Drift mobility techniques for the study of electrical transport properties in insulating solids

JOURNAL OF NON-CRYSTALLINE SOLIDS 1 (1969) 197--214 © North-Holland Publishing Co., A m s t e r d a m

DRIFT MOBILITY

TECHNIQUES

OF ELECTRICAL

TRANSPORT

IN INSULATING

FOR THE STUDY PROPERTIES

SOLIDS

W. E. SPEAR Department of Physics, The University, Dundee, Scotland, U.K.

Received 11 December 1968 The paper reviews in some detail the principles and experimental techniques involved in drift mobility measurements. These are particularly suitable for transport studies in highly resistive, low mobility solids and examples of their application to crystalline and non-crystalline materials are given. A platelet specimen is fitted with electrodes on opposite sides and charge carriers are generated near the top electrode by a fast excitation pulse. Both light and electron pulses have been used and the particular advantages of electron beam excitation are discussed. A steady or pulsed applied field draws one type of carrier across the specimen and the transit time tt is determined either by charge integration or from the observed current transient. This leads directly to the drift mobility. A section of the paper deals with the effects of trapping on the measurements. Shallow centres, possessing a release time constant Zr "~ tt, lead at lower temperatures to a transport controlled by multiple trapping and release. Measurements in this range give information about such centres. Deep traps introduce disturbing polarisation effects and ultimately limit the applicability of the method. Details of a space charge neutralisation technique are given. A different, more "static" method developed by Davis is briefly described. 1. Introduction

I n recent years the range o f solid state research has widened considerably. There has, for instance, been a g r o w i n g interest in b o t h o r g a n i c a n d i n o r g a n i c m o l e c u l a r solids a n d i m p o r t a n t a d v a n c e s have been m a d e in o u r basic unders t a n d i n g o f d i s o r d e r e d structures a n d non-crystalline materials. As far as the electrical p r o p e r t i e s o f solids within these g r o u p s are concerned, the available d a t a indicate t w o p r e d o m i n a n t p r o p e r t i e s : fairly high resistivity and low carrier mobilities. B o t h o f these can present serious e x p e r i m e n t a l p r o b l e m s in a n y meaningful investigation o f electrical t r a n s p o r t . A t t e m p t s have been m a d e to develop m o d i f i c a t i o n s o f the c o n v e n t i o n a l H a l l effect technique which are suitable for m e a s u r e m e n t s on high resistivity solids1). A l t h o u g h the e x p e r i m e n t a l difficulties have been largely overcome, the m a j o r p r o b l e m lies in the m e a n i n g f u l i n t e r p r e t a t i o n o f H a l l d a t a o b t a i n e d on m a t e r i a l s with carrier mobilities b e l o w a b o u t 1 c m 2 sec-1 V - x . 197

198

W.E. SPEAR

The increased localisation of the charge carriers in low mobility solids introduces an entirely new aspect into the transport theory. Holstein 2) and others have treated this problem within the framework of small polaron theory and it is evident that the mechanism of charge transport in such materials may be basically different from the normal type of band conduction found in high mobility semiconductors. Similar fundamental differences affect the interpretation of the Hall constant. The theoretical work 3) on this subject leads to complicated, structure dependent expressions for the Hall mobility. Clearly, Hall effect measurements are no longer the useful and interpretable approach to electrical transport studies which they were in semiconductor physics. Drift mobility experiments, on the other hand, form a very direct approach in an investigation of transport properties. As shown by the work of Spear on vitreous Se 4, 5) and the application of similar methods to organic solids by Le Blanc 6) and Kepler7), drift mobility techniques are particularly suitable for materials possessing high resistivities and low carrier mobilities. They have since been applied to an increasing range of insulating solids and also to liquids. In the following the principles and experimental techniques involved in drift mobility measurements will be discussed in some detail, together with the problems introduced by trapping and space charge effects.

2. Principle of drift mobility measurements Consider first of all a trap free solid in the form of a thin platelet, thickness d, fitted with metallic electrodes T and B as shown in fig. 1. The top electrode is connected to a steady or pulsed source of potential. For the sake of the present discussion we shall assume that T is kept at a positive potential VAwith respect to ground. The bottom electrode is returned to ground through Excitation

E21

iI F--

te <
Irel>>tt 1 Fig. 1.

C

_

--~ AV

1

Illustrates the principle underlying drift mobility measurements on a highly resistive specimen.

DRIFT MOBILITY TECHNIQUES

199

the resistor R which is normally much smaller than the specimen resistance. Free carriers are generated by some form of transient external excitation which will be discussed in the next section. It is essential that the duration of the excitation pulse, t e, should be considerably shorter than the transit time t t of the generated carriers across the specimen. More easily interpretable results are obtained if the absorption depth 6 of the excitation is kept very much smaller than the specimen thickness d. In that case a narrow sheet of charge carriers of one sign is drawn across the specimen. Suppose that N of the carriers generated in a surface area A escape recombination between x = 0 and x = 6. The drifting sheet of charge at x = x' will modify the applied field E A= VA/d and elementary electrostatics show that E1 and E2, indicated in fig. 1, are given by

4nNe( x') EI(Xt)=EA--~- 1--~ ,

(I)

4nNe x' EE(X')= EA+ e A d '

(2)

where e is the dielectric constant of the solid. It can be seen that the drifting carriers perturb the field within the specimen. However, if N is kept sufficiently small, so that the self-field 4nNe/eA ~.EA, the internal field can be taken as VA/d. It should also be noted that this description of carrier transport applies to an insulating solid in which the dielectric relaxation time Zre~ is very much longer than the transit time. In this respect the situation differs fundamentally from the drift of minority carriers in an extrinsic semiconductor such as GeS), where the condition of local space charge neutrality during carrier transit forms a stringent requirement. The insulating material has an obvious advantage over the semiconductor in this respect, because drift mobility measurements on both types of carrier are possible within the same specimen by simply reversing EA. There are essentially two ways in which the transit time of the carriers can be determined. The first relies on charge integration and in this method the time constant CR must be much larger than the transit time t,. C denotes the total capacity across resistor R and includes that of the specimen, the leads and the input to the detecting system. As the generated carriers drift across the specimen, the changing fields E1 and E2 will cause a re-distribution of charge on the electrodes. For the bottom electrode this is according to eq. (2)

Aq = Ne x'/d.

(3)

The potential developing across R is then

Ne AV(t) = Cd vt,

(4)

200

w.E. SPEAR

during 0 < t < tt, where v = d/t t denotes the drift velocity. For t ~ tt, A V remains constant and equal to N e / C as long as t < C R . The typical pulseshape from which t t c a n be obtained is shown in fig. 2a. The linear rising edge implies that N remains constant during the transit, and that the drifting carriers do not interact appreciably with "deep" trapping centres (see section 4).

ql (a) , 0

tt

{t

0

t

i

t>

(d)

i ¢4 . . . . cJ

()

I

'~'

~

0

tt

Fig. 2. Typical pulse shapes observed in drift mobility experiments when the carriers are generated close to the top electrode, O>tt, (b) current pulse, C R ~ tt. In both (a) and (b) deep trapping is absent. (c) and (d) show corresponding pulse shapes when the drifting carriers interact with deep centres.

A l t e r n a t i v e l y , t t can be measured from the duration of the current pulse produced by the drifting carriers. In this case it is necessary to reduce R so that C R < t t. Eq. (3) leads to*

i=

Ne

d

v.

(5)

Therefore AV = R

Ne

d

v

(6)

for 0 < t < t t and A V = O when t ~ t t (see fig. 2b). The choice between these two methods of detection depends largely on the specimen capacity and the order of magnitude of It involved. In general, the integration technique is the more sensitive, particularly if t t lies in the range below about 10-5 sec. For instance, with a single crystal specimen of reasonable thickness (say 400/~m), C will be a few picofarad, provided a cathode follower mounted close to the specimen is used. In this case the transit of about 105 carriers will give an integrated signal of 5 mV. It is worth noting * A more general treatment has been given by Shockley 9) which gives eq. (5) as a special case.

DRIFT MOBILITY TECHNIQUES

201

that with this value of N, the perturbation of the field mentioned earlier is quite negligible as compared to the E A values used. The lower limit of tt that can be measured with any reliability is determined only by the overall rise time of the electronic equipment (say 5-10 nsec). If, on the other hand, we try to display the current pulse with a similar rise time, we shall have to reduce R to a value in the Kohm range. We then would require between 10 7 and 10 8 carriers to obtain a 5 mV current signal, if a typical value of v = 104 cm sec- 1 is assumed in eq. (6). For the measurement of transit times in the msec range, rise times are no longer critical and much larger values of R can be used without affecting the accuracy of the experiment. The sensitivity is then sufficient for most measurements in this transit time range. The advantage of displaying current pulses lies in the fact that in the presence of deep trapping (see section 4) it is normally easier to determine t t and also obtain directly a value for the free liftetime of the carriers. Once the transit time has been measured, the drift mobility is obtained from Iz = d / E A t t .

The safest procedure is to determine t t over as wide a range of applied fields as possible. A graph of l i t t versus E A should be a straight line, which may, however, not pass through the origin (see for instance ref. 4) if a trapped surface charge layer of essentially constant density builds up near the top electrode. /t is obtained from the gradient of the line. The nature of specimen electrodes is of importance but, in our experience, depends to a large extent on the solid under investigation. The type of drift mobility experiment described here relies on a well defined pulse of generated carriers and any effect which tends appreciably to broaden the sheet of carriers must be avoided. This applies particularly to the injection of excess charge from the electrodes during and after the transit of the generated (primary) carriers. In an extreme case, such as a CdS crystal or film with an injecting top electrode, the turnover at t t in the integrated electron signal will be completely absent. Therefore, ideally, the top electrode should be blocking to the charge carrier under investigation and extracting to that of the opposite sign. Artificial blocking electrodes have been used in drift mobility work, but the problem is that they normally tend also to impede the extraction of the opposite type of generated carrier. This is likely to produce disturbing polarisation effects and neutralisation techniques (section 5) are essential. Kepler 7) found that conducting glass electrodes, coupled purely capacitively to the anthracene crystal, led to satisfactory results. Spear and Mort a°) have

202

W.E.SPEAR

used 0.5 #m Pyrex films as a blocking top electrode on CdS crystals. The incident electron beam penetrated this electrode with negligible loss of energy. There is, however, some uncertainty in this arrangement as to the actual potential which develops across the crystal. In our experience it is better to aviod the use of artificial blocking layers and, if possible, to find a metallic electrode giving minimum injection. 3. Methods of excitation

Perhaps the most common method employed for the transient generation of excess carriers is to illuminate the top electrode with a light flash of suitably short duration. The efficiency of electron-hole generation rises rapidly as the photon energy approaches that of the fundamental absorption edge, so that the majority of carriers are generated within less than 1 pm of the illuminated surface. This can be a serious disadvantage. The density of imperfection centres is generally higher near a surface, and these, together with any surface states that might be present, will considerably shorten the carrier lifetimes in the generation region. As a result of enhanced deep trapping and recombination, the effective quantum yield may be low. However, there are exceptions to this argument. Of particular interest in the present context is the high quantum efficiency of vitreous Se films which reaches unity for light having an absorption depth of less than 0.1 pm (ref. 11). Experimentally, the problem consists of finding a light source which produces an intense flash of sufficiently short duration (t e,~ tt) in a suitable spectral range. Commercially available xenon-filled triggerable tubes normally give flashes having a halfwidth between 1 and 10 psec. They are therefore useful in cases when transit times are about 0.1 msec or longer. Their intensity in the visible and near ultraviolet spectral range is ample and filters can be used to isolate appropriate wavelength regions. However, as is frequently the case, free carrier lifetimes are the limiting factor, necessitating thin specimens, shorter transit times and excitation times below 100 nsec. A simple condenser powered spark gap in air will give flash lengths of about 100 nsec, but steady and reproducible operation is difficult to achieve. The design of a number of ultra-short, triggerable flash sources has been published in the literature 12) and some of these are commercially obtainable. Flash durations of 30 nsec down to a few nsec have been achieved. However, the difficulty arises, that with decreasing te the number of photons per flash tends to become too small for the production of a sufficient number of drifting carriers, suitable for measurements with wide band electronic equipment. Ultra-short light pulses from a Q-switched ruby laser have been used for the study of two photon processes and exciton interactions, partic-

DRIFT MOBILITY TECHNIQUES

203

ularly in organic crystalsla). The output intensity would be more than sufficient for application in drift mobility experiments, provided a laser working at a suitable wavelength were available. A second method of excitation involves the use of high energy fast particles, such as electrons or a-particles. The process of carrier generation is now fundamentally different from that in the optical excitation. The breakdown of the incident particle energy proceeds by a series of complex intermediate stages which are difficult to analyse in detail. The problem has been treated by Shockley 14) and more recently by Kleinl~). The quantity that concerns us in the present context is the average energy, e, given up by the incident particles in generating one electron-hole pair. There exists a remarkable correlation between e and the band gap, eg, of the material, which does not seem to depend on the details of the band structure. The correlation graph given in ref. 15 for ten crystalline solids with band gaps below 3 eV, suggests the relation e ~ 2.8 eg. Whether such a relatively high generation efficiency can be achieved generally in a wider range of solids is open to question. For instance, measurements of the generation efficiency under electron beam excitation in a non-crystalline solid, such as vitreous Se16), led to e-~ 18 eV, which amounts to almost 7eg. On the other hand, our recent measurements on a typical molecular crystal such as Xe, using a 40 kV electron beam, gave ~-~26 eV. As the band gap lies between 9 and l0 eV in solid Xe, this value is in agreement with the above relation. Our experience with electron beam excitation suggests that this is a most versatile technique which should be applicable in drift mobility measurements on a wide range of solids. Its main advantages over optical excitation are as follows: (i) There is ample intensity, even with nsec pulses, for the generation of a sufficient number of carriers. The design and construction of a suitable high voltage electron gun with magnetic focussing is a relatively easy matter. In an earlier version of the apparatus we used a mercury wetted contact relay to switch a delay line for the generation of the voltage pulses applied to the modulator grid of the electrode gun. Further details of electron gun and pulse generator are given in a paper by Spear et al. 17). (ii) The depth of the generation region below the top surface can be varied within wide limits by means of the accelerating potential Vc applied to the gun. Ehrenberg and King la) have investigated experimentally the penetration of fast electrons into a number of luminescent materials of different densities. Their curves, showing the energy dissipated per #m per electron as a function of the depth below the surface, provide useful information in the present discussion. In the case of a solid of low density, such as polythene ( p = 1.05 g cm-3), a l0 keV beam will generate practically all electron-hole

204

w.E. SPEAR

pairs within less than 2/~m of the surface. But on increasing Vo to 80 kV, the maximum of the energy loss curve is shifted to 5-~ 45/tm and the majority of carriers will now be produced between 30 and 60/tin below the surface. For a solid of intermediate density (p-~4.5 g cm-3, for instance CdS or vitreous Se), a 10 keV electron beam will generate carriers to a depth of about 0.5 pm, whereas 80 keV electrons will extend appreciable carrier generation to about 15 ktm. It is evident that the electron beam excitation technique permits the control of 6 over quite an appreciable range. As mentioned above this may have advantages if the surface lifetime of carriers is appreciably shorter than that in the volume of the material. In addition, the technique makes it possible to study carrier generation, transport and space charge distribution as a function of 5, particularly in thin film specimens. An investigation of the space charge distribution under electron bombardment in thin Pyrex, As2S 3 and Mica specimens has been carried out by Spear 19) and more recently by Ehrenberg and his collaborators 20). The effect of varying 6 in transport experiments on a vitreous Se specimen (d= 6.95/~m) is illustrated in figs. 3a and b. In the former, a negative potential is applied to the top electrode and

-q

l

.£

0

~

(a)

•

----

-

~-t

(b)

Fig. 3. Integrated pulses observed on a vitreous Se film, 6.95/tin thick, with excitation by 35 keV electrons. Now 5 ~0.4 d. Components hp and hn are produced by the drift of holes and electrons respectively. (a) top electrode negative, (b) top electrode positive.

the integrated electron signal obtained with V 6~- 6 kV (fig. 2a) changes to that shown in fig. 3a at VG--- 35 kV. Electrons and holes are now produced to within a depth of about 3 itm. The component hp, appearing on the oscilloscope trace, is associated with the reverse drift of the generated holes. It can easily be distinguished from the electron component h,, because the hole mobility in this material is appreciably larger than that of the electrons. On reversing VA (fig. 3b), the contributions to the total charge displacement of the electron and hole components are interchanged. At incident electron energies corresponding to practical range values approaching about 1.5 d,

DRIFT MOBILITY TECHNIQUES

205

the carrier generation becomes fairly uniform throughout the specimen and both components tend towards equal height. Measurements of hp and h, as a function of VC can lead to an approximate value for the volume recombination lifetime. In vitreous Se, this is about 2 x 10 -8 sec (ref. 21). (iii) Electron beam excitation largely overcomes the problem of absorption in the top electrode which may be a serious one when optical excitation is used in the "sandwich" cell configuration. A thin evaporated metal electrode may easily absorb almost all the incident light intensity, particularly in the ultraviolet, yet be practically transparent to a 10 keV electron beam. (iv) In transport studies on very wide band gap materials, such as the rare gas crystals, optical excitation of electron-hole pairs is hardly feasible, so that electron or ~-particle excitation is the only solution. The former approach was used recently by Miller, Howe and Spear 22) in a detailed investigation of the electron transport in solid Ar, Kr and Xe. It was found possible by this technique to extend the measurements into the region of low applied fields ( ~ 10 V/cm). This was of considerable importance, because pronounced hot electron effects made it impossible to obtain meaningful carrier mobilities from measurements at higher fields. On the other hand, Pruett and Broida 23) used 5 Mev a particles in similar experiments on rare gas crystals, but found that the low generation efficiency obtainable by this technique restricted their results to the high field range (e.g. E g 15 kV/cm for Ar). The reason for the large discrepancy in e deduced from these two techniques is not clear. The main disadvantage of electron beam excitation lies in the fact that the experiment has to be carried out in a vacuum, 10 -4 Torr or better. If the solid under investigation is mounted in the same system, its vapour pressure has to be sufficiently low in the temperature range of interest. This is frequently the case, but in the rare gas solids vapour pressures of several hundred torr occur near the triple point. This problem was overcome in the work referred to above by growing and investigating the specimen in a small chamber isolated from the main vacuum system. The bottom electrode on which the crystal was grown is made of 6/~m gold plated Mylar foil, stretched tightly over an electron microscope mounting grid. The electron beam passes through this electrode with about 3 0 ~ transmission. The same technique has also been used in work on the rare gas liquids 22) and has probably wider applications to transport measurements in the liquid state. Fig. 4 shows in some detail the experimental arrangement used in drift mobility measurements under electron beam excitation. The electron gun, kept at the negative high tension, is of the tetrode type. This has the advantage that the beam current is practically independent of Vc. The emission from the tungsten hairpin filament F is normally biassed off by the battery B ( ~22 V). A fast rising positive voltage pulse, produced by switching the delay

206

W.E.SPEAR

line D L is fed through the terminated connecting line CL to the modulator grid of the gun and switches on the electron beam for the duration of the pulse. The beam current is simply controlled by the charging potential applied to DL. The mercury wetted contact relay mentioned in (i) above has, in the present design, been replaced by an avalanche transistor, which makes precise triggering possible. The latter is achieved by an optical link consisting

I

:;~

D,"

F

E%, oo i

-vG

r :

[]i

lamp I~

I'

Trigger

]_

,

l

I

IL-.II t__.l l\.,"

]llrec°raerl

Fig. 4. Experimental arrangement used in drift mobility measurements under electron beam excitation. (F) hairpin filament; (DL) delay line; (CL) connecting line; (M) magnetic lens; (S) specimen; (CF) cathode follower; (PA) pre-amplifier.

of a GaAs lamp at ground potential and a photo-transistor and amplifier at l/C. A master unit triggers the beam, the oscilloscope and, when working with pulsed applied fields, the field unit. The system can be run in "single shot" mode or at repetition rates of 50 or 100 ppsec. The electron beam is focussed by the magnetic lens M into a uniform spot of 1-2 mm diameter which just fills the aperture above the specimen S. It is convenient to use a second lens (not shown) which directs the beam into a small Faraday cylinder for measuring directly the number of electrons in the incident pulse. A cathode follower CF is mounted close to the bottom electrode of the specimen. Its output is fed into a wide band oscilloscope, preceded by a preamplifier if necessary. With a sampling plug-in unit the output pulses can be directly recorded on an X - Y recorder. The charge sensitivity of the system is obtained by applying a pulse of known height to the cathode follower input through the small standard condenser Cs ("~ 1 pF). -

207

DRIFT MOBILITY TECHNIQUES

4. The effect of trapping on drift mobility measurements So far it has been assumed (section 2) that we are dealing with a trap-free solid. Unfortunately, trapping effects often present a serious problem in drift mobility studies and ultimately limit the applicability of the transient method. In the following the effect of various regions of the trapping spectrum will be briefly discussed on the basis of the simple model shown in fig. 5./~o is the

1:

Nc

tConducting states

a:d

jUo,no ~ A

N t --

--

/EC

-~ ~__--_~ nt--v~:t _ - -

(~r)~

ShallOWand deep traps

-

Fig. 5. Model used in discussing the effect of shallow and deep trapping centres on drift mobility measurements, r and r~ refer to shallow traps and denote the free electron lifetime and the average time before thermal release respectively, ra and (rr) a are the corresponding quantities for deep traps. mobility of the n o free carriers in the conduction band of the solid. Their lifetime with respect to any particular group of traps, et below the band edge, is T. The probability per sec of thermal release from these centres is denoted by 1/zr. Let us first consider the effect on the measured drift mobility p of a single level of shallow electron traps, characterised by the following conditions: "t'r'~/t, I:,~ t t. It can easily be shown that the electron transit, particularly at lower temperatures, will now be controlled by multiple trapping and release. During the transit,

(7)

nop o = (n o + n,) It.

On the assumption that the carrier densities approach the thermal equilibrium distribution (8)

n, = N t e x p ( e t / k T)"

no

N¢

Eqs. (7) and (8) lead to the drift mobility

P=Mo

[

Nt e x p ( ~ , / k T

I+N~

,1

.

(9)

At sufficiently high temperatures, the probability of thermal release is high, and P~-/~o- With decreasing T, the second term in the denominator of eq. (9)

208

W.E.SPEAR

rapidly becomes the dominant one and

No --- ~o ~ exp(- ~,/kr)

(10)

It follows from eq. (9) that shallow trapping (i.e. z r ~ tt) has no appreciable effect at the high temperature end, and drift mobility measurements will lead to the lattice mobility in the particular band. With decreasing temperature a growing fraction of the measured transit time will be due to the localisation of the drifting carriers in shallow centres. This, however, does not normally lead to any limitation from the experimental point of view. On the contrary, useful information on the density and position of a level of shallow centres can be obtained from an analysis of the results. The transition between the two types of transport has been observed in drift mobility measurements on quite a number of solids such as CdSl°), ZnS z4), monoclinic SeZS), trigonal Se z6) orthorhombic S 37) and iodine2S). Fig. 6 shows a typical example of such measurements on CdS 29), which also indicates the type of information that can be obtained about the shallow defect centres. The measured electron drift mobility is plotted as a function of lIT for two distinct types of CdS crystal (A and B) which differ in their shallow defect structure. The solid curves were calculated from eq. (9), using the values of et and N t given in the caption. Crystal A, having the lowest density of shallow centres, gives drift mobilities which closely follow the lattice curve #0 from 400°K to about 140°K. Below this temperature multiple trapping becomes the predominant effect. Type B crystals differ from those

/do

~

I0 ~

I0 z

if"

,

/

/

B

i

io

} 2

4

5

103IT(T

8 in *z)

10

12

Fig. 6. Temperature dependence of the electron drift mobility in CdS specimens. Solid curves have been calculated from eq. (9). Crystal A: et =0.043 eV, Nt =3.5 × 1015m-Z; crystal A': et = 0.030 eV, Nt "" 1017cm 3; crystal B: et = 0.16 eV, Nt = 5 × 1016cm-3. /to denotes the lattice mobility.

209

DRIFT MOBILITY TECHNIQUES

of type A by a fairly high density of trapping centres situated 0.16 eV below the conduction band. As shown in fig. 6 (curve B), these lead to trap controlled behaviour even above room temperature. The density of the 0.16 eV defects can be reduced by heat treatment and this process has been followed by drift mobility measurements at various intermediate stages29). Fig. 7 shows the temperature dependence of electron and hole mobility in a non-crystalline solid, vitreous Se. This is a very suitable material for drift i

i

: , : x S p e a r (1957,1960', A ~ Hartke (1962) °O°lo.A

7U 10-1

"-~ ... Holes ""~-.w.. ¢ = 0.14 eV .,v.A%x=

.o

10

o

'~,,~

E

|&

L

A

~\

Electrons

°~1.

-3

¢ = 0.26

eV

~",, o~, ~ , ~ o ~ I

10

40=C 20°C O=C -20 °C I

10-4 3.2

I

3.6

I I I

4.0

-40°C -500C, ~

I

4.4

103//T Fig. 7. Temperature dependence of the electron and hole drift mobilities in vitreous Se

films. The results of Spear 4,5) and of Hartke 37) are compared.

mobility experiments and the agreement between the measurements of Hartke aT) and the earlier work of the author4, 5) is remarkably good. Electron and hole transport is an activated process and corresponds to activation energies of 0.26 eV and 0.14 eV respectively. The interpretation of these results is not entirely clear. The hole transport could be explained through eq. (10) in terms of a comparatively large density of similar defects along the Se-chain. However, the results of the small polaron theory z) show that phonon assisted hopping conduction should also lead to an activated temperature dependence. The electron mobility, about 5 x 10-3cm 2 sec -1 V -1 at 20°C, lies well within the range of magnitudes one would expect for this

210

WoE.SPEAR

mechanism, but the experimental evidence available so far does not allow us to distinguish between hopping and trap controlled transport. Let us now consider the second group of centres, the "deep" traps. These are defined in the present context by the condition: (rr)d >>tr Their effect on the measurements will depend on the lifetime zd of the free carriers with respect to deep trapping. If, for instance, zd > tt, then the presence of deep centres will have little effect. With shorter lifetimes, rd'-'/t, there will be a loss of free carriers during the transit, so that N is no longer constant in eqs. (4) and (6), and pulses will have have the form shown in figs. 2c and 2d. If the integrated pulse is displayed, as in fig. 2c, values of z a, t t and p can be obtained from measuring the time t'. This methode has been used in hole transport measurements on CdSl°). If possible, it is more convenient to display the current pulse which leads directly to a value of t t and rd" Fig. 2d is typical of the pulse shapes observed in recent work on electronic transport in liquid, ultrapure S 30). Gibbons and Spear z0 have used an interesting method to determine Td for electrons in orthorhombic S at various depths within the crystal. Electrons are generated in a space charge free crystal and the field is applied for a time T < t t. It is then interrupted for a period ti, which in the experiments could be varied between 50 psec and 100 msec. During this time the carrier cloud at a depth x = p ~ E T interacts with deep trapping centres. When the field is re-applied at T + tl to complete the transit, the change in pulse height provides a direct measure of the number of carriers lost to deep traps in time tl. As expected, the results show a marked decrease in ~d on approaching the specimen surface. Finally, if za is appreciably shorter than tt, e v e n at high applied fields, then the drift mobility methods described can no longer be applied. It may, however, be possible in some cases to overcome this limitation by reducing the specimen thickness. But this will necessitate faster electronic equipment and shorter te- In the extreme case za'~ tt a different experimental approach, briefly discussed in section 6, would seem more suitable.

5. Space charge effects In this section we shall discuss two kinds of space charge effects which are of importance in drift mobility measurements. The first is connected with the presence of deep trapping centres in the volume and particularly near the surface of the specimen. The gradual build-up of charge in such centres during successive transits will modify the internal field, so that the assumption of an essentially uniform field is no longer valid. Experimentally, one observes slow polarisation effects in which the transit signal gradually

211

DRIFT MOBILITY TECHNIQUES

diminishes in size during the first few seconds after switching on the excitation pulses. Occasionally the signal disappears completely and it must be concluded that in this case the resultant field has become extremely small in part or all of the specimen. Similar observations have frequently been made with crystal counters. To eliminate disturbing effects of this kind two precautions are essential: first, the density of generated carriers should be kept as low as is consistent with the sensitivity of the detecting equipment and secondly, space charge neutralisation techniques should be used. A simple, but effective, method consists in running the excitation pulses at a repetition rate of about 1 ppsec with both electrodes earthed. The presence of an internal charge distribution, particularly near the top surface, is indicated by the appearance of a reverse signal, caused by the displacement of generated carriers in the space charge field. This signal decreases as the trapped charges are removed by recombination and normally disappears after a few excitation pulses. The external field is then applied across the specimen, but is removed as soon as the transit has been recorded. This obviously tedious procedure is carried out automatically in the experimental arrangement shown in fig. 4, section 3. The sequence is illustrated in fig. 8. Line (a) represents the output of the trigger unit in the form of short pulses, 10 msec apart. These are divided by 2, 4 (as in (b)) or 8, and this signal is used to trigger the field unit. In the present example a 5 msec field pulse is

Trigger unit

~ms A

VA v

(c)

i

Field pulses

I i

k

(e) I

'

Observed signals 1

'

Fig. 8. Space charge neutralisation technique used in drift mobility measurements22). (a) output of trigger unit (fig. 4), (b) output divided by four, (c) field pulses, triggered by signals (b), (d) electron excitation pulses, triggered from (a) and phase shifted, (e)observed signals: intergated transit pulses, followed by discharge pulses.

212

W.E.SPEAR

obtained at 40 msec intervals (c). The electron excitation pulses (d) are triggered from signal (a) via the optical link, but a variable phase shift unit allows the excitation pulses to be positioned in the centre of the field pulses. Line (e) shows the observed signals. Each integrated transit pulse (not resolved on the msec time scale) is followed by three discharge pulses, so that the transit is observed in an essentially unpolarised specimen. This system has been used with considerable success in our work on the rare gas solids and liquids 22), where surface polarisation presented a particular problem. The second effect to be discussed is connected with the space charge of the drifting carriers themselves. If N is increased sufficiently (which can easily be done with electron beam excitation for most te) the self-field 4rcNe/eA can be made to approach the value of the applied field EA. Eqs. (1) and (2) show that fields E~ and E2 will now be very different and one would expect marked changes in the observed signal. Many and Rakavy 32) have analysed the case of transient space charge conduction on the assumption of a carrier reservoir close to the injecting electrode, so that carriers enter the solid during and after the first transit. The predictions of this model have been substantially verified by Many and his co-workers in their experiments on iodine 28). More recently Papadakis 83) has considered the perturbation of the current flow in the absence of a carrier reservoir, that is under conditions which apply to the drift mobility method described here. The experiments of Gibbons and Papadakis 84) on transient space charge perturbed currents in orthorhombic S are in agreement with these predictions. Fig. 9 shows a typical electron transit signal when 4rcNe/eA~- ½E A. The prominent feature is the cusp at about

0 Fig. 9.

= 0.8 t t

t ~"

Current pulse showing the effect of space charge perturbation on the electron

transit in orthorhombic S. (From a photograph by D. J. Gibbons, thesis, University of Leicester.)

which also occurs under the experimental conditions used by Many et al. The physical reason for this pulse shape is as follows: electrons near the leading edge of the generated cloud experience the larger field E 2 and "run away" from the slower moving carriers. The current will increase until the extraction of the faster carriers causes it to drop beyond the cusp. The 0.8 t t

DRIFT MOBILITY TECHNIQUES

213

position of the cusp in terms of the transit time depends somewhat on the ratio of applied to self-field. If N is kept reasonably constant during the experiment, the cusp forms a useful feature for the accurate measurement of transit time. However, with increased N, effective space charge neutralisation between excitation pulses becomes most important, as is clearly shown by the work on orthorhombic Sa4). 6. A different approach to drift mobility measurements As discussed in section 4, the condition za'~ tt limits the applicability of any method employing fast transient excitation. It would seem, however, that a more "static" method could provide a suitable basis for transport measurements in materials where localisation in deep trapping centres is a predominant effect. The recent work of Davis 3~) is an interesting attempt in this direction. Suppose a surface charge ao (per cm 2) is placed at t = 0 on the free surface of a specimen, such as glass or polythene. The opposite surface rests on a earthed metal plate. Positive and negative carriers injected from opposite sides of the specimen will gradually drift in the field produced by the charge distribution. Davis showed that under certain conditions ao a(t)-

2rrtro 1 + e d - /at,

(11)

where p denotes the resultant mobility of both types of charge carrier. The experiment is carried out in high vacuum, using a comprehensive design of the apparatus which also permits other measurements on the same specimen. Its main feature is a moveable arm which carries the specimen. The charge distribution on the free surface is monitored by oscillating the arm below a probe connected to an electrometer amplifier and oscilloscope. From the calibration36), tr0 and tr(t) can be obtained absolutely and it is also possible to check any lateral spread of the surface charge. The results on 0211 glass are found to satisfy eq. (11) and lead to p'-'10 -8 cm 2 sec - I V - I at 20°C. The temperature dependence of p gives an activation energy of 0.80 eV. The interpretation of these data is a difficult problem, particularly as it is by no means clear whether the mobility refers to an electronic or ionic transport. Nevertheless, it is felt that an experimental approach of this kind, extended to a wider range of very low mobility solids, should lead to more conclusive information about their transport properties.

214

w.E. SPEAR

References 1) See for instance, A. G. Redfield, Phys. Rev. 94 (1954) 526; J. Dresner, J. Phys. Chem. Solids 25 (1964) 505; H. Gobrecht, A. Tausend and G. Clauss, Z. Physik 176 (1963) 155; A. M. Goodman, Phys. Rev. 164 (1967) 1145. 2) T. Holstein, Ann. Phys. (N.Y.) 8 (1959) 343. 3) L. Friedman and T. Holstein, Ann. Phys. (N.Y.) 21 (1963) 494; Yu. A. Firsov, Soviet Phys.-Solid State 5 (1964) 1566; J. Schnakenberg, Z. Physik 185 (1965) 123. 4) W. E. Spear, Proc. Phys. Soc. (London) B 70 (1957) 1139. 5) W. E. Spear, Proc. Phys. Soc. (London) 76 (1960) 826. 6) O. H. Le Blanc, J. Chem. Phys. 33 (1960) 626. 7) R. G. Kepler, Phys. Rev. 119 (1960) 1226. 8) J. R. Haynes and W. Shockley, Phys. Rev. 81 (1951) 835. 9) W. Shockley, J. Appl. Phys. 9 (1938) 635. 10) W. E. Spear and J. Mort, Proc. Phys. Soc. (London) 81 (1963) 130. 11) See for instance, fig. t in J. L. Hartke and P. J. Regensburger, Phys. Rev. 139 (1965) A 970. 12) For instance, H. Fischer, J. Opt. Soc. 51 (1961) 543; R. C. Mackey, S. A. Pollack and R. S. Witte, Rev. Sci. Instr. 36 (1965) 1715. 13) J. L. Hall, D. A. Jennings and R. M. McClintock, Phys. Rev. Letters 11 (1963) 364; K. Hasegawa and S. Yoshimura, J. Phys. Soc. Japan 20 (1965) 460. 14) W. Shockley, Solid State Electron. 2 (1961) 25. 15) C. A. Klein, J. Appl. Phys. 39 (1968) 2029. 16) W. E. Spear, Proc. Phys. Soc. (London) B 69 (1956) 1139. 17) W. E. Spear, H. P. D. Lanyon and J. Mort, J. Sci. Instr. 39 (1962) 81. 18) W. Ehrenberg and D. E. N. King, Proc. Phys. Soc. (Londen) 81 (1963) 751. 19) W. E. Spear, Proc. Phys. Soc. (London) B 68 (1955) 991. 20) W. Ehrenberg and B. Ghosh, J. Phys. (C), in press; C. Bowlt and W. Ehrenberg, J. Phys. (C), in press; C. Bowlt, Brit. J. Appl. Phys. 18 (1967) 1585. 21) W. E. Spear, unpublished. 22) L. S. Miller, S. Howe and W. E. Spear, Phys. Rev. 166 (1968) 871. 23) H. D. Pruett and H. P. Broida, Phys. Rev. 164 (1967) 1138. 24) P. G. Le Comber, unpublished. 25) W. E. Spear, J. Phys. Chem. Solids 21 (1961) 110. 26) J. Mort, Phys. Rev. Letters 18 (1967) 540. 27) A. R. Adams and W. E. Spear, J. Phys. Chem. Solids 25 (1964) 1113. 28) A. Many, M. Simhony, S. Z. Weiss and Y. Teucher, J. Phys. Chem. Solids 25 (1964) 721. 29) G. W. Bradberry and W. E. Spear, Brit, J. Appl. Phys. 15 (1964) 1127. 30) P. Ghosh and W. E. Spear, J. Phys. (C) 1 (1968) 1347. 31) D. J. Gibbons and W. E. Spear, J. Phys. Chem. Solids 27 (1966) 1917. 32) A. Many and G. Rakavy, Phys. Rev. 126 (1962) 1980. 33) A. C. Papadakis, J. Phys. Chem. Solids 28 (1967) 641. 34) D. J. Gibbons and A. C. Papadakis, J. Phys. Chem. Solids 29 (1968) 115. 35) D. K. Davis, in: Proceedings of the Static Electrification Conference (1967). 36) D. K. Davis, J. Sci. Instr. 44 (1967) 521. 37) J. L. Hartke, Phys. Rev. 125 (1962) I 177.