Embed Size (px)
Citation preview
CHARGE CARRIER RECOMBINATION
IN AMORPHOUS SELENIUM FILMS
A Thesis
Submitted to the College of Graduate Studies and Research
in Partial Fulfillment of the Requirements
for the Degree of
Master of Science
in the Department of Electrical Engineering
University of Saskatchewan
Saskatoon
by
CHRISTOPHER JON HAUGEN
Saskatoon, Saskatchewan
May 1995
Copyright © 1994: Christopher Jon Haugen
COPYRIGHT
The author has agreed that the Library, University of Saskatchewan,
may make this thesis freely available for inspection. Moreover, the author
has agreed that permission for extensive copying of this thesis for scholarly
purposes may be granted by the professor who supervised the thesis work
recorded herein, or in his absence, by the Head of the Department or the
Dean of the College in which this thesis work was done. It is understood
that due recognition will be given to the author of this thesis and to the
University of Saskatchewan in any use of the material in this thesis.
Copying or publication or any other use of this thesis for financial gain
without approval by the University of Saskatchewan and the author's
written permission is prohibited.
Requests for permission to copy or make any other use of the material
in this thesis in whole or in part should be addressed to:
Head of Department of Electrical Engineering
University of Saskatchewan
Saskatoon, Canada, S7N OWO
University of Saskatchewan
Electrical Engineering Abstract # 94A408
CHARGE CARRIER RECOMBINATION IN AMORPHOUS SELENIUM FILMS
Student: C. Haugen Supervisor: Dr. S.O. Kasap
M. Sc. Thesis Submitted to the College of Graduate Studies and Research
August 1994
ABSTRACT
The charge transport characteristics of amorphous semiconductors determine how well they will perform in many applications. The product of the charge carrier drift mobility, µ, and deep trapping lifetime, t, also known as the range of the carrier, represents the average distance per unit electric field that a charge carrier will travel in the conduction band before being trapped in deep localized states within the mobility gap. The irc product is therefore an important parameter in predicting the performance of an amorphous semiconductor based device. However, in applications where more than one polarity of electronic charge is involved, charge carrier recombination is also an important consideration. The use of amorphous selenium alloy based films in electroradiography is one such application. This work utilized three different experimental techniques to determine charge carrier drift mobility, deep trapping lifetime and recombination coefficient in stabilized amorphous selenium (a-Se:0.2%As+Cl in ppm) films, suitable for use in electroradiographic systems. The conventional time-of-flight (TOF) method was used to evaluate carrier drift mobility and the interrupted field time-of-flight (IFTOF) technique was used to determine the carrier deep trapping lifetime. The hole range of the amorphous selenium films used was wth=67.54x10-6 cm2V-1, and the electron range was wre=2.68x10-6 cm2V-1. An ambipolar time-of-flight experiment was performed to measure bulk recombination by measuring the fractional change in hole photocurrent as an electron and hole charge packet passed through each other under the influence of an applied field.
TOF and IFTOF measurements were used to characterize charge transport in the samples before the recombination experiment was performed. The ambipolar TOF experiment indicated that the charge carrier recombination process within chlorinated a-Se:0.2%As follows the
ii
Langevin process, originally proposed for recombination of gaseous ions. The predicted Langevin recombination coefficient was Cer=35.2x10-9 cm3s-1, while the experimentally determined Langevin recombination coefficient was CrE=36.6x10-9 cm3s-1. This implies that the carrier mean free path in the films is much less than the recombination radius defined by Langevin. As most photoinduced discharge theories ignore the effect of carrier recombination their development, the measured recombination coefficient can now be used to reformulate these models to include recombination.
in
ACKNOWLEDGMENTS
I would like to extend my sincere thanks to my supervisor, Professor
S.O. Kasap, for his guidance, help and friendship during the course of this
project. My thanks are extended to Brad Polischuk (at Noranda Technology
Centre) for providing the IFTOF measurements and for the many insightful
discussions. I am grateful to Noranda Technology Centre for providing the
sample materials and for supplementary financial help. I would also like to
express my appreciation to NSERC for the financial support I have received.
Finally, I would like to thank my wife Laura for her unfailing support,
encouragement, and patience.
iv
TABLE OF CONTENTS
COPYRIGHT
ABSTRACT ii
ACKNOWLEGDEMENTS iv
TABLE OF CONTENTS
LIST OF FIGURES vii
LIST OF ABBREVIATIONS xi
1. INTRODUCTION 1 1.1 Introduction 1 1.2 Applications of Amorphous Selenium 2
1.2.1 Electrophotographic Photoreceptors 2 1.2.2 Electroradiographic Detectors 5
1.3 Research Objectives 8 1.4 Thesis Outline 9
2. PROPERTIES OF AMORPHOUS SELENIUM 10 2.1 Introduction 10 2.2 Structure of Amorphous Selenium 10 2.3 Band Model for Amorphous Selenium 13 2.4 Optical Properties of Amorphous Selenium 16 2.5 Charge Transport in Amorphous Selenium 19 2.6 Summary 24
3. TIME-OF-FLIGHT AND AMBIPOLAR RECOMBINATION EXPERIMENTS 26 3.1 Introduction 26 3.2 Principles of the Time-of-Flight (TOF) Technique 27 3.3 Transient Trap Limited Theory 35
3.3.1 tc«tx<tT Case 39 3.3.2 High Field Case (tT<Tc) 40
3.4 Summary 41
4. EXPERIMENTAL PROCEDURE 43 4.1 Introduction 43 4.2 Sample Preparation 43 4.3 Ambipolar Time-Of-Flight (TOF) Apparatus 47
4.3.1 Photoexcitation Sources 50 4.3.1.1 Xenon Flash Bulb Source 50 4.3.1.2 Nitrogen Laser Source 53
4.3.2 Timing Signal Generator 56 4.3.3 Digital Delays 59 4.3.4 Bias Application Circuit 59 4.3.5 Voltage Follower Circuit 60 4.3.6 Data Acquisition System 61
4.4 Interrupted Field Time-of-Flight (IFTOF) Apparatus 63 4.4.1 Schering Bridge Network 69 4.4.2 High Voltage TMOS Switch 71
4.5 Summary 72
5. RESULTS AND DISCUSSION 73 5.1 Introduction 73 5.2 Charge Transport Study 73 5.3 Charge Trapping Study 78 5.4 Ambipolar Recombination Experiment 82 5.5 Summary 91
6. CONCLUSIONS 93
7. REFERENCES 97
vi
LIST OF FIGURES
Figure 1.1 The basic steps of the xerographic process: (1)charge, (2) expose, (3) develop, (4) transfer, (5) fix, (6) clean, and (7) erase. 3
Figure 1.2 Typical projection radiographic system for medical imaging 5
Figure 1.3 Development system for electroradiography consisting of a pulsed laser beam and capacitively coupled probe. 7
Figure 2.1 Atomic arrangements in (a) a perfect crystal and (b) a perfect network glass 11
Figure 2.2 Selenium chain molecule and the definition of the dihedral angle 4). The dihedral angle is formed by the planes defined by atoms 123 and 234 12
Figure 2.3 Local structure of amorphous selenium showing chainlike segments of y-Se and ringlike segments of a-Se. 13
Figure 2.4 Various forms proposed for the density of states as a function of energy for crystalline and amorphous semiconductors. (a) crystalline model (b) Mott's model, (c) CFO model, and (d) Davis-Mott model [11]. 15
Figure 2.5 Experimentally determined density of states function N(E) for a-Se [12]. 16
Figure 2.6 Absorption coefficient a and quantum efficiency Tl as a function of the incident photon energy hv for various applied fields F [13,15]. 18
Figure 2.7 Predicted variation of carrier mobility in amorphous solids with energy [16]. 20
vii
Figure 2.8 Energy diagram for an electron bound to a point charge in the presence of a uniform electric field (Poole-Frenkel effect) [21]. 23
Figure 3.1 (a) Simplified schematic and (b) small signal ac equivalent circuit for the Time-of-Flight transient photoconductivity technique, where Cs is the sample capacitance. 28
Figure 3.2 The motion of charge q through dx induces charge dQ to flow through the external circuit. 30
Figure 3.3 Signals from the TOF experiment where (a) and (b) are I-mode signals for the trap free and deep trapping only case and (c) and (d) are V-mode signals for the same cases [20]. 34
Figure 3.4 Current flow with trapping and release processes in a thin slice of thickness dx. 36
Figure 4.1 Schematic diagram of the vacuum deposition system 45
Figure 4.2 Schematic diagram of sputtering system 46
Figure 4.3 Generalized schematic of TOF experiment 48
Figure 4.4 Diagrammatic view of ambipolar TOF experiment apparatus. 50
Figure 4.5 Schematic sketch of xenon flash circuit. 52
Figure 4.6 a)Reverse biased p-i-n measurement circuit. b)Light output Vs time for xenon flash. Horizontal axis: 200ns/div.; Vertical axis: 20mV/div. 53
Figure 4.7 Potential energy curves for lowest triplet states in N2 molecule 54
Figure 4.8 Blumlein circuit used for rapid excitation of N2
laser. 55
Figure 4.9 Triggering requirements for the LN 103 C N2 laser. 56
viii
Figure 4.10
Figure 4.11
Figure 4.12
Figure 4.13
Figure 4.14
Figure 4.15
Figure 4.16
Figure 4.17
Figure 4.18
Figure 4.19
Figure 5.1
Timing signals from Timing Signal Generator. twD, iTi, AT2, and An are adjustable as shown in Figure 4.11. 57
Circuit diagram for TTL trigger signal generator. 58
Schematic of pulsed bias application circuit. 60
Schematic of voltage follower with protection relay. 61
Diagrammatic layout of data acquisition system. The system features include the C1002 CCD camera, Tektronix 2467B oscilloscope, an IBM compatible PC to house the frame storage board and run the DCS01 software, and the Panasonic VW-5350 video monitor. 62
(a)Timing sequence for the application of bias voltage in TOF experiment and (b) the resulting photocurrent waveform. (c)The timing signal for the application of the bias in the IFTOF experiment and (d) the resulting IFTOF photocurrent signal 65
Large displacement current signals are produced when the high voltage bias is switched on and off. This signal must be eliminated for the IFTOF experiment to be successfully implemented. 67
IFTOF experiment schematic based on the Schering bridge network. 68
Schematic of Schering bridge network used to implement displacement current signal free IFTOF measurements. 69
Schematic of TMOS high voltage switch. 71
Conventional I-mode TOF waveforms for a 195.1 gm a-Se:0.2%As film for (a) hole transit and (b) electron transit. The transit times are indicated by tT 75
ix
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
Figure 5.8
Figure 5.9
Figure 5.10
Figure 5.11
TOF plot of transit time versus 1/voltage for holes in a-Se:0.2%As film showing µh =0.125 cm2V-ls-1 76
TOF plot of transit time versus 1/voltage for electrons in a-Se:0.2%As film shoWing 1.4=0.0034 cm2V-Is-1 76
Plot of hole and electron mobility as a function of the applied electric field. The hole mobility shows no observable field dependence. The electron mobility shows a very slight field dependence of the form g em F0.04 77
Typical IFTOF waveform for holes in a 195.1 p.m a-Se:0.2%As film showing i(ti), i(t2), and t1. 80
Logarithm of fractional recovered photocurrent as a function of interruption time for holes in a-Se:0.2%As. 81
Logarithm of fractional recovered photocurrent as a function of interruption time for electrons in a-Se:0.2%As. 81
(a) Simplified schematic sketch of double injection TOF technique for studying recombination and (b) the resulting photocurrent. 85
A typical photocurrent waveform from ambipolar TOF experiment. Insert shows an expanded view of the photocurrent due to the hole packet "riding" the top of the electron packet signal. 86
Schematic diagram of hole and electron packets passing through each other. It is assumed that n(x,t)»p(x,t). 87
Semilogarithmic plot for ihilim versus ae/F for two different stabilized a-Se samples. The slope of the line gives a relative dielectric constant of er=6.35. Correlation coefficient r=0.94.. 91
LIST OF ABBREVIATIONS
a-Se amorphous selenium
a-Si:H hydrogenated amorphous selenium
CCD charge coupled device
CFO density of states model proposed by Cohen, Fritzsche, and Ovshinski.
CuSO4 copper sulphate
DDG digital delay generator
EHP electron-hole pair
ESR electron spin resonance
IFTOF interrupted field time-of-flight
PVC polyvinyl-chloride
PVK:TNF poly-n-vinylcarbazole:trinitrofluorenone
TEA transversely excited atmospheric
TP transient photoconductivity
VAP valence alteration pair.
xi
1 INTRODUCTION
1.1 Introduction
Quantum mechanical theory was developed in the 1920s and 1930s.
The theory of quantum mechanics was readily applied to the study of the
physical behaviour of crystalline solids due to the mathematical simplicities
that resulted when dealing with a periodic structure. This led to the
development of many crystalline-based devices, the most important of which
was the solid state transistor.
However, due to the complexities of applying quantum mechanical
models to non-periodic structures, device physics based on amorphous solids
did not experience the same rapid growth as for crystalline materials. Much
of the theoretical understanding of the properties of non-crystalline
materials has been derived since the 1960s. Despite this, it is quite possible
that amorphous semiconductors will become the basis for the next era of
growth in the microelectronics industry [1]. In general terms, amorphous
materials possess a far greater diversity in their physical properties than do
crystalline materials. Furthermore, the preparation of amorphous solids
does not usually require the same carefully controlled growth techniques.
This provides a tremendous economical advantage for many applications.
1
1.2 Applications of Amorphous Selenium
One group of commercially important amorphous materials are the
chalcogenide glasses and in particular amorphous selenium and its alloys.
Since the first paper published on the photoconductive properties of
selenium in 1873 [2], selenium has gone on to be used in a large variety of
applications including providing sound for early motion pictures,
xerography, electroradiographic detection, and use in TV pickup tubes. Of
these applications, xerography and electroradiography are the most
important for this work.
1.2.1 Electrophotographic Photoreceptors
The electrophotographic, or xerographic, industry started in 1938
with the invention of the electrophotographic copier by Chester Carlson [3].
The industry has since grown into a 100 billion dollar/year commercial
enterprise. Today, it encompasses many different forms of
electrophotography including copying machines, fax machines, scanners,
and laser printers. Amorphous selenium photoreceptors were the first to be
used commercially in the early 1960s and continue to be widely used, though
their importance has recently shifted to electroradiography.
The seven basic steps in the xerographic process are shown in Figure
1.1. The first step is to charge the photoconductor. The most common
method used for the charging process is corona discharge. A high electric
field is applied to a thin wire (corotron) which in turn generates a plasma
around itself. Ions drift from the plasma to the surface of the
2
photoconductor thereby charging it uniformly. Next, the photoreceptor is
light-exposed to the optical image to be reproduced.
(1) Charge
Document Toner Particles
44) RFA) gar) .
(2) Expose
(4) Transfer
Photoreceptor
1 Twee. 1
Photoreceptor 4 (3) Develop
wpIem. !die..
Paper
(5) Fix
6 Lamp
1
Photoreceptor
(6) Clean (7) Erase
Fuser Roller 150-200 e Pressure Roller 40-80
Figure 1.1 The basic steps of the xerographic process: (1)charge, (2) expose, (3) develop, (4) transfer, (5) fix, (6) clean, and (7) erase.
3
The light areas of the image cause the corresponding area on the
photoreceptor to discharge through a photoconductive process, while the
corresponding dark areas remain charged. This creates a latent electrostatic
image on the surface of the photoreceptor. The latent image is then
developed by using electrostatically charged toner particles. The particles
stick to the oppositely charged latent image. The particles are then
transferred to the paper, by positively charging the back of the sheet, and
fused by heating the particles to form the final hard copy. Before another
image can be made, the remaining toner particles must be cleaned from the
photoreceptor and any residual electrostatic charge from the image is erased
by flooding the photoreceptor with a uniform high intensity light.
- The amount of photoconductive discharge that occurs during the
formation of the latent image is determined by the electronic properties of
the photoreceptor. The average distance per unit electric field that a charge
carrier will move in the photoconductor is termed the range of the carrier.
The range is given by the i.rt product where µ is the drift mobility, and ti is
the deep trapping lifetime of the carrier. Consequently, the product of the
applied field and the carrier range will determine the average distance
traveled by the charge. For optimal photodischarge, the photogenerated
carriers must move distances greater than the thickness of the
photoconductive layer. Therefore, the charge carrier drift mobility and deep
trapping lifetime are very important parameters for characterizing the
performance of the photoreceptor.
4
1.2.2 Electroradiographic Detectors
The use of amorphous selenium in x-ray imaging has been well
documented and continues to be a field of intensive research [4,5]. There is
considerable interest in digital electroradiogaphy where an electrostatic
image on an x-ray plate is read and converted to a digital form for computer
storage and processing [6].
The medical imaging application of electroradiography relies on the
differential absorption of ionizing radiation by different tissues in the
human body. A typical projection radiographic systems consists in its most
general form of an x-ray source and an x-ray sensitive detector which is
placed behind the subject as shown in Figure 1.2.
X-ray Detector
X-ray Source
Figure 1.2 Typical projection radiographic system for medical imaging.
5
The patient is exposed to the x-rays and the differential attenuation of
the x-rays in passing through the body modulates the radiation intensity
that reaches the detector. The detector must then store this information
until a visible image can be made. Conventional detectors consist of a
photographic film cassette which is sandwiched between fluorescent screens.
Incident radiation which strikes the screens is converted into light which is
then recorded by the film. The film is then developed using standard
photographic means to view the image.
In electroradiography, the photographic cassette is replaced with a
solid-state, planar, image detector. The detector is charged, similar to the
xerographic process, and when exposed to the x-ray radiation undergoes
photodischarge. This leaves a latent electrostatic image on the surface of
the detector. This image may be read by using the sequential discharge of
the surface by a scanning pulsed laser beam and capacitively coupled
transparent probe system shown in Figure 1.3 [6]. The sampling electrode is
capacitively coupled to the surface of the detector. The electrode assumes a
potential related to the surface charge on the detector and the degree
of coupling. When the laser is focused onto the detector, the charge on the
surface of the detector undergoes photodischarge. The sensing electrode
records a change in charge proportional to the change in surface charge.
The image is reconstructed by correlating the electrode voltage signal with
the path of the laser beam. The image can then be stored and analyzed by a
computer.
Transparent Electrode
Conducting Layer
Pulsed Scanning Laser Beam
+ + ++ ++ a-Se Film
Al Substrate
0
Figure 1.3 Development system for electroradiography consisting of a pulsed laser beam and capacitively coupled probe.
There are three major advantages to the electroradiographic system
over the conventional system. First, by replacing the photographic film, the
process is changed from a chemical to an electronic process. This has
environmental as well as economic implications in that the imaging plates
are fully reusable and the costs of the chemical purchase and reclamation
are removed.
Secondly, research on selenium based x-ray detectors indicates that
they are more sensitive to x-ray radiation than conventional film detectors.
This means that for comparable image quality, the patient is exposed to
lower radiation levels when using the solid state detector. This increases
the safety factor for the patient.
Finally, solid state detectors allow for a higher lateral resolution than
photographic detectors. Light that is generated in fluorescent screens of the
photographic cassettes propagate to the surface of the film through an
isotropic diffusion process, i.e. they spread parallel as well as perpendicular
to the image plane. This limits the resolution on the film. This problem is
overcome in the solid state detector since the charge carriers involved with
electrostatic discharge move along the applied electric field and therefore
perpendicular to the image plane.
Since the imaging process is based on photoinduced discharge, the
range or wr product is a very important material parameter for studying the
detectors used in electroradiography. However, carriers in selenium
electroradiographic detectors are not lost to conduction through deep
trapping alone. Charge carrier recombination may also play an important
role. The x-ray absorption process for amorphous selenium is such that
electron-hole pairs are generated throughout the bulk of the detector. The
application of an electric field causes the electrons and holes to move past
each other, and there is a probability that some carriers recombine. The
recombination coefficient, Cr, is therefore another important parameter for
characterizing the usefulness of a material as a detector.
1.3 Research Objectives
Amorphous semiconductors have been the subject of a great deal of
scientific interest and study. As their use increases, it becomes more
important to understand the physical and electronic properties of this group
of materials. The primary focus of this research is to study charge carrier
recombination in chlorinated a-Se:0.2%As films suitable for use in
electroradiographic systems.
The experimental techniques used were the time-of-flight (TOF)
technique, the interrupted field time-of-flight (IFTOF) technique, and a
8
double flash, ambipolar time-of-flight technique. The results from the TOF
and IFTOF experiments were used to characterize charge transport, i.e. wr
product, in the films. The ambipolar TOF technique was used to directly
measure the amount of recombination that occurred within the samples
when holes and electrons interacted with one another.
1.4 Thesis Outline
This thesis is divided into six chapters. Following this introductory
chapter, a brief review of the various structural, optical, and electronic
properties of amorphous selenium is given in Chapter 2. Chapter 3 provides
the principle of the time-of flight transient photoconductivity technique and
an analytical framework for studying charge transport in a material with a
single species of traps. A description of the ambipolar TOF and IFTOF
measurement systems used in this work is provided in Chapter 4 along with
a description of the sample preparation procedure. Chapter 5 presents the
results from the TOF, IFTOF and ambipolar recombination measurements
performed on amorphous selenium films. Finally, the conclusions drawn
from the results in Chapter 5 are presented in Chapter 6, along with some
recommendations for future work.
2. PROPERTIES OF AMORPHOUS SELENIUM
2.1 Introduction
This chapter deals with the physical properties of amorphous
selenium. The physical structure of amorphous selenium and its energy
band model are described. These determine the optical and electrical
properties the material exhibits. .
2.2 Structure of Amorphous Selenium
Amorphous and crystalline materials have vastly different structures.
Figure 2.1 presents in schematic fashion the atomic arrangement of a
perfectly crystalline material as opposed to a perfect network glass. The
dots in the figure represent the equilibrium positions about which the atoms
oscillate. In a perfect crystal, the bonding arrangement (i.e. bond length and
bond angle) for each atom is identical regardless of the atom's position in the
crystal. The crystalline solid exhibits a translational periodicity and
possesses "long range order". This does not hold for amorphous solids.
Atoms in an amorphous solid have slight variations in bond length and bond
angle which destroy the periodicity for distances greater than a few atomic
radii. The amorphous solid does however exhibit a high degree of short
range order. The valency requirements for each atom in the structure are
10
satisfied and each atom is normally bonded to the same number of
neighbouring atoms.
(a) (b)
Figure 2.1 Atomic arrangements in (a) a perfect crystal and (b) a perfect network glass.
In the crystalline state, selenium can exist in one of two forms,
monoclinic Se (a - Se) and trigonal Se (y-Se). a-Se is composed of Ses rings
while y-Se comprises of parallel Se. spiral chains in a hexagonal structure.
It is natural to assume that the structure of amorphous selenium • would
preserve elements of a-Se and y-Se, that is a mixture of ring and chain
members. Recent studies on the structure of amorphous selenium now
favour a "random chain model" with all the atoms in a twofold coordinated
chain structure. The dihedral angle 4) of this chain remains constant in
magnitude but changes sign randomly [7].
Consider Figure 2.2 with atoms 1, 2, 3 and 4. The dihedral angle 4) is
defined as the angle between two adjacent bonding planes. It is observed in
Figure 2.2 by looking down the bond that connects atoms 2 and 3. In y-Se,
11
the dihedral angle rotates in the same sense in moving along the chain to
give a spiral pitch of three atoms. In a-Se, the dihedral angle alternates its
sign to form a ringlike structure. In the amorphous structure, the sign of
the dihedral angle changes randomly leading to regions that are chain-like
and to regions that are ring-like as in Figure 2.3.
Figure 2.2 Selenium chain molecule and the definition of the dihedral angle (1). The dihedral angle is formed by the planes defined by atoms 123 and 234.
Although the twofold coordinated structure, Se2°, is the most
energetically favourable, thermally derived charged structural defects,
known as Valence Alternation Pairs (VAPs), also exist in the amorphous
state. These VAPs correspond to some of the Se atoms being over- and
under-coordinated [8]. Electron Spin Resonance (ESR) studies have shown
that the lowest energy defects in amorphous selenium (a-Se) do not have
dangling bonds. It has also been calculated that the lowest energy defects
are not singly bonded Sei° or triply bonded Se3° atoms [52]. The lowest
energy defects are charged centres with paired electron spins, Sec and See.
12
These structured defect pairs are the VAP, and they constitute the origin of
localized states within the mobility gap of the material.
Figure 2.3 Local structure of amorphous selenium showing chainlike segments of y-Se and ringlike segments of a-Se.
2.3 Band Model for Amorphous Selenium
The disorder inherent with amorphous materials results in a different
band structure from that of crystalline solids. A number of band models
have been proposed for amorphous materials.
Mott [9] took the first step in generalizing the quantum mechanical
arguments made for the band structure of crystalline semiconductors to
amorphous ones. Mott realized that quantum mechanical solutions for
crystals, that led to a density of states model where electrons existed in
13
bands of extended states separated by gaps with sharp band edges, as in
Figure 2.4(a), were the result of the long range order in the crystal. He
argued that the lack of long range order in amorphous materials would
cause the sharp edged bands in crystalline materials to be replaced by bands
with tails of localized states. Mott further argued that extended states
would exist in amorphous materials at some particular density of electronic
states. This would in turn lead to a sharp increase in mobility at the critical
energy where the extended states began. This concept of a "mobility gap" in
amorphous solids is similar to the band gap concept for crystalline solids.
The density of states model proposed by Mott is shown in Figure 2.4(b).
Mott's original model was further expanded by Cohen, Fritzche, and
Ovshinsky [10]. Their model became known as the CFO Model and is shown
in Figure 2.4(c). This model assumed that the nature of the localized band
tails depends on the extent that the amorphous structures deviated from a
perfect periodicity. They postulated that the degree of disorder in
amorphous solids was greater than that assumed by Mott. As a result, the
band tails would extend through the mobility gap and give rise to a finite
density of states at the Fermi level (i.e. they would overlap). However, this
continuum of states in the gap would not give rise to metallic conduction
properties because the states were still assumed to be highly localized in
space. Finally, the CFO model considered that since amorphous material do
not have the rigid constraints of a crystalline material, each atom would
ordinarily be able to locally fulfill its valency requirements. This would
eliminate any sharp structure in the density of localized states in the
mobility gap.
14
Ec
EF
E v
(a)
(c)
N(E)
N(E)
(b) N(E)
(d) N(E)
Figure 2.4 Various forms proposed for the density of states as a function of energy for crystalline and amorphous semiconductors. (a) crystalline model (b) Mott's model, (c) CFO model, and (d) Davis-Mott model [11].
However, amorphous semiconductors are thought to contain defects
such as impurities and dangling bonds. These may lead to discrete levels in
the mobility gap. This led Davis and Mott to relax the valency condition of
the CFO Model to account for the effects of structural defect [11]. The
Davis-Mott Model is shown in Figure 2.4(d).
15
The currently accepted electronic density of states model, for a-Se is
shown in Figure 2.5 [12]. It was developed from various xerographic and
transient photoconductivity measurements. The high concentration of
shallow traps at energies -0.29eV above Ev and -0.35eV below Ec control
hole and electron drift mobilities through a shallow-trap-controlled band
transport process.
Ec
2.0 -
Ev 0
EF= 1.06 eV ••• *ft
og.
2.22 eV
I.-. I
1011 12 13 14 15 16
101710 10 10 10 10 1018
1019
1020
1021
N(E), cni3eV
Figure 2.5 Experimentally determined density of states function N(E) for a-Se [12].
2.4 Optical Properties of Amorphous Selenium
The task of a photoreceptor is to convert the photons of an incident
light signal into mobile charge carriers. Therefore, the optical properties of
16
a material determine its value as a photoreceptive material. In an ideal
photoreceptor, each incident photon leads to the generation of an electron-
hole pair. Real materials however do not conform to this ideal behaviour.
The first optical property of importance to look at is the optical
absorption coefficient a. Optical absorption in semiconductors is determined
by the probability that a photon will excite an electron across the bandgap
and generate an electron-hole pair (EHP). As such, a depends on the photon
energy and the density of states at the band edges. As long as the photon
energy is less than the gap energy, little or no absorption will occur.
Studies reveal that the optical absorption coefficient of amorphous
selenium exhibits an Urbach edge of the form a=7.35x10-12
exp[hv/0.0058eV]cm-1 [13]. However, at high photon energies, the
absorption coefficient has been found to obey (ahv)-(hv-Eo) [14], where
E0-2.05eV is the optical bandgap at room temperature.
The second important optical property to be looked at is the quantum
efficiency of the photoreceptor. Quantum efficiency determines the
probability that generated EHPs will dissociate to form free electrons and
holes. For crystalline semiconductors, the quantum efficiency is largely
determined by recombination kinetics and is generally independent of
electric field and temperature. This is not the case with amorphous
selenium and many other low mobility solids.
The quantum efficiency of a-Se has a strong electric field dependence
even for photon energies greater than the mobility gap. Figure 2.6 shows
17
the dependence of the absorption coefficient a and the quantum efficiency
on the photon energy hv.
E U
Abs
orpt
ion
Coe
ffic
ient
105
104
103
102
10
1
1
10-1
-2 10
103
104
10-5
101 10-6 1.5 2.0 2.5 3.0 3.5 4.0
Photon Energy hv, (eV) Q
uant
um E
ffic
ienc
y,
Figure 2.6 Absorption coefficient a and quantum efficiency ri as a function of the incident photon energy hv for various applied fields F [13,15].
The mechanism for the field dependent quantum efficiency in
amorphous selenium has been explained by the Onsager theory[15]. The
Onsager theory calculates the probability that an EHP will dissociate, as a
result of diffusion, under an electric field. The quantum efficiency depends
on the electric field F, the temperature T, and the initial separation of the
EHP ro. Thus, the quantum efficiency is given by
18
11=110f(F,T,ro), (2.1)
where f(F,T,ro) is the probability that the EHP will dissociate and lio(hv) is
the quantum efficiency of the intrinsic photogeneration process.
2.5 Charge Transport in Amorphous Selenium
Assuming the existence of disorder-induced localized states within the
mobility gap, a number of charge transport mechanisms exist for amorphous
solids. As shown in Figure 2.7, electrons with energy far in excess of Ec
move in the extended electronic states. Conduction in these states is similar
to that of electrons in the conduction band of crystalline semiconductors. The
mean free path of the electron in these states is much longer than the
average interatomic distance and transport is based on Bloch wave
functions. The predicted mobility for carriers in these states is in excess of
100 cm2V-1s-1.
In the extended states just above the mobility edge, the long range
disorder of the material starts to dominate the transport process. The
carrier mean free path is comparable to the interatomic distance in these
states and charge transport can no longer be regarded as simple band
transport. Electron motion in these states is described as diffusive motion,
similar to Brownian motion [17]. The mobility in these states is of the order
of 1 cm2V-1s-1.
19
CM2V -1S.1
µ>100
1 • • • • • * • •
• •-•-..* 11. < 10 -2
• • • •
11« 10 -2• • •
Figure 2.7 Predicted variation of carrier mobility in amorphous solids with energy [16].
Bloch wave functions do not extend throughout the material in the
localized states below Ec, but decay as exp(-aR) where R is the average
interatomic distance and a defines the rate at which the Bloch wave
function decays. The possibility exists that transport between these
localized states will occur by tunneling between the states. This 'hopping'
transport will depend on the overlap of wavefunctions between nearest
neighbours given by exp(-2aR), an attempt to hop frequency (i.e. phonon
frequency), VPH, and any activation energy, W, associated with the hopping
mechanism. Spear has described the mobility for such 'hopping' transport as
[18],
20
eR 2 wl exp[-20cR]expt—Tri
kT (2.2)
The mobility for the hopping mechanism is estimated to be of the order of
10-2 cm2V-1s-1.
The exact nature of the microscopic mobility has not been conclusively
determined for amorphous selenium. Drift mobility studies have shown that
the thermally activated mobility has no pressure dependence [19]. This has
been used as evidence against a hopping transport mechanism and a
diffusive type transport in the extended states near the mobility edge has
been assumed.
In a material such as a-Se, which has a significant number of
localized states, the microscopic mobility go can be modulated by traps that
lie at lower energy levels with respect to the microscopic conduction level.
The drift of the carriers is periodically interrupted by capture and release
events from these shallow traps. The time spent by the carriers in the traps
effectively lowers the microscopic drift mobility of the carriers. go for such
carriers is reduced by a factor tc/(tc+TR) to µa where tc is the amount of time
the carrier remains free and Tx is the amount of time the carrier remains in
the trap. This conduction mechanism is known as trap-controlled transport
and has been observed in a-Se by examining the drift mobility at low
temperatures [20,50].
Carriers can be captured by three different types of traps: (a) centres
with an opposite electronic charge from the carrier (Coulomb attractive); (b)
21
neutral centres; or (c) centres with the same electronic charge as the carrier
(Coulomb repulsive) [21]. Regardless of the type of trap involved, the
probability that a carrier will become captured is given by
1 _ NTCT, ,LC (2.3)
where tic is the mean free time before the carrier is captured, NT is the
density of traps and CT is the capture coefficient which is dependent on the
species of trap involved.
Charge carriers can be re-emitted from traps by a variety of different
mechanisms. Re-emission from a Coulomb-attractive trap is a thermally
activated process. The probability per unit time for thermal release from
this type of trap is given by Boltzmann statistics as
1 E T 1 = V exp[--
kT R (2.4)
where TR is the mean release time, vpH is an attempt to escape frequency
(phonon frequency), and ET is the depth of the trap below the band edge.
Further, it should be noted that if trap-controlled transport is applicable,
detailed balance considerations relate the trapping and de-trapping times by
a. N pPE ] TR NT
ex kT
22
(2.5)
where Nc is the density of states in the conduction band.
The application of an electric field enhances re-emission from the
trapping centres. The applied field reduces the potential barrier in a
Coulomb-attractive trap through the Poole-Frenkel effect. This is illustrated
in Figure 2.8.
Conduction Band
E - 0
Electron Energy
Trap Ground State
A
SE
Figure 2.8 Energy diagram for an electron bound to a point charge in the presence of a uniform electric field (Poole-Frenkel effect) [21].
The Poole-Frenkel effect leads to a decrease in the potential barrier ET
by an amount 8E given by
8E = 13-if (2.6)
23
where 13 is the Poole-Frenkel constant and F is the applied electric field.
Equation 2.4 must be modified to take this barrier reduction into account
and it becomes
1 I- ET -13,51, zR
= vpllext kT j
2,6 Summary
(2.7)
In this chapter, the physical structure and properties of amorphous
selenium were introduced. Studies have shown that atoms in amorphous
selenium exist in a twofold coordinated chain structure. The dihedral angle
of this chain remains constant in magnitude but changes sign in a random
fashion. Thermally derived defects in the chain (VAPs) also exist in the
amorphous state.
Further, it was shown that the disordered structure of amorphous
materials, such as selenium, leads to a different band model than for
crystalline materials. The disorder in amorphous solids is thought to give
rise to states, localized in space, in the mobility gap of these materials. In
amorphous selenium, the VAP structures are the origins of the localized
states. Theses band structures in turn govern the optoelectronic properties
of amorphous selenium.
The absorption coefficient of a-Se is dependent on the photon energy
of the incident light. The optical gap in amorphous selenium is —2.05 eV,
and photons with lower energy will experience little or no absorption. The
24
quantum efficiency of a-Se is dependent on both the energy of the incident
photons and the applied electric field. The field dependence of the quantum
efficiency has been explained by the Onsanger theory, and it only reaches an
acceptable level at high electric fields and photon energies larger than the
optical gap.
Charge transport in amorphous materials can occur through a variety
of processes. Charge transport studies on amorphous selenium have
suggested that a diffusive type transport in the extended states near the
mobility edge is the dominant process for transport. However, this transport
is further modulated by the existence of shallow traps near the mobility
edge. This reduces the mobility of the charge carriers through trapping and
release events from these shallow traps.
25
3. TIME-OF-FLIGHT AND AMBIPOLAR
RECOMBINATION EXPERIMENTS
3.1 Introduction
Due to their disordered structure, the charge transport properties of
amorphous materials are difficult to model and understand mathematically.
With the use of quantum mechanics, crystalline materials are easily
understood since their long-range order greatly simplifies the mathematical
models involved.
The study of amorphous materials, then, relies heavily on empirical
measurements of the physical and electronic properties of interest. The
Time-of-Flight (TOF) transient photoconductivity experiment provides an
excellent means to study the charge transport properties of low mobility
materials. The principles of this technique will be introduced in this
chapter. The following section will present an analytical framework for
interpreting the resultant TOF waveforms for a material with a single
species of deep traps.
26
3.2 Principles of the Time-of-Flight (TOF) Technique
The Time-of-Flight (TOF) transient photoconductivity experiment
consists of measuring the transient response that occurs due to the drift of
injected charge carriers across a low mobility solid. A simplified schematic
diagram of the TOF experiment is shown in Figure 3.1(a). A thin film, of
thickness L, of the material to be studied is sandwiched between two metal
electrodes, A and B. The top electrode A is connected to a high voltage bias
source Vo which sets up a uniform electric field across the sample. The
bottom electrode B is connected to ground through a sampling resistor R. It
is assumed that, for the present discussion, electrode A is kept at a positive
potential with respect to ground. A thin sheet of free carriers is injected into
the sample through some form of external excitation, and these carriers drift
across the sample under the influence of the applied electric field.
The analysis of the signal is greatly simplified when the absorption
depth 8 of the excitation is much less than the sample thickness L. This
ensures that bulk generation of carriers across the sample does not occur
and that only one type of charge carrier is swept across the sample. This
discussion thus assumes that electrons will be quickly removed from the
sample by the positive potential at electrode A while holes will drift towards
electrode B.
It is also important to ensure that the duration of the excitation tex is
much less than the transit time tT of the carriers. tex determines the initial
width of the charge carrier sheet that will cross the sample. This sheet is
used as a probe to examine charge transport across the thickness of the
27
sample and its width will determine the spatial resolution of these
measurements.
Carrier Injection tex
T ----F 1
w . i ...+. . .±.±..+.+._+±.-11..+.± +.±
F2
1P h
iP
. (a)
(b)
x =0
x=x'
x = L
Figure 3.1 (a) Simplified schematic and (b) small signal ac equivalent circuit for the Time-of-Flight transient photoconductivity technique, where Cs is the sample capacitance.
28
Time-of-flight measurements require that the dielectric relaxation
time, trei, of the material under study be much longer than the transit time
of the carriers. trei represents the time for the extrinsic charge carriers in a
material to decay to their thermal equilibrium number. TOF measurements
rely on the fact that the excess photoinjected carriers are not neutralized by
intrinsic charge carriers while they are drifting across the sample. This can
be assumed to be true when trei » tT. High resistivity amorphous
semiconductors generally fall into this category since they contain few
mobile intrinsic charges at room temperature.
The carriers injected into the sample perturb the applied internal
electric field Fo. The fields F1, behind the charge sheet, and F2, in front of
the charge sheet, as shown in Figure 3.1(a) can be determined at any
position x. By using elementary electrostatics, Spear [22] has shown that
= Fo + Lepow(x
—1j, (3.1)
and that
F = F
+ ep ow x 2 0 e (3.2)
where F0=V0/L is the applied electric field, po is the concentration of injected
carriers (in this example holes) in the charge sheet, w is the width if the
sheet, and e is the dielectric permittivity of the sample. If the amount of
injected charge powA, where A is the area if injection, is kept small enough
so that epow/c « Fo, the internal field can be approximated as being uniform
Fo.F1=F2=Vo/L. This is the small signal condition, and it corresponds to
29
Qo(injected) « VoCs, where Cs is the capacitance of the sample. This
condition limits the number of carriers that can be injected into the sample
for TOF studies. If the small signal condition is not maintained throughout
the experiment, the TOF analysis must be modified to take the space charge
perturbation of the electric field into account [23].
As a charge q drifts within the sample, a charge is induced to flow in
the external circuit. Consider Figure 3.2. The work done moving charge q a
distance dx is given by
dW=F•q•dx, (3.3)
where dW is the work done moving the charge and F is the field in which the
charge is moving. The energy required to do this work must be supplied by
the external source and it is given by
dE = Vo • clQ. (3.4)
dx
dQ
Figure 3.2 The motion of charge q through dx induces charge dQ to flow through the external circuit.
30
Equations 3.3 and 3.4 must be equal to each other according to the
first law of thermodynamics. The following equation can then be written
dQ = qdx L •
(3.5)
Equation 3.5 is known as Ramo's theorem [24]. In practical terms this
shows that the signal measured in the external circuit is due to an injected
charge moving through the sample from electrode A to electrode B. It
follows simply from Equation 3.5 that for a trap free solid, the induced
photocurrent through the sampling resistor is
i ph (t)
ePot,
for t < t,
0 for t t,
(3.6)
Equation 3.6 is valid for both holes and electrons by substituting no for po.
There are essentially two methods of measuring the induced charge
that flows in the external circuit. Figure 3.1(b) shows the small signal ac
equivalent for the circuit in Figure 3.1(a). The induced photocurrent iph(t) in
this circuit must flow through the parallel RC circuit. Let V(s) and Iph(S) be
the Laplace transforms of the voltage signal and photocurrent. For the
circuit shown in Figure 3.1(b), they are related through
31
V(s) — sRCs + 1
IPh
(s). (3.7)
The bandwidth of the measured signal is arbitrarily defined as the
reciprocal of the carrier transit time tT.
The first measurement involves measuring the current pulse
produced by the drifting charge sheet. If RCs«tT then the inverse Laplace
transform of Equation 3.7 leads to
v(t) = Ri ph (t) for RC < tT (3.8)
Equation 3.8 is the so-called I-mode signal because the observed output
signal is directly proportional to the photocurrent. In a trap-free solid, the I-
mode signal rises instantaneously to a constant level when the charge
carriers are first injected and remains so until the charge sheet reaches the
opposite electrode when the signal falls to zero.
The second technique relies on integrating the induced charge Q that
moves through the sampling resistor. Again consider Equation 3.7, but with
RCs»ti, for this case. Taking the inverse Laplace transform gives a signal
ri v(t)=--
Cs j°iP h (t)dt for RCs » tT (3.9)
Equation 3.9 represents the V-mode signal. The V-mode signal is the
integral of the I-mode signal. As such, it will rise in a linear fashion after
32
the charge carriers are injected until they drift across the sample at which
time the signal will flatten and remain constant.
The I-mode and V-mode signals are modified by interactions with the
deep traps that can occur in the mobility gap of amorphous semiconductors.
Deep traps are localized states that exist deep within the mobility gap.
Release times from the deep traps are very long due to the large potential
barrier that carriers must be thermally excited over. These traps can
significantly reduce the concentration of free carriers in the charge sheet as
they drift across the sample. For a given species of trap, characterized by a
mean trapping lifetime 'cc and a release such that carrier release is
insignificant during tr, the number of free carriers will be diminished in an
exponential manner. The photocurrent in Equation 3.6 is then modified as
ePo r t 1 tT
expi — I for t < tTL "Cc J
i ph (t)
0 for t tT
(3.10)
to account for the decrease in the concentration of free carriers. The
resulting I-mode signal is given by
v(t) =
Re Po .r xpl
tT L
0
t I for t < tT— —
j
for t ?_ tT
(3.11)
33
The resulting V-mode signal can be found by integrating the photocurrent
signal according to Equation 3.9. This yields
ePot t 1—ex ---- for t < tT
Cs tT 'CC v(t) =
ePot r CS tT
exp I for t tTt c
(3.12)
A comparison of the trap free and deep trapping signals for I-mode and V-
mode signals is shown in Figure 3.3.
v(t)A v(t)A
t=0 t=t T
(a) v(t)A v(t)A
z I I
t4) t=t T t
(C)
t=t
0:0)
I t=0 t=t T t
(d)
Figure 3.3 Signals from the TOF experiment where (a) and (b) are I-mode signals for the trap free and deep trapping only case and (c) and (d) are V-mode signals for the same cases [20].
34
There are advantages and disadvantages inherent with both the I-
mode and V-mode techniques. For example, I-mode signals readily lend
themselves to the determination of carrier transit times since an abrupt
change in signal magnitude is evident when the carriers exit the sample at
the opposite electrode. V-mode analysis on the other hand can be used to
determine the total amount of charge injected into the sample. Equation
3.12 has also been used to estimate the trapping time of carriers into deep
traps [51].
3.3 Transient Trap Limited Theory
The previous section developed the principles of the TOF experiment.
In this section, a transient trap-limited theory will be developed for trapping
and release from a single set of monoenergetic traps within the mobility gap
of an amorphous solid.
Figure 3.4 represents some semiconducting material. Consider a thin
slice of the material with a thickness dx. If a current due to an electron
charge packet is flowing in the material, the number of electrons in the slice
may increase due to the net flow of electrons into the slice or due to the net
thermal release of trapped electrons within the slice. Recombination effects
may be ignored because only one type of carrier is present in the sample.
This situation can be expressed by the continuity equation as
on(x, t) 1 8J(x, t) SnT (x,t) St e Sx St
35
(3.13)
where n(x,t) is the concentration of free electrons in the sample, J(x,t) is the
net current density flowing into the slice, and nT(x,t) is the density of
trapped electrons in the slice.
x+dx
J(x,t) ►J(x+dx,t)
tc
Figure 3.4 Current flow with trapping and release processes in a thin slice of thickness dx.
There are two components which make up J(x,t). The first component
consists of the drift of electrons under the influence of the applied field.
This is expressed as Jc(x,t)=epon(x,t)F(x,t) where e is the electronic charge,
go is the mobility, and F(x,t) is the electric field. The second component is
due to spatial variations in the concentration of charge carriers and is given
by Jp(x,t)=eD8n(x,t)/Sx where D is the diffusion coefficient. The net current
density is therefore given by
J(x, t) = egon(x, t)F(x, t) + eD Sx •
8n(x, t) (3.14)
The substitution of Equation 3.14 into Equation 3.13 leads to the one
dimensional continuity equation for electrons given by
36
on(x, t) on(x, 45F(x, 0 52 n(x, t) OnT (x,
St oxµ0F(x, + on(x, t) 8x + D 53(2 — St . (3.15)
The expression for SnT(x,t)/8t, known as the rate equation, is
determined by the difference in the instantaneous trapping and release
rates. Given tc and TR as the capture and release times, the rate equation is
SnT (x, t) n(x, t) nT (x, t) St T 'CR
(3.16)
A number of simplifying assumptions can be made to allow for the
simultaneous solution of Equations 3.15 and 3.16. For example, the internal
electric field for small signal TOF measurements is assumed to be uniform.
This means that the 8F(x,t)/5x term may be neglected. The diffusion term
may also be neglected since the magnitude of the diffusion current term is
usually considerably less than the conduction current.
The following initial conditions are required to solve Equations 3.15
and 3.16 simultaneously
and
n(x,0) = NoS(x,0), (3.17)
nT (x,0) = 0 for x > O. (3.18)
These conditions correspond to an impulse of No electrons being injected into
the sample at time t=0 and position x=0. Boundary conditions which take
into account the finite length of the sample must also be used. These are
37
n(x,t)= 0 for x > L, (3.19)
and
nT(x,t)=0 for x>L. (3.20)
Equations 3.15 and 3.16 have been solved by applying these initial
and boundary conditions and by using Laplace transform techniques[251.
This provides an expression for the free electron charge density given by
No I- z 1 No z (t — z)lj (4) 2(t — z)
n(x, — exit i:
— 71SO — z) + 110F ex rcc U(t — z) , (3.21)
where z=x410F, Ii(4) is the hyperbolic Bessel function, U(x) is the unit step
function and 4= (2Vorcz(t— /TR ) itc
Equation 3.21 consists of two components. The first term represents
the charge that remains in the injected packet as it drifts across the sample.
These carriers do not undergo any delay due to trapping and release events
but the number of these untrapped charges does decrease exponentially as
exp(-t/tc) until they reach the opposite side of the sample. The second term
represents those carriers that have been trapped out of the charge packet
and are released back into the conduction band at time t. These carriers will
lag behind the untrapped carriers, due to at least one trapping and release
event, and contribute to the signal at times greater than t=I4toF where go is
the microscopic mobility.
38
The time dependence for the free carriers in the sample can be found
by integrating Equation 3.21 over the length of the sample. However, the
detrapped portion of Equation 3.21 cannot be integrated to give a closed
form for N(t), so limiting or particular cases are used to evaluate the
trapping parameters. These special cases do not pose a problem for
predicting the transient response of charge carriers during TOF experiments
since they can be obtained by making appropriate choices as to sample
thickness, bias voltage, and temperature.
3.3.1 TC«'CR<tT Case
The conditions tc«tT<TR state that the capture time is much shorter
than the time it takes for the fastest carriers to cross the sample determined
by tT=L/µ0F, and that Tx is comparable to tT. These conditions imply that the
carriers will undergo many trapping and release events, from a shallow
species of traps very near to the conduction band edge, before they complete
their transit across the sample. Imposing these restrictions on Equations
3.15 and 3.16 causes the time derivative of the total charge in the conduction
band to vanish over a long time interval. By making use of the principle of
conservation of charge, the total number of free charges in the conduction
band is given by
N = No T c •
'Lc + TR (3.22)
The resulting I-mode photocurrent signal can be found by substituting
Equation 3.22 into Equation 3.6. This expression is
39
eNo Tc tc +TR 'ph for tic < t < tT • (3.23)
tT Tc +TR Tc
This resembles the trap free I-mode case except that the transit time tT has
been increased by a factor of erci-tx)itc. This in turn implies a reduction in
carrier mobility from .to to µ, given by
tc = 011o
t + C TR (3.24)
where the scalar 0 is referred to as the shallow trap-controlled transport
factor. When the mobility of the carriers is reduced by the time spent in the
traps, the transport mechanism is known as shallow trap-controlled
transport.
3.3.2 High Field Case (tT<Tc)
When the applied electric field is sufficiently high, it is possible that
charge carriers will cross the sample without becoming trapped and that the
equilibrium between trapping and release events found in the previous case
will not be reached. The photocurrent signal for this case can be separated
into two terms. The first term represents the drift of carriers in the charge
sheet for t<tT. This current signal has been derived as [21]
eN0 r TR tic +TR t)
I for t < tT. i ph ( t ) I L exp — (3.25) tT ctic +TR t c +TR t ct it
40
If detrapping is neglected by letting TR—>co, then Equation 3.25 reduces to the
simple case of deep trapping only i.e. Equation 3.25 reduces to Equation
3.10.
The second term, for t>tT, represents the response for those carriers
that were trapped and then later released back into the conduction band.
Most of these carriers finish crossing the sample without being trapped
again. The current signal for this case has been derived as[211
eN0 tT p[ t iph (0 =
2 Tctiz ex
'CR
3.4 Summary
for t > tT. (3.26)
The principle of the Time-of-Flight experiment and the transient
response expected for a single species of trap have been introduced in this
chapter. The TOF technique is a powerful method for studying charge
transport in amorphous and low mobility semiconductors. There are
essentially four conditions that must be maintained throughout the TOF
experiment. These are:
1. The absorption depth, 6, of the charge carriers must be much less than the thickness of the sample (8«L).
2. The duration of the injection pulse, tex, must be much shorter than the transit time of the carriers across the sample (tex<<tT).
3. The dielectric relaxation time, trel, must be much longer than the transit time of the carriers (trei»tT).
41
4. Small signal conditions must be maintained throughout the sample (Qo(injecthd)«CsVo).
Furthermore, there are two methods for measuring the charges that
flow in the external circuit during the TOF experiment. These are the I-
mode and V-mode measurements. Each of these techniques has its own
advantages, and the use of one or the other depends on the parameter of
interest in the experiment.
The effect of the many trapping and release events found with a set of
energetically shallow traps is to reduce the mobility of the carriers because
of the time that the carriers spend in the traps. However, for a deeper set of
traps, the photocurrent signal will decay exponentially with a characteristic
trapping lifetime Tc.
42
4. EXPERIMENTAL PROCEDURE
4.1 Introduction
This chapter describes the systems that were used to obtain
experimental data during the course of this work. It consists of three parts.
The first describes the procedures used for fabricating the samples. Next, a
review of previous recombination experiments is conducted before the
present Ambipolar Time-of-Flight (TOF)/recombination measurement
system is introduced. The final section gives a brief overview of the
Interrupted-Field TOF (IFTOF) method used for obtaining the trapping
lifetimes of carriers in Cl doped a-Se:0.2%As films of this work.
4.2 Sample Preparation
The stabilized a-Se alloy films were prepared by conventional vacuum
evaporation onto aluminum substrates. The polymer film used to protect the
Al sheet was first removed by ultrasonic cleaning in a sequence of acetone,
distilled water, methanol, and distilled water baths. The substrate was then
placed in a heated mixture (65 C) of sodium carbonate, sodium phosphate
and distilled water (caustic etch solution) to partially remove the oxide layer
on the surface of the Al substrate. The final cleaning sequence consisted of
the sample being dipped into a nitric acid solution and then washed in
43
repeated cycles of distilled water and detergent solutions. The oxide layer
was regrown on the substrate by placing it in a 300° C furnace for 4-5 hours.
The oxide layer serves two functions. First, it acts as an insulator between
the substrate and selenium film to prevent charge carrier injection from the
electrode into the film [26]. Second, it provides an amorphous base onto
which the film can be deposited. The Al substrate was loaded into the
vacuum deposition chamber and heated to a temperature of 55° -65 ° C by
the substrate heater as described below.
The source material for the a-Se films were xerographic grade, liquid
quenched, vitreous selenium pellets obtained from Noranda Technology
Center, Pointe Claire, Quebec. The purity and chemical contents of the
pellets were verified by the supplier using optical emission spectroscopy.
The purity of the pellets was found to be 99.999%.
A NRC 3117 vacuum deposition system, shown in Figure 4.1, was
used to fabricate the a-Se films. The evaporation chamber was evacuated by
a diffusion pump until a pressure of —10-6 Torr was obtained. The Al
substrate was heated and maintained at a temperature above the glass
transition temperature for a-Se in order to produce films with good charge
transport properties [27]. The selenium pellets were contained in an open
stainless steel boat. A large ac current (100-150 A) was passed through the
boat to heat the pellets. The temperature was maintained at 270° C by
controlling the amount of current through the boat. At this temperature, a
deposition rate of about 2µm/minute was obtained. The substrate and boat
heaters were turned off when deposition was completed and the samples
were allowed to cool slowly before air was let back into the vacuum chamber.
44
The completed films were then allowed to age in the dark, at room
temperature, for a period of 2-3 weeks to allow their physical properties to
stabilize. Samples used for recombination measurements were peeled off
from the Al substrate so that both sides of the film were available for
illumination.
Reflector
T/C Substrate Heater Substrate
Quartz X-tal
T/C
1
_IShutter
• Se enium
tainless Steel Boat
Rotation 4— Platform
150A
Stainless Steel Base
11F Diffusion Pump
Gas
Figure 4.1 Schematic diagram of the vacuum deposition system.
In order to facilitate the TOF/recombination measurements, semi-
transparent Au electrodes were deposited on the samples. The deposition
was carried out in a Hummer VI sputtering system, shown schematically in
Figure 4.2. The sample was loaded into the sputtering chamber of the
Hummer VI which was then evacuated and flushed with argon until a
pressure of 70 millitorr was obtained. A large dc bias voltage (3000V) was
45
applied between the anode and cathode causing the Ar within the chamber
to ionize and form a plasma. The positively charged Ar ions were
accelerated towards the cathode where the Au target was located. The ions
dislodged Au atoms from the surface of the of the target which were
dispersed throughout the chamber and settle on the sample. Masks were
used to define the areas on the sample where the Au was to be deposited.
Cathode Shield
Substrate
Insulator
High Voltage
Argon ions Electrons
4, 4i
Cathode Vacuum ie.„—Chamber Target
Vacuum Pump
Anode
i3) Needle Valve
Argon
Figure 4.2 Schematic diagram of sputtering system.
In the present study, electrodes where sputtered on each side of the
sample so that each could be illuminated. The region outside of the
sputtered electrodes were masked with PVC electrical tape to prevent
photogeneration of carriers in the fringing fields during TP measurements.
The sputtered samples were then mounted onto cardboard backing and
46
electrical connections were made by attaching wires to the electrodes with
highly conductive silver paint.
4.3 Ambipolar Time-Of-Flight (TOF) Apparatus
Time-of-Flight transient photoconductivity (TOF-TP) experiments
were pioneered in the 1950s and 1960s by Brown [28], Spear [20], and
Kepler [29]. They were able to apply the technique to the study of a wide
variety of materials. The power of this experiment is that it allows for direct
measurement of charge carrier mobility. A simplified schematic of the TOF
experiment is shown in Figure 4.3.
The TOF experiment consists of measuring the transient photocurrent
that results when photoinjected charge carriers drift across a
semiconductor or insulator. The most common method of injecting charge
carriers into the sample is a short duration light pulse. The spectral
components of the light pulse must be matched to the energy gap of the
material being studied so that bulk generation of charges does not occur due
to weakly absorbed light components. A number of different sources have
been used to study different materials, and these include xenon flash
lamps[30], N2 flash lamps[31], nitrogen pumped dye lasers[32], and Q
switched ruby lasers[33].
47
Current
tc Time
Output
Figure 4.3 Generalized schematic of TOF experiment.
Variations on the TOF experiment have also been reported. These
include the use of different bias schemes (dc or pulsed bias). Advanced
application of the bias has been used to study the effect of negative bulk
charge on the charge transport properties in the sample[34]. Charge carrier
surface recombination has been examined by delaying the application of the
bias until after the carriers have been photoinjected. This allows the
carriers to interact before they are swept apart by the bias field[35].
A double photoinjection TOF technique was used by Dolezalek and
Spear[36] to study bulk recombination in orthorhombic sulphur crystals.
This experiment involved the photoinjection of one species of carrier followed
by a second injection, on the other side of the sample, of carriers of the
opposite sign. The carriers underwent recombination as the charge packets
drifted through each other. This was evidenced by a reduction in the total
48
photocurrent observed. The recombination experiment performed in the
course of this study is based on the technique used by Dolezalek and Spear.
A schematic of the ambipolar TOF apparatus used was shown
diagrammatically in Figure 4.4. A high voltage bias, V, was applied to the
sample which is grounded through a sampling resistor, RSAMPLE. Following
the application of the bias voltage, mobile charge carriers were photoinjected
into the sample, by the laser only, where they drifted across the sample and
induced a current in the external circuit. The transient current through
RSAMPLE was then measured.
In order to perform the recombination experiment, a second
photoexcitation source was required. This source was used to inject charge
carriers of the opposite sign into the other side of the sample. The xenon
flash was triggered and a negative charge packet was photoinjected into the
sample. While the negative charge packet is drifting towards the positive
electrode, the laser was triggered and injected a positive charge packet
which started to drift towards the negative electrode. The oppositely
charged carriers drifted towards each other and underwent recombination as
the respective charge packets passed through each other. The
recombination event was witnessed by the decay in the external
photocurrent through the sampling resistor.
49
Fiber
tX ENON 'LASER
-Se
Diffuser 4-0-;
r-11 Pulse Bias Circuit
A
SAMPLE
•—g•
Xenon Flash
2
Trigger Signal Generator
CCD Camera O o O 0
U000 000 000
0000 0 0
0 0 0 0
tosc t:1-1- 10.
0 0 0 a a o 0000
0 0
Oscilloscope
Figure 4.4 Diagrammatic view of ambipolar TOF experiment apparatus.
4.3.1 Photoexcitation Sources
Injection of transient charges was accomplished through the use of
optical excitation. Both a xenon flash bulb and a nitrogen laser were used
as photoexcitation sources. The spectral outputs of these sources were
appropriate for use with TP measurements in a-Se alloys.
4.3.1.1 Xenon Flash Bulb Source
The xenon flash source made use of short arc length (1.5 mm) xenon
flash bulbs manufactured by EG&G and Hammamatsu as quiet xenon flash
50
bulbs. The circuit used for obtaining short duration light pulses from the
xenon bulbs is shown in Figure 4.5. The high voltage capacitor, CH, was
connected across the electrodes of the xenon flash bulb. This capacitor was
charged up to 1600V. A pulse transformer was connected to trigger probes
in flash bulb. Capacitor CT was connected in series with a silicon controlled
rectifier (SCR) to the primary of the pulse transformer and was charged to a
voltage of 170V. When the SCR was triggered by the triggering circuit, CT
was discharged through the pulse transformer and a high voltage spike (5-7
kV) was applied to the trigger probes of the xenon flash bulb. The high
voltage spike caused the xenon gas in the spark gap of the flash bulb to
ionize, which in turn lowered the impedance of the spark gap. When the
impedance in the gap had been lowered sufficiently, CH discharged through
the spark gap providing the light pulse. The light from the xenon flash bulb
was passed through a CuSO4 solution filter to remove the undesirable red
wavelengths. These wavelengths would have resulted in bulk generation of
carriers in the samples. The xenon flash bulb circuitry was contained within
well grounded shielding, and RF filters and optocouplers were used to
prevent high-frequency transients from feeding back into the measurement
systems.
The output pulse from the xenon flash circuit was measured with the
reverse biased p-i-n photodiode circuit shown in Figure 4.6(a). The width of
the light pulse, which is shown in Fig 4.6(b), was —140ns at the half power
point. This is much shorter than the typical transit times experienced with
amorphous chalcogenide semiconductors.
51
CuS
O4
SO
LUT
ION
PA
RA
BO
LIC
R
EF
LEC
TO
R
H V
4- NV
LV
TRIG
GE
R
INP
UT
LV
Fig
ure
4.5
S
chem
atic
sk
etch
of
xeno
n fl
ash c
ircu
it.
Oscilloscope
47
a)
p-i-n Diode (S1722-02)
33n
b)
Figure 4.6 a) Reverse biased p-i-n measurement circuit. b) Light output Vs time for xenon flash. Horizontal axis: 200ns/div.; Vertical axis: 20mV/div.
4.3.1.2 Nitrogen Laser Source
The second photoexcitation source was a Laser Photonics LN 103 C
transversely excited atmospheric (TEA) nitrogen (N2) laser. This laser was
capable of providing a 250kW peak power output pulse with a duration of
300 ps at a wavelength of 337.1 Tim.
53
The TEA N2 laser is a 3-level laser system where the laser transitions
occur between the C31Iu (C-state) and the B31Ig (B-state) electronic states in
the N2 molecule, shown in Fig 4.7[37,38]. Electrons are excited from the
ground state to the C-state by impact collisions with external electrons. The
electron lifetime at the C-state is relatively short (-2ns) at atmospheric
pressures, while the B-state is metastable. Therefore cw operation is not
possible and TEA N2 lasers may only operate in a pulsed mode. In order to
achieve population inversion between the C-state and B-state, a very rapid
excitation method is required, in this case, a very fast electrical discharge.
2 15
flu
10
E(eV)
Electron Collision
1.0 2.0 Nuclear Seperation (A)
3.0
Figure 4.7 Potential energy curves for lowest triplet states in N2
molecule [37].
Figure 4.8 shows a simplified schematic circuit for the excitation of a
TEA N2 laser. This circuit makes use of the Blumlein excitation method.
Initially Ci and C2 are charged to the high voltage (HV) potential (10-20kV).
The electrodes in the laser channel are effectively shorted by an inductive
lead. When the spark gap is triggered, Ci is rapidly discharged through the
54
gap. The inductance in the loop is such that a damped oscillation occurs in
the circuit, and a voltage reversal appears on Ci. This causes an overvoltage
and electrical breakdown in the laser channel. With the electric field
transverse to the electrodes, the discharge is so fast that atmosphere glow
discharge and laser action occur on the order of 10-9s.
HV
Trg.
Spark Gap
TLaser Head
C2
Figure 4.8 Blumlein circuit used for rapid excitation of N2 laser.
The LN 103 C laser is triggered by two separate I IL pulses. An
initial pulse of at least 100ns duration must be applied to the Trigger Reg
input of the laser in order to charge it. A second pulse of at least 100ns
duration must be applied to the Trigger Low input, between 30 and 50 i.t.s
later, to fire the laser. If the second pulse does not occur within 50 i.ts, the
laser will self-fire. Figure 4.9 shows the timing requirements to fire the
laser.
55
4- 10011S
+5V
Laser Self Fires
Triggering Window
Trigger Reg
Trigger Low
—mot 4-- 100ns
+5V
0 us 30 us 50 us
Figure 4.9 Triggering requirements for the LN 103 C N2 laser.
4.3.2 Timing Signal Generator
A TTL timing signal generator was used to provide the required
timing control signals for the TP experiments performed
(TOF/Recombination as well as the IFTOF measurements to be discussed
later). The timing signal generator made use of TTL 74123 monostable
multivibrators and TTL 7476 J-K flip flops to produce the control signals
X2, Xi, and Xh which are shown in Figure 4.10. A schematic of the timing
generator is shown in Figure 4.11.
Signal Xi controls the application of the bias voltage used in the TOF/
Recombination experiment. X2 deactivates the amplifier protection circuitry
after the RC transients, created by switching the bias voltage across the
sample, died out. When the measurements are complete, X2 reactivates the
amplifier protection circuitry before the bias voltage is removed by Xi. The
Xd signal is used as a trigger for a set of digital delays that control the
56
triggering of the oscilloscope and photoexcitation source used in the TOF
experiment. The oscilloscope is triggered slightly before the photoexcitation
source so that the baseline is visible before the TP waveform is viewed. In
the recombination experiment, where two photoexcitation sources are used,
the digital delays are used to ensure that the two sources are not triggered
at the same instant, i.e. so that the oppositely charged carriers are not
injected into the sample at the same time. Finally, the signal Xh is used in
the IFTOF experiment. This signal controls the application of the switched
bias source used for IFTOF measurements. The details of the timing
requirements for the IFTOF experiment will be discussed later.
2.2ms 2.2ms
4— 2.2 ms
tic =3.5 - 75 us
t4 =tlaser
-0' t D1
T2
tosc t=0 for IFTOF Time
X h
Figure 4.10 Timing signals from Timing Signal Generator. tND, ATi, AT2, and AT3 are adjustable as shown in Figure 4.11.
57
5V
4K7 4K
lop'-
11
B
CLR
0 >
1,
R/C
us
C
0 3
0
A
5V
OK
K
-i---141-1-4 5V
20K
K
20K
K
95
V
03V
Qsv
B
CLR
R/C
ti
c T
3 5-
A
3
22K
.2 70r
A
CLR
B
A
0
5V
0
4K
7
lOp
r
3
AB
CLR
0 3
a/c
r:
0
A
B
CLR
R/C
CQ
T2
0A
A
—C
r-T
T"
lOa
r IA
, Igo
r
B
CLR
0 3
+
••4
R/C
1
.1
C
AT
I 53
A
AB
CLR
0
4K
7
...a 1
0p
r a/c
ft 1.0
5V
(ii‘r
0
CLR
4K
7 10p
r R
/C
a.
C
B
7
B
CLR
0
R/C
Ft;
A
3-6
3-
3
o]
Y
3
05V
CLR
0 3
R/C
-C
-C
.IK7
A
3V
A B
CLR
0 3
-
R/C
W
C
A B
07
SE
1
J
0
C C
LK
CK
o
CLR
0 5V
••••••••-‹
c —
C
5V
ASE
TJ
0
cLK
K
0
CLR
>—
=1
x 1
a--
--"D
X2
3
7K5
in,
B
C C
LR
R/C
tiA
a 5 a
B
CLR
2
R/C
I.J
C c
.27)." A
V
D.
3
Q3V
fa--C
ASE
T 0
C C
LK
O•
CK
0
cia
3
3
Fig
ure
4.1
1 C
ircuit
dia
gra
m
for TT
L trig
ger sig
nal g
enerato
r.
D)
v
0 X
4.3.3 Digital Delays
The timing delays required for triggering the oscilloscope and
photoexcitation sources were provided by Berkeley Nucleonics Corporation
(BNC) Model 7010 and 7065 Digital Delay Generators (DDG).
The Model 7010 DDG consists of two count chains and various other
support circuits. The first count chain is used to develop the time base
signal that determines the resolution of the DDG. The resolution of the
Model 7010 varies from 0.1 µs to 1 ms giving a range from 0.1 la to 99.999 s.
The second count chain uses the time base signal from the first count chain
to generate the delay signal. The support circuits are used for control
operations, pulse shaping, and other functions as needed.
The Model 7065 DDG operates in a manner very similar to the Model
7010. The major differences between the two units are their resolution and
range. The Model 7065 has a resolution of 1 ns and a range from 1 ns to
999.999 gs.
4.3.4 Bias Application Circuit
A pulsed bias circuit, shown in Figure 4.12, was used to prevent the
build up of bulk space charge in the sample during the time that the bias
voltage is applied in the TOF/Recombination experiment. The bias voltage
was supplied by an EG&G Ortec 556 high voltage supply. The output
voltage from the supply was switched across the sample by a SPST reed
59
relay (EAC 061AY*050CAA). The coil of the relay was energized by the
collector current of a 2N3904 BJT. A 1N914 diode and a capacitor were used
to protect the BJT from an overvoltage state when the current through the
relay coil was interrupted. The pulse bias circuit was well shielded and was
further isolated from the experiment control circuitry by use of a HCPL-2601
opto-isolator on the trigger input. This was done in an attempt to reduce the
feedback of transients into the TOF/Recombination system. The circuit was
activated by a standard TTL pulse applied to the Trigger In input.
9V I --11011F
270 5.6k
HPCL-2601 2N3904 lk
1.8k
1.5k
2N3904 1N914
OnF
High Reed Voltage Relay
In
Figure 4.12 Schematic of pulsed bias application circuit.
4.3.5 Voltage Follower Circuit
+5V
To Sample
The voltage follower circuit shown in Figure 4.13 was used to drive
the long BNC cables that were used to connect the sample and the sampling
resistor to the input terminal of the oscilloscope. A two-stage follower circuit
based on a 2N5484 JFET was used to provide a high input impedance so
that loading effects on the TP signal were minimized.
60
A relay based protection circuit was incorporated to protect the
voltage follower from the large transient voltage that occured when the high
voltage bias was switched across the sample. The protection was provided
by a normally grounded SPDT relay (Potter & Brumfield JWD-172-1). The
relay was used to connect the sample and sampling resistor to the voltage
follower after the displacement currents had time to decay. The protection
relay was triggered by timing signal X2.
X2
4.7k
From () Sample
56pF 2N3904
1_
1N914 56
JWD-172-1
9 V 1100u_a_
T 12vT T 2N5484
1 M
2N2222A
—"Out
560
Figure 4.13 Schematic of voltage follower with protection relay.
4.3.6 Data Acquisition System
The TP waveforms were displayed on a Tektronix 2467B, 400 MHz
single shot bandwidth, analog oscilloscope. The waveforms where then
stored by making use of a DCS01 CCD Camera Data Acquisition System.
This system consists of a Tektronix C1002 charge-coupled-device (CCD)
camera, an IBM compatible PC DX01 video frame storage card, and the
DCS01 software for control and waveform manipulation. The data
acquisition system is shown in Figure 4.14.
61
DXO1 Video Framtlag=g1=E1 Storage Board (in computer)
Panasonic Video Monitor
DCSO1GPH Software
Video Signal
Trigger
V
Computer
Tektronix 2465A/2467B Oscilloscope
0 0 0 0 0 0
00000 000 000 O 000 0 0
o 0 0 000
000000
0 0 0 n° Co° " 3° O o o 0
C1002 CCD Camera
Figure 4.14 Diagrammatic layout of data acquisition system. The system features include the C1002 CCD camera, Tektronix 2467B oscilloscope, an IBM compatible PC to house the frame storage board and run the DCS01 software, and the Panasonic VW-5350 video monitor.
The CCD camera was mounted to the front of the oscilloscope by an
adapter that blocked out external light. The imaging device in the camera
has a sensivity of 2 lux and consists of a planar pixel array. The dimensions
of this array are 490 pixels vertical by 284 pixels horizontal. Light from the
oscilloscope CRT is focused onto the imaging device and the camera converts
the light signal into a RS170 (NTSC) video signal. This video signal is then
passed to the DX01 frame storage board. In order to capture a waveform,
DCS01 software instructs the frame storage board to acquire the video
frame. The frame storage board then converts the captured frame into a 512
by 512 data point matrix which represents the target pixels. The light that
strikes each pixel is recorded in one of 256 gray scales. The DCS01 software
assumes a Guassian profile of the light distribution from the oscilloscope
CRT and from these determines the center of the beam trace. This finally
62
results in a digitized waveform with a record length of 512 data points and a
vertical precision of 12 bits. The overall system accuracy is claimed to be at
least 99%.
The waveforms can be visually monitored on the Panasonic VW-5350
video monitor. The DXO1 frame storage board can pass the RS170 video
signal to any device that will accept it as a video input.
The DCS01 software is a menu driven data acquisition package that
is used to acquire and digitize the signal from the CCD camera. The
software provides calibration routines that can be used to correct for
systematic optical and linearity errors inherent with the camera/oscilloscope
combination. Waveform measurements such as rise and fall times,
frequency, and duty cycle are available as soon as the waveform is acquired.
DCS01 also contains built-in functions to perform numerical calculations
such as waveform addition or subtraction, and integration on acquired
waveforms. The data acquired with the DCS01 software may be stored in
either binary or ASCII formats. This allows for the export of data to other
software packages for further manipulation.
4.4 Interrupted Field Time-of-Flieht (IFTOF) Apparatus
The charge carrier deep trapping lifetime, t, in high resistivity solids
has been measured conventionally by looking at the exponential decay et of
the standard TOF waveform. This method failed with many materials
however because they exhibited a non-exponential decay. This may be
attributed to factors such as space charge build up effects, Poole-Frenkel
barrier reduction effects, or sample inhomogeneity effects. This method also
fails with materials that have long deep trapping lifetime with respect to the
carrier transit time. In these specimens, the TOF photocurrent waveform
does not display a significant decay while the carriers are crossing the
sample and the lifetime cannot be accurately determined.
These limitations in measuring the charge carrier lifetime can be
overcome by the Interrupted Field Time-of-Flight (IFTOF) technique. This
technique has been used successfully by Spear and co-workers to measure
the charge carrier lifetimes in orthorhombic sulphur crystals[39] and a-
Si:H[40] and by Kasap and co-workers in a-Se alloys [27, 41]. The IFTOF
technique involves interrupting the transit of charge carriers as they cross
the sample in the conventional TOF experiment by removing the applied
bias field at some time Ti. Following an interruption time t1, the field is
reapplied at T2=Ti+ti, and the remaining charge carriers are removed from
the sample. A comparison of the standard TOF experiment and the IFTOF
experiment is shown in Figure 4.15. Figure 4.15 (a) and (b) represent the
timing sequence for applying the bias voltage and the resulting photocurrent
waveform for the TOF experiment while Figure 4.15 (c) and (d) represent
those for the IFTOF case. The charge carriers drift a distance x=TiLitt
(where L is the thickness of the sample and tt is the carrier transit time) into
the sample before the bias is removed. The carriers interact with the deep
traps located at x during the interruption time ti. The number of carriers
that become trapped during ti will be reflected in the recovered photocurrent
signal at i(T2). If a single mean free carrier lifetime can be assigned to the
64
v(t) photoexcitation
(a)
i(t) A
time
v(t) A
time (b)
photoexcitation
i(t) •
ti
po. T 2 time
(c)
time (d)
Figure 4.15 (a)Timing sequence for the application of bias voltage in TOF experiment and (b) the resulting photocurrent waveform. (c)The timing signal for the application of the bias in the IFTOF experiment and (d) the resulting IFTOF photocurrent signal.
65
the bias voltage from on/off or off/on produces a large displacement current
signal which decays with the time constant RCs. The magnitude of the
signal could be several hundred volts depending on the bias voltage being
used. This signal is several orders of magnitude larger than the resulting
photocurrent signal and would make it unusable. The displacement current
signals may also be damaging to any electronics used in the detection of the
photocurrent signal. Therefore, some method must be used to eliminate the
displacement current signals to successfully make use of the IFTOF
technique.
HV Switch
Displacement Current Signal -300V
—300V
J -20mV
Photocurrent Signal
Figure 4.16 Large displacement current signals are produced when the high voltage bias is switched on and off. This signal must be eliminated for the IFTOF experiment to be successfully implemented.
A number of different methods have been previously used to
implement the IFTOF technique. A complementary bias technique has been
reported by Kasap and co-workers[41]. During the 1960s, Helfrich and
Mark [42] used a resistance ratio bridge and floating bias supply to
eliminate the displacement current effects in transient space-charge limited
67
measurements. The major disadvantage with this technique is that only
half of the bias voltage appeared across the sample. This problem can be
overcome by making use of a Schering bridge network [43]. A diagrammatic
representation of the IFTOF experimental apparatus, based on the Schering
bridge network, is shown in Figure 4.17. The N2 laser source, trigger
generator, digital delays, and data acquisition system have been previously
discussed in Sections 4.3.1.1 to 4.3.1.3 and 4.3.1.6.
Laser
HV Switch
Xtrg A Xh
td
Fiber
a-Se
Trigger Signal Generator
td
CCD Camera
•0 . * *
• • 0 0 0 . 13000 COO 0013 . 0000 0 0
0 0 0 MI 0 0
• . .0 Oon
Oscilloscope
Figure 4.17 IFTOF experiment schematic based on the Schering bridge network.
68
4.4.1 Schering Bridge Network
A schematic diagram of the Schering bridge and high voltage supply
is shown in Figure 4.18. Two nulling capacitors are required, CNS and CN1,
to eliminate the switching transients between points A and ground. The
floating high voltage supply introduces 'stray' capacitances to ground,
represented by Ci and C2, and these must be taken into account when
balancing the bridge. CI simply adds to CNs so that the balance condition is
C2-I-CNS=CS. CN1 is used to null C2.
Figure 4.18 Schematic of Schering bridge network used to implement displacement current signal free IFTOF measurements.
Good I-mode photocurrent waveforms are obtained by optimizing two
opposing conditions. The I-mode signal measured between the bridge output
and ground is given by vo(t)=R'i(t) where i(t) is the transient photocurrent
and R' is the effective sampling resistance given by R'=RN111/(2RN-FR1). The
optimum output is obtained when Ri is larger than RN which maximizes R'.
This condition must be balanced against the fact that for good I-mode
signals, the time constant of the circuit must be much less than tT so that
69
the signal is not integrated. Laplace analysis of the bridge network,
including the addition of a capacitance CIN across Ri to account for the input
capacitance of the amplifier, relates Vo(s) and I(s) as follows
Vo (s) = [R7 (1 + sR'C')]I(s) (4.2)
where C'.2C1N+Cs+CNi is the effective integrating capacitance. Therefore, in
I-mode operation, the time constant, R'C', must be less than tT.
The variable components CN1, CN2, and RN are used to adjust the
bridge to an optimal balance condition. However, since the Schering bridge
is floating, it is very difficult to balance the bridge so that no displacement
current signal appears. The differences in the high frequency permittivity of
selenium and the ceramic capacitors used to null the bridge also creates
difficulties in balancing the bridge. In order to extract the photocurrent
signals, the following procedure had to be used. First, the bridge was
balanced to a point where the magnitudes of the displacement current and
photocurrent signals were similar. Next, two measurements were
performed, one with photoexcitation and one without. The two resulting
waveforms were acquired and digitally subtracted from each other using the
DCS01 software to provide a net displacement current free photocurrent
signal. This method has been used to extract displacement current free
photocurrent signals in photocurrent reversal measurements on a-Si:H films
[44].
70
4.4.2 High Voltage TMOS Switch
The switching of the bias voltage was accomplished by making use of
two n-channel 1kV TMOS transistors in a totem pole configuration shown in
Figure 4.19. The high voltage source was provided by Eveready dry cell
batteries. The bias voltage is varied by simply changing batteries. The
gate-source voltage for switching each TMOS transistor is provided through
CMOS optocouplers (HCPL-2200) powered by floating 9V batteries. The
floating batteries were used because the maximum gate-source voltage the
TMOS transistors can sustain is ±20V. Common-emitter push-pull driver
circuits were added to the gates of the TMOS transistors to source and sink
gate charge as fast as possible. The switching time for this circuit is
approximately 150 ns. This switching time is considerably shorter than the
transit times encountered in this study.
— To Schering Bridge
Figure 4.19 Schematic of TMOS high voltage switch.
71
The trigger signal for the high voltage switch is provided by the Xh
signal from the trigger signal generator discussed in Section 4.3.1.2. The
interruption time t1 is controlled by varying the RC combinations of the TTL
74123 monostable multivibrators used in the trigger signal generator.
4.5 Summary
In this chapter, a brief description of the sample preparation was
given. Following the thermal evaporation of a-Se alloy pellets onto Al
substrates, Au electrodes were sputtered onto the samples to facilitate
transient photoconductivity measurements.
A TOF transient photoconductivity apparatus was also described.
This apparatus allows the charge transport properties of high resistivity
solids to be examined. By adding a second photoexcitation source and an
extra digital delay, the TOF apparatus can be used to study bulk
recombination in these solids.
Finally, an IFTOF apparatus was introduced to study deep trapping
lifetimes in high resistivity solids. The technique presented allows bias
voltages of up to 1kV to be used.
72
5 RESULTS AND DISCUSSION
5.1 Introduction
The previous chapter described the experimental details of the
ambipolar TOF and IFTOF measurement systems that were used during the
course of this work. This chapter presents the experimental results obtained
using these techniques on chlorinated a-Se:0.2%As electrophotographic films
suitable for x-ray electroradiography. Amorphous Se:0.2%As doped with Cl
is normally referred to as stabilized Se.
It is important to know the charge transport and deep trapping
properties of the materials being studied before performing the ambipolar
recombination experiment. Initially, conventional TOF measurements were
performed to study charge transport in the a-Se films. Next, IFTOF analysis
was used to provide information about the deep trapping that occurred in
the samples. Finally, the ambipolar TOF technique was used to analyze the
recombination effects in the films.
5.2 Charge Transport Study
The assumption that the internal field in the sample, set up by the
applied bias voltage, is uniform must be made in order to perform TOF
73
analysis. When the small signal conditions are met, the field is negligibly
perturbed and remains constant. This is shown experimentally by the
almost rectangular shape of the photocurrent signals for a-Se samples with
long carrier lifetimes. This is the expected shape for a constant field and
drift mobility.
Tabak and Scharfe[45] have shown that the internal field will remain
constant and uniform following the bias application until a transition time
tsc is reached. The transition tithe for a-Se is typically on the order of 100
ms. After tsc, a bulk charge builds up within the sample, due to charge
injection from the contacts, and the field becomes non-uniform. This non-
uniformity may be determined from the Poisson equation dF/dx=p/e.
Photoexcitation in the measurements completed for this work took place a
few milliseconds after the application of the bias voltage to preclude these
field perturbations.
Repeated measurements may result in a build up of trapped bulk
charge in the a-Se film due to the trap release time being very long. This
trapped bulk charge will distort the applied field, again as determined by
the Poisson equation. This can be avoided by performing single shot
measurements and by dark resting the samples in a short circuit condition
between measurements to discharge any bulk charge.
Figures 5.1(a) and 5.1(b) shows the I-mode TOF waveforms for holes
and electrons respectively. The interaction between the drifting holes and
deep traps is minimal. This is evidenced by the lack of any decay in the top
of the hole photocurrent waveform. The electron waveform however, does
74
show some exponential decay. The nature of this waveform can be described
by Equation 3.10 which is restated here in slightly different form as
Iph (t) = Ic, exp[--t ] for t < , (5.1)
where Io is the initial value of the photocurrent and ti is the carrier deep
trapping lifetime. The electron lifetime for this sample was estimated to be
Te.850 gs from this waveform.
tT
4
(a)
tT
12 Time (go 0 100 200 300
(b)
Time (i.ts)
Figure 5.1 I-mode TOF waveforms for a 195.1 gm a-Se:0.2%As film for (a) hole transit and (b) electron transit. The transit times are indicated by tT.
The relationship between the carrier mobility µ. and the measured
transit time tT is given by
LztTV ,
75
(5.2)
20
15
10
5
0 0.000 0.001 0.002 0.003
1/Voltage (V-1)
0.004 0.005
Figure 5.2 TOF plot of transit time versus 1/voltage for holes in a-Se:0.2%As film showing j.th =0.125 cm2V-1s-1.
400
350
300
250
.1" 200
150
100
50
0 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030
1/Voltage (V-1)
0.0035
Figure 5.3 TOF plot of transit time versus 1/voltage for electrons in a-Se:0.2%As film showing ge=0.0034 cm2V-is-1.
76
where L is the thickness of the film, and V is the applied bias voltage.
Figure 5.2 is a plot of tT versus V-1 from TOF transit time analysis for hole
transport The slope of the straight line yields a hole mobility of i.th = 0.125
cm2V-1s-1. Similarly, Figure 5.3 shows an electron mobility of lie = 0.0034
C1112V-IS-1 .
When the drift mobilities of both holes and electrons are calculated
using Equation 5.1 and plotted as a function of electric field, the behaviour
in Figure 5.4 is observed. The hole mobility shows no observable field
4
1.000
0.100
0.010
0.001 1.E+5 1.E+6
F(Vnr')
•gh
1.E+7
Figure 5.4 Plot of hole and electron mobility as a function of the applied electric field. The hole mobility shows no observable field dependence. The electron mobility shows a very slight field dependence of the form peocFo.o4.
77
dependence. However, the electron mobility shows a very slight power law
field dependence of the type 1.1.eccF° where n was experimentally determined
to be n-0.04, which is very small. The exact nature of the electron mobility
field dependence is not yet fully understood. However, for the limited range
of fields used in this work, Ph and ge have both been considered field
independent.
5.3 Charge Trapping Study
The carrier mobility does not completely characterize the charge
transport process in semiconductors. As the carriers drift across the sample,
some of them become trapped in deep localized states within the mobility
gap. Release times from these deep traps is much longer than the release
times from the shallow, mobility controlling traps. This is due to the greater
potential barrier over which the carriers must be thermally excited.
The carrier lifetime ti can be used to provide a measure of how many
carriers are lost from the transport band through deep trapping. This is
extremely important to the recombination study described in the next
section where the trapping effect must be separated from recombination
alone.
The interrupted field time-of-flight experiment provides a means of
measuring the mean carrier lifetime by studying the fractional recovered
photocurrent as a function of interruption time. The measured photocurrent
78
is directly proportional to the concentration of free charge carriers and their
drift mobility. The photocurrent is given by
iph (t) = en(t)µF, (5.3)
where n(t) is the concentration of free carriers and F=V/L is the internal
electric field, which is assumed to be constant (and uniform). As discussed
in the previous section, 11 is a material property and remains constant with
electric field. Measurement of the photocurrent at times ti and t2, just before
and after interruption, therefore provides a direct measure of the fraction of
recovered charge carriers since i(t2)/i(tl)=n(t2)/n(tl). For a single species of
deep traps with a well defined lifetime,
n(t i ) (t 2 — t i )] n(t2)
—ex —ti
(5.4)
Thus the slope of a semilogaritl-unic plot of i(t2)/i(ti) versus ti=t2-ti
gives the deep trapping lifetime. Charge carrier trapping occurs under the
zero-applied field condition, during ti, when using the IFTOF technique. As
such, the lifetime measured when using IFTOF analysis should be
independent of the applied bias voltage. A recent study using IFTOF
techniques has confirmed this fact [46]. There is nonetheless, an internal
field due to the space charge of the injected charge carrier packet. This
internal field is much smaller than the applied field, as the injected charge
is much smaller than CsV where Cs is the sample capacitance.
Figure 5.5 shows a typical IFTOF waveform with i(ti) and i(t2) clearly
discernible. IFTOF measurements were performed on a 195 p.m chlorine-
79
doped a-Se:0.2%As film with an applied bias of 90 V for hole transport and
300 V for electron transport. The interruption time was varied and for each,
a measurement of i(ti) and i(t2) was made. The results of these
measurements are shown in the semi-logarithmic plots of Figures 5.6 and
5.7. The hole lifetime for this sample was found to be th=540.3 ;a and the
electron lifetime is '4=787.2 p.s. These lifetimes seem reasonable when
compared to the conventional TOF waveforms shown in Figure 5.1. The hole
TOF waveform show little or no decay since tT « Th. The electron TOF
waveform on the other hand exhibits an exponential decay. This is to be
expected as tT is of the same order as Te.
0 5 1/ 715 80
i(t2)
8 5 Time (m)
Figure 5.5 Typical IFTOF waveform for holes in a 195.1 p.m a-Se:0.2%As film showing i(ti), i(t2), and t1.
The exponential decay that the photocurrent undergoes, as shown in
Figures 5.6 and 5.7, is predicted by Equation 5.4 and more generally by
Equation 3.25 with 'CR-->00. The experimental verification of the exponential
decay of the photocurrent was described previously by Polischuk[47,48].
80
This can be used as evidence that a single species (i.e. one with a single
trapping time) or set of traps, one for holes and another for electrons, is
responsible for deep trapping in a-Se alloys.
The product of the carrier mobility and the trapping lifetime wc is
known as the range of the carrier. The pr product is a measure of the
average drift length for a carrier per unit electric field before the carrier
becomes trapped. The range of the carriers is an important consideration for
the recombination experiment where the only decrease in free carrier
concentration should be due to recombination and not trapping. For the
samples used in the present study, the hole wc products are such that the
holes lost to trapping are insignificant when compared to the holes which
undergo recombination. However, the electrons have a more limited range
and electron trapping must be taken into account in the recombination
study.
5.4 Ambipolar Recombination Experiment
Processes such as electron-hole recombination play an important role
in the interpretation of the electronic properties of low mobility solids.
Experimental studies on orthorhombic sulphur crystals [36] and PVK:TNF
organic polymer films [49] have suggested that bulk recombination of
electrons and holes in low mobility solids is a diffusion controlled process
that agrees with Langevin's theory of recombination for gaseous ions [50,
51]. It has further been suggested that this diffusion controlled
recombination might be a universal property of low mobility solids.
82
The theory proposed by Langevin was based on the assumption that
the mean free path of the carriers is small when compared to the
recombination radius rc. The latter is defined as the distance where the
potential energy due to Coulombic interactions between the hole and
electron is equal to kT where k is the Boltzmann constant and T is
temperature in degrees kelvin. rc is given by
e2
rc — 47ccoEykT
(5.5)
where Er is the relative dielectric constant of the medium. Assuming Er-6.6,
for a-Se rc-86A at room temperature. The mean free path of carriers, a, at
the mobility edge in a-Se has been estimated to be a.5-10A. It seems likely
that Langevin recombination behavior will be evident in a-Se since rc»a.
When an electron becomes trapped within a radius rc in the Coulomb
field of a hole, it will lose energy due to phonon interactions and
recombination will become highly probable. The recombination coefficient Cr
is directly proportional to the recombination cross-section ar and the relative
velocity of the electron and hole in the Coulomb field vr or Cr=0Arr. The
capture cross section, ar, is simply the surface area of a sphere with radius rc
surrounding the hole. The relative velocity, vr, can be found from the
relation
yr = Fc (14 +
where Fc is the Coulomb field. This leads to
83
(5.6)
mobility. This leads to a photocurrent signal where the current due to the
hole packet "rides" on top of the electron current signal as in Figure 5.8(b).
Hole Injection time t= th
A
+ + ++ + + +
ip h
(a)
lectron Injection time t= to
x4
x=L
(b)
Figure 5.8 (a) Simplified schematic sketch of double injection TOF technique for studying recombination and (b) the resulting photocurrent.
85
A typical photocurrent signal observed during the ambipolar TOF
recombination experiment is shown in Figure 5.9.
Hole Photocurrent
Phot
ocun
ent
(arb
. uni
t
Double Flash Photocurrent
6 Ti (el
100 200 300 400 Time (vs)
Figure 5.9 A typical photocurrent waveform from ambipolar TOF experiment. Insert shows an expanded view of the photocurrent due to the hole packet "riding" the top of the electron packet signal.
Consider Figure 5.10 where a hole charge packet drifts towards an
electron packet under the influence of an external field F. The two packets
meet each other at some time ti and have completely passed through each
other by time t2. Figure 5.10 illustrates the recombination events.
Considering hole drift with respect to the electron packet, at time ti, the hole
packet is at xi and recombination is just about to begin. At time t, the hole
packet is totally within the electron packet and the hole concentration is
decreasing due to recombination. Recombination stops when the hole packet
86
exits the electron packet at X2 at time t2. If Sp and 8n are the changes in the
hole and electron concentrations due to recombination during a small
p
t+ St
LI)2 t2
1 i2
Figure 5.10 Schematic diagram of hole and electron packets passing through each other. It is assumed that n(x,t)»p(x,t).
interval of time St while the packets are interacting At=t2-t1, then the rate of
recombination is,
Sp Sn St = =—Cr n1).
(5.9)
Since Equation 5.9 is symmetrical in both p and n, the concentration
changes from ti to t2 follow
pi I)
87
(5.10a)
or
78n j— = - Cr SP6t'
P2 In— = 1)1
1n = ni
(5.10b)
(5.11a)
(5.11b)
where p and if are some mean value of p and n in At. If p«n at all times so
that 71«n, then Equation 5.11 implies that n2-ni (i.e. there is no significant
change in n) and that the recombination primarily affects p. This is
attainable by maintaining the hole and electron photocurrent approximately
equal since 1.1.«µh which means n»p. Using Equation 5.11a, II can be
substituted for as follows. We can define the width of the electron packet as
AX=X2-X1 and therefore ii-a./(eAx). where ae is the injected negative charge
per unit area. At is related to Ax through the relative velocity of the electron
and hole charge packets where At=Ax/[(.thilte)F]. Substituting for n and At
in Equation 5.11a leads to
In P2 — CrogeP1 'e(Ete )F •
(5.12)
Both F and ae are experimentally determined parameters inasmuch
as F=Vo/L and ae is obtained by integrating the electron photocurrent in the
absence of hole injection and dividing the integral by the electrode area.
During the transit of the electrons across the sample, a small fraction of the
88
electrons may be lost to deep traps within the mobility gap of the material.
This can be accounted for if the electron deep trapping lifetime tie is known
from the IFTOF analysis in the previous section. If Q. is the integrated
electron photocurrent without hole injection then
— exp(— t
+ t2 )
Q. 2t. A t T
exp(---t) (5.13)
where A is the electrode area. There is an upper and lower limit to ae. The
lower limit is due to the n»p requirement. The upper limit is the small
signal TOF requirement so that the internal field F is not space charge
perturbed. Since F remains constant throughout the experiment, the hole
and electron drift velocities remain constant and Equation 5.12 may be
rewritten as
In 'h2 CA
e(11. I-10F (5.14)
If the recombination coefficient is the Langevin coefficient, given by
Equation 5.8, then a substitution into Equation 5.14 will cause the
mobilities to be canceled and simply gives
i h2 In — 1h1
I a. cot, F
(5.15)
and a plot of ln(ihilim) versus ae/F should be a straight line whose slope is
simply -1/(eoer). Thus the fractional change in the hole photocurrent due to
89
recombination is independent of the relative drift mobility of holes and
electrons. This is due to the fact that while the Langevin recombination
coefficient is directly pr'oportional to the relative mobility gr.(gh+ge), the
time duration of the overlap of the electron and hole packets is inversely
proportional to gr.
Figure 5.11 shows a semilogarithmic plot of the experimental ih2/ihi
values versus oe./F where ae, the injected negative charge, and F, the applied
electric field, are user defined experimental parameters. As shown in Figure
5.11, the experimental recombination data confirms the expected Langevin
recombination behaviour as predicted by Equation 5.15. The slope of the
line gives a value of er=6.35. This is very close to the value of er-.6.6 found
from capacitance measurements. This line was fit using the method of least
squares. The correlation coefficient, r, for this line was calculated to be
r=0.94. This verifies statistically the goodness of fit of the regression line.
It is also apparent that there is some scatter in the data but that over
a wide range of ae/F values, the best fit confirms Equation 5.15.
Experimental scatter is due to cre which involves integrating the electron
TOF photocurrent signal in the absence of injected holes. Variations in the
xenon flash output (about 5-15%) cause cre to be scattered by about this
amount. In addition, there are the usual experimental errors in the
measurement of ihdihi and the sample thickness L.
90
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6 00
• Sample 1 (1...1771.un)
ASample 2 (L=1951.tm)
0.5 1.0 1.5 2.0 2.5
CL/F (x10-11Cm'IV -I)
3.0 35
Figure 5.11 Semilogarithmic plot for ih2/ihi versus ae/F for two different stabilized a-Se samples. The slope of the line gives a relative dielectric constant of er=6.35. Correlation coefficient r=0.94.
5.5 Summary
Charge transport, charge trapping, and electron-hole recombination
were examined in chlorinated a-Se:0.2%As electroradiographic films. TOF
measurements were used to study charge carrier mobility. The hole mobility
was found to be 111=0.125 cm2V-1s-1 and the electron mobility was µe=0.0034
cm2v-i s Both hole and electron mobilities were relatively independent of
the applied field.
Deep trapping was investigated by using the IFTOF technique. The
exponential decay of the recovered photocurrent as a function of the
91
interruption time suggests that deep trapping in a-Se is due to a single
species of localized traps within the mobility gap. Combining the results of
the TOF and IFTOF measurements yielded the p:r product or range of the
carriers. This property of the material determines how far a carrier will
travel before being trapped as a function of the applied field. The hole range
was wrh=67,54x10-6 cm2V-1, and the electron range was j.tte=2.68x10-6 cm2V-1.
For the samples being studied, the range of the electrons was such that the
electron trapping effect had to be taken into account during the
recombination experiment.
A double flash ambipolar TOF technique was used to study electron-
hole recombination. The results of the study were in agreement with those
predicted by the Langevin recombination theory. The predicted Langevin
recombination coefficient was Cer=35.2x10-9 cm3s-1. The experimentally
determined Langevin recombination coefficient was CrE=36.6x10-9 cm3s-1.
This result implies that the mean free paths of the carriers are very short
compared to the critical recombination radius. This type of recombination
could be a general property for those materials in which the mean free path
is much shorter than rc.
92
6 CONCLUSIONS
Three different variations of the transient photoconductivity
measurement were used in completing this work. These were the
conventional time-of-flight (TOF), the interrupted field time-of-flight
(IFTOF), and the double flash, ambipolar time-of-flight techniques. These
techniques were applied to chlorinated a-Se:0.2%As electroradiographic
films to study charge carrier transport and recombination. The TOF and
IFTOF experiments were used to study charge carrier drift mobility and
deep trapping lifetime. The ambipolar TOF experiment was used to
examine charge carrier recombination. The combined results from these
three experiments can be used to provide an overall picture of charge carrier
transport in applications, such as electroradiography, where both electrons
and holes are involved.
Considerable effort was put into the design of the ambipolar TOF
experimental apparatus and into the development of a method to analyze
the results from this experiment. The essence of the ambipolar TOF
measurement involved photoinjecting oppositely charged carriers on
opposite sides of a sample. The two injected charge packets drifted towards
each other under the influence of an applied electric field. As the two
packets passed through each Other, some of the carriers underwent
93
recombination. This recombination was evidenced by a fractional change in
the hole photocurrent.
The stabilized a-Se films were initially studied using the conventional
TOF method. These measurements provided a measure of the carrier drift
mobility as well as an indication of the amount of deep trapping expected.
The hole drift mobility, in the samples studied, was found to be
approximately 35 times larger than the electron mobility in the same
samples. The field dependence of the drift mobilities was also examined.
The hole mobility appears to have no field dependence at room temperature.
The electron drift mobility, on the other hand, shows a very slight field
dependence of the type geocF°•04. The origin of this field dependence is as yet
unknown but it is small enough that for a limited range of fields the electron
drift mobility can be assumed to be field independent.
The shape of the I-mode TOF waveforms can be used as a rough
indication of the amount of carrier deep trapping. There was no observable
decay in the hole photocurrent signal. This fact can be used to say that the
hole deep trapping lifetime, th, must be much greater than the hole transit
time, trh. However, the electron photocurrent signal did exhibit a decay.
This means that the electron deep trapping lifetime, tie, must be of the same
order as the electron transit time, tTe.
IFTOF analysis was then used to provide a measurement of the
charge carrier deep trapping lifetimes. The results confirmed that the hole
and electron deep trapping follow an exponential behaviour with a
characteristic trapping time, T. This exponential trapping behaviour implies
94
a single species or set of traps are responsible for carrier deep trapping in
stabilized a-Se. Furthermore, the results confirmed the expectations that
t n,»Th and that t re was of the same order as t e.
The product of the carrier drift mobility, deep trapping lifetime, and
applied field, or wrF, called the Schubweg, provides a measure of the average
drift length for a charge carrier in a material. If this product is greater than
the thickness of the film being used, most carriers will travel across the film
without becoming trapped. In the present study, this was true for holes but
not for electrons. As a result, it became necessary to account for electron
deep trapping when performing the ambipolar recombination experiment.
It was demonstrated that the ambipolar TOF technique implemented
can be used to measure carrier recombination in stabilized a-Se films. An
electron packet of known charge•density per unit area, ige, was injected into
one side of a sample and a hole charge packet was injected into the opposite
side. The two packets drifted towards each other under the influence of an
applied electric field, F. The magnitude of the hole photocurrent was
measured before, ihi, and after, ih2, the packets had passed through one
another. The measured fractional change in hole photocurrent, ih2/ihi, as a
function of ae/F indicated that recombination in chlorinated a-Se:0.2%As
followed a Langevin type behaviour, as defined by the Langevin
recombination coefficient. This result directly implies that the carrier mean
free path, a, in stabilized a-Se, is much less than the critical recombination
radius rc. It is quite probable that this type of recombination is a general
property for materials that meet the a«re criterion, i.e., low mobility
materials. It seems that Langevin's simple formulation for recombination
95
applies to amorphous semiconductors for which, at present, the rigorous
theoretical models are very limited.
Most current photoinduced discharge theories ignore charge carrier
recombination in their formulation. The importance of this work is that the
experimentally determined recombination coefficient can now be used in the
modeling of photoinduced discharge of stabilized a-Se photoreceptors used in
electroradiography, where both electron and hole drifts are involved in the
discharge process.
The combined use of different transient photoconductivity techniques
provides a powerful tool for studying charge transport and recombination in
high resistivity solids. Up to this point, this combination of measurements
has been applied only to stabilized amorphous selenium films. It would be
interesting to perform the same set of experiments on other low mobility
solids, in an effort to confirm the postulate that Langevin type
recombination is a general property for low-mobility materials. The current
experimental systems may have to be modified to incorporate different light
sources that correspond to the mobility gap of the new materials being
studied. It is also possible that the detection electronics may have to be
modified.
96
7 REFERENCES
[1] Ovshinski S.R., "Amorphous semiconductors for microelectronics", Proceedings from SPIE, 617, 1986, pp. 1-9.
[2] Smith W., "Effect of light on selenium during the passage of an electric current", Nature, 7, 1873, pp. 303.
[3] Pai D.M. and Springett B.E., "Physics of electrophotography", Review of Modern Physics, 65, 1993, pp. 163-211.
[4] Boag J.W., "Xeroradiography", Physics in Medicine and Biology, 18, 1973, pp. 3-37.
[5] Aiyah V., Kasap S.O., Polischuk B., and Bailie A., "Doped amorphous selenium based photoreceptors for electroradiography: Determination of x-ray sensitivity", Journal of Non-Crystalline Solids, 164-166, 1993, pp. 777-780.
[6] Davis H.J., Araj N., Rowlands J.A., and Hunter D.M., "A novel, digital radiographic imaging system using selenium plates", Proceedings of the Fourth International Symposium on Uses of Selenium and Tellurium, edited by S. Carapello, Selenium-Tellurium Development Association, New York, 1989, pp. 267-280.
[7] Kasap S.O., "Photoreceptors: The selenium alloys", Handbook of Imaging Materials, edited by A.S. Diamond, Marcel Dekker Inc., New York, 1991.
[8] Kutner M., "Defect chemistry and states in the gap of lone-pair semiconductors", Journal of Non-Crystalline Solids, 31, 1978, pp. 223-240.
[9] Mott N.F., "Electrons in disordered structures", Advances in Physics, 16, 1967, pp. 49-57.
97
[10] Cohen M.H., Fritzsche H., and Ovshinski S.R., "Simple band model for amorphous semiconductor alloys", Physical Review Letters, 22, 1969, pp. 1065-1072.
[11] Mott N.F, and Davis E.A., Electronic Processes in Non-Crystalline Solids, Clarendon Press, Oxford, 1979.
[12] Abkowitz M., "Density of states in a-Se from combined analysis of xerographic potentials and transient transport data", Philosophical Magazine Letters, 58, 1988, pp. 53-57.
[13] Hartke J.L. and Regensburger P.J., "Electronic States in vitreous selenium", Physical Review, 139, 1965, pp. A970-A980.
[14] Davis E.A., "Optical absorption, transport and photoconductivity in amorphous selenium", Journal of Non-Crystalline Solids, 4, 1970, pp. 107-116.
[15] Pai D.M. and Enck R.C., "Onsager mechanism of photogeneration in amorphous selenium", Physical Review B, 11, 1975, pp. 5163-5174.
[16] Marshall J.M., "Carrier diffusion in amorphous semiconductors", Report on Progress in Physics, 46, 1983, pp. 1235-1282.
[17] Cohen M.H., "Review of the theory of amorphous semiconductors", Journal of Non-Crystalline Solids, 4, 1970, pp. 391-409.
[18] Spear, W.E., "Electronic transport and localization in low mobility solids and liquids", Advances in Physics, 23, 1974, pp. 523-546.
[19] Dolezalek F.K. and Spear W.E., "Electronic transport properties of some low mobility solids under high pressure", Journal of Non-Crystalline Solids, 4, 1970, pp. 97-106.
[20] Spear W.E., "Transit time measurements of charge carriers in amorphous selenium films", Proceedings from the Physical Society of London, B70, 1957, pp. 669-675.
[21] Martini M., Mayer J.W., and Zanio K.R., "Drift velocity and trapping in semiconductors -transient charge technique", Applied Solid State Science: Advances in Materials and Device Research, edited by R. Wolfe, Academic Press, 1972, pp. 181-261.
98
[22] Spear W.E., "Drift mobility techniques for the study of electrical transport properties in insulating solids", Journal of Non-Crystalline Solids, 1, 1969, pp. 197-214.
[23] Papadakis A.C., "Theory of space-charge perturbed currents in insulators", Journal of Physics and Chemistry of Solids, 28, 1967, pp. 641-647.
[24] Ehrenberg W. and Gibbons D.J., Electron Bombardment Induced Conductivity, Academic Press Inc., London, 1981, pp. 141-194.
[25] Zanio K.R., Akutagawa W.M., and Kikuchi R., "Transient currents in semi-insulating CdTe characteristic of deep traps", Journal of Applied Physics, 39, 1968, pp. 2818-2828.
[26] Zhang Q. and Champness C.H., "Charge decay in amorphous selenium layers with an intermediate aluminum oxide layer", Canadian Journal of Physics, 69, 1990, pp. 278-283.
[27] Polishchuk B., Kasap S.O., Dodds D., and Yannacopoulas S., "Charge trapping studies in amorphous selenium films by the interrupted transit time time-of-flight technique", Proceedings from the Fourth International Symposium on uses of Selenium and Tellurium, edited by S. Carapello, Selenium-Tellurium Development Association, New York, 1989, pp. 202-218.
[28] Brown F.C., "Temperature dependence of electron mobility in AgCl", Physical Review, 97, 1955, pp. 355-362.
[29] Kepler R.G., "Charge carrier production and mobility in anthracine crystals", Physical Review, 119, 1960, pp. 1226-1229.
[30] Tabak W.D. and Warter P.J., "Field-controlled photogeneration and free carrier transport in amorphous selenium films", Physical Review, 173, 1968, pp. 899-907.
[31] Oda 0., Onozuka A., and Tsubaga T., "Effect of oxygen on electrophotographic properties of selenium", Journal of Non-Crystalline Solids, 83, 1986, pp. 49-62.
[32] Abkowitz M.A., Rice M.J., and Stolka M., "Electronic transport in silicon backbone polymers", Philosophical Magazine B, 61, 1990, pp. 25-57.
99
[33] Gill W.D., "Drift mobilities in amorphous charge-transfer complexes of trinitrofluorenone and poly-n-vinylcarbazole", Journal of Applied Physics, 43, 1972, pp. 5033-5040.
[34] Kasap S.O. and Juhasz C., "Transient photoconductivity probing of negative bulk film space charge evolution in halogenated amorphous selenium films", Solid State Communications, 63, 1987, pp. 553-556.
[35] Mort J., Troup A., Morgan M., Grammatica S., Knights J.C., and Lujan R., "Geminate recombination in a-Si:H", Applied Physics Letters, 38, 1981, pp. 277-279.
[36] Dolezalek F.K. and Spear W.E., "Carrier recombination in orthorhombic sulphur", Journal of Physics and Chemistry of Solids, 36, 1975, pp. 819-825.
[37] Svelto 0., Principles of Lasers, Plenum Press, New York, 1989, pp. 320-327.
[38] Gerry E.T., "Pulsed-molecular-nitrogen laser theory", Applied Physics Letters, 7, 1965, pp. 6-8.
[39] Gibbons D.J. and Spear W.E., "Electron hopping transport and trapping phenomena in orthorhombic sulphur crystals", Journal of Physics and Chemistry of Solids, 27, 1966, pp. 1917-1925.
[40] Spears W.E., Steemers H.L., and Mannsperger H., "Charge lifetimes in amorphous silicon junctions from delayed and interrupted field experiments", Philosophical Magazine B, 48, 1983, pp. L49-L54.
[41] Kasap S.O., Thakur R.P.S., and Dodds D., "Method and apparatus for interrupted transit time transient photoconductivity measurements", Journal of Physics E: Scientific Instruments, 21, 1988, pp. 1195-1202.
[42] Helfrich W. and Mark P., "Space charge limited currents in anthracine as a means of determining the hole drift mobility", Zeitschrift Fur Physik, 166, 1962, pp. 370-385.
[43] Kasap S.O., Polischuk B., and Dodds D., "An interrupted field time-of-flight (IFTOF) technique in transient photoconductivity measurements", Review of Scientific Instruments, 61, 1990, pp. 2080-2087.
100
[44] Konenkamo R., Hermann A.M., and Madan A., "Photocurrent reversal and time-of-flight in amorphous silicon-hydrogen films", Philosophical Magazine B, 48, 1983, pp. L33-L37.
[45] Tabak M.D. and Scharfe M.E., "Transition from emission-limited to space-charged-limited photoconductivity", Journal of Applied Physics, 41, 1970, pp. 2114-2118.
[46] Polischuk B. and Kasap S.O., "A high-voltage interrupted-field time-of-flight transient photoconductivity apparatus", Measurement Science Technology, 2, 1991, pp. 75-80.
[47] Polischuk B.T., M. Sc. Thesis, Charge Transport and Trapping Studies on Amorphous Chalcogenide Semiconductor Films, University of Saskatchewan, Saskatoon, Canada, 1990.
[48] Polischuk B.T., Ph. D. Thesis, Interrupted Field Time-of-Flight Transient Photoconductivity Technique and its Applications to Amorphous Semiconductors, University of Saskatchewan, Saskatoon, Canada, 1993.
[49] Hughes R.C., "Bulk recombination of charge carriers in polymer films: poly-n-vinylcarbozole complexed with trinitrofluorenone", Journal of Chemical Physics, 58, 1973, pp. 2212-2219.
[50] Langevin P., "Ionisation of gases", Annales de Chimie et de Physique, 28, 1903, pp. 287 and 433.
[51] Loeb L.B., The Kinetic Theory of Gases, Dover Publications, Inc., New York, 1961, pp. 585-587.
[52] Kastner M., Adler D., and Fritzsche H., "Valence-aternation mdel for gap states in lone-pair semiconductors.", Physical Review Letters, 37, 1976, pp. 1504-1507.
101
