Title: Study of grown-in defects and radiation-induced defects in GaAs and AlxGa1-xAs /
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Title: Study of grown-in defects and radiation-induced defects in GaAs and AlxGa1-xAs /
Physical Description: xii, 190 leaves : ill. ; 28 cm.
Language: English
Creator: Wang, Weng-Lyang, 1950-
Publication Date: 1984
Copyright Date: 1984
 Subjects
Subject: Gallium arsenide semiconductors   ( lcsh )
Crystals -- Defects   ( lcsh )
Semiconductors -- Effect of radiation on   ( lcsh )
Semiconductors -- Defects   ( lcsh )
Electrical Engineering thesis Ph. D
Dissertations, Academic -- Electrical Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1984.
Bibliography: Bibliography: leaves 182-189.
Statement of Responsibility: by Weng-Lyang Wang.
General Note: Typescript.
General Note: In "AlxGa1-xAs" in title, "x" and "1-x" are subscripts.
General Note: Vita.
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Bibliographic ID: UF00099491
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000491183
oclc - 11961022
notis - ACQ9685

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STUDY OF GROWN-IN DEFECTS AND RADIATION-INDUCED
DEFECTS IN GaAs AND AlxGal_xAs






















By

WENG-LYANG WANG












A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY








UNIVERSITY OF FLORIDA

1984












TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS ................................................ i

SELECTED LIST OF SYMBOLS ........................................ vi

ABSTRACT.......... ........... ............ ....................... xj

CHAPTER

I INTRODUCTION.................................................. 1

II REVIEW OF POSSIBLE NATIVE DEFECTS AND COMPLEXES IN
GALLIUM ARSENIDE ........................................ 6

III EXPERIMENTAL METHODS........................................ 13

3.1 Current-Voltage (I-V) Measurement...................... 13
3.2 A. C. Admittance Measurement........................... 15
3.3 Capacitance-Voltage (C-V) Measurement.................. 17
3.4 Thermally Stimulated Capacitance (TSCAP) Measurement... 18
3.5 Deep Level Transient Spectroscopy (DLTS) Measurement... 19

3.5.1 Principle of DLTS Measurement................... 21
3.5.2 Minority carrier injection...................... 22
3.5.3 Majority carrier injection...................... 22
3.5.4 Defect concentration............................ 25
3.5.5 Activation energy of a deep level defect........ 26

IV DETERMINATION OF POTENTIAL WELL OF DEEP-LEVEL TRAPS USING
FIELD ENHANCEMENT EMISSION RATE ANALYSIS OF NONEXPONENTIAL
DLTS IN GaAs .............................................. 31

4.1 Capture and Emission Process at a Deep-Level Trap....... 32
4.2 Overview of the Theory.................................. 36

4.2.1 Poole-Frenkel effect............................. 36
4.2.2 Phonon-assisted tunneling effect................. 39

4.3 Theoretical Calculations of Emission Rate for
Different Potential Wells................................ 42

4.3.1 Coulombic potential well.......................... 42
4.3.2 Dirac delta potential well........................ 45
4.3.3 Square potential well............................ 47
4.3.4 Polarization potential well...................... 48
4.3.5 Dipole potential well............................ 52










4.4 Theoretical Calculation of the Nonexponential DLTS
Transient for Different Potential Wells................. 56
4.5 Sunmary and Conclusions................................ 65

V MODELLING OF GROWN-IN NATIVE POINT DEFECTS IN GaAs ......... 69

5.1 Introduction........................................... 69
5.2 Theoretical Calculations of Vacancy and Interstitial in
Undoped GaAs............................................ 71
5.3 Thermal kinetic after crystal growth.................... 77
5.4 The Possible Grown-in Point Defects in GaAs for the
As-rich, High Arsenic Pressure Cases.................... 80
5.5 The Possible Grown-in Point Defects in GaAs for the
Ga-rich, Low Arsenic Pressure Cases .................... 81
5.6 Summary and Conclusions................................ 81

VI ON THE PHYSICAL ORIGINS OF EL2 ELECTRON TRAP IN GaAs
(THEORETICAL AND EXPERIMENTAL EVIDENCE) ......... ............... 83

6.1 Review of the EL2 Electron trap in GaAs................. 84
6.2 Theoretical Modelling of the EL2 Electron Trap in GaAs.. 87

6.2.1 Growth process................................... 88
6.2.2 Cooling process.................................. 91
6.2.3 Annealing process................................ 95

6.3 Determination the Potential Well for EL2 Electron Trap
from Field Enhanced Emission Rate Analysis.............. 95
6.4 Sumary and Conclusions................................ 99

VII STUDY OF GROWN-IN DEEP LEVEL DEFECTS VS GROWTH PARAMETERS
IN VPE, LEC, LPE AND MOCVD GROWN GaAs ...................... 100

7.1 Study of Grown-in Deep Level Defects vs Growth
Parameters in the VPE GaAs Layers...................... 100

7.1.1 Introduction................................... 101
7.1.2 Experimental Details............................ 102
7.1.3 Results and Discussions......................... 103
7.1.4 Summary and Conclusions ........................ 116

7.2 Study of Grown-in Deep Level Defects vs Growth
Parameters in the LEC GaAs Layers...................... 117

7.2.1 Intrinsic double acceptor level in LEC
grown p-GaAs.................................. 117
7.2.2 Study of deep level defects vs annealing
temperature in H2 ambient ..................... 119

7.3 Study of Grown-in Deep Level Defects vs Growth
Parameters in the LPE n-GaAs Layers................... 128










7.4 Study of Grown-in Deep Level Defects vs Growth
Parameters in the MOCVD n-GaAs Layers................. 130
7.5 Summary and Conclusions............................... 133

VIII DEFECT STUDIES IN LOW-ENERGY PROTON AND ONE-MEV ELECTRON
IRRADIATED AlGaAs-GaAs SOLAR CELLS........................ 135

8.1 Introduction.......................................... 135
8.2 Experimental Details.................................. 137
8.3 Theoretical Analysis of Lattice Damages Created by
Particles Irradiation................................. 139
8.4 Defect Parameters for the Low-Energy Proton Irradiated
(AlGa)As-GaAs Solar Cells.............................. 147
8.5 Defect Parameters for the One-MeV Electron Irradiated
(AlGa)As-GaAs Solar Cells ...................... 154

8.5.1 Sn-doped GaAs irradiated at room temperature and
post annealed at 2300C ......................... 159
8.5.2 Sn-doped GaAs irradiated at 150 and 2000C cell's
temperature for different fluxes and fl inces... 167
8.5.3 Unped GaAs irradiated at 2000C for 10 and
10 e/cm fluences............................ 167
8.5.4 Undoped GaAs irradiated at room temperature for
different electron fluences..................... 172

8.6 Summary and Conclusions ............................... 176

VIIII CONCLUSIONS.............................................. 178

REFERENCES...................................................... 182

BIOGRAPHICAL SKETCH ............................................. 190











SELECTED LIST OF SYMBOLS


Symbol Definition

A diode area

Al e2a / 8E oE s2 for polarization well.

A2 (1/a ) [Ze2 / (4 s mc2)]2

B Proportionality constant for emission rate.

Co depletion layer capacitance.

C(t) capacitance transient which proportional to electrons
(holes) emitted to the conduction (valence) band for DLTS.

AC capacitance change due to majority (minority) carrier
emission for TSCAP.

AC(t) Co C(t)

d cell thickness.

Dn(Dp) diffusion constant for electrons (holes).

en(ep) emission rate of electrons (holes).

eno emission rate for zero electric field.

enl(en3) one- (three-) dimensional emission rate in the presence of
the electric field.

en matrix elements of the transition for emission rate.

enH total enhancement emission rate.

ent emission rate due to phonon-assisted tunneling effect.

enHC total enhancement emission rate for Coulombic well.

enHD total enhancement emission rate for Dipole well.

enHP total enhancement emission rate for Polarization well.
enHR total enhancement emission rate for Dirac well.

enHS total enhancement emission rate for Square well.

eni (Ei) enhancement emission rate for each electric field Ej.










E energy handgap.

EH 13.6 eV, is the ionization energy of a hydrogen atom.

Ej incident particle energy.

Ett tn t+ A

Et activation energy of the trap level.

Eti ionjzatjon energy of the trap level.

Eth thermal excitation energy or phonon energy.

AEb the activation energy of capture cross section for each
trap.

AEti Poole-Frenkel lowering of the potential barrier.

F electric field.

Fj electric field in each small segment.

Fmax Max. electric field in the p+-n junction.

g degeneracy factor.

X h / 2 T planck constant.

AH enthalpy change.

Id(Irg) the magnitude of a saturation diffusion (generation-
recombination) current.

If(Ir) current due to forward (reverse) component.

Io saturation current.

It total current.

L0(L1) the minority carrier diffusion length for the unirradiated
(irradiated) cell.

LD Debye length.

Ln(Lp) diffusion length for electrons (holes).

L effective diffusion length.

m electron effective mass.

m free electron mass.









mde(mdh) density of state electron (hole) effective mass.

m ideality factor.

M1 the mass of the incident particle.

M2 the mass of the lattice atom.

n electron concentration.

nj intrinsic carrier density.

N the number of GaAs per unit volume.

Na (Nd) acceptor (donor) density.

Nc density of state in the conduction band.

Nt trap density.

N(x) distribution of proton particle.

AN total number of displacement particles.

p hole concentration.

P probability ratio for an electron impinge on the barrier.

P dipole moment.

r mole fraction of [As] to [Ga].

rmax the location of the Poole-Frenkel lowering barrier.

R A Eti / kT

Re the penetration range of electron particle in mg/cm2.

Ro distance separating the charge center.

Rp shunt resistance.

Rs series resistance.

Rp projected range of proton particle.

ARp straggle range of proton particle.

S(T) DLTS signal.

AS entropy change.

tl(t2) time setting by the dual gated boxcar.


viii








TIm the max. energy transferred to the lattice atom.

v velocity of light.

average thermal velocity.

Va applied voltage.

Vbi built in potential.

VD displacement energy.

Vr applied reverse bias voltage.

V(r)[VT(r)] potential well for the trap level when no (an external)
electric field is applied.

w 2 f, frequency radian.

W depletion layer width.

Wo zero bias depletion layer width.

xi proton penetrate depth.

Y(w)[Z(w)] admittance (impedance) as a function of frequency.

Z atomic number of the lattice atom.

a Z / 137

aH(aj) the polarizability of a hydrogen (neutral impurity) atom.

B v/c

Y1 5.405xl0-4 eV/k for GaAs.

Y2 204 for GaAs.
SF the anger between electric field with the dipole moment.

6m the anger for the max. barrier lowering occurs for dipole
well.

od differential scattering cross section.

Sn( p) capture cross section for electrons (holes).

a- capture cross section at very large temperature.

e(t p) electron (hole) fluence.

)i built-in potential.











&) image lowering potential of the Schottky diode.

es dielectric constant of the GaAs.

T carrier emission time constant.

Te effective carrier lifetime.

Tn( ') lifetime of electrons (holes).










Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



STUDY OF GROWN-IN DEFECTS AND RADIATION-INDUCED
DEFECTS IN GaAs AND AlxGal_xAs

By

Weng-Lyang Wang

August 1984

Chairman: Sheng-San Li
Major Department: Electrical Engineering

The objectives of this dissertation are (1) to conduct a detailed

analysis of the grown-in defects and radiation induced defects in GaAs

grown by the LEC, VPE, LPE, and MOCVD techniques under different

growth and annealing conditions, (2) to identify the physical origins

of the deep-level trap in GaAs, and (3) to determine the potential

well of electron traps from analyzing the electric field enhanced

emission rates deduced from the nonexponential DLTS data.

A detailed theoretical and experimental study of the grown-in

defects and radiation-induced defects in GaAs has been carried out in

this dissertation; the main research accomplishments derived from this

research are summarized as follows:

(1) Theoretical and experimental studies of native point defects

in GaAs grown by the LEC, VPE, LPE, and MOCVD techniques under

different growing and annealing conditions have been made in this

research, and the conclusions are listed as follows: (a) high purity

GaAs material can be grown for the low arsenic pressure case under

optimum cooling condition, (b) GaAs grown under a high arsenic

pressure condition will produce more native point defects than lower










arsenic pressure conditions, (c) arsenic antisite (AsGa) defect only

can be observed in GaAs grown under an As-rich or high arsenic

pressure conditions; this defect can not be produced under low arsenic

pressure condition.

(2) A new defect model supported by the experimental data has

been developed in this work to account for the physical origins of the

EL2 electron trap in GaAs. It is shown that the EL2 electron trap may

be attributed to two different types of native defects: One is

identified as the EL2a (i.e., Ec-0.83eV) electron trap, and the other

is designated as the EL2b (Ec-0.76eV) electron trap. The physical

origin for the EL2a level is attributed to the doubly-charged arsenic

antisite (i.e., AsGa +) defect, whereas the physical origin for the

EL2b electron trap is due to the arsenic-antisite-plus-arsenic vacancy

complex (ie., ASGaVAs). Based on this model, the relationship between

the density of EL2a and EL2b trap levels and the [As]/[Ga] ratio in

the MOCVD and VPE grown GaAs was established.

(3) A theoretical model for the nonexponential DLTS response due

to the field dependent emission rate of the trapped charge has been

developed. A comparison of the theoretical calculation of the

nonexponential DLTS response with the DLTS data for each trap level

would allow us to determine the potential well of the trap involved.

This method has been applied to identify the physical origins of the

EL2a electron trap in GaAs.












I. INTRODUCTION


Studies of deep-level defects in GaAs have been extensively

published in the literature. [1-13] Speculations on the physical

origins of defect levels and defect complexes are still very

tentative. It is not even possible to say with any assurance that

simple gallium vacancy (VG) or arsenic vacancy (VAs) can be related

to a particular energy level.

In one respect understanding has been improved. Gallium arsenide

(GaAs) specimens grown by various techniques such as liquid phase

encapsulation (LEC), Bridgmann, vapor phase epitaxy (VPE),

metalorganic chemical vapor deposition (MOCVD), liquid phase epitaxy

(LPE), and molecular beam epitaxy (MBE) are now recognized as likely

to have different properties in terms of energy levels within the

bandgap. In each of these techniques the growth temperature, growth

pressure, growth phase, and cooling rate are usually different. For

examples, GaAs grown by the LPE technique from a gallium melt is

expected to be low in gallium vacancy defects and possibly high in

arsenic vacancy. The LPE GaAs usually contains hole traps with energy

level of Ev+0.71eV (B center), while VPE GaAs grown in the As-rich

conditions always contains an electron trap with energy of Ec-0.83eV

(EL2 level). The reason for observing these trap levels in the LPE or

VPE GaAs is still not clear.

The main objectives of this research are (1) to make a detailed

analysis of the grown-in defects and radiation-induced defects in GaAs

specimen grown by the LEC, VPE, LPE, and MOCVD techniques under

1










different growth and annealing conditions, (2) to identify the

physical origins of the deep-level traps in GaAs, and (3) to

determine the potential well of electron traps by analyzing the field

enhanced emission rates deduced from the nonexponential DLTS response

data.

A detailed theoretical and experimental study of the grown-in

defects and radiation induced defects in GaAs has been carried out in

this dissertation; these include the following: (1) Theoretical

modelling of native defects in GaAs has been developed. GaAs specimen

grown by the LEC, VPE, LPE, and MOCVD techniques under different

growth and annealing conditions have been measured in order to support

this model. The GaAs-samples used in this study include (i) VPE GaAs

epilayers grown on <100>, <211A>, and <211B> oriented semi-insulating

(S. I.) Cr-dopedGaAs substrates with the gas phase controlled by

varying the [Ga]/[As] ratios from 2/1, to 6/1, (ii) LEC n-GaAs

samples prepared for study of the effect of hydrogen heat treatment on

deep-level defects, (iii) LPE GaAs samples grown under two different

temperatures (i.e., 700 and 8000C) and two cooling rates (0.4 and

lC/min.), and (iv) MOCVD GaAs epilayers grown on S. I. GaAs substrate

and S. I. Ge substrates. Theoretical modelling of native point defects

is described in chapter V. Experimental evidence for some of the

native point defects is given in chapter VII. (2) The deep-donor

trap, commonly known as EL2 center, with activation energy ranging

from Ec-0.76 to E -0.83eV, has been observed in GaAs grown by LEC,

VPE, and MOCVD techniques. The EL2 level acts as a recombination

center for lifetime reduction. The physical origin of this electron

trap has been a subject of greater interest in recent years. Although










a large number of papers have been devoted to finding the physical

origins of the EL2 electron trap, unfortunately, none of these

published results offered a consistent and unambiguous explanation for

the observed EL2 trap in GaAs. A detailed theoretical and

experimental study of the EL2 electron trap has been carried out in

this work. The detailed results are discussed in chapter VI. (3)

DLTS signals are often analyzed assuming that the capacitance

transient is exponential.,7'14] However, most of the DLTS signals are

nonexponential transient.[15,16] In this dissertation, we present the

theoretical analysis of nonexponential capacitance transients due to

the electric field dependent emission rate of trapped charge. The

emission rate of trapped charge carriers is enhanced by the Poole-

Frenkel and phonon-assisted tunneling effects in the presence of an

applied electric field. Since the electric field varies with position

within the depletion region of a reverse biased p-n junction, the

emission rate is not constant within the same region. The DLTS

response due to nonuniform emission rates can in general be expressed

as S( ) = E exp(-enitl) Z exp(-enit2). Based on the

nonexponential capacitance transient, theoretical calculations of DLTS

response for deep-level traps in GaAs were made using five different

potential wells; namely, the coulombic well which has a positive

charge state for the empty state, the Dirac well, square well,

polarization well, and dipole well which all have neutral charge

states from different physical origins. A comparison of the

theoretical calculation of the nonexponential DLTS response with the

DLTS data for each trap would allow us to determine the potential well

of the trap involved. This model was applied to the calculations of










the potential well for the EL2a level and other electron traps.

Details of the results are discussed in chapter IV. (4)

Characterization of low energy proton and one-MeV electron irradiation

induced defects in the LPE grown (AlGa)As-GaAs solar cells has been

studied. For the case of low energy proton irradiation, [17 19] the

GaAs solar cells were bombarded under different proton energies (50,

100, 200, and 290 kev), proton fluences (1010, 1011, 5xl011, 1012, and

1013 p/cm2) and Sn-dopant densities (2x1016 and 8x1016 cm-3). For the

case of one-MeV electron irradiation, [20-22] both undoped and Sn-

doped GaAs solar cells were irradiated under different temperatures

(25 and 2000C), fluences (1014, 1015, 5x1015, and 1016 e/cm2), fluxes

(2x109 and 4x1010 e/cm2s), and annealing times (10, 20, 30, and 60

min.). Defects parameters for deep-level traps induced by low-energy

proton and one-MeV electron irradiation are presented in chapter VIII.

Experimental tools employed in this study include the current-

voltage (I-V), capacitance-voltage (C-V), thermally stimulated

capacitance (TSCAP) and the deep-level transient spectroscopy (DLTS)

measurements. From these measurements, one can determine the energy

levels, density of defects, defect profile, and the capture cross

section for each trap level.

Chapter II reviews the possible native defects and impurity

complexes in GaAs. Chapter III presents the experimental details.

Determination of the potential well of deep level traps using field

enhanced emission rate analysis of nonexponential DLTS in GaAs is

described in chapter IV. Chapter V depicts the modelling of the

grown-in native point defects in GaAs. The physical origin of the EL2

electron trap in GaAs is explained in chapter VI. Chapter VII




5




describes the study of grown-in defects vs. growth parameters in VPE,

LEC, VPE, and MOCVD grown GaAs. Defects studies in low-energy proton

and one-MeV electron irradiated (AlGa)As-GaAs solar cells are

discussed in chapter VIII. Chapter IX gives the summary and

conclusions.












II. REVIEW OF POSSIBLE NATIVE DEFECTS AND COMPLEXES
IN GALLIUM ARSENIDE


The number of possible native defects in GaAs is large as may be

seen in table 2.1. None of these native defects has been identified

with any confidence. This is due to the fact that experiments for

studying such defects tend to be too uncontrollable. In addition to

the defects shown in table 2.1, other types of defects such as

impurity defects, impurity complexes defects may also be expected in

GaAs. The impurity complexes are shown in Table 2.2 and 2.3. In

this chapter, we will focus our attention on a few native defects

listed in table 2.1, which are believed to be related to the electron

or hole traps observed in this study.

Defects can be represented by their chemical symbols. For

examples, vacancy is represented by V and interstitial by i.

Subscript indicates the lattice site. Thus, VGa denotes the gallium

vacancy; Gaj represents the gallium interstitial site defect. In

addition to these simple point defects, defect complexes (for example:

VGa-AsGa VGa-) might be expected to form as the crystal cooling down

from high temperature to room temperature. Another type of defect,

namely, the antisite defect must also be considered. The antisite

defects (such as AsGa,++ GaAs--, and AsGa +GaAs--) are believed to be

important native defects in GaAs specimen.

A survey of the literature on the subject of defects in GaAs

grown by the Liquid Encapsulation Czockraski (LEC), Horizontal

Bridgmann-Stockbargen (HB), Vapor Phase Epitaxy (VPE), Liquid Phase

Epitaxy (LPE), Molecular Beam Epitaxy (MBE), and Metalorganic Chemical

6












Table 2.1 Possible native defects in GaAs.



1. One Component Defects:

a. Vacancy: VGa' VAs

b. Interstitial: Gaj, Asj

2. Two Component Defects:

a. Divacancy: VGaVGa VGaVAs, VAsVAs

b. Antisite: GaAs, ASGa

c. Di-interstitial: GajAsj

d. Vacancy-interstitial: VGaGai, VGaASj, VAsGaj, VAAsA

3. Three Component Defects:

a. Antisite-vacancy complexes: AsGaVGa, ASGaVAs, GaAsVGa, GaAsVAs

b. Trivacancy: VGaVAsVGa, VAsVGaVAs

4. Four Component Defects:

a. Antisite-divacancy complexes: VGaAsGaVGa' VAsGaAsVAs

b. Di-antisite: GaAsAsAGa












Table 2.2 Sane hypothetical impurity complexes.



I. Impurity interstitial: Ai

2. Impurity substitutional: AGa, AAs

3. Impurity-vacancy complexes: AGaVGal AGaVAs' AAsVGa AAsVAs

4. Impurity-antisite complexes: AGaAsGa, AGaGaAs, AAsASGa, AAsGaAs



A = Group II impurities (Be, Mg, Zn, Cd)

Group IV impurities (C, Si, Ge, Sn)

Group VI impurities (0, S, Se, Te)

Transition impurities (Ti, V, Cr, Mn, Fe, Co, Ni, Cu)












Table 2.3 Impurity defects in GaAs.


Periodic Table


Group III Group IV Group V

Ga atoms are As atoms are
replaced by replaced by
impurities impurities



* Group I; Li, Cu, Ag, Au

This group of impurities will act as acceptor traps in GaAs.

Each impurity may contain several deep-level traps.

* Group II; Be, Mg, Zn, Cd

This group of impurities will act as shallow acceptor traps in

GaAs.

* Transition Metals; Sc, Ti, V, Cr, Mn, Fe, Co, Ni

The energy level for each of these transition metals has a

downward trend from 1.0eV to 0.15eV above the valence band as

the metal elements change from Ti to Ni.

* Group IV; C, Si, Ge, Sn, Pb

When each of these impurities is on a Ga site, it becomes a

shallow donor level. On the other hand, if the atom is on a

As site, it becomes a shallow acceptor level.

* Group VI; S, Se, Te

This group of impurities will act as shallow donor traps in

GaAs.











Vapor Deposition (MOCVD) techniques showed that only a few electron

and hole traps are common point defects observed in both the bulk and

epitaxial grown GaAs material, while most of the point defects can't

observed in GaAs specimen with different growth processes. Lists of

the electron and hole traps observed in this study compared with

others [23-33] are given respectively in tables 2.4 and 2.5.

It is noted that EL2 (same as EF10, ET1, EB2, ES1) is the

dominant electron trap in the VPE, MOCVD, and bulk grown GaAs, and is

absent in the LPE and MBE grown GaAs epitaxial layers. Trap densities

of EL3, EL5, and EL12 levels are varied by different growth

conditions, and density of these traps can be easily reduced by

annealing. This suggests that they are due to native point defects.

On the other hand, EL11 is not affected by heat treatment; therefore,

the physical origin of EL11 level could be due to an impurity complex.

Crystals grown by different growth techniques are expected to produce

different electron traps, and only a few of them are common and

independent of methods of crystal growth. For example, both EL6

(bulk) and EL7 (MBE) could be the same defect in GaAs, which is not

observed in VPE grown GaAs. ELl0 (MBE) and EL11 (VPE) could be the

same level, yet not seen in bulk GaAs material. Most of these deep

level defects are believed to be either due to the vacancy related

defects, antisite defects or vacancy-impurity complex defects. For

the hole trap level, HL2, HL5, HL7, HL9, and HL11 may be related to

native defects; the other trap levels are related to the impurity

defects.










Table 2.4. Electron traps in n-GaAs.


Cr-doped LPE
as-grown VPE
Electr.irradi.

MBE
Electr. irradi.
MBE
MBE
Electr. irradi.


Cr-doped bulk
VPE


MBE
VPE
Bulk
MBE
VPE
11


3. 5x10-
2.2x10-13
3.0xl101-
8.3x10-13
2.6x10-13
2.6xl0-13
1.7x10-14
1.5x10-14



1.0X10-14
1.2x10-13
11
1.0x10-12
1.2x10-13
1.5x10-13
7.2x10-15
7.7x10-15
6.8x10-15
1.8x10-15
3.0x0-16
4.9x10-12
5.2x10-16
5.7x1013
4.0x10-18


0.86
0.83
0.90
0.71
0.48
0.41
0.30
0.19
0.18
0.12

0.78
0.83
0.58
0.51
0.42
0.35
0.30
0.28
0.23
0.17
0.17
0.78
0.22
0.15
0.37

0.11
0.14
0.20
0.31
0.35
0.52
0.60
0.71
0.76
0.83
0.90


Proton irradi.
ti 11

Electr.irradi.
n-LEC
Proton irradi.
n-LEC
Electr. jrradi.
LEC
LEC, VPE, MOCVD
Electr. irradi.


Bulk
Electr.
VPE


EB1
EB2
EB3
EB4
EB5
EB6
EB7
EB8
EB9
EB10


EL1
EL2 (A)
EL3 (B)
EL4
EL5 (C)
EL6
EL7
EL8 (D)
EL9
EL10
EL11 (F)
EL12 (A)
EL14
EL15
EL16


EF1
EF2
EF3
EF4
EF5
EF6
EF7
EF8
EF9
EF10
EF11


irradi.












Table 2.5 Hole traps in p-GaAs.


Cr-doped LPE
as-grown LPE
Fe-doped LPE
Cu-doped LPE
as-grown LPE
Electr. irradj.


Cr-doped VPE
as-grown LPE
Fe-doped VPE
Cu-doped VPE
as-grown LPE
VPE
MBE
MBE
VPE
VPE


LEC (p)
Electr. irradj.
Proton irradj.
it 11
Electr. irradi.
.1 It

Proton irradi.


Electr. irradj.


5.2x10-16
1.2x10-14
3.4x10-16
3.4x10-14
2.2x10-13
2.0x10-14


3.7x10-14
1.9x10-14
3.0x10-15
3.0x10-15
9.0x10-14
5.6x10-14
6.4xl0-15
3.5x10-16
l.lxl0-13
1.7x10-13


HB1
HB2 (B)
HB3
HB4
HB5 (A)
HB6


HL1
HL2
HL3
HL4
HL5
HL6
HL7
HL8
HL9
HL10


HFO
HF1
HF2
HF3
HF4
HF5
HF6
HF7
HF8
HF9
HF10


0.78
0.71
0.52
0.44
0.40
0.29


0.94
0.73
0.59
0.42
0.41
0.32
0.35
0.52
0.69
0.83


0.082
0.13
0.17
0.20
0.29
0.35
0.40
0.44
0.52
0.57
0.71












III. EXPERIMENTAL METHODS


Experimental tools employed in this study include current-voltage

(I-V) measurement, a. c. admittance measurement, capacitance-voltage

(C-V) measurement, thermally stimulated capacitance (TSCAP)

measurement, and deep level transient spectroscopy (DLTS) measurement.

From these measurements, one can determine the diode characteristics

and the defect parameters such as defect energy levels, defect

densities, and capture cross sections. Each of these measurement

techniques is described as follows:



3.1. Current-Voltage (I-V) Measurement


Measurement of the current-voltage (I-V) characteristics under

forward bias condition can yield useful information concerning the

conduction mechanisms, recombination processes in the space charge

region of a p-n junction diode or a Schottky barrier diode. For a

good p-n diode with no surface leakage, the total current is composed

of the diffusion current in the quasi-neutral region (QNR) and the

recombination current in the space charge region (SCR). When bulk

diffusion current component dominates, the current expression is given

by [34]


If = Id [exp(Va/VT) 1] (3.1)


where Va is the applied voltage; VT = kT/q; and Id is the magnitude of

a saturation diffusion current.









Id = qni2 A [(Dn/LnNa) + (Dp/LpNd)] (3.2)

where nj is the intrinsic carrier density; A is the diode area; Dn

(Dp) is the diffusion constant for electrons (holes); Ln (Lp) is the

diffusion length for electrons (holes); and Na (Nd) is the acceptor

(donor) density. If bulk generation-recombination current dominates,

then the current expression is given by [34]


Ir = Irg exp(Va/2VT) (3.3)

where Irg is the magnitude of a saturation generation-recombination

current.


Irg = qniW / 2Te (3.4)

In Eq.(3.4), W denotes the depletion layer width; e (Tn T )1/2 is

the effective carrier lifetime in the space charge region; [35] Tn (p)

is the lifetime of electrons (holes), defined by


Sn = 1 / (Nto n ) (3.5)


where Nt is the trap density; on (o p) is the capture cross section

for electrons (holes); is the average thermal velocity.

The total current can be expressed as


It= If + Ir = Io exp(Va/m*VT) (3.6)

where I is the saturation current; m is the ideality factor. The

diode ideality factor, m can be used to identify the dominant

current component in a p-n diode. Inspection of Eqs.(3.1) and (3.3)

shows that the bulk diffusion current depends more strongly on

temperature than the recombination current in the junction SCR. Since










the recombination current in the junction SCR is inversely

proportional to the effective carrier lifetimes (and hence directly

related to the defect density in the transition region), measurements

of I-V characteristics under forward bias conditions would allow us to

determine the effective lifetimes in GaAs cells.



3.2. A. C. Admittance Measurement


A useful experimental tool for evaluating shunt (R) and series

resistance (Rs) of a p-n junction diode is by using a. c. admittance

measurement techniques. [36] A p-n junction diode can be represented

by a three element device with shunt resistance, junction capacitance,

and series resistance, as shown in Fig. 3.1. Measurements of the

admittance as a function of frequencies (i.e., 110 kHZ to 700 MHZ)

will enable us to determine Rs, R, and C of the diode. The impedance

of a p-n diode is given by


Z(w) = Rs + (Rp(/jwC) / [Rp + (i/jwC)]}

= RD(w) + jX(w) (3.7)
where

R(w) = Rs + [Rp/(l+w2C2R2)] (3.8)

XD(w) = RpWC / (+w2C2Rp2) (3.9)


The admittance is the inverse of the impedance in a p-n junction

diode, which is given by


Y(w) = 1/Z(w) = {RD(w) / [RD2(w) + XD2(w)

j{XD(w) / [RD2(w) + XD2(w)]} (3.10)





























Figure 3.1 A three element equivalent circuit model for a p-n
junction diode.


-~--N









In the low frequency and high frequency limits,


w + 0, Re Y(w) = 1 / [Rp + Rs] (3.11)

w -=, Re Y(w) = 1 / Rs (3.12)


Thus, from a plot of the Im Y(w) vs. Re Y(w), the series resistance

and shunt resistance of the diode can be determined. The a. c.

admittance technique can be very useful in evaluating the shunt

leakage problems in a p-n diode and allows accurate determination of

the Rs, Rp, and C over a wide range of frequencies.



3.3. Capacitance-Voltage (C-V) Measurement


The capacitance-voltage (C-V) measurement can be used to

determine the background doping concentration in the n- or p-GaAs

epitaxial layers using a Schottky barrier structure or a one-sided

abrupt p+-n (or n+-p) junction. The depletion capacitance across the

Schottky barrier diode is given by


C(Vr) =E sA / W = A {qESNd / [2(0j + Vr kT/q)]}1/2 (3.13)


where a is the dielectric constant of GaAs; (i is the built-in

potential; and Vr is the applied reverse voltage. Equation (3.13)

shows that the depletion capacitance of a Schottky diode is

proportional to the square root of dopant concentration and inversely

proportional to the square root of the applied voltage. If the

inverse of the capacitance square (C-2) is plotted as a function of

the reverse bias voltage Vr, then, the background concentration, can

be calculated from the slope of C-2 vs V using the following

expression











C-2(Vr) = [2 / (qe SA2N)] (D j + Vr) (3.14)


The intercept of C-2 vs. Vr plot with the voltage axis yields values

of dj which is related to the barrier height of a Schottky diode by


Bn = J + V + kT/q -A 4 (3.15)

where

Vn =Ec (kT/q) In(Nd/Nc) (3.16)


and A $ is the image lowering potential of a Schottky diode; Nc is

the density of state in the conduction band.



3.4. Thermally Stimulated Capacitance (TSCAP) Measurement


Another interesting experiment, which is known as the thermally

stimulated capacitance (TSCAP) measurement technique [37,38] will be

described in this section. The TSCAP experiment is carried out by

first reverse biasing a p-n diode or a Schottky diode, and then the

diode is cooled down to the liquid nitrogen temperature (770k). After

temperature reaches 770K, the diode is momentarily zero biased to fill

the majority carrier traps and returned to reverse bias condition, and

the temperature is then raised from 77 to 4000 K. The thermal scan of

capacitance vs temperature plot is taken by an X-Y recorder. A

capacitance step is observed from the C vs T plot if majority or

minority carrier emission is taking place in a trap level with a

certain temperature range. The amplitude of this capacitance step is

directly proportional to the trap density. The trap density for n-

GaAs can be calculated from the following expression











Nt = Nd(2 AC / CO) (3.17)


where CO is the depletion layer capacitance and AC is the capacitance

change due to the majority or minority carrier emission. Thus,

knowing Nd (or Na) and Co at the temperature where the capacitance

step was observed, the trap density can be calculated from Eq.(3.17).

Note that Eq.(3.17) is valid only for the case when Nt < 0.1 Nd. For

the case of large trap density with Nt > 0.1 Nd, a more exact

expression should be used instead.



3.5. DLTS Measurement


The Deep-Level-Transient-Spectroscopy (DLTS) experiment is a high

frequency (20 MHZ) transient capacitance technique, which was

introduced first by Lang in 1974. [7,14] The DLTS scan displays the

spectrum of deep level traps in the forbidden gap of a semiconductor

as positive or negative peaks on a flat baseline as a function of

temperature. Although this kind of measurement is time consuming, it

offers several advantages such as being sensitive, easy to analyze and

capable of measuring the traps over a wide range of depths in the

forbidden gap.

Figure 3.2 shows the schematic block diagram of a DLTS system

used in this study. The DLTS system consists of a sensitive

capacitance measurement apparatus with good transient response, a

pulse generator, a boxcar with dual-gated signal integrator, an X-Y

recorder, and temperature control system for heating and cooling. By










1-


I15 XY x
Wide Band
Lo|Am plifier Recorder







S Device


Figure 3.2 The block diagram of the DLTS system.









properly changing the experimental parameters it is possible to

measure the following parameters:

-The minority and majority carrier traps.

-The activation energy of each defect level.

-The defect concentration which is directly proportional to

the peak height.

-The defect concentration profile.

-The electron and hole capture cross sections for each trap.



3.5.1. Principles of the DLTS Technique


The capacitance transient is associated with the return to

thermal equilibrium of the carrier occupancy in a trap level following

an initial nonequilibrium condition. The polarity of the DLTS peak

depends on the capacitance change after trapping the minority or

majority carriers. Because an increase in trapped minority carriers

in the SCR would result in an increase in the junction capacitance,

the minority carriers trapping will produce a positive polarity peak,

and vice verse. For example, in a p+n junction diode, the SCR extends

mainly into the n-region, and the local charges are due to positively

charged ionized donors. If a forward bias is applied, the minority

carriers (holes) will be injected into this region. Once the holes

are trapped in a defect level the net positive charges in such region

will increase. This results in a narrower SCR width which implies a

positive capacitance change. Thus, the DLTS signal will have a

positive peak. Similarly, if the majority carriers are injected into

this region and captured by the majority carrier traps, which reduces

the local charges, the SCR width will be wider, implying a decrease of









the junction capacitance. Therefore, the majority carriers trapping

will result in a negative DLTS peak. The same argument can be applied

to the n+p junction diodes. All of the samples used in the DLTS

measurements are p+n diodes so that a positive peak represents the

hole trap and a negative peak represents the electron trap.



3.5.2. Minority Carrier Injection


Figure 3.3 shows the injection of minority carriers. Figure

3.3(a) is the injection pulse where V=Vp > 0 during the pulse (ta < t

< tb) and V = VR < 0 outside the time interval (ta, tb). Figure

3.3(b) is a simplified energy band diagram (the band bending due to

the junction electric field is omitted) in quiescent reverse bias

condition (t < ta). Figure 3.3(c) is the saturating injection pulse

(ta < t
filled by holes. Figure 3.3(d) is the transient process during the

period (t>th); the capacitance transient is due to the trapped holes

begin to emit from the trap centers to the valence band by the built-

in electric field.



3.5.3. Majority Carrier Injection


Figure 3.4 shows the injection of majority carriers. Figure

3.4(a) is the injection pulse where V = Vp = 0 during the pulse (ta <

t < tb) and V = VR < 0 outside the time interval (ta, tb). Figure

3.4(b) is a simplified hand diagram in quiescent reverse bias

condition (t < ta). Figure 3.4(c) is the majority carrier injection.

During the pulse period (ta < t < tb), the majority carriers were


















Ia Ib


P++-- -'----- ---E, N

00b 00
b : a:n


--- N

000

C(I)






i-L i


AC(O)


II,


0
C : t Ib


Figure 3.4 The process of majority carrier injection.










injected into the SCR and captured by the majority trap. Figure 3.4(d)

is the transient process for the period (t > tb) in which the captured

electrons begin to emit from the trap centers to the conduction band

and then they are swept out of the SCR by the built-in electric field,

resulting in the observed capacitance transient.



3.5.4. Defect Concentration


The defect concentration is directly proportional to the peak

height as described before, and the peak height is proportional to the

capacitance change A C(0) [ AC(0) is shown in Fig. 3.3(d) and 3.4(d)].

Therefore, the defect concentration Nt is proportional to A C(0) to be

derived as follows: Let C(t) is the capacitance transient[39,40]

which proportional to electron (hole) emitted to the conduction

(valence) band. Then,


C(t) = Aq Es [Nd Ntexp(-t/T)] / [2(Qit + Vr + kT/q)]}1/2

= Co {l [Ntexp(-t/r) / Nd]}1/2 (3.18)


where t is time; T is the carrier emission time constant; Co = C(Vr),

as shown in Eq. (3.13), is the junction capacitance at the quiescent

reverse bias condition. Using binomial expansion and the condition

that Nt/Nd << 1, Eq. (3.18) reduces to a simple form as


C(t) = Co [1 Ntexp(-t/r)/2Nd] (3.19)


Equation (3.19) can be rewritten as


Ntexp(-t/t) = (2AC(t) / CO) Nd


(3.20)









where A C(t) = Co C(t). From the DLTS technique, AC(0) can be

measured. The junction capacitance Co and the background

concentration can be obtained from C-V measurements. Thus, the defect

concentration Nt can be calculated easily by using Eq.(3.20) at t=0.



3.5.5. Activation Energy of the Defect Level


As shown in Fig. 3.5,A C(t) begins to decay after the injection

pulse is over. The decay associates with a specific time constant

which is equal to the reciprocal of the emission rate. For an

electron trap, the emission rate "en" is a functions of temperature,

capture coefficient and activation energy, and can be expressed by
[41,42]


en = (OnNc / g) exp[(Ec Etj)/kT] (3.21)


where Eti is the activation energy of the trap; g is the degeneracy

factor; an is the electron capture cross section which is temperature

dependent [43


a n = o" exp(- AEb/kT) (3.22)


where o, is the capture cross section at very high temperature; AEb is

the activation energy of the capture cross section for the trap. The

emission rate can be written as


en = BT2 exp{[Ec (Eti +A Eb)] / kT)

= BT2 exp [(Ec Em) / kT] (3.23)











AC(t)


T1

r2



T >T
2 1


Figure 3.5 The transient capacitance decay
the injection pulse is over.


exponentially after










where B is the proportionality constant and is independent of

temperature. From this relation, en increases with increasing

temperature. The capacitance transient is rearranged from Eq.(3.19)

as


C(t) = Co(Nt / 2Nd) exp(-t/T)

= AC(0) exp(-t /T ) (3.24)


where T = e -1. Equation (3.24) implies a faster decay of 6 C(t), as

is shown in Fig. 3.5, at higher temperature and a smaller decay time

constant which implies a faster decay of AC(t) as shown in Fig. 3.5.

The same argument can also be applied to the hole trap. The only

difference is that AC(t) has an opposite polarity.

The following is the procedures to deduce the activation energy

of a defect level. We first set tI and t2 in a dual-gated integrator

boxcar, then we can write


C(tl) = C(0) exp(-t1 /T) (3.25)

C(t2) = C(0) exp(-t2 /T) (3.26)


The DLTS scan along the temperature axis is obtained by taking the

difference of Eqs. (3.25) and (3.26) which yields


S( r) = 6 C(0)[exp(-tl / ) exp(-t2 /T )] (3.27)


The maximum emission rate, T max -, is obtained by differentiating

S(T) with respect to T, and let it equal to zero [dS(r ) / d = 0].

The result yields


Smax = (t t2) / n(tl/t2)


(3.28)




29




Under this condition, S(T ) reaches its maximum value at a specific

temperature. The emission rate is given by en = 1 / Tmax for each tl

and t2 setting. By changing tI and t2 several times, a set of

temperatures that correspond to this set of rmax (or emission rate en)

can be obtained as shown in Fig. 3.6. The activation energy of the

trap can be calculated from the slope of the Arrhenius plot [i.e.,

In(en/T2) vs. 1/kT].































150 200 250 300 350 400
T (K)


Figure 3.6 The DLTS thermal
rate windows.


scan of a 100 keV, 1012 p/cm2 proton irradiated sample with different











IV. DETERMINATION OF POTENTIAL WELL OF DEEP-LEVEL TRAPS USING FIELD
ENHANCEMENT EMISSION RATE ANALYSIS OF NONEXPONENTIAL DLTS IN GAAS


Deep-Level Transient Spectroscopy (DLTS) signals are often

analyzed assuming that the capacitance transient is exponential.

However, most of the DLTS signals are nonexponential transient.
[15,16] Nonexponential capacitance transients may occur from (1) the

electric field dependent emission rate of the trapped charge, [44,451

(2) multiexponential decay due to several trap levels with similar

emission rates, and (3) trap density of the same magnitude as that of

the shallow dopant density. [46,47] This chapter will deal with cases

(1) and (2).

To determine the nonexponential capacitance transient due to

electric field dependent emission rate of the trapped charge, Makram-

Ebeid, [48,49] Wang and Li [50,51] have measured the field enhancement

emission rate. In this chapter, we present the theoretical analysis

of nonexponential capacitance transients due to the electric field

dependence emission rate of trapped charge and multiexponential decay.

Emission rate of trapped charge carriers is enhanced by the Poole-

Frenkel effect and phonon-assisted tunneling effect in the presence of

an applied electric field. Since the electric field varies with

position within the depletion region of a reverse biased p-n junction,

the emission rate is not constant within the same region. The DLTS

response due to the nonuniform emission rates can in general be

expressed by S(r) = E exp(-enjtl) E exp(-enjt2). Based on the

nonexponential capacitance transient, theoretical calculations of DLTS

response for the deep-level traps in GaAs are made using five










different potential wells; namely, the Coulombic potential well which

has a positive charge state for the empty state, the Dirac well,

square well, polarization well as well as dipole well which all have a

neutral charge state from different physical origins. A comparison of

the theoretical calculations of nonexponential DLTS response with the

DLTS data for each trap level would allow us to determine the

potential well for the trap involved. This model was applied to the

calculations of potential well for the EL2 level and other electron

traps in GaAs. We found that the EL2 electron trap was due to

Coulombic potential well with a double charge state (i.e., AGa++).

Details of the results are discussed in this chapter.



4.1 Capture and Emission process at a Deep-Level Trap


In the study of electric field dependence of emission rate, it

is important to know the charge state of a trap so that the type of

potential well for such a trap can be determined. The charge state of

a deep-level trap may be either positively charged, neutral, or

negatively charged [10] (i.e., Nt+, Nt or Nt-). For example, if an

electron is captured by a positive donor trap, then the kinetic

equation for the capture process requires that


Nt+ + e = Nto (4.1)


In this case, the capture process is Coulomb attractive. Similarly,

the emission process for the same trap can be written as


Nt = N t+ + e


(4.2)








which again is an attractive process. This attractive capture-

emission process is the feature of a Coulombic potential well. In

GaAs, for example, the deep-level defects such as arsenic vacancy
[52] (VAs) and arsenic antisite [13] (AsGa++) defects have a Coulombic

potential well.

For an empty neutral trap with Nt the capture process is

given by


Nt + e = Nt (4.3)


and the emission process for the same trap is given by


Nt- = Nt0 + e (4.4)


The potential wells for a deep-level neutral trap in a semiconductor

may include Dirac delta potential well, [531 square potential well,

polarization potential well and dipole potential well. [54] The Dirac

delta potential well does not show Poole-Frenkel effect. Neutral

arsenic vacancy (VAs,) defect in a GaAs crystal behaves as a Dirac

delta potential well in the capture-emission process. For the square

potential well, a potential well has a depth of Vo for r < ro and

zero for r > ro. Deep-level defects such as neutral arsenic

interstitial (Asi ) have these characteristics. The potential of a

polarization potential well has the form V(r) = A1 / r4, where

Al = e2 ai / 8E0o52; aj is the polarizability of a neutral impurity

atom, and Es is the relative dielectric constant of the host crystal.

Lax[55] used a polarization potential well to model capture of

electrons and holes by neutral impurities. Tasch and Sah 44] used

this potential well to model the observed field dependence of Au in









silicon. A neutral impurity trap such as AlGao has the properties of

a polarization potential well. A complex of two oppositely charged

centers, each with charge magnitude of Zq, will form a dipole

potential well. The potential is represented by a dipole potential,

V(r) = qr- / 4c0 er with a dipole moment given by P = Z q R ,

where R, is the distance separating the two charge centers. The

antisite pair defect (ASGa +GaAs-) behaves as a dipole potential

well in the capture-emission process.

For the process Nt- + e = Nt--, the trapping process is repulsive

and the trap in Nt- state has a Coulombic energy barrier that the

electron must surmount thermally or tunnel through. Thus one may

expect its capture cross section to be very small (, 10-21 cm2 or

less) and with a strong temperature dependent property.

In DLTS technique, [7,14] electrons captured by trap level

occurred in the quasi-neutral region (QNR) of a p-n diode which has

zero electric field, as shown in Fig. 4.1(a). On the other hand,

electrons emission from a trap level usually take place in the space-

charge region (SCR) of a p-n diode in which high electric field

prevails in this region, as shown in Fig. 4.1(b). The effect of

electric field on the emission process is to enhance the emission rate

by either Poole-Frenkel effect or phonon-assisted tunneling effect to

be discussed in next section. The emission rate enhanced by the

electric field will cause the DLTS response to be nonexponential

transient.




















- - - - - - r -


a:Capture Process


b: Emission Process


Figure 4.1 (a) Electrons captured by trap level are occurred in the
quasi-neutral region of a p-n junction.

(b) Electrons emission from a trap level usually take
place in the space charge region of a p-n junction.









4.2 Overview of the Theory


The emission rate is based on the detailed balance expression,
[41,42] and under zero electric field condition, Eq. (3.23) is

rearranged as


eno = en exp(- Eti/kT) (4.5)


where Etj is the ionization energy of the trap level, and en~ contains

the matrix elements of the transition. Figure 4.2 shows a trap level

under high electric field. There are three basic mechanisms [54]

which affect the emission rate enhancement under high electric field

conditions.

(1) Poole-Frenkel effect, in which electrons climb over a

barrier lowered by the presence of applied electric field.

(2) Phonon-assisted tunneling effect, in which electrons absorb

thermal energy from the lattice, and then tunnel through the

barrier at a higher energy.

(3) Pure quantum mechanical tunneling effect. Since pure

tunneling becomes important only at very high electric fields [56]

(i.e. F > 107 V / cm), we will not consider this effect in our DLTS

analysis.



4.2.1 Poole-Frenkel effect


The Poole-Frenkel and Schottky lowering effects are due to the

lowering of a Coulombic potential barrier by an applied electric

field. The Schottky effect[34] is associated with the lowering of

barrier height of a metal-semiconductor contact. The Poole-Frenkel


















qFr cosO
\/


-Eti


Eti




Eth
SL.


rmax


Phnon assisted
tunneling
SEmission


Figure 4.2 There are three basic mechanisms which affect the emission
enhanced under high field conditions.









effect is associated with the lowering of potential barrier in a deep-

level trap of a bulk semiconductor. Both donor and acceptor traps

would show the Poole-Frenkel effect. The enhancement of emission rate

from a Coulombic potential well due to the Poole-Frenkel effect was

first done in a one-dimensional model by Frenkel, [57] and later

extended to three-dimensional case independently by Harke [58] and

Jonscher. [59] A similar calculation for the polarization well and

dipole well was done by Martin et al.. [54]

In this section we will consider the general case for calculating

the emission rate enhancement due to Poole-Frenkel effect. The

potential for a deep-level trap in an electric field, F, can be

expressed by


VT(r) = V(r) q F r cos(8) (4.6)


where V(r) is the potential of a deep-level trap. For 0 < e < r/2, the

minimum potential was found by setting dVT(r)/dr = 0 at r = rmax.

The lowering of potential barrier due to the presence of an applied

electric field is found by evaluating VT(r) at r = rmax. Thus,


A Eti () = VT(rmax) (4.7)


A one dimensional result is given by setting 6 = 0. The Poole-Frenkel

effect leads to a decrease of the ionization energy, and the one

dimensional thermal emission rate, enl, in the presence of an electric

field can be written as


enl = eno exp[-(Etj Eti) / kT]

= enoexp( A Etj/kT) (4.8)









where eno is the thermal emission rate at zero electric field given by

Eq. (4.5). The three-dimensional calculation requires an integration

over a due to the spatial variation of A Eti (6). For 0 < 6
emission rate is proportional to 6, and for r/2 < < i, it is

assumed that the emission rate does not change with electric field.

Thus,

2, -/2 2 T a
en3/eno=(l/47T)[ I dyJ sin(&exp(A E/kT)d +1 d4 I sin(e)de]
0 0 0 2/2
(4.9)


where en3 is the three dimensional thermal emission rate.



4.2.2 Phonon-assisted tunneling effect


There are several different types of potential wells which may

exist in a deep-level trap, depending on the charge state of a

particular trap. The potential well may be affected by an external

electric field. Figure 4.3 shows a potential well for a trap level

with energy of Eti as a function of the radial coordinate. A trapped

electron can absorb a phonon and tunnel through the barrier. The

tunneling process can be treated by using the WKB [60] (Wentzel-

Kramers-Brillouin) approximation for the potential barrier. The

probability ratio, [61] (or the barrier penetration factor, P) for an

electron impinging on the barrier is given by

x2
P = exp[-2 f k(x) dx]
x2
= exp{-[(8m)1/2 / 2] [V(x)-E]l/2dx} (4.10)
xI






















V(x)


a


0 x x
1 2


Figure 4.3 A trapped electron can absorb a 9honon and tunnel through
the barrier.









where k(x) = [(2m)1/2/] x [V(x)-E]1/2 is positive when V(x) > E. The

potential well for the trap level is V(x). The electron energy is E.

The two turning points, xl and x2, are the fixed points for which

electron energy is equal to the barrier energy of the potential well

for the trap.

A trapped electron can absorb a phonon with energy of exp(-

Eth/kT) and tunnel through the barrier at a higher energy. The

probability of this composite event is


Pc = exp(-Eth/kT) P (4.11)


where Eth is the thermal excitation energy or phonon energy; and P is

given by Eq. (4.10). The emission rate due to phonon-assisted

tunneling effect is given by integrating Eq. (4.11) over the phonon

energy, Eth*


ent = EtITc dEth / kT (4.12)
0

where 1/kT is a normalization factor. The normalized emission rate

enhancement is obtained by dividing Eq.(4.12) by the zero electric

field emission rate en0, which yields

Etj /kT
ent / eno = exp(Etj/kT) Pc dEth / kT
0

= exp[(Eti-Eth)/kT] I Et/kTexp{ [-(8m)1/2/W]
0
x2
I [V(x)-E]dx dEth / kT} (4.13)
x1
Equation (4.13) is a general expression for the emission rate

enhancement due to phonon-assisted tunneling effect.









The total emission rate enhancement is obtained from the sum of

Poole-Frenkel effect and phonon-assisted tunneling effect. From

Eqs. (4.9) and (4.13), one obtains


enH = eno ( en3 + ent ) (4.14)


Vincent et al. [53] and Martin et al. [54] showed that for a Coulombic

well and other potential wells, both the Poole-Frenkel effect and

phonon-assisted tunneling effect, are important over the field range

of interest (104 106 V/cm at 3000 K). Our results are in good

agreement with this observation, as will be shown next.



4.3 Theoretical calculations of the emission rate enhancement
for different potential wells



4.3.1 Coulombic potential well


A donor type electron trap, which has a Coulombic potential well,

is positively charged, Nt+ when it is empty. The capture (emission)

process for a such trap is given by Eqs. (4.1) and (4.2). Assuming an

electron is at a distance, r, from the trap, the attractive force

between a positive trap and the electron is given by


F(r) = -q2 / 4 sosr2 (4.15)


The potential for the trap is obtained by integrating Eq. (4.15) from

infinity to r. Thus,

r
V(r) = I F(r) dr = -q2 / 4 r Eocsr (4.16)
oos









When an external field, F, is applied, the total potential energy as a

function of distance is given by


VT(r) = -q2/4 ioe sr qFrcos() (4.17)


Electron traps such as As vacancy (VAs ) and As antisite (AsGa++)

defects have Coulombic potential well for electrons. Equation (4.17)

can also be applied to an acceptor type hole trap, which also has a

Coulombic potential well. In this case, the Coulombic potential well

is negatively charged when it is empty. The capture process for such a

hole trap is


Nt- + h = Nt (4.18)


and the emission process is


Nto = Nt- + h+ (4.19)


Hole traps such as Ga vacancy (VGa-) and Ga antisite (GaAs-) defects

have a Coulombic potential well for holes. Compared to other types of

potential wells, a Coulombic potential well shows a very large Poole-

Frenkel effect.



4.3.1.1 Poole-Frenkel effect


The Poole-Frenkel lowering potential Eti and the location of

lowering rmax are given by the condition dVT(r)/dr = 0, or


rax = {q / [4 7 EOESF cos(B)]}1/2
S(4.20)
AEtj = q [ q F cos(9) / ( n EOES)]l/2










The Poole-Frenkel effect leads to a decrease of ionization energy

Eti, and the one-dimensional thermal emission rate can be written as


enl = enoexp(A Eti/kT) (4.21)


For a three-dimensional case, the emission rate of a trapped electron

may be obtained by assuming that emission rate is field dependent for

0 < e < t/2 and is independent of electric field for /2 < 0 < ir.

Thus,


en3 = (o/4 ) [I I sin(9) exp(AEtj/kT)de d(
2 -r /2
+I f sin(e)de d ( ] (4.22)
0 0

Integrating Eq. (4.22), and the result is


en3/eno = (1/R2) [eR(r-l) + 1] + 1/2 (4.23)

where


R = q (qF/r EOES)1/2 / kT = Eti /kT (4.24)



4.3.1.2 Phonon-assisted tunneling effect


The phonon-assisted tunneling effect may be evaluated by

substituting Eq. (4.17) to Eq. (4.13). Vincent et al. 153] have

obtained a closed form for the phonon-assisted tunneling effect for a

Coulombic potential well, which reads

(Eti- AEti)/kT
ent/eno = I exp{z z3/2[4(2m)1/2(kT)3/2
0


/ 3qVF] [1 (AEti/zkT)5/3]} dz


(4.25)










The total emission rate is composed of Poole-Frenkel effect and

phonon-assisted tunneling effect


enHC = eno (en3 + ent) (4.26)


Figure 4.4 shows the normalized enhanced emission rate vs. electric

field for the Coulombic potential well for the Ec 0.83 eV electron

trap observed in GaAs. The Poole-Frenkel effect dominates when

electric field is lower than 2 X 104 V/cm, while the phonon-assisted

tunneling effect becomes important for electric fields higher than 2 x

104 V/cm.



4.3.2 Dirac delta potential well


The potential for a Dirac delta well is given by


V(r) = -Vo for r = 0
(4.27)
= 0 for r t 0


In the presence of an applied electric field, the potential is given

by


V(r) = -Vo qFr cos(8) for r = 0
(4.28)
= 0 qFr cos(e) for r t 0


A neutral vacancy trap such as neutral arsenic vacancy (VAs0) may have

a Dirac potential well. For this potential well, the Poole-Frenkel

lowering potential is equal to zero, and only the phonon-assisted

tunneling effect is considered. For the case of a one-dimensional

















M 3.Puole-Frenkel

.1100-
N-




1 2



10








1


4 8 12 16

F (104 V/cm)
Figure 4.4 Normalized emission rate enhancement vs. electric field
for the Coulombic potential well for EL2a electron trap
for phonon-assisted tunneling effect and Poole-Frenkel
effect.


-tU









calculation, cos( ) is equal to 1, and the emission rate enhancement

is obtained by substituting Eq. (4.28) to Eq. (4.13), which yields

Eti /kT
ent/eno = {exp[(Etj-Eth)/kT] }; {exp [-(8m)12/
0

[ (-qFx + Et Eth)1/2 dx] dEth / kT} (4.29)
xl

Equation (4.29) gives an analytical form for the transparency of

triangular barrier of a Dirac well. For the triangular well, xI = 0

and x2 = (Eti Eth) / qF. Integrating Eq. (4.29) over Eth and

letting z = (Etj Eth) / kT, we obtain the enhanced emission rate for

the phonon-assisted tunneling effect

Eti/kT
ent / eno = f exp{z z3/2[4(2m)1/2(kT)3/2/3q$F] } dz
0
(4.30)


The total emission rate due to Dirac well can be expressed by


eHR = eno ( 1 + et) (4.31)


4.3.3 Square Potential Well


The same treatment can be applied to the square well. The

potential of a square well in the presence of an applied electric

field is


V(r) = Vo qFr cos () for r < r
(4.32)
= 0 qFr cos(8) for r > ro


where ro is the radius of the trap. A neutral interstitial trap such

as neutral arsenic interstitial (Asj0) may have such a potential well.


11/








The barrier lowering due to Poole-Frenkel effect is equal to qFro.

The enhanced emission rate for a one-dimensional and a three-

dimensional Poole-Frenkel effect is given respectively by


enl/eno = exp(R)
(4.33)
en3 / eno = (1/2R) x [exp(R) 1] + 1/2


where R = qFr,/kT.

For the enhanced emission rate due to phonon-assisted tunneling

effect, Eq. (4.29) is still valid. In a square well, xl = ro and x2 =

(Etj Eth)/kT. The range of phonon energy, Eth is from 0 to (Eti -

LEti) / kT. Thus, we obtain an expression for the normalized enhanced

emission rate due to phonon-assisted tunneling effect:

(Eti- SEt )/kT
ent/ eno = exp{z-z3/2[4(2m) 1/2(kT) 3/2/3qWF]
0

[1 (qFr/zkT)3/2]} dz (4.34)


The total emission rate is the sum of Eqs. (4.33) and (4.34)


enHS = eno (en3 + t) (4.35)


4.3.4 Polarization potential well


An electron with charge, e, at a distance r from a trap center

with polarizability ,a j, will induce a dipole moment, p = aie/ sr2.

This dipole will produce an attractive force on the charge of

pe / (2 E0 e sr3) = aje2 / (2 e0 s2r5). Thus, the attractive

potential is given by


V(r) = -A1 / r4


(4.36)









where

Al = aje2 / (8 a oEs2)


The polarizability of the atom can be expressed by


oj / aH = (mn/m) ( EH/Eti)2 (4.37)


where Etj is the ionization energy of the trap; EH = 13.6 eV is the

ionization energy of a hydrogen atom; = 0.666 X 10-24 cm3 is the

polarizability of a hydrogen atom; a. is the polarizability of the

trap; mo is the free electron mass; and m is the effective electron

mass. Lax [55] used the polarization potential well to model

capture of electrons and holes by neutral impurities. Tasch and Sah
[44] used this potential well to model the observed field dependence

emission rate of Au in silicon. A neutral impurity trap such as AlGa

has the properties of a polarization potential well. In the presence

of an electric field, the total potential of the polarization well is

given by


VT(r) = -A1 / r4 qFr cos(8) (4.38)



4.3.4.1 Poole-Frenkel effect


The minimum potential is obtained by setting dVT(r)/dr = 0 at r =

rmax, and the result is given by


rmax = [4A1 / qFcos(8)]11/5
(4.39)
AEtj = -1.649 A 1/5 [qFcos(e)]4/5


Emission rate is field dependent for 0 < e < n/2 and is independent of

electric field for i/2








emission rate due to Poole-Frenkel effect can be written as


enl/eno = exp(R) (4.40.a)


for the one dimensional case, and

1
en3/eno = (1/2) x [1 + (5/4) x j Rtl/4exp(R) dt] (4.40.b)
0

for the three dimensional case. Where R = 1.649 Al/5 (qF)4/5 / kT



4.3.4.2 Phonon-assisted tunneling effect


Substituting Eq. (4.38) into Eq. (4.13) and letting z = (Eti -

Eth)/kT yields the normalized enhanced emission rate due to phonon-

assisted tunneling effect:

(Et- &Eti)/kT
ent/eno = I exp{z [(8m)1/2/$] (-Al/r4
0

qFx + zkT)1/2 dx} dz (4.41)


Numerical integration can he carried out by assuming xl = (A1 /

zkT)1/4 and x2 = zkT/qF. The total enhanced emission rate is


enHP = eno (en3 + ent) (4.42)


Note that integrals given in Eqs. (4.40) and (4.41) can not be solved

analytically. The numerical calculations of the enhanced emission

rates as a function of the electric field were shown in Fig. 4.5 for

Ec 0.83 eV trap in GaAs at 3000 K. The Poole-Frenkel effect is

dominant when electric field is lower than 4 x 104 V/cm, while the

phonon-assisted tunneling effect becomes important for electric field

greater than 4 x 104 V/cm.


















=10



m 2

" C 3




E L2 a
1 Polarization well

2 Phonon assisted
3 Poole Frenkel
1-- -


4 8 12 16 20
F (104 V/cm)
Figure 4.5 Normalized emission rate enhancement vs. electric field
for EL2a electron trap in GaAs for phonon-assisted tunneling
and Poole-Frenkel effects.











4.3.5 Dipole potential well


The dipole potential can be represented by a trap center with two

oppositely charged ions, each with charge Zq.


V(r) = r. / 4 7 E oSr2 (4.43)


where is the dipole moment, p = ZqRo; RO is the distance between two

oppositely charges. Antisite pair defect (AsGa +GaAs--) behaves as

the dipole potential well in the capture-emission process. As is

shown in Fig. 4.6, if the applied electric field, F, forms an angle

6 F with z axis, and is polarized along the z direction, then the
total potential becomes


VT(r) = -qPcos(6)/(41 COEsr2) qFr sin (6F)sin (9)cos (1)

qrF cos(%F)cos(6) (4.44)



4.3.5.1 Poole-Frenkel effects


The mininum potential is obtained by setting dVT(r)/dr = 0, which

yields


rmax = {[P cos(e) / (2rco0E)] [F sin(e)sin ) cos(4)

+ F cos(9e) os(6) }1/3 (4.45)


and the change in barrier height is given by


Etj(e, ) = -(3 x 2-2/3) x [P cos(e) / (47 Eo]s)1I/3

x [F sin(eF)sin(e)cos(P) + F cos(6F)cos(e)]2/3

(4.46)



































7^-----------------^
y



I I f





X



Figure 4.6 In dipole potential well, external electric field form
an angle eF with the dipole moment.










Unlike other potentials, the dipole potential experiences a barrier

lowering which is field dependent. The integrals fall into two cases

according to the incident angle Fp.


1. Case 1: 0 < 6p < r/2

The barrier is lowered for T/2 < < w/2.

and for 7/2 < 4 <3 7/2, 0 < 9< tan-1[-cot(6F)/cos ()].

The normalized field enhanced emission rate for this case is given

by

T/2 T/2
en3/eno = (1/2 ) d) I sin(e) exp[- AEtj (e,)]de
-n/2 0

37/2 tan-1 -cot(8F)/cos( )]
+ (1/2n ) I d P ; sin(e)exp[-BAEtj ( ,4)]de
n/2 0

3 w/2
+ (1/2Tn) {1 + [cot(eF)/cos( )]2}-1/2 dp
,/2
(4.47.a)


2. Case 2: i/2 <6 < T

The barrier is increased for r/2 < 4 <3 n/2.

and for /2 < 4 < 7/2, 0 < 6< tan-1 [-cot@F)/cos() ].

The barrier is lowered for -V/2 <
< < 7/2.

The normalized field enhanced emission rate for this case is

given by


en3/eno = 1 (1/2, ) j


2 /2
{1 + [cot(eF)/cos()]2}-2 d1
-T /2


T/2 T/2
+ (1/2rn) d t sin(6)exp[- 86&E i(6(,)]d
-1/2 tan- [-cot(eF)/cos ()] (4.47.b)










For BF = 0, the e dependence disappears, and the problem can be solved

analytically. The barrier lowering simplifies to


Etj = -1.9 (p/4 T E s 3)1/3 F2/3 cos(e) (4.48)


and the normalized Poole-Frenkel effect emission rate enhancement is

given by


en3/eno = (/R) x [exp(R) 1] (4.49)


where

R = 1.9 (p/47nosE)1/3 F2/3 /kT



4.3.5.2 Phonon-assisted tunneling effect


For the potential wells studied here, the one-dimensional

analysis was done for 0 = 0, where the Poole-Frenkel barrier lowering

is dominant. For the dipole well, the maximum barrier lowering occurs

at 8= 8m, where 0 < m < F and q = 0. Now, differentiating Eq.

(4.46) for AEti with respect to 0 att = 0, and setting the result

equal to zero, we obtain a solution for 8m


e m = tan-1 [ {[8 + cos2 (F) 1/2

3 cos(6F)} / 2sin(6F)] (4.50)


Substituting Eq. (4.50) into Eq. (4.44) and Eq. (4.44) into

Eq. (4.13), and letting z = (Eti Eth) / kT, the field enhanced

emission rate due to phonon-assisted tunneling effect can be expressed

as










(Et- AEtj)/kT r2
ent/eno =f exp{z [(m) 1/2/Wf] [-qPcos(6m)
0 r1

/(47noESrr-qrF sin(6F)sin(er qrF cos(9%cos(9)


+ zkT]1/2 dr) dz (4.51)


Here r1 = [(qPcosom / (4zirE6EkT)]1/2 and r2 = zkT / {qF [ sin(Q~)

sin(em) + cos(9F) cos(am)] }. The normalized field enhanced emission

rate due to phonon-assisted tunneling effect and Poole-Frenkel effect

can be calculated by numerical method. The results are shown in

Fig. 4.7. Thus, the total field enhanced emission rate is


enHD = eno (en + ent) (4.52)


Table 4.1 summarizes the potential wells for Colombic well, Dirac

well, square well, polarization well and dipole well. Table 4.2

summarizes the one-dimensional and three-dimensional emission rate due

to Poole-Frenkel effect for five different potential wells. Figure 4.8

shows the emission rate vs electric field for the Dirac well, square

well, polarization well and coulombic well as compared with the zero

electric field values. The enhanced emission rate for the neutral

trap with Dirac well, square well or polarization well, has almost the

same value. However, the enhanced emission rate for the Coulombic

well depends very strongly on the electric field.



4.4 Theoretical calculations of the nonexponential DLTS
transient for different potential wells


From the analysis of field enhanced emission rate, the electric

field dependent DLTS response can be calculated. This is discussed as


















10-






N3
a 2

Z EL2a -
1 Dipole well
2 Phonon assisted
3 Poole Frenkel


.1 -

I I I -
4 8 12 16 20
F(104 V/cm)

Figure 4.7 Normalized enhanced emission rate vs. electric field for
EL2a electron trap in GaAs for phonon-assisted tunneling and
Poole-Frenkel effects.








Table 4.1 Summarize the potential, Poole-Frenkel barrier, and rmax
for five different potential well.


Potential well VT(r) AEtj rmax


Coulombic -q2/(4,roEsr)-qFrcos (0) -q{qF/[nEOS] }1/2 [q/(4r cOsF) ]1/2


Dirac V. -qFrcos(B) for r=0 0 0
-qFrcos(B) for r40


Square Vo-qFrcos(0) for r -qFrcos () for r>ro


Polarization -A1/r4 qFrcos () -1.649AI1/5 (qF)4/5 [4A1/qF]1/5



Dipole -qPcos ()/(4TrE s0r2) (3x2-2/3) [Pcos (e)/(4T g Es) ]1/3 {p/[2 Eoo sos() ]
-qFr[sin( (8)snT0)cos( ) x[Fsin( n )sin(6)co~ ~) xF[sin( ) sin(G)cs, )
+cos(eF)cos(e)] + F cos( F)cos ()] +Fcos(6eFcos(e)] }I







Table 4.2 Summarize the enhancement emission rate of one-dimensional and three-dimensional
Poole-Frenkel effect with diagram for four different potential well.

Potential well R en/eno en3/eno Diagram


Coulombic AEtj/kT exp(R) [exp(R) (R-l)+1]/R2 + 1/2





Dirac 0 0 0





Square A Etj/kT exp(R) [exp(R) 1]/(2R) + 1/2






Polarization AEti/kT exp(R) (5/4)I Rt1/4coh(Rt)dt
0











































4 8 12 16 20
F c 04 V/cm)


Figure 4.8 Enhanced emission rate vs. electric field for EL2a electron
trap in GaAs for Coulombic well, Dirac well, polarization
well, and dipole well.









follows: consider a p+n abrupt junction diode, the electric field is

in general spatial dependent within the depletion region, and can be

expressed by


F = Fmax(l x/W) (4.53)


where x is the distance from the junction; Fmax is the maximum

electric field occurring at the metalallurgical junction of the p+n

diode and is given by


Fmax = qNdw /e oSs (4.54)

where W is the depletion width under reverse bias condition.


W = [2OES (Vbi + Vr) / qNd]l/2

= LD[2(Vbi+Vr)/kT 2]1/2 (4.55)


where LD is the extrinsic Debye length and is given by


LD = [0oEskT / (q2ND)11/2 (4.56)

where Vbi is the built-in potential, which reads


Vbi = (kT/q) ln(ND/nj) (4.57)


where ni is the intrinsic carrier density,


ni= (NcNv)1/2 exp(-Eg/2kT)

= 4.9x 1015 (mdemdh/mo2)3/4T3/2 exp(-Eg/2kT) (4.58)


and Eg is the energy bandgap, which is a function of temperature. [411


Eg(T) = Eg(0) -y1 T2 / (T +Y2) (4.59)










where Eg(0) = 1.519eV, Y1 = 5.405 x 10-4 eV/K, and y 2 = 204 for GaAs.

Electrons which are located in the region between W. (i.e., zero bias

depletion layer width) and W (i.e., reverse bias depletion layer

width) will be emitted into the conduction band when an applied bias

is increased from 0 to -Vr, as is shown in Fig. 4.9. The depletion

width in the junction space charge region is first divided into

equally spaced small segments. In each small segment, the electron

trap density and electric field are assumed constant. For each

electric field (Fi) strength, there is a corresponding enhanced

emission rate, eni(Fj). If one assumes that the electron emission is

exponentially transient within each segment, namely, exp[eni (Fi)]t,

then the total emission transient in the depletion width is equal to

the sum of the individual components, which read


E exp[-eni (Fi) t] (4.60)


Therefore, the DLTS signal can be expressed by


S(r) = exp[-eni(F )tl] Z exp[-eni (Fj)t2] (4.61)


where eni is the electron emission rate within each small segment in

the depletion region, as is shown in Eq. (4.14). Values of enj can be

calculated from Eqs. (4.26, 4.31, 4.35, 4.42, and 4.52) for different

potential wells. From Eq. (4.61), it is noted that the DLTS spectral

response is nonexponential. Figure 4.10 illustrates the DLTS response

for the EL2a (Ec-0.83eV) electron trap in GaAs calculated from Eq.

(4.61) for different potential wells and for zero electric field. The

theoretical calculations showed that the location of DLTS signal peak

for attractive or neutral trap is different along the temperature































EL2QL
-1
en=172 s

1. Coulombic well
2. Dirac well
Square well
polarization well
3. Zero electric field


1-
2 3
LI I
300 350 400
T (K)

Figure 4.10 DLTS response for the EL2a level for Coulombic well,
Dirac well, with zero electric field.










axis. For Coulombic potential well, the DLTS signal peak will occur

at the lowest temperature, while for the neutral trap with Dirac well,

square well, and polarization well will produce identical DLTS signals

at the same temperature. Figure 4.11 shows the DLTS spectral response

for the EL2a electron trap for the case of Coulombic well with

single- and double-charge state along with the experimental results.

Figure 4.12 illustates the DLTS signal for the EL2a electron trap in

GaAs for Coulombic well with a double charge states for different

window rates. Compared the theoretical with experiment DLTS spectral

signal will enable us to determine the potential well for the EL2a

electron trap level. Our results showed that the most probable

potential well for the EL2a trap is the Coulombic well with a double

charge states.



4.5 Summary and Conclusions


We have analyzed the nonexponential capacitance transients due to

electric field dependent emission rate of trapped charge of deep-level

traps in GaAs. A comparison of the theoretical calculations of the

nonexponential DLTS response with the DLTS data for each trap level

would allow us to determine the potential well of the trap involved.

This is one of the methods which may be used to identify the physical

origins of the trap in a semiconductor. From the theoretical analysis

of DLTS response, the conclusions are given as follows:

(1). The location of DLTS signal peak for attractive or neutral

trap is different vs temperature. For Coulombic well, the

DLTS signal peak will occur at the lowest temperature, while































c12
-1- -2



EL2Q
c -1
c =e172 s1

1.Coulombic well with
double charge state

2.Coulombic well with
single charge state







300 350 400
T(K)

Figure 4.11 Nonexponential DLTS response for the EL2a trap for
the case of Coulombic well with single and double
charge states.



























EL2Q
Coulombic well with
double charge state
-1
1. e =34.4 s
2. en 86.6
3. en= 172 n

4. en= 344
5. en= 866





1 2 3 4
300 350 400
T (K)

Figure 4.12 DLTS response for the EL2a trap in GaAs for Couloribic
well with a double charge states for five different
emission rates.










for neutral traps such as Dirac well, square well,

polarization well, and dipole well, the DLTS signals have almost

the same shape and the DLTS peak will occur at the same

temperature.

(2). For Coulombic well, the DLTS signal peak for the double charge

state will occur at a lower temperature than that of the single

charge state.

(3). The shape of the DLTS signal is affected by the capture cross

section. For large capture cross section, the narrow shape of

the DLTS response will occur in the low temperature region.

For small capture cross section, the shape of DLTS response

will become broader and move to the higher temperature region.

(4). The DLTS response is proportional to the background

concentration, and reverse bias. Higher background

concentration and higher reverse bias will result in a bigger

emission rate enhanced due to high electric field dependence.

(5). Nonexponential capacitance transient due to electric field

dependence is expected in the high reverse bias condition. Only

in the very low electric field (<103 V/cm) or in the uniform

electric field condition will DLTS response be exponential.












V MODELLING OF GROWN-IN NATIVE POINT DEFECTS IN GaAs


Theoretical modelling of grown-in native point defects in GaAs is

presented in this chapter. Based on chemical-thermodynamic

principles, expressions for the equilibrium defect concentration as

functions of temperature and arsenic pressure during crystal growth

are derived. Thermal kinetic equations are then employed to predict

the possible native defects in GaAs after crystal cooling. For GaAs

grown under As-rich or high arsenic pressure condition, it is shown

that several native defects such as gallium vacancy (VGa), arsenic

interstitial (Asj), arsenic antisite (ASGa), arsenic antisite-plus-

arsenic vacancy (VAsAsGa) and their complexes may be observed in GaAs

material.



5.1 Introduction


GaAs specimens grown by various techniques such as Liquid

Encapsulation Czockraski (LEC), Vapor Phase Epitaxy (VPE), Liquid

Phase Epitaxy (LPE), Metalorganic Chemical Vapor Deposition (MOCVD),

and Molecular Beam Epitaxy (MBE) are known likely to produce different

defect properties in terms of energy levels within the bandgap of a

semiconductor due to differences in the native defects and trace

impurities or impurity complexes. In each of these techniques, the

growth temperature, growth pressure, growth phase, and cooling rate

are usually different. For example, GaAs grown by LPE technique from

a gallium melt is expected to be low in gallium vacancy defects and

high in arsenic vacancy. The LPE GaAs usually contains hole traps









with energy level of Ev + 0.71 eV (B-center), while the VPE GaAs grown

in high arsenic pressure conditions always contains an electron trap

with energy of Ec 0.83 eV (EL2a level). The reason for observing

these trap levels in LPE or VPE GaAs is still not clear.

In this chapter, we shall introduce the chemical-thermodynamic

principles and thermal kinetic equations to interpret grown-in defects

in GaAs. The use of chemical-thermodynamic principles to analyze

point defects in GaAs was proposed first by Logan and Hurle.[52] They

considered the shallow vacancy as well as shallow interstitial levels.

Bublik [62] modified their model, and applied it to the deep vacancy

level. More recently, Hurle [63] used Frenkel defects instead of

Schottky defects for the arsenic vacancy and arsenic interstitial

defects. During crystal growth, both VGa and VAs Schottky vacancy

pairs are important defects for the undoped GaAs. In the present

work, we use VGa and VAs Schottky vacancy pairs with As-Frenkel

defect to calculate the vacancy and interstitial concentrations during

crystal growth. During crystal cooling from high temperature to room

temperature, thermal kinetic is expected to be the dominant mechanism.

Since the formation energy for antisite defect is very low in the

after-growth condition (VGa + Asj = AsGa, H = 0.35 eV), the anti site

defect is likely to be the dominant defect after crystal growth, as

was proposed by Van Vechten. [64]

From the theoretical analysis of GaAs material grown under As-

rich or high arsenic pressure condition [such as LEC, VPE, and MOCVD

techniques], defects such as arsenic interstitial (Asi), gallium

vacancy (VGa), arsenic antisite (AsGa), arsenic antisite-plus-arsenic

vacancy (VASAsGa), and their complexes may be the dominant defects in


I










undoped GaAs, while, gallium vacancy (VGa), arsenic vacancy (VAs) and

their comlexes may be the dominant grown -in defects in MBE and LPE

GaAs under low arsenic pressure conditions.

Section 5.2 explains the theoretical calculations of vacancy and

interstitial defects in GaAs during crystal growth. Thermal kinetic

equations are described in section 5.3. Section 5.4 discusses the

possible grown-in point defects in GaAs for the As-rich or high

arsenic pressure cases. The possible grown-in point defects in GaAs

for the Ga-rich or low arsenic pressure cases is depicted in

section 5.5. Summary and conclusions are given in section 5.4.



5.2 Theoretical Calculations of Vacancy and Interstitial
in Undoped GaAs


In this section, the chemical-thermodynamic principles [62-69]

are used to derive expressions for thermal equilibrium defect

concentration as functions of temperature and arsenic pressure in

GaAs. Hurle [63] calculated the point defects by considering only As-

vacancy and As-interstitial defects in undoped GaAs. However, it is

known that Ga-vacancy related defects may play an important role in

anti site formation.

In this chapter, we consider several types of point defects such

as arsenic monovacancy, VAs, positively charged arsenic monovacancy

VAs, arsenic interstitial Asj, positively charged arsenic

interstitial Asj+, gallium monovacancyVGa, and negatively charged

gallium monovacancy VGa .

To deal with the problem of native point defects in GaAs, one can

write down the reaction equations for formation of each type of









defects as well as formation of electrons and holes in the crystal.

There is an additional reaction equation which represents the transfer

of atoms between gas and solid phases. For each of these reactions,

there is a mass action which applies in equilibrium. The mass action

can be written in terms of concentrations, and Boltzmann statistics is

used for electrons. To these mass action equations one adds the

condition of charge-neutrality, and the resulting set of equations can

then be solved as a function of arsenic partial pressure. Considering

the defects cited above, one has the following reaction equations.


AsAs + V = As + VAs (5.1)


VAs = VAs + e (5.2)

As = Asi' + e- (5.3)


0 = e- + h+ (5.4)


(1/2)As2(g) + V = Asj (5.5)


0 = VGa + VAs (5.6)


VGa = VGa + h+ (5.7)

Equations (5.1) to (5.4) represent the reactions for forming the

ionized arsenic Frenkel defects. Equation (5.5) denotes the transfer

of arsenic atoms between solid and gas phases. Equation (5.6) shows

the formation of Schottky pairs. Equation (5.7) represents the

ionization of a Ga-vacancy. The mass action relationships

corresponding to the above reactions are given as follows [62,63]









Kfa = [As] [VAs]

= 2.92 x 106 exp(-4.845/kT) (5.8)


Kav = n [VAs] / [VAs]
= 442 exp(-0.27/kT) (5.9)


Kai = n [Vj+] / [Asj]
= 4.9 x 109 x T3/2 exp(-0.4/kT) (5.10)


K = np

= 1 x 10-12 T3 exp(-1.62/kT) (5.11)


KAs2 = [Asi] PAs2-1/2
= 16.4 exp(-1.125/kT) (5.12)


Ks = [Va] [VAs]
= 3.286xl04 exp(-3.6/kT) (5.13)

Kgv = [V Ga-] / [VGa]

= 3.7 x 10-8 T3/2 exp(-0.66/kT) (5.14)


Square brackets in the above equations are used to indicate the

concentration. The AsAs represents arsenic atom at the arsenic site,

and is taken as unity. The partial pressure of As2 in the gas phase

is denoted by PAs2. The equilibrium constants appearing on the right

handside of Eqs. (5.8) through (5.14) have the general form.

K = exp(AS/k) exp(-AH/kT) = Ko exp(-AH/kT) (5.15)

where AS and AH are the entropy and enthalpy changes for each









reaction, respectively. The charge neutrality condition is obtained

from Poisson equation


n + [VGa- = P + [VAs+] + [Asi+] (5.16)


Equations (5.8) through (5.16) are usually solved by Brouwer

approximation. [70] In the present case, we solved Eqs. (5.8) to

(5.16) directly and obtained an expression for n2 as


n2 = Kcv + (KaKfa/KAs2) PAs2-1/2 + KajKiAs2iAs21/2


/ (1 + KqvKsKAs2jAs21/2 / KfaKv) (5.17)


Thus, the electron concentration can be calculated from Eq. (5.17) and

other defect density can also be deduced from n via Eqs. (5.8) to

(5.16). Figure 5.1 shows the defect concentration vs. PAs2 for T =

1000 K. Note that Ga vacancy is the dominant point defect in the

entire As2 pressure range shown. The LPE GaAs is usually grown in the

lower As2 pressure range with PAs2 = 10-8 atm, and defects such as

VGa, VGa-, and VAs+ are the dominant defects. For VPE GaAs with a

corresponding partial pressure of 10-4 atm, defects such as VGa, VGa-

VAs Asj, and Asi are the dominant defects. In the pressure range

between LPE and VPE growth, the concentration of VGa- is equal to the

concentration of VAs+. Figure 5.1 also shows that the grown-in

defects for the VPE and MOCVD techniques are much more than LPE and

MBE growth techniques. Figure 5.2 shows defect density as a function

of growth temperature for PAs2 = 5 x 10-3 atm. The concentration of

VGa- monovacancy and VAs+ monovacancy increases with increasing growth






















































-3
10 110
MOCVD
VPE


10 1
P at m/2
As2
2


2
10 10


Figure 5.1 Defect density
at 1000 K.


vs. As partial pressure for GaAs grown


--3
10


10-5




10-6


10-8


10i \




-4
10
11
LPE
MBE











I I p


-3
5x10 atm.


I I


0.8 0.9


1/T(1000/K)


Figure 5.2 Defect density vs. temperature for
arsenic pressure of 5x10-3 atm..


GaAs grown at an


PAS
As,


-2
10


-3
10


1-5



-6
10


I~ ~ I| I


I |


1. 1.1 1.2 1.3










temperature, but the density of Asj+ mono-interstitial decreases with

increasing growth temperature.



5.3 Thermal Kinetic after Crystal Growth


In general, defects will migrate as the crystal cools down from

the growth temperature. Thus, one would expect defect concentrations

to reach a new equilibrium condition at lower temperature. [64,71]

The enthalpy of a single vacancy migration in GaAs is 1.6 eV. [64,72]

For examples, if the jump attempt frequency is equal to Debye

frequency, then the jump rate will be 4 x 107 s-1 at 1400 K and

5 x 104 s-1 at 1000 K. For example, for a typical crystal to cool

down from 1050 K to 950 K in 10 min., simple vacancy would pass

through more than 108 lattice sites in that period. The migration of

vacancy will produce antisite defects, antisite pairs or impurity

complexes. In LPE grown GaAs samples, we have observed that samples

with faster cooling rate (10 C/min.) would produce more defects than

slower cooling rate (0.40 C/min.). Most of the simple vacancies are

ionized, and may encounter with other defects to form bound complexes.

At room temperature, almost all the vacancies present should be tied

up with other defects to form complexes. To consider the ultimate

fate of a simple point defect introduced during crystal growth,

several types of defects and defect complexes should be considered.

It seems likely that the most common defect complexes will be those

which have no net charge because these would have the greater binding

energy. For example, a negatively charged gallium vacancy and a









positively charged arsenic vacancy may produce a neutral gallium-

arsenic divacancy. This can be expressed by


VGa +VAs =VGaAs (5.18)

In addition, the antisite-divacancy complexes may be formed by the

reaction equations shown below


and 2VAs + GaAs =As GaAs-VAs (5.19)
and

2VGa + AsGa++ = VaAsGa++VGa- (5.20)

The antisite pair defect complexes can be written as


GaAs + AsGa++ = GaAs--AGa++ (5.21)


The interaction of VAs+ (VGa-) with a single acceptor (or donor)

impurity, A- (D+), can be written as


A- + VAs+ = AAs (5.22)


D++ VGa = DGa (5.23)


which should have about the same binding energy as the gallium-arsenic

divacancy complex given by Eq. (5.18).

From Fig. 5.1, it is noted that the concentration of VGa is very

high, and the following reactions are prevailed


VAs + VGa + e = VGaVAs (5.24)


VGa + D+ = DGa


(5.25)









In general, the concentration of positively charged and

negatively charged simple point defects introduced during crystal

growth are not equal. Therefore, the concentration of one type of

simple defects may be exhausted as shown by the reaction Eqs. (5.18)

to (5.25). This can be illustrated by the following kinetic equations.

(1). Arsenic antisite can be formed by Asi+, Asi, VGa-, and VGa.


Asi+ + VGa = AsGa + 2e- (5.26)


As+ + VGa = AsGa +e (5.27)


As + VGa = AsGa++ + 3e- (5.28)


As + VGa = AsGa + 2e- (5.29)


(2). Antisi te-vacancy complexes can be expressed by


VGa + ASAS = AsGaVAs + 4e (5.30)


VG+ AsAs = AsGaAs+++ + 3e- (5.31)


VAs + GaGa + 4e" = GaAsVGa (5.32)

which will occur everytime a vacancy migrates to a nearest neighbor

site.

(3). Impurity-vacancy complexes can be written as


VGa" + AAs = AAsVGa- (5.33)
and


VGa- + DGa+ + e- = DGaVGa-


(5.34)









Equations (5.33) and (5.34) are the interaction of VGa~ with a

acceptor (donor) substitutional sites. For examples, TeAsVGa- defect

complex may be formed in Te-doped GaAs, while, SnGaVGa- and GeGaVGa-

defect complexes may be formed in Sn-doped and Ge-doped GaAs,

respectively.

The VAs+ may migrate to a donor substitutional site, and the

reaction equations is given by


VAs + DGa = DGaVAs (5.35)

Obviously, such reactions act as to compensate the dopant and to

prevent the Fermi-level from approaching either band edge during

crystal cooling.



5.4 The Possible Grown-in Point Defects in GaAs for the
As-rich or High Arsenic Pressure Case


Applying defect modelling to the high arsenic pressure

conditions, the VGa, VGa-, VAAs AS and Asj are found to be the

dominant defects when PAs2 is greater than 10-5 atm [such as LEC, VPE,

and MOCVD techniques]; this is shown in Fig. 5.1. The migration of

VGa VGa-, and VAs+ defects may result in forming complexes given by

Eqs. (5.18) to (5.20) and Eqs. (5.22) to (5.35) after crystal growth.

If we neglect the neutral defect complexes, then native defects such

as AsGaVAs AsGa VGa-" GaAsVGa--, VAs+, Asi+, VGa As, and

impurity complexes DGa AAsVGa-, DGaVGa", DGaVAs are the possible

defects which may be performed in high arsenic pressure conditions.

In As-rich condition, the concentration of VAs+ may be decreased, Asj+









may be increased, and AsGaVAs ++ AGa ++, VGa Asi+, VGa, Asi, and

impurity complexes are the possible defects.



5.5 The Possible Grown-in Point Defects in GaAs for the
Ga-rich or Low Arsenic Pressure Case


Apply defect modelling to the low arsenic pressure conditions.

VGa, VGa-, and VAs are found to be the dominant point defects when

PAs2 is less than 10-7 atm; this is the case for the LPE and MBE grown
GaAs. The vacancies migrate to form complexes given by Eqs. (5.18) to

(5.20), Eqs. (5.22) to (5.24), and Eqs. (5.30) to (5.35) after crystal

growth. If we neglect the neutral defect complexes, then native

defects such as VGa VAs+, GaAsVGa AsGaVAs VGa and impurity

complexes such as: DGa AAsVGa-, DGaVGa-, DGaVAs+ are the possible

defects in low arsenic pressure conditions. The concentration of VGa

is almost equal to that of VAs, as is shown in Fig. 5.1, and the

binding energy for the gallium-arsenic divacancy is very high, as

given in Eq. (5.18). Thus, high purity GaAs can be grown in this case

under optimum cooling condition. In Ga-rich and low arsenic pressure

conditions, the concentration of VGa- and VGa may be decreased,

gallium interstitial may be react with VAs+ to form GaAs. Thus the

possible defects are VAs + GaAs--, and GaAsVGa--- in undoped GaAs

grown under Ga-rich condition.



5.6 Summary and Conclusions


In this chapter, we presented a new defect model for predicting

native point defects in GaAs. During crystal growth, the chemical-









thermodynamic principles are used to derive the density of vacancy and

interstitial defects under thermal equilibrium condition. After

crystal growth, thermal kinetic equations are employed to predict the

antisite, complexes, and impurity complexes. Conclusions are listed

as follows

(1). High purity GaAs material can be grown for the low arsenic

pressure case under optimum cooling condition.

(2). GaAs grown under higher arsenic pressure condition will produce

more native point defects than under lower arsenic pressure

condition.

(3). Native defects such as ASGa' ASGaVAs, VGa, and Asj and impurity

complexes such as DGa AAsVGa-, DGaVGa_ are the possible defects

for GaAs layers grown under the As-rich or high arsenic pressure

condition.

(4). Native defects such as VGa, VAs, GaAsVGa, ASGaVAs and impurity

complexes such as DGa, AAsVGa, DGaVGa, DGaVAs are the possible

defects for GaAs layers grown under low arsenic pressure case.

(5). Native defects such as VAs, GaAs, GaAsVGa and impurity complexes

such as DGaVAs are the possible defects for GaAs layers grown

under Ga-rich and low arsenic pressure conditions.

(6). Arsenic antisite (AsGa) defect only observed in GaAs grown under

As-rich or high arsenic pressure conditions; this defect can not

be produced under low arsenic pressure and Ga-rich conditions.












VI. ON THE PHYSICAL ORIGINS OF EL2 ELECTRON TRAP IN GaAs
(THEORETICAL AND EXPERIMENTAL EVIDENCE)


The activation energy for the EL2 electron trap in GaAs reported

in the literature ranges from E -0.76eV to Ec-0.83eV. The physical

origin of this trap is a subject of great interests in recent years.

A large number of papers has been devoted to this subject. Based on

our theoretical model and experimental results, we found that EL2

level is formed by two electron traps. One is identified as the EL2a

(Ec-0.83eV) electron trap, the other is denoted as the EL2b (Ec-

0.76eV). The physical origin of EL2a level is due to the arsenic

antisite (AsGa) defect, whereas, the physical origin of the EL2b

level is due to arsenic antisite-plus-arsenic vacancy (ASGaVAs)

complex.

Based on the native defect modelling presented in last chapter,

modelling of EL2 electron trap is derived in GaAs material grown under

As-rich or high arsenic pressure case. Furthermore, from calculations

of the trap density for the MOCVD and VPE grown GaAs with As to Ga

mole fraction ratio greater than one, it is found that the density of

EL2a trap is proportional to the mole fraction ratio of (r-1)1/2;

whereas, the density of EL2b trap is proportional to (r-1)1/4, where

r = [As]/[Ga].

The EL2a trap is best fitted to a Coulombic potential well with

double charge state (i.e., AsGa++), this was verified by the Poole-

Frenkel effect and phonon-assisted tunneling effect as observed in the

field dependent electron emission rates using nonexponential DLTS

method.










DLTS measurements were performed on VPE GaAs layers grown on

different orientations [e.g., (100), (211A), (211B)] and LEC GaAs

layers annealed in hydrogen gas at different temperatures [e.g., 200,

300, 5000C]. From the results of our annealing study, it was found

that EL2b trap would disappear, and EL2a trap would emerge in the DLTS

scan at annealing temperature of 500C. This result may be

interpreted by the model of EL2 electron trap to be presented in this

chapter. The experimental evidence which may be used to support the

modelling of EL2 will be presented in chapter VII.

Section 6.1 review the EL2 electron trap in GaAs. Theoretical

model of EL2 electron trap is explained in section 6.2. Section 6.3

discusses the method of determining the potential wells for EL2 trap

levels from analyzing the field enhanced emission rates in the

nonexponential DLTS experiment. Summary and conclusions are given in

section 6.4.



6.1. Review of the EL2 Electron Trap in GaAs


Activation energy of EL2 electron trap covers the energy range

from Ec-0.75eV to Ec-0.83eV as reported by many previous

investigators. [73-91] This trap has been observed in GaAs grown by

the Bridgmann, [77,78] LEC, [79-85] VPE, [86,87] and MOCVD [88-91]

methods as well as high temperature heat-treated GaAs samples. [92]

However, this level was not observed in the LPE [93] and MBE [94]

grown GaAs epitaxial materials. Recent studies of the LEC bulk grown

GaAs reported by Taniguchi et al. [74] have found that Ec-0.77eV

electron trap exists in the front section of LEC GaAs ingot; whereas,









Ec-0.82eV level was the dominant trap level appears in tail section of

LEC GaAs ingot. The same result was reported in MOCVD grown GaAs

epilayers by Watanabe et al.. [75] They found that EL2a (Ec-0.83eV)

was the dominant trap level for GaAs grown at 720 to 7400C, while,

EL2b (Ec-0.76eV) was the dominant trap level for GaAs grown at 630 to

6600C. In their annealing studies, Day et al. [94] reported that EL2b

was observed in as-grown MBE n-GaAs material; this level can be

annealed out at 8000C for 1/2 hour or at 7000C for 1 hour. Whereas,

EL2a was not observed in the as-grown MBE n-GaAs. The EL2a level can

be created by thermal annealing process and its trap concentration can

be enhanced by high temperature annealing. These results indicate

that EL2 electron trap may be due to two different trap levels. One

of them is the EL2a (Ec-0.83eV) electron trap and the other is EL2b

(Ec-0.76eV) electron trap. Our model and experimental evidence have

showm that these two electron traps have different physical origins.

Studies of the LEC grown GaAs [79,95] have shown that n-type

(S.I.) material can be grown only from melts above a critical As

composition, and the EL2a level was native defect observed in this

material. Ga-rich melts were found to yield p-type, low resistivity

GaAs crystal. Ta et al. [79] reported that EL2a level was observed in

As-rich GaAs material. GaAs samples prepared by LPE method are grown

from a Ga-rich solution, whereas, VPE GaAs samples are commonly

prepared in an As-rich gas ambient, in which growth rate and surface

morphology are optimized. [95] The EL2a level was not observed in as-

grown MBE n-GaAs material. [94] However, it was found that EL2a level

can be created and its trap density can be enhanced by high

temperature annealing (above 5000 C). [94] There is clear evidence









that the EL2a trap can only be observed in GaAs grown under As-rich or

high arsenic pressure case. The high arsenic pressure will enhance

the formation of VGa, and As-rich case will increase the number of

Asi. [89] Thus, the EL2a level is associated with gallium vacancy,

arsenic interstitial or their complexes, [96] and is not related to

oxygen impurity complex. [97]

In undoped GaAs material, Watanabe et al. [75,89] have shown that

the concentration of EL2b level is proportional to ([AsH3]/[TMG])1/4.

However, the concentration of EL2a level is proportional to

([AsH3]/[TMG])1/2. They also found that densities of EL2a and EL2b

level would increase with increasing growth temperature for MOCVD

grown GaAs material. Bhattacharya et al. [87] observed a linear

dependence of the EL2a trap density on [As] / [Ga] ratio in MOCVD

GaAs samples. Lagowski et al. [78] have found that the concentration

of EL2a level was increased with increasing As pressure during

Bridgmann bulk growth, while, Miller et al. [86] found that the

density of EL2a level was increased with increasing [AsH3]/[GaCl]

ratio in VPE grown GaAs. Li et al. [21] also found that the density

of EL2a level was decreased with decreasing [AsCl3]/[Ga] ratio in the

Ga-rich VPE GaAs.

In the S-doped GaAs material, Watanabe et al. [75,89] found that

density of EL2b level decreases with increasing dopant concentration

of surfur impurity. The density of EL2a level was found to decrease

with increasing concentration of shallow donor dopants (Si, Se, Te) as

was observed by Lagowski et al.. [78] Donor concentration above a

threshold value (1 x 1017 cm-3) led to a rapid elimination of EL2

trap. [78] This is consistent with our observation [98 in which no









EL2 trap level was detected in MOCVD GaAs samples with Sn dopant

density higher than 3 x 1017 cm-3. If group VI (Se, Te, S) elements

occupy the As lattice site and combined with gallium vacancy to form

antisite-vacancy (AAsVGa-) complexes, then the concentration of VGa

will be decreased. Thus, the probability of forming an arsenic

antisite (ASGa) defect will be greatly reduced. [87] Johnson et al.

[99] used photoluminescene upconversion method to observe EL2a level,

and concluded that this level is due to arsenic antisite defect. The

fact that EL2a level is a donor type defect was also supported by the

observed field dependence of emission rates. [48,73] This is

consistent with the modelling of native point defect described in the

previous chapter. We conclude that arsenic antisite defect is the

only grown-in defect which is observed in As-rich or high arsenic

pressure case, but is not observed in Ga-rich and low arsenic pressure

case. From the experimental evidence, it can be shown that EL2a trap

is due to antisite defect, AsGa formed during the post-grown

cooling, [94,99] as will be discussed further in next section.



6.2. Theoretical Modelling of the EL2 Electron Trap in GaAs


We shall next present a new model for explaining EL2 level vs

different [As]/[Ga] ratio for the MOCVD and VPE grown GaAs samples.

Assuming that the mole fraction ratio of [As] to [Ga] is equal to r,

it can be shown that for r > 1, the concentration of EL2a level is

proportional to (r-1)1/2, and the concentration of EL2b level is

proportional to (r-l)1/4. In this section, the kinetics of EL2

formation in GaAs are described. In the growth process, vacancies,

interstitials and antisites are formed in high temperature thermal









equilibrium. In the cooling process, vacancies migrate to form EL2a

and EL2b electron trap. In the annealing process, EL2b trap level is

transferred to EL2a trap level after thermal annealing. These three

different processes of defect formation in GaAs are discussed next.


6.2.1. Growth process


Defect formation under thermal equilibrium for the case of r > 1.

(a) MOCVD grown GaAs epitaxial material.

Arsine (AsH3) and trimethygallium (TMG) were used as sources

for As and Ga in MOCVD grown GaAs. Let the mole fraction ratio of

arsine to TMG be r, then


[AsH3] / [Ga(CH3)3] = r (6.1)


If we assume [Ga(CH3)3] equal to 1, then [ASH3] will be equal to

r, where the square bracket in Eq.(6.1) represents the mole fraction

of arsine and TMG gas. The reaction of arsine is to decompose into

As4(g) or As2(g), depending on the growth temperature. In general,

arsine will decompose into As4(g) in the epitaxial growth temperature

(below 1000 oC), while arsine will decompose into As2(g) at the melt

growth temperature (above 1400 OC). [64] The growth temperature for

MOCVD process is usually below 1000 oC, and thus the decomposed

reaction of arsine can be written as


AsH3(g) = (1/4)As4(g) + 3/2 H2(g) (6.2)


The chemical reaction of As4(g) and TMG is shown below




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