Title: Investigation of deep level impurities (oxygen and chromium) in bulk gallium arsenide and Au-GaAs Schottky diodes
CITATION PDF VIEWER THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00097579/00001
 Material Information
Title: Investigation of deep level impurities (oxygen and chromium) in bulk gallium arsenide and Au-GaAs Schottky diodes
Physical Description: xii, 73 leaves. : illus. ; 28 cm.
Language: English
Creator: Huang, Chern I., 1940-
Publication Date: 1973
Copyright Date: 1973
 Subjects
Subject: Diodes, Semiconductor   ( lcsh )
Gallium arsenide   ( lcsh )
Semiconductors   ( lcsh )
Transistors   ( lcsh )
Electrical Engineering thesis Ph. D
Dissertations, Academic -- Electrical Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 71-72.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00097579
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000585123
oclc - 14184409
notis - ADB3755

Downloads

This item has the following downloads:

PDF ( 2 MBs ) ( PDF )


Full Text




















INVESTIGATION OF DEEP LEVEL IrmPURITIES
(OXYGEN AN:D Clh;OMIUM) IN bULK GALLIUL-! RSENIDE
AND Au-CaAs 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. F19628-72-C-0363.
















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 CxPACITiANCE-VOLTAGE 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 n-TYPE 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 . .
Current-Voltage Measurement .
Capacitance-Voltage Measurement .
Photocapacitance Measurenent .
Bulk Effect Measurements . .


EXPERIMENTAL RESULTS AD ANALYSES . .


Introduction . . .
Forward Current-Voltage Measurement
Schottky Diodes . . .
Reverse Current-Voltage Measurement


of Au-CaAs

of Au-CaAs


Schottky Diodes .


Transient Capacitance Measurement of Au-GaAs .
Hall-Effect and Conductivity Measurement . .
PHE and PC Measurerent on Chromium-doped n-type GaAs
PME and PC Measurement on O:.:ygen-doped n-type 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 Au-GaAs (n-type)
Schottky barrier diodes at 300 K ...................... 36

2. Summary of the results for Au-CaAs (n-ty'pe) Schottky
barrier diodes deduced from transient dark and photo-
capacitance measurements .............................. 56















LIST OF FIGURES


Figure Page

1. Energy band diagram of a metal-semiconductor (n-type)
contact with an interfacial layer and surface states
(After Cowley and Sze, Reference 21) ............... 6

2. (a) Energy band diagram of a netal-semiconductor
(n-type) contact wiLh the presence of donor-type
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 steady-state illumination: (a) thermal
equilibrium; (b) intermediate injection; (c) high
injection ........................................... 28

6. Test set-up for measuring Schottky barrier diode
current-voltage characteristics ..................... 38

7. Experimental set-up for measuring transient dark and
photocapacitance of che metal-GaAs Schottky barrier
d iodes .............................................. 39

8. Experimental sec-up for the AC PME measurement ...... 41

9. Forward current-voltage relationship of Au-GaAs
(n-type) Schottky diode D-ll at various temperatures 45

10. Forward current-voltage relationship of Au-GaAs
(n-type) Schottky diode D-17 at various temperatures 46


MM








LIST OF FIGURES (continued)


Figure Page

11. I /Ti versus 10O/T for the A'i-GaAs (n-type) Schottky
barrier diodes D-ll and D-17 ....................... 47

12. Reverse voltage-current relationship for the Au-CaAs
Schottky barrier diode D-17 ........................ 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 D-17, D-7 and 0-11. The superscript represents
the values taken at t = 0+ ......................... 57

17. The photo-Hall mobility versus photoconductance for
sample S-3 at 20.8 and 4.2 K ........................ 60

18. The PIE short-circuit current per unit width of
sample per unit magnetic flux density, Ip /B, versus
photoconducrance LG for samples S-1 and
S-2 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 short-circuit current per unit width of
sample per unit magnetic field intensity, I /B,
versus photoconductance for oxygen-doped sample S-3
at 20.8 and 4.2 K .................................. 65

21. The PME apparent lifetime T (i = T = ) versus
photoconductance LG for S-3 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 Quasi-Fermi 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 short-circuit 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 Fermi-level 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 Au-GaAs 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 n-type 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 Shockley-Read 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 Cr-doped GaAs. For the oxygen-doped n-type 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

n-type 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 Au-GaAs 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 gold-doped 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 steady-state 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 semi-insulating 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 oxygen-doped GaAs between 140 and 3000K. The photo-

electronic analysis of high resistivity n-type 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 Cr-doped 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 metal-semiconductor Schottky diode is a powerful tool in

obtaining fundamental deep impurity parameters through its time-varying

capacitance-voltage 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 n-type 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 n-type 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 Hall-effect measurements.
15
Sah et al. reported transient capacitance experiments using gold-
+ +
doped silicon p-n 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

metal-semiconductor Schottkv barrier diodes. In this work, the Au-CaAs

(n-type) 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 steady-state 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 ) n-type 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 metal-semiconductor barriers is mainly

due to majority carriers in contrast to p-n junctions where the minority

carriers are responsible. The theory of current flow over the barrier

of metal-semiconductor contacts is complicated. There are several

mechanisms, namely, thermionic emission,16 diffusion,16,17 thermionic
18 i19
emission-diffusion, thermionic-field 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 current-voltage 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 giv-es

-q''b aV
J = A*T" exp( k )[exp (c)-l] (1)
kT kT'


- 5-




- 6 -


----I-
q ",


qL b qVbi

E-c
- Ef


Fig. 1 Energy band diagram of a mncal-
semiconduccor (n-type) 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 metal-semicondiuccor

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(Vbi-V) 21D] -q 'b 1
J = nC-1 (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 thermionic-diffusion theory.

A low electric field limit for application of this theory is estimated

from consideration of phonon-induced 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 quantum-mechanical reflection and quantum tunneling on the

thermionic recombination velocity near the metal-semiconductor inter-

face. It gives


2(m-1) 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 thermionic-field 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 Au-GaAs

(n-type) 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 metal-GaAs 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 C-V 1825

and I-V 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 5-30A. 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 current-voltage 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 current-voltage behavior in

a wide voltage range and for various physical situations. Andrews and

Lepselter used this model successfully to explain the I-V character-

istics of metal-silicide 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 metal-semiconductor 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

I-V 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 W-GaAs

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 metal-semiconductor

contact properties, namely the capacitance and voltage relation, will





12 -



be studied in some detail. The effect of deep level impurities on

C-V characteristics '.will also be investigated.















CHAPTER III

THE CAPACIT.'JCE-VOLTAGE CHA.-.CTERISTICS OF SCHOTTKY
EAPRIER DIODES I. THE PRESENCE OF DEEP LEVEL I'MURITIES



Incroduction

In metal-semiconductor 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 k--T (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 freeze-out 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 p-n 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 metal-semiconductor C-V

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(1l-ecxp(-ent)] and

, with \(t). Their model has the form


= T[+N_1-exp(-e C)]
AC D n
TL

x(t)Nr
)[l-exp(-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 C-V experiment, they have determined the

energy level for oxygen in n-type 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 metal-semiconductor
(n-type) in the presence of donor-type 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 p-n junction capacitance to the metal-semiconductor 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 Au-GaAs (n-type) 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 metal-semiconductor 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 quasi-Fermi levels in

this region. Inside the depletion region, the constant quasi-Fermi

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 donor-like 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' (l-a)' 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 steady-state 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 acceptor-type 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

n-type 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 n-TYPE 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 C-V

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 Shockley-Read32
34
and Sah-Shockley 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

n-type 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 n-type

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 Sah-Shockley 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 n-type. 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

(ND-nD) = 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

n-type 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 steady-state 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 (np-n+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 power-law 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 (np-ni) (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 black-body 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 10-2 ( ) (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 short-circuit current and photoconductance can be derived as

follows: The photoconductance per unit sample length-to-width 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+C-i)D FY A 2 (49)

The PME short-circuit 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+C-S)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

Shockley-Read 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 short-circuit 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 photo-Hall mobility u .


Summary

After considering the charge neutrality condition in the semi-

conductor, a simple power-law 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 acceptor-type deep level

impurities in the n-type semiconductor, the Shockley-Read 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 n-type oxygen- or chromium-doped 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 TO-1S 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 Cr-doped semi-insulating

n-type GaAs single crystal wafer (total chromium impurity density is
17 -3
1-3x10 cm ) were made by the zone-melting method. The sample dimen-

sions are 0.5xlx0.1 cm for Sample No. 1 (S-l) and 0.4x0.8x0.1 cm for


- 35 -






- 36 -


C
4' o
.:: .-( T --I

II 1 --4O 0
>> -i II O l-i -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 >



F-l




- 37 -


Sample No. 2 (S-2). A third slice was cut from an oxygen-doped semi-
15 -3
conducting n-type GaAs single crystal (n 10 cm ). The dimension
3
for this sample (S-3) 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.


Current-Voltage Measurement

The experimental arrangement for I-V 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'


Capacitance-Voltage Measurement

A system for measuring the transient capacitance and transient

photocapacitance was set up as shown in Fig. 7. It consists of a

Wayne-Kerr B641 Capacitance Bridge, a low noise amplifier, a wave

analyzer, a Perkin-Elmer 98 Monochromator and an X-Y 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 set-up for measuring Schottky barrier
diode voltage-current characteristics.





- 39 -


Null Voltmeter

Biasing Circuit

Device

Monochromator

Capacitance Bridge

Amplifier

X-Y Recorder


2. Thermo-couple

4. He-Ne Laser

6. Temperature Chamber
8. Tungsten Light Source

10. Low Noise Amplifier

12. Wave Analyzer


Fig. 7 Experimental set-up for measuring transient
dark and photocapacitance of the metal-GaAs
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 X-Y

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 C-V relation-

ship. The light source is the He-Ne 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, Hall-effect and Photo-Hall-effect measurements

were performed by using the standard DC method. The measurements were

made at 300 and 80K for S-1 and S-2, at 20.8 and 4.20K for S-3. 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. "Cryo-Tip" Cryogenic System


-- 13


Constant Current Supply
Control Panel
Low Noise Amplifier
Wave Analyzer
DC voltmeter
Electromagnet Power Supply
Potentiometer


Fig. 8 Experimental set-up 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 signal-to-noise

ratio is better than 10.















CHAPTER %' .

EXPERIMENTAL RESULTS ATFD ANALYSES



Introduction

The temperature dependence of Au-GaAs (n-type) Schottky diodes

forward I-V characteristics was measured. Values of the barrier

height were deduced from these measurements. The reverse I-V

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 n-type 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 n-type

GaAs with the presence of deep impurities were investigated.


Forward Current-Voltage Measurement of Au-GaAs Schottkv Diodes

The forward I-V 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 I-V plots for devices D-11 and D-17 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 electro-static 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 D-ll and D-17 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 D-ll and D-17

respectively. The results indicate that the different deep impurities

in n-type 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 Au-GaAs (n-type) Schottky diodes is

0.90 ev.





- 45 -


10-5
I0


(Amp)



10-6



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



10-10
0-10







10-11 1 I I I I
0 0.1 0.2 0.3 0.4 0.5

V (volts)


Fig. 9 Forward voltage-current relationship of Au-GaAs (n-cype)
Schoctky barrier diode D-11 at various temperatures.





- 6 -


1-6
i0


(Amp) 7


10-7



10 8


-8
1






10-9



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
0-11 7 286 1.11
8 273 1.09
/ 9 265 1.09



9
10-12 I I I
0 0.1 0.2 0.3 0.4 0.5
V (volts)


Fig. 10 Forward voltage-current relationship of Au-GaAs (n-type)
Schottky barrier diode D-17 at variouss temperatures.





- 47 -


Amo





S10- 12
-1"
- 10







I
s

T~



S10-13


D-17


D-11


I I I I


II I I I


3.0


103/T (K -1


I
Fig. 11 -versus 10 /T for the Au-CaAs

barrier diodes D-11 and D-17.
barrier diodes D-ll and D-17.


(n-type) Schortkv


2.8


m i I





- 48 -


The Reverse Current-Voltace Measurement of Au-GaAs Schottky Diodes

In Fig. 12, the reverse I-V characteristics for D-17 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
reverse-current 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 metal-silicide 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 I-V behavior. The value of a = 1.44:106 cm for our

device is higher than that of metal-silicide 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
4-1 (-















C .




*1-4






0 0.
-c








Uj











-l4















,.4
I l


- 49 -


e-I 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 Au-GaAs 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 w-r-C- < ] in our

experiments (see a later section), Eq. (2') still can be used to

analyze the C-V data without introducing appreciable error.

With the help of the Hewlett-Packer calculator 9100A and the least

square curve fitting technique, the time constant (or the reciprocal of

the thermal emission rate of electrons),the steady-state 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 D-17 shows rapid increase while that of others remains unchanged.

This can be explained qualitatively by the Poole-Frenkel 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.

1-hen 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
4-1





i-4

X

LU


I I I It I I c-I


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 D-7 seems to indicate an impurity

potential that is more of the Coulomb attractive type. The stronger

field dependent thermal emission rate of D-17 favors a neutral type

potential. Indeed, the deep impurity in D-7 is the donor-type oxygen.1

The bonding force between the oxygen atom and an electron is the Coulomb

attractive type. While the deep impurity in Device D-17 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. D-17
2. D-11
-1)
(sec- 3. D-7









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 -








D-7 (oxygen) E = 0.82 ev (from the conduction
band edge)

D-ll (oxygen) ET = 0.80 ev

D-17 (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 Hall-effect 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

oxygen-doped 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















E-c
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 -----





CD---I






0 C, CL) C:)
SI I I I







v I 0 I I 0 C
CO CoL .

























'-* 0
-7







I. -J LI-I
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 -
D-7 and D-11.
t = 0+


a function of reverse bias voltage for D-17,
the superscript represents the values taken at


(pf-2)


x 10-5


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 D-7 N1 = 2.1:.:101 cm ; = 9.2x10 cm
15 -3 15 -3
D-11 N = 5.66:.:10 cnm = 2.64:-:10 cm
15 -3 =15 -3
D-17 r = 2.03x10 cm N = 2.55:-:10 cm
T D

Comparing these values with those obtained by our Hall-effect measure-

ment on the bulk n-type 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 D-7

r = 3.2 K', for D-11

r = 10 KQ1 for D-17

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.


Hall-Effect, Photo-Hall-Effect and Conductivity Measurements

The dark resistivity for chromium-doped semi-insulating GaAs
sample S- is 1.2x8 -c and 3 8 m for S-2 at 300K. he Hall
sample S-1 is l.2x10 C-cm and 3>40 C-cm for S-2 at 300NO. The Hall





- 59 -


mobility was found to be about 250 m 2/v-sec at 300K. The low Hall

mobility is attributed to the mi:-ed conduction in chromium-doped 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-/v-sec at 3000K. The slight difference in

resistivity between S-1 and S-2 implies that the chromium densities are

not equal in the two samples. Presumably S-1 has slightly lower

chromium impurity density than S-2. This assumption is consistent with

the observation of the PME and PC responses in the two samples, in which

S-1 shows less trapping effect than S-2.

The photo-Hall-effect measurements over samples indicate that the

Hall mobility is a slowly varying function of injection. The photo-

Hall experiments in oxygen-doped n-type 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 /V-sec at 300'K.

The result of the photo-Hall 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 Chromium-doped n-type GaAs

In Fig. 18, IpHE/B versus AG for T = 80 and 3000K for both S-1 and

S-2 is illustrated. It is interesting to note that three well-defined

regions are obtained in I E/B versus AG plot. In the high injection

region (I), I /B is directly proportional to AG for S-1 and S-2 at
PUPI





- 60 -


Scm
1V-s0







10 L


I i I I I


10-5
10


II I


6 x 10-5


LG(mho)



Fig. 17


The photo-Hall mobility versus photoconductance.


-420.

20. 8rK


I I I I I I


I





















800


3000K /
(S-1)


1

(I)


3000
(S-2)


*Mi p/m




10-







10-



I
r 11
PME



- 10-6







10
-71


. I


I I I I


I I I


1010
10


0-9 (-8
10 10)
tG (mho)


1-7
10


10-6
10


Fig. 18 The PHE short-circuit current per unit width of sample per
unit magnetic flu:x density, I E/, versus photoconductance

AG for samples S-1 and S-2 at 80 and 3000K.


- 61 -


1.2





1


800
(S-2)


(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 S-1 and S-2 at SOK and for

S-1 at 300K. The effect of hole trapping at the chromium-acceptor

-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
r-l


-1 I



01 1
D.. t-







01
0LL 4-


I





I II I I


I





- 64 -


300K and 0.084 at 80K for S-2, 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 semi-insulating GaAs.
n p
In the low injection range, another linear region for I E/B versus

AG is observed for sample S-2 (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 Oxygen-Doped N-type 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 oxygen-doped n-type

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 short-circuit current per unit width of sample per
unit magnetic field intensity, I /E, versus photo-

conductance for oxygen-doped sample S-3 at 20.S and 4.2K.


4 .2K


10-5
10

















1-6
10


10-6


' '





- 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 > 10-5 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 oxygen-doped n-type GaAs at 20.8 and 4.2K is

dominated by the band to band radiative recombination. The deep level

oxygen impurities in n-type 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 short-circuit current and the photoconductance

of the samples.





- 67 -


10









(sec)










T
a



10-5
I0


4.2 K


I I I I I I I


I 5 I 1
3 4 5 x 10-5


AG (mho)


Fig. 21


The PHE apparent lifetime T (T = T = T ) versus
a a n p
photoconductance AG for S-3 at 20.8 and 4.2K.


20. 8K


10









(sec)










T
a


10-3
















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

n-type GaAs. The electronic properties of the deep impurity centers

are determined by using the transient dark and photocapacitance

measurements on the Au-GaAs 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 n-type GaAs have been determined by the

photomagnetoelectric and photoconductive measurements. It is concluded

that the chromium impurity centers act as Shockley-Read type

recombination centers. On the other hand, the radiative band to band

recombination mechanism prevails at low temperatures for n-type 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 chromium-doped GaAs. The electron capture probability for

the band to band radiative recombination in oxygen-doped 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 n-type 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 Hall-effect 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 Poole-Frankel effect. The present results indicate that oxygen

is a donor-type impurity and chromium is an acceptor in nature.

(6) The I-V characteristics have been measured both in forward and

reverse bias conditions on the Au-GaAs (n-type) 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

metal-semiconductor 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 freeze-out 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 oxygen-doped GaAs as

a function of temperature would also yield the temperature dependence

of the electron capture probabilities in the band to band radiative

recombination.















BIBLIOGRAPHY


1. B. R. Holeman and C. Hilsum, J. Phys. Chem. Solids, 22, 19 (1961'.

2. C. H. Hurd, Proc. Phys. Soc. (London), 79, 4' (1962).

3. R. H. Bube, J. Appl. Phys., 31, 315 (1960).

4. S. Mayburg, Solid Scate Electron., 2, 195 (1961).

5. T. Kinsel and I. Kudman, Solid State Electron., 8, 797 (1965).

6. R. F. Broom, J. Appl. Phys., 38, 3483 (1967).

7. 0. Madelung, Physics of III-V Compounds, (Wiley, New York, 1964).

8. A. tI. Goodman, J. Appl. Phys., 34, 329 (1963).

9. R. Williams, J. Appl. Phvs., 37, 3411 (1966).

10. Y. Furukawa and Y. Ishibashi, Japan. J. Appl. Phys., 6, 503 (1967).

11. R. R. Senechal and J. Basinski, J. Appl. Phys., 39, 4581 (1968).

12. G. H. Clover, IEEE Trans. Electron. Dev., ED-19, 133 (1972).

13. Y. Zohta, Appl. Phys. Letter, 17, 284 (1970).

14. S. M. Sze and J. C. Irvin, Solid State Electron., 11, 599 (1968).

15. C. T. Sah, L. Forbes, L. L. Rosier and A. F. Tasch, Jr., Solid
State Electron., 13, 759 (1970).

16. H. K. Henisch, Rectifying Semiconductor Contacts (Oxford at the
Clarendon Press, Oxford, 1957).

17. W. Schottky, Natart.iss. 26, 843 (1938).

18. C. R. Crowell and S. M. Sze, Solid State Electron., 9, 1035 (1966).

19. F. A. Padovani and R. Stratton, Solid State Electron., 9, 695 (1966).

20. A. G. Milnes and D. L. Feucht, Heterojunctions and Metal-Semi-
conductor Junctions (Academic Press, New York, 1972), p. 163.


- 71 -





- 72 -


21. A. M. Cowley and S. M. Sze, J. Appl. Phys., 36, 3212 (1965).

22. C. A. 'lead and W. G. Spitzer, Phys. Rev. 134, A713 (1964).

23. C. R. Crowell, H. B. Shore and E. E. Labate, J. Appl. Phys., 36,
3843 (1965).

24. S. M. Sze, Physics of Semiconductor Devices (Uiley-Interscience,
New York, 1969).

25. C. R. Crowell and G. I. Roberts, J. ;ppl. Phys., 40, 3726 (1969).

26. J. Ohura and Y. Takeishi, Japan. J. Appl. Phys., 9, 458 (1970).

27. J. G. SiiLmnons, J. App Phys., 34, 1793 (1963).

28. G. J. Unterkofler, J. Appl. Phys., 34, 3145 (1963).

29. J. M. Andrews and M. P. Lepselter, Solid State Electron., 13, 1011
(1970).

30. J. A. Copeland, IEEE Trans. Electron Dev., ED-16, 445 (1969).

31. A. F. Tasch, Jr. and C. T. Sah, Phvs. Rev. B. 1, 800 (1970).

32. W. Shockley and W. T. Read, Jr., Phvs. Rev., 87, 835 (1952).

33. W. van Roosbroeck, Phys. Rev., 101, 1713 (1956).

34. C. T. Sah and W. Shockley, Phys. Rev.., 109, 1103 (1958).

35. R. N. Hall, Proc. Inst. Elec. Eng. B. Suppl., 17, 923 (1959).

36. J. Blakemore, Semiconductor Statistics (Pergamon Press, New York,
1962).

37. J. Agraz and S. S. Li, Phys. Rev. B. 2, 1847 (1970).

38. J. Agraz and S. S. Li, Phys. Rev. B. 2, 4966 (1970).

39. R. N. Zitter, Phys. Rev.., 112, 852 (1958).

40. S. S. Li, Phys. Rev. 188, 1246 (1969).

41. A. M. Cowley, J. Appl. Phys., 37, 3024 (1966).

42. T. Inoue and M. Ohyama, Solid State Comim., 8, 1309 (1970).

43. S. S. Li and C. I. Huang, J. Appl. Phys., 43, 1757 (1972).
















BIOGRAPHICAL SKFTCH


Chern I Huang was born Hay 25, 194'0, at Taipei, Taiwan. In

June, 1962, he graduated from Cheng-Kung 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 Jui-Yu 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 a-d 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




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs