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PICOSECOND DYNAMICS OF CARRIERS IN AMORPHOUS SEMICONDUCTORS
Z. Vardeny, J. Tauc, C. Fang
To cite this version:
Z. Vardeny, J. Tauc, C. Fang. PICOSECOND DYNAMICS OF CARRIERS IN AMOR- PHOUS SEMICONDUCTORS. Journal de Physique Colloques, 1981, 42 (C4), pp.C4-539-C4-542.
�10.1051/jphyscol:19814116�. �jpa-00220733�
JOURNAL DE PHYSIQUE
Co2Zoqv.e
C4,suppZ6ment au nO1O, Tome
42,octobre 1981 page
C4-539PICOSECOND DYNAMICS OF CARRIERS I N AMORPHOUS SEMICONDUCTORS
Z . Vardeny, J. Tauc a n d C . J. ~ a n z
Division of Engineering and Department o f Physics, Brown University, Providen- ce, Rhode Island 02912,
U.S.A.*MU Planck I n s t i t u t e fur FestkSrperphysik, S t u t t g a r t , F.R.G.
A b s t r a c t . - Using t i m e r e s o l v e d p h o t o i n d u c e d a b s o r p t i o n w i t h s u b p i c o s e c o n d r e s - o l u t i o n we s t u d i e d h o t c a r r i e r t h e r m a l i z a t i o n f o l l o w e d by d e e p t r a p p i n g and r e c o m b i n a t i o n i n a - S i , a-Si:H, a-Si:F, a-Si:H:F and a-As2Seg. I n a-Se and a - A ~ 2 S 3 - ~ S e , ( 0 . 2 5 ( X ( 0 . 7 5 ) t h e o b s e r v e d r e l a x a t i o n s were a t t r i b u t e d t o g e m i n a t e r e c o m b i n a t i o n .
I n t r o d u c t i o n . - A p a s s i v e l y modelocked dye l a s e r p r o d u c i n g s u b p i c o s e c o n d p u l s e s was used t o s t u d y t h e u l t r a f a s t dynamics o f e x c e s s c a r r i e r s by t h e t i m e r e s o l v e d photo- i n d u c e d a b s o r p t i o n i n a - S i , a-Si:H, a-Si:H:F and c h a l c o g e n i d e g l a s s e s : a-Se, a-AspSej and a-As2Sg-,Sex (0.25 ( X ( 0 . 7 5 ) . We found t h a t when t h e e x c i t i n g photon e n e r g y
%up i s l a r g e r t h a n t h e band g a p Eg, t h e p h o t o g e n e r a t e d c a r r i e r s a r e n o t bound t o - g e t h e r and we c o u l d f o l l o w t h e h o t c a r r i e r t h e r m a l i z a t i o n a s w e l l a s t h e c o n s e c u t i v e t r a p p i n g and r e c o m b i n a t i o n p r o c e s s e s . On t h e o t h e r h a n d , when Eg >/F;wp, t h e photo- g e n e r a t e d c a r r i e r s a r e bound t o g e t h e r and t h e i r g e m i n a t e r e c o m b i n a t i o n i s o b s e r v e d . I n some o f t h e s t u d i e d amorphous s e m i c o n d u c t o r s a p o l a r i z a t o n memory a s s o c i a t e d w i t h induced d i c h r o i s m was o b s e r v e d .
E x p e r i m e n t a l . - The dye l a s e r and e x p e r i m e n t a l s e t - u p h a v e b e e n d e s c r i b e d e l ~ e w h e r e . l - ~ The 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 % w p = 2eV w i t h a s i n g l e s i d e e x 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 and r e p e t i t i o n r a t e d - 1 0 6 s - l . We used t h e pump and p r o b e t e c h n i q u e ; t h e p r o b e p u l s e i s d e l a y e d by v a r y i n g t h e l e n g t h o f i t s o p t i c a l p a t h . 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(I)
t o t h a t o f t h e pump beam. A l l e x p e r i m e n t s were done w i t h o p t i c a l l y t h i n samples: d < a a t 2eV, 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 c o n c e n t r a t i o n n v a r i e d from sample t o sample ( a s a - l ) between 5 X 1016 and 1019 cm-3 p e r p u l s e .O r i g i n s o f o b s e r v e d r e l a x a t i o n s . - The proposed e l e c t r o n i c mechanisms f o r t h e t r a n s - i e n t photo-induced a b s o r p t i o n c o e f f i c i e n t h a ( t ) f o r c a s e s : ( a ) Ziwp
>
Eg ( b ) 5 w p<
Eg a r e shown i n F i g . 1. I n c a s e ( a ) h o t c a r - Aa r i e r s w i t h e x c e s s e n e r g y BE a r e e x c i t e d
a c r o s s t h e band gap by t h e pump p u l s e w i t h
%W, energy.hwp. 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 due t o 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 .
c a r r ~ e r s D u r i n g t h i s p r o c e s s 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 s o r p t i o n c r o s s - s e c t i o n Of h o t c a r r i e r s i 3 c r e a s e s 4 w i t h AE
,
i t 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 o p t i c a l method, 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 enough. The e l e c t r o n - h o l e d i s t a n c e a f t e r t h e r m a l i z a t i o n F i g . 1 - Proposed mechanism f o r p h o t o - , ( t h e r m a l i z a t i o n r a d i u s r o ) i s l a r g e r i n c a s einduced a b s o r p t i o n decay ( a ) t h a n t h e Onsager c a p t u r e r a d i u s r c ( a ) Kwp
>
Eg, ( b ) *up<
Eg. and t h e c a r r i e r s move i n d e p e n d e n t l y o f e a c ho t h e r . E v e n t u a l l y , t h e t h e r m a l i z e d c a r r i e r s
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814116
JOURNAL DE PHYSIQUE
d e l a y ( P S )
F i g . 2
-
Time dependence o f t h e p h o t o i n d u c e d a b s o r p t i o n i n a - S i , a-Si:H and a-Si:H:F f o rI I
p o l a r i z a t i o n s . 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 .F i g . 3
-
Same a s i n F i g . 2 b u t f o r a-AszS2.4S 0.6, a-Se and a-As2Sej.w i l l b e removed from t h e b o t t o m o f t h e c o n d u c t i o n band by t r a p p i n g , r e c o m b i n a t i o n o r b o t h . l y 5 I n c a s e ( b ) where .tiw
<
Eg, c a r r i e r s a r e e x c i t e d i n t h e Urbach t a i l ( F i g . I(:)), ro<
rc and t h e e l e c t r o n and h o l e a r e bound t o g e t h e r . I n t h i s c a s e t h e r e c o m b i n a t i o n i s g e m i n a t e and i s o b s e r v e d a s a d e c a y o f h a ( t ) , s i n c e A a ( t ) % n ( t ) .Amorphous S i l i c o n . - T y p i c a l r e s u l t s f o r
I I
p o l a r i z a t i o n a r e shown i n F i g . 2 ; t h e y a r e examples o f c a s e ( a ) . Most samples show a n i n i t i a l nonsymmetric r e s p o n s e around t = 0 t h a t d e c a y s f a s t t o a lower v a l u e A u s . The r e l a t i v e h e i g h t o f t h e measured peak a t t = 0 i s c l o s e l y r e l a t e d t o t h e a v e r a g e i n i t i a l e x c e s s e n e r g y E ( o ) = (6w - % ) I 2 a s s e e n i n F i g . 2 where A % ( s ~ )>
~ E ( s ~ : H )fj
AE(S~:H:F).
When
I
p o l a r i z a t i o n i s u s e d t h e peak i n h a i s r e d u c e d ; t h i s i s a s c r i b e d t o t h e r e d u c t i o n o f t h e c o h e r e n t a r t i f a c t component . 2 9 3 A t l o n g e r t i m e s when s a t u r a t i o n i s r e a c h e d Aas(L)<
Ans([ 1) and t h e d e p o l a r i z a t i o n r a t i o p = Aa( 1
)/Acts([ 1) v a r i e s between 0 . 6 and 0.9.' T h i s shows t 2 a ~ a p o l a r i z a t i o n memory a s s o c i a t e d w i t h p h o t o i n d u c e d d i c h r o i s m c a n e x i s t i n t h e s e 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 . We o b s e r v e d t h a t p -increas- e s w i t h i n c r e a s i n g t h e i n i t i a l e x c e s s e n e r g y AE(0).The d a t a i n d i c a t e t h a t t h e e x c e s s e n e r g y d i s s i p a _ t i o n r a t e by i n t e r a c t i o n o f e l e c t r o n s w i t h phonons d ~ ~ l d t i s f a s t e r i n a-Si t h a n i n a-Si:H. It i s g e n e r a l l y assumed6 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 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 ~ i t h t h e t h e r m a l - i z a t i o n r a t e e x t r a c t e d from t h e d a t a ~ E ( O ) = 0.35eV, to
'
0 . 7 ~ ~ ) . The f i t t o t h e a-Si c a s e shown i n F i g . 2 was done u s i n g a p i m p u l s e r e s p o n s e A ( t ) % a ( t ) where~ ( t ) = o s [ l + (bAE(O)/K) ( 1
-
t / 0 . 7 ) ] f o r t<
0 . 7 p s and o ( t ) = Us f o r t>
0.7ps where b i s t h e enhancement p a r a m e t e r @U = b E ) . From t h e f i t we o b t a i n e d b = 1 . 2 x ~ O - ~ K - I which i s s u r p r i s i n g l y c l o s e t o t h e v a l u e o f 1 . 3 L 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 t 2eV 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 s c a t t e r i n g i n c r y s t a l s . 4A s l o w e r d i s s i p a t i o n r a t e , 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 b y F r 5 h l c c h c o u p l i n g t o p o l a r phonons. The a v e r a g e r a t e o f dAE/dt o v e r a Boltzmann d i s t r i b u t i o n ~ X ~ ( - A E / ~ T ~ ) (where Te i s t h e h o t c a r r i e r s t e m p e r a t u r e ) i n f e g r a t e d o v e r t h e i r - a c t i v e phonon s p e c t r u m was c a l c u l a t e d . T h i s r a t e f i r s t 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 rn_aximum5 of 0 . 1 e V l p s . For a-Si:H shown i n F i g . 2 AE(O) = 0 . 1 eV and t h e t h e r m a l i z a t i o n t i m e t o = l p s .
The f i t t o t h e o b s e r v e d A a ( t ) i s o b t a i n e d u s i n g A ( t ) W ( t ) = o s ( l + a ~ , ( 0 ) ( 1
-
t / 1 . 2 ) 1 f o r t<
1 . 2 p s and o ( t ) = U f o r t>
1 . 2 p s w i t h a = 1 . 7 X ~ O - ~ K - I and Te = 2 @ ( 0 ) / 3 = 800K. A a ( t ) f o r a-Si:H:F was f i t w i t h a s t e p f u n c t i o n j m p u l s e r e s p o n s e A ( t ) = o S u ( t ) . The r e a s o n o f why dAE/dt i s l a r g e r i n a-Si t h a n i n a-5i:H i s unknown a t t h i s t i m e ; one c a n s p e c u l a t e t h a t dAE/dtincreases with increasing disorder as other electron phonon interaction channels may open.
After thermalization, at longer time a slower decay, that cannot be described by a single exponential, of Aa(t) was dbservedl in sputtered a-Si; at lower T this decay is slower. It was attributed to trapping in deep traps or recombination centers.
We observed similar decays in a-Si:F but not in hydrogenated samples. This suggests that F alone does not compensate the dangling bonds effectively.
Chalcogenide glasses.- Typical results for chalcogenide glasses are presented in Fig. 3. The gap Eg for a-As2S2.4 Seo.6 and a-Se at all T is larger than5wp, there- fore, they represent case (b) (Fig. 1). In a-As2Seg E g < 5 w p and it represents case (a) in the chalcogenide group. In the latter case the relaxations are similar as in a-Si:H discussed above. We will concentrate now on case (b). Excited in the Urbach tail, electron and hole are bourid together as a pair with a binding energy e2/4 n ero ( E is thz dielectric constant). The energy above the ground state is
AE* = - K u
-
E + e /4 rrcro. E is not well defined; we took for it the energy wherea = 1o4cK-1. g~ssuming that the energy g d. sipation rate dA~*/dt = hv2 we calculate ro by solving th equation r = (Dhott0)f72 = ( D ~ ~ ~ A E * / ~ v ~ ) ~ / ~ . Taking
got
= 0.1 cm2/s1 and h v = 3 y m e ~ we obtain values of r between 3 to98
(Table I).e values of to = A ~ * / h v ~ are less than 50 femtosecon8s, too short to be observed.
The observed decays are ascribed to recombination.
The Onsager capture radii6 in these materials are r = 80% at 300K and 1 300%
at 80K, considerably larger than ro. Since only a fraction exp[-rc/ro] of carriers C escape the geminate recombination the dominant recombination process is geminate.
The observed decays are exponentials exp[-t/~,] where Tr is longer at smaller Eg.
An important feature of this recombination time rr is that it decreases with de- creasing temperature1 (as shown for a-Se in Fig. 3 and for other chalcogenides in Table I); this is just the opposite of the temperature dependence of the recombina- t ion time observed in a-Si after thermalizationl mentioned above.
Geminate recombination model.- Two models for geminate recombination were considered.
In the first model (usually referred to as time-dependent Onsager model8) the car- riers diffuse towards each other. The number of
was calculated8 to be N(t) = No exp[-rc/ro] [l +
a t-ll2 decay of Aa(t) which is slower at lower the temperature de- pendence of D in amorphous materials), both against the experimental data.
l000
-
Another approach describes the geminate recombinationas a tunneling process1,9 in which ~ ( t ) = ~ ( 0 )
(
exp[-th1
with time constant r r = v 1exp[2&o~, where B - ~ is the extent of the wave function. This model agrees with the observed exponential decays asl 0 0 - well as with the temperature dependence of rr. This
dependence is due to the temperature dependence of Eg
-
which is larger at lower T; consequently ro is smallera
+- and is shorter. A consequence of this model is that r r depends on Eg only, regardless of whether a certain
value of Eg is obtained by changing composition or
o - 8 ~ temperature. This is clearly confirmed by experiment, ~
f - 3 0 0 K as seen in Fig.
4 where^^
is plotted vs. ro. The datao-AS, SJ.xSe, lie on a straight line for almost 3 orders of magnitude
of rr. The fit gives v = 1 1 X 1013s-' and
B - ~
= 2.1%;both parameters have reasonable yfjlues. In the case of a-As Se .hw
>
Eg and ro = rc so that the geminater , i i ~ 2
3
recombinat~on Fime constant becomes very long. Indeed, Fig.
4 -
Decay time r r as shown in Fig. 3, Aa(t) shows no apparent decay up plotted vs. the thermaliza- to 60ps.t ion radius ro for
a-A~2S3-~Se, and a-Se
.
Our results do not contradict the work on the tempera- ture dependence of the luminescence decay in GDJOURNAL DE PHYSIQUE
a - S i : ~ l l i n which d i f f u s i o n had t o b e i n c l u d e d f o r e x p l a i n i n g t h e d a t a on g e m i n a t e r e c o m b i n a t i o n a t h i g h T. I n o u r c a s e t h e e x c i t a t i o n o c c u r s i n t o t h e Urbach t a i l , r o
<<
r c and t h e d i f f u s i o n i s n e g l i g i b l e a t a l l T.We t h a n k F. J a n s e n f o r t h e a-Se and a - A s ~ S e j samples 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 .
*On l e a v e from C h i n e s e U n i v e r s i t y o f S c i e n c e and Technology, B e i i i n g , PROC Reference's.
D. E . A c k l e y , J . Tauc and W. P a u l , Phys. Rev. L e t t .
5,
715 ( 1 9 7 9 ) . Z . Vardeny and J. Tauc, Phys. Rev. L e t t .66,
1223 ( 1 9 8 1 ) .Z . Vardeny and J . Tauc, s u b m i t t e d t o O p t i c s Communications.
K. S e e g e r , S e m i c o n d u c t o r s P h y s i c s , S p r i n g e r , New York, p . 374, 1973.
Z . Vardeny, J . Tauc and C. J . Fang, P r o c . I n t . T o p i c a l Conf. on T e t r a h e d r a l l y Bonded Amorphous S e m i c o n d u c t o r s , C a r e f r e e , A r i z o n a 1981, i n p r i n t .
J . C . K n i g h t s and E . A. David, J . Phys. Chem. S o l .
5,
5 4 3 ( 1 9 7 4 ) . E. M. Conwell i n S o l i d S t a t e P h y s i c s , S u p p l . 9 , Acad., New York,, 1967.K. M . Hong and J . N o o l a n d i , J . Chem. Phys. 6 8 , 5 1 6 3 ( 1 9 4 8 ) . N . F. Mott, E . A. D a v i s , R. A. S t r e e t , P h i l . Mag.
32,
961 ( 1 9 7 5 ) .J . M o r t , I . Chen, M. Morgan and S . Grammatica, S o l . S t . Comm. ( i n p r i n t ) . J. N o o l a n d i , K. M. Hong and R. A. S t r e e t , J . Non-Cryst. S o l .
E,
669 ( 1 9 8 0 ) .TABLE I
Geminate Recombination Decay P a r a m e t e r s i n C h a l o g e n i d e G l a s s e s
Sample
*From D . E. A c k l e y ' s Ph.D. T h e s i s , Brown U n i v e r s i t y , 1979.
