydride VPE
is a complex process. Since the desired band gap energy and
the preferred lattice matching condition are controlled by
the composition of the grown compound, composition control is
of primary concern for hydride VPE users. Composition
control is usually achieved in the process development stage
by empirical tuning of process parameters, in conjunction
with complex chemical equilibrium calculation. This
approach, resulted from the incomplete understanding of the
process chemistry, although not ideal, has nevertheless been
successful enough to make the hydride VPE a viable process
for industrial development and production of In]__xGaxAsvPi-v
heterostructures.
The empirical tuning method, which involves tedious
procedural trial-and-error runs, is quite expensive and time-
consuming. Intelligent maneuvering is crucial to obtaining
fruitful results in this type of process development. The
drawback of this empirical method has been that the result
obtained from one system is not directly applicable to
another reactor system. In order to render the results more
tractable, complex chemical equilibrium calculations have
112

113
been used to predict and to compare with the process
behavior. Complex chemical equilibrium calculations have
been reported capable of predicting solid solution
composition in VPE growth of some III-V compounds. But, in
general, this theoretical approach has not been able to make
accurate predictions for the growth of InGaAsP solutions.
The reason is simply that although hydride VPE is a
thermodynamically driven process the process behavior can
still be significantly affected by mass transfer and chemical
reaction kinetics. Therefore, complex chemical equilibrium
calculations, at best, give a qualitative description of
process performance. Quantitative prediction is very
difficult when each epitaxial reactor is designed and
operated differently and the magnitude of mass transfer and
kinetic effects varies. Another problem that undermines the
creditability of complex chemical equilibrium calculation is
that the result of calculation is sensitive to the choice of
thermochemical data and solid solution model, which are
required to initiate the calculation. Although sometimes it
is possible to explain a set of experimental results by using
a particular set of thermochemical data and solid solution
model, the reverse exercise is usually unsatisfactory. At
the present time, some important thermochemical data that are
needed in the complex chemical equilibrium calculation for
the hydride VPE of In^_xGaxASyP]__v are still being refined
and different solid solution models are being tested for

114
compatibility with the In^_xGaxASyPi_y solution system,
therefore there is actually no reason to expect accurate
description of process behavior by complex chemical
equilibrium calculation.
In the practice of empirical tuning of process
parameters, engineers observe (1) how process results change
with respect to incremental setpoint changes of each and
every one of the process parameters, (2) the fluctuation of
process parameters around their setpoints during a process
run and the effects on process results, and (3) how setpoint
changes affect the observations of (1) and (2). The first
observation can be termed "the process sensitivity to process
parameters". Since all the process parameters are inter¬
related, their influences on process behavior are not totally
independent. "Process parameter sensitivity network" is
determined from the first observation. The second
observation, "the process parameter value fluctuation", is a
inevitable result of process controllers' control mechanisms
compounded with the changing nature of process mechanics. If
the composition of the resulted epitaxial film is of primary
importance, then the observations centered upon the
compositional variation should be conducted. That is, we
should try to determine the "compositional" process parameter
sensitivity network and the magnitude and effect of process
parameter value fluctuation on "compositional control". The
third and last observation is to resolve the optimum

115
operating condition for the objective of controllability of
intended process results. For the development of hydride VPE
of Ini_xGaxASyPi_y, this observation primarily involves the
determination of compositional process parameter sensitivity
network and process parameter value fluctuations at various
sets of process parameter setpoints.
Specifically in hydride VPE of Ir.i_xGaxASy Pi-y, as
explained in section 4.1.3, there are fourteen process
parameters, FH2(Ga), FHCl(Ga), Ts(Ga), e(Ga), FH2(In),
FHCl(In), Ts(In) , e(In), FH2(m), FAsH3(m) , FPH3(m), Tm, Td
and Ptot- It is clear that because of the large number of
process parameters, a large body of experimental runs have to
be done for the practice of empirical tuning of process
parameters, which is extremely cumbersome and undesirable.
What is proposed and reported in the remaining of this
chapter is to apply complex chemical equilibrium calculation
to simulate the empirical tuning exercise. The objective is
to determine the inter-dependencies between process
parameters, to pinpoint the most influential process
parameters and to reveal the direction for the search of
optimum operating conditions. With the result cf such a
theoretical analysis, valuable information is obtained
cheaply and speedily through computer calculation and a
significantly smaller body of experiments has to be conducted
for compositional control studies.

116
The proposed approach, named "process controllability
evaluation(PCE) by complex chemical equilibrium calculation",
is a sound one, although it has been argued in the above that
complex chemical equilibrium calculation does not accurately
describe the process performance and the ambiguity related to
the choice of thermodynamic data and solid solution model
exists. The reason is simple, because this approach merely
tries to determine the relative merits, not the exact
influence on process results, of the process parameters. It
is a qualitative approach and the choice of thermochemical
data and solid solution model has only slight effect on the
obtained information.
In the following sections, the inter-dependencies of
process parameters will be reviewed first, followed by the
definitions and elaborate discussion on the ingredients in
the process controllability evaluation, namely, compositional
sensitivity to equilibrium parameter, range of equilibrium
parameter value fluctuation and quantitative representation
of process controllability. Two PCE studies are also
reported in this chapter, deposition of In>53Ga#47As on InP,
and I n _ 7 4Ga # 2 6A s . 5 6 p . 44 on InP. Based on the results
presented in these studies, the practicality of growing these
ternary and quaternary compounds by hydride VPE at the
studied conditions is discussed. To improve process
controllability, optimum, or better, process conditions
should be searched. The method of analysis aimed at

117
elucidating the direction of search for optimum operating
conditions is presented in the last section of this chapter.
The method, readily applied to the two studied growth
systems, give invaluable insight to the choice of operating
conditions to gain compositional control.
5.1 Interdependence of Process Parameters
in Hydride VPE of InGaAsP
The number of degrees of freedom in the deposition zone
for the growth of InGaAsP by hydride VPE is seven, as
discussed in chapter 4. Depending upon subjective
preference, different "equilibrium parameters" can be used to
initiate a complex chemical equilibrium calculation. One
such set of seven equilibrium parameters has been
conveniently chosen and shall be used for the remaining of
the discussion, namely,
T (deposition temperature)
Ptot (total system pressure)
Cl/H (chlorine to hydrogen ratio)
III/H (group III to hydrogen ratio)
V/H (group V to hydrogen ratio)
Ga/III (gallium to group III ratio)
As/V (arsenic to group V ratio)
Also as presented in chapter 4, there are fourteen
process parameters in the hydride VPE of Ini_xGaxAsvPi__v.

118
FH2(Ga) (hydrogen flowrate in gallium source zone)
FHC1(Ga) (HC1 flowrate in gallium source zone)
Ts(Ga) (gallium source zone temperature)
e(Ga) (reaction efficiency factor in Ga source zone)
FH2(In) (hydrogen flowrate in indium source zone)
FHCl(In) (HC1 flowrate in indium source zone)
Ts(In) (indium source zone temperature)
e(In) (reaction efficiency factor in indium source zone)
FH2(m) (hydrogen input flowrate in mixing zone)
FAsH3(m) (arsine input flowrate in mixing zone)
FPH3(m) (phosphine input flowrate in mixing zone)
Tm (mixing zone temperature)
T¿ (deposition zone temperature)
Ptot (system total pressure)
Since the degrees of freedom are less than the number of
process parameters, it is self-evident that these process
parameters must influence process behavior collectively.
Therefore the fourteen process parameters are inter-dependent
and can be lumped together to form a set of seven independent
functional groups. If using the seven equilibrium parameters
as the functional groups, then the interdependence of the
fourteen process parameters can be resolved by determining
the dependence of equilibrium parameters on process
parameters. The detailed discussion of this subject has also

119
been covered in chapter 4. The interdependence of the
process parameters can be written as follows.
A = ,r1/m = FHCl (Ga) + FHC1 (In)
d 1 ' ' “ (2FH2 (Ga)+2FH2 (In)+2FH2 (m)+FHC1 (Ga)
+FHC1(In)+3FAsH3(m)+3FPH3(m) )
(5-1)
, FHCl(Ga) e(Ga) + FHCl(In) e(In)
d DZd~ ' ' ' (2FH2 (Ga)+2FH2 (In)+2FH2 (m)+FHC1 (Ga)
+ FHC1(In)+3FAsH3(m)+3FPH3 (m) )
FAsH3(m)+FPH3(m)
C1d+C2d=(V/H)=(2FH2(Ga)+2FH2(In)+2FH2(m)+FHC1(Ga)
+FHC1(In)+3FASH-(m)+3FPH0(m) )
,r./TTn = FHCl (Ga) e (Ga)
1 ' ' FHCl(Ga) e(Ga) + FHCl(In) e(In)
(5-3)
(5-4)
(As/V)
FAsH3(m)
FAsH3(m) + FPH3(m)
(5-5)
T =
(5-6)
P = P
tot tot
(5-7;
In the above equations, the left hand side terms are the
equilibrium parameters and the right hand side terms are the

120
lumped groups of process parameters. The process parameters
involved in the same lumped group are dependent in deciding
process outcome.
5.2 Compositional Sensitivity
Define "process sensitivity to parameters" as the change
of process results with respect to parameter setpoint change.
If the composition of the solid solution Ini_xGaxASyPi_y is
chosen as the process result and the parameters are chosen to
be equilibrium parameters T, Ptot' Cl/H, III/H, V/H, Ga/III,
and As/V, then, the definition of " compositional sensitivity
to equilibrium parameters" can be succinctly expressed in
mathematical forms as follows.
compositional sensitivity to temperature T:
dx/dT, dy/dT
compositional sensitivity to pressure Ptot:
dx/d(ln Ptot>' dy/d(In Ptot)
compositional sensitivity to Cl to H ratio Cl/H:
dx/d(ln Cl/H), dy/d(ln Cl/H)
compositional sensitivity to III to H ratio III/H:
dx/d(ln III/H), dy/d(In III/H)

121
compositional sensitivity to V to hydrogen ratio V/H:
dx/d(In V/H), dy/d(In V/H)
compositional sensitivity to Ga to III ratio Ga/III:
dx/d(Ga/III), dy/d(Ga/III)
compositional sensitivity to arsenic to V ratio As/V:
dx/d(As/V), dy/d(As/V)
where dx/dA and dy/dA are derivatives of compositional
dependence on equilibrium parameter A, and dx/d (In B) and
dy/d (In B) are derivatives of compositional dependence on
natural logarithm of equilibrium parameter B. The form of
the differential dA or d(ln B) is chosen according to the
expression for parameter fluctuation, which is to be
discussed in the following sections. Note that the
sensitivities can be evaluated for a chosen set of setpoints,
or a particular operating condition, and these values change
accordingly when setpoints are changed.
5.3 Parameter Value Fluctuation
The parameter values during a process run are not
expected to obey their setpoints at all times. Ideal process
controllers, which adjust parameter values to their setpoints
at zero time transient, do not exist. Therefore, when the
parameter values are different from their setpoints, a

122
certain time period will elapse before the setpoints are
reached. In fact, for almost all cases, the process
parameter values do not really reach the setpoints, but
oscillate around the intended setpoints. Depending upon the
process control mechanisms, the range of fluctuation from the
setpoint varies. Besides the fluctuation associated with the
non-ideality of the process controllers, the process
parameter values can change instantaneously during process
operation even when no changes are made on the setpoints.
One good example is the flowrate fluctuation during valve
turn-on/turn-off cycles. The sudden change of process
mechanics at a valve turn-on/turn-off cycle will change the
established pressure difference across the flow controllers
resulting in drastic increase or decrease of flowrates in the
influenced gaslines. It should be pointed out that this is a
problem of concern in all types of VPE techniques for
heterostructure growth, since in the continuous growth of a
heterostructure, it is unavoidable to have valve turn¬
on/turn-off cycles at the juncture of interphasing when a few
reactant gasflows have to be interchanged between the reactor
and the bypass.
The range of equilibrium parameter value fluctuation is
defined as the maximum difference of equilibrium parameter
value and its setpoint during the process runtime when the
interested process results can be influenced by the
fluctuation. In hydride VPE of InGaAsP, the interested

123
process results are the solid solution composition x and y,
and it is the range of equilibrium parameter value
fluctuation during "deposition" which is of primary concern.
The range of equilibrium parameter value fluctuation can also
be represented as follows.
range of temperature fluctuation: dT
range of pressure fluctuation: d(Ptot)/(P-tot)
or d (In Ptot)
range of Cl/H fluctuation: d(Cl/H)/(Cl/H) or d(ln Cl/H)
range of III/H fluctuation: d(III/H)/(III/H)
or d(In III/H)
range of V/H fluctuation: d(V/H)/(V/H) or d(ln V/H)
range of Ga/III fluctuation: d(Ga/III)
range of As/V fluctuation: d(As/V)
,where dA is the absolute range of parameter value
fluctuation of parameter A and d (In B) is the natural
logarithmic range of parameter value fluctuation of parameter
B.

124
5.4 Process Controllability Evaluation
Process controllability is reflected by the range of
process result fluctuation, which is decided by the magnitude
of process sensitivity and the range of parameter value
fluctuation. In fact, the larger the range of process result
fluctuation, the harder the process is to control, and
therefore the lower the process controllability. Define
process controllability as the inverse of the range of
process result fluctuation. For hydride VPE of InGaAsP
process, the process result is the solid solution composition
x, y. The range of composition fluctuation dx and dy are
defined mathematically as follows.
range of
compositional ==
fluctuation
compositional
sensitivity to
equilibrium
parameter
range of
X equilibrium
parameter
fluctuation
(dx, dy) (dx/dA, dy/dA)
(dA)
or or
(dx/d(ln B), dy/d(ln B)) (d(ln B))
And process controllability can be evaluated for each and
every parameter by the above relationship.

125
5 - 5 Process Controllability Study
5.5.1 InGaAs Lattice-Matched to InP
The lattice matching composition of Ir]__xGaxAs on InP is
x = 0.47. Assuming As/V = 1, T = 973K, Ptot “ 1 atm, Cl/H =
III/H = V/H = 0.001, iterative complex chemical equilibrium
calculation by varying Ga/III gives the result that when
Ga/III = 0.605, x = 0.47 is achieved with supersaturation S/H
= 0.53e-4 .
Using the result of this calculation as a reference,
compositional sensitivity to parameters T, Ptot' Cl/K, III/H,
V/H and Ga/III can be calculated successively by making an
incremental change(1% of the parameter value of the reference
state) on the input value of one parameter while holding
others at constant. The result of this sensitivity
calculation is as follows
parameter sensitivity
T
^tot
Cl/H
III/H
V/H
Ga/III
dx/dT=-0.0141 K-1
dx/d(In Ptot)=0.044
dx/d(In Cl/H)=-0.923e-9
dx/d(In III/H)=0.937e-6
dx/d(ln V/H)=0.152e-4
dx/d(Ga/III)=6.94

126
Note that compositional sensitivity is small to parameters
Cl/H, III/H and V/H. The composition is quite sensitive to
parameters T and Ptot' and extremely sensitive to Ga/III.
First-order quasi-chemical model was used in the calculations
above.
The range of parameter value fluctuation is assumed to
be as follows.
parameter range of parameter value fluctuation
T
dT = 0.5K
ptot
d(Ptot) = 10% Ptot
or d(In Ptot) = 0*1
Cl/K
d(Cl/H) = 10% Cl/H
or d(In Cl/H) = 0.1
III/H
d(III/H) = 10% III/H
or d (In III/H) = 0.1
V/H
d(V/H) = 10% V/H
or d(In V/H) = 0.1
Ga/III
d(Ga/III) = 0.001
With known values of sensitivity and range of parameter
value fluctuation, the range of composition fluctuation and
process controllability can be evaluated. The results are
presented as follows

127
parameter range of process
composition controllability
fluctuation
T
0.00705
141.8
p tot
0.00440
227.3
Cl/H
0.9 23e-10
1.0 8e + 10
III/H
0.937e-7
1.0 7e + 7
V/H
0.152e-5
6.5 8e + 5
Ga/III
0.0694
144.1
Process controllability is small with respect to T,
ptot' Ga/III, and very large with respect to Cl/H, III/H, and
V/H. The next step is to determine the acceptable process
controllability level. For the growth of In^_xGaxAs on InP,
the composition x has to be close to 0.47 to avoid the
generation of dislocation due to lattice mismatch. The
allowable lattice mismatch depends upon the intended
thickness of the InGaAs layer. For the growth of one
micrometer thickness, composition control of mole fraction to
within 0.01 is generally required. Therefore in this case
the acceptable process controllability level is 1/0.01, or
100. All the parameters showed satisfactory process
controllability levels.
In conclusion, the growth of InGaAs on InP at the
specified operating condition with T = 973K, Ptot = 1 atm,
Cl/H = III/H = V/H = 0.001, Ga/III = 0.605 , and As/V = 1
should give satisfactory controllability on InGaAs
composition. Three parameters T, Ptot' and Ga/III are most
influential to compositional control. Process tuning should

128
be carried out intensively around these three parameters.
Note that in this study, the range of Ga/lII fluctuation was
assumed to be 0.001, and with such a strict requirement on
the range of fluctuation the process controllability level of
this parameter was 144.1, which is just above the acceptable
process controllability level(IOC). Therefore, reduction of
the range of Ga/III fluctuation is important for successful
development of InGaAs VPE by hydride method. From section
3.2, it is clear that the equilibrium parameter Ga/III is
determined by four process parameters, namely, FHCl(Ga),
e (Ga) , FHCl(In) and e(In) . Accurate and responsive
controllers should be implemented to control the input
flowrates of HC1 into gallium and indium source zones. Under
equilibrium conditions, both of e(Ga) and e(In) are
independent of temperature and very close to unity above
923K. Therefore, if the source zones are operated at
equilibrium conditions, the range of fluctuation of e(Ga) and
e(In) is effectively reduced to zero. Careful source zone
design, eliminating any possible mass transfer or reaction
kinetic influences to reach source zone equilibrium, is
essential.to successful development of hydride VPE for InGaAs
growth on InP. Lastly, the search for better operating
condition should also be centered on the reduction of the
values of compositional sensitivity to the three most
important parameters T, Ptot an<^ Ga/III. Such a search by
complex chemical equilibrium calculation has been completed

129
for this system and will be presented in the last section of
this chapter.
, process . __ , range of .
controllability composition fluctuation
== 1/dx, 1/dy
From the above equations, it is clear that process
controllability can be improved when sensitivity or parameter
fluctuation is lowered. The value of compositional
sensitivity changes with respect to parameter setpoint
changes. The process that runs at setpoints with the lowest
values of compositional sensitivities is considered the
optimum operating condition since the highest possible
process controllability is realized. It is therefore
important to search for this optimum condition. Besides
changing operating conditions, process controllability can be
boosted by lowering the range of parameter fluctuation. This
is achieved by careful study of the origin of fluctuation
followed by improved process design and process controllers.
With the foundation of the above sections of this
chapter and the methodology of complex chemical equilibrium
calculation reported in the last two chapters, two sample
studies of process controllability of hydride VPE of InGaAsP
have been carried out.

130
5.5.2 InGaAsP Lattice-Matched to InP
Assuming that the lattice constant of In]__xGaxASyP]__y
obeys Vegard's law, the lattice matching condition for
InGaAsP on InP is that x equals to 0.47y, 0 973K, Ptot = 1 atm' Cl/H = III/H = V/H = 0.001, iterative
complex chemical equilibrium calculation by varying both
Ga/III and As/V gives the result that when Ga/III = 0.388 and
As/V = 0.0039, the composition of the quaternary compound is
that x = 0.26, y = 0.56 and supersaturation S/H = 0.55e-5.
Using the result of this calculation as a reference,
compositional sensitivity to parameters T, Ptot' Cl/H, III/H,
V/H and Ga/III can be calculated successively by making an
incremental change on the input value of one parameter while
holding others at constant. The result of this sensitivity
calculation is as follows
parameter sensitivity
T
dx/dT=-0.802e-2 K_1,
dy/dT=0.565e-2 K"1
ptot
dx/d(ln Ptot)=0.142,
dy/d(In Ptot)=-0.199
Cl/H
dx/d(lnCl/H)=-0.3e-10,
dy/d(InCl/H)=.5e-10
III/H
dx/d(In III/H)=0.335e-7,
dy/d(lnlll/H)=-.5e-7
V/H
dx/d(ln V/H)=-0.120e-6,
dy/d(InV/H)=0.17e-6
Ga/III
dx/d(Ga/III)=2.27,
dy/d(Ga/III)=-0.429
As/V
dx/d(As/V)=-58.8,
dy/d(As/V)=83.0
Similar to the study of In.53Ga#47As growth,
compositional sensitivity is small to parameters Cl/H, III/H
and V/H. The composition is quite sensitive to parameters T

131
and Ptot / and extremely sensitive to Ga/III and As/V. In
this calculation the incremental change of parameter input
value was 1% of the parameter value of the reference state.
The range of parameter value fluctuation is assumed to
be as follows
parameter
range of parameter value fluctuation
T
dT = 0.5
'K
ptot
d(Ptot)
= 5% P
tot
or d(ln
ptot)
= 0.05
Cl /H
d(Cl/H)
= 10%
Cl/H
or d(ln
Cl/H)
= 0.1
III/H
d(III/H)
= 10%
III/H
or d (In
III/H)
= 0.1
V/H
d (V/H) =
= 10% V/H
or d(In
V/H) =
0.1
Ga/III
d (Ga/III
) = o.
001
As/V
d(As/V)
= 0.0001
With known values of sensitivity and range of parameter
value fluctuation, the range of composition fluctuation and
process controllability can be evaluated. The results are
presented as follows
parameter
range of III-sublattice
composition fluctuation
dx
process
controllability
on composition x
T
^tot
Cl /H
III/H
V/H
Ga/III
As/V
0.00401
0.00710
0.333e-ll
0.335e-8
0.120e-7
0.00227
0.00588
249.4
140.8
3.00e + ll
2.9 9e + 8
8.33e+7
440.5
170.1

132
parameter range of V-sublattice process
composition fluctuation controllability
dy on composition y
T
0.00282
354.6
P tot
0.00995
100.5
Cl/H
0.466e-ll
2.15e + ll
III/H
0.4 69e-8
2.13e+8
V/H
0.170e-7
5.88e+7
Ga/III
0.C00423
2364.
As/V
0.00830
120.5
Process controllability is small with respect to T,
ptot' Ga/III, and As/V. and very large with respect to Cl/H,
III/H, and V/H. If acceptable process controllability level
is assumed to be 100, the same value as used in the study of
In.53^a.47As growth, all the parameters showed satisfactory
process controllability levels.
In conclusion, the growth of In^746ap26As.56p.44 on InP
at the specified operating condition with T = 973K, Ptot = 1
atm, Cl/H = III/H = V/H = 0.001, Ga/III = 0.338 , and As/V =
0.00339 should give satisfactory controllability on the
growth composition of this quaternary compound. Four
parameters T, Ptot' Ga/III, and As/V are most influential to
compositional control. Extensive process tuning should be
done around these four parameters. Again, strict control on
the range of Ga/III and also As/V fluctuation are noted. The
reduction of the range of Ga/III fluctuation has been
discussed in the last case study. For quaternary compound
growth, tight control on the input flcwrates of both arsine

133
and phosphine, which determine the value of As/V, is a must
for the compositional controllability on both group III and
group V sublattices. The search for optimum operating
condition will be discussed in the next section.
5.6 Process Sensitivity Analysis
Process controllability with respect to a parameter, as
defined in section 5.4, is determined by both the process
sensitivity to the parameter and its range of fluctuation.
Even with the best possible process design, the reduction of
the range of parameter value fluctuation is still limited by
the performance of the available controller devices. For the
most influential parameters it is imperative to search for
operating conditions that the very high degree of process
sensitivity imposed by these parameters can be driven toward
lower values. Suppose empirical tuning starts at a certain
set of process parameter setpoints, engineers are often
interested to know in which direction the setpoints should go
to resolve a better controllable, less sensitive operating
condition. If the starting set of setpoints is used as a
reference state, it is interesting to observe how process
sensitivities of each and every process parameter will change
as a result of setpoint variations.
Denote the process sensitivity at the reference set of
setpoints by subscript 0 as follows

134
parameter
reference process sensitivity
^tot
Cl /H
III/H
V/H
Ga/III
As/V
T
(dx/dT)o, (dy/dT)0
(dx/d(ln Ptot))0/ (dy/d(In Ptot))0
(dx/d(ln Cl/H)) q , (dy/d(ln Cl/H))q
(dx/d(In III/H))o, (dy/d(ln III/H))0
(dx/d(ln V/H))o f (dy/d(ln V/H))q
(dx/d(Ga/III))o, (dy/d(Ga/III))0
(dx/d(As/V))o, (dy/d(As/V))o
Define relative sensitivity as the ratio of the process
sensitivity after setpoints are varied to the process
sensitivity at the reference set of setpoints.
Mathematically, the relative sensitivity can be represented
as in table 5-1.
The relative sensitivity can be evaluated by varying the
input process parameter setpoints and observing the
corresponding process sensitivity after the changes are made.
If the relative sensitivity of the interested parameter is
less than one, then the new setpoints give a more
controllable, less sensitive condition; if it is larger than
one, the new operating condition is less controllable and
therefore undesirable. The evaluation process can be carried
out experimentally or by complex chemical equilibrium
calculation. The approach by complex chemical equilibrium
calculation is adopted here and has been used to evaluate the
relative sensitivities, at a systematic variation of
parameter setpoints, in hydride VPE of In_53Ga<47As lattice-

135
Table 5-1. Definition of Relative Sensitivity
parameter
relative sensitivity
T
(dx/dT)/(dx/dT)q,
(dy/dT)/(dy/dT)g
ptot
(dx/d(ln Ptot))/(dx/d(In Ptot))0'
(dy/d(ln Ptot))/(dy/d(In Ptot))o
Cl /H
(dx/d(ln Cl/H))/(dx/d(In Cl/H))g,
(dy/d(In Cl/H))/(dy/d(In Cl/H))g
III/H
(dx/d(In III/H))/(dx/d(In III/H))0,
(dy/d(In III/H))/(dy/d(In III/H))0
V/H
(dx/d(ln V/H))/(dx/d(In V/H))g,
(dy/d(In V/H))/(dy/d(In V/H))g
Ga/III
(dx/d(Ga/III))/(dx/d(Ga/III)) 0,
(dy/d(Ga/III))/(dy/d(Ga/III))0
As/V
(dx/d(As/V))/(dx/d(As/V))0,
(dy/d(As/V))/(dy/d(As/V))0

136
matched to InP and In # 74Ga # 2 6As . 5 6P . 44 lattice-matched to
InP.
5.6.1 Relative Sensitivities in Hydride VPE of InGaAs
The reference setpoints for this study has been chosen
to be the result reported in section 5.5.1. Results of the
study are conveniently presented in figures 5-1 to 5-5. In
figure 5-1, the relative sensitivities of parameters T, Ptot'
Cl/H, III/H, V/H and Ga/III are reported with the variation
of temperature T, while other parameter values are kept at
the reference setpoints. Ptot' Cl/H, III/H and V/H are
varied, and the relative sensitivities are calculated and
presented in figure 5-2, 5-3, 5-4 and 5-5, respectively. The
calculational procedure is as follows. For each setpoint
variation, Ga/III value is calculated first for the
composition, x = 0.47, followed by the calculation of
compositional sensitivities, as discussed in section 5.5.1.
The relative sensitivities can then be calculated according
the definition. For the sake of convenience, the curves are
numbered to represent each and every parameter; curve 1: T,
curve 2: Ptot' curve 3: Cl/H, curve 4: III/H, curve 5: V/H,
and curve 6: Ga/III.
Since T, Ptot' and Ga/III are the most influential
parameters, the curves 1, 2, and 6 should be carefully
studied for the search of optimum operating conditions. From
figures 5-1 to 5-5, it is observed that, with small to mild

Relative Sensitivities
137
650 70C 750
T (°C)
Figure 5-1. Dependence of relative sensitivities of parameters
T (curve 1), Ptot (curve 2), Cl/H (curve 3), III/H
(curve 4), V/H (curve 5) and Ga/III (curve 6) on T.
The reference setpoint is T = 700 C, Ptot = 1 atm,
Cl/H = III/H = V/H = 0.001 and Ga/III = 0.605.

Relative Sensitivities
138
0.01 C.10 1.00
Plot (atm)
Figure 5-2. Dependence of relative sensitivities of parameters
T (curve 1), Ptot (curve 2), Cl/H (curve 3), III/H
(curve 4), V/H (curve 5) and Ga/III (curve 6) on
Ptot* The reference setpoint is T = 700 C, Ptot =
1 atm, Cl/H= III/H= V/H= 0.001 and Ga/III = 0.605.

Relative Sensitivities
139
0.0001 0.001 0.01
Cl/H (l!!/H=C!/H)
Figure 5-3. Dependence of relative sensitivities of parameters
T (curve 1), Ptot (curve 2), Cl/H (curve 3), III/H
(curve 4), V/H (curve 5) and Ga/III (curve 6) on
Cl/H with III/H = Cl/H. The reference setpoint is
T = 700 C, Ptot = 1 atm, Cl/H = III/H = V/H= 0.001
and Ga/III = 0.605.

Relative Sensitivities
140
0.9S 0.96 1,00
lll/H * 10°
Figure 5-4. Dependence of relative sensitivities of parameters
T (curve 1), Ptot (curve 2), Cl/H (curve 3), III/H
(curve 4), V/H (curve 5) and Ga/III (curve 6) on
III/H. The reference setpoint is T = 700 C, Ptot=
1 atm, Cl/H= III/H= V/H= 0.001 and Ga/III = 0.605.

Relative Sensitivities
141
Figure 5-5. Dependence of relative sensitivities of parameters
T (curve 1), Ptot (curve 2)• Cl/H (curve 3), III/H
(curve 4), V/H (curve 5) and Ga/III (curve 6) on
V/H. The reference setpoint is T = 700 C, Ptot
= 1 atm, Cl/H= III/H= V/H= 0.001 and Ga/III = 0.605.

142
effects on the compositional sensitivities of other
parameters, (1) compositional sensitivity to temperature T is
reduced if Cl/H value is lowered, or if V/H value is
increased, (2) compositional sensitivity to pressure Ptot is
reduced if Cl/H value is lowered, or if V/H value is lowered,
and (3) reduction of compositional sensitivity to Ga/III can
be achieved effectively by lowering T value or by increasing
V/H value. Besides, III/'H should be kept close to Cl/K,
which occurs when source zones are operated at equilibrium,
for lower sensitivity to all parameters.
In conclusion, for better control of InGaAs composition,
Cl/H setpoint should be lowered from 0.001, V/H value should
be increased from 0.001, and deposition temperature should be
lowered from 700 C.
5.6.2 Relative Sensitivities in Hydride VPE of InGaAsP
The reference setpoints are reported in section 5.5.2.
Results of this study are presented in figure 5-6 to 5-10.
In figure 5-6 & 5-7, the relative sensitivities of parameters
T, Ptot' Cl/H, III/H, V/H, Ga/III, and AS/V are reported with
the variation of temperature T, while other parameter values
are kept at the reference setpoints. The relative
sensitivities of group III sublattice composition, x, are in
figure 5-6, and those of group V sublattice composition, y,
are in figure 5-7. Ptot' Cl/H, III/H and V/H are varied, and
the relative sensitivities are calculated and presented in

Relative Sensitivities
143
Figure 5-6. Dependence of x (group III sublattice composition)
relative sensitivities of parameters T (curve 1),
Ptot (curve 2), Cl/H (curve 3), III/H (curve 4),
V/K (curve 5), Ga/III (curve 6) and As/V (curve 7)
on T. The reference setpoint is T = 700 C, Ptot =
1 atm, Cl/H= III/H= V/H= 0.001 and Ga/III = 0.388
and As/V = 0.0039.

Relative Sensitivities
144
T co
Figure 5-7. Dependence of y (group V sublattice composition)
relative sensitivities of parameters T (curve 1),
ptot (curve 2), Cl/H (curve 3), III/H (curve 4),
V/H (curve 5), Ga/III (curve 6) and As/V (curve 7)
on T. The reference setpoint is T = 700 C, Ptot =
1 atm, Cl/H» III/H= V/H= 0.001 and Ga/III = 0.388
and As/V = 0.0039.

Relative Sensitivities
145
• I
0.01 0.10 1.00
Ptot (atm)
Figure 5-8. Dependence of x (group III sublattice composition)
relative sensitivities of parameters T (curve 1),
ptot (curve 2), Cl/H (curve 3), III/H (curve 4),
V/H (curve 5), Ga/III (curve 6) and As/V (curve 7)
on Ptot* The reference setpoint is T = 700 C,
ptct = 1 atm, Cl/H= III/H= V/H= 0.001 and Ga/III =
0.388 and As/V = 0.0039.

Relative Sensitivities
146
Plot (atm)
Figure 5-9. Dependence of y (group V sublattice composition)
relative sensitivities of parameters T (curve 1),
Ptot (curve 2), Cl/H (curve 3), III/H (curve 4),
V/H (curve 5), Ga/III (curve 6) and As/V (curve 7)
on ptot* The reference setpoint is T = 700 C,
Ptot = 1 atm, Cl/H= 111/H= V/H= 0.001 and Ga/III =
0.388 and As/V = 0.0039.

Relative Sensitivities
147
Cl/H (l!l/H=C!/'H)
Figure 5-10. Dependence of x (group III sublattice composition)
relative sensitivities of parameters T (curve 1),
Ptot (curve 2), Cl/H (curve 3), III/H (curve 4),
V/H (curve 5), Ga/III (curve 6) and As/V (curve 7)
on Cl/H with III/H = Cl/H. The reference setpoint
is T = 700 C, Ptot = 1 atm, C1/H=III/H=V/H= 0.001
and Ga/III = 0.388 and As/V = 0.0039.

Relative Sensitivities
148
Cl/H (lll/H=CI/H)
Figure 5-11. Dependence of y (group V sublattice composition)
relative sensitivities of parameters T (curve 1),
Ptot (curve 2), Cl/H (curve 3), III/H (curve 4),
V/H (curve 5), Ga/III (curve 6) and As/V (curve 7)
on Cl/H with III/H = Cl/H. The reference setpoint
is T = 700 C, Ptot = 1 atm, C1/H=III/H=V/H= 0.001
and Ga/III = 0.388 and As/V = 0.0039.

Relative Sensitivities
149
III/H * 103
Figure 5-12. Dependence of x (group III sublattice composition)
relative sensitivities of parameters T (curve 1),
ptot (curve 2), Cl/H (curve 3), III/H (curve 4),
V/H (curve 5), Ga/III (curve 6) and As/V (curve 7)
on III/H. The reference setpoint is T = 700 C,
ptot = 1 atm, Cl/H = 111/H=V/H= 0.001 and Ga/III =
0.388 and As/V = 0.0039.

Relative Sensitivities
150
lll/H * 103
Figure 5-13. Dependence of y (group V sublattice composition)
relative sensitivities of parameters T (curve 1),
ptot (curve 2), Cl/H (curve 3), III/H (curve 4),
V/H (curve 5), Ga/III (curve 6) and As/V (curve 7)
on III/H. The reference setpoint is T = 700 C,
Ptot = 1 atm, C1/H=III/H=V/H= 0.001 and Ga/III =
0.388 and As/V = 0.0039.

Relative Sensitivities
151
• 1
0,0001 0.001 0.01
V/H
Figure 5-14. Dependence of x (group III sublattice composition)
relative sensitivities of parameters T (curve 1),
ptot (curve 2), Cl/H (curve 3), III/H (curve 4),
V/H (curve 5), Ga/III (curve 6) and As/V (curve 7)
on V/H. The reference setpoint is T = 700 C,
Ptot = 1 atm, C1/H=III/H=V/H= 0.001 and Ga/III =
0.388 and As/V = 0.0039.

Relative Sensitivities
152
Figure 5-15. Dependence of y (group V sublattice composition)
relative sensitivities of parameters T (curve 1),
Ptot (curve 2), Cl/H (curve 3), III/H (curve 4),
V/H (curve 5), Ga/III (curve 6) and As/V (curve 7)
on V/H. The reference setpoint is T = 700 C,
ptot = 1 atm, C1/H=III/H=V/H= 0.001 and Ga/III =
0.388 and As/V = 0.0039.

153
figures 5-8 & 9, 5-10 & 11, 5-12 & 13, and 5-14 & 15,
respectively. The calculational procedure is as follows.
For each setpoint variation, Ga/III and As/V values are
calculated first for the composition, x = 0.26 & y = 0.56,
followed by the calculation of compositional sensitivities.
The relative sensitivities can then be calculated according
the definition. The curves are conveniently numbered to
represent each and every parameter; curve 1: T, curve 2:
Ptot' curve 3: Cl/H, curve 4: III/H, curve 5: V/H, curve 6:
Ga/III, and curve 7: As/V.
T' Ptot' Ga/III, and As/V are the most influential
parameters, therefore the curves 1, 2, 6 and 7 were carefully
studied for the search of optimum operating conditions. From
figures 5-6 to 5-15, it is observed that (1) compositional
sensitivity to temperature T is reduced if T value is
increased, Cl/H value is decreased, or V/H value is
increased, (2) compositional sensitivity to pressure Ptot i-s
reduced with increased T, decreased Cl/H and increased V/H,
(3) reduction of compositional sensitivity to Ga/III can be
achieved effectively by increasing Cl/H, and (4) reduction of
compositional sensitivity can be achieved with lowered T,
increased Cl/H, or increased V/H. And as discussed in the
last section, III/H should again be kept close to Cl/H.
In conclusion, T, Cl/H and V/H can be varied to achieve
better control of In#74Ga#26As.56p.44 composition. V/H value
should definitely be increased from 0.001, however the

154
direction of variation for T and Cl/H is not clear. Both
temperature decrease and Cl/H value increase reduce
compositional sensitivity to As/V, but increase compositional
sensitivity to T and Ptot* Cl/H value increase also reduces
compositional sensitivity to Ga/III. A tentative conclusion
is to increase Cl/H from 0.001 for effective reduction of
compositional sensitivity to Ga/III and As/V, and to increase
deposition temperature from 973K, at the same time, to offset
the increase of sensitivity to T and Ptot from increased Cl/H
value.

CHAPTER 6
MODELING OF GA11IUM AND INDIUM SOURCE REACTORS
Gallium and indium source reactors in hydride VPE
represent a class of chemical vapor transport reactors.
Therefore, a generalized approach is adopted in modeling of
this reactor system.
The physical configuration of a chemical vapor transport
reactor is sketched as in figure 6-1. The chemically
reactive gas mixture flows through the horizontally placed
tubular reactor; chemical reactions take place, in general,
in the region where a solid substrate or a boat of liquid
resides. The solid or liquid source material can participate
in the chemical reaction, or serve only as a catalyst to
facilitate surface-catalyzed reactions. A variety of
applications are possible by using chemical vapor transport
reactors. Typical examples are chemical vapor etching of
solid substrate, chemical vapor transport source, chemical
vapor deposition of semiconductor or ceramic materials. Table
6-1 presents a simple chemistry with a single input reactant
and a single gaseous reaction product; the nature of the
chemical reaction on the surface of the condensed phase may
be etching or deposition.
155

156
Reactants
+
/\
i i
i i
i i
Convective
diffusion,
i i
i i
i i
V V
Products
+
Carrier gas
— >
Chemical
Reactions
—>
Carrier gas
Figure 6-1. Typical physical configuration of
chemical vapor transport reactors

157
Table 6-1. Typical chemistry in chemical vapor transport
reactors
Reactant: A
Carrier gas: 0
Substrate material: B
Chemical reaction:
etching: A + B(S) < > C
deposition: A < > E(Sj + C
Gaseous reaction product: C
Representative schematic:
A + 0 >
A, C, 0
A + C + 0

158
In the case of chemical vapor transport of In and Ga,
the reactant A is HCl, the carrier gas 0 is H2 , and the
product C is InCl or GaCl. The predominant chemical reaction
is
HCl + III (i) < > IIIC1 + 1/2 H2 (6-1)
6.1 Thermodynamic Model
Detailed analysis of the complex chemical equilibrium in
the systems of Ga/H/Cl and In/H/Cl has been discussed in
chapter 4. Here, the thermodynamic model of the simplified
case with consideration of only three chemical species in the
vapor phase, H2, HCl and IIIC1, is presented.
The group III monochloride is derived from the reaction
equation (6-1), the equilibrium constant can be written as
P P0*5
IIIC1 H„
Kp = p (6-2)
FHC1
The law of mass conservation dictates that
PIIIC1 + PHC1 = p0HCl (6-3)
where P°HC1 i-s the initial HCl partial pressure at the
reactor entrance. If the carrier gas hydrogen is in great
excess, the partial pressure of hydrogen can be approximated

159
by the reactor system pressure, PSyS. Equations (6-2 and 6-
3) can be solved together to give
K Q
PIIIC1 = P o 5— PHC1 (6-4^
Kp + psys
Equation (6-4) is the simplified thermodynamic model equation
for indium and gallium source reactors in hydride VPE. When
the input HC1 partial pressure is known, equation (6-4)
predicts the output IIIC1 partial pressure from the
thermodynamic point of view. The conversion of HC1 can be
defined as the fraction of HCl reacted with group III metal,
and can be derived from equation (6-4) as follows
P
HCl
P
0
HCl
PIIIC1
P°
HCl
III
Cl
K +P
0.5
sys
(6-5)
Clearly from equation (6-5), the thermodynamic conversion of
HCl is always less than one in gallium and indium source
reactors. Since the chemical reaction, equation (6-1), is
exthothermic, equilibrium constant Kp increases with
temperature. Therefore, the conversion will increase with
increasing temperature and decreasing system pressure.

160
6.2 Nonequilibriuiri Mechanisms
6.2.1 Chemical Reaction Kinetics
Two different reaction routes are proposed here for
chemical reaction between HC1 and group III metal. The first
route is the surface reaction route. As discussed in chapter
3, surface reactions are accomplished through a multi-step
process, including convection, diffusion, adsorption,
reaction, desorption, etc.. The chemical kinetics of a
surface reaction concerns those mechanisms taking place at or
near the surface, i.e. adsorption, surface diffusion, surface
reaction, and desorption.
Since the chemical reaction between HC1 and group III
metal is reversible, the kinetic rate expression should have
two terms, one of the rate of the forward reaction and the
other of the rate of the reverse reaction. The forward
reaction rate through the surface reaction route, F-^s,HCl' is
postulated to have a first order dependence on HC1
concentration (or the partial pressure of HC1).
Rfs,HCl = “ ks PHC1' (6-6)
where ks is the surface reaction constant. The reverse
reaction rate through the surface reaction route, Rrs,HCl can
be derived from the thermodynamic equilibrium conditions when
the net reaction rate is zero, i.e.

161
r£s,HC1 + Rrs,HCl = 0
and
PHC1
IIIC1
,0.5
sys
K
(6-8)
Substituting PhcI i-n equation (6-6) by equation (6-8), and
using equation (6-7), the reverse reaction rate can be
derived.
Rrs,HCl = jT PHC1 psys5 (6-9)
P
Combining equations (6-6 and 6-9), the kinetic rate
expression for the surface reaction route is obtained.
Rs,HCl = r£s,HC1 + prs,HCl o 5
= ~ks PHC1 + ks/Kp pIIICl psvs (6-10)
Equation (6-10) describes the production rate of HCl.
Assuming that IIIC1 is the only chlorine-containing species
resulting from the surface reaction, then the law of mass
conservation dictates

162
rs,HC1 + Rs,IIICl = 0 (6-11)
in which Rs/IIICl i-s tbe rate of production of IIIC1 at the
surface. The rate expression for IIIC1 production can be
derived, simply from equations (6-10 and 6-11), as
Rs,IIICl = ks PHC1 ~ ks/Rp PIIIC1 psys (6-12)
Since PhcI anb PIIIC1 are on tke same order of magnitude, the
reverse reaction rate can be neglected when PSys^’^/KP is
small (less than 10-2).
The second reaction route is the homogeneous reaction
between HC1 and group III atoms in the vapor phase. The
reaction route involves the evaporation of group III atoms
from the melt, and can be important only when the evaporation
rate is high enough and the diffusion of these group III
vapor atoms is fast enough. With high evaporation rate and
fast diffusion, the partial pressure of group III atoms is
approximately equal to the vapor pressure of the group III
melt. If first order kinetics is postulated for the
homogeneous reaction, the rate expression for the production
of HC1 from the homogeneous reaction, P-hc1' can be written as
rHC1 = _k PHC1 + k/Kp PIIIC1 psys
(6-12)

163
where k is the homogeneous reaction rate constant for the
forward reaction. The production rate of IIIC1 from the
homogeneous reaction is also derived as
RIIIC1 = k PHC1 “ k/Kp PIIIC1 psys (6-14)
Again, when system pressure is low or temperature is high,
the reverse reaction can be neglected with PSVs^*^/Kp less
than 0.01.
The evaporation rate of group III atoms can be estimated
from the Hertz-Langmuir equation [46] . If the estimated
evaporation rate is considerably lower than the
experimentally observed HCl conversion rate, then the
homogeneous reaction cannot be the dominant reaction route,
and thus can be neglected. When the estimated evaporation
rate is comparable with the observed conversion rate,
diffusion speed of group III atoms in the vapor phase is
important in determining the influence of homogeneous
reaction on the overall reaction rate. If the diffusion
speed is low, the vaporized group III atoms can be consumed
near the surface, resulting in a surface-reaction-1 ike
condition and consideration of the homogeneous reaction in
the bulk of the vapor phase is unnecessary. only when the
diffusion speed is fast and the evaporation rate is higher
than the observed conversion rate could homogeneous reaction
be the dominant reaction route.

164
6.2.2 Transport Phenomena
Transport phenomena in a multi-component multi-phase
chemical vapor transport reactor is quite complex. It
involves the multi-dimensional transport of momentum, energy
and mass, described by the equation of motion, the equation
of energy and the equations of change. With a specific set
of boundary conditions adopted for a particular reactor
system, these equations can, in principle, be solved together
analytically or numerically to reveal the definitive reactor
behavior. The transport phenomena in the domain of the vapor
phase can be influenced by two types of process conditions.
The process design conditions(e.g., reactor configuration,
flowrates, process temperature, pressure) are chosen by the
process designers and can be adjusted at will. The process
chemistry conditions(e.g., reaction rates, reaction products)
are determined by thermodynamics and kinetics of the process
chemistry and can not be manually manipulated. The
complexity of the transport phenomena in chemical vapor
transport reactors depends on these process conditions. And
the degree of difficulty in modeling the transport phenomena
in the chemical vapor transport reactors also varies. It has
been established that simple reactor models, with possible
analytical solutions, are often preferred in reactor design
and characterization. Therefore, careful adjustment of
process design conditions can be very useful in reducing the
complexity of the transport phenomena and rendering reactor

165
modeling amenable. In this section, the process design
conditions that simplify the transport phenomena in gallium
and indium source reactors are discussed.
6.2.2.1 Hydrodynamic and Thermal Entrance Region Effects
The process design conditions that are relevant to the
momentum transport and the energy transport in gallium and
indium source reactors are presented below.
(1) The temperature profile typically encountered in a
hot-wall chemical vapor transport reactor with external
control of reactor wall temperature is represented as in
figure 6-2. The reactor wall temperature is constant in the
reaction zone, where a solid substrate is installed. The
temperature profile carries a certain slope at both the
upstream and the downstream of the reactor.
(2) The energy flux, delivered as a result the reaction
heat, is usually negligible compared with the energy flux
carried by the gas stream at this high temperature.
(3) There is no temperature gradient in the group III
boat, and the vapor/melt interphase temperature is close to
the wall temperature.
(4) The carrier gas is in great excess, therefore the
momentum flux carried by the gas stream does not undergo
appreciable change as a result of the chemical reactions
occurring in the reaction zone.

166
Reaction Zone
i : Reactor wail temoerature
w
Figure 6-2. Typical temperature profile in hot-wall chemical
vapor transport reactors

167
From conditions (2) and (4) , it is assumed that the
momentum flux and the energy flux are not influenced by the
chemical reactions in gallium and indium source reactors.
Also the momentum transport and the energy transport are
independent from the mass transport. The equation of motion
has to be considered for momentum transport at the entrance
region and the exit region of the reaction zone. The sudden
constriction and expansion of the gasflow conduit, caused by
the melt-containing boat, gives rise to a developing boundary
layer problem. Between the hydrodynamic entrance region and
the hydrodynamic exit region, an axial gasflow with laminar
flow profile is expected. It is, therefore, of practical
interest to estimate the hydrodynamic entry length. The
hydrodynamic entry length, is defined, somewhat
arbitrarily as the length required from the inlet to achieve
a maximum velocity of 99 percent of the corresponding fully
developed magnitude. The hydrodynamic entry lengths inside
conduits have been given by various authors. The results for
laminar flow inside conduits of various cross sections have
been compiled and published by M. N. Ozisik [69]. Table 6-2
presents part of Ozisik's compilation. From table 6-2, it is
possible to estimate the hydrodynamic entry length in the
reaction zone of the gallium and indium source reactors. The
group III source boats can be designed in such a way that the
reaction between HCl and group III melt happens only in the
region where axial laminar flow has been established, i.e.

168
Table 6-2. Hydrodynamic entry length and thermal entry
length L^- for laminar flow inside conduits of
circular and rectangular cross sections.
Cross
Section
Lh/Dh
Re
Lt/Dh
Re Pr
Circular
0.056
0.033
Rectangular
(side lengths:
a & b)
a = 0.25 b
0.075
0.054
a = 0.50 b
0.085
0.049
a = b
0.090
0.041
Dft : hydraulic
diameter
Re : Reynold's
number
Pr : Prantl1s number

169
between the hydrodynamic entrance region and the hydrodynamic
exit region. The approach of adjusted source boat design
limits the complicated hydrodynamics out of the reaction zone
and will be proven effective, in section 6.3, for simplifying
the modeling of mass transport in the reaction zone.
The equation of energy has to be considered for both the
upstream and the downstream regions from the reaction zone,
where sloped temperature profiles exist. From conditions
(1) , (2) and (3) , it is possible to achieve isothermal
gasflows in the reaction zone. Both the thermal entry length
and the thermal exit length have to be taken into account.
The thermal entry length, , is defined, somewhat
arbitrarily, as the length required from the starting point
of the constant wall temperature zone to achieve a transverse
averaged temperature of 99 percent of the wall temperature.
Table 6-2 presents the thermal entry lengths compiled by M.
N. Ozisik [69] for various conduit shapes.
Isothermal laminar axial flow can be achieved in the
reaction zone when the process design conditions, discussed
in this section, are met.
6.2.2.2 Mass Transport in the Reaction Zone
A general equation of change of component i in the gas
phase in this reactor system is given by [70]
3Ci
9 t
+ 7-N. = R.
l l
(6-14)

170
where is the concentration of component i and Rj_ is the
rate of production per unit volume of component i. The molar
flux of component i, Nj_, contains two parts: a convective
flux Cj_V, where V is the velocity, and a diffusive flux Jj_.
Since the reaction zone is operated isothermally and with an
excess of carrier gas, the diffusive flux can be simplified
to pseudo-binary ordinary diffusion according to
Ji = C Dif0 v*i (6-15)
In this expression, D-^q is the binary molecular diffusivity
of component i in carrier gas O, C is the total
concentration, and x¿ is the mole fraction of component i.
The boundary condition along the transverse direction can be
written as
- Ji n = Rs f j_ (6-16)
Here, n is a normal vector of unit magnitude in the direction
from the transverse boundary surface to the interior of the
system and Rs, i is the production rate of component i per
unit area on the liquid metal boundary surface.
Given a reactor geometry, the above equations can be
solved together for if the velocity V and the reaction
rates R^ and Rs, i are specified. As discussed in section
6.2.2.1, with proper process design conditions, the velocity

171
should have only the axial component Vz, which has a laminar
profile and is dependent on the transverse directions x and
y. Under this condition, equation (6-15) can be replaced by
J Ci 3 Ci 2
â–  + Vz(x,y) -yj Dif0 v Ci = Ri (6-17)
The transverse dependence of Vz can be obtained by solving
Poisson's equation for the specific reactor geometry.
6.3 Transport Models
Two transport models have been developed for gallium and
indium source reactors at different operating conditions,
normal pressure, and low pressure (1 torr) . Simplified
equation of change with boundary conditions are solved and
analytical model solutions have been derived in both cases.
These models were used for data analysis in the experimental
characterization of gallium and indium source reactors. The
experimental result and analysis will be presented in chapter
7 and 8. The assumptions and boundary conditions adopted in
developing these models were based on the experimental
conditions.
6.3.1 2-D Convective Diffusion Model
The geometry of the experimental reactor is shown in
figure 6-3. The domain of the modeled reaction zone in

Side view
Front view
Figure 6-3. Side view and front view of the experimental
reactor.

173
rectangular coordinates is shown in figure 6-4a. There are
two transverse directions (x*, y*) and one axial direction
(z*) in the domain. However, the y*-dimension is neglected
in developing the 2-D model because of the zero-flux boundary
condition at the reactor wall.
When the reactor is operated at normal pressure, the
molecular diffusivities are low and the HC1 partial pressure
is relatively high, therefore it is assumed that the
homogeneous reaction is not important in the gas phase
domain. The total flowrate is also high and the Peclet
number (Peclet number is defined as VaL/D where Va is the
average flow speed, L is the length of the reaction zone, and
D is the molecular diffusivity) is larger than 10, so the
axial dispersion term is neglected. The steady state two-
dimensional (2-D) convective diffusion equations for HC1 and
IIIC1 can be derived from equation (6-17) as follows.
C DO 2 C
UHC1 UHC1 , S:ci
vz —* ( )= ( ) —-J ( ) (6-18)
szC OD * r
3 IIIC1 u UIIIC1 9x UIIIC1
The corresponding boundary conditions are as follows,
at x* = 0,
D,
HC1
0 D
• 3 , CHC1
IIIC1 3x* CIIIC1
k -k /K C
) = ( s s )( C1
-k k /K ;kCTTTO,
s s IIIC1
6-19

174
e Z € ( 0, Is )
Figure 6-4. Domain of the modeled reaction zone. a. in
rectangular coordinates, b. in cylindrical
coordinates.

175
and at x*
1 (1 = A/S= ttR/4) ,
( DHC1
0
0
DIIIC1
CHC1 )
CIIIC1
0
0
)
where K
Kp/Psys^
The inlet condition
at z* = 0,
( CHC1
CIIIC1
C°
(LHC1 )
0
Equations (6-18 to 6-21) can be rewritten
variables from the following definitions.
'HC1
1 + K
'HC1
K
1 + K
'HC1
CC =
1 + K
'HC1
- C
IIIC1
1 + K
'HC1
z = z*/i
- X
*
/I
(6-20)
is that
(6-21)
with dimensionless
(6-22)
(6-23)
(6-24)
x
1
(6-25)

176
PeA =
V 1
a
D
HC1
(6-26)
PeC
V 1
a
D
IIIC1
(6-27)
in which Pe¿ is the Peclet number for component i, and Va is
the average axial velocity. Approximating V2 by Va and using
the definitions in equations (6-22 to 6-27), equations (6-18
to 6-21) become
(
PeA
0
0
Pe,
9
3 z
(6-28)
at z = 0, x e (0,1) ,
(6-29)
at x = 0, z £ (0, -j-) ,
( 0 }
(6-30)
at x =
1, Z £ (0, 4p) ,
a
a*
PeC/PeA
)(
a a
a a
° CA
1/K} (CC
) =
0
(6-31)

177
where
k
s
Pe
(6-32)
a
V
A
a
The solution of equations (6-28 to 6-31) involves the proof
of self-adjointness of the partial differential operator by
selecting an appropriate inner product in the two diemsional
Hilbert space [71, 72]. The solution of the eigenfunctions
of the operator gives a complete set of expansion series; and
the corresponding eigenvalues are real and positive. The
formal solution is
Z
i = l
CO
2
sin(Xiv/Pec) sin ( ^/Pe^ ] exp(- y z)
v'PeA sin(Ai/Pec) cos ( Ai vPeA x)
(6-33)
The constant in equation (6-33) can be expressed as
sin (2 A. /Pe )
1
4 A i ‘-peA
sin (2 A VPec)
(6-34)

178
The transcendental equation for the solution of eigenvalues
A.i is derived as
Ai/PeA tan(Ai/PeC)
i /Pec tan(xi^Pec)
K /Pe^ tan(Aiv5e^)
(6-35)
It is convenient to define the HCl conversion n and the IIICl
transport factor t as follows.
n = 1
L)
(6-36)
T
c
IIICl
c
(z*
0
HCl
L)
(6-37)
where the transverse average of C¿ of component i is defined
as
1 *
Jt C. dx
C. = — j (6-38)
By plugging equations (6-36 and 6-37) into equations (6-22
and 6-23), the relationship between the experimental results,
H and T , and the model variables, C^ and Cq, can be
established.

K
1 + K
179
(6-39)
T
( 1 - CC (z=L/l) )
n
K
1 + K
( 1 - CA (z=L/1) )
(6-40)
Using equation (6-33) and following the definition of the
transverse average (equation (6-38)),
Pe + Pe
D = x= “ [—A C [sin ( ^ /Pec) sin ( Aj/Pe^ 3 2exp [-(L/ 1) ]
i = 1 Xi
(6-41)
Equation (6-41) describes the dependence of the reaction
conversion ( t, g ) on the process parameters (Pe^, Pe^, a )
when the process chemistry is known (K) and a specific
reactor design (L, 1) is adopted.
6.3.2 Axial Dispersion Model
Because of difficulties associated with typical reactor
geometries, it is convenient to adopt an axial dispersion
model to describe the reactor performance. Referring to
figure 6-4b, the transverse average of a term @ in the r-9
plane is defined as
@
l ;
A
A
@ dA
(6-42)

180
where A is the transverse area. Similarly, a transverse
boundary average of @ is defined as
I = ' s 9 dS
(6-43)
where S is the transverse boundary length. With these
definitions the transverse average of the equation of change
is
+
a.
9Z
V2Ci
(6-44)
This equation is the axial dispersion model in its rigorous
form. When the system pressure is low, it can be assumed
that the reverse reaction is not important, as discussed in
section 6.2.1. The homogeneous reaction rate R-j_ and the
heterogeneous reaction rate Rst± are both expressed by first-
order rate expressions. With the assumptions of pseudobinary
ordinary diffusion, isothermal and isobaric condition in the
reaction zone, the equation of change, equation (6-44)
becomes
if V*Ci
+ a ^s,i Ci+ kj_ Ci
(6-45)
A dimensionless velocity and concentration based on the
transverse average is defined by = Vz/Vz and ^ = Cj_/C¿.

181
is a function of the transverse directions only, since the
flow is fully developed. But, in general ip is a function of
the axial length. However, the z dependence of ip is weak in
the region downstream from the mass transfer entrance region.
When the flowrate is low and the molecular diffusivities are
high, the Peclet number is small and the mass transfer
entrance region can be reduced. If the reactor length is
considerably longer than the mass transfer entrance region,
it can be assumed that ip is a function of transverse
directions only. In this case, the transverse averaged
equation of change, equation (6-45) can be rewritten as
The semi-circular cross section, shown in figure 6-3a,
of the reaction zone was designed to permit relatively
straightforward development of and \p . An orthogonal
collocation procedure [73] was used to solve Poisson's
equation for this geometry to give the result.
$ = ! (1- |) [1- (-jf") 2] [8.71- 1.06|
where R is the radius. Note that if - 0 at the transverse
boundary and = 1.

182
The transverse boundary conditions are
3^
at 0=0: = 0;
(6-48)
a e
at 0
3Ci _
- + tt/2: Di,0 r 30 - + ks,i ci'-
(6-49)
3Ci
at r = R: —— = 0;
(6-50)
at r = 0
-D
i/O
3Ci
—*
9 r
_ ^s,i Ci
(6-51)
ip can be approximated from the known transverse boundary
conditions and the "Taylor" procedures [74]. The "Taylor"
procedures generate polynomials of (r, 0 ) that satisfy the
transverse boundary conditions. For semi-circular geometry,
the polynomial of the lowest order that satisfies the
transverse conditions is
ip (r, d )
a.r.2 l/3+3/20g
2 R; l + a/8
<4~) a(|) [l-3(-4^)2n
X (1 + 5 a/12)-1
(6-52)
In this expression a is an axial dispersion number defined as
^s,iR/Di,0 and represents the ratio of the surface reaction
velocity to the transverse diffusion velocity. 0 satisfies

183
the boundary conditions and the value of the transverse
average of \¡j is one.
With equations (6-47 and 6-52) , ip and $ are readily
obtained as
— _ 1 + 0.846 ct+ 0.181
(6-53)
i, 1 + 0.464 a + 0.0131a ^
V " 1 + 0.809 a + 0.164a2
(6-54)
It is noted that if the surface reaction rate is zero, a= 0,
then both and ^ are unity and the concentration field is
independent of the transverse directions. This situation
corresponds to homogeneous reaction only. The boundary
conditions in the axial direction are of Danckwerts' type
[75] and given by
(6-55)
at z = L
Di,0 Ci = 0.
dz
(6-56)
C-j^ is the concentration of component i in the inlet gas and
L is the length of the liquid metal boat.

184
Three additional dimensionless numbers appear in this
formulation: Peclet number (Pe), Damkoehler number (Da), and
a geometric aspect ratio ( 3),
defined by
Pe = Va L / Dif0
(6-57)
Da = k¿ L2 / Dif0
(6-58)
8 = S L / A R
(6-59)
An analytical solution of the unreacted HC1 as a function of
dimensionless length, £= z/L,
is given by
12 i Pe
q = exp ( (J4 2 & t dx exp (-
ci
-K0 O + d2 exp (K0 E.) ], (6-60)
where
di = Pe(Pe + K0)[[Pe(l- 4|)
+ K0](Pe + K0)
- [Pe(1- ^|) - K0](Pe -
- K0) exp(~2K0))-1 (6-61)
(6-61)

185
d2 = -Pe (Pe —jj- - Kq) exp (-2Kq) C [Pe (1- ^|) + Kq] (Pe ^ + Kq)
- [Pe (1- 4|) - K0] (Pe - K0) exp(-2K0)3-;L (6-62)
and
K0 = [Pe 2 + 3 a ip + Da]1/2 (6-63)
At the outlet of the liquid metal boat (z = L), the fraction
of unreacted HC1 (Cj_/Cj_®) is determined by the four
parameters, Pe, Da, a and g through the solved model equation
(equation (6-60)). The reactor performance equation provides
a direct relation between the experimentally measured
conversion (Ci/C^O) and the kinetic information (Da, a) for a
specific reactor design and operation (Pe, g).

CHAPTER 7
EXPERIMENTAL STUDY OF GALLIUM AND INDIUM SOURCE TRANSPORT
AT NORMAL PRESSURE
7.1 Literature Review
The performance of gallium and indium source reactors at
normal pressure (1 atm) has been experimentally studied by
several investigators. Ban [21, 76] and Ban and Ettenberg
[77] sampled the outlet vapor stream of Ga and In source
boats by means of a capillary coupled to a time-of-f1ight
mass spectrometer. Measurements of HC1 conversion in carrier
gas E-2 as a function of flowrate, HC1 partial pressure and
temperature were made. The effect of the replacement of H2
by He and of HC1 by CI2 on the transport of Ga were also
studied. The results indicated that GaCl and InCl are the
only chlorides formed. Furthermore, the conversion values
demonstrate that incomplete conversions of HC1 occurs in
their system. The Ga and In transport rates did not change
when different reactants (HC1 or CI2) or different carrier
gases (He or H2) were used. The indium transport rate is
almost always less than the gallium transport rate. The HC1
conversion for an In source reactor has also been studied by
Ban and Ettenberg [77] to show no dependence on HC1 inlet
partial pressure. Karlicek and Bloemeke [78] applied UV
186

187
absorption spectroscopy to measure gallium and indium source
boat effluent concentrations with results consistent with the
previous fluorescence studies [79]. The transport of InCl
from the indium source boat was found to continue for several
minutes after the input HC1 was turned off. The effect
indicates an appreciable amount of InCl dissolved in the melt
indium. The duration of continued InCl transport was said to
depend on the flowrate and the concentration of HC1 used
before HC1 was turned off. A similar effect for continued
GaCl transport from the gallium boat, though not as
pronounced as for InCl, was also observed. The results of
the previous investigations indicate that the mono-chloride
is the major reaction product and non-equilibrium conversion
are often encountered in the range of process conditions used
for hydride deposition of Ga or In containing films.
Furthermore, the strong dependence of conversion on
temperature and flowrate suggest that both mass transfer and
kinetic limitations are responsible for the non-equilibrium
rates.
7.2 Experimental Method
A schematic diagram of the normal pressure experimental
setup is shown in figure 7-1. The source boat was contained
in a 38 mm O.D. quartz tube approximately 130 cm in length
and heated by a three-zone resistance furnace. The furnace

o o
Resistance Heating
o o o o o]
v-
UZT
\j n /
/vr
o o
o o o o o I
= Ga or In
vs
r
V
y
V
mm
V
mm
V Exhaust
'A .
- Dl Water
HCI Collector
Ice/Water Cooling Bath
05
00
Figure 7-1. Schematic diagram of the normal pressure
experimental apparatus.

189
was equipped with external shunts so that a flat temperature
profile across the source boat could be maintained (+_ 2 K) .
The gas manifold system, constructed with stainless
steel tubing and VCR fittings, accepted pure HC1 and
palladium-alloy diffused H2. Gas flows were regulated with
Tylan-brand electronic mass flow controllers. A schematic
description of the gas manifold system is shown in figure 7-
2.
In order to eliminate hydrodynamic and thermal entrance
region effects in the reaction zone, the source boats were
constructed as shown in figure 7-3. The outside diameter of
the semi-cylindrical quartz boats coincided with the inside
diameter of the reactor of the reactor tube to isolate the
gas flow above the melt. The source boat was 10.5 cm in
length. Two similar boats (7.5 cm length), only covered by a
rectangular quartz flat, were placed adjacent to the front
and back of the metal source boat. These boats served as
hydrodynamic and thermal stabilizers which reduced the
effects of entrance region disturbances and provided axial
and laminar flow conditions. Because the thermodynamic and
thermal entry lengths increase primarily with increasing
flowrate, it has been calculated that the assumption of axial
laminar gas flow above the melt is appropriate when the
flowrate of carrier gas H2 is less than 5,000 seem.
The source boat was admitted into the reactor from the
front open end, which was fused with a female sleeved ground-

Figure 7 2. Gas manifold for the experimental system.
190

Figure 7-3. Enlargement of the source boat design.
191

192
joint and could be sealed by the matching male ground-joint
cap. Seal between the joints was achieved by placing rubber
bands around the sleeves; Trapezon-brand grease was used to
prevent gas leakage. Compression O-ring fitting was used to
connect the stainless steel gas tubing and the pyrex glass
tubing, fused onto the ground-joint cap.
Group III chlorides, generated as a result of the source
transport reactions, were collected from the exit end of the
quartz reactor by a series of three ice-bathed cold traps.
Both cold traps were 25 cm long, made of 25 mm diameter pyrex
glass tubing with sealed bottom. The connection tubing
between these traps was 15 mm in diameter. Size 40/50 ball-
socket joints with metal clamps were used exclusively between
the reactor exit end and the first cold trap and between the
rest of the cold traps. The second and third cold traps were
filled with glass rings, 1/4" in both diameter and length, to
improve cooling rate and condensation efficiency. It was
found that if the flowrate of H2 carrier gas was too low,
then the condensation would start in the reactor and
incomplete collection would result. But if the flowrate of
H2 carrier gas was too high, the condensation efficiency
would decrease appreciably and part of the condensable
chlorides could pass the cold traps uncollected. To allow
complete collection of group III chlorides by the described
collection setup, it was determined that the flowrate of H2
carrier gas had to be between 600 seem and 2000 seem. The

193
unreacted HCl in the exhaust was collected by bubbling the
exhaust gas stream out of the cold traps through distilled
water. The exhaust gas from the water bubbler was confirmed
by mass spectrometry to contain only carrier gas H2*
After each experiment the group III chloride condensate
in the cold traps was dissolved in aqua regia and diluted for
atomic absorption spectrometric measurement, from which the
total weight of group III metal in the condensate, or the
transport rate of Ga or In, was deduced. The amount of
gallium or indium in the water bubbler was also measured by
atomic absorption and used to verify the completeness of the
collection of III metal chlorides by the cold traps. The
amount of unreacted HCl was determined by precipitation
titration of chloride ions by the Mohr method [80].
7.3 Data Analysis
Because of the restriction imposed by the collection
technique, the flowrate of H2 carrier gas, chosen for
experimental studies, was 1,000 seem, 1,500 seem and 2,000
seem. The HCl flowrate was 10 seem, 15 seem and 20 seem.
And the studied temperature range was between 999 and 1131 K.
The flowrates were low enough, so that the hydrodynamic
and thermal entrance region effects could be eliminated by
the flat-quartz stabilizers, and ideal axial laminar flow was
established in the reaction zone. The Peclet number of these
flowrates was also high enough (larger than 10) for the axial

194
diffusion in the reactor to be neglected. The mass transport
in the reactor should be well described by the 2-D convective
diffusion model, discussed in section 6.3.1. Therefore,
equation (6-41) was used for data analysis of this
experimental study.
7.4 Results and Discussion
7.4.1 Gallium Source Transport
Transport Rate v.s. Total Flowrate The gallium
transport factor Ga/Cl, defined in equation (6-37) , was
studied at T = 1068 K for three different total flowrates
with identical input H2 to HC1 ratio. These flowrates were
1,000 seem H2 + 10 seem HC1, 1,500 seem H2 + 15 seem HC1 and
2 , 000 seem H2 + 20 seem HC1. The experimental result,
presented in figure 7-4, show a strong dependence on the
total flowrate. Equilibrium gallium transport is also
indicated in figure 7-4 by the broken line, and non¬
equilibrium conversion was clearly observed in these
experimental conditions.
Transport Rate v.s. Input HC1 Concentration By fixing
the H2 flowrate and varying the input HC1 flowrate, the
effect of input HC1 concentration on gallium transport factor
was determined. As shown in figure 7-5, the input HC1
concentration was varied in the range 0.5 < %HC1 < 1.0 for H2
flowrates of 1,500 seem and 2,000 seem. The transport factor

195
r otai
Howraíe
k i
V-ri < I
Figure 7-4. Gallium transport factor (Ga/Cl) versus total
flowrate at T = 1068 K and HC1 flowrate/H2
flowrate = 0.01. The broken line shows the
maximum gallium transport at equilibrium. The
solid curve is the result calculated from
transport model equation (6-41), with rate
constant ks deduced from figure 7-8. The dotted
curve is the result calculated from the diffusion-
limited case of transport model equation (6-41).

196
Ga
Cl
Figure 7-5.
#:1500sccm H2
2000sccm
Gallium transport factor (Ga/Cl) versus percent
HC1 in the input flow at T = 1068 K. The broken
line shows the maximum gallium transport at
equilibrium. The solid curves are the results
calculated from transport model equation (6-41),
with rate constant ks deduced from figure 7-8.

197
showed no dependence on the input HC1 concentration in both
cases, indicating a linear relationship between the input HC1
flowrate and the group III chloride transport rate. This
result validates the assumption of the first-order rate
expression, used in the development of model equation (6-41).
Transport Rate v.s. Temperature The temperature
dependence of the gallium transport rate was extensively
studied in the temperature range 999 < T < 1131 K, and the
gallium transport factor was calculated and shown in figure
7-6. Since the gallium transport factor was found to be
independent of the input HC1 concentration, the HC1 flowrate
for the temperature dependence study was fixed at 10 seem
while different H2 flowrates, 1,000 seem, 1,500 seem and
2,000 seem, were used. As was expected, the gallium
transport rate increases with increasing temperature and
decreasing H2 flowrate. However, equilibrium conversion (the
broken line in figure 7-6) was not achieved even at the
highest temperature and lowest flowrate used in this study.
Unreacted HC1 The unreacted HCl was collected in the
water bubbler and determined by precipitation titration of
chloride ions. The HCl conversion, as defined in equation
(6-36) , is plotted in figure 7-7. Similar dependencies of
HCl conversion on temperature, flowrate and input HCl
concentration were obtained. Theoretically, the HCl
conversion should be equal to the gallium transport factor
(equation (6-41)) if gallium monochloride is the only product

198
o : 1000 seem H2 + 10 seem HCI
o : 1500 seem H2 + 10 seem HCI
# : 2000 seem H2 + 10 seem HCI
Figure 7-6. Gallium transport factor (Ga/Cl) versus
temperature at various flowrates. The broken
line shows the maximum gallium transport at
equilibrium. The solid curves are the results
calculated from transport model equation (6-41),
with rate constant ks deduced from figure 7-8.

HCI Conversion
199
o : 1000 seem H2 + 10 seem HCI
• : 1500 seem H2 + 10 seem HCI
* : 2000 seem H2 + 10 seem HCI
T (K)
Figure 7-7. HCI conversion versus temperature of gallium
source reactor. The broken line shows the maximum
gallium transport at equilibrium.

200
of the source transport reaction. Results in figures 7-6 and
7-7 show that the gallium transport factor was closer to the
KC1 conversion at higher temperature and lower flowrate, or
when the reactor was operated closer to equilibrium
condition. It was realized that since product sampling was
done far from the reaction zone where the reaction products
had cooled down considerably from the reaction temperature,
the chemical composition of the product gas could have
changed appreciably as a result of the chemical reactions
during the course of transport. The experimentally observed
HC1 conversion, therefore, can be very different from that at
the immediate exit of the reaction zone. The gallium
transport factor was, however, preserved during the transport
process since no deposit was observed along the transport
path between the reaction zone and the sampling devices. The
exact chemical composition of the product gas was unknown,
but should be primarily gallium monochloride when both the
gallium transport factor and the HCl conversion was found
close to equilibrium prediction, i.e. at low flowrate(1000
seem H2), or at temperature higher than 1050K.
Determination of Rate Constant The experimental result
in figure 7-6 was reduced by equation (6-41) to determine the
first-order kinetic rate constant ks. The diffusion
coefficients of HCl and GaCl in H2 were taken [81] to be
D (cm2/sec)
HC1,H
5.32 x 10
-1
P(atm)
1.664
T (K)
(7-1)

201
and
Gael ,H.
(cm/sec) = 2.87 x 10
-5
P(atm)1
T (K)
1.736
(7-2)
The calculated values of the first order rate constant are
plotted in figure 7-8 as a function of reciprocal absolute
temperature. The results are too scattered to give a linear
relationship between the rate constant and reciprocal
absolute temperature. It was discovered later that the
gallium transport rate in this experimental study could be
explained by a diffusion-limited model and the calculation of
kinetic rate constant could be very sensitive to experimental
error. The calculated rate constant in figure 7-8 is,
therefore, accurate only within its order of magnitude. An
attempt was made to compare the results in figure 7-8 with
Ban's [76] experimental data. The dimension of the reactor
used in Ban's experiments was estimated first. The reported
HC1 conversion was assumed to be equal to the gallium
transport factor(equation (6-41)) and reduced by the 2-D
convective diffusion model to yield the rate constant. The
calculated rate constant from Ban's data, also shown in
figure 7-8, has the same order of magnitude as the ones from
this study. A least square fit of these calculated rate
constant was finally performed and the rate constant was
determined to be

202
T (K)
1150 1100 1050 1000 950
r\ _ <
Figure 7-8. First order rate constant of gallium source
reaction, ks (cm/sec), versus reciprocal absolute
temperature, deduced from experimental results in
figure 7-6 or Ban’s data [71] and equation (6-41).
The straight line approximates the temperature
dependence of the rate constant, and is given by
2.12 x 105 exp (-11,575/T (K)).

203
ks (cm/sec) = 2.12 x 10^ exp (-11,575/T (K)) (7-3)
Using model equation (6-41), the diffusion coefficients,
equations (7-1) and (7-2), and the rate constant, equation
(7-3), the reactor performance can be calculated for any
given condition. The result of this calculation is given in
figures 7-4, 7-5 and 7-6 by the solid curves. These solid
curves clearly demonstrate that the 2-D convective diffusion
model satisfactorily fits the experimental data. The dotted
curve, shown in figure 7-4, is the predicted reactor
performance from the diffusion-1 imited model, which
represents a special case of equation (6-41). The closeness
of the solid and the dotted curves indicates that the gallium
transport process in the studied conditions is almost
diffusion-limited and the reaction kinetics has only a slight
effect on the transport rate.
7.4.2 Indium Source Transport
Transport Rate v.s. Total Flowrate The indium transport
factor In/Cl, defined in equation (6-37), was studied at T =
1068 K for three different total flowrates with identical
input H2 to HC1 ratio. The flowrates were 1,000 seem H2 + 10
seem HC1, 1,500 seem H2 + 15 seem HC1 and 2,000 seem H2 + 20
seem HC1. The experimental result, presented in figure 7-9,
shows a strong dependence on the total flowrate. Equilibrium
indium transport is also indicated in figure 7-9 by the

204
T otai
Flowrate
Figure 7-9. Indium transport factor (In/Cl) versus total
flowrate at T = 1068 K and HCl flowrate/H2
flowrate = 0.01. The broken line shows the
maximum indium transport at equilibrium. The
solid curve is the result calculated from
transport model equation (6-41), with rate
constant ks deduced from figure 7-13.

205
broken line, and non-equilibrium conversion was clearly
observed in these experimental conditions.
Transport Rate v.s. Input HC1 Concentration By fixing
the H2 flowrate and varying the input HC1 flowrate, the
effect of input HC1 concentration on indium transport factor
was determined. As shown in figure 7-10, the input HC1
concentration was varied in the range 0.5 < %HC1 < 1.0 for H2
flowrates of 1,500 seem and 2,000 seem. The transport factor
showed no dependence on the input KC1 concentration in both
cases, indicating a linear relationship between the input HC1
flowrate and indium chloride transport rate. This result
validates the assumption of the first-order rate expression,
used in the development of model equation (6-41).
Transport Rate v.s. Temperature The temperature
dependence of the indium transport rate was extensively
studied in the temperature range 999-1131 K, and the indium
transport factor was calculated and shown in figure 7-11.
Since the indium transport factor was found to be independent
of the input HC1 concentration, the HC1 flowrate for the
temperature dependence study was fixed at 10 seem while
different H2 flowrates, 1,000 seem, 1,500 seem and 2,000
seem, were used. As expected, the indium transport rate
increases with increasing temperature and decreasing H2
flowrate. However, equilibrium conversion (the broken line
in figure 7-11) was not achieved even at the highest
temperature and lowest flowrate used in this study.

206
In
C¡
# : 1500 seem H2
^ : 2000 seem
% HCI input
Figure 7-10. Indium transport factor (In/Cl) versus percent
HCI in the input flow at T = 1068 K. The broken
line shows the maximum indium transport at
equilibrium. The solid curves are the results
calculated from transport model equation (6-41),
with rate constant ks deduced from figure 7-13.

207
o :1000sccm H2
® :1500sccm H2
# : 2000sccm
+ 10 sccm
+ 10 sccm
+ 10 sccm
HCI
HCI
HCI
Figure 7-11. Indium transport factor (In/Cl) versus
temperature at various flowrates. The broken
line shows the maximum indium transport at
equilibrium. The solid curves are the results
calculated from transport model equation (6-41),
vith rate constant ks deduced from figure 7-13.

208
Unreacted HC1 The unreacted HC1 was collected in the
water bubbler and determined by precipitation titration of
chloride ions. The HCl conversion, as defined in equation
(6-36), is plotted in figure 7-12. Similar dependence of HCl
conversion on temperature, flowrate and input HCl
concentration was obtained. Theoretically, the HCl
conversion should be equal to the indium transport factor
(equation (6-41)) if indium monochloride is the only product
of the source transport reaction, and could be less that the
indium transport factor if higher chlorides, other than
monochloride, appear as reaction products. Good agreement
between figures 7-11 and 7-12 indicates that indium
monochloride should be the dominant reaction product in the
studied conditions(also see discussion in section 7.4.1).
Determination of Rate Constant The experimental result
in figure 7-11 was reduced by equation (6-41) to determine
the first-order kinetic rate constant ks. Equation (7-1) was
used for the diffusion coefficient of HCl in H2* The
diffusion coefficient InCl in H2 was approximated to be
InCl ,H.
(cm/sec) = 2.73 x 10
-5
P (atm)-1
T (K)
1.7
(7-4)
The calculated values of the first order rate constant are
plotted in figure 7-13 as a function of reciprocal absolute
temperature.
The results show a linear relation with

HCI Conversion
209
o : 1000 seem H^ + 10 seem HCI
© : 1500 seem + 10 seem HCI
Figure 7-12. HCI conversion versus temperature of indium
source reactor.

210
T (K)
1150 1100 1050 1000 950
1/T X 103 (K~1)
Figure 7-13. First order rate constant of indium source
reaction, ks (cm/sec), versus reciprocal absolute
temperature, deduced from experimental results in
figure 7-11 and equation (6-41). The temperature
dependence of the rate constant is given by
4.13 x 106 exp (-12,851/T (K)).

211
reciprocal absolute temperature and the rate constant was
determined to be
ks (cm/sec) = 4.13 x 10^ exp (-12,851/T (K)) (7-5)
Using model equation (6-41), the diffusion coefficients,
equations (7-1) and (7-4), and the rate constant, equation
(7-5) , the reactor performance can be calculated for any
given condition. The result of this calculation is given in
figures 7-9, 7-10 and 7-11 by the solid curves. It is clear
that these solid curves match the experimental results
satisfactorily. In order to understand the importance of
both the diffusion and the kinetic mechanisms for the
determination of indium transport rate in the studied
conditions, the calculated results of the kinetically-
limited model and the diffusion-limited model are presented
in figure 7-14 by the dotted curves. The combined effect of
these nonequilibrium mechanisms is realized in model equation
(6-41) and described in figure 7-14 by the solid curve.
The results and analysis of the normal pressure
experiments shows that the 2-D convective diffusion model is
adequate in describing the reactor performance in a
flowthrough reactor at the studied operating conditions. The
group III transport factor showed a first-order dependence on
input HC1 concentration which indicated that the overall
reaction rate could be dominated by two possible processes;

212
Flowrates : lOOOsccm Hg + 10 seem HCI
T (K)
Figure 7-14. Experimental results, obtained at H2 flowrate
1,000 seem, HCI flowrate = 10 seem and
temperature range, 943 < T < 1131 K. The solid
curve shows the calculated result from equation
(6-41), considering both diffusion and kinetic
limitations. The dotted curves show the
calculated results from two special cases, the
diffusion-limited case and the kinetically-
limited case, of equation (6-41).

213
namely, molecular diffusion, and first order reaction
kinetics. Both processes exist in source reactors and one of
the two processes can be dominant depending upon reactor
design and operation. Flowthrough reactor design should be
carried out under two criteria, minimum material(group III
metal) requirement and maximum process reproducibility.
These two criteria, however, appear to be against each other
since maximum process reproducibility entails long boats to
ensure equilibrium conversion and incurs problems in trying
to minimize material requirement. The difficulty in source
reactor design is, therefore, to choose the appropriate
reactor geometry and reactor length to satisfy the above
criteria. With the determined rate constants for
gallium(equation (7-3)) and for indium(equation (7-5)) source
reactor performance can be easily simulated and reactor
design can be checked numerically for improvements. In
general, diffusion limitation should be eliminated or reduced
to achieve efficient reactor operation which implies a
kinetically controlled reactor. Since reaction kinetics only
controls the local reaction rate, therefore, when the reactor
residence time is long enough, equilibrium conversion is
obtained and the overall reaction rate(group III transport
rate) will follow the thermodynamic trend becoming
temperature insensitive.

CHAPTER 8
EXPERIMENTAL STUDY OF GALLIUM AND INDIUM SOURCE TRANSPORT
AT LOW PRESSURE
8.1 Equilibrium Calculations
No recorded study of gallium and indium source transport
at low pressure (about 10-3 atm) could be found in the
literature. In order to establish the maximum achievable HC1
conversion, to identify possible reactant and product species
at reduced pressure and to compare them with those at normal
pressure, complex chemical equilibria in the Ga/H/Cl and
In/H/Cl systems were computed. Three degrees of freedom
exist in this system and independent variables were chosen as
pressure, temperature and the gas phase Cl/H ratio since
these quantities are each constant during source operation.
Equilibrium compositions in the Ga/Cl/H and In/H/Cl systems
were computed at values of Cl/H = 2.5xl0-3 and pressure of 1
and 10-3 atm as a function of temperature in the range 950 <
T < 1250 K. A stoichiometric algorithm was used to compute
values of the equilibrium partial pressures. The chemical
species and their thermochemical data have been presented in
chapter 4. It is recognized that a small solubility of metal
chlorides in the melt exists, but the activity of the metal
214

215
should be close to unity and therefore the slight solubility
should not greatly influence the equilibrium composition.
The calculated equilibrium compositions as a function of
reciprocal absolute temperature for the Ga source boat at 1
atm pressure are shown in figure 8-1 and at 10-3 atm in
figure 8-2. At both pressures the HC1 conversion is high
(about 99.99%) and is higher at the lower pressure. For all
conditions investigated, the major gallium species is the
monochloride. Increasing the source temperature gave higher
HC1 conversions and decreased the partial pressures of other
gallium chlorides, primarily because of entropic effects.
Since the equilibrium conversion of HC1 was nearly complete
and GaCl was the dominant gallium vapor species, the
equilibrium transport rate of gallium is almost independent
of source temperature and directly proportional to the inlet
HCl molar flowrate. To produce controllable and reproducible
transport rates, it is therefore desirable to operate the
source boat at conditions which achieve equilibrium
conversions. Decreasing the pressure from 1 atm to 10-2 atm,
gave a decrease in the partial pressures of the minor gallium
chlorides. These results suggest that overall reaction
investigated in the low pressure experimental work should
involve only the production of gallium monochloride. As the
temperature increased the partial pressure of elemental
gallium increased, and since the vapor pressure of liquid Ga
is independent of system pressure, the relative amount of

Partial Pressure P¡ (10 Natm)
216
S
a
10
i
f~r
/ i
i
4
Figure 8-1. Calculated equilibrium partial pressures in the
Ga/H/Cl system as a function of temperature at
P = 1 atm and Cl/H =,0.025.

Partial Pressure P¡ (10 Natm)
217
950 850 750 T(C)
8 9 10
1/T (K"1)* 10 4
Figure 8-2. Calculated equilibrium partial pressures in the
Ga/H/Cl system as a function of temperature at
P = 10“3 atm an¿ cl/H = 0.025

218
elemental gallium in the vapor increased significantly with a
decrease in total pressure. The homogeneous reaction, which
was neglected in the normal pressure reactor modeling, could
play an important role in the low pressure source zone
transport.
Similar calculations were performed for an indium source
boat and the results are given in figure 8-3 (1 atm pressure)
and figure 8-4 (10“3 atm pressure) . The equilibrium HC1
conversion is shown to be nearly independent of temperature
(about 99.95%) but less than that calculated for gallium.
The values of the equilibrium partial pressures of the other
chlorides of indium were higher than those above the gallium
boat. By operating the experimental reactor at low pressure,
the other indium chlorides were still trace species. The
major difference between the gallium and indium systems was
the relative importance of the elemental vapor species. For
the indium system at 1250 K, the equilibrium indium partial
pressure was nearly equal to the partial pressure of indium
monochloride.
8.2 Experimental Method
A schematic diagram of the low pressure experimental
arrangement is shown in figure 8-5. The general aspect of
the reactor system is the same as those described in section
7.2. The gallium source boat was 11 cm in length and the
indium boat was 10.5 cm in length. A 12 1/s mechanical pump

Partial Pressure P¡ (10 Natm)
219
8 9 10
1 /T (K-1) * 10 4
Figure 8-3. Calculated equilibrium partial pressures in the
In/H/Cl system as a function of temperature at
P = 1 atm and Cl/H = 0.025

Partió! Pressure P¡ (10 Natm)
220
950 850 750 T(C)
8 9 10
1 /T ÍK"1') * 10 4
Figure 8-4. Calculated equilibrium partial pressures in the
In/H/Cl system as a function of temperature at
P = 1.0“3 atm and Cl/H = 0.025

Mass
Sampling Spectrometer
Three-Zone Furnace Tube Head
Exhaust
Figure 8-5
Schematic diagram of the low pressure experimental
apparatus.
221

222
was used to provide low pressure operation (about 10”3 atm).
After loading a source, the reactor was first vacuum baked
and then purged with nitrogen. Preliminary studies
established operating conditions that gave significant
reaction rate limitations in the temperature range of
interest. Flowrates were 200 seem H2 and 10 seem KC1 with
reactor pressure of 0.51 Torr (Ga) and 0.68 (In). Under
these conditions approximately 1 hour was required before a
steady-state conversion was measured.
Unreacted HCl was detected by sampling the gas just
beyond the third boat by a di f f er en t i a 11 y-pumped mass
spectrometer arrangement. Under the conditions of these
experiments the transverse variation in the concentration of
HCl was shown to be negligible. The sampling tube (9 mm O.D.
quartz) had a tapered nozzle (about 100 urn orifice) and was
pumped by a 120 1/s diffusion pump. At the low reactor
pressure used, molecular flow was established within a short
distance after the nozzle, thus minimizing parasitic
reactions in the sampling apparatus. The resulting molecular
beam was collimated and directed towards the ionization
chamber of the quadruple mass spectrometer (EAI Quad 250 mass
spectrometer head). The electron impact energy used was 69
eV. The vacuum chamber housing the mass spectrometer head
was maintained at a pressure of around 10-s Torr by a 250 1/s
ion pump.

223
Calibration of the mass spectrometer was performed by
measurement of the HC1+ ion intensity as a function of inlet
HC1 partial pressure and temperature at constant total
flowrate without the liquid metal placed in the middle boat.
The HC1+ ion intensity was found to vary linearly with the
HC1 partial pressure and to be nearly independent of the
sampling temperature.
8.3 Data Analysis
Laminar gas flow was achieved above the source boat at
the low flowrate used in these low pressure experiments.
Also because of this low flowrate, the Peclet number is small
(around 1) , therefore axial diffusion is important and the
mass transfer entrance region is short. Under this
circumstance, the axial dispersion model, discussed in
section 6.3.2, describe the reactor performance well.
Equation (6-60) was used for data analysis in these low
pressure experiments.
8.4 Results and Discussion
8.4.1 Gallium Source Reaction
For the source boat design and values of operating
parameters used in the experimental measurement of HC1
conversions, incomplete HC1 reaction was observed. The
percent HCl consumed at various reaction temperatures is

224
shown in figure 8-6 for a H2 flowrate of 200 seem at a
pressure of 0.51 Torr. As expected, the HC1 conversion
increased with increasing source temperature.
Reaction rate constants were determined from the
measured conversions by application of equation (6-60). The
major difficulty with interpreting the rate data derived
from this equation is that Da, which contains the homogeneous
rate constant, and a , which is proportional to the
heterogeneous rate constant, are present in a coefficient as
a linear combination. Thus, it is not possible to separately
determine values of both of these rate constants if they are
both important. Although both reaction paths can coexist, it
is highly unlikely that the rate constants have similar
values of activation energy and pre-exponential factor.
The measured HC1 consumption data was first reduced for
the case of Da = 0 (negligible homogeneous reaction rate).
Equation (7-1) was used for the interdiffusion coefficient of
HC1 in H2. The calculated values of the first order rate
constant are plotted in figure 8-7 as a function of
reciprocal absolute temperature. The results show a linear
relation with reciprocal temperature and the values of the
activation energy and pre-exponential factor, as determined
by linear regression, are 32.7 KJ/mol and 3.61 x 104 cm/sec,
respectively. An analogous treatment of the data with the
assumption of a= 0 (negligible heterogeneous reaction rate),
presented in figure 8-8, also showed linear behavior and the

MCI Consumption (%)
225
950
80
70 —
60
50 —
40
50
8
850
750
T(C)
s
10
1/7 (K~1)* 1C 4
Figure 8-6. Measured percent HC1 consumption versus reaction-
temperature in the Ga/HCl/H2 reaction system.
H2 flowrate = 200 seem, HC1 flowrate = 10 seem
and P = 0.51 Torr.

sec
226
950
850
750
E
a*
T(C)
O
1 /T CK-1) * i.O 4
Figure 8-7. First order rate constant ks (cm/sec), versus
reciprocal absolute temperature as determined
from reduction of data in figure 8-6 with equation
(6-60) and assuming Da = 0. The rate constant is
given by ks = 3.61 x 10^ exp (-3,930/T(K)).

sec
227
950 850 750 I (C)
£ 9 1C
1/7 (K"1) * iO 4
Figure 8-8. First order rate constant, k (sec-l), versus
reciprocal absolute temperature as determined
from reduction of data in figure 8-6 with
equation (6-60) and assuming oC = 0. The rate
constant is k = 6.23 x 10^ exp (-3,750/T(K)).

228
regression values of the activation energy and pre¬
exponential factor were determined to be 31.2 KJ/mol and 6.23
x 1C)3 sec“l, respectively.
The reaction rate expression determined above does not
identify a specific mechanisms, however, the low values of
the calculated pre-exponential factors suggest that rate
limiting reaction involves a heterogeneous reaction. A
possible homogeneous mechanism consists of vaporization of
gallium and reaction with HCl. The maximum rate of
evaporation of pure Ga is given by the Hertz-Langmuir [46]
expression. Combing this expression with the molar flux of
HCl used in this study, the measured HCl conversion , and the
vapor pressure of pure Ga [46] , a temperature 1323 K is
required to provide sufficient elemental gallium vapor to
react with the inlet HCl. This temperature is greater than
the experimental temperature range. Furthermore, the
calculated activation energy (31.2 KJ/mol) is considerably
different from the enthalpy of vaporization of gallium (272
KJ/mol).
8.4.2 Indium Source Reaction
Studies similar to those performed with gallium were
also made with liquid indium. The measured HCl consumption
is shown in figure 8-9 as a function of reciprocal absolute
temperature. The data was analyzed by application of
equation (6-60) . The results of the data reduction for the

ICI Consumption (%)
229
950 850 750 T(C)
2 10
1/T (K~1) * 10 4
Figure 8-9. Measured percent HCl consumption versus reaction
temperature in the In/HCl/H2 reaction system.
H2 flowrate = 200 seem, HCl flowrate = 10 seem
and P = 0.68 Torr.

230
case of a = 0 is given in figure 8-10 and for Da = 0 in
figure 8-11. The calculated rate constants shown in figures
8-10 and 8-11 clearly indicate two competing reaction
mechanisms exist with crossover at 1123K. With an assumption
of only homogeneous reaction (figure 8-10), the calculated
activation energy and pre-exponential factor are 57.7 KJ/mol
and 1.04 x 10® sec”l at low temperatures and 123.6 KJ/mol and
6.2 x 10® sec-1 at high temperatures. The values of the
activation energy and pre-exponential factor extracted from
figure 8-11 (heterogeneous reaction) are 62.2 KJ/mol and 1.8
x 10® cm/sec at low temperatures and 157.8 KJ/mol and 5.7 x
101® cm/sec at high temperatures.
It is believed that at low temperatures a heterogeneous
reaction limitation exists and at high temperature a
homogeneous one. The pre-exponential factor determined for
the high temperature homogeneous reaction case is appropriate
for a gas phase reaction. Furthermore, the temperature
calculated from the Hertz-Langmuir expression at which there
is a sufficient rate of indium vaporization to react with the
inlet molar flowrate of HC1 flow is 1119K [46] . Above this
temperature the maximum evaporation rate of indium is greater
than the HC1 transport rate and the reduced pressure should
give rapid gas phase mass transfer. This temperature value
nearly coincides with the measured crossover temperature.
The interpretation that reaction is limited by a homogeneous
reaction at high temperatures is consistent with the

231
950
850
750 T(C)
o
CD
V)
Figure 8-10. First order rate constant, k (sec~l), versus
reciprocal absolute temperature as determined
from reduction of data in figure 8-9 with
equation (6-60) and assuming <*- = 0. In the high
temperature range k = 6.2x10^ exp (-15,050/T(K))
and in the low temperature range k = 1.04 x 10-
exp (-7,020/T(K)).

sec
232
10,000
1,000
8
s
10
1/T (K"1) * 10 4
Figure 8-11. First order rate constant ks (cm/sec), versus
reciprocal absolute temperature as determined
from reduction of data in figure 8-9 with
equation (6-60) and assuming Da = 0. In the high
temperature range ks= 5.7x10^ exp (-19,210/T(K))
and in the low temperature range ks = 1.8 x 106
exp (-7,630/T(K)).

233
experimental observation of a metallic deposit (presumably
indium) on the cold reactor exit parts.
The reaction of molecular chlorine with liquid indium at
low temperature has been studied by Balooch et. al. [82] by
modulated beam mass spectrometric methods. A reaction
mechanism based on dissociative adsorption of chlorine was
proposed and gives significantly higher rates than determined
here. A nonlinear InCl transport rate as a function of input
HC1 was measured by Donnelly and Karlicek [79]. For the
experimental conditions used in our study, the gas phase
concentration of HC1 at the surface is nearly constant and
thus the dependence of reaction rate on HC1 concentration was
not determined. These results suggest a more complex
reaction mechanism exists for InCl production than for GaCl
production.

CHAPTER 9
CONCLUSIONS AND RECOMMENDED FUTURE WORK
9.1 Conclusions
The suitability of employing hydride vapor phase epitaxy
to prepare quaternary compound semiconductor In]__xGaxASyP;]__y
is judged by the material quality the process can deliver.
Composition and thickness of the epitaxial layer are the most
important material quality factors for InGaAsP devices. Two
layers of process design considerations decide the
controllability and reproducibility of these two material
factors. The first layer concerns how the material quality
is dictated by process thermodynamics and the nonequilibrium
mechanisms(mass transfer and reaction kinetics) and the
second layer concerns how to design process equipment and
process operation condition in order to achieve the desired
thermodynamic, mass transfer, and reaction kinetic
environment. Three process design issues that have been
identified are (1) the investigation of optimum process
operation range, (2) the investigation of source zone
reaction kinetics, and (3) the investigation of deposition
reaction kinetics. Resolution of these issues will complete
the required information for process design considerations.
234

235
Fourteen process parameters can influence the complex
chemical equilibrium in hydride vapor phase epitaxy; namely,
the input hydrogen flowrates in the gallium source zone, the
indium source zone, and the mixing zone, the input HCl
flowrates in the gallium source zone and the indium source
zone, the temperatures of the gallium source zone, the indium
source zone, the mixing zone, and the deposition zone, the
system pressure, and the transport factors of the gallium
source zone and the indium source zone. Except for the
source zone transport factors, which are determined by the
mass transfer and reaction kinetics, the rest of the process
parameters can be selected by process engineers before each
run. The fourteen process parameters collectively influence
the thermodynamics in the deposition zone through a smaller
set of "equilibrium parameters."
Thirty nine chemical species were considered in the
development of complex chemical equilibrium calculation for
the In/Ga/As/P/H/Cl system and their thermochemical data was
compiled. Four solid solutions models, the ideal solution
model, the strictly regular solution model, the delta lattice
parameter model and the quasi-chemical model, were reviewed
for Ini_xGaxAs^_yPy. The characteristic feature of this
solid solution is that the distribution of the nearest
neighbor pairs is not uniquely determined by the apparent
composition (x, y). Only the quasi-chemical model considers
this unique feature and the preferential occupation of

236
lattice sites by short range clustering of like-atoms and was
adopted in the subsequent calculations.
Complex chemical equilibrium calculation was used to
resolve the first process design issue. Two target
compositions of practical importance were studied. In the
preparation of composition In>53Ga>47As (lattice-matched to
InP) ternary compound, the deposition zone temperature,
system pressure, and the Ga/III molar ratio in the deposition
zone are apparently the critical control parameters. At T =
973K, Ptot = 1 atm, Cl/H = III/H = V/H = 0.001, and Ga/III =
0.605, the target solid solution composition, In#53Ga#47AS,
results at equilibrium. At this process condition,
composition control to within 2% of the target composition
could be achieved when the temperature control was within
0.5K, the pressure control was within 10% of the preset
value, and the Ga/III ratio could be controlled to within
0.1% of the specified value. Different process conditions
give different degrees of process controllability and can be
objectively compared by relative sensitivities. For the
calculated condition for InGaAs (lattice-matched to InP)
growth, the process controllability can be improved by
lowering Cl/H ratio, increasing V/H ratio and lowering the
deposition zone temperature. In another case of preparation
of In # 74Ga # 2 6 As . 5 6P . 4 4 ' lattice-matched to InP, quaternary
compound, the critical control parameters are the deposition
zone temperature T, the system pressure, Ga/III ratio and

237
As/V ratio in the deposition zone. Equilibrium at T = 973K,
ptot = 1 atm, Cl/H = III/H = V/H = 0.001, Ga/III = 0.388, and
As/V = 0.0039 results in the target composition of the solid
solution, In^74Ga#26As.56p.44 • Control to within 2% of the
target composition, at the calculated condition, could be
achieved if the temperature control was within 0.5K, the
pressure control was within 5% of the preset value, the
Ga/III ratio was within 0.1% of the specified value and the
As/V ratio could be controlled to within 0.01%. Relative
sensitivities were calculated for different process
conditions and the compositional controllability of these
process conditions was compared. T, Cl/H, and V/H can be
varied to achieve better control of In%74Ga#26^s.56p . 44
composition. V/H value should be increased from 0.001. Cl/H
ratio should be increased for effective reduction of
compositional sensitivity to Ga/III and As/V, and the
deposition temperature should be increased, at the same time,
to offset the increase of sensitivity to T and Ptot' as a
result of the increased Cl/H value.
Characterization and modeling of gallium and indium
source reactors in hydride VPE was attempted to resolve the
second issue. Two transport models were developed
considering the nonequilibrium mechanisms of convective
diffusion and reaction kinetics in the source reactor. These
models were used to reduce the experimental data and to
establish the reaction rate expressions. When the input

238
flowrates are high, the diffusion coefficients are small, a
two-dimensional convective diffusion model with the
consideration of only surface reactions satisfactorily
describe the reactor performance. The 2-D convective
diffusion model met the operating condition in the study of
normal pressure experimental reactor and was subsequently
used to reduce the normal pressure experimental data. When
the input mass flowrates are low and the diffusion
coefficients are high, axial diffusion is important, the mass
transfer entrance region is short, and the transverse
dependence of the concentration field does not vary much in
the axial direction. With these assumptions, which are
appropriate for the low pressure experimental conditions, the
axial dispersion model was developed with the considerations
of both heterogeneous surface reaction and possible
homogeneous reaction.
The reaction rate of HC1 with liquid gallium and indium
at normal pressure was studied in a flowthrough reactor. The
source boat was specially designed to avoid hydrodynamic and
thermal entrance region effects above the source boat. The
reactor effluent exhausted into a series of three ice-bathed
cold traps where gallium or indium chlorides was collected
for measurement. Unreacted HCl in the exhaust was collected
by bubbling the exhaust gas stream out of the cold traps
through distilled water. After each experiment, the III
metal chloride condensate was dissolved in aqua regia and

239
diluted for atomic absorption spectrometric measurement, from
which the total weight of group III metal in the condensate,
or the transport rate of Ga or In, was deduced. The amount
of Ga or In in the water bubbler was also measured by atomic
absorption and used to verify the completeness of the
collection of III metal chlorides by the cold traps. The
amount of unreacted HC1 was determined by precipitation
titration of chloride ions. The transport rates were found
to vary linearly with the input KCl concentration, indicating
diffusion and/or first-order kinetic limitations. The group
III transport factor was found closer to the HC1 conversion
at low hydrogen flowrate, 1000 seem, or high temperature,
>1050K. Because of the possible chemical reactions during
the course of transport and cooling of the product gas flow
from the reaction zone to the sampling devices, the exact
chemical composition in the reaction zone could not be easily
traced. When the group III transport factor approaches
equilibrium value, however, the dominant chemical species
should be group III monochlorides. The transport rate of
gallium was found to be most strongly dependent on the
carrier gas flowrate, less on the reactor temperature, and
proportional to the input HC1 partial pressure. All of the
above suggests a possible diffusion-limited process. With
the assumption of a first-order surface rate expression, the
experimental data was reduced by the two-dimensional
convective diffusion model to give rate constant at the

240
temperature range 943-1131K. The determined rate constant
was close to those deduced from the data reported by Ban [76]
in an independent study. The rate expression is given by,
ks (cm/sec) = 2.12 x 10^ exp (-11,5 7 5/T (K) ) . The indium
transport rate was found to be strongly dependent upon both
the carrier flowrate and the reaction temperature. Similar
to gallium transport, the indium transport rate is also
linearly proportional to the input HC1 flowrate, which
validates the assumption of a first-order rate expression.
From the reduction of the indium transport rate data, the
surface reaction rate constant was obtained, ks (cm/sec) =
4.13 x 106 exp (-12,851/T (K) ) . With the rate constant, the
model equation could be used to predict the source reactor
performance at other process conditions.
Mass transfer limitation was eliminated significantly by
operating at reduced pressure. The reaction rate of HC1 with
liquid Ga and In, the HC1 consumption, at reduced pressure
was measured by mass spectrometry. A single reaction rate
expression can describe the reaction of HCl with gallium and
it is believed to be a heterogeneous reaction. A first-order
surface reaction rate constant, ks (cm/sec) = 3.61 x 104
exp(-3,930/T(K)), was determined as a function of temperature
for the reaction of HCl with Ga. The results of measurements
with the indium source boat were somewhat different with two
mechanisms apparently competing. At temperatures above 1120
K, homogeneous reaction of HCl with In vapor is proposed as

241
the limiting reaction; the rate constant is determined to be
k (sec-1) = 6.2 x 108 exp (15,0 5 0 / T ( K) ) . At temperatures
below 1120 K, a heterogeneous reaction is suggested as the
dominating reaction route, with the rate expression ks
(cm/sec) = 1.8 x 108 exp(-7,630/T(K)).
6.2 Discussions and Suggested Future Work
In resolving the source reaction kinetics, experiments
were conducted in both normal pressure and low pressure
conditions. The deduced rate expressions from these two sets
of experiments were apparently different. The normal
pressure experimental results agreed with the previous
findings that have been reported in the literature. Also
consistent with common belief in hydride process practice,
the gallium reaction rate at normal pressure was found to be
more efficient than the indium reaction rate. The reaction
of HC1 with Ga and In at reduced pressure has never been
investigated before this study. The rate constants
determined from this low pressure experiments were
consistently higher than those found from the normal pressure
experiments. Moreover, the production of InCl seems to be be
more efficient than that of GaCl at low pressure conditions.
Two possible explanations are speculated for this observed
discrepancy. The group III transport reaction through the
surface reaction route is considered to be very sensitive to
the surface condition of the group III melt.
If sufficient

242
oxygen or water existed in the reactor, the liquid group III
surface could be appreciably oxidized causing a decrease of
the effective reaction surface area or completely changing
the dominating reaction mechanisms. Low pressure reactor is
less susceptible to the oxidation problem because the reactor
is usually vacuumed at room temperature and much lower oxygen
or water content could exist in the reactor. The other
possible reason is that fundamentally different reaction
mechanisms exist for normal pressure and low pressure
reactions. For example, the role of hydrogen may be to
compete with HC1 for surface adsorption or to boost the
reverse reaction rate. In both cases, lower reactor pressure
reduces hydrogen partial pressure in the reactor and could
lead to the reaction rate enhancement as observed in this
study.
Detailed experimental studies of the effects of oxygen,
water and carrier gas on the reaction between HC1 and Ga and
In at both low pressure and normal pressure conditions are
essential to resolve this discrepancy. However, from the
standpoint of process design of source reactors for hydride
process, it should be expected that the operation of an In
source boat at elevated temperature and low pressure will
present difficulties with In metal deposition in the
deposition zone which is at a lower temperature.
What will be interesting and technologically important
is to study indium and gallium transport at normal pressure

243
from an In/Ga alloy source boat. As was pointed out in the
process controllability studies, one of the most stringent
parameters in compositional control is the Ga/III ratio in
the deposition zone. An alloy source presents the
possibility of achieving the required gas phase makeup for a
specified composition growth.
Transient behavior of source reactors during HCl turn¬
on /turn-off period and setpoint changes is also of great
interest to hydride process designers for achieving sharp
junction at heterostructure interphase in a "single-barrel"
reactor.
It will be of strategic value to equip the process
development and operation of every hydride vapor phase
epitaxial reactor with an expert-system computer simulation
program. Complex chemical equilibrium analysis, process
controllability analysis, simulation of reactor transport
phenomena and chemical reaction kinetics, which are relevant
to the process performance, should be implemented in this
expert-system simulation package. By itself, this program
can be used to evaluate different process design and
operation options that concern process designers. The
expert-system can be even more powerful in a process/product
development environment, where a large database of process
response and product quality can be established. The program
can serve process engineers as an expert in selecting the
optimum operation condition for a certain product

244
specifications or suggest the area of problems that more
research should be carried out. A constantly updated expert-
system process simulation program will indeed be the best
solution for process design in hydride vapor phase epitaxy.

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BIOGRAPHICAL SKETCH
Julian J. Hsieh was born January 24, 1959, in Kaoshiung,
Taiwan. His family later moved to Taipei, Taiwan, where he
received his primary and high school education. He graduated
from National Taiwan University with a bachelor of science
degree in chemical engineering in 1980. After serving in the
Republic of China Marines Corps for two years, he was
admitted to the University of Florida to pursue graduate
degrees in chemical engineering. His graduate research has
been focused on reactor modeling, reaction thermodynamics,
process design and hydride vapor phase epitaxy of III-V
compound semiconductor. After receiving his Doctor of
Philosophy degree, Julian will be working at AT&T Bell
Laboratories in Murray Hill, New Jersey.
250

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is in fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Timothy
Associat
Chemical
ndérson, Chairman
Pirofessor of
Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is in fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
£
Lewis E. Johns
Professor of
Chemical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is in fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
HongZPTQliit
Professor oí
Chemical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is in fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
féng S./Li
Professor of
Electrical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is in fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Ranganathan Narayanan
Associate Professor of
Chemical Engineering

This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
lUStjjJ- 0-'
April 1988 Dean, College of Engineering
Dean, Graduate School



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