OPTICAL PICOSECOND STUDIES OF HOT CARRIERS IN AMORPHOUS SEMICONDUCTORS

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OPTICAL PICOSECOND STUDIES OF HOT CARRIERS IN AMORPHOUS SEMICONDUCTORS

Z. Vardeny, J. Tauc

To cite this version:

Z. Vardeny, J. Tauc. OPTICAL PICOSECOND STUDIES OF HOT CARRIERS IN AMOR- PHOUS SEMICONDUCTORS. Journal de Physique Colloques, 1981, 42 (C7), pp.C7-477-C7-482.

�10.1051/jphyscol:1981758�. �jpa-00221695�

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suppZQment au nOIO, Tome 42, octobre 1981 page C7-477

O P T I C A L PICOSECOND S T U D I E S O F HOT CARRTERS I N AMORPHOUS SEMICONDUCTORS

2.

Vardeny and J. Tauc

Division of Engineering and Department of Pfiysics, Brolim University, Providence, Rhode Island, 0291

A .

Abstract.- Thermalization of photogenerated carriers in a-Si, a-Si:H, a-AsgSe3 and a-Se was studied by measuring the photoinduced absorption with subpicosecond resolution. The thermalization process can be described by Frshlich interaction with polar phonons in a-Si:H and a-As2Seg but not in a-Si. Using photon energy of 2eV, the excess energy dissipation rates were determined to be 0.5 eV/ps in a-Si, 0.1 eVIps in a-Si:H, 0.2 e ~ / ~ s in a-As~Seg and less than 0.05 eVIps in a-Se.

Introduction.- Hot carrier relaxations in semiconductors occur on a time scale of 10-LLs, therefore pico and subpicosecond laser spectroscopy provides a unique tool for measuring directly these ultrafast processes. The lack of detectors and elec- tronics that are fast enough to resolve re- sponses in the pico and subpicosecond ranges necessitates the use of correlation tech-

niques,l such as the pump and probe technique

shown in Fig. 1. The sample is hit by a

b strong pump pulse that changes its optical

constants; the response is probed by a weak probe pulse delayed by a time

. ^{The delay}

Sample

is generated by a longer optical path of the

CT

probe relative to that of the DumD. This . .

is produced mechanically with a translational Fig. 1 - The pump and probe experi- stage. In the case of laser systems having ment. The delay between the robe high repetition rates one obtains the desired

and pump pulses is produced by a range of

by periodically scanning the translational stage. stage over the corresponding length.

Hot carrier relaxation due to polar phonon dissipation mechanism was investigated extensively in ~ a ~ and to a lesser degree in ~ s ~ - ~ d ~ e Shank et al.' . ~ concluded from picosecond reflectivity measurement that an electron-hole plasma having an initial excess energy of about 1 eV loses energy at a rate of approximately 0.4 eVIps. Using induced transmisison spectra in G ~ A S ~ hot carriers with excess energy of about 0.1 eV were shown to relax to the lattice temperature (80K) in about 4 ps. Increasing the overall sensitivity by using probe frequencies close to the band edge,4 relaxation of warm carriers

= l 0 meV) was followed up to 250 PS;

it was experimentally verified that the polar dissi ation rate decreases when the excess energy is smaller, in agreement with theory.! In a non-polar crystal such as Ge the electron-phonon interaction is much smaller and r'e maximum dissipation rate was found6 to be about 50 meV/ps.

The first investigation of hot carrier relaxation in amorphous semiconductors was reported by our group very recently.' In the crystalline materials mentioned above, the hot carrier relaxation could be followed by measuring optical transmission because of the band gap renormalization and band filling effects. Due to the much more complicated electronic band structure, especially near the band (mobility) edges and very large effective masses, the existence of these plasma effects in amorphous semiconductors appears doubtful. In this case we could follow7 the hot carrier relaxation processes using the dependence of the hot carrier absorption cross section

on its excess energy A E . Theories that deal with this effect in

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981758

C7-478 JOURNAL DE PHYSIQUE

c r y s t a l s were d e r i v e d by s e e g e r 8 and E l c i e t f o r t h e Boltzmann and Fermi-Dirac d i s t r i b u t i o n s .

Ex e r i m e n t a 1 . - The pump and probe t e c h n i q u e was used w i t h a c a v i t y dumped p a s s i v e l y mo:e-locked dye l a s e r d e v e l o p e d by I p p e n and shank.' T h i s l a s e r p r o d u c e s l i n e a r l y p o l a r i z e d l i g h t p u l s e s a t h %

2eV w i t h a s i n g l e s i d e e x p o n e n t i a l s h a p e and t p

0.6 - 0 . 8 ps d u r a t i o n , 1-2 n J e n e r g y p e r p u l s e and r e p e t i t i o n r a t e 1 0 4 - 1 0 ~ s - ~ . The p r o b e beam p a s s e d t h r o u g h a p o l a r i z a t i o n r o t a t o r and i t s p o l a r i z a t i o n was e i t h e r p a r a l l e l ( 1 1 ) o r p e r p e n d i c u l a r (l) t o t h a t o f t h e pum p ^beam. A l l e x p e r i - ments were done w i t h o p t i c a l l y t h i n amorphous f i l m s : d < a - ( d 1 s t h e t h i c k n e s s and a i s t h e a b s o r p t i o n c o e f f i c i e n t a t 2 e ~ ) , s o t h a t t h e p h o t o g e n e r a t e d c a r r i e r con- c e n t r a t i o n n v a r i e d from sample t o sample ( a s U - l ) between 5

1017 and

per p u l s e .

The pump p u l s e ~ r o d u c e d a change o f t h e a b s o r p t i o n c o e f f i c i e n t Aa = A T / T ~ . ^{I n}

g e n e r a l , A a can b e n e g a t i v e ( b l e a c h i n g ) o r p o s i t i v e ( i n d u c e d a b s o r p t i o n ) ; i n amorphous s e m i c o n d u c t o r s , we a l w a y s o b s e r v e d L a > 0 .

Response t h e o r y . - I n t h e l i n e a r r e s p o n s e t h e o r y 1 , 9 Aa(T) i s t h e sum o f two t e r m s ; y : ~ ) g i v e n by t h e c o n v o l u t i o n o f t h e i m p u l s e r e s p o n s e f u n c t i o n A ( t ) w i t h t h e i n t e n s i t y a u t o c o r r e l a t i o n f u n c t i o n G ( T ) , and B(') ( " c o h e r e n t a r t i f a c t " ) by t h e c o n v o l u t i o n of A ( t ) w i t h t h e pump and probe e l e c t r i c f i e l d s . B(T) i s a s h a r p l y d e c r e a s i n g symmetric f u n c t i o n around

0

i n o u r e x p e r i m e n t s i t h a s a s i m i l a r s h a p e a s G(T) . TO o b t a i n A ( t ) one h a s t o s u b t r a c t t h e c o n t r i b u t i o n o f B(T) from t h e measured and t o d e c o n v o l u t e t h e r e s u l t u s i n g t h e known s h a p e o f G(T) measured e . g . by second harmonic gener- a t i o n c o r r e l a t i o n e x p e r i m e n t i n a n o n - l i n e a r c r y s t a l s u c h a s KDP.

When i n f o r m a t i o n a b o u t A ( t ) a t v e r y s h o r t t i m e s i s n e e d e d , a n a c c u r a t e e v a l u a t i o n o f

d i s e s s e n t i a l . T h i s c a n b e done by m e a s u r i n g b o t h

4 1 and A y

A ( t ) i s a f o r t h r a n k m a t r i x A i j k g , ( t ) which i s , w i t h i n a f a c t o r p r o p o r t i o n a l t o t h e i m a g i n a r y p a r t X'' of t h e t i m e dependent e l e c t r i c a l s u s c e p t i b i l i t y t e n s o r X(1) ( t , w , - U ) . I n i s o t r o p i c media ~ ( 3 ) ( t , w , - w ) h a s o n l y two i n d e p e n d e n t e l e m e n t s and t h e r e l a t i o n X

+ 2X h o l d s . 1 ° I t h a s b e e n shown9 t h a t i n t h e

I I c a s e b o t h y,, azzX%,I a::Y8etermfxg8 by Axx, , w h i l e i n t h e I c a s e Y r i s a s s o c i a t e d w i t h Axxy and 6 ~ w i t h Axpy . Defining1' t h e d e p o l a r i z a t i o n f a c t o r

P'

Axxyy/A.+xxx

Y ~ / $ , I t h e r e l a t i o n LIB! I

Axyxy/Axxxx

( 1 - 8 ) / 2 i s o b t a i n e d f o r i s o t r o p ~ c m a t e r i a l s . I f

> 1 1 3 , 81 1 s r e d u c e d more t h a n Y_L r e l a t i v e t o t h e I I c a s e and i s c o m p l e t e l y e l i m i n a t e d i f P = 1 .

B a s i c Model.- We s t u d i e d A ( t ) i n a - S i , a-Si:H, a-Si:H:F and t h e c h a l c o g e n i d e g l a s s e s a-Se and a-AspSeg. I n some c a s e s , t h e induced a b s o r p t i o n r e s p o n s e Aa(T) c a n b e s e p a r a t e d i n t o two r e g i o n s : a f a s t r e s p o n s e t h a t we a s s o c i a t e w i t h h o t c a r r i e r t h e r m a l i z a t i o n , and a s a t u r a t i o n a s c r i b e d t o t h e r m a l i z e d c a r r i e r s w i t h l i f e t i m e s l o n g e r l l t h a n t h e d u r a t i o n o f o u r e x p e r i m e n t ( a b o u t l o o p s ) .

The b a s i c i d e a t h a t we u s e d f o r i n t e r p r e t i n g t h e d a t a i s t h a t a n e x c i t e d c a r r i e r

h a s a h i g h e r o p t i c a l a b s o r p t i o n c r o s s s e c t i o n t h a n a n e l e c t r o n i n t h e v a l e n c e band

( c l o s e t o t h e t o p ) .

amorphous m a t e r i a l , where t h e k - v e c t o r c o n s e r v a t i o n r u l e i s n o t a p p l i c a b l e , o n l y

t h e d e n s i t y o f t h e f i n a l s t a t e s i s i m p o r t a n t ; i t i s l a r g e r f o r a n e l e c t r o n c l o s e

t o t h e bottom o f t h e c o n d u c t i o n band (and a h o l e c l o s e t o t h e t o p o f t h e v a l e n c e

band) t h a n f o r v a l e n c e - c o n d u c t i o n band t r a n s i t i o n s c l o s e t o t h e e x t r e m a . Changes

o f

produced by t h e a b s o r p t i o n e d g e s h i f t d u e t o t h e t e m p e r a t u r e i n c r e a s e

a s s o c i a t e d w i t h t h e a b s o r p t i o n o f t h e pump p u l s e h a v e much l o n g e r r e l a x a t i o n t i m e s ,

and a l s o a r e n o t e x p e c t e d t o show any p o l a r i z a t i o n memory e f f e c t s . The l a t t e r i s

a l s o t r u e f o r some o t h e r c o n c e i v a b l e "bulk" e f f e c t s such a s band gap r e n o r m a l i z a -

t i o n and band f i l l i n g .

F i g . 2 - P h o t o i n d u c e d a b s o r p t i o n d e c a y A a ( r ) i n F i g . 3 - Same a s i n F i g . 2 , a-Si:H (CH

1 0 % ) f o r I ( and I p o l a r i z a t i o n s . b u t f o r a - S i .

S o l i d c u r v e s : e x p e r i m e n t a l , d o t t e d c u r v e s : c a l c u l a t e d .

Hot c a r r i e r t h e r m a 1 i z a t i o n . - I n F i g s . 2 and 3 f a s t d e c a y s o f A ~ ( T ) a r e shown i n h y d r o g e n a t e d and non-hydrogenated a-Si. Curves ( a ) and ( b ) c o r r e s p o n d t o 1 1 and

I p o l a r i z a t i o n r e s p e c t i v e l y , and show a maximum i n Aa around

0 t h a t d e c a y s -

t o a s t e a d y v a l u e Ass a t l o n g e r t i m e s ; from Ass i n F i g s . 2 and 3 we e s t i m a t e t h e a b s o r p t i o n c r o s s - s e c t i o n u s

3

1 0 - ' ~ c m ~ which i s c l o s e t o f r e e c a r r i e r

0

i n a-Si ( 2 x 10-18cm2 a t 2 eV and 8 0 ~ ~ ~ ) . The d e p o l a r i z a t i o n f a c t o r

P = A a s l l A a s l I i s s e e n t o b e 0 . 7 5 i n a-Si and 0 . 7 i n a-Si:H s a m p l e s and shows t h e e x i s t e n c e o f p o l a r i z a t i o n memory i n t h e s e amorphous m a t e r i a l s f o r s u r p r i s i n g l y l o n g t i m e s ; a t t h i s p o i n t , i t s o r i g i n i s n o t c l e a r l y u n d e r s t o o d . Curve ( c ) i s Aa l

- P-'A~& which i s e q u a l t o ( 3 ~ - 1 ) 8 1 /2 ~ ( ~ 5 8 / 6 i n o u r c a s e )

t h i s c u r v e d i r e c t l y g i v e s t h e c o h e r e n t a r t i f a c t ; welkound t h a t f o r o u r t r a n s f o r m l i m i t e d p u l s e s t h i s c u r v e i s i n d e e d s i m i l a r t o t h e measured

. I n o u r c a s e B I i s ( 1 - p ) / 2

118 o f 6 1 1 b u t s t i l l a peak o f

i s s e e n i n a-Si c a s e

( F i g . 3 ( b ) ) . T h i s r u l e s o u t t h e p o s s i b i l i t y t h a t t h e o b s e r v e d peak around

0 i s c a u s e d by t h e c o h e r e n t a r t i f a c t a l o n e w h i l e A ( t ) i s a s t e p f ~ n c t i o n . ~ A ( t ) must t h e r e f o r e c o n t a i n a f a s t d e c a y .

C We c a n e x p l a i n t h e f a s t component a s h o t c a r r i e r a b s o r p - t i o n and Ass a s a b s o r p t i o n by t h e r m a l i z e d c a r r i e r s . The proposed mechanism is i l l u s t r a t e d i n F i g . 4 . When t h e photon e n e r g y &hp ( = 2 eV) i s l a r g e r t h a n t h e band gap

~ ~ r n

Eg ( ~ 1 . 8 eV f o r a-Si:H a n d = 1 . L e V f o r a-Si) h o t c a r r i e r s h a v e an i n i t i a l e x c e s s e n e r g y AE(O)

(!up-EE)/2 > 0 .

These c a r r i e r s t h e r m a l i z e t o t h e b o t t o m o f t h e band b y l o o s i n g t h e i r e n e r g y t o phonons. D u r i n g t h i s p r o c e s s carriers t h e y c a n r e a b s o r b l i g h t . S i n c e t h e o p t i c a l a b ~ r t i o n

c r o s s - s e c t i o n o f h o t c a r r i e r a i n c r e a s e s w i t h AE,g.8 it i s p o s s i b l e t o o b s e r v e t h e f a s t t h e r m a l i z a t i o n p r o c e s s by m e a s u r i n g A a ( r ) p r o v i d i n g t h e s y s t e m ' s r e s p o n s e i s f a s t E, enough. It i s p l a u s i b l e t o assume t h a t h o t c a r r i e r s i n

amorphous s e m i c o n d u c t o r s a r e i n e x t e n d e d s t a t e s and t h e r e - f o r e t h e i r o p t i c a l p r o p e r t i e s c a n be d e s c r i b e d s i m i l a r l y a s i n c r y s t a l s .

I n t h i s i n t e r p r e t a t i o n , from t h e d e c a y d u r a t i o n we c a n ob- F i g . 4 - Proposed mech- t a i n t h e r a t e o f t h e a v e r a g e e n e r g y d i s s i p a t i o n o f h o t anism f o r p h o t o i n d u c e d c a r r i e r s R

dAE/dt. The d a t a i n d i c a t e t h a t

i n a-Si a b s o r p t i o n d e c a y a s s o c - ( F i g . 3 ) i s f a s t e r t h a n i n a-Si:H ( F i g . 2 ) .

was gener- i a t e d w i t h h o t c a r r i e r a l l y assumed13 t h a t t h e t h e r m a l i z a t i o n r a t e i n amorphous t h e r m a l i z a t i o n . s o l i d s i s t h e h i g h e s t p o s s i b l e r a t e a s s o c i a t e d w i t h phonon

e m i s s i o n h v 2 . Our r e s u l t s show t h a t t h i s i s t h e c a s e f o r

a - S i ; hv2 a v e r a g e d o v e r i t s phonon s p e c t r u m g i v e s 0 . 5 eV/ps i n agreement w i t h t h e

C7-480 JOURNAL DE PHYSIQUE

-

r a t e o b t a i n e d from t h e d a t a : AE(0) 0 . 3 eV , t h e r m a l i z a t i o n t i m e t o = 0 . 7 ~ ~ . However, a n a n a l y s i s o f t h e d a t a f o r a-Si:H ( ~ i g . 2) g i v e s R = 0 . 1 eV/ps which i s c o n s i d e r a b l y s l o w e r t h a n h v 2 .

The t h e r m a l i z a t i o n r a t e s R h a v e t o b e compared w i t h t h e c a r r i e r - c a r r i e r d i s s i p a - t i o n r a t e

which depends on t h e c a r r i e r d e n s i t y and e x c e s s e n e r g y ; 5 under t h e c o n d i t i o n s o f o u r e x p e r i m e n t s RC was a b o u t 0 . 3 e ~ / p s . I f R < RC, h o t c a r r i e r t e m p e r a t u r e Te c a n b e d f i n e d , 1 4 t h e c a r r i e r d i s t r i b u t i o n f(b'E)

e x p ( - ~ E / k ~ ~ ) and t h e s t a n d a r d t h e o r y B f o r

c a n b e used

T h i s i s t h e c a s e i n a-Si:H b u t n o t i n a-Si.

A s l o w e r R t h a t c a n e x p l a i n t h e r e s u l t s i n a-Si:H i s p r o v i d e d by F r u h l i c h c o u p l - i n g t o p o l a r phonons.5 The i r a c t i v e ( p o l a r ) phonon o s c i l l a t o r s t r e n g t h d S ( v ) c a n b e d e t e r m i n e d from t h e a b s o r p t i o n c o e f f i c i e n t a ( v ) i n t h e f a r i r :

d S ( v )

n r a ( v ) ~ / ~ % 2 ( n i s t h e i r r e f r a c t i v e i n d e x ) . R a v e r a g e d o v e r t h e Boltzmann d i s t r i b u t i o n f f ~ E ) was c a l c u l a t e d u s i n g n r

3!g1and a ( v ) from R e f . 15.

The r e s u l t i s shown i n F i g . 5. The dependence o f t h i s r a t e on Te f o r a-Si:H h a s t h e f a m i l i a r s h a p e o f t h e p o l a r d i s s i p a t i o n ; f i r s t Rpol i n c r e a s e s s h a r p l y w i t h Te and around Te

2000K r e a c h e s a b r o a d maximum o f 0 . 1 e V l p s , which i s o n l y f o u r t i m e s weaker t h a n t h e measured r a t e f o r C - G ~ A ~ . ~

F i g . 5 - R 01 c a l c u l a t e d f o r F i g . 6 - The n o n - e q u i l i b r i u m d i s t r i b u t i o n a-Si:H a t !

^80K. f u n c t i o n ~ ( A E ) a t t

0 ( a p p l i c a b l e t o a - S i ) .

I t s t i m e dependence i s i n d i c a t e d . Both c u r v e s ( a ) and ( b ) i n F i g . 2 were f i t w i t h

f o r t <-1.2 p s and ~ ( t )

f o r

> 1 . 2 p s w i t h a

1 . 7

L O - ~ K - ' ,

T e ( O j = 2 b ' ~ E ( 0 ) / 3 k = 8 0 0 ~ , w i t h t h e p u l s e s h a p e deduc2d from c u r v e ( c ) , and w i t h B A = 1/8f3ll . By c h a n g i n g t h e hydrogen c o n t e n t CH we change Eg and t h e r e f o r e

T e ( 0 ) . The measured7 dependence o f Te(0) on CH i s i n agreement w l t h t h i s i n t e r - p r e t a t i o n w i t h

i n d e p e n d e n t o f CH. The v a l u e o f % i s c l o s e t o

$ =

1 . 3

I O - ~ K - ~ c a l c u l a t e d f o r h o t c a r r i e r a b s o r p t i o n a s s i s t e d by o p t i c a l d e f o r - m a t i o n p o t e n t i a l i n c r y s t a l s a t 2 e ~ . * I n o u r a n a l y s i s we d i s r e g a r d t h e l o n g t a i l o f T e ( t ) s i n c e o u r d a t a a r e n o t s e n s i t i v e enough t o r e v e a l t h i s w e l l known5 f e a t u r e o f t h e p o l a r d i s s i p a t i o n mechanism.

I n a-Si where Te c a n n o t be d e f i n e d we a s s u m g t h a t & o ( t f i s p r o p o r t i o n a l t o t h e a v e r a g e c a r r i e r e x c e s s e n e r g y i%(t) (ha = bAYI). The i n i t i a l n o n - e q u i l i b r i u m d i s t r i b u t i o n f u n c t i o n f @ E ) was t a k e n t o be p r o p o r t i o n a l t o t h e p r o d u c t o f t h e i n i t i a l and f i n a l d e n s i t i t e s o f e l e c t r o n s t a t e s ( a s s u m i n g t h a t t h e m a t r i x e l e m e n t s a r e i n d e p e n d e n t of AE). For s q u a r e - r o o t d e n s i t i e s f h E )

m ^*up -

shown i n F i g . 6 . I n c a l c u l a t i n g X ( r ) we d i s ~ g a r d t h e change:of f Efu; E

c a r r i e r - c a r r i e r i n t e r a c t i o n s and assume t h a t bE changes w i t h t i m e a c c o r d i n g t o d%/dt

0 . 5 e V / p s , s o t h a t f r e t a i n s i t s s h a p e b u t moves w i t h t i m e t o s m a l l e r A E , a s shown i n F i g . 6 . The c a l c u l a t e d h ~ l t p i s a d e c r e a s i n g f u n c t i o n o f t t h a t

we a p p r o x i m a t e d by a l i n e a r d e c a y o f 0 . 7 ps d u r a t i o n . Curves ( a ) and ( b ) o f

F i g . 3 were s i m u l t a n e o u s l y f i t w i t h

reason why R is larger in a-Si than in a-Si:H is not known at this time; one can speculate that R increases with increasing disorder as more electron-phonon interaction channels may open.

D E L A Y ( p s ) D E L A Y ( P S )

Fig. 7 - ^~a

^for I 1 polarization in a-As2Seg Fig. 8 - Same as Fig. 7 at T

300K and T

80K. but for a-Se

Chalcogenide Glasses.- We observed hot carrier thermalization also in some chalco- genide glasses. Figure 7 shows A~(T) in a-As2Se3 and Fig. 8 in a-Se, both for 1 I

polarization. The fast decay seen around

0 is more pf_onounced in a-As2Se3 than in a-Se. >is is consistent with the difference in AE(0): Eg(a-AsqSe3

=

1.75 eV and AE(O) ' 0.12 eV; Eg(a-Se) $ 2 eV and AE(O) is smaller than in a-AspSe3. With decreasing temperature Eg increases, X(O) decreases and so does the peak height at

0 for both samples. From Ad, we estimate us (os = ~ a ~ / n ) to be 2xl0-17cm2 for both samples which is larger than in a-Si and a-Si:H

(

3

10-18cm2).

a-AssSe3.- From the data of Fig. 6 we estimate t o = 0.6 ps, which together with hE(0)

0.12 eV results in

0.2 eV/ps. This rate is smaller than R

hv2 =

0.4 eV/ps, and therefore we conclude that in a-AszSeg (similarly as in a-Si:H) the dissipation rate is slower than the maximum rate allowed by phonon emission.

The changelgf Eg with temperature in these chalcogenide glasses is about

0.7 meV/K; E at 80K is 1.9 eV andT~(0) is only 50 meV, much smaller than at

300K. The temperature dependence of Eg is the reason why the peak height at^ g = 0

decreases with decreasing temperature. Slnce

at 80K remains approximately the

same as at T = 300K, the dissipation rate R at 80K is slower. The decrease of R

with decreasing m(O) or ~ ~ ( 0 ) ) is in agreement with the known shape of R ~ E )

for polar dissipation.' We conclude that the dissipation mechanism in a-As2Se3

is through polar phonons.

C7-482

The peak h e i g h t a t

0 i s l a r g e r i n a-As2Sej t h a n i n a-Si:H a l t h o u g h E ( o ) i n b o t h c a s e s h a v e comparable v a l u e s ; t h i s i m p l i e s a l a r g e r v a l u e o f . A l s o a s

i s l a r g e r t h a n i n a-Si:H. T h i s s u g g e s t s t h a t t h e e l e c t r o n - p h o n o n i n t e r a c t i o n a s s o c i a t e d w i t h t h e photon a b s o r p t i o n i s s t r o n g e r i n a-AspSe3. Rpol deduced from t h e d e c a y e x p e r i m e n t i s l a r g e r i n a-As2Se3 t h a n i n a-Si:H i n agreement w i t h t h e l a r g e r i r o s c i l l a t o r s t r e n g t h i n a-AspSej.

a-Se.- S i n c e =(O) i n a-Se i s c l o s e t o z e r o i t i s n o t s u r p r i s i n g t h a t t h e peak a t r

0 i s much lower compared t o a-AsgSeg. The t h e r m a l i z a t i o n t i m e i s found t o b e a b o u t 1 p s and t h e d i s s i p a t i o n r a t e R < 0 . 0 5 eV/ps i s much s l o w e r t h a n i n a-AsqSej.

It i s a l s o m u c h s l o w e r t h a n hv2

0 . 5 eV/ps i n a-Se. T h e s e d a t a i n d i c a t e t h a t R f o r v e r y s m a l l BE(0) i s n o t t h e maximum r a t e hv2 deduced b e f o r e from t h e depend- e n c e o f t h e quantum e f f i c i e n c y on t h e a p p l i e d e l e c t r i c f i e l d i n a-Se.16

At 80K E i s 2.2 eV, which i s l a r g e r t h a n h p . T h e r e f o r e t h e d e c a y i n A & ) shown i n F i g . g c a n n o t b e h o t c a r r i e r r e l a x a t i o n . We a t t r i b u t e t h i s d e c a y w i t h a t i m e c o n s t a n t o f a b o u t 8 0 p s t o g e m i n a t e r e c o m b i n a t i o n . T h i s o c c u r s i f < ^{Eg when}

t h e photon i s a b s o r b e d i n t h e Urbach t a i l and t h e e l e c t r o n - h o l e p a i r 1 s bound t o g e t h e r . l l We o b s e r v e d t h i s c a s e i n many c h a l c o g e n i d e g l a s s e s 1 1 ; i t i s d i f f e r e n t from t h e c a s e 6% > Eg d i s c u s s e d i n t h i s p a p e r f o r which t h e d i s s i p a t i o n o f t h e e x c e s s e n e r g y 4T%-Eg 1 s o b s e r v e d .

We t h a n k F. J a n s e n f o r t h e a-Se and a-As2Se3 s a m p l e s and T. R. K i r s t and J . S t r a i t f o r a s s i s t a n c e w i t h t h e e x p e r i m e n t s . T h i s work was s u p p o r t e d i n p a r t by NSF g r a n t DMR-79-09819 and t h e NSF M a t e r i a l s R e s e a r c h L a b o r a t o r y program a t Brown U n i v e r s i t y . R e f e r e n c e s

1 . E. P. I p p e n and C . V. Shank, i n U l t r a s h o r t L i g h t P u l s e s ( e d i t e d by S. L. S h a p i r o ) S p r i n g e r , New York,

8 3 ( 1 9 7 7 ) .

2. C. V. Shank, D. H. Auston, E. P. Ippen and 0 . Teschke, S o l i d S t a t e Commun. 26,

567 ( 1 9 7 8 ) .

3.

V. Shank,

L. F o r k , R. F . Lehny and J . Shah, Phys. Rev. L e t t . ftl, 112 ( 1 9 7 9 ) 4.

Von d e r L i n d e and R. Lambrich, Phys. Rev. L e t t . 42, 1090 (1979).

5 . E. M. Conwell i n S o l i d S t a t e P h y s i c s , Supp. 9 , Acad. P r e s s , New York 1967.

6. A. E l c i , M.

S m i r l and

M a t t e r , Phys. Rev. -, 191 ( 1 9 7 7 ) . 7. Z . Vardeny and

Tauc, Phys. Rev. L e t t . 5, 1223 ( 1 9 8 1 ) .

8 . K. S e e g e r , Semiconductor P h y s i c s , S p r i n g e r , New York, p. 374 ( 1 9 7 3 ) . 9.

Vard.1

J . Tauc, O p t i c s Commun. ( t o b e p u b l i s h e d ) .

10. S. A. Akhmanov and

K o r o t e e v , Sov. Phys. Usp. 20, 899 ( 1 9 7 8 ) . 11. D. A . A c k l e y , J . Tauc and

P a u l , Phys. Rev. L e t t . 43, 715 ( 1 9 7 9 ) . 12. J. F. R e i n t j e s and J. C. McGroddy, Phys. Rev. L e t t . 30, 9 0 1 ( 1 9 7 3 ) . 13. J . C. K n i g h t s and E. A. D a v i s ,

Phys. Chem. S o l i d s 35, 5 9 3 ( 1 9 7 4 ) . 14. J. Shah, S o l i d S t a t e E l e c t r o n i c s 21, 4 3 ( 1 9 7 8 ) .

15. M. H. Brodsky and A. L u r i o , Phys. Rev. g , 1646 ( 1 9 7 4 ) .

16. R. C. Enck and G. P f i s t e r i n P h o t o c o n d u c t i v i t y and R e l a t e d Phenomena, e d i t e d

by

Mort and

P a i , E l s e v i e r , New York, p. 215 ( 1 9 7 6 ) .