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The study of photoconductivity effects in semi-insulating gallium arsenide using microwave reflection technique

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Order N um ber 9111077
The study o f photoconductivity effects in sem i-insulating gallium
arsenide using m icrowave reflection technique
Wang, Ming-Shan Marshall, Ph.D.
Rensselaer Polytechnic Institute, 1990
UMI
300 N. Zeeb Rd.
Ann Arbor, MI 48106
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THE STUDY OF PHOTOCONDUCTIVITY EFFECTS IN SEMI-INSULATING
GALLIUM ARSENIDE USING MICROWAVE REFLECTION TECHNIQUE
by
Ming-Shan Wang
A Thesis Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the Degree of
DOCTOR OF PHILOSOPHY
Major Subject: Electrical Engineering
Approved by the
Examining Committee:
Ronald J. Gfotmann, Member
Thomas P . Crowley, Membe
Toh-Ming Lu, Member
Rensselaer Polytechnic Institute
Troy, New York
August 1990
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CONTENTS
page
LIST OF TABLES ........... .......................... vi
LIST OF FIGURES ........
viii
ACKNOWLEDGEMENT ....................................
xvi
ABSTRACT ............................................ xvii
CHAPTER 1 INTRODUCTION .............................
1
1.1 Semi-insulating Gallium Arsenide Substrates ..
3
1.2 Microwave Measurement Techniques ............
5
1.3 Scope of the Research .......................
9
CHAPTER 2 SEMI-INSULATING GALLIUM ARSENIDE AND ITS
PHOTOCONDUCTIVITY ...............................
10
2.1 Introduction ................................
10
2.2 Gallium Arsenide Material ...................
12
2.2.1
Properties of Gallium Arsenide .......
2.2.2
Growth of Semi-insulating Gallium
13
Arsenide ............................. 23
2.2.3
Imperfections in Semi-insulating
Gallium Arsenide .....................
2.2.4
EL2 Concentration by Near-infrared
Absorption ......... ..................
2.2.5
32
39
Carbon Localized Vibrational Mode
Absorption ...........................
45
2.3 Photoconducitivty of Semi-insulating Gallium
Arsenide ....................................
2.3.1
General Concept ......................
ii
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46
45
2.3.2
Trapping and Recombination Centers ....
2.3.3
Photo-induced Excess Carriers in
50
Semiconductor ........................
2.3.4
53
Above-band-gap Photoconductivity in
Semi-insulating Gallium Arsenide .....
2.3.5
58
Below-band-gap Photoconductivity in
Semi-insulating Gallium Arsenide ..... 63
CHAPTER 3 MICROWAVE MEASUREMENT SETUP AND ITS
CALIBRATION .....................................
68
3.1 Introduction ..................................68
3.2 Conductivity and Lifetime Measurement
Principles ....................................69
3.2.1
Simple Reflection Setup ..............
3.2.2
Measurement Setup with 3dB Hybrid
Bridge
3.2.3
3.3
3.4
............................
70
75
Experimental Considerations and Results
78
Ka-band MeasurementSystems .................
gi
3.3.1
System for Large Detected Signals ....
g2
3.3.2
System for Small Detected Signals ....
100
Choke-FlangeRectangularWaveguide ..........
102
3.4.1
Introduction ........................
3.4.2
Choke-Flange and Flat-Flange Rectangular
Waveguides ...........................
3.4.3
102
106
Transverse-Electric Mode Assumption ... m
3.5 Photoconductivity Evaluation for Non-uniform
Illumination
.............................
iii
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H
5
3.5.1
General Equations for Uniform
Illumination .........................
3.5.2
119
Area Factor for A Small Circular
Illumination .........................
123
Sensitivity Factor ...................
133
CHAPTER 4 EXPERIMENTAL RESULTS AND DISCUSSIONS .....
139
3.5.3
4.1 Introduction ...............................
139
4.2 EL2 Concentration Measurement Using NearInfrared Absorption ........................
141
4.3 Dark Resistivity Profiling in Semi-insulating
Gallium Arsenide ...........................
150
4.3.1
Basis of Measurement Technique ......
151
4.3.2
System Calibration and Measurement
Results .............................
154
4.4 Below-band-gap Transient Microwave
Photoconductivity ...........................
155
4.4.1
904 nm Pulsed GaAs Laser Response .....
159
4.4.2
1060 nm Pulsed YAG Laser Response .....
170
4.4.3
Photoconductivity Model With an
Additional Donor Level ...............
173
4.5 Above-band-gap Steady State Microwave
Photoconductivity ...........................
4.5.1
4.5.2
189
Correlation with LVM Carbon
Concentration .......................
191
Recombination Mechanism .............
194
iv
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4. 6 Photoinduced Microwave Deep Level Transient
Spectroscopy (PMDLTS)
4.6.1
.......................
210
Transient Photoconductivity Due to
Trapping Centers .....................
212
4.6.2
Technical Backgrounds for DLTS ........ 215
4.6.3
Experimental Results .................
225
CHAPTER 5 CONCLUSIONS ..............................
239
CHAPTER
REFERENCES ...............................
247
.1 Chapter1 ....................................
247
6
6
6.2
Chapter 2 ....................................
249
6.3
Chapter3 ....................................
259
.4
Chapter4 ....................................
259
6
v
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L IS T
OF
TABLES
Page
Table 2.2.1
Properties of GaAs at room temperature (300K)
......................................... 14
Table 2.2.2
Ionization energies of impurities in GaAs
Table 2.2.3
Simple intrinsic defects found in GaAs .. 20
Table 2.2.4
Apparent activation energy and capture cross
17
section of electron and hole traps observed
by DLTS .................................21
Table 2.2.5
Calibration factors for the total carbon
acceptor LVM absorption line in GaAs ....
Table 3.3.1
47
Operation characteristics of two laser diodes
......................................... 97
Table 3.5.1
The normalized reflected and dissipated
microwave power and the sensitivity factor in
the low conductivity range .............
Table 4.2.1
124
The product at, the transmittance, and the
sensitivity quantity at1060 nm obtained from
equation (2.2.18)
Table 4.2.2
......................
144
Measurement results from optical absorption
at A.i=1060 nm and ^2=1320 nm. N + E L 2 and N°el 2
are in
Table 4.4.1
10^
cm-^ .......................
148
Parameters needed to fit the BBG transient
microwave response for different temperatures
.........................................183
vi
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Table 4. .2
Paremeters needed to fit the BBG transient
microwave response for different wafers
....................................
Table 4. .1
185
Thermal emission rate and the corresponding
temperature obtained from the PMDLTS
measurement.... .........................
Table 4 .6 .2
229
Results of PMDLTS measurement deduced from
the data in Table 4.6.1 .................. 231
Table 4 .6 .3
Electron concentration n(x) and Fermi level
due to ion implantation as a function of
depth x from
thesurface ...............
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236
LIST OF FIGURES
Page
Figure 2.2 .1
Unit cube of GaAs crystal lattice ..... 16
Figure 2.2 .2
Liquid encapsulated Czochralski pulling
techniques ............................ 25
Figure 2.2 .3
Experimental arrangement for low pressure
liquid encapsulated compounding of GaAs 27
Figure 2.2 .4
Experimental arrangement for high pressure
liquid encapsulated compounding of GaAs 28
Figure 2.2 .5
Resistivity of LEC GaAs as a function of the
arsenic fraction in the melt .........
30
Figure 2.2 .6 The dependence of EL2 concentration as
determined by optical absorption on the melt
stoichiometry ......................... 31
Figure 2.2 .7
Room-temperature electron (squares) and hole
(filled circles) optical cross sections.
Also shown is hole optical cross section
(open circles) from Chantre et al...... 41
Figure 2.3 .1 Fermi levels and demarcation levels for an
insulator .............................
52
Figure 2.3 .2
Semiconductor wafer illuminated by light55
Figure 2.3 .3
Above-band-gap photoconductivity model for
semi-insulating GaAs ..................
Figure 2.3 .4
50
Below-band-gap photoconductivity model for
semi-insulating GaAs ..................
viii
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55
Figure 3.2.1
Schematic diagram of simplified measurement
setup .................................. 71
Figure 3.2.2
Microwave measurement setup consisting of a
3dB hybrid bridge for nulling purpose ..
77
Figure 3.2.3 Normalized reflected power (square of the
reflection coefficient) vs conductivity of
25 mil thick Si wafer at 35 GHz ........ 82
Figure 3.2.4
Detector voltage decay of bare silicon wafer
with (a) maximum attenuation,
(b) nulling
dark signal and (c) log scale plots .... 84
Figure 3.2.5
Detector voltage decay of SI-GaAs wafer with
(a) maximum attenuation,
(b) nulling dark
signal and (c) log scale plots ......... 86
Figure
3.2.6 Lifetime measurement on silicon solar cell
sample using (a) microwave reflection
technique and (b) open circuit photovoltage
decay method .......................... 89
Figure
3.3.1 Microwave measurement setup for large
detected signals ......................
Figure
3.3.2 Four-port junction 3dB hybrid bridge ...
Figure
3.3.3 Characteristic curve of an HP crystal
detector ..............................
Figure
93
94
98
3.3.4 Microwave measurement setup for small
detected signals ......................
ix
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101
Figure 3 .4.1
Choke-flange and direct contact coupling
between two rectangular waveguide sections
.......................................
Figure 3 ,4.2a
Reflected
104
microwave power asa function of
spacing S (0-20 mm)
using the choke-flange
and flat-flange waveguides ............
Figure 3 ,4.2b
Reflected
microwave power asa function of
spacing S (0-5 mm) using the
choke-flange
and flat-flange waveguides ............
Figure 3. 4.3
107
108
Reflected microwave power as a function of
wafer thickness for the choke-flange and
flat-flange waveguides ................
Figure 3. 4.4
no
Configurations for the microwave reflection
measurement using the choke-flange waveguide
where (a) the wafer is cut and fitted into
the waveguide, and (b) the wafer is placed
outside the waveguide ...... ...........
Figure 3. 4.5
113
Reflected microwave power transients by
using configurations in Fig.3.4.4a and
Fig.3.4.4b ............................
114
Figure 3. 4.6
Log scale of the transients in Fig.3.4.5
116
Figure 3. 5.1
Transmission line representation of the GaAs
wafer for the calculation of the reflected
microwave power .......................
Figure 3. 5.2
121
Normalized reflected power vs photo­
conductivity of the wafer .............
x
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122
Figure 3 .5.3
Schematic definition of the area factor for
the small circular illumination .......
126
Figure 3 ,5.4a Theoretical and experimental area factors.
The experimental data are taken with a
constant photon flux density on the wafer
128
Figure 3. 5.4b Theoretical and experimental area factors.
The experimental data are taken with a
constant photon flux, but various photon
flux density, on the wafer ............
Figure 3. 5.5
Schematic diagram showing the calculation of
the illumination radius which equals
microns +
Figure 3. 5.6
0
100
.2 h ........................
135
A typical transmittance spectrum for undoped
LEC-grown semi-insulating GaAs wafers ..
Figure 4. 2.2
131
Normalized sensitivity factor as a function
of the illumination radius d ..........
Figure 4. 2.1
129
142
Comparison between the unionized EL2
concentration obtained from our measurements
and the one obtained from Spectrum Inc.
Figure 4. 3.1
149
Calibration of the system by relating the
normalized microwave response to the dark
resistivity of the SI-GaAs wafer ......
Figure 4. 3.2
155
Mapping data of microwave crystal detector
voltage and dark resistivity for a SI-GaAs
wafer .................................
xi
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157
Figure 4 . 1.1 A typical BBG transient microwave response
using 904 nm GaAs diode laser .........
Figure 4. .2
160
Arrhenius plot of In ( z * T 1//2) for determining
the activation energy of an at EL2 level 163
Figure 4.4 .3
The log scale plot of Fig.4.4.1. The slope
in the tail corresponds to the decay time
constant 1/Cn (Ng-N^)
155
Figure 4.4 .4 Comparison between the net shallow acceptor
concentration determined from BBG transient
microwave response and the LVM carbon
concentration .........................
^55
Figure 4.4 .5 The normalized peak BBG microwave response
vs the unionized EL2 concentration ....
Figure 4.4 .6
159
A typical BBG transient microwave response
using 1060 nm YAG laser ...............
171
Figure 4.4 .7 The log scale plot of Fig.4.4. 6 . The slope
in the tail corresponds to the decay time
constant 1/Cn (Ng-N^)
Figure 4.4
.8
^72
The magnitude of the pulsed 1060 nm response
vs the magnitude of the pulsed 904 nm
.response ..............................
Figure 4.4 .9
^74
The energy diagram of the proposed
photoconductivity model where the additional
donor level is located between the Fermi
level and Ec-1.17 eV ..................
xii
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Figure 4 .4.10aA typical curve fitting according to
equation (4.4.10) with n^ (0)/n2 (0)=0.3 and
Cn2=2xl0"5 c m V s
....................... 179
Figure 4 ,4.10bA typical curve fitting according to
equation (4.4.10) with n-^ (0) /n2 (0) =0 .02 and
Cn2=l.4xl0-5 cm-Vs .....................
180
Figure 4. 4.11 Electron mobility for SI-GaAs from
Ehrenreich (1959) and Stillman (1976) .. 182
Figure 4. 4.12 The energy diagram showing the transition of
electrons from the second EL2 level .... 187
Figure 4. 4.13 Optical cross sections for the two EL2
levels in GaAs. an° (triangles) and dp0
(filled circles) aremeasured at
(filled triangles) at
78 K. dp2°
85 Kand CJn2° (open
circles) at 150 K. Also shown (full curve)
is the data obtained in p-type material by
Lagowski (1985)
Figure 4. 5.1
.....................
190
Correlation between the ABG steady state
microwave response and the LVM carbon
concentration .........................
Figure 4. 5.2
Mapping of ABG steady state microwave
response across two 3" SI-GaAs wafers ..
Figure 4. 5.3
ig3
195
Mapping of shallow acceptor concentration
across two 3" SI-GaAs wafers using the
straight line in Fig.4.5.1 as a calibration
.......................................
xiii
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196
Figure 4. i.4
Equivalent circuit for calculating the
photoconductance G
induced byABG light from
microwave reflection coefficient ....... 199
Figure 4. .5
ABG steady state microwave response vs
photon flux density for a low carbon wafer
202
Figure 4.5 .6
Normalized Ntotal vs surface recombination
velocity S assuming T=200 ns, D=130 cm^/s,
and a= 1 0 4 cm- 1
Figure 4 .6 .1
.................. ......204
Transient photoconductivity signal and
weighting function
of lock-inamplifier 217
Figure 4 .6 .2 Function A(p) in equation (4.6.10)
function of p.
A(p) is maximum at
as
a
p=2.51,
and is half of its maximum at p=0.527 and
9-66
Figure 4 .6 .3
. 219
Theoretical curve for the output A(p)
assuming three trapping levels located at
0.2, 0.3 and 0.4 eV below the conduction
band ...................................
Figure 4.6 .4
221
Transient photoconductivity signal and the
harmonic weighting function of lock-in
amplifier .............................
Figure 4 .6 .5
Function A(p) in equation (4.6.11)
function of p.
as
223
a
A(p) is maximum at p=5.02,
and is half of its maximum at p=1.054 and
19.32 .................................
xiv
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224
Figure 4.6.6 Block diagram of the photoinduced microwave
deep level transient spectroscopy (PMDLTS)
measurement ............................ 226
Figure
4.6.7 A typical PMDLTS response using 1060 nm YAG
laser on an ion implanted sample ....... 228
Figure
4.6.8 Arrhenius plot of ln(T^/en ) vs 1000/T for
the three levels found using 1060 nm YAG
laser ...................................230
Figure
4.6.9 Typical PMDLTS response using 633 nm HeNe
laser on an ion implanted sample ....... 233
Figure
4.6.10 Arrhenius plot of ln(T^/en ) vs 1000/T for
the level found using 633 nm HeNe laser
.......................................
xv
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234
ACKNOWLEDGEMENT
It is my pleasure to thank my advisor Professor Jose
M. Borrego for his guidance and encouragement throughout
the course of this work.
I also wish to thank the members
of my doctoral committee for their keen interest
work.
in the
I thank Dr. Subhas Bothra, Hemant Bhimnathwala, Mike
Heimlich for numerous discussions and suggestions during
the course of this work,
valuable help.
and Krishna K. Parat
for many
The supply of SI-GaAs wafers by Paul J.
Pearah from Spectrum Technology Incorporated is gratefully
acknowledged.
I give most special thanks and unending gratitude to
my parents, Pang-Hi Wang and Cwei-Mei Chang Wang, to whom I
owe a great deal.
Bae-Jan N. Wang,
I am especially grateful to my wife,
for her encouragement and understanding
during the preparation of this manuscript.
This work was partially supported by the Solar Energy
Research
Institute under contract XL-5-05018-2, the New
York State Energy Research and Development Authority under
agreement No. 970-ERER-ER-87, and New York State Center for
Advanced Technology at
RPI.
This
support
is gratefully
acknowledged.
xvi
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ABSTRACT
Photoconductivity effects of undoped semi-insulating
gallium arsenide is studied,
from which the material can
be characterized using microwave reflection techniques
without making any contact.
consisting
acceptor
of
a
level,
above-band-gap
deep
A photoconductivity model,
donor
is proposed
(ABG)
level
and
EL2
and
used
to
and below-band-gap
reflection
techniques
(BBG)
allows
shallow
explain
and steady state photoconductivity response.
microwave
a
a
the
transient
The use of
contactless
characterization of resistivity, shallow acceptor (carbon)
concentration, and deep levels of SI-GaAs materials.
The measurement performed using microwaves essentially
provides
two
semiconductors:
evaluate
important
pieces
of
information
conductivity and lifetime.
quantitatively
the
conductivity
of
In order to
induced by
a
monochramatic light the choke-flange rectangular waveguide
is used as a probing element.
When a SI-GaAS wafer backed
by a metallic short is placed near to the open-end of the
choke-flange
rectangular waveguide the electromagnetic
field distritribution can be assumed to be TE^ q mode, and
therefore
the
photoconductivity
of
the
wafer
can
evaluated from the measured reflected microwave power.
xvii
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be
During the course of this study we have used more than
20
LEC-grown
undoped
SI-GaAs
wafers,
concentration ranging
from less than
c m “ 3,
photoconductivity
to
check
the
with
carbon
3x10-^ to 7x10^^
model.
Good
correlations have been found between 1) the BBG steady
state
microwave
resistivity,
2)
photoconductivity
the
ABG
steady
and
the
state
dark
microwave
photoconductivity and the LVM carbon concentration, and 3)
the
slow time constant
of the BBG transient microwave
photoconductivity and the LVM carbon concentration.
correlations
can
photoconductivity
be
explained
model
and
are
by
These
using
useful
to
the
the
non-destructive characterization of SI-GaAs.
The BBG transient microwave response shows an initial
fast decay after the light is turned off which can not be
explained by using the photoconductivity model.
In order
to explain the initial fast decay an additional deep donor
level is incorporated into the photoconductivity model
which is studied at different temperatures.
A new characterization technique, called photoinduced
microwave deep level transient spectroscopy PMDLTS,
is
introduced and demonstrated to be capable of detecting
deep levels in ion-implanted SI-GaAs materials.
However,
in bulk SI-GaAs wafers no deep level was found to be above
xviii
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the EL2 by using this technique.
xix
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CHAPTER 1
INTRODUCTION
Characterization
research,
of materials
transient
include
The conventional characterization
photoluminecence
spectroscopy
measurement,
after
categorized
destructive.
deep
depending
upon
characterization
into
two
Although
level
capacitance-voltage
and secondary ion mass spectroscopy
techniques,
materials
(PL),
(DLTS), Hall effect measurement,
optical absorption measurement,
These
for the
development and manufacturing of semiconductor
materials and devices.
methods
is essential
groups:
the
(SIMS).
usability
procedure,
destructive
destructive
(C-V)
can
and
techniques,
of
be
non­
such as
DLTS, Hall effect, and C-V, have been more widely used in
the
industrial
non-destructive
and
university
characterization
laboratories,
techniques
are
more
attractive from a manufacturing point of view because the
serviceability of materials will not be affected by the
characterization
procedure,
and
among
them
1
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are
photoluminecence and optical absorption techniques.
The
capability of non-destructive characterization of these
two techniques lies on the fact that both of them utilize
optical signals rather than electrical signals to detect
defect levels and material's properties.
Recently there have been an increasing interest in
developing new non-destructive techniques which utilize
microwaves together with optical signals to characterize
semiconductor materials.
The term "microwave" refers to
electromagnetic waves in the frequency range from a few
hundred
MHz
to
a
few
hundred
wavelengths ranging from
Testings
100
GHz,
cm to
conducted at microwave
1
corresponding
to
mm in free space.
frequencies
have been
widely used in the metals and dielectrics industries to
solve
a variety
problems.
of
materials
and
product
evaluation
Since most of semiconductor substrates can be
treated as lossy dielectrics, the use of microwaves as a
characterization
technique
becomes
applicable
on
semiconductor materials.
A non-destructive
characterization technique using
microwaves and optical signals has been conducted in the
microwave and the solar cell laboratories at Rensselaer
Polytechnic Institute by Prof.
Gutmann since 1985.
J. Borrego and Prof.
R.
The technique allows the evaluation
2
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of
process-related
semiconductor
or
materials
bulk
properties
and
many
of
different
successful
research
results have been published (Borrego and Gutmann 1987a and
1987b) .
This study is a continuation of that research
program with an emphasis on photoconductivity
effects in
semi-insulating gallium arsenide (SI-GaAs) bulk materials.
This material
research
(SI-GaAs) has been the subject of intensive
because
it
is
used
as
a
substrate
performance GaAs integrated circuits.
for
high
The importance of
SI-GaAs materials will be described in more detail in the
next
section.
applications
materials
In
section
of microwave
1.2
will
techniques
and the advantages
characterization tool.
we
on
describe
the
semiconductor
of using microwaves
as a
Finally, the purpose and the scope
of this study will be given in section 1.3.
1. 1 Semi-insulating
Gallium
Arsenide
Substrates
Gallium arsenide has been a subject of research in
many industrial and university laboratories for more than
two decades.
high
The high mobility (compared to silicon) and
saturated
semiconductor
drift
velocity
devices
could
have
meant
operate
at
that
GaAs
microwave
frequencies where silicon devices are unable to function.
Many GaAs devices and circuits are fabricated in a high
quality epitaxial layer which is grown on the top of a
3
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semi-insulating substrate with a buffer layer in between.
The
availability
substrates
of
allows
semi-insulating
low parasitics,
(107 -10®
device
direct ion implantation techniques,
ohm-cm)
isolation by
and true monolithic
circuit implementation.
The high resistivity property of semi-insulating GaAs
materials has been
midgap
deep
shown to be greatly dependent
levels
(Martin
1980
and
Johnson
upon
1983) .
Chromium has been used for many year as a midgap electron
trap for compensating donors such as silicon (Hyder 1982,
Oshima
1984 and Winston
undoped
semi-insulating
rapidly
decreasing.
1983),
GaAs,
Large
but with the advent of
the
use
diameter
of
chromium
(up to
100mm
is
in
diameter) undoped semi-insulating GaAs crystals can now be
grown
using
commercially
Melbourn high-pressure,
puller
manufactured
Cambridge, England.
available
instruments,
e.g.
liquid-encapsulated Czochralski
by
Cambridge
Instruments
Ltd.,
The availability of large-diameter,
semi-insulating GaAs substrates has spurred the growing
use of gallium arsenide in discrete devices and integrated
circuits for microwave, millimeter-wave,
and digital
development
applications.
of
GaAs
A major
technology
is
optoelectronic,
impediment
in the
inhomogeneities
regarding residual impurity concentration and intrinsic
defect distribution.
To improve the fabrication process
4
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and increase the yield in manufacturing high-performance
GaAs
IC's,
technique
a
reliable
and
non-invasive
is
required
to
detect
the
diagnostic
non-uniform
distribution of defects.
1. 2 Microwave
Microwave
powerful
Measurement
techniques
Techniques
have
non-destructive
been
widely
used
characterization
dielectrics and metals industries
as
method
a
in
(Bahr 1982) , and more
recently have been applied to semiconductor research and
industrial environments
(Chen 1988 and Kunst 1987).
The
use of microwave techniques as a contactless method to
measure the photoconductivity lifetime of semiconductor
material was first demonstrated on germanium by Ramsa,
Jacob and Brand in 1959.
Since then, various versions of
this technique have also been applied to Si
(Mada 1979,
Beck 1986, Borrego 1987a, and Kunst 1986 and 1988), GaAs
(Hasegawa 1984, Cummings 1986,
and Wang 1989),
ZnS
(Kalikstein 1968 and Kramer 1972).
the
microwave
characterization
CdS,
and
The idea behind
technique
is
that
observed change of the measured microwave power,
the
which
could be reflected or transmitted,
is a function of the
conductivity
test.
of
samples
under
Since
the
conductivity (or photoconductivity if an external light is
used)
of the sample is directly related to its carrier
5
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concentration,
determined
a number of material's properties can be
by
observing
microwave power.
the
change
of
the
measured
Many measurements have been made using
this technique and among them are carrier concentration
(Braslau 1984), mobility
resistivity,
(Braslau 1984 and Bothra 1989),
photoconductivity
(Bhatnagar
1983
and
Kalikstein 1968), carrier lifetime (Tiedje 1983 and Kunst
1985),
surface
defect
level
recombination
concentration
(Yablonovitch
(Fujisaki
1986),
1986
and
and Shimizu
1982).
Although many different apparatuses have been used,
the microwave measurement setup is basically operated in
either a reflection or a transmission mode.
Operation in
the transmission mode usually requires a special shaping
of the sample to fit into a waveguide section
1960), which is sometimes cumbersome.
(Jacobs
Operation in the
reflection mode has been favored in recent years because
it
allows
the
test
microwave apparatus
Special
applications
sample
to
be
placed
outside
the
and no sample shaping is demanded.
such
as
cooling
(Chen
1988)
and
spatial mapping (Hasagawa 1984) can be performed by using
a microwave setup operated in the reflection mode.
Besides that the microwave technique is essentially
non-destructive
and contactless,
there
are many
6
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other
advantages
of
using
this
technique
semiconductor materials.
layer
condition
can
in
For examples,
be
evaluated
characterizing
(1) the surface
by
using
an
above-band-gap light to generate excess carriers near the
surface,
(2 ) the bulk condition can be evaluated by using
a below-band-gap light to generate excess carriers in the
bulk,
(3)
high
spatial
resolution
can be
focusing the light into a small spot,
achieved by
(4) the measurement
setup can be incorporated into a process line facility for
on-line monitoring,
(5) rapid measurement can be taken,
(6 ) various sample size and thickness can be used, and (7)
many process-related and material's
evaluated.
properties
can be
Thus it is interesting to investigate and to
explore the capability and the application of using the
microwave
technique
in
the
characterization
of
semiconductor materials.
1.3 Scope
A
of
the
research
techniques
in
Research
program
the
of
using
microwave
characterization
of
reflection
semiconductor
materials has been developed for many years at Rensselaer
Polytechnic Institute.
and
solar
cell
The research done in the microwave
laboratories
includes
defect-free
zone
(DFZ) in Czochralski-grown (CZ) silicon wafer (Jensen 1986
and Lo
1988),
undoped
and chromium
doped
LEC
SI-GaAs
7
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materials (Heimlich 1987), the effect of ion implantation
processing on SI-GaAs (Campbell 1988), and measurements of
resistivity, lifetime and mobility of GaAs, InP and HgCdTe
materials
the
(Bothra 1990) .
program
with
This study is a continuation of
an
emphasis
on
the
study
of
photoconductivity effects in undoped liquid-encapsulated
Czochralski
The
(LEC)
purpose
of
semi-insulating GaAs bulk materials.
this
research
conductivity effects,
excitations,
in
characterize
SI-GaAs
acceptor
is
to
1)
study
photo­
above-band-gap and below-band-gap
semi-insulating
materials
(carbon) concentration,
GaAs materials
and 2)
- resistivity,
shallow
and deep levels - using
microwave reflection techniques.
This study is organized in the following way.
2 describes
materials,
the
photoconductivity
including
general
Chapter
of undoped
concepts
about
SI-GaAs
gallium
arsenide materials and the photoconductivity of solids.
A
photoconductivity model for SI-GaAs is proposed from the
two-energy-level defect model.
Both above-band-gap and
below-band-gap photoconductivities of SI-GaAs are derived
from the photoconductivity model, which will be later used
to
interpret
evaluate
microwave
the
the
measurement
model.
measurement
In
results
Chapter
setup
and
3
as
we
its
well
as
describe
to
the
calibration.
Experimental considerations in the lifetime measurement
8
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are given in section 3.2 together with some experimental
results.
Two Ka-band measurement setups, the choke-flange
rectangular waveguide, and the area factor for nonuniform
illumination are given in sections 3.3-3.5, respectively.
The
experimental
results
and discussions
are
given
in
chapter 4, including near-infrared EL2 concentration, dark
resistivity measurement of SI-GaAs, above-band-gap steady
state photoconductivity,
conductivity,
level,
and
below-band-gap transient photo­
photoconductivity model with an additional
a
"photo-induced
new
characterization
microwave DLTS".
technique
called
Many discussions
are
given to check the validility of the photoconductivity
model.
The conclusions and future works are summarized in
chapter 5.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 2
SEMI-INSULATING GALLIUM ARSENIDE
AND ITS PHOTOCONDUCTIVITY
2 .1 I n t r o d u c t i o n
Undoped semi-insulating GaAs crystals can be grown on
a reproducible basis by controlling the arsenic fraction
in
the
melt
concentration
to
be
from
in the
0.48
undoped
to
SI-GaAs
0.51.
grown
The
EL2
from this
composition ranges from SxlO1^ cm"^ to 2x10-*-® cm'^.
This
concentration is normally larger than the concentration of
net residual shallow acceptors, and hence a compensation
between the donor level EL2 and the net shallow acceptors
results.
Most
of the
electrical
properties
of the
undoped
SI-GaAs can be explained by using a three-energy-level
defect model which involves a shallow acceptor level,
shallow donor
level
and a deep donor
level
a
at around
10
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E c-0.7
eV.
normally
Since
small
concentration,
the
shallow
compared
to
donor
the
concentration
shallow
is
acceptor
the shallow donor will remain ionized and
the defect model can be simplified to a two-energy-level
defect
model,
acceptor
i.e.
level
acceptors.
acceptor'
with
a
deep
a
donor
level
concentration
plus
of
In this study we normally refer
as
'shallow acceptor'
for
a
net
single
shallow
'net shallow
simplicity
unless
stated specifically.
A photoconductivity model has been proposed for the
undoped SI-GaAs
using the two-energy-level model which
illustrates the transition of electrons during and after a
pulse of light.
When above-band-gap
(ABG) light, a light
with photon energy larger than the band gap of GaAs,
used
the
optical
energy
is
absorbed
to
is
create
electron-hole pairs from band to band.
When light with
photon energy larger than 0.7 6 eV but
smaller than the
band gap of GaAs, or below-band-gap
(BBG)
light,
is used
the optical absorption is mainly due to the deep donor
level
EL2.
The
photoconductivity
resulting
from
the
above-band-gap and below-band-gap illuminations contains
an
important
parameter,
lifetime,
which
is
directly
related to the concentration of shallow acceptors.
The
relationship between the photoconductivity and the shallow
acceptor concentration of the undoped SI-GaAs is derived
11
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from the photoconductivity model, and the details will be
described in this chapter.
2 .2 Gallium
Arsenide
Material
Gallium arsenide has been a subject of research in
many industrial and university laboratories for more than
two decades.
The high electron mobility
cm^/v-s @ 300K)
GaAs
(more than 7000
(compared to silicon) make it possible for
semiconductor
devices
to
operate
at
microwave
frequencies where silicon devices are unable to function.
The
ability
substrates
circuit
to
produce
allows
undoped
low parasitics
implementation.
The
(resistivity > 10 7 ohm-cm)
semi-insulating
and true
GaAs
monolithic
semi-insulating property
of the undoped GaAs results
from a compensation between the
deep donors, known as EL2
(Martin 1977), and the residual shallow acceptors, mainly
carbon
(Holmes
1982) .
The
conventional
method
to
determine the concentrations of EL2 and the carbon of the
SI-GaAs material is the near infrared (NIR) and the local
vibration mode (LVM) optical absorption, respectively.
In this section we begin with a brief description of
the GaAs properties
native defects.
including the impurities
and many
Next we will describe the growth of the
undoped SI-GaAs whose electrical properties are found to
12
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strongly depend on the melt stoichiometry.
the two major defects,
section 2.2.3,
The nature of
EL2 and carbon is discussed in
together with the compensation mechanism
for semi-insulating GaAs.
Finally, the optical absorption
measurements for determining the concentrations of the EL2
and the carbon are described.
2.2.1
Properties
of
Gallium arsenide
Gallium
Arsenide
is a III-V compound semiconductor
which is composed of elements Ga and As from Columns III
and V of the periodic chart.
This material was
first
created by Goldschmidt in the 1920s (Goldschmidt 192 9).
A
recent review article on the intrinsic, major properties
of GaAs
lists
1982) .
Further information about GaAs may be found in
many
over
references
four hundred references
(Willardson
1965,
Milnes
(Blakemore
1973,
Hilsum
1961, Madelung 1964, and Howes 1985).
Table 2.2.1 lists a few important properties of GaAs
at room temperature
(300 K)(Sze 1981).
the
is
GaAs
material
characterized
As can be seen,
by
a
relatively
high-electron mobility and large energy band gap.
These
properties make it an ideal candidate for high-frequency,
high-temperature,
and
applications.
GaAs
The
radiation-resistant
crystal
is
composed
13
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device
of
two
Table 2.2.1 Properties of GaAs at room temperature
(300 K) (Sze 1981).
Properties
GaAs
Atoms/cm3
4.42xl022
Atomic weight
144.63
Breakdown field
~4xl03 V/cm
Density
5.32 g/cm3
Dielectric constant
13.1
Effective density of states
in conduction band Nc
4.7xl017 cm- 3
Effective density of states
in valence band Nv
7.OxlO18 cm- 3
Electron affinity
4 .07 V
Energy gap
1.424 eV
Intrinsic carrier concentration
1.79x106 cm- 3
Lattice constant
5.6533 A
Melting point
1238 C
Mobility (Electrons)
8500 cm 3 /V-s
Mobility (Holes)
400 cm3 /V-s
Specific heat
0.35 J/g-C
Thermal conductivity
0.4 6 W/cm-C
14
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face-centered
cubic
(fee)
sublattices,
with
each
sublattice containing only one type of element, Ga or As
atoms.
These two sublattices are offset with respect to
each other by a quarter of the diagonal of the fee cube.
Such a crystal configuration is called zincblende and is
shown in Fig.2.2.1.
pressure,
the
At room temperature and atmospheric
distance
between
nearest-neighbor
Ga-As
pairs is 0.245 nm.
Several types of structural imperfections can occur in
the
GaAs
crystal
impurities,
complexes.
lattice,
interstitials,
including
vacancies,
substitutional
antisites,
and
Substitutional impurity occurs when a foreign
atom intentionally (by doping) or unintentionally replaces
either Ga or As at a regular lattice site.
atoms may remain neutral,
The foreign
promote electrons as donors,
acquire electrons as acceptors,
or act as charge traps.
The type of behavior that an impurity exhibits in the GaAs
lattice
generally
ionization
energy.
depends
Many
upon
its
impurities,
valence
both
state
and
shallow and
deep, are present in the form of complexes with gallium or
arsenic.
Both active and inactive complexes have been
identified in GaAs, and little is known of the manner in
which they are incorporated into the lattice.
lists
the
impurities
in
GaAs
together
ionization energies and conductivity types
Table 2.2.2
with
their
(Ghandhi 1983,
15
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Figure 2.2.1
Unit cube of GaAs crystal lattice.
16
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Table 2.2.2 Ionization energies of impurities in
(Ghandhi 1983, Milnes 1973, and Partin 1979).
Impurities
Donors(eV)*
Acceptors(eV)**
S
0.0061
Se
0.0059
Te
0.0058
Sn
0.0060
C
0.0060
0.026
G©
0.0061
0.040
Si
0.0058
0.035
Cd
0.035
Zn
0.031
Be
0.028
Mg
0.028
Li
0.023, 0.05
0
0.4, 0.75
Co
Cu
0.16, 0.56
0.14,0.24,0.44
Cr
0.79
Mn
0. 90
Fe
0.38, 0.52
Ca
0.16
Ni
0.35, 0.42
Au
0.09
Ag
0 .11
* from bottom of conduction band
** from top of valence band
17
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Milnes 1973, and Partin 1979).
It is interesting to see
that some amphoteric impurities
from group IV
(carbon,
germanium, silicon) can be either n-type dopant when they
substitute Ga atoms or p-type dopant when they substitute
As atoms.
The detection of the native defects in GaAs is a very
complicated problem and has been the subject of numerous
articles
(Bourgoin 1988 and its references).
It is only
by the conjunction of several techniques that a complete
picture of a given defect can be obtained.
The classical
techniques of defect characterization used in the case of
GaAs include:
(Lang
1974),
deep level transient
photocapacitance
spectroscopy
transient,
optical
(DLTS)
DLTS
(Chantre 1981), optical absorption, photoluminecence and
electron paramagnetic resonance
Bourgoin 1983).
provide
a
(EPR)
(Lannoo 1981 and
None of the these techniques is able to
complete
set
of
information
necessary
to
identify a defect and to deduce its electronic properties.
Therefore,
they
must
be
used
in concert,
which
often
raises more problems because different techniques require
different sample preparation and probe different regions
of the sample.
For instance, DLTS probes a surface region
of conductive doped materials while optical absorption and
EPR probe the whole material.
18
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With the help of electrical and optical techniques, in
particular EPR, a number of simple point defects have been
reasonably
well
identified.
Table
2.2.3
lists
six
intrinsic defects found in GaAs materials, together with
the characterization techniques and the references.
Among
these intrinsic defects the As antisite and its complex
have
received enormous
candidate
for
the
semi-insulating
attention because they
most
GaAs
important
crystals.
defect
The
are the
EL2
history
in
the
and
the
identification of EL2 will be discussed in more detail in
Section 2.2.3.
In addition to the above identified intrinsic defects,
many native defects have been characterized using DLTS
technique in different GaAs materials: bulk, vapor-phase
epitaxy
(VPE), liquid-encapsulated
metalorganic
chemical
molecular-beam epitaxy
(LPE)
materials.
concentration,
The
vapor
Czochralski
deposition
(LEC),
(MOCVD),
(MBE), and liquid-phase epitaxy
DLTS
activation
technique
energy,
and
provides
capture
the
cross
section of defects which are electrically active and the
results are summarized in Table 2.2.4 for various types of
studied materials
(Bourgoin 1988).
As can be seen a large fraction of the observed traps
appear to be characteristic of a single mode of growth,
19
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Table 2.2.3
Simple intrinsic defects found in GaAs
(Bourgoin 1988).
Defects
Characterization
References
technique
VAs
DLTS, EPR
Pons (1985)
Bardeleben (1986)
Loualiche (1984,1984b)
VAs- A sjl
DLTS
Pons (1979, 1984, 1985)
Thermal stability
Stievenard (1984,1986,
1986b)
Loualiche (1984)
As Ga
GaAs
EPR
Bardeleben (1985)
Thermal stability
Kaufmann (1984)
DLTS, IR absorption Elliott (1982)
Luminescence
Yu (1982,1982b)
AsGa+ VAs
DLTS, EPR
Bardeleben (1986b,1987)
As.
Thermal stability
Stievenard (1986b)
20
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Table 2.2.4 Apparent activation energy and capture cross
section of electron and hole traps observed by DLTS
(Bourgoin 1988).
Electron traps
Label
oC
al (10_14cm-2)
Ea (eV)
EL2
10
0.82
EL3
10
0.57
EL4
100
0.51
EL5
20
0.42
EL6
150
0.35
EL8
EL9
ELIO
EL12
EL14
EL16
Ell
EI2
EI3
EB1
EB7
E
E
E
M3
M4
EA2
EA6
EA7
0.8
0.7
0.7
500
0.05
0.0004
0.07
1
2
3.5
1.7
30
6.4
1500
3
1
0.05
/
0.1
0.27
0.22
0.17
0.78
0.21
0.37
0.43
0.19
0.18
0.86
0.30
0.74
0.26
0.42
0.61
0.31
0.52
0.18
0.14
Material
References
VPE,bulk,MOCVD
LEC(In doped)
A s h b y (7 6),S a k a i (74)
S h e n g (85)
Bhattacharya(80)
K itagawara(86)
VPE,bulk
A s h b y (76)
LEC(In doped)
Kitagawara(86)
MBE,MOCVD
W a t a n a b e (83)
Blood(83),M a r t i n (77)
V P E , L E C (In doped) A s h b y (76)
Kitagawara(86)
Bulk, MBE
Kitagawara(86)
M a r t i n (77)
LEC(In doped)
VPE,MBE
M i r c e a (75),B l o o d (83)
VPE
M i r c e a (75)
VPE,MBE
M i r c e a (75),Blood(83)
VPE,MBE,bulk
M i r c e a (75),D a y (81)
Bulk
M a r t i n (77)
VPE
M a r t i n (77)
VPE
L e fevre(77)
VPE
L efevre(77)
VPE
L e f e v r e (77)
LPE(In doped)
L a n g (75)
MBE
L a n g (76)
MOCVD
S a k a i (74)
LEC(In doped)
Kitagawara(86)
MOCVD
Watan a b e (83)
MOCVD
Buchwald(87)
MOCVD
Buchwald(87)
Bulk
A u r e t (8 6)
Bulk
A u r e t (86)
Bulk
A u r e t (86)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.2.4 (continued) Apparent activation energy and
capture cross section of electron and hole traps observed
by DLTS.
Hole traps
Label
HT1
HS1
HS2
HS3
HB1
Oa (10"14cm"2 )
Ea (eV)
Material
0.04
0.0005
0.44
0.58
0.64
0.44
VPE
LPE
LPE,VPE
LPE
0.05
0.78
LPE,VPE
0.71
LPE,VPE
0.00002
HB2
HB3
0.035
0.52
LPE,MBE
HB4
3.5
0.44
LPE,VPE
HB5
20
0.40
LPE,bulk
♦
HL3
HL6
HL7
HL12
H
HA6
0.3
5.5
0.65
1.3
/
2
0.59
0.32
0.35
0.27
0.57
0.18
VPE
VPE
MBE
LPE
MOCVD
Bulk
References
S a k a i (74)
H a segawa(75)
Hasegawa(75)
H a segawa(75)
Kitagawara(86)
L a n g (75)
H e n i n i (86)
Mitonneau(77)
L a n g (75)
M i t o n n e a u (77)
L a n g (75)
M i t o n n e a u (77)
Lang(75)
M i t o n n e a u (77)
L a n g (75)
M i t o n n e a u (77)
M iton n e a u (77)
Miton n e a u (77)
M i t o n n e a u (77)
M i t o n n e a u (77)
W a t a n a b e (83)
Auret(86b)
22
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indicating
defects.
that
they
hardly
be
simple
intrinsic
Only one defect is consistently observed in all
practical materials:
intrinsic defect.
have
can
been
it is EL2 and is believed to be an
Although many electron and hole traps
detected,
no
systematic
performed on these defects.
studies
Consequently,
have
been
none of them
have been identified with the exception of EL2 because of
its significant role in semi-insulating GaAs materials.
2.2.2
Growth
Single
techniques
of
Semi-insulating
crystals
of
utilizing
GaAs
melt
have
and
Gallium
been
Arsenide
grown
solution
by
many
approaches,
including horizontal and vertical Bridgman (Parsey 1982),
gradient freeze (Plaskett 1971), Czochralski
(Czochralski
1918), liquid encapsulated Czochralski
(Metz 1962),
vertical
melting
1982).
float-zone
(Yamenidijian 1982),
from
1959),
horizontal-zone
and by magnetic LEC
(Jacob
The most widely used techniques today encompass
modifications
freeze,
(Weisburg
(LEC)
of
and LEC,
elements.
horizontal
Bridgman
(HB),
gradient
usually employing in situ compounding
In this
section
we
concentrate
on LEC
growth techniques because their development for the growth
of bulk
semi-insulating
GaAs
has
resulted
in readily
available sources of large-diameter round wafers suitable
for use in standard semiconductor process equipment. This
23
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
achievement has significantly improved the manufacturing
technologies
dislocation
of GaAs
density
integrated circuits
of wafers
grown
by
although the
LEC method
is
higher than that of horizontal Bridgman grown wafers.
The
LEC technique
was
experimentally by Metz et al.
volatile
Mullin
PdTe
et
al.
crystal,
(1968),
first
(1962)
applied to
and
adapted
demonstrated
for
III-V
for
the growth of
materials
the
use
by
with
pyrolytic boron nitride (PBN) crucibles by Swiggard (1977)
and AuCoin (1979). In the liquid encapsulated Czochralski
process, the crystal is grown in the vertical direction by
slowly pulling the ingot from a melt
(see Fig.2.2.2). The
melt consists of molten GaAs and is confined by an inert
molten
layer of boric oxide
(B2 O 3 ) that
floats on the
surface of the melt. The growth process begins when a high
quality GaAs seed penetrates the boric oxide and contacts
the melt
which
is
contained
(SiC>2 ) or PBN crucible.
rotated
in either the
in a high-quality
quartz
The seed and the crucible are
same
or
opposite
directions
to
eliminate azimuthal thermal gradients. The diameter of the
crystal is controlled by the pull rate, typically 5-10 mm
per hour, and ocher operating parameters.
The LEC process may be subdivided into low pressure
LEC and high pressure LEC. The low pressure LEC process
24
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
inert atmosphere
\
high
seed
quality
pyrolytic boror
nitride (PBN)
r.f. coil
/
GaAs crystal
O
O
O
O
o
o
o
o
O
GaAs melt
O
O
O
susceptor
Figure 2.2.2
Liquid encapsulated Czochralski pulling
techniques.
25
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
was first investigated by Pekarek
(1970) who described a
process for synthesizing GaAs in a Czochralski puller at
nitrogen pressures
of 1.5 atm.
Figure 2.2.3
shows the
diagram of the low pressure LEC arrangement where arsenic
contained
in
a
quartz
ampoule
was
vaporized
and
transferred via a quartz tube into heated Ga covered by
molten
B2 O 3 .
fundamentally
Since
low
smaller
pressure LEC machines,
pressure
and
less
LEC
machines
expensive
than
are
high
it seems likely that these will
dominate in the future.
T. R. AuCoin (1979) and D. A. Rumsby (1979) described
a high pressure
in situ compounding/Czochralski growth
process
yields
which
reproducible basis.
semi-insulating
GaAs
on
a
The arrangement for the widely used
high pressure LEC process today
is shown
in Fig.2.2.4
where the in situ compounding and LEC growth are carried
out in the following manner. Stoichiometric quantities of
high
purity
gallium
and
arsenic
[six
9's
(0.999999)
purity] are loaded into PBN crucibles which, unlike quartz
crucibles,
can be cleaned and reused.
The Ga, which is
solid to just above room temperature, is loaded on the top
of the As so that the liquid Ga will encapsulate the As.
Starting with a chamber pressure of 600 psi the crucible
is heated to between 450 and 500 degree C, at which point
the B 2 O 3 softens, flows over the charge of Ga and As, and
26
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
quartz ampoule
growth chamber
/
pulling rod
heater
GaAs seed
arsenic
susceptor
crucible
r.f. c o i l \ ^
\°
o
o
o
o
Figure 2.2.3
h
x
O
O
Ga melt.v.v
o
o
o
Experimental arrangement for low pres
liquid encapsulated compounding of GaAs.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
high pressure
inert atmosphere
Ga matal
shielding
pyrolytic boron
nitride (PBN)
As granules
thermocouple
Figure 2.2.4
Experimental arrangement for high pres
liquid encapsulated compounding of GaAs.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
seals at the crucible wall. The pressure is then increased
to
-1000
psi
approximately
reaction
and
the
temperature
800 degree C,
(GaH q u i d
where
is
raised
to
a strong exothermic
+ Assolid = GaAssolid)
occurs.
The
presence of the boric oxide and the use of high argon
overpressures
prevent
significant
loss
of
As
due
to
sublimination and evaporation during and subsequent to the
exothermic synthesis. The GaAs melt is effectively sealed
by the boric oxide, suppressing not only As loss but also
shielding the melt against contamination from the crucible
and growth ambient. When the reaction is completed,
the
temperature is increased to above the melting point of
GaAs and the pressure is reduced to ~50 psi. A single­
crystalline ingot is gradually pulled from the melt in the
same manner as in the conventional Czochralski technique.
Semi-insulating GaAs (107 -10® ohm-cm resistivity) can
be grown using LEC techniques without additional doping
and its high resistivity has been shown to be greatly
dependent
Holmes
upon
(1983)
the melt
has
shown
stoichiometry
that
the
(Holmes
melt
1982b).
stoichiometry
controls the compensation in undoped GaAs and that the
free
carrier
concentration
depends
upon
the
balance
between EL2 and the residual carbon acceptors.
Figures
2.2.5 and 2.2.6 show the dependence of the resistivity of
LEC
GaAs
and
the
concentration
of
EL2
in
29
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
GaAs,
10*
• •• ••
10*
2**
••
10'
RESISTIVITY. B-cm
10*
»
10
p-TYPI
SfMMNSULATIMd
10*
10*
Critical AS
Composition
10*
101
o
10-'
0.42
a0
o
J
0.44
Stoichiometric
Composition
L
i
0.46
0.46
i
L
0.90
i
L
0.92
0.94
ARSENIC ATOM FRACTION IN MELT
Figure 2.2.5
Resistivity of LEC GaAs as a function of
the arsenic fraction in the melt (Holmes 1982b).
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
29x10’*
StoteMoiMMe
20 x10’
*
3
’ 9 * ’ O’*
*
1 0x10’ *
3x10’*
0.47
0.4
0.40
0.90
041
0.32
0.33
044
ARSENIC ATOM FRACTION IN MELT
Figure 2.2.6
The dependence of EL2 concentration as
determined by optical absorption on the melt
stoichiometry (Holmes 1982b).
31
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
respectively,
upon melt stoichiometry.
It is seen that
both the resistivity and the EL2 concentration in GaAs
increase as the arsenic fraction in melt increases. As
indicated in Fig.2.2.5,
the material is semi-insulating
above and p-type below a critical As concentration in the
melt
- approximately
concentration,
5 x 10-*-5
from
as
0.475 As
shown
atom
fraction.
The EL2
in Fig.2.2. 6 , increases
from
to 1 . 1 x 1 0 ^ - ^ cm-^ as the As atom fraction increases
about
normally
acceptors,
residual
0.48
larger
to
0.51.
than
This
the
EL2
concentration
concentration
of
is
residual
therefore a compensation between EL2 and the
acceptors
is
attained
and
the
material
is
semi-insulating.
2.2.3
Imperfections
in
Semi-insulating
GaAs
EL2 level
The
high
semi-insulating
r e sistivity
GaAs
property
crystals
is
of
achieved
undoped
through
a
delicate balance between the antisite-related defect EL2
and residual shallow acceptors.
detected
in
n-type
material
The EL2 level was early
by
using
a
transient
capacitance technique (Williams 1966, Blanc 1961, and Sze
1968), and was then rediscovered using DLTS (Mircea 1975).
The
unusual
persistent
behavior
quenching
of
of
GaAs
the
materials,
namely
photoconductivity
32
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
at
a
low
temperature
(Lin
1976),
is
attributed
to
the
transformation of the EL2 defect into a metastable level
(Vincent 1982).
The EL2 level was first thought to be
related to oxygen impurity but careful studies revealed
that
there
was
no
correlation
between
concentration and the 0 concentration
the
EL2
(Martin 1982 and
Huber 1979).
The microscopic
structure
active research area.
identification
came
of the
The first
with
the
EL2
level
is
an
step towards the EL2
electron
paramagnetic
resonance (EPR) detection of the spectrum associated with
the As antisite and the demonstration that this spectrum
has the same metastable behavior as EL2
1983) .
At that time,
(Weber
1982 and
atomic models started to flourish
all based on this observation: the isolated AsGa (Kaminska
1985), the pair of AsGa
(Lagowski 1982),
(Wager
1987,
(Figielski 1985), the Ga vacancy
a complex involving AsGa and vacancies
Yuanxi
1982,
and
Lagowski
complex involving AsGa and interstitials
Spaeth
1987).
Among
these
proposed
1983),
and
a
(Meyer 1986 and
models
the
most
popular atomic configurations were the isolated AsGa, the
AsGa+vAs complex (Baraff 1985 and Mochizuki 1986), and the
A s g a +As^
complex
controversies
(Bourgoin
still
remain
1988).
today
However,
many
regarding
the
identification of the EL2 atomic structure.
33
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
unlike
years.
electrical
its atomic
characteristics
structure,
of the
EL2
have been known
level,
for many
From DLTS measurement the capture cross section
for an electron Gn at the EL2 level has been measured in a
rather
large
temperature
range
(50-270
K)
(Mitonneau
1976) .
On =
5 x 1 0 _19+
6 x 1 0 ~ 15
exp [-0.066 (eV)/kT]
(cm2)
(2.2.1)
The hole capture cross section at the EL2 level has been
evaluated to be
Gp = 2x10” ^® cm^ (Mitonneau 1976) .
The
energy level of
the EL2, measured from the bottom of
the
conduction band,
depends on the temperature and is given
by Martin et a l . (1980) as:
E (EL2) = 0.759 - 2.37xl0~4 T (eV)
Mircea
and Mitonneau
level EL2 is a donor.
charge state of
(1976)
(2.2.2)
proved
that
this
deep
It has been well accepted that
this level is
0 /+
the
with the concentration
of the single charged EL2 approximately equal to that of
residual
shallow
experimentally
Ev+0.54
eV
that
acceptors.
EL2
It
introduces
(Silverberg 1988b,
was
a
Logowski
also
second
1985,
found
level
at
and Weber
34
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1982)
which has the charge state of +/++.
charged EL2 was
The double
found to be the dominant hole trap in
p-type bulk GaAs with a hole capture cross section Gp^ =
(1±0.5)xlO--^ cm^
(Logowski 1985).
However,
in n-type or
SI materials the deep level EL2 should be either neutral
or single charged.
In this study we refer "EL2 level" as
the one at Ec-0.75 eV, and "second EL2 level" as the one
at Ev+0.54 eV.
.Recently it has been argued that the charge state of
the EL2 level is +/2+ and not 0/+ because the experimental
evidence
has
been
double-charged
presented
acceptor
in
for
the
presence
undoped
SI-GaAs
concentrations of at least 2xl015 cm~3
of
a
with
(Bardeleben 1988).
This argument, however, has not been widely accepted since
most
of
the
electrical
properties
of
SI-GaAs
explained by the balance between the EL2
residual shallow acceptors
(Chichibu 1987,
can
be
level and the
Sargent 1988,
and Tang 198 9); which implies the charge state of the EL2
level is 0/+.
Carbon
Carbon,
chemically
impurity
as
determined by
identifiable,
in
undoped
LVM,
is
the predominant,
electrically active background
semi-insulating
LEC
GaAs.
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
concentration of carbon usually ranges from SxlO1^ to lO1^
cm-^.
The source of carbon in LEC grown GaAs crystals is
the B 2 O 3 encapsulant, polycrystalline Ga and As charges,
crucible,
and graphite susceptor.
Hunter et al.
have shown that the use of wet B 2 O 3
(500 ppm H 2 O) results
in materials with low carbon concentrations,
SxlO1^ cm“3, while dry B 2 O 3
including
the
may
have many
electrical
less than
(100-150 ppm H 2 O)
materials with carbon as high as SxlO1^ cm“^.
concentration
(1984)
effects
properties,
produces
The carbon
on the material,
such
as
carrier
concentration, mobility, and resistivity (Chichibu 1987),
thermal conversion
(Ohkubo 1988),
and the activation of
implanted Si (Chen 1984).
Other Background Impurities
From
secondary
measurements
impurities,
the
ion
mass
concentration
spectrometry
of
other
(SIMS)
background
such as S, Mg, Cr, Mn, and Fe, is very low.
In particular, the Si concentration is consistently less
than about
1 x1 0 ^
cm-^ which results from crystal growth
without a quartz crucible.
from about
1 x1 0 *-^
B 2 O 3 encapsulant.
to
Boron is present in a range
6 x 1 0 -^
crrT^ and it comes from the
The incorporation of boron has been
shown to depend on the water content of the encapsulant,
decreasing as the water content increases
(Oliver 1981).
36
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Although boron is the predominant chemical impurity, it is
iso-electronic
indicating
with
that
boron
Ga,
and
is
no
evidence
electrically
was
active
found
(Holmes
1982) .
.Compensation Mechanism
To develop a model for the electrical compensation in
terms of the concentration of predominant electrically
active centers in the SI-GaAs material, the concentration
of
shallow
and
first-principle
ionization
deep
centers
theoretical
of EL2
produces
an
were
related
through
considerations.
ionized
The
center plus
an
electron in the conduction band
Unionized EL2 <=> Ionized EL2 + e
According
to
the
principle
of
detailed
(2.2.3)
balance,
the
concentration of ionized centers Nj, the concentration of
electrons n, and the concentration of unionized centers Ng
are related by the following equation:
n N
Nu
where
Nc
is
= N
the
c
exp(-AE/kT)
effective
density
(2.2.4)
of
states
in
37
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
conduction band and AE is the energy level of EL2.
equal
to the net
acceptor
concentration,
given
Nj is
as the
difference in concentration between shallow acceptors Na
and shallow donors Nd
Nx = Na — Nd
(2.2.5)
The concentration of acceptors is given as the sum of the
concentrations of carbon and other residual acceptors NaR
N
= [carbon] + NR
cl
(2.2.6)
cl
The concentration of unionized centers is equal to the EL2
concentration as determined by optical absorption.
is
only
EL2
centers
which
are
occupied
by
That
electrons
contribute to the optical absorption process
N0 = [EL2]
By substituting
(2.2.5)
(2.2.7)
through
(2.2.7)
to
(2.2.4),
the
following expression for the free electron concentration
is obtained in terms of the predominant
centers
SI-GaAs material:
38
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
in the
[EL2 ]
n = Nc exp(-AE/kT)
(2.2.8)
([carbon] +
- Nrf)
This expression can be rewritten in the following form:
n
en [EL2]
(2.2.9)
where en and Cn are the thermal emission rate and capture
rate for an electron in the EL2 level, respectively.
This
expression can be further rewritten, in terms of the total
EL2 concentration N^, as:
Therefore, the electron concentration is controlled by the
concentration of the EL2 and the net acceptors.
2.2.4
EL2 Concentration by Near-infrared
Absorption
The variation
of the EL2
concentration
in SI-GaAs
substrates will affect the uniformity of bulk material's
property,
such as resistivity,
as well as active layer's
properties, such as implanted layer activation and device
39
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
performance.
has
been
The activation of the Si ion implantation
found
to
increases
with
increasing
concentration by 1% for each lxlO1^ cm-^ of EL2
EL2
(Brierley
1988).
The threshold voltage of field-effect transistors
(FETs)
fabricated
on
SI-GaAs
substrates
using
ion
implantation technique has been observed to be dependent
on the EL2 concentration of the substrate.
The voltage
decreases with increasing EL2 concentration by a rate from
-15 mV/10-'-^ cm-^ to -33 mV/101^ cm-^ (Alt 1988) .
Since semi-insulating GaAs materials have a very high
resistivity, conventional characterization techniques such
as
DLTS
can
not
concentration.
be
The
used
for
measuring
most
common
method
the
used
EL2
to
quantitatively determine the EL2 concentration was the
infrared
(IR) absorption at 1 |lm as suggested by Martin
(1981).
Recently the
spectral
dependence
of both
the
electron and hole photoionization cross sections of EL2
has been accurately measured, therefore the concentration
of ionized and unionized EL2
(Silverberg 1988).
capture
cross
centers
can be determined
The spectral dependence of the optical
section
of electron <7n° and of hole Cp°
determined from the photocapacitance transient technique
at
300
K is shown
in Fig.2.2.7.
For a photon
energy
larger than 1.1 eV the optical absorption is mainly due to
the transition
of electrons
from the EL2
level
40
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to the
Photon energy
Figure 2.2.7
<e\/
Room-temperature electron (squares) and
hole (filled circles) optical cross sections.
Also
shown is hole optical cross section (open circles)
from Chantre et al. (1981) (Silverberg 1988).
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
conduction band.
Since most of the EL2 centers in SI-GaAs
materials are neutral
(unionized)
the EL2 concentration
can be approximately determined by
«*L2
“
N EL2
(2.2.11)
0n
where CCE L 2 is the optical absorption coefficient and NE L 2
is the total EL2 concentration.
In order to evaluate the ionized and unionized EL2
concentrations both the electron and hole optical capture
cross
sections
have
to be
taken
into
account
for the
optical absorption coefficient as:
<*EL2
where
f is the
level.
If
=
N EL2
rf<
electron
the
+ U-fJOp ]
occupancy
absorption
data
(2.2.12)
fraction on the EL2
are
taken
wavelengths,
it is a simple matter to solve
both
NE E 2
f
and
and
the
results
are
at
two
(2 .2 .1 2 ) for
given
in
the
following:
f
_______________ °
W
2 )GP (1>
-
- < ( 2 )J - ^ (
________________
2) 101(1) - «£(!)]
(2.2.13)
42
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and
a EL2
_(l) [o°(2 ) - o°(2 ) ]
N.EL2
o°(
2 )o°(i)
P
n
a°(
2 )o°(i)
n
p
(2.2.14)
However,
the
determined
total
EL2
independently
concentration
by
energy at which On° = G p ° .
using
can
also
a particular
be
photon
For T = 295 K these optical
capture cross sections are 4.9xl0-1^ cm2 at hi) = 1.04 eV
and, for T = 78 K, Gn° = Gp° = 2.9xl0- 1 7 cm2 at hi) = 1.08
eV.
These data are recommended for quick and accurate
determination
of
the
total
EL2
concentration
in
test
samples and wafer mapping applications.
The optical absorption coefficient a is deduced from
the optical transmittance measurement.
If the incident
photon flux is normal to the semiconductor wafer which has
parallel
surfaces,
the total transmittance T due to the
reflection on the surfaces and the absorption in the bulk
is given by:
(1 - R)
1 - R
exp(-at)
(2.2.15)
exp(-2at)
43
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where t is the wafer thickness and R is the reflectance at
both
the
front
(air
(semiconductor to air)
to
semiconductor)
faces of the sample.
and
rear
For normal
incidence the reflectance is given by:
(n - l)2
R = ------(n + 1 )
(2.2.16)
where n is the refractive index of the semiconductor.
refractive
index
for
GaAs
materials
at
300
expressed by the following empirical equation
K
can
The
be
(Blakemore
1982).
n 3oo<hl)> = J
Equation
3 78
1 -1 0 + ------ 1------ 2
1 - 0.180(ht)
(2.2.17)
(2.2.15) is a quadratic equation for exp(at)
and the absorption coefficient can be solved as:
1
(1-R) 2
a = — ln{ -— r —
t
2T
therefore,
[1
+
1
+
4R T
(1-R)
^
]}
(2.2.18)
the EL2 concentration can be determined using
proper optical capture cross section data.
44
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.2.5
Carbon Localized Vibrational Mode Absorption
Liquid encapsulated Czochralski grown, semi-insulating
GaAs substrates contain carbon shallow acceptors as the
major
residual
evidence
electrically
that
active
substitutional
impurity.
carbon
in
Direct
GaAs
is
predominantly on the As sublattice has been obtained from
Fourier transform infrared (FTIR) spectroscopy absorption
measurements of the carbon-induced localized vibrational
mode
(LVM)
(Theis 1982).
Carbon acceptors
(CA s ) exhibit
an absorption due to LVM mode at 580 cm- 1 at 300 K and 582
cm- 1
at
70
K.
calibrate
the
function
of
absorption
There
strength
carbon
have
of
been
this
several
attempts
absorption
line
concentration
coefficient
a
is
[C].
expressed
mid-infrared spectroscopy uses wave number
in
to
as
a
Since
the
cm"-'-
and
(1) in cm--*-) as
its spectral variable, then
J
a du = «xA) =
cm"2
(2.2.19)
where f is the temperature-dependent calibration factor in
__-|
cm ± .
For some quick, low-resolution measurements, the
total
absorption
(aA)
means
the
product
of
the
peak
absorption 0Cmax and the full width at half-maximum (FWHM)
A.
45
R eproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
The
calibration
factor has
researchers using different
been
assessed by
calibration methods
1983, Hunter 1984, Homma 1985, Brozel 1986,
1989).
Table
calibration
2.2.5
factors
lists
the
results
For low temperature
evaluated the
different
As
(1986) the calibration factor
LVM absorption
calibration
SxlO1^ and
(T<77 K) it has been
increases by ~60%
compared to the one at room temperature.
(1989)
and Sargent
of
for the CAs LVM absorption band is between
found that the total
(Theis
obtained at room temperature.
suggested by Brozel et al.
llxlO1^ cm- 1 .
many
factors
Sargent et al.
fRT for room
temperature and fLT for T < 100 K, and recommended that
fRT £ l . 6 fLT = (13 ± 3) x 1015 cm'1
which
gives
a
realistic
connection
(2.2.20)
between
300
K and
low-temperature measurements.
2.3 Photoconductivity of Semi-insulating Gallium
Arsenide
2.3.1
General
Concept
Early research in the field of photoconductivity was
concentrated primarily on photoconductive materials, such
46
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Table 2.2.5 Calibration factors for the total carbon
acceptor LVM absorption line in GaAs.
Authors
Calibration factor (cm -1-)
Theis et al.(1983)
31-41 x 10 15
Hunter et al.(1984)
11
Homma et al. (1985)
9.5 ±2.9 x 1015
Brozel et al.(1986)
8
Sargent et al.(1989)
13 ± 3 x 1015
x
±
2
1 0 15
x
1 0 15
47
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as selenium
(Piersol 1927),
cuprous oxide
and thallous sulfide
(Case 1920).
photoconductivity
has
characterization
been
techniques
for
(Pfund 1916),
Recently the study of
applied
to
evaluating
properties of semiconductor materials.
various
electrical
Examples of these
techniques are photo-induced transient spectroscopy (PITS)
and microwave photoconductivity measurements (Kunst 1986).
The
study
of
the
photoconductivity
determining the electrical properties
is
useful
in
of semiconductor
materials because the photoconductivity relates to the
carrier concentration and mobility in a direct manner. The
conductivity of an insulator or semiconductor is expressed
as
a = q(|ln + npp)
(2.3.1)
where n and p are the concentrations of free electrons and
holes,
respectively,
hole mobilities.
and (ln and (ip are the electron and
In a homogeneous material in which n and
p are uniform throughout the material,
photoconductivity
a+Aa results when absorbed radiation increases the value
of n and p from nQ and pQ in the dark to nQ+An and pQ+Ap
in the light:
a+Aa = q [(In(no+An) + (ip (po+Ap) ]
(2.3.2)
48
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In insulators the values of An and Ap may be much larger
than the corresponding free carrier concentrations in the
dark, while in semiconductors the effect of radiation can
be
considered as a small perturbation
on a large dark
carrier concentration.
The
lifetime
of
photoexited
carriers
is
the
key
parameter for an understanding of photoconductivity.
If
light falling on a semiconductor creates G electron-hole
pairs per second per unit volume of the semiconductor,
then
where
Xn
lifetime
G X n = An
(2.3.3 a)
GX
(2.3.3 b)
p
= Ap
is the lifetime of an electron,
of
a
hole.
Equation
and
(2.3.2)
Xp
is the
for
the
photoconductivity can then be rewritten as
A a = Gq(Ll
X + (1 X )
^ 'n n
'p p
(2.3.4)
This relation shows why the lifetime is the key parameter
in photoconductivity.
49
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2.3.2
Trapping
It
is
and
Recombination
important
distinguishing
recombination
to
between
center
know
a
in
Centers
the
trapping
criterion
center
semiconductors
for
and
because
a
the
presence of trapping or recombination centers might have a
significant effect on photoconductivity.
is
to
be
considered
as
a
trapping
Whether a center
center
or
as
a
recombination center depends on the relative magnitudes of
(1 ) the probability of thermal
freeing of the trapped
carrier, and (2 ) the probability of recombination with the
carrier of opposite sign.
For example these centers will
act like electron trapping centers if
(2.3.5)
or like recombination centers if
(2.3.6)
where nt is the concentration of centers occupied by an
electron,
p is the
free hole
concentration,
Cp is the
capture rate for a free hole by a center occupied by an
electron, Cn is the capture rate for a free electron by a
50
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center occupied by a hole, and Et is the energy difference
between the conduction band and the level of centers.
It is convenient to define a demarcation level which
separate trapping and recombination
electron
(hole)
demarcation
is
level,
located
it
at
has
ejected
to
the
the
equal
recombinding with a free hole
thermally
centers.
When
electron
(hole)
probability
(electron)
conduction
an
of
and of being
(valence)
band.
Figure 2.3.1 shows schematically the relationship between
the demarcation levels and the steady state quasi-Fermi
levels
for an insulator,
or semi-insulating
GaAs,
for
which the concentration of photoexited carriers is much
larger
than
carriers.
the
The
concentration
quantitative
of
thermally
relationships
excited
between
the
demarcation levels and the steady state quasi-Fermi levels
are given as:
E
fn
= E
dn
Cp
+ kT ln(-£-)
C n
(2.3.7)
n
and
C p
E fp = E.d p - kT ln(-E-)
c n
(2.3.8)
n
Since a demarcation level is determined by the values of
Cn and Cp
of the
center
involved,
it
is
important
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to
electron Fermi level
electron demarcation level
hole Fermi level
h
t
i i
\
t
f
A
k
♦
I Efn
^
E dn
I II
1
III
k
hole demarcation level
k
k
E fP
E^
dp
1
Figure 2.3.1
an insulator.
r
ir
IV
i
Fermi levels and demarcation levels for
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
realize that each different type of center has its own
demarcation levels associated with it.
As indicated in Fig.2.3.1 the energy gap is separated
into
four
demarcation
electron
traps.
regions
by
levels.
traps;
Levels
the
Levels
levels
quasi-Fermi
located
located
levels
in
region
in region
and
I are
IV are hole
located in region III are recombination
levels by definition of the demarcation levels.
Levels
located in region II act as recombination centers because
they can not capture electrons, while hole capture leads
to
recombination
(hence,
they
are
hole
recombination
levels).
2.3.3
Photo-induced Excess Carriers in
Semiconductors
Before
considering
the
effect
of the
presence
of
defect levels on the photoconductivity of semi-insulating
GaAs,
excess
we
first
carriers
derive
the
equation
in a semiconductor
for photo-induced
wafer.
There
are
basically three equations which govern the photoeffects in
semiconductors, namely
equation,
1 )continuity
equation,
and 3) charge neutrality equation.
2
)transport
Consider a
semiconductor wafer whose area is very large compared with
its thickness d,
with its upper surface normal to the
53
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illumination as shown in Fig.2.3.2. Assuming no electric
field and linear bulk recombination with lifetime T, the
change
in the photo-induced excess
obtained
from
the
combination
electrons
of
the
n can be
continuity
and
transport equations and it satisfies the equation:
dn
dt
where
Dn , a
d n
n
d X
X
= D -------- + a N , e
n- 2
ph
and Np^
are
-a x
electron
(2.3.9)
diffusion
constant,
optical absorption coefficient and photon flux density,
respectively.
In the steady state the above equation is
simplified to:
_
d2n
D n—
n
= — - a N phe
dx
This
equation
boundary
can
-ax
(2.3.10)
x
be
solved
conditions which
in
conjunction
with
in this case are the
the
surface
recombination conditions:
x=0
where
Dn
S is the
surfaces
of
j
= Sn;
surface
the
x=d
dX
wafer.
Dn
*
recombination
After
= -Sn
(2.3.11)
dX
the
velocity at both
excess
electron
54
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light
x=0
wafer a. t, D
x=d
Figure 2.3.2
Semiconductor wafer illuminated by light.
55
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concentration n(x)
is solved using
(2.3.10) and (2.3.11)
the total excess electron concentration Ntctaj_ per unit
area can be obtained by integrating n(x) from
0
to d, and
the result is given as (Moss 1966) :
d
0
)
(2.3.12)
coth (d/2L)
where L is diffusion length (DnT)^^^. This expression may
be evaluated for various particular cases as will be shown
in the following.
Case I: Infinite surface recombination velocity
If the surface recombination velocity S is very high,
or infinite, equation (2.3.12) can be simplified to
Nt o t a l
- (XL (1+e
d
) tanh (—— )) (2.3.13)
Since the wafer thickness d is normally much larger than
the diffusion length in GaAs, the hyperbolic tangent term
in
(2.3.13)
is
equal
to
one
and
the
above
equation
56
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becomes:
N total
aL (1+e
-ad
))
(2.3.14)
where the total electron concentration Ntotal, depending
on the value of the absorption coefficient, could vary by
an order of magnitude.
Case II: Zero absorption coefficient
Another extreme
when the
optical
such that ad «
condition
absorption
1 and aL «
for equation
coefficient
(2.3.12)
is
is negligible,
1.
It is a simple matter to
of
light
rewrite (2.3.12) as
which means
the
absorption
energy
is uniform
through the wafer thickness and, therefore, the number of
electrons per unit area is equal to the product of the
generation rate per unit area Nphad and the bulk lifetime
X.
57
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2.3.4
Above-Band-Gap Photoconductivity in Semiinsulating Gallium Arsenide
When a semi-insulating GaAs wafer is illuminated by an
above-band-gap light electron-hole pairs will be generated
near
the
front
surface
of
the
wafer
as
the
optical
absorption coefficient is large for above-band-gap light.
Since the electron mobility is much larger than the hole
mobility in GaAs we consider only the effect of electrons
in determining the ABG photoconductivity.
After the light
is off, the excess electrons in the conduction band will
recombine
through
a
mechanism
with
the
excess
recombination
together
with
holes
in
process.
the
This
resulting
valence
band
recombination
photoconductivity
effects will be discussed in the following.
In order to explain the ABG photoconductivity, as well
as BBG photoconductivity given
in the next
section,
a
photoconductivity model has been proposed for SI-GaAS from
the two-energy-level
defect model,
i.e.,
level EL2 and a shallow acceptor level.
recombination
center
in
this
model
is
a deep donor
Since the only
the
EL2
the
recombination of the excess carriers will take place in
this level (the recombination through shallow acceptors is
unlikely to happen and will be considered in chapter 4).
Assuming that the main recombination mechanism is the fall
58
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of
the
electrons
from
positively ionized
change
in
obtained
the
conduction
band
to
the
deep donors as shown in Fig.2.3.3, the
excess
from
the
electron
equation
concentration
(2.3.9)
except
can
be
that
the
recombination term
is now Cnn (Na-Ncj+n)instead of n/T as
was assumed, and it
is given by:
“
at
where
and
= D n—
n
N . e "“x - C n ( N
~ + a
2
P*1
"ax
n
'
a
- N .+ n )
d
(2.3.16)
'
and Na are the concentrations of shallow donors
shallow
acceptors,
respectively,
and
Cn is
the
electron capture rate in the EL2 level. To make the above
equation linear the excitation level is assumed to be low
so that the excess electron concentration n is much less
than Ng-N^. Equation
(2.3.16) will have the same form as
(2.3.9) with bulk lifetime X equal to 1/Cn (Na~Ncj) .
With
a
low
level
steady
state
excitation
and
an
infinite surface recombination velocity, the total excess
electron
concentration
absorption ( ad »
per
unit
area
under
strong
1 ) can be obtained from (2.3.14) as:
(l/cm2)
(2.3.17)
59
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Ec
•
•
• •
Nc, n
Ed
Nd
• ••••••
•
• • • •
o o
Figure 2.3.3
Nt, nt
Na
N,
Above-band-gap photoconductivity model
for semi-insulating GaAs.
60
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The photoconductance of the wafer can be calculated as:
G = ^ „ N ,o,.1 = ^ „ 7 ^ L7
(2.3.18)
1 + aL
If the value of aL is much greater than one, which is true
for an above-band-gap light and a diffusion length of a
few |J.m, the photoconductance will be proportional to the
square root of the bulk lifetime and is given by:
N „h &
0 = q ^n ^
q |i„ N h
= -
“7^
It
will
be
“7 ^
shown
in
/
(2.3.19)
V Cn (
section
3.2.1
that
the microwave
response is proportional to the photoconductance of the
wafer (Borrego 1987a and 1987b), therefore the ABG steady
state
square
microwave
root
inversely
of
response
the
low
proportional
to
will
level
the
be
proportional
excitation
square
root
to
lifetime
of
the
the
or
net
shallow acceptor concentration Na-N^.
After the ABG light is off the excess carriers will
recombine through the EL2 as well as at the surface of the
wafer.
Assuming the excess carriers are distributed in a
region near the front surface an effective lifetime
of the excess carriers can be approximately given by
61
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l
l
sa
= — + -----xe ff
„
x
1 + aL
where
the
term
recombination.
Sa/ (1 + OCL)
(2.3.20a)
is
due
to
the
surface
[Note that the above equation is valid
when the wafer thickness W is much larger than L or a-^.
If a - 1
>> W, then another approximation should be used,
i.e.,
is
=
true
+ (7l^D/4 W^) .]
for 850 nm light
Assuming aL »
on GaAs,
the
1, which
above
equation
becomes:
1
S
= — + —
t
It
is obvious
effective
L=50
(1m) .
e ff
that
(2.3.20b)
X
when
S is
large
lifetime becomes very short
As a result
(> 10^
cm/s)
the
(around 5 ns for
the ABG photoconductivity will
decay very fast after the light is turned off.
It is possible to passivate the surface or to put an
electron mirror at the surface, such as n+ layer or AlGaAs
layer,
so that the surface recombination velocity can be
reduced by
several orders
of magnitude.
When this
is
done, e.g., S < 1000 cm/s, the ABG photoconductivity will
decay with a time constant of the bulk lifetime
X.
62
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This
»
is the result of (2.3.20b) if
S/L.
In steady state
the ABG photoconductivity can be obtained from (2.3.12) by
neglecting S and the result is given by
G = q(l Nt o t a l. = q|i Np h X
which is larger than the G in
1+aL.
the
(2.3.21)'
(2.3.18)
Since this factor is large,
steady
state
significantly
ABG
by
typically around 50,
photoconductivity
reducing
the
by a factor of
surface
will
increase
recombination
velocity.
2.3.5
Below-Band-Gap Photoconductivity in Semiinsulating Gallium Arsenide
When
the
SI-GaAs
wafer
is
illuminated
by
a
below-band-gap light with photon energy larger than 0.7 6
eV, both electrons and holes will be excited from the EL2
level
to
the
conduction
band
and
the
valence
band,
respectively. The optical absorption coefficient as stated
in (2 .2 .1 2 ) is given here again as:
a EL2
=
+ U-fXfp ]
N el2
(2.3.22;
which can be rewritten in terms of the concentrations of
63
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unionized EL2 centers N °E L 2 and ionized EL2 centers N+EE2
«EL2
=
N EL2<
+
(2.3.23)
NEL2<
Since the optical capture cross section for a hole in the
EL2 level is small compared to the one for an electron at
the wavelength used
(904 nm) and most of the deep donors
are unionized, the photoconductivity is mainly due to free
electrons
in
the
conduction
band.
This
transition
of
electrons between the conduction band and the EL2 level is
shown in Fig. 2.3.4.
Similar to the ABG excitation,
the
number of free electrons in the conduction band under BBG
illumination will vary in the way described by equation
(2.3.16), and it is:
-\2
—
-)t
vt
= D — J + a N . e'ax- C n ( N -N. + n)
n -x2
9X
Ph
n
v
a
d
(2.3.24)
where a is the absorption coefficient of BBG light. This
absorption coefficient is given as
Gn °
(Nt-Na+Nd-n) where
Nt is the total concentration of EL2 centers. The thermal
emission rate is neglected in the above equation because
it
is very
small
compared with the
optical
generation
rate.
The absorption coefficient for BBG light is usually
64
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• •
m m
Eh
• •
Figure 2.3.4
NL.
v»n
A A
Nh
• ••••••••
Nt , n t
• •
Na
N.
Below-band-gap photoconductivity model
for semi-insulating GaAs.
65
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small and ad is much less than one
mil thick SI-GaAs wafer.
( ad «
1 ) for a 25
The steady state value of the
total excess electron concentration per unit area Nto1:a2_
during the light pulse,
infinite
surface
assuming low level injection and
recombination,
can
be
obtained
from
(2.3.15) as:
o° N , ( N - N
N total = N
SSp h t
X ao'Qd —
+ N .) d
(2
3 25}
(2.3.25)
C (N -N ,)
n '
d'
a
where x = 1/Cn (Na-Ncj) is the low-level injection lifetime.
The above equation has been used to determine the dark
resistivity of SI-GaAs materials at room temperature using
microwave detected photoconductivity (Borrego 1988), which
will be described in chapter 4.
After the light pulse is off, the excess electrons in
the conduction band will recombine with the ionized EL2
and the concentration of free electrons will decay to its
equilibrium value.
photoconductance
In order to investigate the transient
the
absorption
of
the
BBG
light
is
assumed to be uniform through the wafer thickness. This is
a good approximation since ad is about
904
nm
light
transient
and
a
25
mil
photoconductance
thick
during
0.01
when using the
SI-GaAs
the
wafer.
light
pulse
varied in the following way:
56
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The
is
4-^- = q j u d 4-^- = q JLL d [ o° N , (N - N
n dt
n
L n
ph v t
a + N.d - n )
'
- C n n ( N - N d + n)]
(2.3.26)
When the light is off the term consisting of Np^ becomes
zero,
and
the
photoconductance
will
decay
to
zero
according to the following equation (Bube 1960):
q ^ d „ oe C"<N--N')‘
G(t) ------------------------a
where
nQ
is the
d
initial
value
concentration when the BBG light
case of
(2.3.27;
of the
excess
electron
is turned off.
low level excitation where
nQ «
In the
(Ng-N^) , the
above equation reduces to a single exponential decay with
the decay time constant corresponding to the concentration
of the net shallow acceptors, i.e. X = l/Cn (Na-Nci) . If the
excitation level is high, the transient signal in (2.3.27)
will not be a single exponential decay.
However,
after
some time t the exponential term in the denominator can be
neglected
and
the
photoconductance
will
exponentially
decay with the same time constant as were in the case of
low level excitation.
67
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CHAPTER 3
MICROWAVE MEASUREMENT SETUP AND
ITS CALIBRATION
3 .1 Introduction
As mentioned before microwave techniques
useful
for
the
semiconductors.
it
is
non-destructive
characterization
of
To correctly use the microwave technique
necessary
semiconductors
are very
to
but
have
also
a
of
knowledge
not
microwaves
only
because
of
the
interpretation of the experimental data depends on the
experimental arrangement and environment.
performed
using
important
pieces
microwaves
of
essentially
information
conductivity and lifetime.
The measurement
of
provides
two
semiconductors:
A quantitative evaluation of
the conductivity of the wafer is possible only when the
relationship between the conductivity and the measured
microwave signal is well determined.
This is tentatively
done by finding the scattering parameters of a widely used
68
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parallel-plate taper-tip antenna which is placed between
the semiconductor wafer and waveguide components
1990).
(Bothra
Since the deduction of the scattering parameters
is time-consuming and the application of these parameters
is
restricted
to
a
particular
arrangement
of
the
measurement setup, a conventional open-ended rectangular
waveguide isrecommended andis used during
this study.
the course of
We prefer the open-ended waveguide rather
than the taper-tip antenna as a sensing element because
the electromagnetic problems associated with the waveguide
are
easier
relationship
to
solve, and
therefore
a quantitative
between the conductivity of the wafer and the
measured microwave power can be obtained.
3.2 Conductivity and Lifetime Measurement
Principles
The excess carrier lifetime in various silicon wafers
has
been
measured
by
using
the
microwave
technique developed in our laboratories
reflection
(Borrego 1987).
The operation of this technique is based on detecting the
decay
of the microwave
reflected power
following the
introduction of excess carriers by a pulsed light source.
The main advantage of this technique is that there is no
need to make contacts to the sample or shape the sample in
a particular way, therefore the microwave technique can be
69
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readily
used
in
characterization.
many
laboratories
However,
for
lifetime
it should be noted that the
observed lifetime from the microwave reflection technique
can be the true lifetime x, half of the real lifetime x/2,
or some other values depending on the arrangement of the
microwave setup.
It is the purpose of this section to
provide the theoretical basis of the microwave reflection
measurement
and establish some guidelines to setup the
microwave measurement system.
We will also demonstrate
the measured lifetime of silicon and SI-GaAs wafers in two
extreme
cases:
attenuator
and
X
and X/2 by the proper
sliding
short.
The
setting
on an
measured microwave
lifetime is verified by comparing its value to the one
obtained
from
an
independent
photovoltage
decay
measurement on silicon solar cell samples.
3.2.1
Simple
Figure
simplified
Reflection
3.2.1
Setup
shows the measurement principle of a
measurement
system
which
consists
of
a
directional coupler for measuring the reflected power from
the semiconductor wafer.
A CW microwave source generates
a forward wave with power Pj_ which is directed to the
semiconductor sample by a microwave antenna or waveguide.
This wave is partly reflected by the semiconductor and its
power
is detected by
a square-law
detector through
70
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a
Semiconductor
wafer
Pu l s e d
laser light
CW microwave
source
Incident power P
' V
Directional
coupler
Antenna or
waveguide
Square-law detector
I
Metallic
Oscilloscope
Figure 3.2.1
Schematic diagram of simplified
measurement setup.
71
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
directional coupler.
a
,
The semiconductor wafer is considered to be a lossy
dielectric of conductivity
thickness W.
dielectric constant er, and
The wafer is backed by a lossless metallic
contact which serves as an electric short and reflects the
microwave power.
conductivity
In most of the cases measured, the dark
is
very
small
compared
conductivity and is assumed to be zero.
dark
reflection
since
a
all
the
coefficient
incident
to
the
light
Therefore the
T s has a magnitude of one
power
is
reflected.
When
the
conductivity of the semiconductor is increased to a value
due
to
photoinjection
of
carriers
the
reflection
coefficient Ts at the sample changes by a small amount ATS
due to the increase
in power dissipated as:
(3.2.1)
The above equation can be written as:
(3.2.2)
where 0 is the angle of r s* Ars .
If |Ars l « c o s 0 one can
approximate (3.2.2) by:
72
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IAT I
-1—
(3.2.3)
2 cos0 Pj
Note that the value of cos0
to
the
way
we
assign
coefficient in (3.2.1).
is always positive according
the
change
in
the
reflection
If the operator on the left hand
side of (3.2.1) is '+' the value of cos6 will be negative.
The
power
dissipated
in
the
semiconductor
can
be
calculated by the volume integral of the conduction loss
as:
(3.2.4)
v
where E(x,y,z) being the electric field in the sample and
V being the volume where excess carriers are generated.
If the conductivity is assumed to be uniform the power
dissipated
will be proportional to the conductivity,
and so will the small change of the reflection coefficient
|ATS I a s :
|Ar
The
microwave
(3.2.5)
| «= P d oc o
system between
the
detector
and the
73
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
surface
of the
reciprocal
sample
two-port
can be
network
parameters Sllr S1 2 and s2 2 *
reflection
coefficient
rD
considered
described
by
as
a
linear
scattering
The relationship between the
at
the
detector
and
the
reflection coefficient Ts at the sample is given by:
r = s
s2 r
12.s
4-
(3.2.6)
1 - S22r s
Making a Taylor series expansion in the above equation and
retaining only the first term we obtain:
S2
ArD = --------------------------------------(3.2.7)
(1 - s22rs)
Combination of (3.2.5) and (3.2.7) gives:
lArD |oe |Ar |oc0
(3.2.8)
Assuming a square-law detector, the voltage output of
the detector during the light, VD ^L , is proportional to
the square of the total reflection coefficient magnitude
as:
V D.L =
K
l r D
+
A r D
|2
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
< 3 -2 -9 >
where K being a proportionality constant governed by the
characteristic of the detector and the received microwave
power.
The voltage output of the detector, when the light
is off, VD^D , is:
V D.D=K l r D |2
Combination of
(3.2.9)
<3'21°)
and
(3.2.10)
gives the change in
the detector voltage:
a v d = k (2 lrD I lArD Icose + lArD P ) « |ArD I
where
0
that
|rD IcosG »
(3.2.11)
is the angle of TD *ArD , and it has been assumed
proportional
larD I.
to the
Since
excess
the
conductivity
carriers
generated
a
is
it will
decay with the same time constant X as the carriers decay.
From the combination of
(3.2.8)
and
(3.2.11)
concluded that the measured transient
it can be
voltage
from the
detector will decay in the same way as the carriers decay
even if the decay is not a single exponential.
3.2.2
Measurement
Setup
with
3dB
Hybrid
Bridge
The microwave measurement setup that we have used for
75
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
determining the lifetime of excess carriers by monitoring
the decay of the microwave reflection is schematically
shown in Fig.3.2.2.
The setup consists of a 3dB hybrid
bridge which allows the measurement to be performed in
different ways.
be given
in the next
measurement
microwave
A complete description of this setup will
section and here only the major
principles
power
are
discussed.
entering port
The
incident
of the bridge
1
splits
equally into two parts which come out of port 2 and port 3
of the bridge.
When the attenuator connected to the port
3 of the bridge
is set to its maximum attenuation no
reflected
will
power
enter
port
3.
Therefore,
the
microwave power that can be detected at port 4 is only the
reflected power from port 2.
The previous analysis for a
simplified measurement system can be applied in this case
and the observed lifetime of the detector voltage decay
will be the same as the carrier decay lifetime.
If the attenuator and the sliding short are adjusted
such that the reflection coefficient ^
to the reflection
conditions,
the
coefficient ^
at port 3 is equal
at port
2
in the dark
detector will sense no microwave power
because the reflected power from ports 2 and 3 canceled
each
other
before
photoconductivity
of
arriving
the
sample
port
is
4.
When
modulated
due
the
to
photoinjection of carriers, the reflection coefficient at
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35 GHz
FREQUENCY
■#
METER
MICROWAVE
GENERATOR
CRYSTAL
DETECTOR
DIGITAL
VOLTMETER
A
ATTENUATOR
-2 0 d B
HYBRID
CRYSTAL
DETECTOR
PULSER
SLIDING
SHORT
LASER
DIODE
WR-28 WAVEGUIDE
.<r~
SEMICONDUCTOR
SAMPLE
DIGITAL
OSC.
TRIGGER
SOURCE
I
X -Y -Z
MICROPOSITIONER
IBM PS2
COMPUTER
Figure 3.2.2
Microwave measurement setup consisting
of a 3dB hybrid bridge for nulling purpose.
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
port 2 changes by an amount Ar2 .
The detector at port 4
is able to detect this variation as:
lr 2+Ar 2- r 3l2- Ia f2I2
avd= k
(3.2.12)
where F 2 = r 2 by nulling the output of the detector.
Similar
to
proportional
ArD
to
in
the
the
conductivity
photoinjection of carriers.
of A V D
is
simplified
proportional
G
system,
Ar2
induced
by
is
the
As a result, the decay curve
to
the
square
of
both
the
photoconductivity decay curve and the excess carrier decay
curve.
Assuming a single time constant t in the excess
carrier
decay,
the
photoconductivity
and
the
detected
voltage can be expressed as:
o ( t ) = o( 0 ) exp( -tH )
(3.2.13)
A V D( t ) = A V D( 0 ) e x p ( - 2 t /x )
(3.2.14)
which shows that the detector voltage decays with a time
constant T/2 .
3.2.3
Experimental
Considerations
and
Results
When comparing the two microwave setups in Figs.3.2.1
78
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and 3.2.2/ it seems that the simplified measurement setup
is favored over the one with the hybrid bridge for its
simplicity and the direct deduction of the excess carriers
lifetime.
However,
there
are
at
least
two practical
situations in which the simplified setup is unable to give
the correct lifetime.
First, if the angle between rD and
ArD
as
is
not
constant
was
assumed
in
(3.2.11)
the
measured voltage could have a longer or shorter decay time
constant depending on the way the angle changes.
situation
can
happen
when
conductivity
is
large
enough
propagation
so
that
the
the
modulation
to disturb
change
in
of
This
the
the microwave
the
reflection
coefficient has not only a time-varing magnitude but also
a time-varing phase angle.
(3.2.11)
decay
lifetime.
larDP
term in
can become significant and the observed voltage
will
lifetime
In addition
contain
decay
and
two
the
components:
other
one
one
with
with
the
half
of
true
the
Therefore the resulting time constant will be
some value between T and T/2 .
The combined result from a time-varing phase angle 0
and non-negligible ArD gives a very complicated voltage
decay and the observed lifetime could be very different
from the real one.
t ne
3dB
hybrid
coefficient T
2
-
This problem can be avoided by using
bridge
to
cancel
the
dark
reflection
By nulling the detector voltage in the
79
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
dark condition the detector will measure a signal which is
proportional to
|Ar2 I2 and has half of the time constant
T/2 , regardless what the phase angle
Another
0
is.
situation where the use
of the 3dB hybrid
bridge becomes practical is when it is desirable to filter
out
the
operate
DC
in
microwave
its
power
square-law
so
that
region
the
detector
during the
transient
signal.
The proportionality
(3.2.12)
will no longer be a constant when the microwave
power
going
square-law
to
the
factor K
can
detector
detection.
exceeds
The
in eqs.(3.2.9)-
the
distortion
limit
due
for
to
a
the
power-dependent factor K gives a different voltage decay
curve from the true decay curve of excess carriers.
course
before
Of
it is possible to attenuate the microwave power
the
detector,
however
sensitivity of the measurement.
this
will
degrade
the
On the other hand, the
use of a 3dB hybrid bridge will remove the DC microwave
power and allows the entire square-law region be used for
detecting the time varying microwave power.
One
final
note
should
be
mentioned
here.
The
condition in (3.2.3) is valid only when the amount of the
change in the reflection coefficient
is small.
change of the reflection coefficient
is not
If the
small,
the
relationship between the reflection coefficient and the
80
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
conductivity becomes more complicated and requires the
knowledge of the microwave propagation through the sample.
Assuming a quarter-wavelength thick sample with a shorting
plane on its back surface, the reflection coefficient of a
plane wave incident on the front surface will vary from
to
-1
1
when the conductivity of the sample changes from
zero to
infinite.
conductivity
There
where
the
is a turnover point
reflection
for the
coefficient
has
a
minimum magnitude (see Fig.3.2.3 for the example of 25 mil
thick silicon wafer).
the
Equation
(3.2.8) is valid only in
regions where the conductivity
is low
(o <
0.001
ohm-cm- 1 ) or the conductivity is high ( <5 > 10 ohm-cm-1) .
If
of
the conductivity of the sample changes from one side
the turnover point
to another
side,
the
reflection
coefficient will varies in a quite different manner from
monotonous
decay.
This
has
been
observed
during
our
experiment when a high intensity illumination is applied
and should be excluded from the lifetime measurement.
The results of the previous developed theory have been
corroborated by two sets of measurements taken with the
microwave
setup
measurements
was
in
Fig.3.2.2.
taken
on
some
The
first
bare
semi-insulating gallium arsenide wafers.
set
silicon
of
and
The light source
used to create excess carriers in the semiconductors is a
54 W pulsed GaAs laser diode which emits light at 904 nm
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
u
<u
25
>
—4
<44
m il
Si w a f e r
CC
Conductivity (1/ohm-cm)
Figure 3.2.3
Normalized reflected power (square of
the reflection coefficient) vs conductivity of 25 mil
thick Si wafer at 35 GHz.
82
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and
operates
Because
at
of
pulse
the
durations
difference
from
in
50
the
to
200
energy
gap
ns.
of
semiconductors, the generation mechanism for the silicon
wafer
is
a
band-to-band
excitation, and
is to
reflection
intrinsic
One of the purposes of using these two
show the
technique
characterization.
for
capability
a
wide
of the microwave
range
and
of
lifetime
The results from the measurements on
the real lifetime and half of the lifetime
Figs.3.2.4
or
it is an extrinsic excitation in the case
of SI-GaAs wafer.
materials
generation,
3.2.5
for the
silicon
are shown in
and the
SI-GaAs
samples respectively.
The detector voltage decay shown in Fig.3.2.4 (a) was
taken
when
the
attenuator
is
set
to
the
maximum
attenuation and it represents the true decay of the excess
carriers
according
to the preceding
discussion.
The
measurement of the same excess carriers decay was also
carried out by nulling the reflection coefficients during
the
dark
condition
Fig. 3.2 .4 (b) .
and
result
is
shown
in
It is clearly seen that the decay of the
voltage in Fig.3.2.4(b)
F ig.3 . 2 . 4 (a).
the
If
the
is much faster than the one in
voltage
in
Fig.3.2.4(b)
is
proportional to the square of the voltage in Fig.3.2.4(a),
the logarithm of the normalized voltage in Fig.3.2.4(b)
will be twice of the logarithm of the normalized voltage
83
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.6
(a)
>
6
1.2
-
0.8
-
4)
O'
(Q
0
>
u
Q
u 0.4
o
v
vJ
V
Q
-
0.0
4
6
8
10
12
14
Time (microseconds)
1.6
(b)
>
e
~
1.2
o
O'
TJ
o
>
u
O.a
0
a
o 0.4
<
uu
V
J \
0.0
0
i
2
I
4
I
6
I
8
!
10
I
12
I
14
L
16
18
20
Time (microseconds)
Figure 3.2.4
Detector voltage decay of bare silicon
wafer with (a) maximum attenuation,
(b) nulling dark
signal and (c) log scale plots.
84
R eproduced with permission o f the copyright o w n e r Further reproduction prohibited without pemrissioh.
0
>»
■o
'J
V
a
3
0)
<0
o
3
CO
O'
0
-i
0.2
0.4
0.6
0.3
Tine (microseconds]
Figure 3.2.4 (continued) Detector voltage decay of
bare silicon wafer with (a) maximum attenuation,
nulling dark signal and (c) log scale plots.
85
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(b)
40
v
®
30
a*
i>
20
u
o
j :o
cj
* u
<u
0)
a
i
0.8
1.6
2.4
3.2
4.0
Time (microseconds)
I
0
|
0.8
|
|
1.6
|
i
i
2.4
i
3.2
i
4.0
Time (microseconds)
Figure 3.2.5
Detector voltage decay of SI-GaAs wafer
with (a) maximum attenuation,
(b) nulling dark signal
and (c) log scale plots.
86
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2
l.ocj Scale
ot Decay
-1
3
_
C
c
0.3
L .5
.4
3.2
4.0
Time (microseconds)
Figure 3.2.5 (continued) Detector voltage decay of
SI-GaAs wafer with (a) maximum attenuation,
(b)
nulling dark signal and (c) log scale plots.
87
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
in Fig.3.2.4(a).
This
condition
is confirmed by the
result shown in Fig.3.2.4(c) where the logarithm of the
two voltages in Figs.3.2.4(a) and 3.2.4(b) are compared.
The results using a SI-GaAs wafer were obtained and are
shown in Figs.3.2.5(a), 3.2.5(b)
and 3.2.5(c)
for the
excess carrier lifetime decay, half of the lifetime decay,
and the logarithm of the two decays, respectively.
An
independent
lifetime was
evaluation
carried out
of the
in silicon
photovoltage decay method.
excess
carriers
solar cells by
a
The open circuit photovoltage
of a PN junction after excess carrier injection will decay
as:
£at = — T
where
X
is
the
excess
<3-215>
carrier
lifetime.
The
above
equation shows that the open circuit photovoltage will
decay by kT/q or 0.02585 V at room temperature for every
lifetime X.
The measured photovoltage decay of a silicon
solar cell sample is shown in Fig. 3.2. 6 (b) where it is
clearly seen that the curve consists of an initial linear
decay and a second faster decay.
The initial linear decay
of the photovoltage is due to the recombination of the
excess carriers in the bulk and is used to extract the
88
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
i
30
<0
cn
|Q
fa)
o
>
u
±oj
CJ
V
fa)
<v
a
20
10
0
0
20
40
60
80
100
Time (microseconds)
800
>
E
V
O'
iQ
fa!
o
(b)
600
400
>
u
O
fa>
o
(U
fal
<u
a
200
\
200
400
600
800
1000
Time (microseconds)
Figure 3.2.6 Lifetime measurement on silicon solar
cell sample using (a) microwave reflection technique
and (b) open circuit photovoltage decay method.
89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
bulk lifetime of the excess carriers.
The second part of
the photovoltage decay is attributed to the recombination
in
the
depletion
several lifetimes
region
which
(Mahan 1981).
deduced from Fig.3.2. 6 (b)
decay
of
the
silicon
becomes
after
A lifetime of 18.9 (Is is
which shows
solar
dominant
cell
the photovoltage
after
excess
carrier
injection with GaAs laser.
The microwave reflection measurement was carried out
on
the
same
solar
photo-illumination.
cell
with
the
same
level
of
The detector voltage decay as shown
in Fig.3.2.6(a) gives a time constant of 19.5 p.s which is
obtained with a maximum attenuation
in the attenuator.
This
the
value
agrees
photovoltage decay.
very
well
with
one
from
the
The same agreement has been found for
other solar cell samples and it can be concluded that the
measured time constant using microwave technique is the
true excess carrier lifetime.
In summary,
reflection
it has been demonstrated that microwave
measurements
are
able
to
evaluate
the
recombination lifetime of photo-injected excess carriers
in semiconductors.
This technique can measure either the
lifetime
of
or
half
the
lifetime
depending
measurement setup and the applications.
in the
reflection coefficient
on
the
When the change
due to photoinjection
90
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
is
very small compared to the reflection coefficient in the
dark, the simple measurement setup which directly measures
the reflected power from the sample is usually used.
The
measurement with nulling the dark reflection coefficient
is required when the simple assumptions are not valid:
including a small change in the reflection coefficient,
constant phase angle 0 in (3.2.11), and square-law region
detection.
setup
as
It is always desirable to have a measurement
the
one
in Fig. 3.2.2
because
both
x and X / 2
measurements can be performed on the same sample to verify
the validity of the measurement.
3 .3 Ka-band
Measurement
Systems
In this section we will describe two Ka-band microwave
reflection
setups
which
have
been
used
for
the
photoconductivity measurements on SI-GaAs materials.
The
first measurement setup is normally used when the change
in the photoconductivity produces a signal larger than
mV in the crystal detector.
transient
1
Both the steady state and the
photoconductivity
responses
can be measured
using this measurement setup where the detected voltage of
the reflected microwave power is directly connected to and
displayed on a digital oscilloscope.
de t e c t o r
voltage
due
to
the
In the case that the
change
in
the
photoconductivity is less than 1 mV the second measurement
91
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
setup becomes necessary where the detected voltage
measured synchronously by using a lock-in amplifier.
is
The
measurement sensitivity of the second setup is greatly
improved
although
a
temporal
information
on
the
of
the
photoconductivity becomes difficult.
3.3.1
System
Figure
for
Large
Detected
3.3.1
shows
a
measurement
setup
Signal
schematic
used
for
diagram
detecting
the
large
photoconductivity signal induced by the light pulse.
The
system is basically a microwave bridge using a 3 dB hybrid
bridge.
The
hybrid
bridge
is
a
four-port
junction
consisting of a E- and H-plane arms as shown in Fig.3.3.2.
Such a junction displays the power dividing properties of
the E- and H-plane tees and has the advantage of being
completely matched at all its ports.
The application of
the hybrid bridge in the microwave system includes the
receiving
mixer,
phase
shifter,
discriminator (Gandhi 1981).
and
the
microwave
The operation of the hybrid
bridge is described by its S-matrix:
0
1
1
0
1
0
0
1
1
0
0
-1
0
1
-1
0
92
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(3.3.1)
35 GHz
CRYSTAL
DETECTOR
FREQUENCY
METER
MICROWAVE
GENERATOR
D I GITAL
VOLTMETER
ii
ATTENUATOR
-20dB
1
ISOLATOR
3
HYBRID
TEE
4
2
SLIDING
SHORT
L
CRYSTAL
DETECTOR
I
PULSER
A
WR-28 WAVEGUIDE
LASER
DIODE
1
SEMICONDUCTOR
SAMPLE
%
DIGITAL
OSC.
TRIGGER
SOURCE
X-Y-Z
MICROPOSITIONER
IBM PS2
COMPUTER
Figure 3.3.1
Microwave measurement setup for large
detected signals.
93
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
E -a rm
2
H -a rm
Figure 3.3.2
Four-port junction 3dB hybrid bridge.
94
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A 160 mW Gunn diode oscillator operating at 35 GHz '
provides the CW microwave power which is applied to port 1
of the bridge through an isolator.
to
the
Gunn
reflected
power
oscillator.
frequency
oscillator
from
The isolator connected
is used to
the
bridge
attenuate
and
all
protect
the
the
The microwave frequency is calibrated using a
meter
Fig.3.3.1.
and
An
a
crystal
attenuator
detector
and
a
as
sliding
shown
short
in
are
connected to port 3 of the hybrid bridge and they are used
for nulling the microwave reflection of the sample under
dark conditions.
The optical fiber connected directly to
the laser diode is inserted into the WR-28 rectangular
waveguide such that the wafer can be placed at the end of
the
waveguide
for
photoconductivity
a
quantitative
(see section
evaluation
3.5.1).
The
of
the
reflected
microwave power from the wafer is detected by a crystal
detector connected in port 4 of the bridge.
output
of
the
detector
enters
a
The voltage
Tektronix
digital
oscilloscope with a 300 MHz bandwidth and in term the
digital output signal from the oscilloscope is acquired
and recorded in an IBM PS/2 computer for further analysis.
Two
different
light
sources
have
been
used
inducing photoconductivity in SI-GaAs materials.
for
One of
them is a GaAs laser which emits a monochromatic light at
904
nm
and
is
used
to
produce
the
below-band-gap
95
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photoconductivity.
The other light source is an AlGaAs
laser emitting light at 850 nm which is lower than the
direct band gap cut-off wavelength of 880 nm for GaAs
materials
at room temperature.
Both
laser diodes are
driven by the laser pulsers which allow a variable laser
current
and
light
pulse
width.
The
operating
X
,
characteristics of the two lasers are given in Table 3.3.1
which shows the emission wavelength
I^h'
maximum operating
current
threshold current
Imax
at maximum output
power Pmax, and laser pulse duration Tp .
The crystal detector we have used is an HP detector
which,
when
used
in
conjunction
with
a matched
load,
exhibits a square-law characteristic for input powers less
than 10 mW.
In other words the measured detector output
voltage is linearly proportional to the input microwave
power for a small input microwave power.
shows
the measured voltage-power
Figure 3.3.3
characteristic
of the
crystal detector that we have used and it is seen that the
detection
of
the
microwave
power
does
not
follow
square-law for a high input microwave power.
the
Under dark
conditions the semi-insulating wafer reflects almost all
microwave
power
back
and
it
is
very
common
that
the
detection of the microwave power is beyond the square-law
region
of the
detector.
In order to
obtain
a. linear
relationship between the time varying microwave power and
96
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Table 3.3.1
Operation characteristics of two laser
diodes.
Laser
A,(nm)
rth <A >
•’■max
pmax
Tp(ns)
AlGaAs
850
13
60
54
50
GaAs
904
11
40
31
50
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1000 1
i
u
100
s
K
»4
2
C6
O
H
a
u
t*
a
a
-20
-10
0
MICROWAVE
Figure 3.3.3
POWER
10
20
(dBm)
Characteristic curve of an HP crystal
detector.
98
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the corresponding time varying detector voltage the change
in the microwave power AP due to the photoconductivity
should be small compared to the dark reflected power PQ .
Consider a detector voltage VQ in the non-square-law
region which corresponds to an input power PQ in the dark
condition.
The change in the input power AP due to the
photoconductivity of the wafer will cause a change in the
detector voltage AV.
Assuming the changes, Av and AP, are
small
VQ
compared
to
characteristic curve at
and P0
and
the
slope
of
the
(V0 ,P0 ) is s, the output voltage
and the input power of the crystal detector can be related
by:
(3.3.2)
Making a Taylor series expansion in the above equation and
retaining only the first two terms we obtain
(3.3.3)
o
which shows that the change in the detector voltage is
linearly proportional to the change in the input power.
It
should be noted that the value
of s is one
99
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in the
square-law
region
and
is
less
than
one
beyond
the
square-law region as can be seen in Fig.3.3.3.
3.3.2
System
Figure
for
3.3.4
Small
shows
Detected
a
Signal
schematic
diagram
of
the
measurement setup which has been used for detecting a very
small
change
in
the
detector
output
voltage.
This
arrangement is mainly used for measuring the steady state
below-band-gap photoconductivity which requires a light
duration larger than 1 |is.
The light source we have used
is a yittrium-alluminum-garnet
(YAG)
laser which has a
maximum output power of 2 W and emits a CW monochromatic
light
at
1.06 urn or
1.32
modulated by an optical
optical
fiber through
urn.
The
CW laser
light
is
chopper and is coupled to the
a fiber coupler.
The alignment
between the YAG laser and the fiber coupler is essential
and is usually achieved with the aid of a visible He-Ne
laser.
The modulation frequency of the laser light can be
as high as 30 KHz which corresponds to a pulse duration of
33 |ls.
Since
the
laser
power
is
low
the
induced
photoconductivity is very small and so is the change in
the
detector
detector
voltage.
voltage
The
due
observed
to
the
variation, of
change
in
100
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the
the
35 GHz
MICROWAVE
GENERATOR
I
FREQUENCY
METER
t i
ATTENUATOR
-20dB
ISOLATOR
HYBRID
SLIDING
SHORT
FIBER
COUPLER
YAG
LASER
WR-28 WAVEGUIDE
SEMICONDUCTOR
SAMPLE
|CHOPPERj
LOCK-IN
AMP.
DIGITAL
VOLTMETER
CRYSTAL
DETECTOR
r
u
Figure 3.3.4
CHOPPER
CONTROLLER
X-Y-Z
MICROPOSITIONER
Microwave measurement setup for small
detected signals.
101
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
photoconductivity ranges typically from a few mV to a few
tenths of mV which can be barely seen on the oscilloscope.
By using a lock-in amplifier the sensitivity of measuring
a small AC voltage is increased to be in the range of 50
(IV.
Therefore the steady state below-band-gap microwave
response
using
the
low power
We
can
also
measured.
photoconductivity
setup.
YAG
roughly
laser
can be
estimate
the
easily
minimum
G that can be detected by using this
As will be shown in section 3.5.1 the normalized
dissipated microwave power Pd/Pj_n is equal to 54a.
assume
= 100|IV and P^n = IV, then a will be in the
order of
1 0 “® 1 /ohm-cm.
3 .4 Choke-Flange
3.4.1
If we
Rectangular
Waveguide
Introduction
As mentioned before both the open-ended rectangular
waveguide and the taper-tip parallel-plate antenna can be
used for receiving the reflected microwave power from the
wafer
in
the
microwave
open-ended
rectangular
advantages
over
the
reflection
waveguide
previously
parallel-plate antenna.
measurement.
has
two
developed
The
significant
taper-tip
Firstly, the sensitivity of the
open-ended rectangular waveguide is much higher because
the propagation loss
in the waveguide
is usually very
102
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small
while
propagation
space.
the
taper— tip
loss due to
antenna
suffers
a
serious
its power radiation into
free
Secondly, the electromagnetic problem is easier to
solve for the open-ended rectangular waveguide, therefore
a quantitative analysis relating the reflected microwave
power
to
the photo-induced
becomes feasible.
conductivity
of the wafer
In addition a high spatial resolution,
which has been considered as the key advantage of the
taper-tip parallel-plate antenna, can be achieved for the
open-ended rectangular waveguide by controlling the size
of the illuminated spot on the wafer.
Two
types
of
flanges
are
rectangular waveguide sections:
(2) the flat-flange.
commonly
used
in
the
(1 ) the choke-flange, and
The more complicated choke-flange is
designed for the choke-flange coupling
(see Fig.3.4.1)
which provides a better connection between two rectangular
waveguide
sections
than
the
direct
contact
coupling
because clean, flat, parallel surfaces are hard to achieve
and maintain.
Choke-flange couplings consist essentially
of a series-branching transmission line whose length is
one-half wavelength, thus presenting zero series impedance
to the main line.
chosen
to be
The depth d of the outer groove is
a quarter
wavelength
in
order
that
the
minimum- current point will occur at the contact.between
the choke-flange and the flat-flange.
103
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Choke-Flange Coupling
Figure 3.4.1
Direct Contact Coupling
Choke-flange and direct contact coupling
between two rectangular waveguide sections.
104
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During
the
non-destructive
microwave
reflection
measurement the wafer is usually backed by a metallic
short and is placed close to the flange of the rectangular
waveguide.
waveguide
It is found that the choke-flange rectangular
is
more
suitable
to
use
in
the
microwave
reflection measurement because the reflected microwave
power is almost independent of the wafer thickness.
The field distribution in the wafer adjacent to the
choke-flange
o f .the
rectangular
waveguide
is
a very
complicated problem and is usually considered as TE-j_q
mode.
During the course of this study it has been found
that the reflected microwave signal taken with the wafer
outside is very similar to the one with the wafer inside.
This result strongly supports the assumption of the TE 10
propagating
wave
quantitative
conductivity
which
is
relationship
of the
later
between
adjacent
wafer
used
to
the
and
derive
a
photo-induced
the
dissipated
microwave power.
In the next section we will describe the experimental
results
taken
with
the
choke-flange
and
flat-flange
waveguides and show why the first one is favored for a
non-destructive
experimental
measurement.
results
will
In
be
section
given
to
3.4.3
some
support
the
105
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assumption of a TE^ q propagating mode in a sample adjacent
to the choke-flange waveguide.
3.4.2
Choke-Flange and Flat-Flange Rectangular
Waveguides
Although
the
choke-flange
rectangular
waveguide
performs better than the flat-flange rectangular waveguide
in connecting two waveguide sections,
it has't been very
clear which of the two will serve better when they are
incorporated into the microwave reflection measurement.
In order to
determine which waveguide
suitable
use,
to
a
few measurements
flange
are
taken
different air spacing and wafer thicknesses.
wafer
is
placed
outside
non-destructive purpose,
the
is more
using
Since the
waveguide
for
a
the variation of the reflected
microwave power due to different wafer thicknesses
or
different spacing between the waveguide flange surface and
the metallic short becomes
measurement.
An
ideal
a major concern during the
candidate
for
the
open-ended
waveguide should be insensitive to the wafer thickness and
the quality of the contact between the wafer
and the
waveguide flange.
Fig.3.4.2
shows the measured reflected microwave
power as a function of the spacing S between the waveguide
106
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CHOKE-FLANGE
FLAT-FLANGE
\
I
s
H
X
a
u
§
h
g
5
10
15
20
SPACING S (mm)
Figure 3.4.2a
Reflected microwave power as a function
of spacing S (0-20 mm) using the choke-flange and
flat-flange waveguides.
107
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"*• CHOKE-FLANGE
FLAT-FLANGE
SPACING S (mm)
Figure 3.4.2b
Reflected microwave power as a function
of spacing S (0-5 mm) using the choke-flange and
flat-flange waveguides.
108
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
flange and the metallic
short using the two different
waveguide
is
flanges.
rectangular
It
waveguide
seen
suffers
that
a
the
flat-flange
serious
loss
in
the
reflected microwave power when the spacing S is larger
than
0.2
waveguide
mm.
However
receives
the
almost
choke-flange
all the
rectangular
reflected microwave
power up to a spacing of 3 mm which corresponds to an
electrical
length
sli g ht ly
l ar ge r
quarter-wavelength of TE10 mode in air.
than
one
Since most of the
test wafers are 25 mil thick which corresponding to one
quarter-wavelength of TE1Q mode,
it is conceivable that
the use of the choke-flange waveguide is better because of
the higher reflected microwave power..
It is also interesting to see in Fig.3.4.2a that the
measured
reflected
microwave
power
of
both
waveguide
flanges shows the same periodic response when the spacing
S is greater than 3 mm.
The period appears to be one
half-wavelength of the free space which implies that the
plane wave propagation dominates in this range.
Another
waveguide
significant
over
the
advantage
flat-flange
reflected microwave power
of
the
waveguide
is relatively
choke-flange
is
that
the
insensitive to
both the wafer thickness and the quality of the contact
between the waveguide flange and the wafer.
Fig.3.4.3
109
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40
O CHOKE-FLANGE
■ FLAT-FLANGE
%
20
'
10
-
3
3
5
a
18
■ ■
T
T
t
20
22
24
— r
26
28
WATER THICKNESS (mil)
Figure 3.4.3
Reflected microwave power as a function
of wafer thickness for the choke-flange and
flat-flange waveguides.
110
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shows the measured reflected microwave power using two
different types of waveguide flanges for different wafer
thicknesses.
gives
a
It is seen that the choke-flange waveguide
higher
and
more
uniform
response
than
the
flat-flange waveguide.
Since all the measured wafers are
bulk
GaAs
semi-insulating
microwave
power should
microwave
power; thus
be
the
materials
the
the
reflected
the
incident
of the
reflected
same as
variation
microwave power due to the change in the wafer thickness
should be
minor.
This is true
for the
choke-flange
waveguide but not for the flat-flange waveguide.
It was also observed during the measurement that the
condition of the contact between the waveguide flange and
the wafer surface is tremendously critical to the measured
reflected power when using the
flat-flange waveguide.
However the use of the choke-flange waveguide does not
have
the
same
electrically
problem because
the contact
rather than physically.
As
is
made
a result the
choke-flange waveguide is more suitable to incorporate
into the microwave
reflection measurement
setup for a
convenient and reliable measurement.
3.4.3
Transverse-Electric
Mode
Assumption
When a piece of wafer is shaped and fitted into the
111
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rectangular
waveguide
as
shown
in
Fig.3.4.4a,
the
electromagnetic field distribution inside the wafer will
be TE 10 mode.
However in the real application the wafer
is placed outside the waveguide as shown in Fig.3.4.4b and
the
field
distribution
complicated.
inside
the
wafer
becomes
more
A knowledge of this field distribution is
important because the measured dissipated microwave power
is related not only to the photoconductivity of the sample
but
also
to
conditions
the
it
fields
has
been
inside
the
observed
wafer.
that
the
In
dark
reflected
microwave power of the configuration in Fig.3.4.4b is as
high as the one measured without putting the wafer.
implies
that
the microwave
radiation
direction of the wafer is very small,
along the
This
radial
if there is any.
Since point A in Fig.3.4.4b represents an electrical short
it is suggested that the field distribution does not vary
much from Fig.3.4.4a to Fig.3.4.4b.
Another evidence to support the transverse-electric
mode
assumption
is
given
by
comparing
the
reflected
microwave power of the configurations in Figs.3.4.4a and
3.4.4b.
Fig.3.4.5 shows this comparison where the curve
having a higher value is taken with the wafer inside the
waveguide and another one is taken with the wafer outside
the
waveguide.
Considering
the
fact
that
the. photon
intensity of the higher curve is 1.07 times larger than
112
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(b)
w a fe r
metallic
short
Figure 3.4.4 Configurations for the microwave reflection
measurement using the choke-flange waveguide where
(a) the wafer is cut and fitted into the waveguide, and
(b) the wafer is placed outside the waveguide.
113
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.071
.086
voltage
(volts)
.056
.048
.036
.026
OUT
.013
.003
■
40
60
120
160
200
240
280
320
360
400
Time (nanoseconds)
Figure 3.4.5
Reflected microwave power transients by
using configurations in Fig.3.4.4a and Fig.3.4.4b.
114
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
that of the lower one, it is found that the ratio of the
peak value of the two curves is about 1.2.
dissipated microwave
power
goes
as the
Since the
square
of the
electric field, the electric field of the lower curve is
90% of that of the higher one.
in
Fig. 3.4.4b
is
a
very
It means the configuration
good
approximation
to
the
configuration in Fig.3.4.4a and the assumption of the TE10
mode appears to be reasonable.
As
the
lifetime
measurement
is
concerned
it
is
desirable to compare the transient response obtained from
the
two
Fig. 3 . 4 .6
configurations
plots
the
log
in
Figs.3.4.4a
scale
of
the
and
two
3.4.4b.
curves
in
Fig. 3.4.5 with the same normalized peak value and it is
seen that both curves have the same slope.
Since the
lifetime information extracted from the two configurations
in Fig.3.4.4 are the same one can simply place the wafer
outside
the
choke-flange
waveguide
for
a
quick,
non-destructive lifetime measurement as was described in
section 3.2.
3.5 Photoconductivity Evaluation for Non-uniform
Illumination
The taper-tip parallel-plate antenna was originally
designed to have a high spatial resolution by confining
115
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LOG SCALE
OF TRANSIENT
8
4.9
OUT
3.9
3
2.9
2
1 .5
■
1
.9
40
60
80
100
120
140
160
160
200
TIME (nanoseconds)
Figure 3.4.6 Log scale of the transients in Fig.3.4.5.
116
R eproduced with permission o f the copyright ow ner. Further reproduction prohibited without permission
the
electromagnetic
aperture.
energy
in
a
physically
reduced
In the case of rectangular waveguide there is
no easy way to confine the electromagnetic energy in a
small area except the use of a resonant iris (Ragan 1948)
which
will
introduce
more
distribution analysis.
measurement,
complexity
in
the
fields
However, in the photoconductivity
a high spatial resolution becomes possible
for the rectangular waveguide because it can be achieved
optically by controlling the size of the illuminated spot
on the wafer.
When
the
waveguide
is
entire
cross
uniformly
section
of
illuminated
a
rectangular
the
dissipated
microwave power due to the photoconductivity of the wafer
can be calculated by assuming a T E ^
propagating wave.
The dissipated power will decrease by some factor if the
illumination
illumination
is
at
not
uniform,
the
e.g.
center
of
a
small
the
circular
waveguide.
A
quantitative relationship between the dissipated microwave
power and the photoconductivity of the wafer is important
because
it allows the evaluation of the photo-induced
carrier concentration from the measured power dissipation.
It
is
the
propose
of
this
section
to
1)
derive
a
quantitative relationship between the dissipated microwave
power and the photoconductivity
of the wafer
uniform and nonuniform illumination and
2
for both
) corroborate the
117
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developed
theory
by
the
experimental
data
which
are
obtained by using SI-GaAs wafers.
In section
3.5.1
the
reflected microwave
power
is
calculated for a wide range of conductivity assuming an
uniform illumination across the whole waveguide.
3.5.2
deals with a more complicated case,
Section
that is only a
small circular area is illuminated by an external light
source.
An area
factor which relating the dissipated
power of the circular illumination to that of the uniform
illumination is defined for a general purpose.
Both the
theoretical derivation and the experimental studies have
been carried out to determine this area factor and a good
agreement has been found for an illumination radius up to
0.9 mm.
In section 3.5.3 a photoconductivity-independent
proportionality
between
the
constant,
reflected
called sensitivity
microwave
photoconductivity is derived.
useful
in the
sense that
power
factor
change
and
S,
the
This sensitivity factor is
the photoconductivity
can be
directly determined from the measured dissipated power.
It will be demonstrated that the theoretical result agrees
with the experimental data with a low photoconductivity
and a small light area.
118
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3.5.1
General
Equations
For
Uniform
Illumination
Let the photo-induced conductivity be uniform over the
entire waveguide area due to an uniform illumination on
the
wafer
which
properties.
The
has
uniform
propagation
optical
and
constant
and
electrical
the
wave
impedance of the wave propagating inside a GaAs wafer,
assuming a TE 10 mode, is given by:
(3.5.1)
(3.5.2)
Y
where
a is larger dimension of rectangular waveguide
(7.112 mm for WR-28 waveguide)
0)
is microwave frequency
( 2.199 x 1011 rad/s at
35 GHz )
\L is permeability ( 1.256 x 10" 6 H/m )
<J is photo-induced conductivity ( in
1 /ohm-cm
)
e is permittivity ( 1.16 x 10-10 F/m for GaAs )
From the transmission line theory the input impedance
looking
into the
front
side
of the
GaAs
wafer
expressed as:
119
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can be
eYt-e _Yt
Zh = Zretanh(yt) = Z
“ rE-----------TE
(3.5.3)
where the GaAs wafer is backed by a metallic short as
shown in Fig.3.5.1.
The reflection coefficient resulting
from a mismatch in the
impedances
ZQ and Zin is simply
given by:
n
<3-5-4)
0
where ZQ is the wave impedance inside the waveguide and
its value can be calculated by setting a = 0 and e = 8.85 x
10~ 1 2
F/m
eqnSi
Fig. 3. 5.2
(3.5.1) and (3.5.2).
plots the normalized reflected power Pr/I?in
= r x r* vs
photoconductivity
ranging
from
ohm-cm —■1
-*■.
. seen that the reflected microwave power
It is
1 0 -3
to
102
varies with the wafer thickness for a conductivity less
than 0.1 ohm-cm- 1 .
ohm-cm - 1
For the conductivity larger than 0.1
all the wafers
show a very similar normalized
reflected power response.
The reason for this is that
when the conductivity of the wafer
is larger than
0.1
ohm-cm - 1 the skin depth of the wafer becomes less than 25
mil at 35 GHz.
Therefore the reflected power is mainly
determined by the wafer's
conductivity
rather than the
120
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
GaAs wafer
WR-28 waveguide
Figure 3.5.1
Transmission line representation of
the GaAs wafer for the calculation of the reflected
microwave power.
121
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.0
.8
.€
-*■ 20.4 mil
21 mil
—
22 mil
23.5 mil
.4
N
.2
s
.0
,001
.01
.1
1
10
100
PHOTOCONDUCTIVITY (1/ohm-can)
Figure 3.5.2
Normalized reflected power vs photo­
conductivity of the wafer.
122
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
thickness.
If the photoconductivity is so low such that the wafer
behaves like a lossy dielectric, the electric field inside
the
wafer
will
photoconductivity.
be
almost
independent
of
the
In this case the microwave dissipation
is directly proportional to the photoconductivity of the
wafer.
The normalized reflected power is calculated and
tabulated in Table 3.5.1 for a conductivity ranging from
10-5 to 10-3 ohm-cm”-'-.
It is seen that the
ratio is
proportional to the conductivity a with a proportionality
constant of 54 i 1.
3.5.2
Area Factor For A Small Circular
Illumination
Very
often
material's
distribution.
there
properties
is
interest
but
also
not
in
only
their
in
the
spatial
Any characterization technique which can be
utilized for a mapping purpose has to have a high spatial
resolution.
A convenient way to increase the spatial
resolution of the microwave reflection technique is to
reduce the illumination area to a small circle such that
the change of the reflected microwave power is attributed
to the photoconductivity of that small circular area only.
However,
a derivation of the quantitative relationship
123
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 3.5.1 The normalized reflected and dissipated
microwave power and the sensitivity factor in the
low conductivity range.
Pr /pin
P /P.
d in
a
(1/ohm-cm)
S
n
.99945
.00055
.00001
55
.9989
.0011
.00002
55
.99836
.00164
.00003
54.7
.99781
.00219
.00004
54.7
.99727
.00273
.00005
54.6
.99673
.00327
.00006
54.5
.99618
.00382
.00007
54.5
.99564
.00436
.00008
54.5
.9951
.0049
.00009
54.4
.99455
.00545
.0001
54.5
.98914
.01086
.0002
54.3
.98376
.01624
.0003
54.1
.97841
.02159
.0004
54
.97309
.02691
.0005
53.8
.96779
.03221
.0006
53.7
.96253
.03747
.0007
53.5
.95729
.04271
.0008
53.4
.95208
.04792
.0009
53.2
.9469
.0531
.001
53.1
124
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
between the dissipated power and the photoconductivity in
the small area becomes very complicated since the simple
transmission
line
model
which
assumes
an
uniform
equations
derived
conductivity is no longer valid.
In
order
to
use
the
general
previously, one may define an area factor AF as the ratio
of the dissipated microwave power when a small circular
area is illuminated to that when an entire waveguide area
is
under
the
same
illumination.
schematically shown in Fig.3.5.3.
factor
can
be
applied
to
This
definition
is
The concept of the area
different
levels
of
photoconductivity although the following discussions are
mainly given for a low level condition.
If the level of the photoconductivity is kept low,
that is less than 1% of coe or 2.5 x 10-3 ohm-cm-1 for the
GaAs wafer, the electromagnetic field distribution in both
cases can be assumed to be the same as that in the dark
condition.
If
the
small
circle
is
centered
transverse plane of the rectangular waveguide,
in
the
the area
factor can be calculated by the definition as:
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ii
b
G
0
1
“
r
small circular illumination
dissipated power = Pd (d)
uniform illumination
dissipated power = pd,u
area factor AF = Pd(d) / Pd u
Figure 3.5.3
Schematic definition of the area factor
for the small circular illumination.
126
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
, JI-7
-J J J
•JJJ
E2 ( x , z ) dx dy dz
°
f«*>
<3-5-5>
E 2(x,z) dxdydz
o o o
7CX
with E ( x , z ) = Ew cos( — ) sin( pzz )
where Ew is the maximum electric field in the GaAs wafer
and the electric field is taken as if in a non-conducting
material because of the low photoconductivity.
that
the
area
factor
is
independent
It is seen
of
the
photoconductivity and contains only one geometric variable
which
is
the
illumination
radius
d.
The
result
of
equation (3.5.5) is plotted in Fig.3.5.4a as a function of
the illumination radius d.
Once the illumination radius
is known, the equivalent dissipation power PdfU under an
uniform
illumination
can
be
obtained
from
Pd (d)/AF.
Therefore the photoconductivity in the small circular area
can be
found
in the
same way as
described
in section
3.5.1.
The theoretical calculation of the area factor has
been corroborated by measuring the dissipated microwave
power for different
illumination radii with a constant
photon flux density.
The radius of the illuminated circle
127
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06
2
i
THEORETICAL CURVE
3
ucu
a
H
H
a
o
a
H
EXPERIMENTAL DATA
0 .0
0.5
1.0
ILLUMINATION RADIUS
Figure 3.5.4a
1.5
2.0
(non)
Theoretical and experimental area factors.
The experimental data are taken with a constant photon
flux density on the wafer.
128
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1
.8
.6
a
u
THEORETICAL CURVE
.4
.2
H
S3
o
S3
H
EXPERIMENTAL DATA
.0
0.0
0.5
1.0
1.5
2.0
ILLUMINATION RADUIS (mm)
Figure 3.5.4b
Theoretical and experimental area factors.
The experimental data are taken with a constant photon
flux, but various photon flux density, on the wafer.
129
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is varied by changing the distance between the optical
fiber and the wafer as depicted in Fig.3.5.5.
It should
be pointed out here that a spatial resolution of 25 mil
can be achieved when the distance h is only 1 mm.
The
illumination intensity is readjusted every time after the
optical
fiber
is
moved,
by
monitoring
a
silicon
photodetector placed at the end of the waveguide.
adjustment
of
the
illumination
intensity
has
This
to
be
deliberately performed to insure a constant illumination.
For uniform illumination in the WR-28 waveguide the
height h should be at least 17.5 mm.
The peak microwave
dissipated power for an uniform illumination is measured
using a 904 nm, 40 ns light pulse.
The same measurements
are taken for h = 2, 3, 4, 6, and 8 mm which correspond to
an illumination radius of 0.5, 0.7, 0.9, 1.3, and 1.7 mm,
respectively.
The normalized peak dissipation power, or
the experimental area factor,
is plotted in Fig.3.5.4a.
It is seen that there is a very good agreement between the
theoretical
illumination
and the
radius
experimental
up
to
0.9
area
mm.
factors
After
for an
that
the
experimental data shows a lower value for the area factor.
This discrepancy
could be due to some degradation of the
electric field in the illuminated area when this area is
larger
than
n x
(0.9mm)2
but
not
larger
than
the
rectangular waveguide area, and more detailed analyses are
130
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200
m icrons op tical fib e r
WR-28 rectangular
waveguide
numerical
aperture=0.2
GaAs wafer
2d
Figure 3.5.5
Schematic diagram showing the calculation
of the illumination radius which equals 100 microns + 0.2h.
131
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
required for further understanding.
In order to eliminate the possible error caused by
adjusting
the
illumination
intensity
during
the
above
measurement of the experimental area factor, an alternate
method is used to determine the experimental area factor
without
the
adjustment
of
the
photon
flux.
The
illumination radius d is varied by changing the distance
h
between
the
optical
fiber
and
the
wafer.
The
photoconductivity of the wafer varies as 1/d^ because of a
constant photon flux.
The experimental area factor can be
found a s :
Pd(d)
P (d)
2
AF = - ± _ - _±__ oc P (d) d2
*d,u
a
(3.5.6)
where Pd (d) is the measured microwave dissipation power.
The experimental area factor together with the theoretical
one
is
plotted
in
Fig. 3.5.4b,
with
a
scaling
on
the
experimental area factor data so that the lower part of
the experimental data agree with the theoretical data.
is
seen
that
the
illumination radius
same
discrepancy
occurs
for
It
the
larger than 0.9 mm as was shown in
Fig.3.5.4a.
132
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3.5.3
Sensitivity
Factor
It has been shown that the microwave dissipated power
Pd is proportional to the photoconductivity a of the wafer
when
the photoconductivity
sensitivity
between
factor
the
S
Pd
photoconductivity
and
can
as
the
the
be
is
low.
One may
proportionality
a
so
directly
that
define
a
constant
the
induced
determined
from the
measured dissipated microwave power Pd .
Once again let the photoconductivity be low and assume
that the electric field inside the wafer is the same as it
were in the dark.
The dissipated microwave power due to
the small circular illumination can be expressed as:
t
Pd ( d ) = 4 a
d
VZ7
JJ J
E2 ( x , z ) d x d y d z
o o o
t
f2 2
d v d - y
=4aJ*J
J
( T E 0cos(““ ~ ) s*n( Pz z ) )2 d xd y dz
(3.5.7)
o o o
where Eg is the maximum electric field in air and T is the
ratio of the maximum electric field in the GaAs wafer to
Eg.
The total input microwave power Pin is given as:
133
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W2 4a
(3.5.8)
where
ZTE
is the
normalized
wave
sensitivity
impedance
factor
of the TE10 mode.
which
A
is defined as the
ratio of Pd to P^CT can be written as:
(3.5.9)
This
normalized
function
of
Fig.3.5.6.
the
In
sensitivity
factor
illumination
order
to
is
radius
directly
plotted
d
as
as
shown
evaluate
a
in
the
photoconductivity equation (3.5.9) can be rewritten as:
Pd( d ) = Sn( d ) P h a = S ( d ) c
(3.5.10)
where S(d) is the sensitivity factor relating the measured
dissipated microwave power to the photoconductivity of the
wafer.
An example of determining the photoconductivity using
the sensitivity factor is given in the following.
illumination
radius
be
0.9
mm
which
is
Let the
obtained
134
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by
40
30
20
10
0
0.0
0.5
1.0
ILLUMINATION RADIUS
Figure 3.5.6
1.5
2.0
(mm)
Normalized sentivity factor as a
function of the illumination radius d.
135
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adjusting the distance between the optical fiber and the
wafer to be 4 mm.
The Pd and Pin are measured to be 7 mV
and 295 mV respectively using an HP crystal detector.
photoconductivity can be determined from the Pa/^in
The
power
ratio and the calculated normalized sensitivity factor as
following:
P.( 0.9 mm)
7
a _ p jnSn(0.9m m ) " 295 x 10.57 "
This
photoconductivity
_3
22x10
can
( 1/ohm-cm)
be
estimated
(3.5.11)
from
an
independent measurement where the carrier concentration is
determined
density.
from
the
measurement
of
the
photon
flux
The photon flux at the surface of the wafer is
measured using a photodiode and an optical attenuator.
The current passing through the silicon photodiode FND-100
produces a voltage of 42 mV for a 50 ohm termination which
corresponds
to
a current
of
8.4
x
10-4 A.
Since the
absolute sensitivity of FND-100 is 0.62 A/W at 900 nm, the
photodiode received a total photon power of 1.35xl0-3 W.
The photon power coming out
attenuated
reaching
by
the
consideration.
determined
system,
an
optical
silicon
from the optical
filter
ORIEL
photodiode
fiber
51000
for
a
is
before
safety
The attenuation of the optical filter is
to be
156
at
904
nm using
a monochrometer
as a result the original photon flux coming out
136
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from the optical fiber is:
^ ■ ('-35Xi037eV)('-6) "
I0'7^
^,,2)
where 1.37 eV is the energy of photon at 904 nm.
Since
the photon flux is detected over a 1 mm2 aperture area the
photon flux density can be calculated as:
N.
— ---- = 9.5 x 1019 (
p* detector area
The photoconductivity
2
s cm
)
(3.5.13)
induced in the GaAs wafer by the
short illumination at 904 nm can be approximated as:
At
o = q(lnn = q(xn
J
At
C ^ N ^ N ^ d t = qH„o°NEL2
j
dt
= y q H noJNE L 2 At = 2.9x 10"3 ( 1/ohm-cm)
(3.5.14)
where |ln= 6500 cm2/s-V, an° =1.5 x 10-16 cm2, Nel 2=1016 cm-3,
At= 40 ns, and the factor 1/2 results from a triangular
increase in the photon flux density.
The agreement in
determining the photoconductivity as shown in (3.5.11) and
(3.5.14)
is fairly good considering so many calculations
and assumptions are involved.
In conclusion,
this study
137
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shows that it is possible to determine quantitatively the
photoconductivity of the wafer directly from the measured
dissipated
microwave
power
for
both
uniform
non-uniform illuminations.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and
CHAPTER 4
EXPERIMENTAL RESULTS AND
DISCUSSIONS
4 .1 Introduction
In order to
SI-GaAs,
check the photoconductivity model
consisting
of
shallow acceptor level,
a deep
donor
level
EL2
for
and
a
many LEC-grown undoped SI-GaAS
wafers were measured under ABG and BBG excitations.
These
wafers contain a wide range of carbon concentration, from
less than 3xl0-*-^ to 7x10^5 cirT^, determined by the LVM
absorption measurement.
between
1)
the
BBG
Good correlations have been found
steady
state
conductivity and the dark resistivity,
state
microwave
concentration,
photoconductivity
and
3)
the
time
microwave
photo­
2) the ABG steady
and
the
constant
LVM
of
carbon
the
BBG
transient microwave photoconductivity and the LVM carbon
concentration.
Since
the photoconductivity model
can
explain all these correlations, it is considered that the
139
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model is valid.
While the above correlations can be found they only
exist under certain conditions.
The examples are 1) a BBG
light pulse of a few |is long is required in the dark
resistivity
required
measurement,
in the ABG
temperature
2)
steady
larger than
transient measurement.
low
level
excitation
state measurement,
220 K is required
is
and
3)
in the BBG
These constrains are based on the
experimental observation and the photoconductivity model
of SI-GaAs, and they will be discussed in this chapter.
In
addition,
the
measurement
result
of
EL2
concentration using near-infrared absorption will be given
in section 4.2.
A new technique introduced as a part of
checking the photoconductivity model, called photoinduced
microwave deep level transient spectroscopy (PMDLTS), will
be described in sections 4.6.
All
chapter
the
microwave
were
measurements
performed
maximum attenuation.
by
setting
described
the
in
attenuator
steady
illumination
state
to
Therefore the decay of the microwave
response represents the actual excess carrier decay.
ABG
this
and
BBG
transient
measurements
is all over the waveguide
cross
In
the
section,
although a better spatial resolution can be achieved.
140
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4.2 EL 2
Concentration
Measurement
Infrared
Absorption
The
concentration
EL2
semi-insulating
GaAs
of
wafers
some
has
Using
of
been
our
Near-
undoped
measured
near-infrared optical absorption technique. A
\asing
description
of how to determine the EL2 concentration from the optical
transmittance has been given in section 2.2.4.
found that the EL2
concentration determined
It is
from this
technique is very sensitive to the value of the measured
transmittance which depends
on the calibration
of the
system as well as the surface condition of wafers.
this
section
we
will
demonstrate
how
to
modify
In
the
equations described in section 2.2.4 to the determination
of
the
concentrations
of
ionized
and
unionized
EL2
centers.
After a SI-GaAs wafer is carefully loaded into the
spectrophotometer (PE 330, PERKIN-ELMER) the transmittance
data
is
automatically
plotted
against
wavelength ranging from 900 nm to 2000 nm.
shows
a
undoped
typical
transmittance
SI-GaAs
wafers.
wavelength
is
larger
It
than
spectrum
is
1600
seen
nm
the
the
optical
Figure 4.2.1
obtained
that
when
for
the
transmittance
approaches its maximum value which corresponds to a zero
absorption
(a=0) .
When the wavelength is close to 900 nm
141
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o
o
<M
o
o
CM
O
O
o
s
dp
O
2DNVMIWSNVH1
142
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
wafers.
GaAs
semi-insulating
H
LEC-grown
o
undoped
s
A typical
a
4.2.1
o
Figure
o
transmittance
spectrum
for
o
o
the
transmittance
decreases
abruptly because the
light
energy becomes very close to the energy gap of GaAs which
is 1.42 eV or 873 nm in wavelength.
The proper
concentration
range
is
for the
from
1000
determination
nm
to
1400
nm
of the
EL2
where
the
absorption of light energy is mainly attributed to the EL2
centers.
As indicated in (2.2.13) and (2.2.14) the total
EL2 concentration N E L 2 and the occupancy factor f can be
determined by measuring the absorption coefficient a at
two different wavelengths.
The concentration of ionized
EL2, n+el2' anc* unionized EL2, N°EL 2 f centers can be then
calculated by:
»,*
-
EL2
m
EL2
„ „ _ <W
^~ ^
Q
V
NEL2. = N„r
,f =
EL2
2)gn(1) - (W
1> < < 2 >
Q
D
2)an(1) " °n(2)ap<1)
g teL2<1 > ^ < 2 >
-
a°(2)a°(i) P
n
„
(4.2.1)
«aL2<2 > < < 1 >
(4.2.2)
a n (2 ) ° p < 1 )
One major difficulty encountered here is the variation
of
the
optical
absorption
coefficient
a
uncertainty in the value of the transmittance.
be
better
product
understood
of the
by
absorption
seeing
Table
coefficient
4.2.1
due
to
an
This can
where
the
a and the wafer
143
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Table 4.2.1
The product at, the transmittance (T),
and the sensitivity quantity at 1060 nm obtained from
equation (2.2.18).
at
T
(8 at/at) / (8t /t )
0.351
0.355
-2.59
0.200
0.42
-4.39
0.100
0.471
-8.5
0.081
0.482
-10.40
0.060
0.494
-14.12
0.030
0.512
-27 .7
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
thickness
t,
the
transmittance
T,
and
a
sensitivity
quantity are listed for a wavelength of 1060 nm according
to
(2.2.18).
The sensitivity quantity is defined as the
ratio of the percentage change of the product at to the
percentage change of the transmittance T.
For example,
when the product at is 0.351 the sensitivity is equal to
-2.59, which means the product at will decrease by 2.59%
for a 1% increase in the transmittance.
It is seen that
the sensitivity quantity is very high for a low at value,
which implying that the deduced at value is less reliable.
In our measurements the value of at is around 0.08
because the wafer thickness is around 25 mil
which
is
considered
measurements.
too
thin
for
optical
(0.635 mm)
absorption
The sensitivity quantity typically ranges
from 5 to 10 for the wavelengths used in our measurements.
Since the resolution in the reading of the transmittance
is about 0.5% the possible error in calculating the at
could be
as
high
as
2.5%
to
5%.
In addition
to the
resolution of the system there are two other factors that
might affect the accuracy of the transmittance value.
first factor is the calibration of the system,
The
i.e., the
accuracy in the absolute value of the transmittance.
The
second factor is the surface condition of the wafer under
test.
If the front and back surfaces are not parallel or
there are some spots on the surfaces which will deflect
145
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the optical beam the measured transmittance will not be
the
same as when the
surface
conditions
were
perfect.
Therefore the at can not be calculated simply from the
measured transmittance and the following modification is
recommended.
The
relationship
between
the
optical
absorption
coefficient a and the transmittance T has been given by:
2
(1 - R) exp(-at)
T = -------E-1 - R exp(-2at)
(4.2.3)
At 1800 nm the absorption of the light energy is almost
zero and (4.2.3) becomes:
(4.2.4)
'18 0 0
R1 8
Combining
(4.2.3)
and
(4.2.4)
00
we
obtain
a normalized
transmittance as:
(1 ~
'
i 8 0 0
1 - R 18
T
'
_ (1 - R)
1 80 0
00
exp(-at)
l - r2 exp(-2at)
................. (4.2.5)
146
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The above equation makes the absorption coefficient be
insensitive to the error in the absolute value of the
measured transmittance.
For example if the reading of the
spectrophotometer gives only 90% of the true transmittance
value the absorption coefficient will be still correct by
using (4.2.5) but will be incorrect by using (4.2.3).
The
absorption coefficient can be solved in the same manner as
(2.2.18) with T be replaced by Tn as:
(4.2.6)
]}
Table 4.2.2 shows the measurement results using two
different wavelengths
( ^ = 1060 nm,
= 1320 nm).
The
transmittance at 1800 nm is measured for each wafer for a
normalization purpose.
Once the a's at
and X
2
are
determined the concentration of the ionized and unionized
EL2 centers can be obtained by using
(4.2.1) and
centers
is
(4.2.2).
(2.2.13),
(2.2.14),
The concentration of unionized EL2
found to be
around
101 ® cm“ ^ which
is the
typical value for undoped LEC-grown SI-GaAs wafers.
The
unionized EL2 concentration obtained from our measurement
is compared to the one measured by Spectrum Inc. using a
thick adjacent wafer.
This result is presented in Figure
4.2.2 where a good correlation is observed.
EL2 concentration
The higher
(about 20% higher) by Spectrum Inc. is
147
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Table 4.2.2
Measurement results from optical absorption
at ^ = 1060 nm and A,2=1320 nm. N + E L 2 and N ° E L 2 are in lO1^
-3
cm J .
A.“ 1800 nm
^ = 1 0 6 0 nm
^2“1320 nm
T
T
T
1
0.535
0.472 1.2
0.519 0.218
1.1
0.54
1.3
2
0.548
0.497 0.945
0.533 0.206
0.85
1.1
-
3
0.523
0.475 0.999
0.51
0.92
0.36
1.06
4
0.523
0.485 1.127
0.523 0.21
1.03
0.65
1.1
5
0.538
0.477 1.15
0.523 0.187
1.06
0.1
1.23
6
0.55
0.498 0.926
0.537 0.146
0.86
0.5
1.13
7
0.534
0.482 0.98
0.52
0.9
0.6
-
8
0.52
0.47
0.507 0.177
0.94
0.3
-
11
0.553
0.497 1.073
0.54
1.0
-
1.33
12
0.556
0.507 1.04
0.543 0.185
0.96
0.38
1.27
22
0.538
0.477 1.12
0.523 0.183
1.0
0.1
1.14
26
0.54
0.496 0.68
0.529 0.093
0.64
-
0.88
27
0.54
0.48
0.526 0.159
1.0
-
1.27
sample
a(cm-1)
1.027
1.09
N°EL2
N+
“ EL2
a(cm-1)
0.176
0.186
0.153
N°
N EL2
(Spectrum)
148
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
<
1.2«+16
s
o
X
o
M
5
ti
X
u
u
2
o
o
CM
w
Q
U
X
D
CO
<
w
s
EL2
CONCENTRATION
Figure 4.2.2
FROM
SPECTRUM
INC.
(cmA-3)
Comparison between the unioinzed EL2
concentration obtained from our measurements and the
one obtained from Spectrum Inc.
149
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
probably due to the use of different optical capture cross
sections in their measurements.
A final note should be mentioned here.
The ionized
EL2 concentration obtained from (4.2.1) is not as reliable
as the unionized EL2 concentration obtained from (4.2.2).
The reason is that the numerator in
the
subtraction
(4.2.1)
consists of
of two very close quantities;
thus any
minor error in the absorption coefficients will cause a
significant error in the value of the N+EL2 •
does not happen to
(4.2.2)
However this
and, therefore, the unionized
EL2 concentration is more reliable for a given error in
the a's.
4.3 Dark Resistivity Profiling in Semi-insulating
Gallium Arsenide
Evaluation of the dark resistivity of semi-insulating
GaAs has been a difficult problem because of its high
resistivity.
the
dark
techniques.
The standard technique used for evaluating
resistivity
is
by
means
of
Hall
effect
However the high resistivity of the material
causes problems in the fabrication of ohmic contacts to
the
sample
as well
as
the
instrumentation
measuring the voltages across the contacts.
is desirable to develop a non-destructive,
needed
for
Therefore it
contactless
150
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
technique for the evaluation of the dark resistivity of
SI-GaAs materials at room temperature.
In this section we will demonstrate how to use the
microwave
reflection
resistivity profile
consists
technique
to
obtain
of SI-GaAs wafers.
the
dark
The technique
of measuring the photoresistivity variations
using microwave reflection which is induced in the SI-GaAs
wafer using monochromatic below-band-gap radiation.
Under
appropriate illumination level it is theoretically shown
that the induced photoresistivity is proportional to the
dark resistivity.
More than ten SI-GaAs wafers were used
in our measurement and it has been found that the measured
microwave
response
resistivity
is
obtained
highly
from
correlated
Hall
to
the
measurement.
dark
Proper
calibration of the microwave system allows us to obtain a
quantitative spatial profile of the dark resistivity of
the
wafer
from
a
photoresistivity.
measurement
The
spatial
of
the
resolution
induced
of
this
technique is limited by the illuminated area which could
be as small as 30 mil.
4.3.1
Basis
of
Measurement
Technique
In order to understand the basis of the measurement
technique,
we assume that the defect model
of SI-GaAs
151
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
consists of a deep donor
concentrations
(EL2) and a shallow acceptor in
Nt and N a , respectively.
Under
dark
condition the free electron concentration nD is controlled
by the rates of the thermal emission from the EL2 level
en^Nt-Na“nD^ anci the recombination to the EL2 level.
At
thermal equilibrium the nD is usually much smaller than Na
and it is given by:
n
e (N - N )
= — ------ —
D
Cn N a
(4.3.1)
where en and Cn are the emission rate and capture rate
coefficients, respectively, associated with the EL2 level.
With the
sample
illuminated by monochromatic
light
of
photon energy less than the bandgap and larger than 0.7 6
eV,
below-band-gap photoconductivity
is induced in the
wafer which is mainly due to the excitation of electrons
from the EL2 level to the conduction band.
The reasons
for this are that 1) the electron capture optical section
G °n
the
is larger than the hole capture cross section
light
energy
concentration
is
we
used,
usually
2)
larger
the
than
G °p
unionized
the
ionized
for
EL2
EL2
concentration, and 3) the electron mobility is much higher
than the hole mobility.
Assuming that the light induced
electron concentration nL is much less than Na , then its
expression can be obtained from (2.3.23) as:
152
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Combining
(4.3.1)
and
(4.3.2)
the ratio of the light to
the dark electron concentrations is equal to:
nL
(Jn° Np h
(4.3.3)
n
Since
the
absorption
light is very small,
absorbed
uniformly
coefficient
for
a below-band-gap
it can be assumed that the light is
throughout
the
wafer
thickness
and
surface condition does not have any effect on the induced
photoconductivity.
Because of this uniformity (4.3.3) can
be rewritten in terms of the resistivity under dark pD and
illuminated
conditions:
o
Pd
an Np h
(4.3.4)
Pl
The above equation indicates that it is possible to
determine
the
dark
resistivity
of
SI-GaAs
wafers
by
measuring the induced photoresistivity if the values of
en' ^ n '
anc* photon flux density Np^ are known.
Another
153
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
possibility is to calibrate the microwave system used for
measuring the photoresistivity with wafers of known dark
resistivity.
uncertainty
The advantage of this approach is that the
in
the
above-mentioned
parameters
can be
avoided and, therefore, it is used in our measurement.
should be mentioned
that
(4.3.4)
is also valid for the
case of a three-energy-level defect model
i.e.,
It
for SI-GaAs,
for the case of having a shallow donor in addition
to the deep donor and shallow acceptor levels, as long as
the
shallow
donor
remains
essentially
empty
during
illumination.
4.3.2
System
The
Calibration
microwave
system
and
we
Measurement
have
used
Results
for
the
dark
resistivity measurement is the one shown in Fig.3.3.4.
A
CW YAG laser emitting a monochromatic light at 1060 nm is
used
to
excite
photoresistivity.
the
steady
state
below-band-gap
The whole system has been calibrated
using more than ten SI-GaAs wafers whose resistivity was
obtained by using Hall effect techniques on nearby wafers
from the ingot.
The calibration consisted in relating the
voltage output of the crystal detector during the light
pulse
to
the
wafer
dark
resistivity
and
thickness.
Assuming that the electric field inside the wafer has a
sinusoidal distribution with its zero at the rear surface
154
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of the wafer, a normalized microwave response (in mV) for
each wafer can be obtained by normalizing the detector
voltage
to
thickness
(4t/A,) (1-sinc (47tt/^,) ) where t is the wafer
and
X
is
the
microwave
wavelength.
The
normalized microwave response which is proportional to the
light electron concentration n^ is inversely proportional
to
the
dark
resistivity
of
the
wafer.
Figure
4.3.1
compares the normalized microwave response with the dark
resistivity obtained from Hall effect measurement and it
shows a very good correlation between the two quantities.
With the system properly calibrated it can be used for
spatial profiling the dark resistivity of the
SI-GaAs.
Figure 4.3.2 shows the crystal detector voltage during the
light pulse as a function of position for a typical wafer.
The same figure shows the corresponding dark resistivity
obtained
from
calibration.
the
detector
It
is
voltage
believed
that
and
by
the
system
using
this
measurement system the dark resistivity of the SI-GaAs can
be profiled with a spatial resolution of a few tens of
mils which will be limited by detector sensitivity.
4.4 Below-band-gap Transient Microwave
Photoconductivity
The
photoconductivity
of
undoped
SI-GaAs
155
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
wafers
5
10
M
SB
0
0«
01
a
CO
a lo p e — 1
*
x
o
OQ
a
10
Q
U
N
10
DARK
Figure 4.3.1
RESISTIVITY
(ohm-cm)
Calibration of the system by relating
the normalized microwave response to the dark
resistivity of the SI-GaAs wafer.
156
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5
0
~
c
r
LU
in
z
o
o.
in
•6x10
(o h m -c m )
60
^
40 -
o
CD
CO
■2x10
DARK
Q
[
30 -
LU
c
r
_l
<
r
o
RESISTIVITY
LU
20
z
0
200
DISTANCE
Figure 4.3.2
400
FROM
600
800
CENTER ( m i l s )
Mapping data of microwave crystal
detector voltage and dark resistivity for a SI-GaAs
wafer.
157
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
induced by
a below-band-gap
light
with photon
energy
larger than 0.7 6 eV is mainly due to the excitation of
electrons from EL2 centers to the conduction band.
steady
state
the
number
of
free
electrons
In
in
the
conduction band is controlled by the optical generation
from the unionized EL2 centers and the recombination to
the ionized EL2 centers.
by
terminating
the
When this balance is destroyed
light
source
the
number
of
free
electrons will decreases to its equilibrium value in the
dark through a recombination process.
In order to understand the transient situation the
three-energy-level defect model for undoped SI-GaAs is
used
as
the
photoconductivity
model
where
the
only
recombination mechanism is the fall of the electron from
the conduction band to the ionized EL2 centers.
From this
model it can be shown that the decay time constant of the
transient is inversely proportional to the net shallow
acceptor
concentration.
We
have
compared
the
concentration of net shallow acceptors determined from the
below-band-gap transient response with the one from the
LVM
absorption
measurement.
It
is found
correlation between these two quantities
that
the
is very good,
nearly one-to-one.
During the below-band-gap transient measurement
158
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an
initial fast decay has been observed in all our SI-GaAs
wafers.
This initial fast decay typically ranging from 25
ns
60
to
ns
can
three-energy-level
not
be
explained
photoconductivity
using
model.
the
It
is
suggested that the initial fast decay is caused by some
deep
levels
other
photoconductivity
than
model
the
EL2
which
level.
involves
an
A
new
additional
defect level is tentatively proposed and its discussion
will be given in section 4.4.3.
4.4.1
904
nm Pulsed
GaAs
Laser
Response
There are two kinds of pulsed lasers which we have
used for exciting the below-band-gap photoconductivity in
SI-GaAs.
The
first
one
is
a 31
W
GaAs
diode
laser
emitting light at 904 nm with a tunable pulse width up to
50 ns.
the
During our measurements the photon flux density on
surface
of
the
wafer
is
adjusted
such
that
the
dissipated microwave power during the light pulse is no
more than 10% of the total incident microwave power.
The
reason for this is to avoid any distortion on the crystal
detector
voltage
caused
by
characteristic of the detector.
transient
SI-GaAs
microwave
wafer
is
response
shown
in
the
non-square-law
A typical below-band-gap
obtained
Fig.4.4.1
for
an
where
undoped
the
peak
dissipated power is around 10% of the incident microwave
159
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
150
1
100
100
200
300
400
Time (ns)
Figure 4.4.1
A typical BBG transient microwave
response using 904 nm GaAs diode laser.
R eproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
power.
By
using
the
three-energy-level
photoconductivity
model it has been shown that after the pulsed BBG light is
off, the photoconductance will decay to zero according to
the following equation:
-C„(N-N.)t
n '
a
d'
q n nd n e
G(t) = -------------- 2------------------------------c_(N,-NH)t
/ i i i
j
1+<i r V (1'e
a
where
nQ
is the
>
d
initial
value
(4.4.1)
of the
concentration when the BBG light
excess
electron
is turned off.
After
some time t the exponential term in the denominator can be
neglected
and
the
photoconductance
will
exponentially
decay with a time constant X = 1/Cn (Na-N^)
where Cn is
equal to the product of the electron capture cross section
an and the thermal velocity vt^ as:
Cn= a vth = 3.6x10 9 7 7 exp (-0 .066 (eV)/kT)
(4.4.2)
At room temperature the value of Cn is 4.9x10“ ^ cirrVs
which gives a decay time constant of 200 ns for 1015 cm-^
net shallow acceptor concentration.
acceptor
concentration
wafers
For high net shallow
( >
4x10^
cm- ^)
exponential decay time constant becomes too short
161
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
( less
than 50 ns) to be clearly observed in the BBG transient
microwave
response
at
room temperature.
increase the decay time
constant
In order
to
of the BBG transient
microwave response the SI-GaAs wafer is cooled down to 200
to 240 K at which the electron capture rate increases by a
factor of 2 to 5, and as a result, the exponential decay
time constant increases 2 to 5 times when compared to the
one at room temperature.
The temperature dependence of the electron capture
rate
as
given
in
(4.4.2)
has
been
corroborated
by
measuring the decay time constant of the BBG transient
microwave response at different temperatures.
wafer used in this measurement
has
The SI-GaAs
a shallow acceptor
concentration of O ^ S x l O 1^ Cm-^ determined from a decay
time constant of 690 ns at room temperature.
The decay
time constants at 280 K, 260 K, and 240 K are measured to
be 780 ns,
1140 ns,
and 1320 ns, respectively.
Figure
4.4.2 shows the Arrhenius plot of the product of the decay
time constant, x, and the root of temperature.
The slope
of the data points gives an activation energy of 0.06 eV
which agrees with the one (0.066 eV) shown in (4.4.2) .
should
be
noted
that
the
main
purpose
of
doing
It
this
experiment is not to determine precisely the activation
energy of the electron capture cross section,
confirm
that
equation
(4.4.2)
can
be
but is to
used
162
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
at
low
10.0
slope = 0.70
3.2
3.4
3.6
3.8
4.0
4.2
1000/T
Figure 4.4.2
Arrhenius plot of ln(T*T1/2) for determining
the activation energy of an at EL2 level.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
temperature
for
evaluating
high
carbon
concentration
wafers.
By knowing the electron capture rate the net shallow
acceptor concentration can be determined from the measured
decay time constant.
Figure 4.4.3 shows the log scale
plot of the BBG transient microwave response in Fig.4.4.1
from which the decay time constant can be determined using
the
tail
of
the
log
curve.
Figure
4.4.4
shows
the
comparison between the net shallow acceptor concentration
determined from the BBG transient microwave response and
the carbon concentration of the adjacent wafer obtained
from
LVM absorption measurement.
For the wafers with a
carbon concentration lower than the detectable limit of
LVM absorption measurement
( < 3x10-^ cm~^ ) the result is
presented using a data line instead of a data point as
those shown in the lower-left part of Fig.4.4.4.
A
very
good
correlation,
nearly
one-to-one,
is
obtained from Fig.4.4.4 and it verifies the validity of
the microwave technique which utilizes a pulsed BBG light
for measuring the concentration of net shallow acceptors
in SI-GaAs wafers.
measurement
acceptor
is more
Note that the BBG transient microwave
suitable
concentrations
for measuring
than
high
low shallow
shallow
acceptor
concentrations because the exponential decay time constant
164
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6.0
5.0
£3
0)
•r-1
c 4.0
uErhti
£ 3.0
rcS
O
C/3
0
75
150
225
300
Time (ns)
Figure 4.4.3
The log scale plot of Fig.4.4.1.
The
slope in the tail corresponds to the decay time
constant l/Cn (Na-Nd).
165
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
n
i
<
9
10
14
X
M
U
X
o
o
X
t*
a»
M
O
y
<
o
*
s
0}
10
(9
CQ
ffl
Figure 4.4.4
LVM
CARBON
CONCSNTRATION
(ca*-3)
Comparison between the net shallow
acceptor concentration determined from BBG transient
microwave response and the LVM carbon concentration.
166
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
l/Cn (Na-N^) is longer in the former case.
that
Ng-N^
correlates
concentration
and the
acceptor
SI-GaAs,
in
very
well
carbon
it
is the
is
concentration of shallow donor
with
From the facts
the
LVM
dominant
concluded
carbon
shallow
that
the
in our wafers is very
small.
Although
the
three-energy-level
photoconductivity
model describes very well the decay behavior in the tail
of the BBG transient it can not explain the magnitude and
the
initial
response.
the
fast decay of the BBG transient microwave
If the free electrons are generated only from
unionized
EL2
centers
under BBG
illumination
the
photoconductance will vary according to:
(4.4.3)
If the width of the light pulse is so short such that the
excess carriers is much smaller than (Na-Nd ) then
(4.4.3)
becomes:
dG
dt
(4.4.4)
167
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
or
G = qu. d
Therefore
the
proportional
peak
to
(4.4.5)
[
<y° Nph (N
•
-Na+N.)
]
L n
' t
cr 1
At
BBG
microwave
(Nt - N a + N cj)
and
response
it
can
will
be
used
be
for
evaluating the unionized EL2 concentration.
However
response
really
we have
and
the
found that
unionized
correlated.
quantities
where
EL2
Figure
the
the
peak
peak
BBG microwave
concentration
4.4.5
BBG
shows
microwave
are
not
these
two
response
is
normalized to (4t/X.) (1-sinc (47Tt/A,) ) with t being the wafer
thickness
and X
unionized EL2
optical
being
the
microwave
concentration
absorption.
A
is
wavelength.
The
determined by means
possible
reason
for
of
this
discrepancy is that the free electrons are excited from
more than one defect level.
concentration
of
lO1^
Especially for an electron
cm- ^
many
defect
levels
with
concentration less than 1 0 ^ cm"^ might have contribution
to the total excess electrons in the conduction band.
In addition,
observed
BBG
for all our undoped SI-GaAS wafers the
transient
microwave
response
contains
an
initial fast decay which is faster than the one described
by the ideal decay equation
decay
not
(4.4.1).
This initial fast
has a time constant of 25 ns to 60 ns and it can
be
explained
using
the
three-energy-level
168
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
H
<0
8
200
40 ns, 904 nm light
0t
w
2
E
6
M
s
8
150
100
0e+0
5e+15
le+16
2e+16
2e+16
UNIONIZED EL2 CONCENTRATION (cmA-3)
Figure 4.4.5
The normalized peak BBG microwave
response vs the unionized EL2 concentration.
169
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
photoconductivity model.
mentioned above
response
Together with the discrepancy
it is believed that the BBG transient
involves
some
other
defect
levels
which
are
sensitive to the BBG light, and more discussions will be
given in section 4.4.3.
4.4.2
1060
nm
Pulsed
YAG
Laser
Response
The photon energy of the 904 nm GaAs laser is 1.37 eV
which is very close to the band gap of SI-GaAS,
at room temperature.
1.42 eV,
It was suspected that the initial
fast decay observed in the BBG transient response could be
caused by
a possible
transition
of electrons
shallow acceptors and the conduction band.
between
To investigate
this possibility a yttrium-aluminum-garnet
(YAG)
laser
at
which
emits
a monochromatic
light
corresponding to a photon energy of 1.17 eV,
pulsed
1060
nm,
is used.
Fig.4.4.6 shows a typical BBG transient microwave response
using the pulsed YAG laser with its log scale plot shown
in Fig.4.4.7.
Because the transient response contains the
same initial fast decay as the one using 904 nm light, the
possibility of exciting carriers
from shallow acceptor
levels to the conduction band can be discarded,
Ec-1.17 eV is far above the valence band.
since
From Fig.4.4.7
we can also determine an exponential decay time constant
using the tail of the curve.
The decay time constants
170
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80
60
40
20
0
0
100
200
300
400
Time (ns)
Figure 4.4.6
A typical BBG transient microwave
response using 1060 nm YAG laser.
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6.0
£ 5.0
0
,\
CO
2
4.0
x= 210 ns
E-<
M-l
° 3.0
0
'
—
i
rd
U
cn
2.0
0
150
75
225
300
Time (ns)
Figure 4.4.7
The log scale plot of Fig.4.4.6. The slope
in the tail corresponds to the decay time constant
l/Cn (Na-Nd) .
172
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
obtained from 1060 nm light are the same as those obtained
from 904 nm light.
Therefore, as the net shallow acceptor
concentration is concerned both 904 nm and 1060 nm light
can be used.
The
magnitude
of
the
pulsed
1060
nm
response
is
compared to the magnitude of the pulsed 904 nm response
for several
Fig.4.4.8.
SI-GaAs wafers and the
result
is shown in
A linear relationship is found which implies
the carrier generation mechanism in both cases
is the
same.
4.4.3
Photoconductivity Model With an Additional
Donor Level
In order to explain the magnitude and the initial fast
decay of the BBG transient microwave
response we have
proposed a photoconductivity model for SI-GaAs which has a
deep donor level in addition to the three levels: shallow
donor, shallow acceptor and EL2 level.
Figure 4.4.9 shows
an energy diagram of the proposed photoconductivity model
where the additional
donor level
Fermi level and above Ec-1.17eV.
is located below the
Let the additional donor
level have a total concentration of N 2 and among them the
concentration
of
ionized
centers
is n 2 .
condition the
concentration of the
In the dark
ionized centers
173
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
is
5!
80
§
0«
w
3
06
H
40
§
a
20
o
VO
o
OB
a
vo
Figure 4.4.8
0
20ns,
904am
GaAs
30
20
10
LASER
RESPONSE
(mV)
The magnitude of the pulsed 1060 nm response
vs the magnitude of the pulsed 904 nm response.
174
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Hd
“
A
A
Nd
Nt,«t
• ••••••
*2
Ea
N2
Na
— — —
N„
Figure 4.4.9
The energy diagram of the proposed
photoconductivity model where the additional donor
level is located between the Fermi level and
Ec-1.17eV.
175
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
almost zero because the additional donor level is below
the Fermi level.
Under the illumination of a BBG light
the number of r\2 could become significant and it will
change according to the following equation:
dn 2
(4.4.6)
dt
where CJn 2 ° and Cn 2 are the optical capture cross section
and
the
electron
capture
rate
associated
with
the
additional donor level,
respectively,
and n is the free
electron concentration.
The difference between n and n 2 ,
denoted as n-j_, is the number of the extra empty centers in
the EL2 level besides those for compensating net shallow
acceptors.
The change of the concentration n-j_ during the
BBG light pulse can be written as:
dn i
dt
where
all
the
(4.4.7)
G°N
. (Nt -N a +Nd -n,)
- Cn n (Na -N.+n,)
n ph
1'
d
1'
parameters
have
their
Assuming n^ and n 2 are much smaller than
usual
meanings.
and Nt the
change in the electron concentration n can be obtained by
combining (4.4.6) and (4.4.7) as:
176
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
d(n1+n2)
dn
dt
dt
(4.4.8)
Equation
(4.4.8)
shows that
electron
concentration
n
the growth of the
during
the
light
excess
pulse
is
determined by the optical generation from the EL2 centers
as well as the optical generation and the recombination
associated with the additional donor level.
As a result
the peak transient microwave response induced by a 40 ns
BBG
light
can
not
be
correlated
to the
unionized EL2
concentration.
Now let's consider the problem of the initial
decay.
After
the
light
is
off
the
excess
fast
electron
concentration will decay by recombining with the empty
centers
in
the
EL2
and
the
additional
donor
levels
according to
The
above
equation
can
be
rewritten
as
two
coupled
differential equations
177
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(4.4.10a)
(4.4.10b)
The actual BBG transient microwave response can be fitted
using
(4.4.10a)
and
(4.4.10b)
by
knowing
the
initial
electron concentration n (0) =n^ (0)+n2 (0) , Cn and Na~Ncj, and
by assuming a ratio ni( 0 )/n2 (0 ) and the electron capture
rate Cn 2 • The initial electron concentration is determined
from
the
dissipated
microwave
Chapter 3 and is around 1 0 ^
power
as
described
in
cm- ^ in our measurements.
Figure 4.4.10a shows the result of a typical curve fitting
with n ^ (0)/n2 (0)=0.3 and Cn 2 = 2 xl0 -^ cm^/s.
The new photoconductivity model can explain both the
magnitude and the initial fast decay of the BBG transient
microwave
model.
response
better
than
the
three-energy-level
The new model can also predict the (NQ-Nd ) related
decay time constant in the tail of the transient response
because after some time t the concentration n 2 will be
very small and equation (4.4.9) becomes:
(4.4.11)
178
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.0
0.8
CD
TS
3
-P
• iH
*H
a
0.2
0
200
400
600
800
1000
Time (ns)
Figure 4.4.10a
A typical curve fitting according to
equation (4.4.10) with n^ (0)/n2 (0)->0.3 and Cn2*2xl0“^
cm^/s.
179
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 .0
0
200
400
600
800
1000
Time (ns)
Figure 4.4.10b
A typical curve fitting according to
equation (4.4.10) with n^ (0)/n2 (0) “0.02 and Cn2“ 1.4x10 **
cm^/s.
180
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
which has a decay time constant of l/Cn (Na-Nd ).
Besides,
the introduction of the additional level should not affect
the result in the BBG steady state measurement.
This is
because that the lifetime of the additional level is very
short
and,
therefore,
in
steady
state
the
photo­
conductivity is mainly due to the EL2 level.
In order to investigate the temperature dependence of
the capture rate Cn 2 the BBG transient microwave response
is taken from 77 K to 300 K.
The electron concentration
n( 0 ) is determined from the dissipated microwave power and
the
temperature-dependent
Fig.4.4.11)
(Stillman
1976
electron
mobility
and Ehrenreich
1959).
(see
The
ratio n 1 (0 )/n2 (0 ) and the capture rate Cn 2 needed to best
fit
the
measured transient
response
temperatures are listed in Table 4.4.1.
at
different
Also listed in
Table 4.4.1 is the electron capture cross section for the
additional donor level deduced by using a thermal velocity
of
6x1 0 ^
cm/s (Sze 1981) .
It is found that the
electron capture cross section for the additional donor
level is in a range from
larger
than
the
one
10-11
for
to
the
1 0 "^-^
EL2
cm^ which is much
level.
The
ratio
n-j_ (0)/n2 (0) is found to be around 0.3 when
T ^ 260 K and
is almost zero below 200 K.
an indication
This could be
that the two deep donor levels have different temperature
dependencies
for the optical capture cross section and
181
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a
10
i
>
CM
io n iz e d
<
im p u r ity
8
*
*
>4
H
«
H
p o la r
e ffe c tiv e
10
o p tic a l
m o b ility
H
M
50
100
150
200
250
300
350
TEMPERATURE (K)
Figure 4.4.11
Electron mobility for SI-GaAs from
Ehrenreich (1959) and Stillman (1976).
182
R eproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
400
Table 4.4.1
Parameters needed to fit the BBG transient
microwave response for different temperatures.
T(K)
nx (0)/n2 (0)
Cn 2 (cm3/s)
On2<cm2)
77
<0.02
7xl0-5
1.3xl0-11
100
<0.02
8xl0“5
1.3xl0-11
120
<0.02
0.3xl0"5
4.5xl0-11
140
<0.02
0.6xl0-5
8.5xl0-11
160
0.02
lxlO-5
1.3xl0“12
180
0.02
1.2xl0~5
1.5xl0~12
200
0.02
1.4xl0-5
1.6xl0“12
220
0.15
1.7xlQ~3
1.9xl0"12
240
0.2
2.2xl0“5
2.3xl0"12
260
0.3
2.5xl0“5
2.5xl0“12
280
0.3
2.2xl0“5
2.2xl0-12
300
0.3
2.OxlO”5
1.9xl0”12
183
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
when T < 200 K most of the 40 ns BBG light energy is
absorbed
by
transient
the additional
and its
Fig.4.4.10b
curve
donor
level.
fitting at
for comparison
with
A
typical
200 K is shown
the
one
at
in
room
temperature.
Six
wafers
concentrations
n ]_ (0) / n 2 (0)
with
were
different
used
and the
temperatures.
for
capture
shallow
determining
rate C n 2
at
acceptor
the
ratio
different
The result is shown in Table 4.4.2 where
the average values for the ratio and the capture rate are
calculated.
the order of
The magnitude of the capture rate Cn 2 is in
1 0 “^
cm-Vs,
and the ratio n ^ (0 )/n 2 (0 ) is
almost zero below 200 K.
In addition to the temperature we have also varied the
photon flux density of the BBG light to check the validity
of the new photoconductivity model.
According to (4.4.9)
the free electron concentration will have an initial decay
time constant of
T.
^
1
= -----------------Cn
a
~
+
(4.4.12)
Cn 2 V ° >
If the optical capture cross section C7° n 2
is independent
of photon flux density Nph , then since n 2 (0 ) will increase
184
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Table 4.4.2
Parameters needed to fit the BBG transient
microwave response for different wafers.
sample
2
4
5
10
12
21
N fl(cm- 3 )
1.5el5
1 . 4el5
4 .5 e l 4
2 . 9el4
3e l4
4el4
T(ns)
14 0
150
450
700
680
510
n 1 (0)/ n 2 (0)
-
-
0.4
0.3
0 .3
0 .3
0.33
C n2 (cm3/,s>
-
-
3e- 5
2e-5
5e-5
4e-5
3.5e-5
n 1 (0 )/ n 2 (0)
0.3
0.4
0.4
0.25
0.2
0.2
0.3
C n2 <cn,3/ s )
4 e-5
1 . 5e-5
2. 5 e - 5
2. 5 e - 5
5e-5
3e-5
3e-5
n x (0) / n 2 (0)
0.4
0.3
0.25
0.02
0.02
0.25
0.2
C n2 (cm3 /s)
5e-5
6e-5
4e-5
2. 4 e - 5
8e-5
2 . 5e-5
4 . 7e-5
n x (0) / n 2 (0)
0.02
0.02
0.01
0.0 2
0.02
0. 02
0. 02
C n 2 (cm3 /s)
8e-5
12e-5
7e -5
10e-5
12e-5
10e-5
10e-5
nj (0) / n 2 (0)
0. 01
0.02
0.01
0.02
0. 02
0.02
0.02
C n 2 (cm3/s>
1.5e-5
7e-5
5e-5
8e-5
8e-5
1 ,5 e- 5
5e-5
300 K
250
K
200 K
150 K
100 K
185
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
average
with increasing photon flux density the initial decay time
constant
will
density.
If
decrease
(0)
is
with
increasing
saturated
by
photon
some
flux
reasons
the
initial decay time constant will remain constant for any
further increase in the photon flux density.
However,
decay
we have not seen a decrease in the initial
time
increased.
constant
when
the
photon
flux
density
is
The observed Xj_n .j_t almost remains constant and
slightly decreases
for a very low photon
The reason for this decrease in
flux density.
could be attributed
to a Np^-dependent optical capture cross section which has
a
slightly
higher
Therefore,
for
low photon
flux
density.
slightly decreases for a very low photon
flux density.
0°n2
value
We are unable to explore the dependence of
on the photon flux density Nph because Nph can be
varied only by a factor of 3 to 4, and this topic should
be investigated further.
A possible candidate for the additional donor level is
the second EL2 level at Ev+0.54 eV.
can absorb
should be
904 nm light
and the
Because this level
electron
large due to the double
capture
charged state.
rate
The
energy diagram showing the transition of electrons from
the EL2 and second EL2 levels is depicted in Fig.4.4.12.
Assuming the number of electrons excited from neutral EL2
186
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N c ,n
• •
ISU
• • • • •
}Nt
E0
• • • • •
Na
N.
second EL2 level
Figure 4.4.12
The energy diagram showing the transition
of electrons from the second EL2 level.
187
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and from single charged EL2 centers is n 2 ,
centers is
then the concentrations of the neutral EL2, single charged
EL2
and
the
double
charged
EL2
Na-Ncj+n1-n2 , and n2, respectively.
are
N t - N a + N d “ n l'
The rate equations for
such a system, as illustrated in Fig.4.4.12, are given by:
dn
—d —
t
= <T°
N (Nt -Na +N
-n ) - Cn n '(Na -Nd +n 1 -n 2 )
n p h
d l '
(4.4.13)
dn
d T = < 2Nph(Na-Nd+nr n2) - cn2n n 2
(4.4.14)
where & n 2 ° anc* c-:n2 are t^ie optical capture cross section
and the electron capture rate associated with the second
EL2 level, respectively, and n =n 2 +n2 is the free electron
concentration.
After the light is off the concentration n
will decay according to
dn
d(ni+n2)
— = -= - n [Cn(Na-Nd+nr n2) + Cn2n2]
which becomes identical to
Therefore,
(4.4.9)
(4.4.15)
if n-^, n2 << (Na"^) .
the result given in Table
4.4.1
obtained by
assuming an additional donor level is applicable to the
case of double charged EL2.
From our measurement it appears that n2 is larger than
188
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n-j_ in a 40 ns pulse of 904 nm light.
Assuming that the
generation terms dominate in (4.4.13) and (4.4.14), then
an 2 ° should be larger than cn° by at least an order of
magnitude because
than Ng-N^.
is about an order of magnitude larger
However,
optical cross
Silverberg
(1988) has measured the
sections using photocapacitance transient
measurement where it shows an°(at 78 K) is larger than
an 2 °(at 150 K) by more than an order of magnitude
Fig.4.4.13).
Besides,
we have
compared the
(see
40 ns BBG
microwave response at low temperature ( around 150 K) with
LVM carbon concentration.
double
charged
EL2,
then
If the additional level is the
a
correlation
between
the
microwave response and the carbon concentration should be
found because n 2 »
n^ at low temperature.
However,
no
correlation has been found and therefore the additional
level can not be the double charged EL2.
4.5 Above-band-gap Steady State Microwave
Photoconductivity
In this section, the steady state photoconductivity of
undoped SI-GaAs wafers induced by an above-band-gap light
is studied.
From our measurements it has been found that
the ABG steady state microwave response correlates very
well with the LVM carbon concentration;
response
the microwave
is inversely proportional to the
root
189
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of the
GaAs: EL2
k
0.6
0.8
1.0
1.2
1.4
Photon energy (eV)
Figure 4.4.13
Optical cross sections for the two EL2
levels in GaAs. On° (triangles) and CTp° (filled circles)
are measured at 78 K. Op 2 ° (filled triangles) at 85 K and
CTn 2 ° (open circles) at 150 K (Silverberg 1988). Also shown
(full curve) is the data obtained in p-type material by
Lagowski (1985).
190
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
carbon
concentration.
This
is
a
consequence
of
the
photoconductivity model we have been using and the result
can
be
applied
to
the
determination
of
the
shallow
acceptor concentration in SI-GaAs materials as well as its
spatial distribution across the wafer.
The relationship between the ABG steady state response
and the carbon concentration can be explained by assuming
that the deep donor EL2 is the recombination center and
the limiting factor in the recombination process is the
fall of the electron from the conduction band to the EL2,
or assuming that the recombination is through the shallow
acceptor
carbon
recombination.
recombination
analysis
is
by
means
of
Shockley-Read-Hall
(SRH)
In order to determine which of the two
assumptions
given
to
is
relate
right,
the
a
ABG
quantitative
steady
state
photoconductivity to the shallow acceptor concentration
and it will be discussed in section 4.5.2.
4.5.1
Correlation
with
LVM
Carbon
Concentration
The light source that we have been using for exciting
above-band-gap photoconductivity is a 54 W pulsed AlGaAs
laser diode which emits light at 850 nm and can be pulsed
to 50 ns with rise and fall times of around 5 ns.
Under
the ABG excitation electron-hole pairs are generated only
191
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near the front surface of the wafer because the absorption
coefficient a for 850 nm light is large, around 104 cm- 1 .
Since the surface recombination velocity is very large,
the
effective
lifetime
of the
excess
carriers
is very
short (a few ns or less), and therefore it is assumed that
the ABG excitation reaches a steady state during the 50 ns
pulse width.
Nearly
20 undoped
LEC-grown
SI-GaAS
wafers
with
a
carbon concentration ranging from 3xl0-*-4 to 7x10-*-^ cm-^
were used in the ABG measurement.
Figure 4.5.1 shows the
ABG steady state microwave response
of LVM carbon concentration.
(in mV) as a function
Note that the lower the LVM
carbon concentration is, the higher the ABG steady state
microwave
response
will
be,
and
that
is
one
of
the
advantages of the microwave technique over LVM absorption
measurement.
A very good correlation has been found in
Fig.4.5.1 and the data points can be passed by a straight
line with a slope equal to -0.5.
This means that the ABG
steady state microwave response is inversely proportional
to
the
root
of
the
LVM carbon
concentration
which
is
nearly the same as the net shallow acceptor concentration.
There
o ut
here.
wafer
are
two
considerations
Firstly,
is d e t e r m i n e d
the
LVM
from the
which
carbon
should
be
concentration
pointed
of
each
LVM absorption measurement
192
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
on
100
%
u
CO
SLOP*
SB
-0.5
O
0<
CO
&
si
CO
01
(9
a
10
14
10
LVM
Figure 4.5.1
CARBON
CONCENTRATION
(cmA-3)
Correlation between the ABG steady state
microwave response and the LVM carbon concentration.
193
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
adjacent
wafer
and
it
is
believed
that
the
concentration of carbon will not vary significantly in a
small portion of a SI-GaAs ingot.
Secondly, since the ABG
microwave response depends on the front-surface microwave
electric
field
dependent,
the
intensity
which
is
measured microwave
wafer-thickness
response
has
to be
corrected for different wafer thicknesses.
Fig.4.5.2 shows the mapping of the ABG steady state
microwave response over two 3" undoped SI-GaAs wafers.
Wafer#24751.130
5.6x10^5
with
cm-3 shows
an
LVM
carbon
concentration
7% standard deviation
of
in the ABG
steady state microwave response while wafer#12851.094 with
an LVM carbon
concentration of 3xl014 cm-^ 'shows
standard deviation.
ABG
steady
state
u niformity
concentration.
in
9.5%
The degree of the variation of the
microwave
the
response
distribution
of
reflects
the
the
carbon
Using the straight line in Fig.4.5.1 the
ABG steady state microwave response can be converted into
a more informative quantity,
concentration,
i.e.,
the absolute carbon
and the mapping of carbon concentration
using this conversion is shown in Fig.4.5.3.
4.5.2
Recombination
Mechanism
In this section discussions will be given to check the
194
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
%
M
96
0
01
m
CO
n m
« 12851.094
I" <
s * * v ♦
• •>
♦ V
-
60
-
-
40
X•
X
m m
# 24751.130
n
w
o
a
10
20
— r~
30
DISTANCE
Figure 4.5.2
“1—
40
■nr
50
60
(mm)
Mapping of ABG steady state microwave
response across two 3" SI-GaAs wafers.
195
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10 16
."W
i
lmStoautMiPm!uP,rf^^
<
a
a
t*
2
M
U
2
O
O
WATER
10
# 24751.130
15.
•******
•«*
«
2
O
s
6
WATER
10 1 4 .
— I—
10
—i
20
r~
30
DISTANCE
Figure 4.5.3
#
— i
40
12851.094
1
—
50
60
(mm)
Mapping of shallow acceptor concentration
across two 3" SI-GaAs wafers using the straight line in
Fig.4.5.1 as a calibration.
196
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
validity
of the photoconductivity
model.
During
our
experiment it has been observed that the ABG steady state
photoconductance is inversely proportional to the root of
the
shallow
acceptor
concentration.
This
could
be
explained by a recombination through the EL2 or, as will
be shown later, through the shallow acceptors.
In order
to decide which of the two recombination mechanisms is
true,
a quantitative analysis will be given to evaluate
the ABG steady state photoconductance G.
Recombination through deep donor EL2
In this model
the assumptions
are
1)
excess holes
recombine very fast with the unionized EL2 centers, and 2)
the excitation level is low (less than lO1^ cm"^) so that
the ionized EL2 concentration is almost the same as the
shallow
acceptor
concentration.
Since
the
surface
recombination velocity is very high for undoped SI-GaAs (S
> 10® cm/s)
the total electron concentration per unit
area, Ntotaj_, can be expressed as:
It is seen that Ntotal can be evaluated in two independent
ways:
1) from photoconductance G, or 2) from photon flux
197
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
density Nph and electron lifetime Tn = l/Cn (Na-Nd)
The
photoconductance
microwave
G
is
determined
from
the
reflection coefficient T using the equivalent
circuit shown in Figure 4.5.4.
Since the excess electrons
are confined in a thin layer region close to the surface,
the photoconductance
element.
G can be
represented by a lumped
If the wafer thickness is a quarter-wavelength
the photoconductance G may be expressed
as:
i - r
° i +r
G = Y -----
where
YQ
is
the
propagating wave,
mode.
The
(4.5.2)
characteristic
admittance
of
the
and is equal to 1/471 ohm- -*- for TE^ q
reflection
coefficient
is
obtained
by
the
microwave power ratio, i.e., T = [Pr (light)/Pr (dark)]1/2,
and from our measurement it is equal to 0.9.
Therefore G
is
1
1-0.9
-4
G = --- (------- ) = 10
471
1 + 0.9
Using
an
electron
mobility
of
1
(— )
Q
6500
(4.5.3)
cm^/V-s
the
total
electron concentration Ntotal is approximately equal to
10-*-■*• cm- ^ .
198
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4.5.4
Equivalent circuit for calculating the
photoconductance G induced by ABG light from microwave
reflection coefficient.
199
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The second way to evaluate Ntotal is from photon flux
density Np^ and electron lifetime Tn .
The photon flux
density
around
has
been
determined
to
be
2 xl 0
4^
photons/cm^-s as following:
( j ) (35 W)
19
Nph = ------- — ---------------- — = 2x10
P
(1.6x10 19C) (1.45 eV) (4 cm2)
where the factor
(1/2)
200 ns,
Dn = 130 cm^/s,
becomes
around
deduced
from
supports
the
electron-hole
(4.5.4)
s
which agrees
photoconductance
assumption
If we use Tn =
and (X = 104 cm- 1 , then Ntotal
1044 cm-^,
pairs
cm
is due to the mismatch in £, and
the laser power is measured about 35 W.
the
photons
that
is through
G.
the
the
with the value
This
agreement
recombination
EL2
level.
of
If we
assume the excess electrons have an uniform concentration
n over a distance of diffusion length Ln = (DnTn )4//^ = 50
|lm, then the concentration n will be equal to Nt0tal/Ln =
2xl04^ cm~3.
This confirms the the previous assumption of
having a low level excitation (less than 1044 cm-^) during
the ABG illumination.
If the photon flux density is increased to a level
where the excess carrier concentration becomes comparable
or larger than the shallow acceptor concentration,
200
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
then
the lifetime of excess electrons will decreases.
The ABG
steady state photoconductivity response will no longer be
linearly proportional to the photon flux density as stated
in (2.3.19), but will be less.
the photoconductivity
is more
This decreasing effect in
obvious
wafers than high carbon wafers.
ABG
steady
state
microwave
for
low
carbon
Figure 4.5.5 shows the
response
as
a function
of
photon flux density measured by using a low carbon wafer,
[C] ® 3 x 1 0 ^ cm”3 .
a
linear relationship is observed for
a low photon flux density and, after Np^ is larger than
SxlO1^ (cm^-s)- 1 , the photoconductivity
away
from
the
quantitative
linear
analyses
line.
Together
given above
starts
with
to bend
all
the
it is appropriate to
conclude that the
recombination of the excess
induced by an ABG
light
carriers
is through the deep donor EL2
level.
Before we leave this section it is desirable to study
the effect of the surface recombination velocity on the
ABG
steady
expression of
state
photoconductivity.
The
general
is given here again:
201
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
5
30 SB
0
H
<
04
H
20-
01
01
at
w
10
-
s
o
04
,
2.0*+19
PHOTON
Figure 4.5.5
1
6.0«+l 9
FLUX
1
1.0«+20
DENSITY
----1.4«+20
(l/cmA2-s)
ABG steady state microwave response vs,
photon flux density for a low carbon wafer.
202
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Since ad is much greater than one for the ABG light, the
above equation can be reduced to:
Nt o t a l
2 2
axs + a l
Np h.Xn
l - a
2
l
2
(4.5.5)
( i ----------------- )
l + s•/t/d
When S = 0, Ntota]_ = Nphxn •
We can' therefore, define a
normalized quantity, normalized N^0|-a]_, as:
2 2
^ axs + a l
Ntotal(S)
Normalized Nt o t a l - ---------kj
/ Q = fl \
total
^
1 + Syfx/D
2----2 2
a L - 1
(4.5.6)
If we know the value for x, D, and a, then the normalized
Ntotal can
plotted as a function of S, and it is shown
in Fig.4.5. 6 for X=200 ns, D=130 cm^/s, and a=10^ cm--*-.
It is not
surprising to see that the value of S has a
strong influence on Ntotal, or the photoconductance.
203
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
This
10°
101
SURFACE
Figure 4.5.6
102
103
104
RECOMBINATION
105
VELOCITY
106
107
(cm/s)
Normalized Ntotal vs. surface recom­
bination velocity S assuming T=200 ns, D=130 cm^/s, and
a=104 cm-1 .
204
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
plot essentially can be used for evaluating the surface
recombination velocity of a passivated sample by comparing
the ABG
steady
state
responses measured on the
sample
before and aft'er the passivation.
The
surface
recombination
velocity
S has
a strong
effect on the effective lifetime Xe f f = (X- ^+S/L)
, in
addition
S
to
reduced by
transient
the
ABG
steady
some
means
of the
ABG
state
such that
response
response.
X"1
will
constant equal to the bulk lifetime
»
S/L,
have
Xe f f
=
X
If
is
then the
a decay
time
= l/CnNa .
In
order to check the photoconductivity model as well as to
evaluate the bulk lifetime in SI-GaAs,
have
been
tried
to
improve
the
several approaches
surface
recombination
velocity.
We have tried to reduce S by putting a coating of
sodium
sulfide
[Na2S+9H20]
(Yablonovitch
1987)
or
making a n+ layer at the surface of the SI-GaAs wafer.
has been
found that the use of sodium sulfide
by
It
coating
increases the ABG steady state response by a factor of 2
to 3 but with no improvement in Xeff.
for this
is that the
A possible reason
surface recombination velocity is
still very high since the LEC SI-GaAs material usually
exhibits a high dislocation density.
that
the
ABG
steady
state
response
It has been shown
obtained by
205
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
using
n +-n-n+-SI structures is much higher than the one from
n+-n-SI structures,
implying that the interface between
the n epilayer and the SI substrate has a large interface
recombination velocity (Bothra 1990).
The
response
different.
after making
a n+
layer
is
somewhat
The n+ layer was formed by Si ion implantation
or S diffusion into SI-GaAs substrates.
The wafers with
the two different n+ layers show a similar ABG response,
i.e.,
no
improvement
in
both
amplitude
and
Te ff •
Following the short decay time constant Teff there is a
very long decay time constant, (is to ms, which is believed
to be due to the presence of traps.
n+
layer
velocity
does
not
improve
the
The reason that the
surface
is probably because of the
recombination
damages
introduced
during the process and the high interface recombination
velocity due to poor quality of the SI substrate
1990) .
(Borrego
These damages could be responsible for the long
decay time constant as well as a few deep levels found in
the ion implanted wafer using PMDLTS technique,
(see next
section for PMDLTS technique).
Recombination through
Another possible
recombine
is
by
shallow acceptor
carbon
w a y in w h i c h t h e e x c e s s
means
of
the
carriers
Shockley-Read-Hall
206
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
will
(SRH)
recombination
(Shockley 1952 and Hall 1952'
shallow acceptor carbon.
through the
The recombination rate R of this
process is given by
np - n.
R = -----------(n+n.)T
+ (p+pjT
1
po
c
r l
no
where
(4.5.7)
n(p) = electron(hole) concentration
nj_ = intrinsic carrier concentration
Tno = ^ n Nr^"""^ with Nr being the concentration of
the recombination centers
T p o
= (CpNr) w i t h
Cp being hole capture rate
n^ = Nce x p (-(Ec-Er)/kT) with Er being the energy
level of the recombination centers
p x = Nvexp(-(Er-Ev )/kT)
n l (Pi ) is defined to be the equilibrium concentration of
electrons
level
were
(holes)
at
that
the
would be
recombination
obtained
level
if the Fermi
Er .
Since the
energy level of carbon is very close to the valence band,
(Er-Ev )=0.026 eV, the value of p^ is usually much larger
than n, p, and n-j_.
Equation (4.5.7) can be simplified to
2
R = — —
Pixno
(4.5.8)
207
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where we assume n = p »
n^.
In steady state the electron concentration satisfies
the equation:
n2n
o
D ---3 9x2
n2
(X N e
-ax
(4.5.9)
which is similar to (2.3.10) except that the recombination
term
is
(4.5.9)
not
n/T,
is
equation
a
and
but
is
given
second-order,
it
can not be
by
(4.5.8) .
Equation
nonlinear,
nonhomogeneous
solved with
a closed
form
solution.
However, if we assume that the term on the left
hand side
is small
other side,
This
compared with the two terms
on the
then n (x) can be solved in a simple manner.
assumption
is
made
by
the
following
estimation.
Since the boundary condition at the surface, x=0, is
9n
D — = Sn
a 3x
with n(0) = 1 0
n(x)
7
(4.5.10)
cm— 7 , the distribution of excess carriers
in a region very close to the surface can be solved
as :
208
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
s
n (x) = n (0) exp ( —
x)
(4.5.11)
a
Using Da = 20 cm2/s and S = 10^,
the maximum value of
Da 0 2n/5x2) is around 7x10-^ l/cm3-s, where we assume the
maximum value occurs at x = 1 |Llm.
The generation term
OO
(XNphexp (-ax) at x = 1 (im, however, has a value of l O ^ to
1023 l/cm3-s using Np^ = 1 0 ^ to 102® l/cm2-s.
Therefore
it is very large compared with the diffusion term.
By neglecting
electron
the diffusion term the
concentration
Nt o p a j_ per
obtained by integrating n(x)
unit
total
area
excess
can
be
from 0 to d, and the result
is given a s :
ft
al =
I n <x>
(x) dx =
" f
- 2 ,
\ /
l -~ ~ ~
o
Using fno=
(cnNa)
“no v
^ntva
(4.5.12)
' the photoconductance of the wafer can
be obtained as
G - <3 H A c i
= 2<^„. /
n
The
above
equation
shows
that
a
the
ABG
steady
state
response will be inversely proportional to the square root
209
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of the shallow acceptor concentration N a , which is the
same
result
as
obtained
from
(2.3.19)
where
the
recombination process is through EL2.
If we substitute the values for Ntotaj_, a , and Np^
we had for the case of recombining through the EL2,
(4.5.12)
into
and use pn = 2.5x10^-® cm-®, then the value of fno
becomes 3.7xl0-1® s.
rate at
cm®/s
as
It means that the electron capture
shallow acceptor
since
Tno
=
carbon
l/Cn N a .
is as
This
large
value
as 2x10“ ®
for
Cn
is
unreasonably high and therefore this recombination model
should be discarded.
4.6 Photoinduced Microwave Deep Level Transient
Spectroscopy (PMDLTS)
There
are many
different
characterization
which have been used to characterize deep
variety of semiconductor materials.
Transient Spectroscopy
(DLTS)
methods
levels
in a
Among them Deep Level
has been widely used for
determining the type, concentration, energy level, and the
capture cross section of deep levels in semiconductors
(Lang 1974).
The DLTS technique consists of probing the
capacitance transient after an injection of carriers into
the
depletion
layer
formed
metal-semiconductor barrier.
by
a
p-n
junction
or
a
Therefore it requires the
210
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formation of metallic contacts to the doped semiconductor
material.
In order for characterizing semi-insulating materials
alternate methods,
involving current transients produced
by light pulsed in bulk material (or Schottky structures),
were introduced.
Optical Transient Current Spectroscopy
(OTCS) was first introduced by Hurtes et a l . (1978)
then by Martin and Bois
(1978).
and
This method consists of
illuminating the sample through a semitransparent metal
layer and then observing photocurrent transients in bulk
material.
Photoinduced
Transient
introduced by Fairman et al.
Spectroscopy
(PITS)
(1979) is somewhat different.
The sample is illuminated by the light beam directly and
the
transient
current
is
measured
through
two
ohmic
contacts fabricated on the front surface of the sample.
Conceptually the OTCS and PITS are similar to the DLTS
except
that
they
can
be
used
for
semi-insulating
materials.
One of the features of the photoconductivity model is
that there is no deep level between the EL2 level and the
conduction
band.
In order to check
this
situation
a
contactless technique should be used because many defects
could be introduced from alloying contacts.
application
of
microwave
Recently, the
techniques
to
211
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
characterization of deep levels has been demonstrated by
Fujisaki
et
al.
in
1986.
The
advantage
of
using
microwaves over the DLTS, OTCS and PITS is that it is a
nondestructive and contactless method, and, therefore, it
can be applied to conductive as well as semi-insulating
materials.
In this section,
a similar technique called
Photoinduced Microwave Deep Level Transient Spectroscopy
(PMDLTS)
is
developed
photoconductivity
model
as
a
for
part
of
undoped
checking
SI-GaAs
and
the
the
details will be given in section 4.6.3.
4.6.1
Transient Photoconductivity Due to Trapping
Centers
In the presence
of trapping
levels
the
transient
photoconductivity will be affected by a filling of the
traps
during
trapped
the
light
pulse
carriers
after
the
and
light
an
emission
pulse.
of
the
Since
the
emission rate at the trap level is usually slower than the
lifetime of the material, the transient photoconductivity
usually consists of a long decay tail with a decay time
constant equal to the inverse of the emission rate.
To
derive the equation of the transient photoconductivity we
consider an electron trapping level with a concentration
of
.
The number of the trapped electrons, n^, will vary
according to:
212
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where en j_ and Cn ^ are the emission rate and the electron
capture
rate
respectively,
associated
with
the
trapping
level,
and n is the free electron concentration.
We assume that due to independent recombination processes
the electrons have a lifetime Tn with 1/Tn »
cni(Ni-ni ) •
Then while the light is on, n = GTn, as shown in (2.3.3a),
and
dn.
= - em ,n,1 + GTn Cni,(N.-n.)
l
l
(4.6.2)
where G is the generation rate for the light excitation
that
puts
electrons
assumption here,
into
of course,
thermal equilibrium value.
N
n
the
conduction
band.
An
is that n = Gtn >> nQ , the
The solution to (4.6.2) is
i
"
<e m
+
G T nc n l > t
= ------------ (1 - e
1 + eni./GTn Cni.
)
(4.6.3)
where the boundary condition is n^=0 at t=0.
When
the
light
is shut
off,
equation
(4.6.2)
213
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
will
becomes dn^/dt = -enin^ and the solution will be
N i
- ( e n i + G V n i ’tp
n. (t) = -----(1 - e
1
1 + eni./GTn Cni.
-e nit
)e
(4.6.4)
where tp is the width of the light pulse and t=0 is at the
end of the light pulse.
If tp is long enough such that it
is much larger than 1/ (enj_+GTnCn j_) < then
N i
n. (t) = ------------ e
1
1 + e ni./GTn Cni.
(4.6.5)
The free electron concentration n is related n^ by:
dn
after the
n
= e„.n. - C_.n (N. -n.) --Tn
light
is off.
We
(4.6.6)
can solve
for n by using
(4.6.6) and (4.6.4), assuming that 1/Tn »
Cnj_(N^-n^.), and
the result is
ni
N i
n (t) = — ;-----------(1 - e
T - e
1 + eni./GTn Cni.
n
-<e ni+GTnc ni)t p
- e nit
) (e
-e
-t/T„
ni
+ n (0)e
(4.6.7)
214
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
)
where n(0)
is the initial value of n when light is off.
It can be shown that n(t)
function of t
is a monotonically decreasing
(Look 1983).
The second term in
(4.6.7)
represents an initial fast decay after the light is shut
off.
Normally
en j_ is
much
smaller
than
1/Tn
and
therefore, after some time t, n(t) will decay with a time
constant of l/en^.
This slower decay time constant could
be in the range of |ls to ms and is a strong function of
temperature.
The
evaluation
of
en ^
at
different
temperatures gives the information of the associated deep
level and it is the basis of DLTS-related characterization
techniques.
4.6.2
The
Technical
operation
Background
of
for
DLTS
DLTS-related
characterization
techniques relies on measuring the thermal emission rate
en (T) of levels as a function of
temperature.
There are
several means of measuring the thermal emission rate: by
capacitance
(DLTS), by photocurrent
by photoconductivity (PMDLTS).
(PITS and OTCS), and
It is well known that the
theoretical expression of en (T) includes the value of the
capture cross section cn and of the activation energy
corresponding to a given level.
If an can be thermally
activated with an activation energy Eg. and E^ has a linear
temperature dependence of Ej_ (T) =Ej_Q-(XT (Martin 1986), then
215
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
en (T) will has the following expression:
en (T) = ynT2 [anoognexp (a/k) ]exp (
(4.6.8)
kT
where Gnoo is the value of Cn for T=°°, gn is the degeneracy
factor and yn is a constant equal to 2.28x10^ cm ^s
in
GaAs
(Martin
1977) .
The
plot of l n ( e n / T ^ )
^
as
a
function
of 1/T yields theapparent electron capture cross
section
(7na = <5noc,gn exp (a/k)
as
activation energy Ena=Ej_0+E0 .
and Ena, are actually the
well
as
the
apparent
These two parameters, Gna
'signature' of a trap, even if
they do not have a direct physical meaning.
There
are
emission
a number
rate
en (T)
at
evaluated (Sundaram 1984).
of
ways
in
different
which
the
thermal
temperature
can
be
The method we have been using
is the one that utilizes a lock-in amplifier as a detector
(Miller
1977) .
The
output
voltage
of
the
lock-in
amplifier is proportional to the average of the product of
the
input
signal
shown in Fig.4.6.1.
and the
square
weighting
function
as
Assuming that the microwave transient
photoconductivity has a decay time constant Tn=l/en and it
is pulsed at a frequency f,
the output
voltage
lock-in amplifier can be calculated from
216
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of the
exp (-ent)
T = 1/f
—
■■■1 ■
►
+1
-1
Figure 4.6.1
Transient photoconductivity signal and
weighting function of lock-in amplifier.
217
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 /2 f
A
=
1/f
exp (~ent))
(I exp(-ent) o
1/2 f
f
f
en
-e
( 1 - exp(
(4.6.9)
2f
Let en/f = P the above equation can be rewritten as:
1
A(p)
P 2
(1 - exp(- — ))
(4.6.10)
P
The output A (p) is equal to zero when p = 0 or °° and it
has a maximum value of 0.2 when p = 2.51
Fig.4.6.2.
as
shown
In other words, when the output A(p)
in
reaches
its maximum the thermal emission rate en (T) = 2.51f where
f is the frequency of the input and the reference signals.
By
using
two
different
frequencies
f^
and
f2
the
corresponding thermal emission rats en -^(T^) and ^n2 ( ^ 2 ^
can be determined at temperatures
and T2 , respectively,
and consequently Ena and Gna can be solved.
There is an alternate way to determine the value of
Ena and O na without
4.6.2
shows
that
changing the
the
output
A(p)
points at p = 0.527 and p = 9.66.
frequency
has
f.
Figure
two half-maximum
At these two points the
corresponding thermal emission rates are en i(T-]_) = 0.527f
and
en 2 ^ T 2^
=
9*66f,
respectively.
By
knowing
218
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the
0.3
CM
<
CM
*»*
<x
I
04
N
0
1
0.2
p-2.51
II
p«*0.527
p-9.66
£
2
0
Figure 4.6.2
4
6
8
10
12
Function A(p) in equation (4.6.10) as
a function of p.
A(p) is maximum at p=2.51, and is
half of its maximum at p*°0.527 and 9.66.
219
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
temperatures
T-^ and T 2
at two half-maximum points
the
value of Ena and ana for a deep level can be solved in the
same manner as before.
Since
function
the thermal
of
activation
the
emission
temperature
energy
Ena
of
rate
as
the
en (T)
well
as
is a strong
the
associated
apparent
level,
each
trapping level will cause a maximum in the output A(p) at
a different
lock-in
temperature.
amplifier
output
A theoretical
A(p)
curve
is plotted
for the
in Fig.4.6.3
assuming that there are three trapping levels with Ena =
0.2 eV, 0.3 eV and 0.4 eV.
levels
have
the
same
We also assume that all three
initial
concentration
of trapped
electrons and the same apparent capture cross section ana
= 5x10“ -*-® cm^ .
For a fixed pulsing frequency it is seen
that the maximum output A(p) = A(p)max occurs at a higher
temperature
for
a deeper
trapping
level.
It
is
also
interesting to see that the maximum output A(P)max shifts
towards
a higher
increased,
and
temperature
that
this
when
shift
the
becomes
frequency
larger
f is
if the
associated trapping level is deeper in the bandgap.
Very often a light source which has a 50% on-off duty
cycle is used for modulating the photoconductivity in the
PMDLTS measurement.
advantage
of
long
This
filing
kind of
pulse
light
width
source
and
it
220
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
has an
can
be
0.3
f-10 Hz
9
0.2 eV
f-20 Hz
eV
0.4 eV
<
0.2
►4
Z
o
M
W
CO
E4
a
s
cu
100
200
TEMPERATURE
Figure 4.6.3
3 0 0
(K)
Theoretical curve for the output A(p)
assuming three trapping levels located at 0.2, 0.3
and 0.4 eV below the conduction band.
221
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
generated
However,
easily
by
means
of
chopping
a
CW
light.
instead of the chopper frequency f, a harmonic
frequency of 2f should be used as the reference frequency
in
the
lock-in
amplifier.
Figure
4.6.4
shows
the
modulated photoconductivity and the harmonic frequency 2f.
The output voltage A(p) of the lock-in amplifier becomes:
1
A (p)
P 2
(1 - exp (- — ))
(4.6.11)
P
where p has the same meaning as en /f.
is plotted as
a function
of p
Equation
(4.6.11)
in Fig. 4. 6.5 where
the
maximum output A(p) = A(p)max = 0.1018 occurs at p = 5.02
and the half-maximum output A(p)
1.054 and 19.32.
Therefore,
= 0.0509 occurs at p =
during the temperature scan
the output of the lock-in amplifier will have a maximum
when
(4 .6 .1 2 )
max
where Tmax is the temperature at which the maximum output
occurs, and it will have a half-maximum when
en (T1) = 1.054 f
(4.6.13a)
en (T2) = 19.32 f
(4.6.13b)
222
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
frequency = 2f
Figure 4.6.4
Transient photoconductivity signal and
the harmonic weighting function of lock-in amplifier.
223
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CM
0.10
'
cu
0.08 -
a,
p-5.02
0.06 '
0.
H
0.04 '
p-1.054
0.02
p-19.32
-
CU
0.00
4
0
8
12
16
20
24
P
Figure 4 . 6 . 5
Function A ( p )
a function of p .
A(p)
in equation ( 4 . 6 . 1 1 )
is maximum at p = 5 . 0 2 ,
as
and is
half of its maximum at p = 1 . 0 5 4 and 1 9 . 3 2 .
224
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where
T-^ and T2
are
the
temperatures
at
which
the
half-maximum outputs occur.
4.6.3
Experimental
Results
A block diagram for the PMDLTS measurement is shown in
Fig.4.6.6 where
reference
a lock-in amplifier,
frequency,
semiconductor
is
sample
used
is
as
slowly
a
with 2f harmonic
detector.
cooled
from
The
room
temperature down to 77 K by pouring liquid nitrogen into
the container during the measurement.
A thermocouple
attached to the metallic block underneath the sample is
used for monitoring the sample's temperature.
Both the
output of the lock-in amplifier A(p) and the thermocouple
are connected to an X-Y recorder with which a PMDLTS plot
of
A(p)
vs
temperature
T
can
be
obtained
when
the
temperature scan is completed.
We have measured undoped SI-GaAs wafers as well as the
SI-GaAs wafer with an ion implantation layer on the top
using two different light sources: 1060 nm YAG laser and
633 nm HeNe laser.
The 1060 nm light can be absorbed all
through the wafer thickness, while the 633 nm light can
only penetrate
the
first
0.2 (im from the surface.
A
typical PMDLTS plot using 1060 nm YAG laser is shown in
Fig. 4.6.7.
The sample which has been used is a SI-GaAs
225
R eproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
ATTENUATOR
35 GHz
MICROWAVE
GENERATOR
ISOLATOR
HYBRID
SLIDING
SHORT
WR-28 WAVEGUIDE
FIBER
COUPLER
HeNe
LOCK-IN
AMP.
Figure 4.6.6
CHOPPER
CONTROLLER
THERMOCOUPLE
SEMICONDUCTOR
SAMPLE
LIQUID
NITROGEN
Block diagram of the photoinduced
microwave deep level transient spectroscopy
(PMDLTS) measurement.
226
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
wafer with an ion implantation layer,
top.
150 KeV Si, on the
A Hall pattern has been fabricated on the implanted
layer, and after that the rest of the implanted layer was
etched away.
The
curve
in Fig.4.6.7
was taken
in the
implanted area and it shows a large peak (level A) and two
small peaks (levels B and C).
peaks
appearing
from
220
There seem to be many other
K to
300
K,
but
since
they
overlap each other no identification can be made.
Table 4.6.1 lists the thermal emission rate en (T) as
well as the temperature T at which en (T) was taken.
values of the en (T) and
T
of level A was determined by
using the maximum and the half-maximum points,
levels B and C, the peak temperatures
and 300 Hz were used.
thermal
emission
temperature
is
rate
equal
en (T)
to
while for
(the temperature at
which a peak in the PMDLTS plot occurs)
144,
The
Keeping
at f = 20,
50,
in mind that
the
corresponding to the
5.02f
according
to
peak
(4.6.12) .
Fig.4.6.8 plots ln(T^/en ) vs 1000/T for the three levels
and from which the values of Ena and Gna can be determined
and are listed in Table 4.6.2.
Compared to levels B and C
level A has a much larger Gna and it could be the same
level as the one observed from PITS measurement which has
Ena = 0.15 eV and Gna = 8xl0--*-^ cm^
(Fairman and Oliver
1980).
227
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
16
14
D
U
12
10
C/3
Z
o
Ok
cn
U
OS
03
H
8
6
4
2
0
300
200
100
TEMPERATURE (K)
Figure 4.6.7
A typical PMDLTS response using 1060
nm YAG laser on an ion implanted sample.
228
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.6.1
Thermal emission rate and the corresponding
temperature obtained from the PMDLTS measurement.
level
A
B
C
D
X(nm)
f (Hz)
en (1/s)
T (K)
1060
300
316
87.2
300
1506
93.4
300
5796
100.8
20
100.4
142
50
251
148
144
723
158
300
1506
166
20
100.4
200
50
251
210
144
723
225
300
1506
235
12
60.2
85.1
20
100.4
87.6
34
170.7
88.4
70
351.4
93.4
99
497
95.0
1060
1060
633
229
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
level C
6-
level B
5-
a
"s.
<
E4
4
3
level A
0
H
T
10
1000/T
Figure 4.6.8
12
(1/K)
Arrhenius plot of ln(T^/en ) vs 1000/T
for the three levels found using 1060 nm YAG laser.
230
R eproduced with permission of the copyright owner. Further reproduction prohibited w ithout permission.
Table 4.6.2
Results of PMDLTS measurement deduced
from the data in Table 4.6.1.
level
X(nm)
En a <eV)
On a (cm2 )
A
1060
0.15
5.5xl0"14
B
1060
0.18
7. OxlO**17
C
1060
0.27
6.5xl0~17
D
633
0.13
1.5xl0“15
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The PMDLTS measurement has been also taken
in the
etched area where the implanted layer was removed.
The
microwave photoconductivity shows a square response which
simply follows the modulation of the light source.
No
transient photoconductivity response has been seen and the
output of the PMDLTS measurement shows no distinguishable
peak.
The same result has been obtained when using the
undoped SI-GaAs wafer.
three
levels
we
have
It is therefore believed that the
seen
are
introduced by
the
ion
implantation process and they are located in the region
that is very close to the surface and can be removed by an
etching process.
The PMDLTS response using 633 nm HeNe laser is somehow
different.
Figure 4.6.9 shows such a response using the
same sample as the one for Fig.4.6.7.
There is only one
level (level D) can be distinguished at around 90 K.
The
Arrhenius plot of ln(T2/en ) vs 1000/T for level D is given
in Fig. 4.6.10 with the data
and the
Tables 4.6.1 and 4.6.2, respectively.
likely to be the
one,
result
listed
in
This level is very
denoted as EA7,
found by Auret
(198 6) in undoped n-type GaAs from DLTS measurement.
The
level EA7 has Ena = 0.14 eV and Cna = lxlO-1^ cm^ and it
is related to the surface damage in the region of less
than 0.28 |lm.
As for the SI-GaAs wafer as well as the
etched area the 633 nm light shows no sign of traps.
232
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10
D
<
8
U
CO
2
0
01
CO
u
6
OS
CO
4
H
Q
S
a*
2
0
300
200
100
TEMPERATURE (K)
Figure 4.6.9
Typical PMDLTS response using 633 nm
HeNe laser on an ion implanted sample.
233
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
c
9
"n*
4.0“
CM
<
3.0-
10.0
10.5
11.0
1000/T
Figure 4.6.10
for the level
11.5
12.0
(1/K)
Arrhenius plot of ln(T2/en ) vs 1000/T
found using 633 nm HeNe laser.
234
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Usually the use of a below-band-gap light can detect
more
deep
levels
in
above-band-gap light.
the
implanted
material
than
an
As shown in Table 4.6.2 more deep
levels can be detected by using 1060 nm YAG laser than
using 633 nm HeNe laser.
The reason for this is that the
excess carriers created by the 633 nm light are confined
in
a
region
where
the
Fermi-level
is
close
to
the
conduction band; thus all the trapping levels which are
below the Fermi-level can not empty themselves after the
light
pulse.
This
can
be
further
understood
by
considering the variation of the Fermi-level in an ion
implanted sample.
the
Si ion
Assuming the doping profile N(x) due to
implantation
into
SI-GaAs
has
a
Gaussian
distribution as:
Q
,-1 .X"Rp.2
) ]
N(x) = - = ---- expt— (
J 2 k Ar
Arp
v
(4.6.14)
y
p
where Q is the dose in ions/cm2 , Rp the projected range,
in cm, and ARp the straggle,
in cm.
Let's also assume a
19
dose of 1.5x10^^
cm— 9 , implantation energy of 150 KeV, Rn
ir
=
0.1
Jim
and
concentration,
function
of
ARp
=
n(x),
depth
0.05
|lm,
then
can be obtained from
x
from
activation or n(x) = N(x).
the
surface,
the
electron
(4.6.14)
as a
assuming
100%
This is shown in Table 4.6.3
235
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.6.3
Electron concentration n(x) and Fermi
level due to ion implantation as a function of depth
x from the surface.
x (Hm)
n(x)(cm“3)
Ec-Ef (eV)
Ec-Ef (eV)
Ec-Ef (eV)
T=300 K
T=200 K
T=100 K
0.1
lxlO17
0.04
0.016
—
0.15
6xl016
0.05
0.025
0.003
0.20
1.4xl016
0.09
0.050
0.016
0.25
lxlO15
0.16
0.095
0.039
0.30
3.4xl013
0.25
0.15
0.068
0.35
3.7X1011
0.36
0.23
0.107
0.40
1.5xl09
0.56
0.33
0.15
236
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
from x = 0.1 Jim to 0.4 Jim.
Also shown in Table 4.6.3 is
the Fermi-level calculated from
E
- E
c
f
n (x)
= - kT ln( -- —
N
T
n (x)
=
'
k
T
l n (
------------ T
T
9x10
-
^
7
>
(
4
- 6
- 1 5 )
T
for three different temperatures, T = 100 K, 200 K and 300
K.
The position of the Fermi-level determines whether a
trapping level can reemit completely the trapped electrons
after the light is off.
For example,
at 200 K,
levels
which are located below Ec - 0.15 eV in energy and less
than 0.3 |lm in position will not empty themselves after
the light pulse because they are below the Fermi-level.
Therefore if the photoinduced carriers are confined in a
region less than 0.3 Jim, which is almost true for 633 nm
HeNe
laser,
then
the
transient
photoconductivity
will
never show the release of the trapped electrons from those
levels.
detect
As a result the use of 633 nm light can only
a
limited
number
of
trapping
levels
in
the
implanted sample.
In
conclusions,
the
PMDLTS
technique
has
237
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
been
demonstrated to be capable of detecting deep levels
semiconductors.
in
The use of 1060 nm YAG laser can detect
three levels in ion implanted SI-GaAs samples while 633 nm
HeNe laser can detect only one level.
wafers
there
is no sign of trapping
In bulk SI-GaAs
levels
in the BBG
photoconductivity response and no deep level above the EL2
level was detected using PMDLTS.
This result disagrees
with the one obtained from PITS measurement where many
deep levels above the EL2 level have been observed.
From
the result of our measurement as well as the fact that the
two-energy-level defect model can explain the resistivity,
it
is
believed
that
the
deep
levels
observed
in PITS
measurement are due to the alloy of metallic contacts and
do not exist in as-grown LEC annealed SI-GaAs substrates.
238
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{
CHAPTER 5
CONCLUSIONS
During this study, we have explored the capability of
microwave reflection techniques in measuring the lifetime
and photoconductivity of semiconductors.
We have also
successfully applied the microwave reflection technique to
the evaluation of the photoconductivity model for semiinsulating gallium arsenide and to the characterization of
SI-GaAs wafers,
acceptor
including the dark resistivity,
concentration,
implantation.
and
deep
levels
shallow
due
to
ion
Many important results are summarized as
following:
Chapter 3:
1)
evaluating
The microwave
excess
conductivity
contacts.
of
The
carrier
reflection technique
lifetime
semiconductors
observed
as
without
lifetime
from
well
is useful
as
photo­
making metallic
the
microwave
reflection technique can be the true lifetime X, half of
239
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
in
the true lifetime T/2, or some other values depending on
the arrangement of the microwave setup.
In most of the
cases the attenuation of the attenuator is set to maximum
and
it
will
result
in
a
true
lifetime
decay
in
the
microwave response.
2)
The
suitable
to
choke-flange
incorporate
into
rectangular
the
waveguide
microwave
is more
reflection
measurement than the flat-flange rectangular waveguide for
a convenient and reliable measurement.
flange
rectangular
waveguide
is
When the choke-
used
the
reflected
microwave power is insensitive to the wafer thickness and
the spacing between the wafer and the waveguide flange.
The
advantages
of
using
the
choke-flange
rectangular
waveguide over the taper-tip parallel plate antenna are 1)
much higher sensitivity, 2) simpler electromagnetic fields
distribution,
spatial
3)
simple
resolution
arrangement,
can be
and
achieved by
4)
the
same
controlling the
light spot.
3)
The
assumption
of
TE-^q
mode
inside the SI-GaAs wafer has been accepted.
propagation
This is done
by comparing the microwave responses obtained with 1) a
piece of wafer, 3.5 by 7 mm, inside the waveguide and 2) a
wafer
outside
amplitude
the
waveguide.
In both
and the decay time constant
cases
the peak
of the microwave
240
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wave
response are nearly the same.
4)
A quantitative evaluation of photoconductivity has
been given for both uniform and non-uniform illumination.
An area factor,
defined as the ratio of the dissipated
microwave power when a small circular area is illuminated
to that when an entire waveguide area is under the same
illumination,
has
been
derived
to
evaluate
the
photoconductivity in the small circular area.
We have
also
as
derived
a
sensitivity
factor,
defined
the
proportionality constant between the dissipated microwave
power
direct
p^
and the
photoconductivity
determination
a,
which allows
of the photoconductivity
a
from the
measured dissipated microwave power.
Chanter 4:
1)
EL2
concentration
of
SI-GaAs
wafers
determined from optical absorption measurement.
has
Because
the wafer thickness t is very small for optical absorption
the
absorption
coefficient
a
is very sensitive to any
error in the measured transmittance.
A new measurement
scheme utilizing a normalized transmittance, normalized to
the
transmittance
at
1800
nm,
is
developed.
The
absorption coefficient a obtained using the new scheme is
insensitive to the error in the system as well
241
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as the
been
condition of wafer surfaces.
Therefore the measured EL2
concentration is more accurate.
2)
obtain
Microwave
reflection technique has been used to
the
resistivity profile
dark
in
SI-GaAs
wafer.
This technique consists of measuring the photoresistivity
variations which is induced in the
below-band-gap radiation.
SI-GaAs wafer using
The light pulse should be at
least a few (is long to insure a steady state condition.
good correlation has been found between the BBG
A
steady
state response and the dark resistivity and it can be used
for
profiling
the
dark
resistivity
in
SI-GaAs.
The
correlation confirms the validity of the two-energy-level
photoconductivity model.
3)
Both
1060
nm
and
904
nm
transient
microwave
responses show an initial fast decay and a second slower
decay.
the
The shallow acceptor concentration deduced from
slower
correlation
decay
with
time
the
constant
LVM
carbon
shows
a
one-to-one
concentration.
The
initial fast decay as well as the peak response can not be
explained
using
the
two-energy-level
model
and
is
attributed to the presence of an additional defect level.
This additional
level
is located below Fermi
level and
above Ec~1.17 eV, and has a very large electron capture
rate,
around 10“ ^ cm^/s.
It is also found that at low
242
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
temperature, below 200 K, the energy of 40 ns 904 nm light
pulse is absorbed mainly by the additional level, not by
E L2.
The second EL2 level located at Ev +0.54 eV is not
the additional level although the model with the second
EL2 level has the same transient equation.
4) The above-band-gap steady state microwave response
correlates very well with the LVM carbon concentration
which
is ranging from 3x10-*-^ to 7xl0^^ cm-^.
The ABG
steady state photoconductivity can be explained by using
the
two-energy-level
recombination
center.
model
The
with
EL2
limiting
as
the
factor
main
in
the
recombination process is the fall of electrons from the
conduction band to the EL2,
and,
therefore,
the bulk
lifetime is given by (CnNa)~-*- for low level excitation.
quantitative
analysis
of the ABG photoconductivity
A
is
given and its result supports the photoconductivity model.
5) The ABG microwave response shows a very short decay
time constant
(only a few ns)
after the light
is off.
This is because of the high surface recombination velocity
(£ 10^ cm/s)
at the surface as well as the high optical
absorption coefficient.
In order to see the bulk lifetime
decay we have tried to reduce the surface recombination
velocity by passivating the surface or by putting a n+
layer to the wafer.
A thin layer of sodium sulfide was
243
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
used to passivate the
successful.
SI-GaAs
surface
and
it was not
The reason is believed to be due to the high
dislocation density in LEC GaAs.
The use of n+ layer,
formed by Si ion implantation or by S diffusion, did not
improve the surface recombination velocity because many
damages were induced during the process.
6)
The
correlation
between
the
ABG
steady
state
response and the LVM carbon concentration can be also
explained by the Shockley-Read-Hall recombination through
carbon.
A
quantitative
analysis
evaluate the ABG photoconductivity.
has
been
given
to
The result showed an
unreasonable value for the electron capture rate at carbon
and, therefore, this model is discarded.
7) A new characterization technique,
called PMDLTS,
has been developed to check the photoconductivity model.
It is demonstrated to be capable of detecting deep levels
in ion implanted SI-GaAs materials.
The use of 1060 nm
YAG laser can detect three levels in ion implanted SI-GaAs
samples while 633 nm HeNe laser can detect only one level.
In bulk SI-GaAs wafers there is no sign of trapping levels
in BBG photoconductivity response and no deep level above
the EL2
level was detected using PMDLTS.
disagrees with the
where many
deep
one obtained
levels
This
result
from PITS measurement
above the EL2
level
have been
244
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
observed.
It is then believed from our measurement that
the deep levels observed in PITS measurement are due to
the
alloy
of
metallic
contacts
and
do
not
exist
in
as-grown LEC annealed SI-GaAs substrates.
The following are a few improvements suggested for the
microwave system.
These improvements will enhance the
capability of the system.
1)
Adding
a
temperature
controlled
stage
or
cryosystem to precisely vary the sample temperature.
is
useful
not
only
for
the
PMDLTS
but
also
evaluation of temperature dependent parameters
a
This
for
the
such as
electron capture rate.
2)
Using an automatic micropositioner to move the
wafer in two or three dimensions.
By doing so the two
dimensional mapping of the dark resistivity as well as the
shallow acceptor concentration can be easily obtained.
These mappings would be useful in the study of materials
properties
due
to
different
growth
conditions
or
fabrication processes.
3) Since the energy of +/++ EL2 is Ev+0.54 eV, the use
of a 1400 nm pulsed laser light will not excite electron
from +/++ EL2 to the conduction band and therefore there
will be no initial fast decay in the BBG response.
is
suggested
to
verify
the
photoconductivity
involving the second EL2 level.
245
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
This
model
When using a pulse of 850 nm light the bulk lifetime
can be measured by passivating the surface of SI-GaAs that
we
have
not been
able
to
achieve
dislocation density in SI substrate.
grow
a
few |im semi-insulating
structure
on the
SI-GaAS
because of
high
It is desirable to
epilayer
substrate.
in a n+-SI-n +
The
SI epilayer
should be high quality and dislocation free such that the
lifetime
is equal
to
l/Cn N a
according to
the
photoconductivity model.
Deep levels of other materials,
such as InP,
studied by using the PMDLTS technique.
can be
The technique is
essentially non-destructive and contactless and therefore
is
useful
processed
contacts.
caused
by
in characterizing
materials
For
without
the
as-grown
the
demand
example the effects
deposition,
diffusion,
as well
of
metallic
to the deep
ion
as
levels
implantation,
annealing could be studied using the PMDLTS technique.
245
R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
or
CHAPTER 6
6.1
REFERENCES
Chapter 1
Bahr, A.J., Microwave Nondestructive Testing Methods,
Gordon and Breach Science:New York, 1982.
Beck, G. and M. Kunst, Rev. Sci. Instrum. 57, 197 (1986).
Bhatnagar, P.K. and V.N. Ojha, Solar Cells 8, 197 (1983).
Borrego, J., R. Gutmann, N. Jensen, and 0. Paz,
Solid-State Electronics 30, 195 (1987a).
Borrego, J., R. Gutmann, C.S. Lo, M. Heimlich, and 0. Paz,
Proceeding of the U.S. Conf. on GaAs Manufacturing
Technology, 101 (1987b).
Bothra, S., Solar Cells, 27, 437 (1989).
Bothra, S., Ph.D. Thesis, Rensselaer Polytechnic
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Braslau, N., paper presented at Int. Symp. GaAs and
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Campbell, C.S, Master Thesis, Rensselaer Polytechnic
Institute, 1988.
Chen, M.C., Journal of Applied Physics 64, 945 (1988).
Cummings, K., S. Pearton, and G. Vella-Coleiro, Journal of
Applied Physics 60, 1676 (1986).
247
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fujisaki Y., Y. Takano, and T. Ishiba, Jpn. Journal of
Applied Physics 25, L874 (1986).
Hasegawa, H., H. Ohno, H. Shimizu, and S. Seki, Journal of
Electron. Mater. 13, 931 (1984).
Heimlich, M.C.,-Master Thesis, Rensselaer Polytechnic
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Hyder, S.B. and W.W. Hooper, Journal of Crystal Growth 56,
369 (1982).
Jenson, N., Master Thesis, Rensselaer Polytechnic
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Johnson E.J., J.A. Kafalas, and R.W. Davies, Journal of
Applied Physics 54, 204 (1983).
Kalikstein, K., B. Kramer, and S. Gelfman, Journal of
Applied Physics 39, 4252 (1968).
Kramer, B., S. Gelfman, and K. Kalikstein, Physical Review
B 6, 556 (1972).
Kunst, M. and A Werner, Solid State Communication 54, 119
(1985).
Kunst, M. and G. Beck, Journal of Applied Physics 60, 3558
(1986) .
Kunst, M. and G. Beck, Journal of Applied Physics, 63,
1093 (1987).
Lo, C.S., Ph.D. Thesis, Rensselaer Polytechnic Institute,
1988.
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