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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Indium gallium arsenide phosphide   ( lcsh )
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Thesis (Ph. D.)--University of Florida, 1988.
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Includes bibliographical references.
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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 LSIEH


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 Hsieh















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
















TABLE 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......... 36
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
4.2.1 Solution Thermodynamics............ 86









4.2.2 Solid Solution Models............. 89
4.2.2.1 Ideal Solution Model...... 94
4.2.2.2 Strictly Regular Solution
Model ..................... 96
4.2.2.3 Delta Lattice Parameter
Model...................... 100
4.2.2.4 First Order Quasi-Chemical
Model..................... 104

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....... ............................. 155
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.......... 186
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









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















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 Inl-xGaxAsyPl-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 diffusionless

conditions, low pressure (< 1 Torr) experiments were carried

out in the temperature range 973-1223 K. The HC1 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 Inl-xGaxAsyP1-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 Inl-xGaxAsyPl-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











zone reaction kinetics were two areas of particular interest

in the process design of hydride VPE of InlxGaxAsyP1-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 Inl-xGaxAsyPly. 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

Inl-xGaxAsyP1-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-ically the solid solution composition

controllability, can also be evaluated through the aid of

complex chemical equilibrium analysis. Controllability

studies for two technologically important Inl-xGaxAsyP-_y

compound compositions are reported in chapter 5.












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 Inl-xGaxAsyPi-y are

suggested.















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.

















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
effective
mass


0.15 m0

0.12 m0

0.082m0

0.067m0

0.042m0

0.077m0

0.023m0

0.0145m0


0.70m0

0.79m0

0.98m0

0.60m0

0.48m0

0.44m0

0.64m0

0.40m0

0.40m0


indirect band gap

direct band gap


.54625

.56611

.61355

.54495

.56419

.60940

.58687

.60584

.64788


2.45(I)

2.16(I)

1.58(I)

2.261(I)

1.42(D)

0.81(D)

1.35(D)

0.36(D)

0.236(D)


AlP

AlAs

AlSb

GaP

GaAs

GaSb

InP

InAs

InSb


(I):

(D) :


3.027

3.178

3.400

3.452

3.655

3.820

3.450

3.520

4.000











When more than one element from group III or group V is

distributed on group III or group V lattice sites,

IIIxIIIl-xv or IIIVyV1-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 + al x + a2 x2 (2-1)



where Eg,0 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 AyBzCl-y-zD, where A, B and C are group III

elements, or the type AByCzD1-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











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 ACyD1-y and x mole fraction of BCyD1-y, or 1-y

mole fraction of Al-xBxC and y mole fraction of Al-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-xBxCl-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 a0 of the alloy Al-xBxC1-yDy is given by



a0 = (l-x)y aAD + xy aBD + x(l-y) aBC
+ (l-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











Eg = (l-x)y EgAD + xy EgBD + x(l-y) Eg,BC
+ (1-x)(1-y) Eg,AC. (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, AlGaInAs and AlGaInP.

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
















AL As




Alz Ga In-,x-z As

Ga As GaIn As I/ n As
(1.2ev / ean s V)

S0.9

Ga In As o', 05
0.8
5.6 0.7
N V' '\ '0.6

5Y 5.5 0.5 Y


0.3
S.5 0.2

0.1
5,. 0















Figure 2-1. The compositional plane for Inl-xGaAsyP1-y at
300K [61. The boldface solid line represents the
GaAs-lattice matching composition The boldface 0. 0.2
broken line represents the InP-lattice matching
2.25eV0)\ (1.35eV)


Aix Ga. InI _X-Y P




At P





Figure 2-1. The compositional plane for Inl-xGaxASyPly 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.











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 Inl-xGaxAsyPl-y/InP heterojunction 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










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 cm2/V-sec have been recorded [8-101 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 heterojunction 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























p InP
p-InP p-InP
P InGaAs

n InGaAs n InP



n- InP
n InP
In Substrate
Substrate


i



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., GaC1 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

trichloridee" 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(l) + HC1 <---> GaCl + 1/2 H2.


(3-1)









Source
Zone
1050-1150K


Mixing
Zone
1100-1200K


Deposition
Zone
950-1050K


HCI + H -

AsH 3+ H
3 2 --


Substrate


HCI+ H2


HCI + H2


AsH 3+ PH3 + H 2--
3 3 2


Figure 3-1. Schematic diagrams of hydride VPE processes.
a. growth of GaAs. b. growth of Inl-xGaxAsyPl-y.


I Ga


I Ga
~J~


F 77 I









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 950-

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)


GaC1 + AsH3 <---> GaAs(s) + HC1 + H2


(3-6)










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 general

chemical formula Inl-xGaxAsyP1-y can also be grown by this

technique. Figure 3-1b shows the schematic diagram of a

reactor used for growing Inl-xGaxAsyPliy 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 gasoline, 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



rl: 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, rt, is equal to rl+r2+r3+r4. 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 = X1 + X2 (3-13)



1-x = (r3+r4)/rt = X3 + X4 (3-14)


1-y = (r2+r3)/rt = X2 + X3


(3-16)











y = (rl+r4)/rt = X1+ X4 (3-17)



where



Xi = ri/rt, i=1,2,3 & 4 (3-18)



(Xl, 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 Inl-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











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, GaAsyP1_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,










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

GaAsyP1-y alloys for a wide range of doping concentrations

and its versatility to grow multi-layer structure, hydride

VPE was adopted industrially in the mass production of

GaAsyP1-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

In-lxGaxAsyP1-y is exemplified as in figure 3-1b. 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











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











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 AsCl3 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 HCI + 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 AsCl3. 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










increasing electron mobility were obtained. This result

seemed to agree with Dilorenzo's explanation of silicon

incorporation in chloride VPE. When additional HCl 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 AsC13 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 As4. 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,











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 HCI flowrate over gallium was

increased a higher purity in the epitaxial film was achieved.

When a secondary HC1 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 HC1 probably does

react with SiO2 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 HC1

flow, thus reducing acceptor incorporation and compensation.

An aging effect of the HC1 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 HC1 tank, the studies on the influence of HC1

concentration on silicon donor level by a secondary HC1 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).











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 GaC1 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 Inl-xGaxAsyPly

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











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 Inl.xGaxAsyPl-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











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

Inl-xGaxAsyPl-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 As4 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 GaC1 have

the relationship,











PGaCl = K1 PHC1 (3-21)


in which K1 is the equilibrium constant for reaction equation

(3-1). The chlorine balance equation is



POHC1 = PHCl + PGaCl, (3-22)


where POHC1 is the HC1 partial pressure in the input flow.

From equations (3-21) and (3-22), PGaC1 and PHC1 can be

solved.



PHC1 = 1/(1+K1) POHCl (3-23)



PGaCl = K1/(1+K1) POHCl (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 Td. Clearly, if equilibrium is reached in the

deposition zone, then











P (P + ss)
Kd(Td) H 0.25 =C 0.25 (3-26)
pe e (P Ga- ss)P 1/4 ss)
GaCl As4 4



where Kd is the equilibrium constant for equation (3-5), Pei

is the partial pressure of gas species i at equilibrium, and

ss is defined as the amount of supersaturation 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.



ss Vf V
Rg RTd A (3-27)
9 R Td As



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).

Besides, the actual deposition rate is influenced by mass

transfer, chemical kinetics and residence time in the











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











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 kinetically-limited. 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











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, ro 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

diffusion-limited 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. Kinetically-limited processes are also

affected by the surface properties of the condensed phase











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 Inl-xGaxAsyPl-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















































Deposition Zone
Reaction Kinetics


Deposition Zone
Mass Trans.er


Composition
Controllability


Growth Rate
Reproducibility


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











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










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 Inl-xGaxAsyP1-y. 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/Cl are

involved. Specifically for hydride VPE of Inl-xGaxAsyP1-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









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 III-

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 10-10, 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











Table 4-1. Possible chemical species in In/Ga/As/P/H/Cl
system*.


Name


Symbol


Gallium

Indium

Gallium Chlorides



Indium Chlorides



Arsenic

Phosphorous

Arsenic Hydrides

Phosphorous
Hydrides

Hydrogen/Chlorine

Gallium Arsenide

Indium Arsenide

Gallium Phosphide

Indium Phosphide


Ga, Ga(l)

In, In(1)

GaC1, GaCl2, GaC13,

Ga2Cl2, Ga2Cl4, Ga2C16

InCl, InCl2, InCl3,

In2Cl2, In2Cl4, In2C16

As, As2, As3, As4

P, P2, P3, P4

AsH, AsH2, AsH3


PH, PH2, PH3

H2, H, HC1, Cl, C12

GaAs(s)

InAs(s)

GaP(s)

InP(s)


* Unless indicated
phase.

(1): liquid phase

(s): solid phase


otherwise all species are in the gas











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




























CN
-4


,0


El

CN




u
+


1 (N
SI















4 'J
C-.4
-r( U
O









U E-4





m
! rU


a) +E




> +
o u




E

c +
(U







C +
4
.i 0


4-1 II
0



I I
(U
- a

> 0
E



(U


a)




-4

a
r-4


4 -
a)














I




cn






-4
0


it










r4
u
N









U
0
O





-4

-4
U


0




rU





0
CM


0 0





o o
I-4

- 1 -


I I


* *0
0 0 0 0 0


a 0



o0 0


I I







C *
* m m


N

c
'0









CDM
0 0 0







'.0









o












O 4
'0






0 0 *





CM m


0c 00 0 C








00 0 0


r-
Itr


v o


I I


0 o 0 0


r- CN
Ln .0
r-l4
CN CM
N (N

0 0N





v~o r-
110 I-

Ln LA

o oV



c 00


cr LA
8,i i-
rI -


-4 -4 CM -4

SU UC) U CN
(U '9 C (0 (0 (0 (0
C D '-4 -4 D CD CD


-4000
ON 0C 0 0
UN >0 k.0 (N
( -'. -4
0


00 *
*
; r-4


, P OD
r- -4


mo o


00


r-4
0










co

* *
o o





- 4
CO



CM

0
o
0.0









o -
(N U
(


%o r- 40 r- co OD co o
IV qr qw "W qw qw IMP






















o aL

















0 0 C
0 0 0 0 0 0


I I


LA

+






N
E-4












+
-I










+
U









E-4






E-I

.-1


0
0
U





II




r+
c-



-l

U


Ln

O-





o N N





-1 1-4 N







4N r-4

U U NM
C-
, i i -i >-


n Ln m
LO Ln LA

"W (M *q? Ul V 'L** Ln Lr
*'a LA LA LA LA LA LA LA


S*0
0 0


0 0 0 0 0


O co 0
0 a% 0 0 0
W CMN -4 C(N -4
S0 0 0 O 0

0 I 0 0 0 0
I I


0 0 0 0 0 0 0 0


C(
Ln
C(
-4
*
0 0
I


.-I











co rC
0 *
.~* ~ i


* *
O o o o o o


-4


*
0 0


qqT










(N

0 0
-4 kO


4 D





-1


i-4
U m
N N m af 3 B E 4
S U 1 (2 ( (Nf < (12 (1


0 0 0 0 0 0




-I
(N
r-

















r- r- 0o
Ln Li in

q^r C14 c( tn
Ln n LAn Ln LO

















o o 0 0 0


E-4




+

NE-
I






cr)
r-4
Ln














+


U











0
U





















r-4
o








41
a












r(





0
U
0
IIr

sJ

0)
O-


0
(U





































u
U
o

















.0





0
r-


U






.-1

U







o
U


00
O CO

N 00






O
'0 ,-
o- .-g


Ln Ln








o o


o0

















o o





0 o




O 'o


In Ln LO %o D





'0

S0 0 0 0





o 0 0>
n m u>

o0 0 0 0
I I I


o O 0 0 0





D c
N T. 0
rCO
(N CN







CN 0 (N r-
* : (M r- 0

i T ^o m


0 U). I G 0

C 3 Cwc a C Q -
r. (a r cN cn a% r-I N U -
- C.5t-4Y j 2U U


Oo
0
Ln




00
00
Cn

*








N *





















N m
2 A


o o 0






* o 0
0 0 0









51

Table 4-3. Selected values of standard state enthalpy of
formation and absolute entropy at 298 K,
o o
AHf(298K) (kcal/mole) S(298K) (cal/mole- K)

o o
Hf(298K) ref S(298K) ref


Ga 65.0 46 40.375 46

Ga(1) 1.3 47 14.2 47

In 57.3 46 41.507 46

In(1) 0.8 47 15.53 47

GaCI 17.1 48 57.236 48

GaC12 39.0 48 71.668 48

GaC13 -102.4 48 77.515 48

Ga2C12 56.1 48 83.681 48

Ga2C14 -148.5 48 103.031 48

Ga2C16 -228.9 48 116.9 48

InCl 16.7 49 59.3 49

InCl2 58.4 45 73.4 45

InC13 90.0 56 82.3 56

In2C14 -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












(continued)


AH ref ref
Hf(298K) ref S(298K) ref


P

P2

P4

AsH

ASH3

PH

PH2

PH3

GaAs(s)

InAs (s)

GaP(s)

InP(s)

H2

H

HC1

Cl

C12


75.62

34.34

12.58

58.

16.

56.2

25.9

1.3

-19.54

-14.29

-23.93

-14.73

0.

52.103

-22.063

28.992

0.


38.98

52.11

66.89

51.

53.22

46.9

50.8

50.24

16.05

17.84

10.96

14.18

31.207

27.391

44.643

39.454

53.29









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


P P
GaC1 H
K9 (T) = 2 (4-1)
PGaC P


PGa C14
K1O(T) = P (4-2)
GaC1 GaC1


0.5
P P
GaC1 H
K (T) = (4-3)
GaCl PHC


PGa C16
K16(T) = 2 (4-4)
GaC13











Table 4-4. Chemical reactions in hydride VPE of InGaAsP


applicable*
number reaction temperature
zone


1 GaCI + 1/4 As4 + 1/2 H2 <---> GaAs(s.s.)# + HC1

2 InCl + 1/4 As4 + 1/2 H2 <---> InAs(s.s.)# + HC1

3 GaCI + 1/4 P4 + 1/2 H2 <---> GaP(s.s.)# + HCl

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 GaCI + 2 HC1 <---> GaC13 + H2


10 GaCI + GaC13 <---> Ga2C14


11 InCl + 2 HCI <---> InC13 + H2


12 InCl + InC13 <---> In2C14


13 InCl + HC1 <---> InCl2 + 1/2 H2


14 GaCI + HC1 <---> GaC12 + 1/2 H2


15 2 InC13 <---> In2Cl6


16 2 GaC13 <---> Ga2Cl6


17 2 InCl <---> In2C12


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


(Cont'd)












applicable*
number reaction temperature
zone


18 2 GaCI <---> Ga2C12 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 <---> C12 s(Ga),
s(In),
m, d

30 GaCI <---> Ga + Cl s(Ga),
m, d

31 InCl <---> In + Cl s(In),
m, d

32 Ga(l) + HC1 <---> GaCl + 1/2 H2 s(Ga)

33 In(l) + HC1 <---> InCl + 1/2 H2 s(In)


s(Ga): Ga source zone
s(In): In source zone
m: mixing zone
d: deposition zone

# (s.s.): InGaAsP solid solution











PGa2Cl2
K18(T) = 2 (4-5)
GaC1



K27(T) = -P-H (4-6)
2
PH


K (T) = (4-6)


SHC
P P




K29(T) = -Cl2 (4-8)
PC1



K30(T) = (4-9)



P PP
GaC1 H
K32(T) = p (4-10)
HC1




In the equations above, Ki(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.











P + 2(P + P + P ) + 3P
GaC1 + GaCl Ga Cl C GaC1l
2 a2Cl2 2 3
+ 4P + 6P + P + PC
Ga2C14 Ga2C16 HC1 Cl
As(Ga) = (Cl/H) = 2PH22Cl
H HC1 H (4-11)




The summation of the vapor pressure of the twelve vapor

species is equal to the total pressure, Ptot, i.e.



tot G aCl GaC12 GaCl + Ga2C1 + Ga2C4 + Ga2Cl6
+ PGa + P + P + PH + PCI + P
Ga H HCl H Cl Cl2 (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.













K11(T)










K13(T)




K15(T) =





K17(T) =





K27 (T) =




K28 (T) =


K29 (T) =


K31(T) =


K33(T) =


InCl3 H2
2
P P
InCl HC1


PIn2C14

PInCl3 InCl
3

p0.5
P P
2 2
InCI2 H2
P P
InCI HC1


pInC1
L 6
2
InCl


pIn I

22
2
InC1


2
H



P PC
H Cl
SHC1


C12
2
C1


p p
PIn PCl
InCI


pp 0.5
InC1 H,

PHC


(4-13)




(4-14)





(4-15)




(4-16)





(4-17)





(4-18)




(4-19)


(4-20)


(4-21)


(4-22)















As(In) = (Cl/H) =


P + 2(P~ncI + + PCl2
InCl + 2(PfnCl2 InCl 2 + 3PInC13
+ 4P In + 6PIn + P + PC1
In 2Cl4 In2 C1 + PH (4-23)C
2P +P +P
H HC1 H (4-23)
2


Ptot = PInCl + InCl2 + InCl3 In2C12 +In2C14 In2Cl6
+ Pn + PH + HC + P + P + P (4-24)
In H HCl H Cl C12 (4-24)
22


Mixing zone There are 33 chemical species in the vapor

phase of the mixing zone; GaCI, GaC12, GaC13, Ga2C12, Ga2C14,

Ga2C16, Ga, C, InC3, In2CC, In2CC, InCl I2C4 2C16, In,

AsH3, AsH2, AsH, As, As2, As3, As4, PH3, PH2, PH, P, P2, P3,

P4, H2, HC1, H, C1 and C12. 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.


PAs4
K5(T) P 2
As2



0.5 1.5
P P
As2 H
K6 (T)
AsH3


(4-25)






(4-26)













K7 (T) =


K8 (T) =





K19(T) =




K20(T) =





K21(T) =




K22(T) =




K23(T) =





K24(T) =




K25 (T) =


0.5 1.5
P2 H2
2 2
PH3


0.5
P P
AsH H
2 2
AsH3


P P
AsH H2

AsH3


P 0.5
PH2 H2
P P


PH H2







PAs2


p 2
As3

As2 PAs4
P P
















p
2P 2
2
P


PP
p
2
P2


(4-27)


(4-28)





(4-29)




(4-30)





(4-31)




(4-32)




(4-33)





(4-34)




(4-35)











2


4 2



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, Bl,, B2m,

C1m, and C2m can be written as follows.



A = (Cl/H) =
PH c+P c+P +P +2(P +P +P +
PHC1Cl GaCl InCl GaC1 InC1 Ga Cl
2 2 2 2
P +P ) +3(P +P ) +
In2Cl Cl GaC1 InCl +
2 2 3 3
4(P Cl +PInCl) +6(P Cl +P Cl
Ga2C14 InC1 Ga2C16 In2C16
(4-37)
2P H+PH+P+HCI3PAsH3 +3P PH+2(PPH +2P AsH+P PH+PAsH)
H ~HHC1 AsH PH PH AsH PH AsH
2 3 3 2 2



Bl = (Ga/H) =
P +P +P +P +2P +2P +2P
PGaPGaCl GaC1 +GaC3 2PGa2C1 2PGaC1 +2PGa2C16
2 3 2 2 2 4 2 6 (4-38)
(4-38)
P +P +P +3P +3P +2P +2P +P +P
H H HC1 AsH PH AsH PH AsH PH
2 3 3 2 2



B2 = (In/H) =

P +P +P +P +2P +2P +2P
In InCl InC12 InC13 2In2C12 In2C14 2In2Cl6
S 3 2 H HC As PPH+P(4-39)
PH +PH+P +3P +3P +2P +2P +P +P
H H HC1 AsH PH AsH PH AsH PH
2 3 3 2 2











Clm = (As/H)m =


(4-40)
PH2+PH+PHC1I+3PAsH3+3PPH3+2PAsH2+2PPH2 +PAsHPPH



C2m = (P /H)m =

PH +PH2 +PP +p +2P +3P +4P
APH PH PH P APS A A PsAs
(4-41)
P +P +P +3P 3+3P +2P +2P +P +P
HH HHC1 jAsH 3PH 3 AsH +PH 2AsH PH
2 3 3 2 2



The summation of partial pressure of the 33 vapor

species equals to the total pressure, Ptot-


= P+P +P +P +P +P +P
Ptot PH PHC1 PH Cl PCl GaC1 GaC1 GaC1
+PGa2C12+P Ga2ClP Ga2C16 +PGa+P InC+P InC12

+PInC13 +PIn2C12 +PIn2C14 +PIn2Cl6 +PIn+P AsH3
2 2 3 4 3
+PAsH2 +PAsH+PAs+PAs2 +PAs3PAs +PPH 3+PPH2

PP+P +Pp P +P +P P (4-42)











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.











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 Inl-xGaxAsyP1-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



a P
GaAs HC1
K1 (T) = a 25 0.5 (4-43)
1 P0.25 0.5
GaC1 As4 H2



K2 (T) = pInAs Hl (4-44)
2 0.25 0.5
InCl As4 H2
4 2


GaP HC1
K (T) = HC1 (4-45)
3 T 0.25 0.5
GaC1 P H2


a P
InP HC1
K4 (T) = 0.5 5 (4-46)
4 0.25 0.5
InC1 P H2



where ai is the activity of binary component i in solid

solution Inl-xGaxAsyP1-y. The ai's are dependent upon the

solid solution composition (x, y), and temperature T. The

solution thermodynamics of solid Inl-xGaxAsyPl-y ,which

elucidates the dependence of ai'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



Ga+PGaCl GaC12 GaCl3+2PGa2C12+2PGa2C14+2PGa2C16

In InCl InC1 PInC13+2PIn2C12+2PIn2C14+2PIn2C16
-P AsH-P AsH-P AsH-P As-2P -3P -4P
AsH AsH As As Asq
3 2 2 3 4
-P H-P -P -P -2P -3P -4P
PH PH PH P P P P
3 2 2 3 4
D = (4-47)
2P +P +P +3P +3P +2P +2P +P +P
H 2H HC1 AsH 3PH 3 AsH PH2 AsH PH



When values of the deposition zone temperature, Td, system

pressure Ptot, parameters D and Ad (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

P aP Ga+P GaC+PGaC +2PGa +2P Ga +2PGaC
Ga GaCI GaC12 GaC114 G2C1
Y = (4-48)
Y P +P P 2 2 2 4 2 +P (4-48)
Ga GC GaC1P GaC12 Ga2Cl GaCC1 Ga2C1
2 3 22 24 26
p +p +p +p +2P +P 2P +2P
In InC InC2 nC 2PIn C 2PIn 2C14 +2PIn2C16



P +P +P +P +2P +3P +4P
AsH 3AsH +AsH As 2As 3As As
3 2 2 3 4
Z = (4-49)
P AsH+P AsH+PAsH+P As+2P +3P +4P + (4-49)
AsH AsH As As As As
3 2 2 3 4
P +PH +P +Pp+2P +3P +4P
PH PH PH P P P P
3 2 2 3 4



Therefore, complex chemical equilibrium can also be

defined by a set of chosen values of Td, Ptot, Ad, D, Y, and

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.










Table 4-5. Equilibrium Parameters


Equilibrium Parameters
Zone

Symbol Definition


gallium source zone As(Ga) Cl/H
Ts(Ga) temperature
Ptot pressure


indium source zone As(In) Cl/H
Ts(In) temperature
Ptot pressure


mixing zone Am Cl/H
Bi, Ga/H
B2m In/H
C1m 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
Ptot pressure












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 HC1

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 FHC1(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



P +P +P +P +
PGaPGaCl GaC1 +GaC 1

F,* 2PGa C1 2Ga2C1 2Ga2C16
F Ga(Ga) = FH(Ga) 2 22 (4-53)
2P H+PHC +PH
H HCl H



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












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, FC1(In), are given by



FH(In) = 2FH2(In) + FHC1(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 according to


F In(In) = FH(In)


P +p +P +P +
In +InC InCl +InCl
2 3
2P +2P +2P
In2Cl2 In2Cl4 In2Cl6
2P +PHC +PH
H2 HCl H


(4-58)


The indium transport e(In) is defined by


e(In) = FIn(In) / FC1(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) = FC1(Ga) + FCl(In)


(4-61)


FGa(m) = FGa(Ga) = e(Ga) FC1(Ga)


(4-62)












FIn(m) = FIn(In) = e(In) FCl(In)


FAs(m) = FAsH3


FP(m) = FPH3


(4-64)


(4-65)


The equilibrium parameters Am, B1m, B2m, C1m and C2m are

related the transport rates and can be written as follows.


Am =



B1m =



B2m =



C1m =



C2m =


FC1(m) / FH(m)


(4-66)


FGa(m) / FH(m)


FIn(m) / FH(m)


FAs(m) / FH(m)


FP(m) / FH(m)


(4-67)


(4-68)


(4-69)


(4-70)


From the equations presented above, it is clear that there

are seven process parameters in the mixing zone; FH2(m),

FAsH3, FPH3, Tm, Ptot, e(Ga) and e(In). When values of

FH(Ga), FC1(Ga), FH(In) ,FC1(In), and the process parameters

are specified, the seven equilibrium parameters, Am, Blm,

B2m, C1m, C2m, Tm and Ptot can be evaluated and the complex

chemical equilibrium in mixing zone is completely defined.


(4-63)









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), FCl(m), FGa(m), FIn(m), FAs(m) and FP(m).



Ad = FCl(m) / FH(m) (4-71)



D = (FGa(m) + FIn(m) FAs(m) FP(m)) / FH(m) (4-72)



Y = FGa(m) / (FGa(m) + FIn(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) + FIn(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

Inl-xGaxAsyP1-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 Ad also remains unchanged throughout

the deposition zone.

The deposition zone temperature, Td, and the system

total pressure, Ptot, are the only process parameters in the

deposition zone. With specified Td, Ptot, and values of the

transport rates at the deposition zone inlet, FH(m), FCl(m),

FGa(m), FIn(m), FAs(m), and FP(m), equilibrium parameters Td









74

Ptot, Ad, D, 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

VPE of Inl-xGaxAsyP1-y; FH2(Ga), FHC1(Ga), Ts(Ga), e(Ga),

FH2(In), FHC1(In), Ts(In), e(In), FH2(m), FAsH3, FPH3, Tm,

Td, and Ptot.












Table 4-6. Process parameters


Process Parameters
Zone

Symbol Definition


gallium source zone FH2(Ga) H2 input flowrate
FHCl(Ga) HC1 input flowrate
Ts(Ga) temperature
Ptot pressure


indium source zone FH2(In) H2 input flowrate
FHC1(In) HC1 input flowrate
Ts(In) temperature
Ptot pressure


mixing zone e(Ga) Ga transport factor
e(In) In transport factor
FH2(m) H2 input flowrate
FAsH3 AsH3 input flowrate
FPH3 PH3 input flowrate
Tm temperature
Ptot pressure

deposition zone Td temperature
Ptot 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 o
Ka = H ai = exp ( ) = exp (RT (4-77)
i=l i=1



where ai is the activity of chemical species i, ui is the

stoichiometric constant of i in the reaction, pi is the

standard Gibbs free energy of i, and n equals the total

number of chemical species involved in the reaction. The
0
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 o
A =( AH TS + 1T C dT
S i= i Af(298K) S(298K) 298K p,i

T IT dT (4-78)
298K p,i T ( )



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.









77

4.1.4.2 Complex Chemical Equilibrium Calculation

Gallium source zone Assuming that q1 = PH20-5 and q2

PHC1 PH2-0-5, then the partial pressure of each chemical

species in gallium source zone can be rewritten in terms of

q1, 92, and temperature dependent equilibrium constants.



H2 = q (4-79)


PHC1 = qq2 (4-80)

0.5
PH = K27 q1 (4-81)


-0.5
PC1 = K28K27 q2 (4-82)
P1 = K K05 q (4-82)

C 29 (4-83)28


PGaCl = K32 K2 (4-84)
2 2 2


Ga2C2 = K18K32 q2 (4-85)

P 2
GaC2 = K4K32 q2 (4-86)


=Ga2Cl K 10KK32 q (4-87)


GaC3 = K9K32 q (4-88)

PGa 2 2 6
GaC6 = K16K K32 q (4-89)

-1 0.5
PGa = K30K32K28 K27 (4-90)











Substituting equations (4-79 to 4-90) in equations (4-11 & 4-

12),


-0.5 3
(q1+K32+K28K27 )2 + K9K322
2 -1 2 2
+(K K 2 +K K +K 2
+29 2827 18K32+K4K32) q2
2 4 2 2 6
A+K 10 K32 2 +K16K9K322
As(Ga) = 0.5 2 (4-91)
s 0.5 2
(q2+K27) q1 + q1



2 0.5 -0.5
tot 1 +K27 1+(K32+K28K27 q2 +
2 -1 2 2
(K29K28K27 +K18K32 +K14K32 2








can be solved together numerically for ql 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)
P3 2 4
=16 K7K3 2 2 (4-94)
2 2 17 32 2












nC2 = K3K33 q2 (4-95)


P 2 4
In2Cl4 1= K 12K1K3 q (4-96)

P 3
InCl = K K 3q (4-97)


P 22 6
PIn2C = K 5K K3 q2 (4-98)
2 6 15 11 33 2

-1 0.5
P = K K K K (4-99)
In K31K33 28 27



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,


A (In) =
s


-0.5 3
1+K33+K28K27 2 +K K33 2
2 -1 2 2
(K9K28K27K17K32K13K33) q2
2 4 2 2 6
+K K K2 q +K K K q
12 11 33q2K15 11 33q2
0.5 2
(q2+K275) q + q1
2 27 1 1 ^


2 0.5 -0.5
tot 1 K27 q1+(K33+K28K27 ) 2 +
2 -1 2 2
(K29K2827 17K33K13K33 2
3 2 4
K11K33 2 +K12K11K332 + 2+
2 2 6 -1 0.5
K K2 K2 q K + K K K
15 11 33 2 31 33 28 27


(4-100)


(4-101)


Solution of equations (4-100 & 4-101) by the Newton-Raphson

method gives the values of ql 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 q3 = PAs 0.25, q4 = Pp 0.25,
4 4
q5 = PGaC1 and q6 = PInCl, then the partial pressure of the

chemical species in mixing zone can be written in terms of

ql1 q2, q3, 9q4 95 and q6 as follows.



PGaCl = 5 (4-102)

P 2
2GaC = K18q (4-103)


GaC12 = K 4 q5 q2 (4-104)


P 2 2
PGaCl4 = K0K9 q 2q (4-105)
2 4 10K9 5 q2


GaC = Kgq q2 (4-106)
P 2 2 4

PGaCl6 = K 6K q5 q2 (4-107)
2 6 16K 9 5 q 2

-1 0.5 -1
P K K 1 K 0.5 -1 (4-108)
Ga 30 2827 5 2 (4-108)


PInCl = 6 (4-109)

P 2
In2C12 = K7 q6 (4-110)


P 2
InC12 = K13 q q2 (4-111)


PnC = 2
In2C14 = K12,1 6 2 (4-112)
2 4 121 q6 q2












InC3 = KI, q6q2 (4-113)


P 2 2 4
In2C6 = K 1 6K q q q4 (4-114)


-1 0.5 -1
P = K 5 1 q (4-115)
In 31 28 27 2 6 (4-115)

P 4
As4= (4-116)


P 0.5 -0.25 3
3 = K 5 K5 q(4-117)


P -0.5 2
As2 = K05 q3 (4-118)


P 0.5 -0.25
PAs = 5 K q3 (4-119)
23 5 3

P -1 .25 3
AsH3 = K61 K5 q3 q1 (4-120)


P -1 -0.25 2
AsH2 = K19K6 K5 q3 q1 (4-121)


-1 -0.25
AsH = K20K6 K'25 (4-122)

P 4
4 = 4 (4-123)


P v0.5 -0.25 3
P3 = K26 K q4 (4-124)


P -0.5 2
Pp = K05 4 (4-125)


P 0.5 -0.25
P K25 K7 4 (4-126)

P 1 K-0.25 3
SPH K K q q (4-127)
3 8 7 4 1









82

P -1 0.25 2
PH2 = 21K K7" q4 q1 (4-128)


PpH = K22K8 K 25 q4q (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 q1, q2, q3, q4, q5, and q6, 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 ql, q2, and

q3 presented in the last two sections,


-1 -1
P = K1 a q ql (4-130)
GaC 1 GaAs 2 34-13


PGaCl = Ks K 2 a2 q q- (4-131)
-2 2 1 1 G 2 3




PGa2C4 = KoK9KI aGaAs q2 q3 (4-133)
PGaCl =K K a q q2 q (4-132)
2 14 1 GaAs 2 3(4-13

P -2 2 4 -2
Ga2C4 = K0K9 aGaAs 2 3 (4-133)

P -1 3 -1
GaC1 = K K a q q (4-134)
3 9 1 GaAs 2 3

P 2 -2 2 6 -2
Ga C1 K K K a q q (4-135)
2 6 16 9 1 GaAs 2 3











-1 0.5 -1 -1
P = K K K a q
Ga 30K28 27 1 GaAs 3


P= K1 aIs 2 qq3
InCI 2 InAs 2 3


P Cl
In2Cl2


PInC1

P
In2C14


-2 2 2 -2
S17 K2 aInAs 2 3

-1 2 -1
13 K2 aInAs 2 q3

-2 2 4 -2
=K2K11K2 aInAs 2 q3


P -1 3 -1
PInC1 K11 K2 a q2 q3
3 11 2 InAs 2 3


P
In Cl
2 6


2 -2 2 6 -2
= K K a qAs q3
15 11 2 InAs 2 3


-1 0 5 -1 -1
SK K K K a q
31 28 27 2 InAs 3

-4 4 4 -4 4
= K K aGaP a GaAs
3 1 GaP GaAs 3

0.5 -0.25 -3 3 3 -3 3
= K K K K a a q
26 7 3 1 GaP GaAs 3

-0.5 -2 2 2 -2 2
= K K Ka aP aGaAs q3
7 3 1 GaP GaAs 3

0.5 -0.25 -1 -1
5 K K K1 a aAs
25 7 3 1 GaP GaAs


P -1 -0.25 -1 -1 3
PH = K K K Ka a q q
3 8 7 3 1 GaP GaAs 3 q


P -1 -0.25 -1 -1 2
PH2 = K21K K7 K3 KlaGaP aGaAs 3

-1 -0.25 -1 -1
PH = K K K Ka a q q,
PH = K22 8K 7 3 1 GaP GaAs q3 1


PIn

P
PP4


PP3


PP2

Pp
3


P
P


(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 ql, q2, and q3. When aGaAs,

aGaP, aInAs (and ainP) are specified, the equations can be

solved for ql, q2, and q3. The complex chemical equilibrium

of deposition zone is calculated by an iterative algorithm,

which is succinctly explained in figure 4-1.











START


Read Process parameters: Td, Ptot
& Mixing Zone Transport Rates:
FH(m), FC1(m), FGa(m), FIn(m), FAS(m), FP(m)


Calculate Equilibrium Parameters: Ad, D


Initial Guess: x, y


Calculate Activities: aGaAs, ainAs, aGaP, ainP
(by Solid Solution Model)


Solve qj, q2, q3
(by Newton-Raphson method)


Calculate Partial Pressure: Pi's


Calculate Equilibrium Parameters: Y, Z


Calculate Supersaturation: S
& Composition of Deposited Solid: xcalc, Ycalc
(by eqs.(75 & 76))


Xcalc = x ?
Ycalc = Y ?

YES


PRINT OUT



STOP
"S-T


:.dust
x, y


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 xi denote the mole fraction of component i in a

homogeneous solution of C components, then



x1 + x2 + x3 + ....... + x = 1 (4-151)



Let W denote an extensive property of the mixture, then the

intensive property wi of component i can be derived from the

basic thermodynamic relationship,



i= ( (4-152)
Ni T, P, Nj(j3i),



where T is temperature, P is pressure and Ni is the amount of

component in the mixture. If Ni has the unit moles, then wi

is called a partial molar property. Therefore the partial

molar Gibbs free energy, gi, or chemical potential, vi, is

simply



gi = gi = ( (4-153)
aNi T, P, Nj(joi),



The partial molar entropy, si, the partial molar enthalpy,

hi, the partial molar volume, vi and the partial molar heat











capacity, Cpi, are derived from the chemical potential i by

classical thermodynamics.


Si = p i/ T


(4-154)


hi = Mi T( Ii/ T)


(4-155)


vi = i/ P



Cpi = T( si/ T) = -T( i/ T2)


(4-156)



(4-157)


Besides its use of conveniently evaluating other partial

properties, the chemical potential is useful in formulating

phase equilibrium. Consider two homogeneous mixtures Al and

A2 of C components at equilibrium, the system of phase

equilibrium equations can be written as follows.


TA1 = TA2



PA1 = PA2



1i,Al = "i,A2, i = 1, 2, 3, ...... C


(4-158)



(4-159)



(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 p0i denote the chemical potential of pure

component i at temperature T and pressure P of interest, then

relative activity ai of component i in the mixture is defined

by the relationship,



ai = exp (( Pi- 0ji)/RT) (4-161)



Clearly, ai 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. P i

can be rewritten in terms of pOi and ai,



Pi = 10i + RT In(ai) (4-162)


Substituting equation (4-162) in equation (4-160) and

cancelling u0i 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, N1, N2, ...., NC) is known, all of

the partial molar properties can be readily derived.

Furthermore, if the standard chemical potential u0i(T, P) is

known, relative activity ai is obtained.









89

4.2.2 Solid Solution Models

The solid solution models used for type Al-xBxC1-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, nAC, nBC, 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 system

behavior from the limited amount available information.

The Al-xBxC1-yDy 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, and nBD represent the number of nearest

neighbor pairs AC, AD, BC, and BD, respectively. These

numbers are related to the number of constituent atoms, NA,

NB, NC, and ND, as follows.


nAC + nAD = z1 NA


(4-164)











nBC + nBD = Z1 NB (4-165)



nAC + "BC = Z1 NC (4-166)



"AD + nBD = Z1 ND (4-167)



, where z1 (= 4) is the number of nearest neighbors for each

atom in the zinc-blende lattice structure. The number of

constituent atoms, NA, NB, NC, and ND, 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 = (l-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, NB, NC, and ND by equations (4-168 to 4-

171) into equations (4-164 to 4-167), is written as follows.











"AD = (l-x) (z N) nAC


nBC = (1-y)(zI N) nAC


nBD = (x+y-1)(z1 N) + nAC


(4-173)


(4-174)


It is obvious from equations (4-172 to 4-174) that nAC, nAD,

nBC, and nBD 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 nAC,

nAD, nBC, and nBD are specified, x, y, and N can be readily

calculated by


x = (nBC + nBD)/(nAC + nAD + nBC + nBD)



Y = (nAD + nBD)/(nAC + nAD + nBC + "BD)



N = (nAC + "AD + "BC + nBD)/z1


(4-175)



(4-176)



(4-177)


If a completely random distribution is assumed, the number of

nearest pairs is given as follows.


nAC = (1-x)(1-y) zI N


(4-178)


nAD = (1-x) y ZI N


(4-172)


(4-179)











nBC = x (1-y) z1 N


nBD = x y z1 N


(4-181)


The molar ratio of the binary components Xij (i=A,B; j=C,D)

is defined by


Xij = (nij/zl) / N


(4-182)


In the case of random mixing, Xij's are evaluated as


XAC = (1-x)(l-y)



XAD = (l-x) y



XBC = x (l-y)


(4-183)


(4-184)


(4-185)


XBD = x y


(4-186)


The extensive Gibbs free energy G of the solid solution

Al-xBxCl-yDy is given as a function of nAC, nAD, nBC, nBD,

and T. From equations (4-172 to 4-174), it is obvious that G

can also be written as a function of nAC, 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).


(4-180)