Scattering studies of photostructural changes in chalcogenide glasses

Scattering studies of photostructural changes in chalcogenide glasses

Journal of Non-CrystallineSolids 59 & 60 (1983) 899-908 North-HollandPublishingCompany 899 SCATTERING STUDIES OF PHOTOSTRUCTURAL CHANGES IN CHALCOGE...

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Journal of Non-CrystallineSolids 59 & 60 (1983) 899-908 North-HollandPublishingCompany

899

SCATTERING STUDIES OF PHOTOSTRUCTURAL CHANGES IN CHALCOGENIDE GLASSES S.R. ELLIOTT Department of Physical Chemistry, University of Cambridge, Lensfield Road, Cambridge, U.K. Structural changes which occur in chalcogenide glasses upon absorption of bandgap l i g h t have been investigated using neutron d i f f r a c t i o n . The f i r s t part of t h i s paper describes studies by small-angle neutron scattering of the i r r e v e r s i b l e photostructural changes which occur in obliquely evaporated amorphous chalcogenide f i l m s . The second part deals with the reversible photostructural e f f e c t observed in chalcogenide glasses, investigated by conventional neutron d i f f r a c t i o n and EXAFS experiments. The various models which have been proposed f o r the photostructural e f f e c t are discussed in the l i g h t of these experimental r e s u l t s . I. INTRODUCTION Chalcogenide semiconducting glasses, containing a large proportion of chalcogen atoms (S, Se or Te) together with As or Ge, are distinguished by the fact that i l l u m i n a t i o n with l i g h t having photon energies comparable to the bandgap induces a host of s t r u c t u r a l and concomitant o p t o - e l e c t r o n i c , chemical and mechanical changes. gories 1'2'3 "

These photo-induced effects may be divided into two cate-

irreversible

phous thin f i l m s , and

changes produced in as-deposited evaporated amor-

reversible

changes produced in well-annealed films or

melt-quenched glasses which can be annealed out by heating the sample to the g l a s s - t r a n s i t i o n temperature.

We have studied both forms of photostructural

change, and the results of our s t r u c t u r a l i n v e s t i g a t i o n s are reported here. The f i r s t

part of the paper deals with a study of the i r r e v e r s i b l e photodensi-

f i c a t i o n which occurs in obliquely evaporated amorphous chalcogenide thin f i l m s . The second part deals with conventional neutron d i f f r a c t i o n and EXAFS studies of the reversible photostructural e f f e c t in melt-quenched chalcogenide glasses. 2. IRREVERSIBLE PHOTOSTRUCTURAL CHANGES 2.11ntroduction I r r e v e r s i b l e , o p t i c a l l y - i n d u c e d s t r u c t u r a l changes are often observed in asprepared, vapour-deposited amorphous chalcogenide thin f i l m s .

Two cases may

be distinguished, f o r which the films e i t h e r consist of molecular units weakly bonded together, or are macroscopically inhomogeneous.

The former case is

exemplified by As2S3 : the predominant vapour species are in fact 4'5 As4S4 and As4S3 (not As4S6), together with S2. When deposited onto a cool substrate, the r e s u l t a n t f i l m consists of an imcompletely polymerized aggregate of such 0022-3093/83/0000-0000/$03.00 © 1983 North-Holland/Physical Society of Japan

S.R. Elliott / Scattering studies of photostructural changes

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molecular units 6'7, mainly bonded together weakly by Van der Waals forces. The e f f e c t of i l l u m i n a t i o n with bandgap l i g h t (or of thermal annealing) is to increase the degree of polymerization and c r o s s - l i n k i n g , causing the structure to be more akin to that of the melt-quenched glass, as shown by X-ray d i f f r a c tion 1'2, and EXAFS and Raman spectroscopy. 7 The other type of amorphous chalcogenide f i l m which e x h i b i t s i r r e v e r s i b l e photostructural changes is that produced by oblique vapour deposition, and is the subject of this part of the paper.

Many materials when deposited as thin

films by evaporation at oblique angles of incidence ( p a r t i c u l a r l y onto lowtemperature substrates) are macroscopically inhomogeneous and e x h i b i t a columnar growth morphology8; the columnar growth has been postulated to occur as a r e s u l t of self-shadowing of the incident evaporant beam.8

Obliquely evaporated

amorphous chalcogenide films ( p a r t i c u l a r l y Ge chalcogenides) also appear to be macroscopically inhomogeneous, and furthermore e x h i b i t some s t r i k i n g photoinduced changes. 9

I r r e v e r s i b l e photodensification (equivalent to a photocon-

t r a c t i o n in thin f i l m s ) has been observed, the magnitude of the change increasing with increasing angle of deposition, ~; for ~ = 80o , the percentage increase in density has been found to be 19% f o r GeS2 and 12% f o r GeSe2 f i l m s , respectively.

Concomitant photo-induced changes in the o p t i c a l properties of

o b l i q u e l y deposited chalcogenide films have also been observed.

The Urbach

edge is observed to s h i f t to lower energies (by O.32eV for GeS2 and O.13eV f o r GeSe2 f o r ~ = 80o films 9, and changes in the o p t i c a l constants, n and k, are also observed

(An/n = 8% f o r GeS2, 3.5% f o r GeSe2, and Ak/k = 30% f o r GeS2,

20% for GeSe2, f o r ~

80o f i l m s 9 ) .

The v i b r a t i o n a l properties of the films

are also changed by the absorption of bandgap l i g h t , as evinced in the far-IR absorption spectra I0, and even the chemical c h a r a c t e r i s t i c s of the films s u f f e r photo-induced changes, e.g. in the rate of chemical etching. I I In summary, the largest photo-induced changes are observed in those films deposited at the largest angles of incidence, and furthermore the presence of S or Ge tends to increase the magnitude of the changes, while As or Se (and p a r t i c u l a r l y Te) tend to decrease the e f f e c t .

For films deposited at oblique

angles of incidence, a large component of the photo-induced changes are i r r e v e r s i b l e in nature.

For example, for as-deposited ~ = 80o f i l m s , i t has been e s t i -

mated9 that a proportion of about 67% of the observed photo-optical changes is i r r e v e r s i b l e , the rest being reversible :

i t is i n t e r e s t i n g to note that the

size of the reversible component in ~= 80o films is about the same as the

total

magnitude of the (completely reversible) changes observed in well-annealed = 0° films. The presence of the i r r e v e r s i b l e component of the photo-effect in o b l i q u e l y

S.R. Elliott/ Scattering studies of photostruetural changes

901

deposited films is obviously closely related to the p a r t i c u l a r microstructure e x i s t i n g in such f i l m s . Thus, in order to reach a complete understanding of the photo-effects, i t is essential to investigate the microstructure, which we have chosen to do using small-angle neutron scattering (SANS). The system which we have studied is a-Ge25Se75, the composition which has been shownl~o e x h i b i t the largest photo-effects. 2.2. Experimental Thin films (=2~m) of a-Ge25Se75 were deposited onto s i l i c a substrates by evaporation of powdered bulk glassy Ge25Se75 at a rate of =20~ s - l ,

using a con-

f i g u r a t i o n which ensured that the rate of deposition was approximately constant f o r a l l angles of deposition (~=0-80° , r e l a t i v e to the f i l m normal). The measurements reported here were performed on the DI7 SANS d i f f r a c t o m e t e r at the ILL, Grenoble, using neutrons of IOX wavelength and with the area detector positioned 1.4m from the sample. This configuration maximizes the neutron f l u x at the detector and gives a Q range from 2wlO-3X -I to 2.5wlO-2X - I . Counting times of about 6h were required f o r the 2~m thick f i l m s . 2.3. Results SANS was observed from a l l the films studiedl~ but the scattering i n t e n s i t y was greatest f o r those f i l m s deposited at the largest angles of incidence, i . e . ~=80°. A contour p l o t showing the scattering i n t e n s i t y r e s u l t i n g from the normal incidence of neutrons on an ~=80° f i l m is shown in f i g . l ( a ) . The SANS is markedly a n i s o t r o p i c , and is d i r e c t evidence f o r the presence of structural inhomogeneities which are anisotropic in shape r e l a t i v e to the f i l m normal. The inhomogeneities are elongated r o d l i k e voids (or low-density regions), which delineate the columnar morphology of the high-density regions, but which do not necessarily l i e p a r a l l e l to the d i r e c t i o n of the o r i g i n a l evaporant beam. An empirical r e l a t i o n s h i p between the angle of the evaporant beam d i r e c t i o n ( at e to the f i l m normal) and the columnar growth d i r e c t i o n ( at B to the f i l m normal), namely

tan ~= 2tan B , has been shown to be obeyed for a wide v a r i e t y

of materials 8. For an ~=80°film, this rule predicts that B=70°. The SANS f o r such a f i l m , rotated through 70°with respect to the neutron beam, is shown in fig.l(b).

The contour p l o t shows that the scattering is more nearly i s o t r o p i c ,

although the contours are not p e r f e c t l y c i r c u l a r . Either the columnar growth d i r e c t i o n in the films is i n c l i n e d at,an angle of more than 70° to the normal, or the columns (or voids) themselves are e l l i p t i c a l ,

not c i r c u l a r , in cross-sec-

t i o n . On the present evidence, these two a l t e r n a t i v e s cannot be distinguished. In p r i n c i p l e , SANS measurements allow the spatial dimensions ( i . e . shape) of each void, and the t o t a l void volume, to be determined. Straightforward quantit a t i v e analysis (using, e.g. the Guinier approximation) is precluded in the present case because of the presence of both p o l y d i s p e r s i t y in void sizes and

S.R. Elliott/ Scattering studies of photostructural changes

902

i n t e r p a r t i c l e interference: a Guinier p l o t of In S(Q) v.s. Q2 is not l i n e a r in any region of Q measured (see f i g . 2), and so a single radius of gyration cannot be assigned to the voids. Instead, we have used a simple model to i n t e r p r e t the data. We have used a model

14

in which the voids are regarded as a set of independent

e l l i p s o i d s each scattering independently, but modified assuming that there is a d i s t r i b u t i o n of void sizes 13. The voids are taken to be e l l i p s o i d s with semiaxis lengths AI=A2
g(x)=e -x / / ~ , where x:(A °-

A i ( x ) ) / A ° 6 . The f r a c t i o n a l p o l y d i s p e r s i t y parameter,~, is taken to be the same f o r a l l semiaxes. Hence, the t o t a l scattering cross-section for an assembly of independently scattering e l l i p s o i d a l voids in a sample, each having a d i s t r i bution of semiaxis lengths given by g ( x ) , i s l 3 : 0002

-~

=

7~

"

f

oo

-~

L

(QR) °

cosi>]

dx

(I)

where N is the t o t a l number of voids, ~ is the neutron s c a t t e r i n g length per unit volume(assuming that the difference in scattering lengths between bulk and e l l i p s o i d is ~, the composition-weighted average for the bulk, i . e . the e l l i p s oids are voids), and

QR:~QxAI)Z+(QvA2)Z+(QzA3)2]I/2 .

© ~ a ~ x

I

I x 0°

Ineufrron 9beam

~dl-+ 9¢ -k

Ig,l .-Y defec I ' o r / ~

-~

~ d

©

10

Id i

~

~

'

I

I

5

10 I'5 I0~ 02[A~]

20

FIGURE 1 FIGURE 2 Contour plots of SANS from evaporated Sector-averaged SANS data (points) f o r an a-Ge95Se75films, obtained with the neuas-deposited ~=80°a-GegKSe75film.Each tron~ normal to the f i l m : ( a ) As-deposited point in I~I is the me~fi of a l l detecf i l m evaporated at e=80*;(b) Same as (a) t o r c e l l s in a sector 15°wide whose but with neutrons at 7 ~ t o f i l m normal; average angular value is ~. Contin(c) After i r r a d i a t i o n ; ( d ) A f t e r annealing, uous lines are f i t s using eq. I. The Contours are a f a c t o r of 2 apart, and scattering geometry is shown in i n s e t , are plotted l o g a r i t h m i c a l l y . T h e s c a t t where Bis the angle the e l l i p s o i d s ering geometry is in inset of f i g . 2, make r e l a t i v e to the f i l m normal.

903

S.R. Elliott/ Scattering studies of photostruetural changes A fit

to the data f o r an ~=80~ f i l m using eq.l is shown in f i g . 2, y i e l d i n g

values f o r the long semiaxis length A3=I20X, and f o r the cross-sectional semiaxis length A2=60X , with a f r a c t i o n a l p o l y d i s p e r s i t y 6=0.4. The measured density of o b l i q u e l y deposited films decreases d r a m a t i c a l l y with increasing angle ~ of the evaporant beam direction~ a feature also e x h i b i ted by our f i l m s . The SANS also increases markedly with increasing ~, as shown in f i g . 3, i n d i c a t i n g that the proportion of void volume increases with increasing ~. For the ~=80°film, we have estimated that the void volume f r a c t i o n is 47+ 5%. For comparison, the measured density d e f i c i t of the f i l m (with respect to one evaporated at the same time with ~=~) is 34+10%. The discrepancy between these values could be due to uncertainty in the value f o r A1 obtained from the model f i t s ,

and also to the fact the as-prepared ~ = ~ f i l m s also contain some

( a l b e i t small) proportion of void volume. i0s

"°°

-

o

I++

20 °

* 80°

++

_i¢ c

+ as-deposited

~ 103 -8o

~

o l I~,~,

".÷÷ + + +

":,o

+++++

~ 102

L~

I

xxtSx x

~lee

:o

o • ~xo °

°.o:';

ol'

10°

**

g@

5

÷÷ ÷÷÷+

+ ÷

o,~

e.e@$,

g ~J

+

GO ++ ÷

4--

103[ +++

]k

o illuminated • anneated

~+~++

+

o@

1#



5 iga~Of)-, 15

I~0

'0 5 I~.J(~2)

15

FIGURE 3 Sector-averaged SANS data (c=O°) for

FIGURE 4 Sector-averaged SANS data(c=40 °) f o r an as-deposited a-Ge2~Se75 films evaporated m=80 a-Gep~SeTK f i l m in as-deposited, at the angles (~) Tnd~cated,taken with i l l u m i n a t ~ , &~d subsequently annealed the neutron beam normal to the f i l m . states. The e f f e c t on the SANS of i l l u m i n a t i o n of an m=80°film f o r 22h with bandgap l i g h t from a IkW Xe arc-lamp is shown in f i g . l ( c ) .

The degree of anisotropy and

the overall level of scattering are both decreased markedly by i l l u m i n a t i o n . This e f f e c t is also shown in f i g . 4 where the sector-averaged SANS is seen to have decreased by about an order of magnitude a f t e r i r r a d i a t i o n . Annealing the i l l u m i n a t e d f i l m f o r I0 min. at 250 °C (Tg=220 °C) reduced the scattering intens i t y and anisotropy somewhat f u r t h e r ( f i g s . l ( d ) and 4). We propose, along with Chopra et a l ] 5, that the i r r e v e r s i b l e photodensification of o b l i q u e l y deposited chalcogenide films is caused by the collapse of the intercolumnar voids. SANS evidence indicates that a f t e r i l l u m i n a t i o n , the overall void volume decreases and, moreover, the remaining voids are approximately i s o t r o p i c in shape. (Unfor-

904

S.R. Elliott/ Scattering studies of photostructural changes

tunately, the present SANS data for the photodensified films do not have s u f f i c i e n t l y good s t a t i s t i c s to warrant detailed f i t t i n g ,

as in f i g . 2.) The collapse

of the voids is caused, most probably, by optical e x c i t a t i o n of the chalcogen lone-pair p-~ o r b i t a l s (and possibly also dangling bonds), resulting in substant i a l structural reconstructions. 3. REVERSIBLE PHOTOSTRUCTURALCHANGES 3.1. Introduction Photo-induced structural and optical changes, which are removed by annealing at Tg, have been observed in many As- and Ge-chalcogenide glasses and annealed 3 amorphous thin film~'~'3but n o t in c r y s t a l l i n e chalcogenides (e.g. As2S3). The photo-optical changes generally involve a s h i f t of the Urbach absorption edge to lower energies ("photodarkening"), the changes again being larger in alloys containing Ge and S than those containing As or Se. This compositional dependence is strongly correlated 3 with the bond i o n i c i t y . The reversible photostructural (PS) effect has be~n much less studied than the photo-optical effects. One of the few direct structural studies has been on evaporated a-As2S3 films, for which X-ray d i f f r a c t i o n has shown3that the "pre-peak" at Q:I~ -I decreases in i n t e n s i t y and shifts s l i g h t l y to larger Q, the effect being larger i f i l l u m i n a t i o n takes place at low temperatures. Unfortunately, data extending to higher values of Q have not previously been reported, and since the structural o r i g i n of the pre-peak in chalcogenide glasses is s t i l l

uncertain,

(and hence any PS change on i t is therefore uninterpretable), the structural mechanism underlying the reversible PS e f f e c t remains unknown. Other i n d i r e c t structural studies have investigated changes in IR absorption spectral~ but such results are also d i f f i c u l t to i n t e r p r e t in terms of a microscopic structural mechanism. Thus, we decided to study the reversible PS effect in chalcogenide glasses by conventional neutron scattering and EXAFS experiments. Some preliminary results have already appeared 17. 3.2. Experimental Glassy As2S3 and As2Se3 were prepared by melting the pure elements in evacuated s i l i c a ampoules in a rotating tube furnace and quenching in a i r . The glasses were annealed at Tg and powdered to a grain size =l~m. The As2Se3 sample for the neutron d i f f r a c t i o n study was sealed i n vacuo and illuminated using a IkW Xe lamp. Heat f i l t e r s were employed, transmitting l i g h t of energy E>I.75eV onto the sample for 89h; the powdered sample was continuously stirred during i l l u m i n a t i o n whilst being held at 77K. The sample was transferred to a narrow-wall V container a f t e r warming to room-temperature p r i o r to measurement. All neutron scattering data was taken at room-temperature on the D2 powder diffractometer at the ILL, Grenoble.After measuring the scattering intensity for =40h for the illuminated

S.R, Elliott/ Scattering studies of photostructural changes

905

sample, i t was then annealed i n s i t u at Tg, and scattering data for the annealed sample were then taken. The neutron wavelength used was 1.22~, thereby l i m i t i n g the maximum value of Q to be 8.7~-] The data were corrected f o r scattering due to the container and m u l t i p l e scattering. Samples of glassy As2S3 f o r EXAFS were prepared by dispersing the powdered glass in " d u r o f i x " glue and forming a thin tape. The measurements were performed at the Synchrotron Radiation Source at Daresbury. The measurements were taken in transmission with the sample held at 77K. The annealed sample was measured first,

then illuminated f o r 9h by l i g h t from a IkW Xe arc-lamp passed through a

CuSO4-solution f i l t e r ( t r a n s m i t t i n g photon energies >2.2eV).The EXAFS spectrum of the i l l u m i n a t e d sample was then taken. 3,3. Results Differences in the neutron structure f a c t o r S(Q) were observed in the prepeak as seen previously# but also up to the largest value of Q measured ( f i g . 5 i n s e t ) , implying that the PS e f f e c t is caused by changes in the l o c a l structure. This is more c l e a r l y seen in the Fourier transform of S(Q),also shown in f i g . 5 . On i l l u m i n a t i o n , the f i r s t

peak decreases in r by =0.02~ and also increases in

height; in contrast the second peak also moves to lower r (by =0.01~) but decreases in height. There are also smaller changes in the higher l y i n g peaks. One mechanism f o r the reversible PS e f f e c t is the double-well model~ in which a chalcogen atom moves from i t s e q u i l i b r i u m position to another metastable s i t e under the action of l i g h t , as a r e s u l t of a change in the chalcogen lonepair i n t e r a c t i o n s . Whilst such a model predicts a change in the second peak of the RDF as a r e s u l t of an increase in (chalcogen) bond-angle d i s t o r t i o n s (in agreement with inferences from IR v i b r a t i o n a l spectral6), i t would not be expected that the As-Se bond-length should change, as appears to be the case from our neutron d i f f r a c t i o n studies; a bond-breaking model seems to be therefore needed. One such model is the " s e l f - t r a p p e d exciton" modell# wherein the o p t i c a l l y excited electron-hole pair causes an As-Se bond to break and a Se-Se bond to form; ~e net r e s u l t is a p a i r of metastable defects, Se~ and As2. In this process, f o r every As-Se bond broken, 2 As and 1Se bond-angles are l o s t and 3 Se bond-angles are created. Since 0(Se)=95 ° and O(As)~lO0 ° , t h i s implies that i l l u mination should decrease the high-r side of the second peak in G(r). Moreover, 2 Se-Se and 1 As-As d i r e c t second-neighbour c o r r e l a t i o n s are l o s t , and 3 As-Se second neighbours are created. The neutron scattering lengths are b(As) =6.73 and b(Se)=7.95 (lO-15m), and since a peak in the RDF due to c o r r e l a t i o n s between atoms i and j is proportional in height to bib j , this implies that the overall magnitude of the second peak should decrease, as is observed. The f i r s t peak is predicted to i n c r e a s e in height,(since an As-Se bond is converted into a Se-Se bond f o r every defect pair formed), and this is also seen experimentally.

S.R. Elliott/ Scattering studies of photostructural changes

906

2! AnneoLed Itlumino,ted

100

~J '~i"

j~" / ~ //i J i~ ~ " ~,/~, J~

f,1,oo

- - Ann~led ..... IItuminQted

2(

o:

IC

OOi

Q.=

-I0.(

'UI/

_, 25

, 50

75

r Ik)

FIGURE 5 Reduced RDF f o r annealed and i l l u m i n ated glassy AsgSeq obtained by neutron d i f f r a c t i o n . The Tnset shows the d i f f erence in S(Q) (annealed-illuminated).

O0 00

10

20

30

40

r

(~}

FIGURE 6 Fourier transform of the EXAFS taken at the As K-edge of glassy As~S~, before and a f t e r i l l u m i n a t i o n . Th~ ~lane-wave approximation has been used.

Another possible model is that in which two As-Se bonds are broken simultaneously, and 1 As-As and 1 Se-Se bond are formed instead. In this model, a l l the atoms retain t h e i r normal valence and remain uncharged, but the chemical shortrange order, presumed to e x i s t in the annealed glass, is p a r t i a l l y destroyed. This model predicts that the f i r s t

peak in the RDF should remain more-or-less

unchanged in height, or perhaps s l i g h t l y lower and broader, and t h a t , since the number and type of bond-angles are conserved a f t e r the bond rearrangement, the high-r side of the second peak should remain unchanged. On the basis of the present data, therefore, the self-trapped exciton model is marginally favoured.The preliminary EXAFS data f o r glassy As2S3 ( f i g . 6),taken at the As K-edge, i n d i c ate a small decrease in the f i r s t

peak on i l l u m i n a t i o n (consistent with As-S

bonds being transformed to S-S bonds), and quite marked changes in the region of the second and t h i r d neighbour distances to a given As atom, which may be cons i s t e n t with e i t h e r bond-breaking model. Detailed peak-shape f i t t i n g

following

planned high-resolution neutron scattering experiments should solve the problem. ACKNOWLEDGEMENTS The author is grateful to his collaborators Drs. T.Rayment, S.Cummings, G.N. Greaves and A.F.Wright and Messrs. A.J.Lowe and T.G.Fowler. Financial assistance from SERC,BP and the Royal Society is also g r a t e f u l l y acknowledged. REFERENCES I ) J.P.De N e u f v i l l e , i n : Optical Properties of Solids, ed.B.O.Seraphim (NorthHolland,Amsterdam,1976) pp.437-472. 2) J.P.De N e u f v i l l e , S.C.Moss and S.R.Ovshinsky, J.Non-Cryst. Sol. 13 (1973/4)191 3) K.Tanaka, J. Non-Cryst. Sol. 35-36 (1980) 1023.

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4) A.J.Leadbetter, A.J.Apling and M.F.Daniel, J.Non-Cryst. Sol. 21 (1976) 47. 5) S.A.Solin and G.N.Papatheodorou, Phys.Rev. B15 (1977) 2084. 6) A.J.Apling, A.J.Leadbetter and A.C.Wright, J. Non-Cryst. Sol. 23 (1977) 369. 7) R.J.Nemanich, G.A,N.ConnelI, T.M.Hayes and R.A.Street, Phys. Rev. B18 (1978) 6900. 8) A.G.Dirks and H.J,Leamy, Thin Solid Films 47 (1977) 219. 9) S.Rajagopalan, K.S.Harshavardhan, L.K.Malhotra and K.L. Chopra, J. Non-Cryst. Sol. 50 (1982) 29. I0) K.S.Harshavardhan, S.Rajagopalan, L.K.Malhotra and K.L.Chopra, J. Appl. Phys. 54 (1983) 1048. I I ) B.Singh, S.Rajagopalan and K.L.Chopra, J. Appl. Phys. 51 (1980) 1768. 12) K.L.Chopra, K.S.Harshardhan, S.Rajagopalan and L.K.Malhotra, Sol.State Comm. 40 (1981) 387. 13) T.Rayment and S.R.Elliott, Phys. Rev. 928 (1983) To appear. 14) G.S.Cargill, Phys. Rev. Lett. 28 (1972) 1372. 15) 8.Singh, S.Rajagopalan, P.K.Bhat, D.K.Pandya and K.L.Chopra, J. Non-Cryst. Sol. 35-36 (1980) 1053. 16) Y.Utsugi and Y.Mizushima, J. Appl. Phys. 49 (1978) 3470; J. Appl. Phys. 50 (1979) 1494. 17) S.R.Elliott, T.Rayment and S,Cummings, J. de Phys. C9 (1982) 35. 18) R.A.Street, Sol. State Comm. 24 (1977) 363.