INVESTIGATION OF DEEP LEVEL IrmPURITIES
(OXYGEN AN:D Clh;OMIUM) IN bULK GALLIUL! RSENIDE
AND AuCaAs SCHOTT'Y DIODES
By
CHERN I HUANG
A DISSERTATION PRESENTED TO THE GRADUATE
COUNCIL OF THE LrUIVERSITY' OF FLORIDA II PARTIAL
FULFILLMENT OF THE REOUIRiENi:TS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1973
ACKI'OWL L UC;GILT S
The author wishes to express his sincere appreciation to the
members of his supervisory committee: Dr. S. S. Li, Dr. F. A.
Lindliolm, Dr. E. R. Chenette, Dr. A. D. Sutherland and Dr. T. A. SCOLL
for their guidance and encouragement throughout this research. The
author also gratefully acknowledges the helpful discussions with Dr.
C. T. Sah.
The research that resulted in this dissertation was part of a
larger effort; therefore, the author is indebted to his fellow co
workers for their generous cooperation, and, in particular, theauthor
wishes to mention H. F. Tseng, R. F. Notta, T. H. Smith, W. A. Lukaszek
and C. F. Hiatt.
The author acknowledges the competence of Mrs. Vita Zamorano tho
typed this manuscript.
This investigation was supported by the Advanced Research Projects
Agency, U. S. Department of Defense and monitored by the Air Force
Cambridge Research Laboratories under contract No. F1962872C0363.
TALLE OF CONTENTS
Page
ACKNOWLEDGMENTS . . . . . ii
LIST OF TABL S . . . . .. . .
LIST OF FIGURES . . . ... ... .. .i
LIST OF S'YM OLS . . . . ... . v. iii
ABSTRACT . . . . ... . . xi
Chapter
I. INTRODUCTION . . . . ... . 1
II. CURRENT TRANSPORT IN SCHOTTKY CARRIER DIODES ..... 5
Introduction . . .. .. ........ 5
Current Transport Theory . . . 5
Interfacial Layer Effect . . . 8
Field Dependence of the Barrier . . 9
Surface States Effect . . . . 11
III. THE CxPACITiANCEVOLTAGE CHARACTERISTICS OF SCHOTTKY
BARRIER DIODES IN THE PRESENCE OF DEEP LEVEL IILPURITIES 13
Introduction . . . . 13
Review of the Existing Models ........... 14
Transition Processes in Deep Impurity Centers .. 17
Dark Transient Capacitance . . ... 19
Transient Photocapacitance . . ... 22
Summary . . . . . 23
IV. RECOMBINATION A*;D TRAPPING PROCESSES IN BULK nTYPE GaAs
IN THE PRESENCE OF DEEP LEVEL IMPURITIES . ... 24
Introduction . . . .. .. 24
Charge Neutrality in Semiconductors . ... 25
Trapping and Recombination Processes Through Deep
Level Impurities . . . ... 27
Radiative Recombination in the Host Crystal ... 30
TABLE OF CONTENTS (Continued)
Chapter
IV. Continued
Carrier LifetinLe Measurement Using PME and PC Effects
Summary . . . . . .
V. EXPERI ENTS . . . . . .
Preparation of Devices . .
Sample Preparation . .
CurrentVoltage Measurement .
CapacitanceVoltage Measurement .
Photocapacitance Measurenent .
Bulk Effect Measurements . .
EXPERIMENTAL RESULTS AD ANALYSES . .
Introduction . . .
Forward CurrentVoltage Measurement
Schottky Diodes . . .
Reverse CurrentVoltage Measurement
of AuCaAs
of AuCaAs
Schottky Diodes .
Transient Capacitance Measurement of AuGaAs .
HallEffect and Conductivity Measurement . .
PHE and PC Measurerent on Chromiumdoped ntype GaAs
PME and PC Measurement on O:.:ygendoped ntype GaAs
VII. CONCLUSIONS . . . . . .
Summary . . . . . .
Suggestions for Further Study . . .
BIBLIOGRAPHY . . . . . . .
BIOGRAPHICAL SKETCH . . . . . .
Page
. . . . 4 8
LIST OF TAb'.LS
Table Page
1. Basic physical parameters of typical AuGaAs (ntype)
Schottky barrier diodes at 300 K ...................... 36
2. Summary of the results for AuCaAs (nty'pe) Schottky
barrier diodes deduced from transient dark and photo
capacitance measurements .............................. 56
LIST OF FIGURES
Figure Page
1. Energy band diagram of a metalsemiconductor (ntype)
contact with an interfacial layer and surface states
(After Cowley and Sze, Reference 21) ............... 6
2. (a) Energy band diagram of a netalsemiconductor
(ntype) contact wiLh the presence of donortype
deep level impurities ....... ........ .........
(b) Spatial distribution of charges ................. 16
3. The energy band diagram and (a) four thermal and
(b) four optical transition processes between the
deep level impurity and Lhe conduction band
(After Sah et al.,Reference 15) ..................... 1i
4. Localized states introduced by the shallow and deep
level impurities in the forbidden band for a semi
conductor. The centers are shown in their available
charge states ........................................ 26
5. Energy band diagram for a semiconductor doped with
Jeep level acceptor impurities in thermal equilibrium
and under steadystate illumination: (a) thermal
equilibrium; (b) intermediate injection; (c) high
injection ........................................... 28
6. Test setup for measuring Schottky barrier diode
currentvoltage characteristics ..................... 38
7. Experimental setup for measuring transient dark and
photocapacitance of che metalGaAs Schottky barrier
d iodes .............................................. 39
8. Experimental secup for the AC PME measurement ...... 41
9. Forward currentvoltage relationship of AuGaAs
(ntype) Schottky diode Dll at various temperatures 45
10. Forward currentvoltage relationship of AuGaAs
(ntype) Schottky diode D17 at various temperatures 46
MM
LIST OF FIGURES (continued)
Figure Page
11. I /Ti versus 10O/T for the A'iGaAs (ntype) Schottky
barrier diodes Dll and D17 ....................... 47
12. Reverse voltagecurrent relationship for the AuCaAs
Schottky barrier diode D17 ........................ 49
13. The actual measured capacitance as a function of time 51
14. The thermal emission rate of electrons as a function
of average electric field. The subscription pH
denotes that the transient photocapacicance method
was being employed to obtain the data .............. 52
15. The thermal emission rate of electron as a function
of temperature (103/T) between 285 and 3160. The
data were taken at V = 6 volcs ..................... 5
16. A plot of C as a function of reverse bias voltage
for D17, D7 and 011. The superscript represents
the values taken at t = 0+ ......................... 57
17. The photoHall mobility versus photoconductance for
sample S3 at 20.8 and 4.2 K ........................ 60
18. The PIE shortcircuit current per unit width of
sample per unit magnetic flux density, Ip /B, versus
photoconducrance LG for samples S1 and
S2 at SO and 300 K ................................. 61
19. The PME apparent lifetime T the electron lifetime
T and the hole lifetime i versus photoconductance
L at SO and 300 K ..... ........................ 63
20. The PME shortcircuit current per unit width of
sample per unit magnetic field intensity, I /B,
versus photoconductance for oxygendoped sample S3
at 20.8 and 4.2 K .................................. 65
21. The PME apparent lifetime T (i = T = ) versus
photoconductance LG for S3 at 20.8 and 4.20K ... 67
LIST OF S'Y; iOLS
A Area of the Schottkv diode
A*
3
B Magnetic flux density
B Capture probability of electron for direct band gap
semiconductor (see Eq. (45))
b U/p
C, Ci Capacitance of a capacitor in general and at bias
voltage V. respectively
1
o 
cn, c Capture rate of neutral and negative impurities
respectively
c c Total electron and hole capture rates respectively
n p
D D D Effective, electron and hole diffusion constants
a n p
respectively
D Surface state density
s
d Thickness of the bulk sample
EC, EV Conduction and valence band edges respectively
Ef, E QuasiFermi level and energy band gap of a semiconductor
respectively
ET Thermal activation energy of deep level impurity
E Electric field intensity
e e Electron and hole thermal emission rates respectively
n p
E, E. Dielectric constants of the semiconductor and the
interfacial layer respectively
AC Photoconductance
h Plank's constant
viii
I, Ia
S sat
J, J
sat
k
K,
m
m m"
NC NV
NT
N, N
nD
n, p
o a.
n.
1
nl' Pi
An, Ap, AnD,
ANI etc.
An
o
nT' PT
"nT PT
q
AQ
R
PMFE shortcircuit current
Current and saturation current respectively
Current and saturation current densities respectively
Boltzmann's constant
See Eqs. (40) and (42)
Diode voltage dividing factor (see Eqs. (3) and (10))
The free and effective masses of electron respectively
The density of states effective masses for electron and
hole respectively
Effective density of states for the conduction and
valence bands respectively
Density of shallow donor
Density of deep level impurity
Density of negative and neutral deep impurities
respect ively
Density of unionized shallow donor
Nonequilibrium electron and hole densities respectively
Thermal equilibrium electron and hole densities
respectively
Intrinsic carrier concentration
Effective electron and hole densities respectively when
the Fermilevel coincides with the trap level
Excess densities over respective thermal equilibrium
densities
Excess carrier density at the illuminated surface
Electron and hole concentrations at the deep impurity
centers respectively
Electronic charge
Variation of charge density
Recombination rate (see Eqs. (41) and (46))
r Resistance
C
n
C
P
S S Electron and hole capture cross section respectively
T Temperature
r See Eq. ('0)
T Ta Large injection carrier, electron, hole and apparent PHE
lifetimes respectively
U, Up, UH Electron, hole and Hall mobilities respectively
V VR Applied voltage and reverse bias voltage respectively
Vbi V'i Diffusion potential (see Fig. 1) and apparent diffusion
potential respectively
V See Eq. (S)
vt Electron thermal velocity
a' b' 4'bo Apparent, actual and intrinsic barrier heights of metal
semiconductor Schottky diode respectively
to Energy level at the surface (see Fig. 1)
ft See Eq. (22b)
A See Fig. 2(a)
Ai Thickness of the interfacial layer (see Fig. 1)
xt See Fig. 2(a)
X Electron affinity
e
n
e +e
n p
p(:) Charge density
W Depletion layer width
A Potential across interfacial layer (see Fip. 1)
Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy
INVESTIGATION OF DEEP LEVEL IMPURITIES
(OXYGEN ANiD CHROMIUM) IN BULK GALLILPI ARSENIDE
AND AuGaAs SCHOTTKY DIODES
By
Chern I. Huang
March, 1973
Chairman: S. S. Li
Major Department: Electrical Engineering
The roles that the deep level impurities, chromium and oxygen,
play in the recombination and trapping processes of the photoinjected
carriers in bulk ntype GaAs have been investigated by using photo
magnetoelectric (PME) and photoconductive (PC) effects at various
injection ranges and temperatures. A generalized theory for the PRE
and PC effects is developed, taking into account the variation of
carrier lifetimes with injected carrier density and the trapping of
holes in the chromium levels, by using a ShockleyRead type recombination
and trapping model. The experimental results have yielded the dependence
of the carrier lifetimes on injections over a wide injection range in
the Crdoped GaAs. For the oxygendoped ntype GaAs, it is found that
at low temperatures the band to band radiative recombination mechanism
prevails. The experimentally obtained capture probability compares
favorably with Hall's radiative recombination model.
: i
The electronic properties of o::ygen and chromium impurities in
ntype GaAs such as the thermal activation energies, the thermal
emission rate, the capture cross section of electrons and the
dependence of the chermai emission rate on static electric fields
are obtained from the transient dark and photocapacitance measurements
on the AuGaAs Schottky barrier diodes in which the GaAs substrates
are doped either with oxygen or chromium.
CHAPTER I
INTRODUCTION
Since gallium arsenide (GaAs) has shown superior electrical
properties such as high electron mobility, high breakdown field and
lower shallow level impurity ionization energy over those of silicon,
better understanding of its physical properties has become an
enthusiastically pursued subject.
In reality and potentiality, GaAs finds wide application in solid
state devices. The device characteristics are greatly influenced by
the existence of deep level impurities in GaAs which is either inherited
from the crystal growing processes or intentionally doped. The
situation is similar to that of golddoped silicon. The progress in
the applications of GaAs, where the concentration of a deep level
impurity is abundant,will be furthered by a complete understanding of
its electrical properties. In this material the impurity centers make
a substantial contribution to the density of charge centers that
fluctuate with carrier injection. This is due to its ability to commu
nicate with the excess electrons in the conduction band of the semi
conductor.
Although considerable work has been published concerning the
trapping and recombination properties of defects in semiconductors,
relatively few are dealing with GaAs. The most effective method for
studying the trapping and the recombination mechanisms is the carrier
 1 
lifetime measurement. Amcng available methods, the photomagneto
electric (1':E) and the photoconduccive (PC) effect measurements
performed under steadystate condition are the favorite ones for
obtaining rhe excess carrier lifetimes and consequently for under
standing the transport mechanism.
The PiME and PC effects in undoped semiinsulating and semi
conducting GaAs single crystals were first reported by Holeman and
1 9
Hilsum. Hurd reported the experimental results of the Dember and
PME effects in oxygendoped GaAs between 140 and 3000K. The photo
electronic analysis of high resistivity ntype GaAs was given by Eube.3
It has also been shown that the minority carrier lifetimes of the more
heavily doped samples are controlled by band to band radiative
recombination,while the minority carrier lifetimes of high resistivit,
samples are determined by recombination centers lying in :he middle of
4 5
the band gap. A more recent study on the photoconductivity of high
resistivit GaAs and Crdoped GaAs was given by broom.6 in all these
works, the roles that oxygen and chromium have played in the excess
carrier recombination and trapping have not been specifically
determined. There is lack of understanding about the basic physical
properties of the deep impurity centers which is believed to have
caused high resistivity in GaAs.
Most recently, the properties of deep level impurity in GaAs have
received noticeable attention in the literature. It has also become
clear that the metalsemiconductor Schottky diode is a powerful tool in
obtaining fundamental deep impurity parameters through its timevarying
capacitancevoltage relationship.
 1)
 3
With respect to the understanding of semiconductor properties via
8
Schottky barrier diodes, Goodman presented the first comprehensive
descriptions of the contact characteristics in terms of the capacitance
voltage relationship of the diode. Although the deep level impurity
effect was included, no detailed transient consideration vas given in
his treatment. However, an interesting transient behavior in the high
frequency capacitance of the Schottky barrier diode on ntype GaAs vas
C9,10,11I,1'
observed. '1 This behavior has been interpreted as a result of
the existence of deep level impurities in CaAs. The electron capture
cross section, the thermal emission rate of electrons and the thermal
activation energy of deep impurity can presumably be obtained from the
9,10,11 ,12
transient time constant. 0,11,12 However, the results for GaAs are
not in good agreement. For example, the determined thermal activation
13 11
energy for oxygen in ntype GaAs ranges from 0.57 ev to 0.9 ev from
the conduction band edge, comparing with the value of 0.8 ev obtained
14
by optical and Halleffect measurements.
15
Sah et al. reported transient capacitance experiments using gold
+ +
doped silicon pn step junctions (either p n or n p junction).
According to their model, the electronic properties of impurity centers
in semiconductors such as energy level, multiplicity of charge state,
thermal and optical capture cross sections, and emission rates of
electrons can be obtained. Their model applies equally well to the
metalsemiconductor Schottkv barrier diodes. In this work, the AuCaAs
(ntype) Schottky barrier diodes are fabricated with substrates doped
either with c:< Len or chromium. The transient capacitance experimental
results are : 'yzed by using the model proposed by Sah et al.
The objective of this research is to study the transport,
recombination and trapping mechanisms of steadystate photoinjected
carriers associated specifically with oxygen and chromium impurities.
The electronic properties of these impurity centers, such as thermal
activation energy, thermal emission rate, capture cross section of
electrons and dependence of the thermal emission rate on static
electric fields are also investigated.
In Chapter II, the current transport theory of the metal
semiconductor Schottky barrier diode is studied. Since the low carrier
14, 15 3
concentration (n = 10 10 cm ) ntype GaAs substrates have been used
for diode construction, it is expected that the depletion layer of the
diodes will be relatively wide. Therefore, the most probable mechanism
of electron transport at the interface is by thermionic emission over
the barrier. Being limited by imperfect CaAs technology, the diodes
fabricated are not ideal. Thus the interfacial layer and surface state
effects are also considered. In Chapter III, following a brief review
of the existing transient capacitance models, the method for determining
the deep impurity physical properties is discussed. Chapter IV contains
recombination models describing the excess carrier behavior in the
presence of deep impurities. The experimental procedures are described
in Chapter V. Chapter VI gives the experimental results and their
analyses. Conclusions and suggestions for further study are given in
Chapter VII.
 4
CHAPTER II
CURRENT TPRANSPORT IN SCHOTTKY BARRIER DIODES
Introduction
The current transport in metalsemiconductor barriers is mainly
due to majority carriers in contrast to pn junctions where the minority
carriers are responsible. The theory of current flow over the barrier
of metalsemiconductor contacts is complicated. There are several
mechanisms, namely, thermionic emission,16 diffusion,16,17 thermionic
18 i19
emissiondiffusion, thermionicfield emission and field emission.
20, 1
There are also some factors such as interfacial layer," surface
states '', and image force lowering of the barrier that could cause
deviations from the ideal case. The energy band diagram of such a
physical system is shown in Fig. 1. However, the identification of
these factors with currentvoltage characteristics of a Schottky
barrier diode has been extremely difficult. Generally, one must
specify the range of applied bias voltage and temperature before a
relationship among current, voltage and temperature can be established.
Current Transport Theory
Ignoring the effect of image force and electron collisions within
16
the depletion region, Bethe's thermionic emission theory gives
q''b aV
J = A*T" exp( k )[exp (c)l] (1)
kT kT'
 5
 6 
I
q ",
qL b qVbi
Ec
 Ef
Fig. 1 Energy band diagram of a mncal
semiconduccor (ntype) contact with
an interracial layer and surface states.
(After Cowley and Sze, Ref. 21)
I
 7 
where
A* = "qm:k
3
h
Assuming that the carrier concentration at the metalsemicondiuccor
interface and the edge of the depletion region are unaffected by the
17
current flow, the total current derived from the diffusion cheory7 is
S, 1/2
q D N C q(VbiV) 21D] q 'b 1
J = nC1 (2)
kT c JkT kT I
where the electron collisions are considered.
1S
Crowell and Sze incorporated Schotcky's diffusion theory and
thermionic emission theory into a single thermionicdiffusion theory.
A low electric field limit for application of this theory is estimated
from consideration of phononinduced back scattering near the potential
energy maximum. A high electric field limit associated wich the
transition to thermionic field emission is obtained by considering the
effect of quantummechanical reflection and quantum tunneling on the
thermionic recombination velocity near the metalsemiconductor inter
face. It gives
2(m1) qVbi k Vi 1/2 ]I
J = J expl (1 1 1 ex p( )1 (3)
sat m kT % bkT'
where
(t dV (4)
S kT d(inJ)
q 9qb,
sat = A*T exp( (5)
The value of m is determined by the type of emission over or through
the potential barrier. For pure thermionic emission m*l. For other
cases m takes on a more complicated form.
 8 
Another derivation has been given by Padovani and Strattonl9
covering the cases of thermionicfield emission and field emission.
The temperature dependence of current flow over a Schottky barrier is
fully discussed.
Since the carrier concentration of GCAs used in this work is in
14 15 3
the order of 10 10 cm the depletion layer width for AuGaAs
(ntype) Sckioctkv barrier is of the order of 100ml at zero bias.
Accordingly, the most probable mechanism of electron transport is by
thermionic emission. In the later part of this chapter, the thermionic
emission theory will be explored further.
Experimental evidence indicates that the metalGaAs surface has
a peak density of surface states near one third of the band gap from
22
the valence band edge. The presence of surface states causes field
dependence of the barrier height.23 This in turn affects the CV 1825
and IV characteristics of the diode. Because of the imperfect CaAs
technology, there exists an interfacial layer between metal and CaAs.
Experimental results have connected the barrier height of the Schottky
20
diode with thickness of the interfacial layer. Thus the surface states
and interfacial layer effects will also be discussed.
Interfacial Layer Effect
The metal contacts evaporated onto the chemically etched surface
under the ordinary laboratory conditions cannot be thought to be ideally
20 26
intimate; there exists an interfacial layer. The thickness of the
layer is estimated to be 530A. It has been assumed by many authors,
19
for simplicity, that the layer is electrically transparent. 9 This is
S1827
true under high electric field. The currentvoltage relation at
 9 
27
very low bias voltage has been overlooked. Simmons2 derived a formula
for the electric tunneling effect through a potential barrier of
arbitrary shape existing in a thin insulating film.
For very lot: applied voltage, the turneling resistivity is constant
(i.e., contact is ohmic). The interfacial layer can be treated as a
high resistance series resistor. Its resistance value depends on the
thickness of the layer, equivalent barrier height and dielectric
27,28
constant of the layer. 28
In view of this ohmic behavior, the thermionic emission theory
gives
2 qb (qV
J = A*T exp( T )[exp( kT1 (6)
where m is a voltage dividing factor. It is worth noting that m is
essentially a function of interfacial layer resistivity and Eq. (6) is
mkT
valid for low reverse bias voltage. At very low voltage, V << ,
q
Eq. (6) becomes
Tb qV (6a)
J = A*T exp( ) ) (6a)
which shows a linear relation between J and V.
Field Dependence of the Barrier
As mentioned in the previous section, the interfacial layer plays
an important role at very low bias voltage. At high reverse voltage,
Eq. (6) becomes
J = A*T exp( ) (7)
kT
which predicts that the reverse current would exhibit saturation.
However, this prediction is not consistent with the experimental
 10 
18,19 ,9
results. 18 9 It is found that the potential barrier ib is slightly
dependent upon the applied electric field.
Among barrier lowering mechanisms, the image force barrier
lowering gives24
1/2
(.,,) = ( ) (S)
image
where
2q1N V 1/2
E (. )
I:T C
V = (1 + n
e b q D
On the other hand, the barrier lowering due to the equilibrium electro
static charge distribution (dipolo l:,'er) prevailing at the contact can
be expressed as'
( static + (9)
static
Here a Maclaurin series expansion is used and a is an adjustable
empirical parameter.
Combining Eqs. (6), (S) and (9), the reverse current is given by
J A*T 2exp +( )1 + E [exp() )~ (10)
WK bo 0,_ mkTU
This equation should be able to cover the currentvoltage behavior in
a wide voltage range and for various physical situations. Andrews and
Lepselter used this model successfully to explain the IV character
istics of metalsilicide Schottky diodes. Since their diode fabrication
process virtually eliminates the interfacial layer, the value of m is
nearly equal to unity.
 11 
Surface States Effect
The effect of surface states on the current transport is shown in
23
the form of barrier height lowering. Crowell ec al. have obtained
d"b qD i 1
d +  1 (11)
K 1
for the metalsemiconductor contact with both the surface states and
d .; b
the interfacial layer. If d is appreciable in comparison with the
width of the semiconductor depletion region, the surface states effect
cannot be overlooked.
From Eq. (3) we see that m is a characterization parameter for the
IV relation. It is especially meaningful in the forward bias
condition with V > 3T Since both A* and 4b are electric field
q b
dependent, a small deviation of m from unity should occur and
dV kT d(LnA.) L''b E '1b E 1
Lm T dnJ = 1 2qV d(LnE) .4V 2V e 2 Vj
In this equation, the contribution due to the second and third
terms alone is small. It is shoun that m equals 1.04 for the WGaAs
diode.2" From Eq. (11) we can see chat if the surface state density D
d 4 b
is high, d = 0. A greater deviation of m from unity car, only be
explained through an adjustable parameter rt. The physical origin of .
29
could be the electrostatic dipole or the interfacial layer.
Since the current transport is not the main subject of this study,
no further exploring will be pursued. In Chapter VI we shall present
some experimental results to substantiate the points raised in this
chapter.
In the following chapter another aspect of the metalsemiconductor
contact properties, namely the capacitance and voltage relation, will
12 
be studied in some detail. The effect of deep level impurities on
CV characteristics '.will also be investigated.
CHAPTER III
THE CAPACIT.'JCEVOLTAGE CHA..CTERISTICS OF SCHOTTKY
EAPRIER DIODES I. THE PRESENCE OF DEEP LEVEL I'MURITIES
Incroduction
In metalsemiconductor contact, the conduction and valence bands
of the semiconductor are brought into a definite energy relationship
with the Fermi level in the metal. This relationship serves as a
boundary condition on the solution of Poisson's equation in the
semiconductor.
Using abrupt junction appro::imation, the following relation is
obtained
C= D (13)
S kT (l+.n C
b q ND]
I 1q DI (13a)
[2V (
Eq. (13a) can be rewritten in the form
2V
I = e (14)
C2 qaND
or
" 1
2 (d(C )) (15)
D qc dV
If the donor concentration ID is uniformly distributed throughout
the semiconductor, hen from Eq. (), the slope of a plot of C versus
the semiconductor, chen from Eq. (14), the slope of a plot of C versus
 13 
 14 
V for reverse bias yields the donor concentration. The barrier height
can be obtained from the extrapolated intercept of the relationship on
the voltage axis. If ;D is not a constant spatially, one can still
utilize the differential capscitance method to determine the doping
profile from Eq. (15). However, the presence of the deep level
impurities in GaAs makes it difficult to interpret the measured capaci
tance. This is due to the fact that the deep impurities do not respond
to the high frequency test signals, yet its influence on the diode is
9 10 I],1
observable.'10'11,12 Previous reports deal with the following physical
situations at a temperature higher than the freezeout temperature of
the deep impurity states: First of all, the diode is placed at zero
bias, such that the deep impurity centers are filled with electrons.
After applying reverse bias, the deep impurity centers in the depletion
region of the diode start to ionize or deionize. This process, in turn,
causes the diode capacitance to vary according to the characteristics
of the deep impurities.
Several models have been suggested to describe the situation, but
the results are not in good agreement. In the following section, the
existing models are reviewed. A model which is originally for deep
level impurities in pn step junction will be discussed in some detail.
It shall be proved experimentally in Chapter VI that it applies equally
well to the Schottkv barrier diode.
Review of the Existing Models
The first detailed treatment of the metalsemiconductor CV
properties was presented by Goodman. The effects of an insulating
interfacial layer between the metal and semiconductor and of traps
(deep level impurities) in the depletion region have been evaluated.
 15 
11
Goodman's model was modified by Senechal and Basinski by taking
into account a more sophisticated charge distribution. Using a
simplified energy band diagram (Figs. 2(a) and 2(b)), a small variation
in DC voltage is given by
Q qND AAW qN AMW
A V  +  (16)
C CA >.
14 (O)
This equation can be rearranged as
2 +N) (T) C (17)
EA
where C = is the high frequen:_y capacitance. This is Zohta's basic
13
model.13 Senechal and Basinski replaced :T with NT(1lecxp(ent)] and
, with \(t). Their model has the form
= T[+N_1exp(e C)]
AC D n
TL
x(t)Nr
)[lexp(ent] C1 (18)
Experimentally, this is a fairly complicated equation. In order
to obtain the value of e several approximations are needed (i.e.,
1 2CC2 2 o 2
V = V V C = and AC = C C ). To obtain the accurate
S 1' C1+C 2 1
values for AV, C and AC requires small step variation in V. This,
in turn, makes capacitance measurement lack necessary accuracy.
Nevertheless, from the above CV experiment, they have determined the
energy level for oxygen in ntype GaAs to be 0.9 ev below the conduction
12
band edge. An extension of their theory was derived by Glover to
include nonuniform impurity distribution in the semiconductor.
All of the models discussed above have involved capacitance versus
ime measurement. On the other hand, ta13 has combined the Senechal
time measurement. On the other hand, Zohta has combined the Senechal
 16 
qllT
qND
 :* ;
0 X
t
(b)
Fig. 2 (a) Energy band diagram of a metalsemiconductor
(ntype) in the presence of donortype deep
level impurities
(b) Spatial distribution of charges.
 17 
asinski1 and Copeland's3 models and has been able to derive deep
impurity information without resorting to the transient measurement.
Their results will be evaluated and compared in a later chapter (see
Table 2).
In the following section, by extending the model by Sah et al.15
on the pn junction capacitance to the metalsemiconductor Schoctky
barrier diode capacitance, a straightforward and simple method is
presented for determining the deep impurity parameters. In the mean
time it is necessary to discuss the electron transport associated with
the deep level impurity centers prior to studying a special physical
situation.
Transition Processes in Deep Impurity Centers
9
As first suggested by Williams, the transient phenomenon in
capacitance on the AuGaAs (ntype) Schottky barrier diode is due to
the emptying of the filled deep impurity centers in the depletion
region. To facilitate the discussion of the processes involved, the
energy band diagram of the semiconductor with single level deep impurity
centers is shown in Fig. 3. There are eight possible thermal and
optical processes associated with the deep impurity centers and excess
15
carriers. The rate equation is given by
dnT
d = (cn + e)PT (p + e)nT (19)
d n n T
Here denotes the rate of change in electron concentrations in the
dt
deep impurities. The exact solution for Eq. (19) is complicated and can
only be obtained by solving the continuity and rate equations
simultaneously.
 18 
=I1
EC
I TT
Fig. 3. The energy band diagram and
(a) four thermal and (b) four optical
transition processes between the deep
level impurity and the conduction band.
(After Sah et al., Ref. 15)
 19 
However, with the case we are dealing here, a simplification is
possible. For the metalsemiconductor Schottky barrier structure, the
charge distribution in the depletion region is sho.wn in Fig. 2(b).
Charge neutrality is assumed outside of the depletion region 0 < x < w.
This approximation allows the use of constant quasiFermi levels in
this region. Inside the depletion region, the constant quasiFermi
level approximation is still adequate, since all that is necessary for
simplification is the depletion condition n = p = 0. Then the race
equation becomes
dn
dr e T n (e +ep) (19a)
Here the totality condition N = n +P is used. The solution of Eq.
(19a) subject to the initial condition of nT(t=0) = 0 is
e
n(t) = n+ep) + (ene)e:.:p[(e+e )t] (20)
This time dependence of charge density in the depletion region
contributes to the transient phenomenon in the capacitance.
Dark Transient Capacitance
The high frequency capacitance of a Schottky barrier diode is
given by
= dQ() =
dV(W) W
The main task in deriving the capacitance expression is to obtain
the depleticn region width W. In the presence of donorlike deep level
impurities, the net charge distribution can be approximated by (see
Fig. 2(b))
o(x) = q[ND +
p(x) = qND
o(x) = 0
After solving
width is5
 20 
Ne
Ten
(e +ep)
n p
for 0 < x < x
t
for x < : < W
for >
for x > W
Poisson's equation, the total depletion layer
W i' (la)' 2 !"2
W= ((N 1 ) r 2c '
TD 'T
+ (2c/q) [(ND+T) bi +V T(1 't}, '
D + T
e
S n (22a)
e +e
n p
E E
,* (22b)
"t q
At large reverse bias voltage, the depletion width becomes
2c (V +V ) '
W = (22c)
(ND TIN T)
Then, for an ideal Schottky barrier diode, the high frequency
capacitance can be expressed as
qeA2 (ND+n ) )!
C = 22(bi+Vn) (23)
By combining Eqs. (20) and (23), the transient capacitance for the
condition of e >> e
n I
C(t) = 2 bi+VR) [1D+N (exp(e n))
q= A2( D+ )
2(Vbi+VR)
1T e +(et]!;
1 +N)exp(e t)
"D T J
and
(21a)
(21b)
(21c)
where
(22)
(24a)
 21 
where VR is a unit step applied voltage.
The initial capacitance (t = 0 ) is
C(0+) q nD (25)
bi R)
and the final steadystate value is
qcA(iD +1T )1
C(t=") = (26)
2(Vbi+V R
A2 D (V^
In addition, if the capacitance values are taken at times such
that
NT
T
( )exp(ent) << 1
then from Eqs. (20) and (24) the time varying capacitance is an
exponential function of time:
C(t) = bi 1 i ( )exp(e t) (27)
(bi R) RDT n
From Eqs. (25) and (26), the shallow and deep impurity doping
concentrations can be determined, while the transient time constant is
obtained from Eq. (27).
The time constant of the transient capacitance gives us the value
of the thermal emission rate of electrons from the deep impurities. It
is worth noting that the thermal emission rate is not an equilibrium
value. Under the influence of an electric field, the impurity potential
barrier is lowered by an amount LE. Thus the thermal emission rate is
given by31
e (E) = e (0) exp[.E/kT] (28)
n n
where
22 
E E
e (0) = ( Sexp ) (29)
n C tSn kT
and the statistical weighting factor has been assumed to be unity. If
the emission rate is independent of the electric field, the activation
energy of the deep impurity states can be obtained through the measure
ment of the temperature dependence of the emission rate by using Eq.
(29). The transient capacitance of Eq. (27) would also show true
exponential dependence on time and the electron capture cross section
S can also be calculated from Eq. (29).
For the case of acceptortype deep level impurities, the time
dependence of the capacitance can be expressed as
.2
C(t) = 2(C [V ) [ e:.:p(ent)] 1/2 (30)
bi+k R
Again, the values of ND ,T and e can be determined by Eq. (30)
from the measurements of time constant, the initial and final values
of capacitance.
Transient Photocapacitance
In the dark transient capacitance measurement, the deep donor
impurity centers were filled with electrons initially at zero bias
condition. The filling of electrons at the deep impurity centers can
also be achieved by shining the interband light (h. > E ) onto the top
g
surface of the device which is reverse biased at a certain voltage.
Upon reaching the steady state, the recapture of photoinjected
electrons by the deep impurities in the depletion region is balanced by
the thermal release of electrons from the impurities. Ihen the light
is removed, the thermal release of the remaining captured electrons
from the deep impurities causes the change in Lhe diode capacitance.
 23 
From the time constant of this transient capacitance measurement, the
thermal emission race can be obtained.
Summary
We have demonstrated in this chapter that some parameters of the
deep level impurity can be obtained by using transient capacitance
measurement. These parameters are important to the kinetic behavior of
excess carriers. For example, if there is only one electrically active
impurity level, the lifetime of holes in low level injection in an
ntype semiconductor is
1
T = (31)
tpT
Here the values of S and N are determinedby the transient capacitance
p T
measurement. In the next chapter, the behavior of excess carriers in a
semiconductor with the presence of deep impurity centers will be
examined.
CHAPTER IV
RECO:MII1.1;ATION: AD TRAPPING PROCESSES
II; BULK nTYPE GaAs IN THE PRESENCE
OF DEEP LEVEL I:mPURITIES
Introduction
In the previous chapter, the properties of deep level impurities
in a semiconductor are studied in terms of its thermal activation
energy, electron emission rate and capture cross section through CV
relationship in a Schottky diode. However, the deep impurity can also
serve as a trapping or recombination center for excess carriers in the
32
semiconductor. A complete review of the effects of trapping on
33 "39
carrier transport is done by van Roosbroeck,33 while ShockleyRead32
34
and SahShockley models provide the necessary trapping and
recombination statistics. In the case of the deep impurity not being
an effective recombination center, Hall's band to band radiative
recombination model5 is applicable.
The most effective method for studying the trapping and the
recombination mechanisms is the carrier lifetime measurement. We
choose the photomagnetoelectric (PME) and the photoconductive (PC)
effects to measure the carrier lifetimes, and investigate the effects
of chromium and oxygen on the transport of excess carriers in bulk
ntype GaAs.
In this chapter, a generalized theory to account for the observed
PME and PC effects on chromium and oxygen doped GaAs is developed by
 24 
 25 
considering the carrier lifelines as a function of the injection and
the effect of trapping. Based on this theory, we are able to determine
the properties of chromium and oxygen as recombination and trapping
centers.
Charge Neutrality in Semiconductors
In steady state injection, the emission and capture of carriers by
the impurity centers cause the charge in such centers to change from
its equilibrium values. Utilizing the energy band diagram for an ntype
semiconductor with one shallow level donor and one deep level acceptor
impurities shown in Fig. 4, the requirement of charge neutrality gives
p + (ND nD) T = 0 (32)
By subtracting the thermal equilibrium contribution we have
Lp = An + LnD + T (33)
34
Applying SahShockley statistics to this physical situation we
obtain
(n+n )c0
N = Nn (34)
T T 
(p+P1)C
and
N = N + N (34a)
T T T
Consider the case of undercompensation (ND > NT) at temperatures
low enough that the semiconductor is an extrinsic ntype. The
36
quantities nI, p and p are negligible and the statistics give
NT
n = nT "o (35)
D T
Also from Eqs. (34) and (3a) we obtain
 26 
Ec
ED
ET
Ev
nD D T T
Fig. 4 Localized states introduced by the
shallow and deep level impurities
in the forbidden band for a semi
conductor. The centers are shown
in their available charge states.
 27 
No = N (36)
T T p+n (36)
where
o
c
n
c
P
Realizing that in thermal equilibrium
(NDnD) = NT + nD T (37)
th. eq.
and
(N;) = NT (38)
th. eq.
the charge neutrality equation (Eq.(33)) can be rewritten as
ApNT ND 1
Ap + n n + An NT ( n + An) (39)
Ap+ny T D T 0o
Therefore, the density of carriers trapped in the impurity states
is a function of the injected carrier densities. If the density of
these traps is larger than the excess carrier density, the charge in
them will play an important role in preserving the charge neutrality
under the steady state injection. This has been shown by Agraz and
37,38
Li.738 In a certain injection range we can define the parameters F
and such that
Lp = rAn (40)
T
where r = l<1 for hole trapping.
n
Trapping and Recombination Processes Through Deep Level Impurities
In order to understand the charge states in the acceptor levels
under dark and illumination conditions, an energy band diagram for the
ntype semiconductor is presented in Fig. 5. In thermal equilibrium,
I i
Oo
*
o
0
IO
r,
o
t.:
I
I
( l
(e
1u
 28 
0
00
00
0
O0 <
00
00
O
O
U nJ
LO
eI
el
0.
Ce:
C* U

1 c
0 Q0
oL
w.u
I 
) r) .
> .0
,a I
w c
.t C
LI >. O
4 U 
CJ 'U
Q)C

o 
co~
OCE
C E C
0 3 1
E .0
VI 4 .0
ro
0 3
n 1*
r1r*
(0 3
o cLCa
.fl 4 1.
iijta 
4
C
II
F
ID I0
 29 
the acceptor levels are occupied by the conduction electrons (see Fig.
5(a)) and are in negative charge state. For steadystate injection,
the free holes in the valence band are captured by the negatively
charged acceptor centers due to the Coulomb attractive potential. As a
result, these trapped holes :ill tend to destroy the charge balance in
the localized and band states. This is true for the case when the
acceptor density is much higher than the thermal equilibrium electron
concentration. The impurity centers tend to serve as recombination
centers.
3/
The recombination rate is
O 
14 c c
2 Tnp
Rc c (npn+c
Sco( (n+nl)+c (p+pl)
n 1 p 1
N c
S("onP + pO nP
A An = (41)
T 1
n p
The carrier lifetimes depend on the injected carrier density as we
have seen in the above equation. This dependence can be expressed in
terms of a powerlaw relationship between T and An, that is
T = KAn (42)
n
in certain injection ranges. In the high injection region, the charge
states in localized and band states are essentially controlled by the
injected carrier densities. The electron and hole lifetimes are equal
and independent of injection. The trapping constant F is equal to
unity and F = 0. In other injection ranges, it is still possible to
37,38
ha'.'e = O, although it usually assumes values other than zero.
 30 
Radiative Recombination in the Hose Crystal
If che semiconductor is heavily doped or if che deep level
impurities in a semiconductor are in a neutral charge state, the
recombination mechanism is most likely to be the band to band radiative
recombination. In a nondegenerate semiconductor, the race at which
excess electrons and holes disappear is proportional to che product of
the electron and hole concentrations. Thus che recombinacion race is
R = B (npni) (43)
For large injection, An >> no, Ap >> po'
R = B rngp (4r)
The capture probability B can be evaluated cheorecically by
r
setting the equilibrium rate of radiative recombinacion equal to the
total amount of blackbody radiation absorbed by the crystal due to
band to band process. It has been derived by Hall35 and is given by
Sm 3/2 m m 3003/2
B = 0.58 x 102 ( ) (1 + + )( ) E (45)
r +mh me mh T g
The band to band radiative carrier lifetimes for large injection
are defined in terms of the recombination rate
R = A = p (46)
T T
n p
and are
1 1
T = = (47)
n p B An B Ap
r r
It is noted here that internal absorption will increase the apparent
radiative lifetime in samples which are thick compared to the absorption
distance for the recombination radiation. Equations (46) and (47) also
 31 
indicate that the capture probability B can be determined at various
temperatures by measuring carrier lifetimes at certain injection ranges.
In the following section, the method for obtaining the quantities Tn'
T B and An will be presented.
p' r
Carrier Lifetime Measurement Usine PME and PC Effects
The theory for the PME effect involves the solution of the
continuity equation for the carriers injected at the illuminated
surface. Detailed descriptions of the physical system have been given
by van Roosbroeck and Agraz and Li.37 In this section, we shall
present a generalized theory to account for the trapping effect in the
presence of deep level impurities in bulk semiconductors.
With the help of Eqs. (40) and (42), the generalized expressions
for PME shortcircuit current and photoconductance can be derived as
follows: The photoconductance per unit sample lengthtowidth ratio is
given by
AG = q (f p n + w Ap)dy
o
SAn DaD d(n)
= qu n (An + ) aAn (48)
b (2 /n D Rd(An))1
o a
2D F
where D = n is the effective diffusion constant and
a r+b
R = (L) Anl' (4Sa)
We obtain the general expression for photoconductance AC by solving
Eqs. (48) and (48a).
C+6+1
n
AG = [h][(t+Ci)D FY A 2 (49)
The PME shortcircuit current per unit width IPME ls
PIlE
 32 
aAn
I = q. p(l+b)B f D d(An) (50)
= 2qy (l+b)D FBLAnC (51)
p p o
The relationship between I and LG can now be derived from Eqs. (49)
and (51) by eliminating An from these two equations. The result
fields
1 [
(I+C+r )2 +L+I 1'r + :+I
I = 2q (l+b)BrD l+C') (52)
PME p p 4(1+CS)D pF q J
This general expression of IpHE versus AG is rather important since
it provides a direct correlation among the measureable quantities IpME'
Sn' B and AC, and allows us to make a direct comparison of the
theoretical prediction with the experimental results.
In general, the electron and hole lifetimes are functions of
injection. In order to determine the lifetimes as functions of
injection, it is necessary to define an apparent lifetime T in the
a
I expression. This can be achieved by rewriting Eq. (52) into
I F, (D a A LG (53)
a
where
2 2(C+?1)
1 (1+ (54
a 2D ] 2 (1+e)D p qJn
is the PRE apparent lifetime.
To deduce the electron and hole lifetimes from the F.IE apparent
lifetimes, we make use of the following relation in the presence of
trapping39
trapping
 33 
T np+T An T +FT
n p = n
T=  = 2T (55)
a Ln+Sp 1+F p
where we assume F = p < 1.
n
In essence, i is a parallel sum of T and I and is controlled
a n p
by the shorter of the two lifetimes. Subsequently, the remainder of
the parameters r and K: can be deduced by using Eqs. (49), (53) and (5.4).
Since we have made use of Eq. (40), we are assuming that the
ShockleyRead type recombination mechanism is dominant; ho'.'ever, the
generalized theory is equally applicable to the case of band to band
radiative recombination processes. In this particular situation, by
1
setting F = 1 (i.e. T = w no trapping), : B and B = 1 in Eq.
n p r
(52), we obtain an expression for the PME shortcircuit current for the
radiative recombination. It can be written as
B
I (r )CG2 (56)
PME 6 qn
where the electron and hole mobility ratio b is assumed to be much
greater than unity. Comparing this equation with Eq. (53) we obtain
the electron and hole lifetimes for band to band radiative recombination
2
q n
T= T = 72D ( ) (57)
n p p B G
r
This equation shows that the electron and hole lifetimes are
inversely proportional to the square of the photoconductance under a
large injection condition.
We can also rewrite Eq. (56) into
6(qun) IPM E
B = ) (58)
r (AG)2 B
(AG)
This equation provides a simple method for determining the capture
probability B M'hich is obtained by the concurrent measurements of
r
I M/B, AG and the photoHall mobility u .
Summary
After considering the charge neutrality condition in the semi
conductor, a simple powerlaw relation between An and lp is established.
Bv taking into account the variation of carrier lifetimes with injected
carrier density and the effect of trapping, a generalized theory for
the PME and PC effects is then developed. For acceptortype deep level
impurities in the ntype semiconductor, the ShockleyRead type
recombination model is used to interpret the recombination process. On
the other hand, Hall's band to band radiative recombination model is
used for the semiconductor in the presence of neutral deep impurity
centers.
 31 
CHAPTER V
EX:PERlIENTS
Preparation of Devices
GaAs wafers were ntype oxygen or chromiumdoped single crystals
with faces in the (111) plane. The samples were mechanically lapped and
chemically etched in a solution of 3:1:1:H SO,:H202:H 0 at 900C. Ohmic
contacts were provided on the rear surface by evaporation of indium,
and alloying at 3750C in a hydrogen atmosphere. The front face was
chemically polished prior to evaporation of a gold dot in an area of
2
approximately 3 mm The gold evaporation was performed in a vacuum
S
with the background pressure of 5x10 torr.
The packaging of the device was made by using a TO1S transistor
header. By applying silver paste, the ohmic contact side of the diode
was "glued" onto the header (collector terminal). After gold wire
connections were made, the diodes were baked at 110C for 24 hours.
The basic physical parameters of typical devices fabricated are
summarized in Table 1.
Sample Preparation
Two slices of rectangular bar cut from a Crdoped semiinsulating
ntype GaAs single crystal wafer (total chromium impurity density is
17 3
13x10 cm ) were made by the zonemelting method. The sample dimen
sions are 0.5xlx0.1 cm for Sample No. 1 (Sl) and 0.4x0.8x0.1 cm for
 35 
 36 
C
4' o
.:: .( T I
II 1 4O 0
>> i II O li i
., LI I 7
0 , IT I 0
c
. : Z X I J
EC
U
C
I I ' I 7
I C1. U Q
u u
E ,
'D CC
',A1
olM
>
*r40 U aO. 0 '.
ci I
rj i
0U 0O I 
)t U
>cZ
U1)
0
a(i
0.
cI
OC)
m 0
En L.
m m
M
Cv I
ui O
0 Q
U l
. I
1
f
o >
Fl
 37 
Sample No. 2 (S2). A third slice was cut from an oxygendoped semi
15 3
conducting ntype GaAs single crystal (n 10 cm ). The dimension
3
for this sample (S3) is 0.3Sx0.Sx0.04 cm3. The samples were
mechanically lapped with silicon carbide ponder on all six faces and
chemically etched on the illuminated surface by using a solution of
3 H2SO :H20 :H 0. Ohmic contact was made by indium allowing in
hydrogen atmosphere at 3750C.
CurrentVoltage Measurement
The experimental arrangement for IV measurements is shown in
Fig. 6. The device impedance rD is always greater than the precision
resistors r and r The input impedance of the digital voltmeter
s1 s2
is much greater than r and r also. The current flowing through
s s2
the diode can be calculated by VC/rs (i = 1,2). The voltage across
I
the diode is obtained by VD VC'
CapacitanceVoltage Measurement
A system for measuring the transient capacitance and transient
photocapacitance was set up as shown in Fig. 7. It consists of a
WayneKerr B641 Capacitance Bridge, a low noise amplifier, a wave
analyzer, a PerkinElmer 98 Monochromator and an XY recorder. The
system is calibrated such that the deviation from the balanced value
of the capacitance bridge, AC = C(t)C(t==), is linearly proportional
to the DC output of the wave analyzer.
The transient capacitance measurement procedure is as follows:
(1) At a certain reverse bias voltage, after the steady state is
reached, apply a small signal (< 10 mV) at 100 KHz to null the bridge.
 38 
1
Power Supply
Thermocouple
Temperature Chamber
Precision Resiscor
(10 6 + 1I')
2. Device
4. Null Voltmeter
6. Precision Resistor
(103 1")
8. Digital Volcmecer
Fig. 6 Test setup for measuring Schottky barrier
diode voltagecurrent characteristics.
 39 
Null Voltmeter
Biasing Circuit
Device
Monochromator
Capacitance Bridge
Amplifier
XY Recorder
2. Thermocouple
4. HeNe Laser
6. Temperature Chamber
8. Tungsten Light Source
10. Low Noise Amplifier
12. Wave Analyzer
Fig. 7 Experimental setup for measuring transient
dark and photocapacitance of the metalGaAs
Schottky barrier diodes.
 40 
(2) Leaving the bridge as it is, remove the bias voltage (so that the
diode is at zero bias). The null detector has maximum deflection.
(3) After waiting for 10 minutes, the same reverse bias is suddenly
applied to the diode. The bridge is restored to the balance position
gradually, and the behavior of restoration is recorded on an XY
recorder.
(4) The data are then analyzed according to Eqs. (24) and (30).
Photocapacitance Measurement
The system and procedures for measuring transient photocapacitance
are essentially the same as those used for measuring the CV relation
ship. The light source is the HeNe laser with a wavelength of 6329A.
In steps (2) and (3) above, the removing andapplying bias voltages are
replaced by shining the light on the diode and removing the light from
the diode respectively. The rest of the steps are the same.
Bulk Effect Measurements
The resistivity, Halleffect and PhotoHalleffect measurements
were performed by using the standard DC method. The measurements were
made at 300 and 80K for S1 and S2, at 20.8 and 4.20K for S3. The
technique for measuring the PIE and PC responses using the DC method is
40
described in detail by Li. For the case of small injection, an AC
system was set up. The system assembly is illustrated in Fig. 8. First
of all, the system was calibrated such that the DC output of the wave
analyzer is linearly proportional to the signal. The tungsten light
source was chopped at 400 Hz and the PME and PC signals picked up from
the sample were passed through the amplifier and a ;.'a.'e analyzer. The
system provides a maximum voltage gain of 105, which allows us to
 .1 
W1
l1u
1. Light Source
2. Light Chopping Hechanism
3. Water filter
4. Focusing Lens
5. Electromagnet
6. Sample
7. "CryoTip" Cryogenic System
 13
Constant Current Supply
Control Panel
Low Noise Amplifier
Wave Analyzer
DC voltmeter
Electromagnet Power Supply
Potentiometer
Fig. 8 Experimental setup for the AC PHE measurement.
42 
measure a relatively small signal. The smallest signal current
10
detected is in the magnitude of 10 amp, and the signaltonoise
ratio is better than 10.
CHAPTER %' .
EXPERIMENTAL RESULTS ATFD ANALYSES
Introduction
The temperature dependence of AuGaAs (ntype) Schottky diodes
forward IV characteristics was measured. Values of the barrier
height were deduced from these measurements. The reverse IV
measurement was used to study the effect of the interfacial layer.
The transient capacitance measurements of the Schottky diodes were
performed between 285 and 316K. From the temperature dependence of
the time constant, the thermal activation energies of the deep level
impurities such as oxygen an chromium in ntype GaAs were determined.
The capture cross sections for electrons were also calculated from the
time constant data.
The bulk effect measurements were performed to obtain the
functional dependence of carrier lifetimes on the excess carrier
injection. The recombination mechanisms of excess carriers in ntype
GaAs with the presence of deep impurities were investigated.
Forward CurrentVoltage Measurement of AuGaAs Schottkv Diodes
The forward IV relation of a Schottky diode by thermionic
3kT
emission theory for V > is
q
_2 (bo 4 + a e_.1p( q) (59)
Tex kT bo E + mk
 43 
 44 
The IV plots for devices D11 and D17 at different temperatures are
shown in Figs. 9 and 10 respectively. From the slope of these lines,
the values of m are calculated through the equation
m = dV) (60)
kT d(nJ)(
which are included in Figs. 9 and 10. The appreciable deviation of m
values from unity could be caused either by the electrostatic dipole
or the voltage dividing nature of the interfacial layer; however, the
exact cause for this nonideal result still cannot be determined.
Now, if we extrapolate the En I versus V plots to the small
voltage region till they intercept the '=0 ordinate as shown in Figs.
9 and 10, we can obtain the saturation current I (see Eq. (7)). In
sat
0 3
Fig. 11, En (I /T ) versus 10 /T for Dll and D17 is illustrated.
sat
The slope of these plots yields the barrier height b. The values of
the barrier height are 0.87 ev and 0.86 ev for Dll and D17
respectively. The results indicate that the different deep impurities
in ntype CaAs have no effects on the values of che barrier height.
These values are within the difference of gold work function ;.m and
electron affinity of GaAsx. It is known that
S= 4.7 5.2 ev for Au
X = 4.07 ev for GaAs
and thus
bo = v = 0.63 1.13 ev
bo m *
The reported barrier height for AuGaAs (ntype) Schottky diodes is
0.90 ev.
 45 
105
I0
(Amp)
106
11
3
If
8
No. T m
1 330.60K 1.21
6 2 320 1.18
3 310 1.15
10 297 1.11
5 289 1.09
6 271 1.02
1010
010
1011 1 I I I I
0 0.1 0.2 0.3 0.4 0.5
V (volts)
Fig. 9 Forward voltagecurrent relationship of AuGaAs (ncype)
Schoctky barrier diode D11 at various temperatures.
 6 
16
i0
(Amp) 7
107
10 8
8
1
109
No. T m
5/ 1 345K 1.32
210 2 336 131
10
3 325 1.26
4 316 1.26
7 5 306 1.20
6 296 1.19
011 7 286 1.11
8 273 1.09
/ 9 265 1.09
9
1012 I I I
0 0.1 0.2 0.3 0.4 0.5
V (volts)
Fig. 10 Forward voltagecurrent relationship of AuGaAs (ntype)
Schottky barrier diode D17 at variouss temperatures.
 47 
Amo
S10 12
1"
 10
I
s
T~
S1013
D17
D11
I I I I
II I I I
3.0
103/T (K 1
I
Fig. 11 versus 10 /T for the AuCaAs
barrier diodes D11 and D17.
barrier diodes Dll and D17.
(ntype) Schortkv
2.8
m i I
 48 
The Reverse CurrentVoltace Measurement of AuGaAs Schottky Diodes
In Fig. 12, the reverse IV characteristics for D17 at 3000K is
shown. Experimental data are illustrated by the circles while the solid
line represents the theoretical prediction of Eq. (10) with the
following parameters:
14 3
N = 2.7 x 10 cm3 m = 9
27 6
A* = 4.4 amp/cm /K' a = 1.4 x 10 cm
= 0.85 ev
'bo
For V > 0.15v, the tenn (exp(&)l] dominates the behavior of
SmkT
reversecurrent I. This is in accord with the existence of an inter
facial layer. The value of m is related to the thickness of the layer
27
and the equivalent barrier height. Instead of solving the complicated
tunneling problem, this empirical parameter m serves as a merit factor.
For metalsilicide Schottky diodes, the problems of interfacial layer
79
and surface imperfection do not exist and m value is unity." For
comparison, the prediction with m = 1 is also included in Fig. 12.
In the range of higher voltages, the barrier lowering mechanisms
dominate the IV behavior. The value of a = 1.44:106 cm for our
device is higher than that of metalsilicide Schottky diodes. This
indicates that the dipole layer effect is strong in our device. The
dipole layer is thought to be a fundamental consequence of electronic
wave function penetration from the metal into the forbidden gap of the
79
semiconductor. Perhaps the existence of the deep level impurities
has enhanced this effect.
J a
O
o
r4
0 Li
M
to
r"
On
> m
41 (
C .
*14
0 0.
c
Uj
l4
,.4
I l
 49 
eI CMJ
I E
= u
E
I I
co
I
CDi
0
I
0O
C
.. . .. p I I I I I I
 50 
Transient Capacitance Measurement of AuGaAs Schottkv Diodes
The transient capacitance measurements were performed between
285 and 316K. A typical capacitance C = C(c)C(t=) versus time t
is illustrated in Fig. 13. In the previous section, the experimental
results have indicated the existence of a high resistance interfacial
8
layer in series with the device. Then the measured capacitance C' is
C' = (61)
l+ 2'r' C
where r is the equivalent series resistance. Since wrC < ] in our
experiments (see a later section), Eq. (2') still can be used to
analyze the CV data without introducing appreciable error.
With the help of the HewlettPacker calculator 9100A and the least
square curve fitting technique, the time constant (or the reciprocal of
the thermal emission rate of electrons),the steadystate capacitance
C(t=) and the initial capacitance C(t=0 ) were obtained (Eqs. (25),
(26) and (27)).
Field Dependence of Thermal Emission Rate of Electrons
The thermal emission rate of electrons e as a function of the
n
average applied electric field is shown for several devices in Fig. 14.
At low electric field, the thermal emission rates remain constant for
all devices. At higher electric field, the thermal emission rate of
Device D17 shows rapid increase while that of others remains unchanged.
This can be explained qualitatively by the PooleFrenkel effect (field
assisted thermal ionization).31
An electron is bound to the deep level impurity atom by some
potential which may either be Coulomb's attractive or neutral potential.
1hen an electric field is applied, the effect on the impurity potential
 51 
U 0
E
C
0
*u
U
Cu
0
CU
ct
.C,
ao
E
J)
co
3
ro
14
*^
(3)D (m = 3)o
( d)
 52 
E
U
LUi
41
i4
X
LU
I I I It I I cI
J 0
1t U
l r
0.
UJ~I
0 O
SOO
>w
a)
C4 V
vC
.LJ
U LI
0 C"
0)
C.
HO
cu %l
Sm
L,
o *
.l
Wa)>!
I I
C I
I I 1 I I
 53 
is to lower the barrier that the trapped electron must overcome in
order to escape from the deep impurity atom. This then increases the
thermal emission rate since it requires less energy to release the
electron. It is reasonable to assume that the potential barrier
lowering by electric field is more effective on the neutral type
potential. This is because of the nature of loose bonding between an
electron and the neutral atom. The slighter field dependence of the
experimental results of Device D7 seems to indicate an impurity
potential that is more of the Coulomb attractive type. The stronger
field dependent thermal emission rate of D17 favors a neutral type
potential. Indeed, the deep impurity in D7 is the donortype oxygen.1
The bonding force between the oxygen atom and an electron is the Coulomb
attractive type. While the deep impurity in Device D17 is an acceptor
1!.
type chromium,4 the bonding potential is neutral type. Our
experimental results agree with these arguments.
The thermal emission rates of electrons determined by the transient
photocapacitance method using interband light (h.>E ) are also included
g
in Fig. 14. The slight difference in magnitudes could be due to small
temperature variations between two separate measurements. They do
indicate similar general trend.
Thermal Activation Energy of Deep Level Impurities
The temperature dependence of the thermal emission race of electrons
is illustrated in Fig. 15. The data were taken at a bias voltage where
the emission rate is not field dependent. From Eq. (29) we can
determine the thermal activation energy of the deep impurities by
calculating the slope of tn(en) versus 1/T (see Fig. 15). The results
for three devices are
1.0
1. D17
2. D11
1)
(sec 3. D7
0.1
e
n
1
3
0.01
1 I I I I I I I
3.1 3.2 3.3 3.4 3.5 3.6
3 r
10 /T ( )
Fig. 15
The thermal emission rate of electron as a function .of
temperature. (103/T) between 235 and 316K. The data were
taken at V = 6 volts.
 54 
D7 (oxygen) E = 0.82 ev (from the conduction
band edge)
Dll (oxygen) ET = 0.80 ev
D17 (chromium) E = 0.74 ev
Hence, in this measurement :,'e have concluded that the thermal activation
energies for oxygen and chromium in GaAs are 0.81 ev and 0.74 ev from
the conduction band edge respectively. These values are in good
agreement with those obtained by the optical and Halleffect measure
ments. They are O.SO ev and 0.73 ev for oxygen and chromium
respect tively.
Calculation of Capture Cross Section
17 3
Using v = 10 cm/sec, iL 4.7 :: 10 cm and the values of e
t C n
and FT determined above in Eq. (29), the electron capture cross section
S is obtained
n
14 2
for chromium impurity S = 4.8 : 10 cmn
n
and
13 "
for oxygen impurity S = 8.0 10 cm"
n
These results also reflect the acceptor nature of chromium impurity and
the donor nature of oxygen impurity. The capture cross section for
oxygendoped samples determined by the present work is much larger than
previously reported values. This is due to the fact that the value of
ET for oxygen in Eq. (29) used by previous authors is considerably
smaller than the value we obtained from the present result (for
comparisons, see Table II).
Determination of Shallow and Deep Level Impurity Concentrations
2 ?
The C(t=0) versus V and C(t=) versus V are shown in Fig. 16
for the devices under study. Although there e:.ists a high resistance
 S55 
 56 
o
0
CD
C)
0
0 U
in
oCQ
o
1
Q C/)
 cu
" 4
 U
Ec
Q U
ri
CI
C. C
U U
I .
C)E
/C
C "
C LL
1 0
ra
.4
L.4
CC
Q
ca
E
o U
E I I I I 0 I 0
o. _o 1 7
.7
0
4 4 
CDI
0 C, CL) C:)
SI I I I
v I 0 I I 0 C
CO CoL .
'* 0
7
I. J LII
u TI I 7 I I I
0 0C
O N 1 N N C
L3 J C)4 _e
S0 0O U O 0 0 0 0
Q.C G.
C0
<: T  0 0
I En > *j I
C r I C: I f mi to C& c r
< > 4 4 C U *H
U E 3 u > C a
N H N r 3 L cIr
 57 
0 2 4 6 8 10 12
(volts)
Fig. 16
1
A plot of C 
D7 and D11.
t = 0+
a function of reverse bias voltage for D17,
the superscript represents the values taken at
(pf2)
x 105
1/C2
 5S 
2
interfacial layer as a series resistor, the slope of C versus V still
gives the shallow and deep impurity concentrations through Eqs. (25)
8
and (26). The results are as follows:
15 3 14 3
for D7 N1 = 2.1:.:101 cm ; = 9.2x10 cm
15 3 15 3
D11 N = 5.66:.:10 cnm = 2.64::10 cm
15 3 =15 3
D17 r = 2.03x10 cm N = 2.55::10 cm
T D
Comparing these values with those obtained by our Halleffect measure
ment on the bulk ntype GaAs samples, they are in good agreement (see
Table 1).
2
The intercept of the C2 versus V plot on the voltage axis should
be the diffusion potential of the diode. However, the existence of a
high resistance interfacial layer makes the apparent diffusion potential
25,41 8
V'. higher than the intrinsic value V It has been shown that
bi bi
V. 2r2 d(l/C')J (62)
bi i Vbi dV
From Fig. 16 and Eq. (62), the series resistance r can be estimated
(Vbi = 0.9 ev). They are
r = 4 K' for D7
r = 3.2 K', for D11
r = 10 KQ1 for D17
These values are much larger than those of the ideal devices.
Nevertheless, they have had no appreciable effects on determining the
properties of deep impurity centers.
HallEffect, PhotoHallEffect and Conductivity Measurements
The dark resistivity for chromiumdoped semiinsulating GaAs
sample S is 1.2x8 c and 3 8 m for S2 at 300K. he Hall
sample S1 is l.2x10 Ccm and 3>40 Ccm for S2 at 300NO. The Hall
 59 
mobility was found to be about 250 m 2/vsec at 300K. The low Hall
mobility is attributed to the mi:ed conduction in chromiumdoped GaAs
occurring at room temperature, as pointed out by Inoue and Ohyama.42
The electron mobility can be calculated from the conductivity
expression given in Ref. ('2), and the result for the present case is
found to be n = 1000 cm/vsec at 3000K. The slight difference in
resistivity between S1 and S2 implies that the chromium densities are
not equal in the two samples. Presumably S1 has slightly lower
chromium impurity density than S2. This assumption is consistent with
the observation of the PME and PC responses in the two samples, in which
S1 shows less trapping effect than S2.
The photoHalleffect measurements over samples indicate that the
Hall mobility is a slowly varying function of injection. The photo
Hall experiments in oxygendoped ntype GaAs samples have been conducted
at T = 4.24K and 20.8K respectively. The electron density in these
14 15 3
samples measured at 3000K varies from 10 to 10 cm The electron
mobility pn is 3500 cm /Vsec at 300'K.
The result of the photoHall mobility data is displayed in Fig. 17
for T = 4.2 and 20.80K. Note that the electron mobility is near
<5
constant for AG 105 mho but increases with increasing light intensity.
0.2 5
The present result shows that u varies with AG for AG > 10 mho.
PME and PC Measurement on Chromiumdoped ntype GaAs
In Fig. 18, IpHE/B versus AG for T = 80 and 3000K for both S1 and
S2 is illustrated. It is interesting to note that three welldefined
regions are obtained in I E/B versus AG plot. In the high injection
region (I), I /B is directly proportional to AG for S1 and S2 at
PUPI
 60 
Scm
1Vs0
10 L
I i I I I
105
10
II I
6 x 105
LG(mho)
Fig. 17
The photoHall mobility versus photoconductance.
420.
20. 8rK
I I I I I I
I
800
3000K /
(S1)
1
(I)
3000
(S2)
*Mi p/m
10
10
I
r 11
PME
 106
10
71
. I
I I I I
I I I
1010
10
09 (8
10 10)
tG (mho)
17
10
106
10
Fig. 18 The PHE shortcircuit current per unit width of sample per
unit magnetic flu:x density, I E/, versus photoconductance
AG for samples S1 and S2 at 80 and 3000K.
 61 
1.2
1
800
(S2)
(II)
(III)
.. I
11
10
S I
I I I I I I I I I I I I I I Ia I I
 62 
300K. The excess electron and hole densities are much higher than the
thermal equilibrium carrier concentration n and the electrically
O
active chromium density. The charge neutrality condition is essentially
controlled by the excess electron anJ hole densities. The carrier life
3?
time is independent of injection and the effect of trapping is
completely negligible. As a result, the conditions given by Eqs. (40)
and (42) are reduced to
An = Ap (i.e. F = 1, C = 1)
and
S = T = T (i.e. = 1)
n p 0
where T is the carrier lifetime and high injection as defined by
32 10
Shockley and Read. In this case i = T = T = 2.5x10 sec. (Fig.
n p m
19).
In the intermediate injection region (II), I ME/R varies with
1 ?
G This is observed for both samples S1 and S2 at SOK and for
S1 at 300K. The effect of hole trapping at the chromiumacceptor
1/3
levels (F<1, 0=1), and the dependence of T on An leads to the
n
observed relation. Under the conditions of C=1, S= 1/3 and rF 1
Eq. (54) becomes43
S 6' 1/5 2/5
D r 5,C
4 _
With the help of Eq. (55) T is deduced and the results are shoi.n in
Fig. 19. The parameters T n, and K: are calculated from Eqs. (42),
(54) and (55).
The computed values of F and : are fairly constant over the entire
intermediate injection range. The value of r is found to be 0.18 at
 63 
c .. C
I 1
I Ii
I j
/
/
0
/
/ I
/
I
/
I I
C
n
III I I I I
Cf
C
0 o
010
C)
C)r
I C
/ c
C
0
/'/
//'
/* H
/ .
s h
1 1 1 I I
CO
r"
O
Li
a
CC
cLa
EC o
o
4.1
C9 0
*r
.C U)
CL
j1
E E
l C
C l 0
.I
rl
1 I
01 1
D.. t
01
0LL 4
I
I II I I
I
 64 
300K and 0.084 at 80K for S2, which shows th3t the ratio of T /T is
n p
about 5.5 at 300K and about 12 at 80K. These results are in good
agreement with the statement by Holeman and Hilsum in that the:' predicted
a rating of r /T < 10 for semiinsulating GaAs.
n p
In the low injection range, another linear region for I E/B versus
AG is observed for sample S2 (Fig. 18). In this region, the effect of
trapping is negligible (i.e. F = 1 and 1 = 1) and 6 = 0. The results are
21 = = = 2.2 x 10 9 sec.
a n p
This is also included in Fig. 19. The injection (over five orders
of magnitude) dependency of carrier lifetimes discussed by Agraz and
38
Li has clearly been demonstrated in this experiment.
PME and PC Measurement on OxygenDoped Ntype GaAs
A plot of IpME/B versus AG for T = 4.2 and 20.S"K is shown in
Fig. 20. From this plot it is found that I E/B varies with AG which
is in good agreement with the prediction given by Eq. (56). By using
Eq. (58) and data in Figs. 17 and 20, the capture probabilities for band
to band radiative recombination are calculated for oxygendoped ntype
GaAs. The results yield
8 3
B = 1.15 x 108 cm /sec at T = 20.S3
r
7 3
B = 1.23 x 107 cm /sec at 4.2K
r
To compare the above experimental values of the capture probabili
ties with those predicted by Hall's direct radiative recombination
formula, we use Eq. (45) to compute B for CaAs at ..20K and ?O.SoK;
the results are
8 3
B = 1.07 x 10 cm /sec at 20.Sc
r
7 3
B = 1.18 x 10 cm /sec at 4.2K
r
 65 
P.IE/nB
I
P~1 E
20.8K
I I I I I I I 1 I
10
U I I I I I I
10
AG (mho)
Fig. 20
The PME shortcircuit current per unit width of sample per
unit magnetic field intensity, I /E, versus photo
conductance for oxygendoped sample S3 at 20.S and 4.2K.
4 .2K
105
10
16
10
106
' '
 66 
Here e/m = 0.068, m /m = 0.5, and E = 1.51 ev have been used.
e o h o g
The above result shows thac che values of E determined from the
r
PME and PC measurements are in e:.:cellent agreement with those computed
from Hall's direct radiacive recombi;ation formula (Eq. (:5)). In
addition, our results also show thuL the capture piobiability B depends
r
3/2
on T for the temperature range from 4.2K to 20.8K, in accord with
the prediction of Eq. (45).
The electron and hole lifetimes can be determined from Fig. 20 and
< 5
Eq. (53). The result is plotted in Fig. 21. Note that for LG 105
mho, i is proportional to AG in accord with the prediction given by
Eq. (57). However, for ZG > 105 nho, r varies with LG The change
in slope of i versus AG is due to the fact that n also changes with AG
0r) 5
for high light intensity (i.e., p aAG for AG > 10 mho).
Estimation of excess carrier density can be obtained from Eq. (3a) of
i10 3
reference (43) for the present case and they are An = 2.5 x 10 cm
12 3 5
at 20.80K and 2.16 x 10 cm at 4.20K for AG = 105 mho. These values
are much higher than the equilibrium electron densities at both
temperatures. Thus the high injection condition is justified for the
present case.
In conclusion, we have shown that the photoinjected excess carrier
recombination process in oxygendoped ntype GaAs at 20.8 and 4.2K is
dominated by the band to band radiative recombination. The deep level
oxygen impurities in ntype GaAs are neither acting as recombination
centers nor as trapping centers for the excess carriers. The radiative
capture probabilities can be determined readily from concurrent
measurements of the PME shortcircuit current and the photoconductance
of the samples.
 67 
10
(sec)
T
a
105
I0
4.2 K
I I I I I I I
I 5 I 1
3 4 5 x 105
AG (mho)
Fig. 21
The PHE apparent lifetime T (T = T = T ) versus
a a n p
photoconductance AG for S3 at 20.8 and 4.2K.
20. 8K
10
(sec)
T
a
103
CHAPTER \'I
CON;CLUS IO:S
Sunmma r
In this work, we have demonstrated a systematic method for
characterizing the deep level impurities, oxygen and chromium, in
ntype GaAs. The electronic properties of the deep impurity centers
are determined by using the transient dark and photocapacitance
measurements on the AuGaAs Schottky diodes. The recombination and
trapping parameters are derived from the carrier lifetime measurements.
The results are summarized as follows:
(1) The roles that the deep level impurities, chromium and oxygen,
have played in the recombination and trapping processes of the photo
injected carriers in bulk ntype GaAs have been determined by the
photomagnetoelectric and photoconductive measurements. It is concluded
that the chromium impurity centers act as ShockleyRead type
recombination centers. On the other hand, the radiative band to band
recombination mechanism prevails at low temperatures for ntype CaAs
doped with oxygen impurities.
(2) The experimental results have yielded the dependence of the carrier
lifetimes on injected excess carrier densities over a wide injection
range in the chromiumdoped GaAs. The electron capture probability for
the band to band radiative recombination in oxygendoped GaAs is also
obtained experimentally.
 68 
 69 
(3) The impurity doping concentrations determined by the transient
capacitance method are in good agreement with those obtained by Hall
effect measurement (see Table 11.
(4) The thermal emission rates of electrons from negatively charged
chromium impurities and neutral oxygen impurities have been measured.
i
They are in the order of 0.07 sec (see Table 2). From the temperature
dependence of these emission rates, the thermal activation energies for
r
oxygen and chromium in ntype GaAs have been determined. They are
0.31 and 0.7' ev from the conduction band edge for oxygen and chromium
levels respectively. These are in good agreement with the values
14
determined by optical and Halleffect measurements. This kind of
accuracy was not achieved by using other transient capacitance models.
For comparisons, the results obtained by the previous authors are
included in Table 2.
(5) The electric field dependence of the thermal emission rates of
electrons was also measured; the results can be explained qualitatively
by the PooleFrankel effect. The present results indicate that oxygen
is a donortype impurity and chromium is an acceptor in nature.
(6) The IV characteristics have been measured both in forward and
reverse bias conditions on the AuGaAs (ntype) Schottky barrier diodes.
From small bias data, it shows the existence of an interfacial layer
between gold and GaAs. The intimacy between metal (Au) and semi
conductor can be determined experimentally. The field dependence of
the effective barrier height also shows up in the form of absence of
true saturation in the reverse characteristics. The barrier lowering
is caused by the image force and the electrostatic dipole layer in the
metalsemiconductor contact. It seems that the dipole layer effect is
enhanced by the presence of deep impurities.
 70 
(7) The existence of the interfacial layer introduces a high resistance
equivalent resistor in series with the Schottky diode. This has
prevented the device front having ideal characteristics. Ho'.ever, we
can still use the device and transient capacitance method to determine
the electronic properties of the deep impurity centers in a semi
conductor as we have demonstrated in this work.
Suggestions for Further Study
The results from more extensive study on the transient photo
capacitance, using band to impurity monochromatic photon excitation
technique and performed at a temperature below the freezeout tempera
ture of the deep impurity centers, would be very informative on the
optical properties of the oxygen and chromium impurities in GaAs.
Combining this information with the excess carrier lifetime measurement
over a wide injection range, a complete understanding of the recombina
tion and the trapping mechanisms of excess carriers in GaAs in the
presence of oxygen and chromium impurities can be obtained. Further
more, the experimental techniques presented in this work are applicable
to determine the electronic properties of other impurities in GaAs or
in other semiconductors.
An experimental study of the PME effect in oxygendoped GaAs as
a function of temperature would also yield the temperature dependence
of the electron capture probabilities in the band to band radiative
recombination.
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BIOGRAPHICAL SKFTCH
Chern I Huang was born Hay 25, 194'0, at Taipei, Taiwan. In
June, 1962, he graduated from ChengKung University with the degree
of Bachelor of Science in Electrical Engineering. Immediately after
graduation he served in the Navy for one year. Following his dis
charge from the service, he accepted a position at his alma mater as
an assistant instructor.
In September, 1964, he started to pursue the graduate study at
Iowa State University, Ames, Iowa. He earned the degree of Master of
Science in May, 1967. From May, 1966, to August, 1963, he was employed
by Collins Radio Company, Cedar Rapids, Iowa, as an engineer. In
August, 1968, he moved to Ft. Lauderdale, Florida, to work for Bendix
Avionics Division. Since September, 1969, he has worked as a graduate
assistant in the Department of Electrical Engineering and has pursued
his work toward the degree of Doctor of Philosophy until the present
time.
He is a member of the Institute of Electrical and Electronic
Engineers. He is married to the former Jennifer JuiYu Cheng and is
the father of one son.
 73 
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Sheng S. Li, Kihairman
Assistant Professor of Electrical Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Fredrik A. Lindholm
Professor of Electrical Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Eugen R. Chenette
Professor of Electrical Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Alan D. Sutherland
Professor of Electrical Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope ad quality, as a dissertation for the degree of
Doctor of Philosophy.
Thomas A. Scott
Professor of Physics
This dissertation was submitted to the Dean of the College of
Engineering and to the Graduate Council, and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
March, 1973 ^ .
Dean, Graduate School
