Carrier injection in amorphous silicon devices

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PROEFSCHRIFT

ter verkrijging van de graad van

doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus,

Prof.drs. P.A. Schenk

in het openbaar te verdedigen

ten overstaan van een commissie aangewezen

door het College van Dekanen

op maandag 19 september 1988

te 16.00 uur

door

HENDRIK MARTINUS WENTINCK

geboren te Rotterdam

natuurkundig ingenieur

r

TR diss

1657

v

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CARRIER INJECTION IN

AMORPHOUS SILICON DEVICES

H.M. WENTINCK

TR diss

1657

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CARRIER INJECTION IN

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Dit proefschrift is goedgekeurd door de

promotor Prof.dr. M. Kleefstra

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CONTENTS

CHAPTER 1 GENERAL INTRODUCTION

1.1 1.2

1.3

1.4

History 1 Properties of amorphous silicon 3

1.2.1 Electrical properties 4 1.2.2 Optical properties 21 Recombination studied using the time-resolved 25

microwave-conductivity experiment

Scope of thesis 40

CHAPTER 2 FABRICATION OF AMORPHOUS SILICON DEVICES

2.1 Introduction 2.2 The deposition system 2.3 Fabrication of devices

2.3.1 Deposition

2.3.2 Contacts and photolithography

43 45 50 50 57

CHAPTER 3 SPACE-CHARGE-LIMITED CURRENTS IN P-I-P STRUCTURES

3.1 Introduction

3.2 Space-charge-limited current theory 3.3 Numerical simulations

3.4 Experimental results

3.5 Stability of p-i-p structures 3.5 Conelus ions 59 62 68 79 89 93

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4.2 Theory 98 4.2.1 Calculation of the generated current 99

4.2.2 Determination of the electric field 103

4.2.3 Drift mobility and diffusion 104

4.3 Experiment 109 4.4 The Schottky barrier 113

4.5 The p-i interface 130 4.6 Conclusions 138

APPENDICES

NUMERICAL SOLUTION OF THE SEMICONDUCTOR DEVICE 139 OPERATION IN THE STATIONARY SITUATION

DETERMINATION OF VARIOUS EQUATIONS IN CHAPTER 4 159

REFERENCES 175 SUMMARY 197 SAMENVATTING ACKNOWLEDGEMENTS 199 201 BIOGRAPHY 203

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CHAPTER 1

GENERAL INTRODUCTION

1.1. History

Hydrogenated amorphous silicon (a-Si:H) or for shortly amorphous silicon has come of age during the preceding decade. Since Spear and Le Comber (1975) demonstrated that a-Si:H could be succesfully doped with phosphorus and boron, this semiconductor has been of interest to many researchers. Firstly, because a-Si:H opened up interesting possibilities for the fabrication of cheap, thin-film electronic devices on large substrates, such as solar cells and drivers for liquid crystal displays. Secondly, because of its scientific attractions, such as: a continuously adjustable bandgap through alloying the material with nitrogen, carbon and germanium, efficient optical transitions, a usable carrier-diffusion length and, as previously mentioned, the capability of employing n- and p-type dopants.

That a-Si:H could be succesfully doped was surprising at the time. No doped amorphous semiconductors had been known prior to 1975, and, as Mott had intuitively explained, the absence of periodic steric constraints in an amorphous material could allow the normal valency of any impurity atom to be completely satisfied. It appeared that the succesful doping of amorphous silicon was due to the incorporation of hydrogen. The hydrogen saturates the dangling bonds in the material and lowers the density of energy states in the bandgap so that a small fraction of the dopant atoms which are not incorporated according to their valency can shift the Fermi level significantly in the direction of the conduction or valence band. In the following years it became clear that the dopant atoms create also extra energy states in the

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bandgap. Street (1985a), Street et al. (1986,1987) and Stutzmann et al, (1987a) proposed that these energy states are an essential feature of the doping mechanism and that the structure is not free from lattice constraints.

Over the last decade, substantial progress has been made in the understanding of the properties of amorphous silicon. Although many questions remain to be answered, the main properties of the material are now partly understood. Some of the experiments which have led to the present level of understanding are discussed in the following section.

If it is difficult to describe the material itself, the

description of electronic devices such as solar cells and thin-film transistors is even harder. The development of these devices led to the fabrication of structures with layers as thin as a few nanometers. Progress in the understanding of the devices has been hindered because detailed structural information is lacking, interfaces between the different layers of the structure are sensitive to the execution of fabrication steps, and the equations which govern the electrical characteristics of the devices are difficult to solve. Generally, the equations can only be solved numerically with computer programs which have only recently become available and are only occasionaly

obtainable, see Schwartz (1982) and Hack and Shur (1985).

Despite these problems, the technology base for amorphous silicon continues to grow at a rapid rate. Due to the great industrial interest, electronic devices such as solar cells and thin-film

transistors have become fashionable and are now partially understood. In 1976 Carlson and Wronski reported the first amorphous-silicon solar cell. In 1987 several companies in the United States, Japan and Europe established either amorphous-silicon solar-cell pilot

production or full-scale manufacturing plants, see, for example, Wallace (1987). Two companies established a roll-on-roll-off process,

see Ovshinsky (1987), and Jacobsen et al. (1987). The conversion efficiency of the solar-cell panels was about 7 %. In 1987 40% of the solar cell market was based on amorphous-silicon devices. While manufacturers were focussing on lowering fabrication costs, see Schmitt (1986), Ovshinsky (1985) was working on high efficiency and

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-3-CHAPTER 1: GENERAL INTRODUCTION

obtained 13 % efficiency for a triple-junction stacked solar cell in the laboratory. Nakano et al. (1987) obtained an efficiency of 11.7 % for a single-junction solar cell with a textured, transparent front contact and a silver back contact. They also achieved a

remarkable increase in the collection efficiency for the short wavelength by applying a super-lattice p-type contact.

A situation similar to that of the solar cells is that of amorphous silicon thin-film transistors for matrix addressing of liquid-crystal displays. In practically all flat-screen color TV's, amorphous silicon is used. Further, the material appears to be suitable to use in other devices, such as image sensors,

photoreceptors and mass storage systems, see for example Pankove ed. (1984).

Unfortunately, there has been little improvement in the

fabrication of the amorphous-silicon germanium alloy with a bandgap smaller than 1.5 eV. The use of such an alloy is crucial to the

achieving of high efficiency in solar cells. Another problem affecting amorphous silicon is the light-induced degradation or the Staebler-Wronski effect as discovered by Staebler and Staebler-Wronski (1977). This metastable effect, which can be annealed out at moderate temperature, is still poorly understood although it became clear that electron hole recombination can create defects. It seems that the effect is an inherent property of amorphous silicon; the concentration (SiH„) polymeric chains is correlated with the degradation rate, as was concluded from infrared absorption that correspond to the bending modes of these chains, see for example Fortmann et al. (1986).

1.2. Properties of amorphous silicon

The literature on the properties of amorphous silicon and its alloys is extensive. General introductions to the field of amorphous silicon have recently been published by Joannopoulos and Lucovsky, eds. (1984) and by Pankove, ed. (1984). The proceedings of the International

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Conference on Amorphous and Liquid Semiconductors (1987), the proceedings of conferences on solar cells, such as the IEEE Photovoltaic Specialist Conferences and the European Solar Energy Conferences, the proceedings of the MRS conferences and conferences on displays, such as the symposia of the Society of Information Display, are all partly dedicated to amorphous silicon. INSPEC (1984) compiled the properties of amorphous silicon. Each year, the journal Solar Cells publishes an extensive amorphous silicon bibliography.

Therefore, the following two subsections provide only an outline of those properties which are relevant to this thesis. The outline is restricted to the description of the electrical and optical properties in subsection 1.2.1 and subsection 1.2.2.

1.2.1. Electrical properties

In this subsection the following properties of hydrogenated amorphous silicon are discussed : the density of energy states in the bandgap, and the transport and recombination of electrons and holes.

Density of energy states.

The electrical and optical properties of an amorphous semiconductor are predominantly determined by energy states in the bandgap, since these states act as traps and recombination centers for excess carriers. The density of energy states, that is the number of energy states per unit volume per unit energy N(E), is therefore an important parameter.

The first picture we have of the density of energy states is from Spear and Le Comber's (1972) field-effect experiment The experiment demonstrated that the Fermi level in a-Si:H could be moved by applying an electric field. Since the field-effect experiment probes energy states in the first hundred nanometers from the interface with the isolator and, therefore, also energy states related to the interface,

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this experiment gives an upper limit for the bulk density of these energy states.

A sketch of the density of energy states is shown in figure 1.1. It is a composite, pieced together from various experiments. The valence- and conduction-band density of energy states were measured with the use of x-ray photoemlssion spectroscopy and inverse

photoemission spectroscopy, respectively, see Jackson et al. (1985). The position of the valence- and conduction-band density of energy states with respect to the Fermi level could be determined within an error of about 0.1 eV. There are no well-defined band edges, but the density of energy states decreases smoothly but strongly to low values in the band tails. These band tails are due to disorder in the

structure. The energy levels E and E are the mobility edges of the conduction band and the valence band, and define the mobility gap. The mobility-edge concept originates from Mott (1967) who first pointed out its existence in weakly and moderately disordered systems. The mobility edge separates the localized energy states in the bandgap from the extended energy states outside the bandgap where the carrier transport is assumed to take place. The position of the mobility edges in respect to the band edges is not very well known since there is hardly experimental information on the density of energy states at the mobility edge. From inverse photoemission spectroscopy, the density of states at the conduction band mobility edge was found to be

21 -3 -1

4 - 8 . 1 0 cm eV . Other estimations of the density of energy states 20 21 -3 -1

at the mobility edge vary between 5.10 and 5.10 cm eV , see for example Hourd and Spear (1985), Marshall et al. (1987a), and Mott

(1987). The density of energy states at the valence-band mobility edge is believed to be in the same range. Because of these uncertainties, the mobility gap is not precisely known. If, as usual, the mobility gap is taken as twice the conductivity activation energy where the thermoelectric power changes sign, the mobility of undoped amorphous silicon is about 1.7 eV, see Stuke (1987).

Within the tails, away from the mobility edges, the density of energy states decreases strongly in some tenths of electron volts. The valence-band tail-state distribution is usually described by

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w h e r e N ( E ) is the d e n s i t y o f energy states at the v a l e n c e - b a n d edge

energy E (eV) a n d E (eV) the characteristic decay energy o f the

b a n d t a l l . F o r t h e c o n d u c t i o n b a n d tail, a similar e x p r e s s i o n w i t h a c h a r a c t e r i s t i c d e c a y energy E , is o f t e n used. E is a b o u t 0.05 e V , J OJ CO V O E is a b o u t 0.025 eV. C O ~ 10 10 10 10 --2.5 I extended —„^states

—

_ E I ■ I I I mobility gap \valance conduction / \ band toil band tail /

v

o T k

/ E

defect states /

I

'

extended states

—

c — -1.5 •0.5 0 0.5 E(eV)

Fig. 1.1 S k e t c h o f the density o f energy states N ( E ) as a

f u n c t i o n o f the energy E . T h e correlation energy U is the energy

difference b e t w e e n the two-electron D~ energy state and the one

e l e c t r o n D e n e r g y state o f the dangling b o n d s .

T h e e x p o n e n t i a l form o f the tail-state distributions is b a s e d u p o n

T i e d j e s (1981) i n t e r p r e t a t i o n o f the anomalous strong d i f f u s i o n o f

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below. Further support for the exponential form comes from optical absorption measurements, see subsection 1.2.2.

The valence-band tail is somewhat broader than the conduction band tail due to the fact that the bonding energy states are more sensitive to bond angle variations in the structure than the anti-bonding energy states. From optical absorption spectra of high-quality amorphous silicon with various hydrogen concentrations of 9 - 14 %, see Cody

(1984), and from theoretical calculations, see Allan and Joannapoulos (1984), it can be concluded, that hydrogen removes energy states from the top of the valence band tail.

The exponential form for the density of energy states in the band tails is not only used for amorphous silicon but also for various other amorphous semiconductors, since it facilitates the modelling of the carrier transport in these materials significantly. However, recent time-of-flight experiments on hole and electron transport which provide information about the tail-state distributions suggest,

significantly different tail state distributions for amorphous silicon. Possible distributions derived from these experiments, are depicted in figure 1.3 and are discussed below.

Around midgap, there is a significant density of defect-related energy states which depends on the conditions under which the material was fabricated. Extensive work on defects in amorphous silicon led to the conclusion that the paramagnetic center which can be observed by electron-spin resonance measurements, and which is usually identified as the dangling bond, is the predominant defect center. This

conclusion is based on the comparison of the spin resonance signal with the photoluminescence quantum efficiency, see for example Street et al. (1981), Dersch et al. (1981a,1983), with the diffusion length of excess carriers, see for example Street et al. (1983), and with subbandgap absorption, see for example Jackson and Amer (1982). The

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comparison extends over a range of 5.10 - 5.10 defects per cubic centimetre. There is no experimental evidence for a significant density of other energy states around midgap which are spinless. Therefore, the discussion is confined to the dangling bond.

The dangling bond is a defect which can be positive (D ) , neutral (D ) , or negative (D ). Important parameters are the energy

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distribution of the D energy states and the correlation energy which is the energy difference between the two-electron D energy state and the one-electron energy D state. In view of the general importance of the dangling bond, it is suprising that there is still so much

controversy over the values of these parameters. Le Comber and Spear (1986) compiled the published values for the energy of the D and the D" state. To summarize, the values fall into two groups which locate the neutral D energy state either 1.2 to 1.3 eV or 0.9 to 1.0 eV below the conduction-band mobility edge E . The location of D 1.2 to

1.3 eV below E is mainly based on subbandgap photon absorption by Jackson and Amer (1982) and Johnson and Biegelsen's (1983)

photodepopulation-induced electron-spin resonance measurements and Lang and Cohen's (1982) transient capacitance measurements on diodes. Allan and Joannapoulos's (1984) theoretical ab-initio calculations sustain this location. On the other hand, charge collection efficiency measurements on p-i/-n and p-7r-n diodes by Spear et al. (1984),

advocate a position of D 0.9 - 1.0 eV below the bandgap. Here v and

7T stand for lightly phosphorus-doped, n-type and lightly boron-doped, p-type material. The authors correlate the change in the majority and minority lifetimes in the u and it layers with the charge in the defect

energy states which is determined by the dopants. Support for this theory comes from the strong increase of the steady-state

photoconductivity in lightly phosphorus-doped material. This is interpreted as an increase of the electron lifetime due to the decrease of neutral and positively-charged dangling bonds, see for example Vanier (1984). Further support comes from the study of light-induced metastable defects by means of space-charge-limited currents in n-i-n structures by Shauer and Kocka (1985). They concluded that D" lies 0.6 eV below E . From the difference in the position of D and

c r

the Fermi level, they deduced that D lies 1.0 eV below E .

whether the measurements which are performed on doped material provide information about dangling bond levels in undoped material, as in the case of Lang and Cohen and Spear et al. is questionable. Doping does not only shift the Fermi level but also creates extra dangling bonds which can have different energy levels. Further, it should be noted that Street (1984a) does not observe an increase in the

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majority-carrier lifetime in doped material in contrast with Spear, and that for n-type material hole transport can be the recombination rate limiting factor, see Main et al. (1987).

Transport

It is common to explain the carrier transport in amorphous silicon by the multiple-trapping model. In this model, it is assumed that carriers move solely in the extended energy states above the mobility edge and that they are immobile in the localized band-tail energy states. When carriers are traversing an amorphous silicon film they become dispersed due to the statistics in the trapping in and the thermal release from the localized energy states. The diffusion depends on the temperature, the electric field and the distance covered, and can become very strong when the temperature decreases. The strong diffusion is often called anomalous dispersion.

The following parameters are involved in the description of the multiple-trapping transport: the extended-state mobility of the

2

carriers /i (m /Vs) , the distribution of the localized energy states

° 2

N(E), and the capture cross-sections a (m ) and the escape rate

coefficients 1/ (s ) of the localized energy states. The capture cross-section o of state of the m-th kind is related to the capture

m 3

rate constant C (m /s) through the relation C = a .v_, with

m ' 6 m m th

vty. (m/s) the carrier thermal velocity which is normally chosen to

be 10 cm/s. Since the thermal velocity of electrons and holes is unknown, it may be asked whether the capture cross-section is not a somewhat misleading expression. The capture rate constant C is related to the escape rate constant u through the detailed balancing

principle. For the conduction band-tail energy states:

v = N .C .exp[(E - E )/k.T] with N - N(E ).k.T the effective density

m c m r L m c ' c v c J

of conduction band energy states and k.T (eV) is Boltzmann's constant times the absolute temperature. /i , C and v depend (weakly) on the

temperature, C and i/ depend also on the energy of the localized energy state. Usually, p , C and v are taken constant.

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The anomalous dispersion is also observed in other amorphous semiconductors and was explained successfully for the first time by Scher and Montroll (1975) through the introduction of a waiting-time-distribution function ^(t). This function is related to the average escape probability of carriers. Although Scher and Montroll calculated this function for carriers which hop between iso-energetic sites with random positional distribution, they noticed that any transport mechanism generating a suitable waiting-time distribution function leads to anomalous dispersion. From subsequent studies of, see it became clear that the multiple-trapping transport mechanism can generate a suitable function i/>(t) and therefore anomalous dispersion,

provided that the localized tail states are distributed over a sufficient range of energy, see for an overview Marshall (1983).

The development of the multiple-trapping model and the description of anomalous dispersion in general is, from an experimental

standpoint, mainly based on the time-resolved photo-conductivity or the time-of-flight experiment in the configuration found in figure 1.2 as was explored by Spear (1969). In this experiment, a pulse of

carriers is injected (normally by a short light pulse) on one side of a film. The carriers move through an applied electric field to the opposite side, thereby generating a current in the circuit connected to the structure. The current is monitored as a function of time and is measured for various temperatures and applied bias voltages.

Fig. 1.2 Typical configuration for the time-of-flight experiment.

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From these measurements, it is possible to derive the transport parameters, such as the extended-state mobility, the tail-state distribution, and the capture cross-sections, albeit with prior knowledge about the temperature dependence of the extended-state mobility and temperature- and energy-dependence of the capture cross-sections and the escape-rate coefficients. The time resolution of the experiment determines which interactions of electrons in extended energy states with localized energy states can be monitored. The very fast interactions of electrons in extended energy states with

localized energy states within 0.1 eV below E or above E , occuring -10 c v within 10 s have not been probed by this type of time-of-flight experiment so far. Detailed information about the density of energy states in this energy range is missing and the following discussion concerns localized energy states deeper in the mobility gap.

In general, the derivation of the density of energy states from the time-of-flight experiments involves complex equations and is cumbersome, see for example Michiel et al. (1983) and Marshall (1983). Therefore, approaches leading up to more tractable and transparent equations, but also to quite different interpretations, were examined by several authors. For example, by Tiedje et al. (1981) (see also Tiedje (1984) for an overview) who observed anomalous dispersion both for electrons and holes. For electrons, anomalous dispersion was only observed below room temperature. For holes, anomalous dispersion was observed even above room temperature. Tiedje et al. explained the current transients from exponentially-decreasing tail-state distributions away from the mobility edges towards midgap, as in equation (1.2.1), both for the conduction-band tail and the valence-band tail. In their analysis, they assumed temperature- and

energy-independent capture cross-sections and applied the thermalization approximation of Tiedje and Rose (1981) and Orenstein and Kastner

(1981), see subsection 1.2.3. Contrary to Tiedje et al., Spear and Steemers (1983), Hourd and Spear (1985), and Spear et al. (1987) found no significant dispersion for the electron transport for temperatures above 150 K. They explained their measurements through a different tail-state distribution and assumed that electrons in the extended energy states interact primarily with localized states

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0.14 eV below the mobility edge. Within 1 ns, electrons in the extended energy states and in these localized energy states are in thermal equilibrium with each other. Accidentally, Tiedje and co-workers and Spear and co-co-workers obtained an extended-state mobility

2

p of about 10 cm /Vs. Silver and Adler (1985) interpreted the

time-of-flight measurement and other current transient effects in a third 2

way and claimed /i > 100 cm /Vs. However, there are several objections to the interpretation of Silver et al., see for example

Michiel et al. (1986).

From studies of Marshall et al. (1983), Michiel et al. (1983), Marshall and Street (1984), and Michiel and Adriaenssens (1984), it became clear that only the prominent features of the localized energy state distribution can be determined with any confidence from the analysis of the time-of-flight measurements. This was illustrated by Monte Carlo simulations of time-of-flight measurements by Marshall et al. (1983) who calculated the temperature and thickness dependence of the dispersion parameters a. and a„ for rather different tail state

distributions. The dispersion parameters describe the shape of the current transients according to I « t 1 before the transit time

(except for very short times), and I <x t 2, after the transit time, see also figure 1.2. At the transit time the first carriers reach the opposite electrode. The transit time is normally observed by a kink in the log I - log t plot. It was found that only a is sensitive to

changes in the energy distribution. However, in the experiment an accurate determination of a„ is very difficult. The simulations showed further that the exponential distribution of localized states, as proposed by Tiedje et al. is not a prerequisite to explain the

experimental data. Rather, in the case of the electron transport, the temperature dependence of Q „ as derived from the measurements of Tiedje et al. and Kirby and Paul (1984) indicated a tail-state

distribution with a sharp cut-off. Computer simulations of Michiel et al. (1986), see also Davis et al. (1986) indicated a similar tail-state distribution.

A recent study by Marshall et al. (1986,1987a) of the electron transport studied by using time-of-flight measurements over a wide range of temperatures and applied electric fields confirmed this idea.

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The temperature- and field-dependence of the carrier transit time and the dispersion parameters a. and a„ indicated a tail-state

distribution varying linearly with the energy between 0.08 and 0.14 eV below E . The extended-state mobility was estimated

c 2

to be p - 20 cm /Vs.

A more pronounced tail-state distribution was also advanced by Nebel and Bauer (1987), applying the same technique as Michiel et al., and Vanderhaghen and Longeaud (1988), applying a somewhat different

2 technique. They derived an extended-state mobility of about 10 cm /Vs

2 and 25 cm /Vs, respectively. Ë _ )20 l18

1 1

--• / " -1

b / /

/ /

♦/ /

-/

+

■{ + + + +

+ /

7\

/a

/

-I -0.3 -0.2 -0.1 0 E-EcleV) F i g . 1.3 V a r i o u s m o d e l s for t h e v a l e n c e - a n d c o n d u c t i o n - b a n d t a l l , b a s e d o n t i m e - o f - f l i g h t m e a s u r e m e n t s , ( a ) : T i e d j e e t a l .

(1981), (b): Marshall (1986), (c): Marshall (1987b). The density of energy states as derived from the Spear and Le Comber's field-effect experiment is represented by the crosses.

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The previous discussion shows that there are uncertainties in the interpretation of time-of-flight experiments applied to electron transport in amorphous silicon. They are due partly to the analysis applied to the data and partly to the material differences in the investigated specimens as can be concluded from the differences in the observed dispersion. However, a rough picture describing the electron transport by the multi-trapping model, can be given. The data indicate

2

an extended-state mobility of 10 - 50 cm /Vs, a tail-state

distribution extending about 0.15 eV into the mobility gap, tail-state capture cross-sections of 10 - 10 cm and an attempt-to-escape

12

frequency prefactor v of about 10 s. This picture corresponds with

the general observation that there is no anomalous dispersion for electrons at room temperature, see also chapter 4.

It should be noticed that the multiple-trapping model cannot predict other carrier transport features in amorphous silicon, such as the the Hall effect sign, which is reversed both for electrons and holes. This was observed by Le Comber et al. (1977) for n-type and p-type

amorphous silicon and by Dresner (1980) for undoped amorphous silicon in darkness and under illumination. In the case of undoped amorphous silicon the signal is always p-type although it is known from other transport experiments that the majority carriers are electrons. The

2

Hall mobility /i is /JU ~ 0.1 cm /Vs below 360 K and temperature

n H

independent. Above 360 K, /*„ is exponentially activated, according to 2

/iu = 7.9 exp(-0.13/k.T) cm /Vs. This behaviour of the Hall mobility

H

favors a transport model in which electron transport takes place in a set of energy states spatially modulated in energy with a mean barrier height of 0.13 eV, see Dresner (1984). At low temperature, the

electrons tunnel through these barriers; at high temperature, they move by thermally activated hopping. This model resembles that of Overhof and Beyer (1981) which is based on a detailed study of the activation energies for conduction and thermopower. Although the reverse sign of the Hall effect can be understood from hopping conduction, see Emin (1977), it is noted that there is no firm theoretical basis for a proper understanding of this phenomenon. It probably excludes only models which assume that long-range potential

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fluctuations of 5 - 10 nm dominate the electron scattering and determine the mobility. As has been pointed out by Mott (1984), classical behaviour in long-range potential fluctuations does not yield a reverse sign of the Hall effect.

The electron extended-state mobility M can in principle also be

obtained from

Ho - ao/[q.k.T.N(Ec)] ^ (1.2.2)

where a is the pre-exponential factor in the expression of the

conductivity of amorphous silicon, q the elementary change and N(E ) is the density of states at the mobility edge E . It is assumed that hole transport can be ignored since undoped amorphous silicon is slightly n-type. Unfortunately, the determination of the pre-exponential factor a from the temperature dependence of the

conductivity a, using

aQ = a.exp[(Ec - Ef)/k.T] (1.2.3)

where E_ is the Fermi level, is hampered by the strong temperature dependence of the position of the Fermi level in respect to the conduction band mobility edge, i.e. E - Ef. Experimentally, assuming

E„ - E to be constant, a wide range of a is obtained for different

f c ° o

samples. This is due partly to side effects such as band bending at the surfaces of the samples, see Solomon et al. (1978), and partly to the density of states determining the temperature shift of the Fermi level in respect to the mobility edge. Accepting a value for the

3 -1 -1

observed pre-exponential factor a , = 2.3x10 ohm cm , and after

r r o obs

correcting for the temperature dependence of E - E_, one obtains - 1 - 1 c r

a - 150 ohm cm , see Stuke (1987). This is in agreement with Thomas

and co-workers's theoretical calculations, see Muller and Thomas (1984) and Fenz et al. (1985). Recently, Mott (1987) sustained this

20 21 -3 -1

value for a . Taking N(E ) = 5.10 - 5.10 cm eV equation 1.2.2

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Experimental data on hole transport is rather limited. Time-of-flight measurements of Allan (1978) and Tiedje et al. (1981,1983) and Street (1982), show a dispersive hole transport, which can be explained by an exponential tail-state distribution, as described by equation (1.2.1). From a fit to the temperature dependence of the hole transit time,

2 12 -1 Tiedje obtains , u - 1 cm /Vs, T - 500 K, and v - 10 s .

J ^o ' c o

However, recent measurements of Marshall et al. (1987b), indicate 2

/i = 10 cm /Vs, and an approximate Gaussian form for the valence band-tail distribution at least for between 0.25 and 0.45 eV from the valence-band mobility edge.

whether transport of electrons and holes takes place in the extended states above the mobility edge or predominantly through thermally-activated hopping between localized energy states near the mobility edge is usually not important in the description of the electrical conduction in amorphous silicon devices in the steady state; neither are the precise tail-state distributions. In practice, as long as the quasi Fermi level is not close to the mobility edge, it is sufficient to assume an appropriate tail-state distribution and extended-state mobility.

In the steady state a drift mobility can be defined. The electron drift mobility /i is given by /i =n .n/n where n is the electron

density in the extended states and n is the density of electrons in the localized states. An analogue equation holds for holes. At room temperature, the electron- and hole-drift mobilities are about

2 -3 2

1 cm /Vs and 10 cm /Vs. The hole-drift mobility is rather limited due to the large fraction of trapped holes in the valence band tail. The limited hole-drift mobility implies a decrease in the performance of devices, such as solar cells.

Recombination

Carriers generated by light or other excitation sources, or injected by applying a bias voltage on a device, undergo several relaxation processes, namely: hot carrier thermalization, trapping, and

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recombination. The methods currently applied to the study of these processes are time-resolved photolumlnescence, time-resolved photo-absorption and time-resolved photoconductivity. Time-resolved photolumlnescence Is based on the radiative transitions of the electrons from the conduction band-tail energy states to the valence-band tail energy states. Time-resolved photo-absorption is based on the different optical transition probabilities for trapped and excited carriers. Here, a second light pulse is used to probe changes in the photo-absorption caused by a preceding light pulse. Time-resolved photoconductivity is often performed In p-i-n structures by the time-of-flight technique described before.

Several conclusions can be drawn from these studies. First, there are several different recombination mechanisms operative in amorphous silicon. The relative importance of each depends on the the material properties and on the experimental conditions. The most important recombination in the bulk of the material occurs via defect energy states which lie close to midgap and belong to dangling bonds, and via the conduction- and valence-band tail energy states.

The contribution of the recombination through defective energy states to the total recombination depends on the concentration and the capture cross-sections of these states, and on the carrier transport to these states. At low temperatures, the relaxation processes which occur just after the electron-hole pair generation determine the contribution of the various recombination processes to the total recombination. The carriers trapped in the band tail energy states, are immobile and tail-to-tail recombination, either through radiative or through nonradiative tunneling prevails. Radiative tunneling can be observed from photolumlnescence. At elavated temperatures, the

carriers diffuse by multiple-trapping or by thermally-assisted hopping to the defective energy states, which form an effective recombination path.

Thermalization of hot carriers down to the mobility edge, occurs in the time scale of a picosecond, as is indicated by the picosecond time-resolved photo-absorption measurements of Vardeny and Tauc (1981) and Fauchet et al. (1986). The subsequent thermalization into the band-tail states was studied by Orlowski and Scher (1985) through

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time-resolved photoluminescence measurements, and by Vardeny et al. (1983), and Fauchet et al. (1987), through transient photo-absorption measurements in the 1 ps - 5 ns time domain.

Orlowski and Scher explained the temperature dependence of the initial decay of the high-energy photoluminescence signal attributed to tail-to-tail recombination, by electron hopping down into the band tail at temperatures between 20 and 100 K. Assuming an exponential band-tail distribution, the experimental data fit well to a theory describing this electron hopping for a hopping rate-prefactor of

13 -1

3.10 s and a relaxation energy width involving single hops of 20 meV, which is close to the peak in the acoustic phonon density. The nearest-neighbour hopping time is about 60 picoseconds. Multiple-trapping is unlikely to play a role in the relaxations at these temperatures. Only at 180 K, is the release time comparable to the observation time.

From the recovery time of the sub-bandgap absorption in transient photo-absorption measurements at room temperature, Fauchet et al. conclude that states 100 meV below the mobility edge can be populated by direct trapping within 1 - 2 ps, and by indirect trapping as through multiple trapping, within 10 ps. Vardeny et al. conclude from the temperature dependence of the decay of the above bandgap

absorption that geminate recombination is unlikely to occur above 80 K. Geminate recombination is the recombination of a generated electron-hole pair before they become separated. This conclusion is in agreement with room-temperature charge-collection efficiency

measurements in reverse biased solar cells, see for example Carasco and Spear (1983), see also Crandall (1984). Based on the Onsager model of geminate recombination, see Onsager (1938), the charge-collection efficiency measurements indicate that the zero-field generation efficiency is in excess of 90 X. According to the Onsager model, the distance over which the electron and hole become separated before the thermalization process has been completed, should be larger than the

2

Onsager radius r = q /(4ir.e.k.T) with q the elementary charge, e the dielectric constant, and k.T the thermal energy. In amorphous silicon the Onsager radius is about 5 nm at 300 K and 17 run at 80 K. Assuming

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the Einstein relation to be valid and a hot-carrier thermalization 2

time of 1 ps, this implies a hot-carrier mobility of 10 cm /Vs at 300 K, which is of the order of the extended-state mobility as deduced from time-of-flight experiments. The absence of significant fast geminate recombination at 80 K suggests a greater hot-carrier mobility but, in this case, carrier trapping should be properly taken into account.

Further information about the thermalization of carriers into the band tail can be deduced from the low-energy photoluminescence decay. At low temperatures amorphous silicon exhibits a strong broad

photoluminescence peak at 1.4 eV, which can be ascribed to the tail-to-tail recombination, see Street (1984b) for an overview. Whether this tail-to-tail recombination is geminate or nongeminate is not clear, according to Dunstan (1984,1985) who argued that distant-pair or non-geminate recombination cannot be ruled out in these

experiments. The distant-pair recombination is due to the build-up of a metastable carrier population in the tail states, during the

experiment. This population can be expected from the very wide range of photoluminescence decay times at low temperatures, see Tsang and Street (1979), and Hong et al. (1981). The wide range of

photoluminescence decay times can be explained by a tunneling rate which depends exponentially on the separation of the trapped electron and hole and a sufficiently broad distribution in this separation. Deconvolution of the luminescence decay at various temperatures by Hong et al. resulted in an initial separation distribution with a broad peak at 5 nm, under the usual assumption of a prefactor of the

8 -1

radiative tunneling rate of 10 s . The peak decay rate is of the -3 -4

order 10 - 10 s. At 10 K, the luminescence intensity drops rapidly 17 -3

when the defect density concentration exceeds 10 cm . This indicates that the critical transfer distance is about 10 nm, in agreement with the initial separation distribution.

At higher temperatures the recombination through the dangling bonds seems to dominate the recombination. Unfortunately, there is only very indirect experimental information about the competing nonradiative tail-to-tail recombination. Although it can be expected that the nonradiative tunneling rate depends exponentially on the

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separation of the trapped electron and hole, the prefactor of the nonradiative tunneling rate is unknown and can vary by many orders of magnitude, see for example Mott (1978).

Remembering the present uncertainty about the energy level of the most dominant defect, the dangling bond, and about the transport mechanism of the carriers, it is not suprising that the published values on the transition probabilities, expressed in capture cross-sections, are different. The results of Street's (1984a) charge

collection measurements and of Dogmane and Spear's (1986) steady-state double-injection experiment, both applied to relatively thick (>5 /im) p-i-n structures, are tabulated in table 1.1. Street measured the collected charge by means of the time-of-flight experiment, see also chap. 4. The capture cross-sections were derived from the formula CT.V , = n /(N,, ./i.r) where the p.r product was derived from the

experiment. The dangling bond concentration N,, was determined by ESR measurements. Dogmane and Spear derived the capture cross-sections from the mutual dependence between the electron and hole

photocurrents, each injected from the opposite sides of the reversed biased structure. They assumed a dangling bond concentration of

1 5 - 3

2.10 cm , which was plausible although it was not verified by other means. The table shows a main discrepancy in the hole capture cross-sections. Further, it can be seen that Coulombic capture-cross section is not much larger than the neutral capture cross-section.

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Table 1.1 Capture cross-sections for dangling bonds. a° and a are the electron and hole capture cross-sections of the

D center, a and a are the electron and hole capture

cross-sections of the D and D centers.

process

a (cm-2)

Dogmane & Spear

Street e •* D o '• -' a n ixicf15 2.7xl0~15 + e ■* D + a n 5.5xl0~15 15xl0~15 h -* D° o a P l.lxlO"16 8xl0"1 5 h -* D~ a P 2.7xl0"16 -15 20x10 1.2.2. Optical properties

In this subsection the photo-absorption spectrum of amorphous silicon is discussed. Time-resolved photo-absorption and time-resolved

photoluminescence were discussed in the previous subsection since they mainly provide information about carrier relaxation and recombination. For a general introduction to photo-absorption in amorphous silicon, the reader is referred to Cody (1984) and Amer and Jackson (1984).

Figure 1.4 shows the photo-absorption spectrum for a typical specimen of good quality 1 ftm thick amorphous-silicon film fabricated in our

laboratory. The absorption spectrum was measured by J.S. Payson of Energy Conversion Devices Inc. (USA) by photothermal deflection spectroscopy. This form of spectroscopy is based on the measurement of the temperature increase due to the light absorption in the film. Photothermal deflection spectroscopy has proved to be a sensitive and

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relatively simple tool for the characterization of amorphous silicon films. Jackson and Amer (1982) applied it for the first time to amorphous silicon.

1.4 1.8 hv(eV)

Fig.1.4 The photo-absorption spectrum of amorphous silicon, measured by J.S. Payson. The optical absorption coefficient a

is a function of the photon energy hv.

The absorption spectrum shows some features typical for amorphous semiconductors, see for example Mott and Davis (1979). First, there is no well defined optical bandgap, as in the case of crystalline

semiconductors. Instead, the spectrum exhibits three regions,

indicated in figure 1.4 as region A, B and C. Region A is the region which is thought to be above the optical bandgap. In this region absorption occurs predominantly by transitions between the valence band and the conduction band states. The absorption coefficient a is

above 10 - 10 cm

It is common to fit the spectrum in this region to the Tauc plot, see Cody (1984),

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(a.h.i/)1/2 - const.(h.i/ - E ) (1.2.3)

g

with h.i/ (eV) the energy of the absorbed photon which is Planck's constant times the photon frequency. The optical gap as defined by E is about 1.65 eV for this material. The optical bandgap as defined by equation 1.2.3 is not the mobility gap. Coincidentally, the optical gap coincides with the mobility gap within the error with which the latter can be estimated.

-1 -3 -1

Region B extends from o;^ -n 1 cm to a ~ 10 cm and exhibits an

exponential rise in the absorption as the energy of the absorbed photon increases. This region is usually called the Urbach edge, and is a consequence of the structural disorder in the material. It is closely related to the band-tail distribution. A recent theoretical study by Dersch et al. (1987) of a tight-binding model for a

disordered two-band semiconductor originated by Abe and Toyozawa, showed that for a short-range disorder potential, the photo-absorption tail is essentially determined by the density of energy states. For a long-range disorder potential, the absorption tail, which has been shown to be exponential, is dominated by the optical matrix elements. Unfortunately, it is still unclear how much the long-ranged disorder contributes to the total disorder in undoped amorphous silicon, see previous subsection. Experimentally, Jackson et al. (1985) obtained the optical dipole-matrix elements by comparing the photo-absorption optical spectra with the density of energy states determined from other experiments. From this comparison they obtained matrix elements independent of photon energy for 0.6 - 3.4 eV within the error of about 50 1 in their measurements. Thus, assuming constant

optical-matrix elements, the Urbach edge reflects the tail-state density. Because the conduction-band tail-state distribution is sharper than the valence-band tail-state distribution, the Urbach edge reflects the latter one. For the specimen of figure 1.4, the characteristic energy E which describes the absorption in this region according to

a = const.exp(h.i//E ) (1.2.4)

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Region C, where a is about 1 cm , is associated with the

defective energy states in the bandgap. As was discussed in the previous subsection, there is a remarkable correlation between the number of defects which can be estimated by separating the subgap defect absorption from the exponential band-tail absorption and the number of defects which can be obtained from electron-spin resonance

(ESR) measurements, and which are identified as dangling bonds. The subbandgap defect absorption or the excess optical absorption a due

to gap-states is given by

a = a - a .exp(h.i//E ) (1.2.5)

ex o r ' o

where a and E are obtained from a fit to the exponential absorption

in region B. Assuming again constant optical dipole matrix elements

a is related to the defect density concentration N by

ex J s J

N = 8.1015.f a .dE (1.2.6)

Jc ex

-3 15 N is expressed in cm . The factor 8.10 follows from the calculation of the optical matrix elements, see Amer and Jackson

(1984). The integral is taken over the region C. For this specimen, 16 - 3

N = 10 cm , which is typical for a good quality film. It should be noted that photothermal deflection spectroscopy also probes the

11 12 -2 surface states. Surface defect densities of 10 - 10 cm , see Jackson et al. (1983), can be expected and can not be ignored in this case. Therefore, N should be considered as an upper limit for the bulk density of energy states.

Accepting the idea that the dangling bonds are the predominant defect states, the correlation energy U for the silicon dangling-bond defect was estimated from the comparison of the photo-absorption spectra of undoped and phosphorus doped amorphous silicon, see Jackson (1982). U was found about 0.35 eV. Because two different materials were compared with each other, a recent combination of ESR and photo-absorption measurements applied to the same material, led to what is probably a better estimation for the correlation energy, which is U = 0.2 ± 0.1 eV, see Stutzmann and Jackson (1987).

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1.3 Recombination studied using the time-resolved microwave-conductivity experiment.

In this subsection, a typical phenomenon of amorphous semiconductors, that is the dispersion in the recombination process of electrons and holes, is discussed in the light of the results of the time-resolved microwave-conductivity experiment. Werner and Kunst (1984) applied this experiment for the first time to amorphous silicon. The experiment discussed here, was performed in collaboration with M.P. de Haas and J.M. Warman of the Reactor Institute of Delft

University of Technology, see Warman et al. (1988), and was applied to undoped amorphous silicon fabricated under standard conditions

described in chapter 2. A short description of the experiment is followed by a tentative explanation of the results.

In the time-resolved microwave-conductivity experiment, the electrical conductivity of the material is measured through the absorption of microwaves. The conductivity depends on the

concentration of electrons and holes. The electrons and holes are generated by irradiation by a 3 MeV electron beam pulse from a Van der Graaff accelerator of typically 10 ns duration, after which they disappear through recombination. Thus, the recombination process can be monitored through the measurement of the microwave absorption as a function of time. The advantage of this means of measurement is that electric contacts usually complicating the study of recombination processes can be avoided. The apparatus has been extensively described by de Haas (1977) and Warman (1982). A short account of the microwave cell containing the amorphous silicon is given here since it is the first time that a configuration of stacked amorphous-silicon films, as depicted in figure 1.5, was investigated by means of this experiment.

The microwave cell is the short circuit of a 7.11 x 3.56 mm waveguide. It is completely filled with 0.5 mm thick, 17 mm long Corning 7059 glass plates. Four of the glass plates are coated on both sides with 2 pm thick amorphous silicon films. Incident microwave

power (~ 100 mW, Ka band 26 - 40 GHz) is absorbed and reflected in the cell. The reflected power is detected by a diode and amplified.

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ELECTRON BEAM

WAVE GUIDEi

Fig. 1.5 Microwave cell containing amorphous-silicon films deposited on glass plates. The direction of the electric field F is perpendicular to the films.

The 3 MeV electron beam irradiates a region of 10 mm at the end of the microwave cell. The advantage of the electron-hole generation by 3 MeV electrons is that the generation profile is practically constant over a depth of 4 mm in a material with a density of 2.5 g/cm , that is within 30 X, see De Haas (1977), chapter 6, which is important for the quantitative analysis of a nonlinear recombination process. In

addition, no holes in the cell wall are required since a considerable number of the electrons can pass the wall. These holes, necessary if light is used as generation source, would hinder a quantitative analysis as they would distort the microwave pattern in a complicated way. Defect creation was found to be of no influence on the observed transients for the beam doses applied to this sample. This was concluded from the reproducibility of the transients after several experiments. The maximum beam dose is much smaller than the 3 MeV

o

electron beam doses of 0.6 and 1.2 G/cm which were applied by Street et al. (1979) and Voget-Grote et al. (1980) to amorphous silicon for the investigation of radiation induced defects. These doses led to

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18 19 -1

about 4x10 and 2x10 defects cm" , respectively. Although the electron fluence of about 10 C/s in the transient-microwave

conductivity experiment is much greater than the electron fluence used by these authors, it can be argued that the difference in the fluence Is of minor importance at these doses. Assuming that defect creation

13 -3 is linear to the beam dose, it is expected that 10 defects cm were created. Further, it can be shown that the production of Frenkel pair

12 -3

defects is less than 10 cm for a maximum dose of 100 nC applied to this sample, see for example Lehmann (1977), chapter 7.

The figures 1.6 and 1.7 show the electron concentration as a function of time at room temperature for different beam doses applied to this sample. The time resolution of the experiment Is about 1 ns. In figure 1.7, the transients of figure 1.6 are depicted on a double-logarithmic scale. Irradiation of a sample of uncoated glass resulted only in a transient during the pulse as illustrated by the shaded area In figure 1.6 for the highest beam dose. Therefore the transients following the pulse do originate from the amorphous silicon regions in these figures. The electron concentration in the pulse is quite high as compared with the electron concentration in a solar cell under AMI

15 -3 illumination which is about 10 cm

Actually, the measured signal corresponds to the absorbed

microwave power as a function of time. The calculation of the electron concentration from the absorbed microwave power is based on the

following assumptions. Firstly, the generated electron and hole concentration can be calculated from the beam dose and the relation between the electron-hole-pair formation energy E (eV) and the bandgap energy E (eV): E = 2.73xE + 0 . 5 . This relation was found applicable to a large number of materials, see Alig et al. (1980) and results in a pair formation energy of 5.1 eV for amorphous silicon with a bandgap 1.7 eV. The beam dose was measured with a reference cell. Secondly, the microwave signal of a transient originating from a very weak beam dose -not depicted in these figures- showing negligible decay, corresponds to the generated electron concentration. The hole contribution to the microwave absorption can be disregarded since significant more holes are trapped in deep traps than electrons (the distinction between deep and shallow traps is discussed below).

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0 20 M) 60 80 100 120 140 160 180 tins)

Fig. 1.6 The electron concentration as a function of the the time t for various doses. The shaded area represents the response of the glass plates for the highest beam dose. The inserted figure depicts the transients divided by the beam dose. The dashed-dotted lines in this figure result from the model.

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2 9

-CHAPTER 1: GENERAL INTRODUCTION

_ 10

1 10 10 10 10 t (ns)

Fig. 1.7 The electron concentration as a function of time t for various doses. The transients are identical to those of figure 1.6 but are here presented on a double logarithmic scale. The dashed lines are t" fits to the data, a is the

dispersion parameter.

Two striking features can be seen from the figures 1.6 and 1.7. First, the maximum electron concentration increases sublinearily with the excitation, indicating a biniolecular recombination process involving both electrons and holes. The biniolecular recombination seems to

15 -3 become important in electron concentrations above 10 cm , in agreement with Orlowski (1985). Second, there is dispersion in the recombination. The dispersion is manifested in the electron decay showing approximately a power law t behaviour between 1 and 1000 ns, as can be seen from figure 1.7. At longer times the electron

concentration decreased even slower. The t decay form was also observed in time-resolved-photoluminescence measurements, see for example Street et al. (1981), in time-resolved photo-absorption measurements, see for example Kirby et al. (1982), Pfost and Tauc

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(1983), Wake and Amer (1983) in time-resolved photoconductivity measurements, see for example Main et al. (1987), Fuhs (1985), and Werner and Kunst (1987), and in the time-resolved

microwave-conductivity measurements, see Werner and Kunst (1984,1986). In general, the dispersion parameter a is a function of the temperature, and depends on the material properties, such as the density of energy states. For a beam dose of 105 nC and for temperatures of 373, 293 and 197 K,, a was 0.68, 0.62 and 0.21 respectively. Figure 1.6 suggests

that a is weakly dependent on the beam dose, in correspondence with

the transient-photoconductivity measurements of Werner and Kunst (1987), and Orenstein et al. (1982), who investigated a-As.Se.. Since a is a phenomenological parameter and the decay is the result of a very complex process, the dependence of a on the beam dose can not be

easily explained.

A tentative explanation of the results, following Tauc (1984), Main (1987) and Werner and Kunst (1987), is based on a model which assumes that a considerable number of holes can be trapped in "special" energy states (in the valence band tail) which are not easily accessible to the generated electrons. The model is based partly on the very slow photocurrent decay or, equivalently, on the very long electron lifetime in slightly n-type doped amorphous-silicon films. It is noticed that the physical origin of such states, if they exist at all, has not been identified yet. The trapped holes are thermally released with a broad range of release times to energy states at the valence band mobility edge and contribute again to the holes which can recombine more easily with the electrons. It is shown that the temporary storage of holes in these special states provides a mechanism for the power-law behaviour of the electron concentration decay. Electron trapping in and release from conduction-band tail states is disregarded here, since the fastest decay time in the transients seems to be longer than the time in which electrons are trapped in and released from the conduction-band tail states, see subsection 1.2.2. Thus, the electrons are thought to be all in one state at the conduction-band mobility edge.

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As was discussed by Main et al. (1987), a rigorous calculation includes all the hole and electron reactions with these special energy states and the recombination centers. However, this calculation is rather elaborate. Alternatively, the demarcation energy concept in the thermalization approximation as developed by Orenstein et al.

(1981, 1982) and by Tiedje and Rose (1981) was applied to this problem.

The thermalization-approximation reduces the number of equations considerably through the introduction of the demarcation energy E,(t). The demarcation energy separates tail states between E and E,(t), from which the holes are released more than once in the elapsed time t after excitation, from the deeper states above E ,(t), where a hole is unlikely to be thermally released in the time t. The average thermal release time T ( E ) for a trapped hole in a tail state with an energy E - E above the mobility edge, is given by

r(E) = z^.expKE - Ev)/k.T] (1.3.1)

12 -1

v is the attempt-to-escape frequency and is about 10 s . The

demarcation occurs at' an energy where the trap release time, T ( E ) is equal to the delay after the excitation, t. Thus

E.(t) - E + k.T.ln(i/ .t) (1.3.2) d v o

As can be seen from equation 1.3.2 the demarcation energy moves away from the mobility edge E .

The trapped hole concentration varies with the time for two reasons. Firstly, because of hole trapping. If the capture rates of these energy states do not depend on the energy, the trapped hole occupation probability f depends on the time according to

^ = C°.(l - f).p (1.3.3)

C is the energy-independent capture rate and p - p(t) is the "free" hole concentration. The second reason that the trapped hole

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dependence of the demarcation energy E,(t). Since a trapped hole above E,(t) is unlikely to be thermally released in the time t, holes above E,(t) are thought to be trapped until time t. Consequently, the holes between E and E,(t) are thought to be free since they are released more than once in time t. The trapped-hole concentration is then

Ef

? t

- f . J N

(E).dE (1.3.4) Ed(t)

Assume an exponential energy distribution for these special energy states

N*(E) - N*.exp[-(Ev - E)/k.TQ] (1.3.5)

Substitution of Eq. 1.3.5 into Eq. 1.3.4, with E,(t) given by Eq. 1.3.2, yields

p„ = f.N*.k.T .(v .t)'a (1.3.6)

r t v o o v /

* -a

with a = T/T and N (E-) is very small. The t dependence of p is the

basis for the dispersion observed in the recombination process, see Orenstein et al. (1981) and Tauc (1984). For k.T ~ 50 meV, a is about

0.5. For t 4- 0 , p in equation 1.3.6 goes to infinity. This "problem" can be solved by considering the holes which are thermally released to the valence-band mobility edge within the time tf, that is, the holes

between E and E,(t_) = k.T.ln(i/ . t„) to be free and in one state, just as the electrons. The value of tf is of the order of the time

resolution of the measurement or of the order of the fastest decay time. It is clear that the value of t- has implications for the values of the parameters which describe the recombination process. Thus

Ef

pt = f. f N(E).dE-f.Nt (t < tf) (1.3.7a)

Ed(tf)

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EF pt - f. ƒ N(E).dE = f.Nt.(^-)'a (t > tf) ( Ed(t) f 1.3.7b) with N = k.T .N .exp[-E.(t.-)/k.T ] (1.3.7c) t o v r L d f ' oJ x

The Eqs. 1.3.7a and 1.3.7b lead to the following rate equations

d pt df

dT-3?

N

t

( t <

V

( 1

'

3

-

8 a )

|

£

= S.N

t

.(tr-f.|.

a

.(^)-

a

-

1

(t>t

f

) (1.3.8b)

where df/dt is given by Eq. 1.3.2. Consequently, the rate equations for the holes and electrons are

^ d

P-S = P-S - r

p

- S T <^-*>

g = g - r n (1.2.10)

g, r and r describe the electron and hole generation and recombination, respectively. To simplify the problem further, disregarding the transport of the "free" holes to the recombination centers, the free holes and electrons can recombine either via bimolecular recombination or via dangling bonds. The dangling bonds are assumed to be single defect centers. This assumption is disputable if the occupation of the dangling-bond energy states changes

appreciably with the time, which is the case for the high beam doses as was noticed by Halpern (1986). In the frame of a tentative

explanation of the experimental results this assumption is useable. In contrast with the bimolecular recombination, recombination via defect centers exhibits saturation effects which are related to the

occupation of these centers. The recombination terms r and r are p n r - C, . . n . p + C°.f2 C. N . c.

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r = C, . .n.p + C".(l-f" ).N. ...p (1.3.11b)

n bim r p def def r v

df

with ,^aer - (n.C° - p.C")/N. e (1.3.11c) dt n r p ' def

C, . is the bimolecular recombination constant, C and C are the _{bim ' n p} capture-rate constants for the electron into the neutral defect and the hole into the negative defect, respectively. N, „ is the defect concentration, f. f is the electron occupation probability for the

defect.

The equations 1.3.8, 1.3.9, 1.3.10 and 1.3.11 with the initial condition n(0) = 0, p(0) =0, p (0) = 0, f(0) = 0 , fjefo= 0 can be

solved numerically by means of a standard Runga Kutta method. The

c\ ft "\

values of the parameters C and C were taken 10 cm /s, which is of the order of the capture rate coefficients of the dangling bond energy states, see table 1.1 (The capture cross-sections a in table 1.1 are

related to the capture-rate coefficients C by the relation C = a .v ,

where v , = 10 cm/s is the thermal velocity). The parameters N, _, C, . , a and t,. were adiusted until a reasonable fit was obtained. The

b lm f J

great variation in beam doses reduced the ambiguity with which these parameters could be chosen. The parameters which fit the model to the experimental results are tabulated in table 1.2.

Although the measurements and the model are in a preliminary stage, a few conclusions can be drawn. First, the model can be fitted to the experiment for values of C , and a which fall within the range

of published values. The concentration of the special energy states N is comparable with the valence-band tail states concentration. The

-9

value t_ = 10 ns implies that the dispersion observed here, originates from energy states that lie farther from the valence-band mobility edge than 0.2 eV assuming a thermal

12

attempt-to-escape frequency v — 10 s. The defect density N

-is of the order expected for th-is quality of amorphous silicon. The value of the parameter C, . is of the same order as the value

r bim

which Werner and Kunst estimated. The value of C, . is less

b i m

than the value which would be expected on the basis of a

diffusion-controlled reaction with the Onsager radius as reaction

radius. This model was applicable to systems with d r i f t

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mobilities of the same order of magnitude as in the present case, see Warman (1982). Disregarding the hole drift mobility, this model

2 yields, for an electron drift mobility /i » 1 cm /Vs,

-7 3-1

C, . = /i.q/e - 1.5x10 cm s where e is the permittivity of amorphous silicon. The discrepancy suggests that there is an energy barrier which hinders electron hole recombination.

Table 1.2 Values for the parameters which fit the model to the experimental results in figure 1.6.

PROCESS hole trapping biraolecular recombination recombination via defects PARAMETER

a

4

N t CO Dim def defo C° n P VALUE 0.7 1.10-9 5.1017 4.10-9 5.10-9 2.1015 0 1.10-8 1.10-8 s -3 cm J cm-Vs o cm /s cm cm-Vs cm-Vs

Hole trapping was found to be essential to slow down the decay of the transients of the higher beam doses. The defects were necessary to obtain the initial decays of the low beam doses but were not important for the decays at the higher beam doses. From the simulations it was found the the fit of the highest beam dose was sensitive to the precise values of the parameters C, . , t_, C , and N indicating that the model presented here should be improved. At the moment it can only be speculated which assumptions should be improved first. It should be

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noticed that dispersion can be caused by many other mechanisms also, and further study of the recombination process is suggested to identify the source of the dispersion. More elaborate calculations, such as were done by Main et al. (1987), are then required.

Electron drift mobility

The electron drift mobility which can be derived from this experiment falls within the scope of values published in the literature and agrees well with the electron drift mobility determined from a time-of-flight experiment applied to the amorphous silicon deposited under the same conditions. Figure 1.8 shows the frequency dependence of the fractional change in the reflected power P (W) per unit beam charge AP/(P.Q) taken at a time of 10 ns after the pulse for a constant beam charge Q (C). The data show the typical interference type of

variations with frequency, characteristic of this type of measurement.

26 28 30 32 3<, 36 38 Frequency (GHz)