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
*
* |