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SPIN-DEPENDENT RECOMBINATION AT DISLOCATION DANGLING BONDS IN Si
V. Kveder, Yu. Ossipyan, A.I. Shalynin
To cite this version:
V. Kveder, Yu. Ossipyan, A.I. Shalynin. SPIN-DEPENDENT RECOMBINATION AT DISLOCA- TION DANGLING BONDS IN Si. Journal de Physique Colloques, 1983, 44 (C4), pp.C4-345-C4-352.
�10.1051/jphyscol:1983441�. �jpa-00223060�
JOURNAL DE PHYSIQUE
Colloque C4, suppl6ment au n09, Tome 44, septernbre 1983 page C4-345
SPIN-DEPENDENT R E C O M B I N A T I O N AT DISLOCATION D A N G L I N G BONDS I N S i
V.V. Kveder, Yu.A. Ossipyan and A . I . Shalynin
I n s t i t u t e o f S o l i d S t a t e P h y s i c s , Academy o f S c i e n c e s o f t h e U.S.S.R., 1 4 2 4 3 2 C7nernogoZovka, Moscow d i s t r . , U.S.S. R.
RBsum6
- La
recombinaison dependant du spin des porteurs l i b r e s par 1' inter- m-
e des liaisons pendantes dues aux dislocations e s t Btudi6e en fonction de l a temperature e t de l t i n t e n s i t 6 de l a luniBre sous des champs magnetiques de 0,04, de 3,3 e t de 12,s m e . L1analyse des r d s u l t a t s conduit 2 proposer un modBle fond6 sur l e concept de recombinaison v i a l e s l i a i s o n s pendantes aprss une capture preliminaire sur des niveaux interm6diaires peu profonds dus pro- bablement au potentiel de d6formation de l a dislocation.
A b s t r a c t
-
S p i n - d e p e n d e n t r e c o m b i n a t i o n o f f r e e c m r i e r s v i a d i s - location d a n g l i n g bonds (DDB) i s i n v e s t i g a t e d a s a f u n c t i o n o f t e m p e r a t u r e a n d l i g h t i n t e n s i t y i n m a g n e t i c f i e l d s o f 0 . 0 4 , 3 . 3 and 1 2 . 5 k o e . On t h e b a s i s o f an a n a l y s i s of t h e d a t a o b t a i n e d , a model o f t h e e f f e c t i s p r o p o s e d i n which u s e i s made o f t h e c o n c e p t o f r e c o m b i n a t i o n v i a DDB w i t h p r e l i m i n a n y c a r r i e r c a p t u r e a t t h e i n t e r m e d i a t e s h a l l o w l e v e l s d u e , p r e s u m a b l y , t o t h e d e - f o r m a t i o n p o t e n t i a l o f t h e d i s l o c a t i o n .I n t r o d u c t i o n
I t i s known t h a t p l a s t i c d e f o r m a t i o n o f S i - c r y s t a l a t 650 - 700 OC
c r e a t e s s p e c i a l t y p e o f p a r a m a g n e t i c c e n t e r s , s o - c a l l e d D - c e n t e r s , which a r e S i - b r o k e n bonds i n some d e f e c t s 11,21. A n a l y s i n a t h e ESR
s i g n a l o f D - c e n t e r s , t h e i r c o n c e n t r a t i o n i s ND : 4 x 1 0 ~ 6 ~ r n - ~ a t 300
-
50 K f o r a d i s l o c a t i o n d e n s i t y o f a b o u t 2 x 1 0 9 cm-2 a n d i s p r o p o r t i o n a l t o t h e d i s l o c a t i o n d e n s i t y . The e n e r u y s p e c t r u m s u q g e s - t e d f o r D - c e n t e r s u s i n g photo-ESR d a t a o b t a i n e d a t 100 K 131 m a i n l y c o n s i s t s o f two n a r r o w b a n d s ( f i g . 1 ) . Band 1 h a s b e e n a t t r i b u t e d t o b r o k e n b o n d s , band 2-
t o b r o k e n bonds ( D - c e n t e r s ) , o c c u p i e d by a d d i t i o n a l e l e c t r o n s .By i n v e s t i a a t i n a t h e ESR s i a n a l o f n e u t r a l p h o s p h o r o u s atoms i n g l a s - t i c a l l y deformed c r y s t a l s and c o n m a r i n a it w i t h t h a t from D - c e n t e r s , it w a s shoo~n t h a t t h e number o f e l e c t r o n s c a p t u r e d by D - c e n t e r s d i d n o t e x c e e d 0.2 N 11
1 .
H a l l e f f e c t d a t a s u s g e s t t h e same c o n c l u s i o n . The DLTS d a t a 14y c o n f i r m t h i s a n d shows t h a t D - c e n t e r s must b el o c a l i z e d i n d i s l o c a t i o n c o r e s ( o r v e r y c l o s e t o them) o r i n some c l a s t e r s w i t h h i g h d e n s i t y s o t h a t t h e Coulomb b a r r i e r , c a u s e d by c a n t u r e d e l e c t r o n s o r h o l e s , r e s t r i c t s t h e i r o c c u p a t i o n .
More t h a n t h a t , t h e d a t a f o r t e m p e r a t u r e d e p e n d e n c e o f m a g n e t i c s u s - c e p t i b i l i t y shows d e v i a t i o n from c u r i e low between 20 and 50 K , which c o r r e s p o n d s t o t h e d i m i n i s h i n g e f f e c t i v e number o f s p i n s a t low tem- p e r a t u r e s 15
[ .
The a n i s o t r o p y of s p e c t r u m a l s o s l i g h t l y c h a n q e s a n d a t T<
20 K c o r r e s p o n d s t o b r o k e n bonds i n d i s l o c a t i o n c o r e s 161.S i n c e D - c e n t e r s a r e d e e p s t a t e s ( a s d e e p a s 0 . 4 eV) e l e c t r o n r e d i s t r i - b u t i o n between them o r o t h e r p r o c e s s e s c h a n s i n g t h e e f f e c t i v e number o f s p i n s ( e x c h a n g e i n t e r a c t i o n f o r example) c a n o n l y a c c u r t h r o u g h a d i r e c t o v e r l a p of t h e b r o k e n bonds wave f u n c t i o n s . S i n c e a l l t h e s e d a t a f i t w e l l w i t h what c a n ke e x p e c t e d f o r t h e c h a i n o f d i s l o c a t i o n d a n g l i n g bonds (DDB) one c a n p r o p o s e t h a t D - c e n t e r s c o r r e s p o n d s t o c h a i n s o f DDB.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983441
C4-346 JOURNAL DE PHYSIQUE
S i n c e DDB can a c t a s a deep t r a p s w i t h a l a r g e c a p t u r e c r o s s s e c t i o n b o t h f o r e l e c t r o n s and h o l e s , t h e y s h o u l d b e v e r y e f f e c t i v e a s r e - corcbination c e n t e r s . I n o r d e r t o o b t a i n a d d i t i o n a l d a t a about t h i s
~ ' ~ ' " ' " " ' " " " ' " " ' ~ ' ~ ' " ' ~
FIG. IF i g . 3 : F i g . 2: G-VALUE
1
-
i s ESP-spectrum f o r D - c e n t e r s ,r e c o m b i n a t i o n p r o c e s s and t h e n a t u r e of D-centers we have i n v e s t i g a - t e d i n t h i s work t h e i n f l u e n c e of s a t u r a t i o n t h e D-centers ESR on t h e r e c o m b i n a t i o n t i m e ( s o - c a l l e d s p i n dependent r e c o m b i n a t i o n (SDR))
.
Such k i n d of e f f e c t h a s been found f i r s t by Lepine f o r t h e s u r f a c e r e c o m b i n a t i o n i n S i 171. Then we found SDR f o r D-centers i n S i a t low t e m p e r a t u r e 181 and Wosinski and F i g i e l s k i found SDR i n p l a s t i c a l l y deformed S i a t room t e m p e r a t u r e 191. More r e c e n t l y e x p e r i m e n t s o f t h i s k i n d have been r e p o r t e d f o r amorphous S i f i l m s (Solomon e t a l l
1101).
Experimental method and R e s u l t s
S i c r y s t a l s grown by a n o n c r u c i b l e zone m e l t i n vacuum doped w i t h 1033 cm-3 boron were p l a s t i c a l l y deformed by 2 % i n compression a l o n g
<110> a t 680 OC. From TEM d a t a a d i s l o c a t i o n d e n s i t y of ( 1 . 5 t o 3 )
*
l o 9 cm-2 was o b t a i n e d .
HF m a g n e t i c f i e l d (F = 110 Mc/s, 9 . l o 3 Mc/s o r 3.6.104 M C / S ) a p p l i e d t o t h e sample p e r p e n d i c u l a r t o t h e d . c . magnetic f i e l d Ho and a weak w h i t e l i g h t was u s e d t o produce p h o t o c o n d . u c t i v i t y . A S i f i l t e r w i t h a t h i c k n e s s 1 mrn was p l a c e d i n f r o n t o f sample t o p r o v i d e a homo- geneous g e n e r a t i o n o f f r e e c a r r i e r s . The photocond.uctivity 6(Ho) of t h e sample was measured a s a f u n c t i o n of a p p l i e d d . c . m a g n e t i c f i e l d Ho w i t h and w i t h o u t HF-magnetic f i e l d and t h e d i f f e r e n c e A6(Ho) was accumulated by computer.
F i g . 2 shows a t y p i c a l SDR-spectrum ( t h a t i s A6(Ho)/G) and ESR-spec- trum f o r D-centers.
So f a r a s D-centers ESR spectrum c o n s i s t s of i n d i v i d u a l s p i n p a c k e t s 151
,
t h e ESR s i q n a l can b e s a t u r a t e d o n l y l o c a l l y d u r i n g t h e sweeping-5.8 -4.0 -3.0 -2.8 -1.0 0.0 7. 0. 11. 1% 15.
g r I T H nMULATIDN
AuITnw nonULATIrW LOG ( H: ) [ARB. UNITS1 ASPIN-LATTICE TIME . 0 LG(6'*)
+SDRTI)IE
F i g . 3: F i g . 4 :
The dependence of SDR-signal on The r * and r, v a l u e s V.S. t h e
HF-power sample c o n d u c t i v i t y .
T = 1 . 4 K; Ho = 0.33 T .
Ho o v e r . I t means t h a t t h e a m p l i t u d e of SPR spectrum d o e s n ' t c o r r e - spond t o t h e t o t a l e f f e c t . I n o r d e r t o o b t a i n t h e r i g h t magnitude f o r SPR, w e a p p l i e d a d d i t i o n a l m a a n e t i c f i e l d HM s i n ( 2 n f n t ) p a r a l l e l t o Ho w i t h a m p l i t u d e H# g r e a t e r t h e n t h e spectrum w i d t h and w i t h f r e - quency f M g r e a t e r t h e n ( 2 ~ c r * ) - ~ , where t * i s some c h a r a c t e r i s t i c t i m e f o r SDR ( i n s i m p l e s t model r * i s T I - s p i n - l a t t i c e r e l a x a t i o n t i m e ) . Indeed a s one can s e e a t f i g . 3 , it c a u s e d i n c r e a s i n g t h e SPR s i g n a l by f a c t o r 2 t o 4 . The v a l u e of r * was c a l c u l a t e d from t h e experimen- t a l l y measured c u r v e s A6/6 V . S . f M .
Our measurements show t h a t t h e r * and r l depend o n l y on l i g h t i n t e n - s i t y b u t n o t on t e m p e r a t u r e i n r a n g e 1.3 t o 10 K and l i g h t i n t e n s i t y s u s e d . F i g . 4 p r e s e n t s t h e dependence o f r l and r * on sample c o n d u c t i - v i t y , measured a t T t h e r * and A6/6 on t e m p e r a t u r e f o r F = 1.4 K . A t l a s t , F i g . 5 p r e e n t s dependences of = 110, 9.10
3
and 3 . 6 ~ 1 0 ~ Mc/s.D i s c u s s i o n and p o s s i b l e i n t e r p r e t a t i o n of d a t a
For D-centers w e have found t h e SDR-signal which h a s t h e same s h a p e as ESR-spectrum and t h e a m p l i t u d e which i s a l m o s t independent on d . c . magnetic f i e l d i n t h e r a n g e from 4 0 t o 1.2 103 Ce. The c h a r a c t e r i s t i c t i m e c o n s t a n t T* of SDR i s n o t i c a b l y l o n g e r t h e n s p i n - l a t t i c e r e l a x a - t i o n t i m e f o r D-centers.
S e v e r a l t h e o r e t i c a l models were moved t o e x p l a i n SDR. The s i m p l e s t one c o n s i d e r t h e t r a p i n g f r e e e l e c t r o n s t o t h e p a r a m a g n e t i c c e n t e r s w i t h s p i n S = 1/2 p r o v i d i n g t h e f i n a l s t a t e w i t h S = 0 . I f t h e s p i n - o r b i t i n t e r a c t i o n i s n o t l a r g e , r e c o m b i n a t i o n t r a n s i t i o n w i l l con- s e r v e t o t a l s p i n . I t means t h a t t h e i n i t i a l c o n f i g u r a t i o n must b e a l s o S = 0 f o r t h e t r a n s i t i o n t o t a k e p l a c e .
I n d . c , magnetic f i e l d b o t h e l e c t r o n s and c e n t e r s have a p o l a r i z a t i o n
JOURNAL DE PHYSIQUE
. -
F i g . 5A: F i g . 5B:
SDR-time t * v . s . t e m p e r a t u r e . SDR-signal V . S . t e m p e r a t u r e f o r S o l i d l i n e 1 i s t h e o r y . s e v e r a l v a l u e s of Ho.
S o l i d l i n e 2 i s e x t r a p o l a t i o n S o l i d l i n e i s t h e o r y . f o r -q.
PS
-
Ho/TS. S i n c e t h e p r o j e c t i o n o p e r a t o r f o r s i n g l e t i s nS=1/4-
S,
.
SD, t h e a v e r a g e p r o b a b i l i t y f o r r e c o m b i n a t i o n i s WR = 1/4 WRS ( I - p e p D ) . S a t u r a t i o n ,of ESR means t h a t PD-
0 and s h o u l d l e a d t o i n c r e a s e i n r e c o m b i n a t i o n r a t e .T h i s model, however, has a l m o s t n o t h i n g t o do w i t h d a t a o b t a i n e d f o r i t p r e d i c t s t h e A6/6 @ (Ho/T) and r* = t l and g i v e s t h e maximal v a l u e of e f f e c t which i s much lower t h e n t h e e x p e r i m e n t a l o n e . The assuming a s p i n l a r g e r t h a n 1 / 2 d u e t o d i r e c t 111
1
o r i n d i r e c t 1121 ferromag- n e t i c exchange i n t e r a c t i o n s between D-centers c a n e x p l a i n t h e l a r g e r v a l u e of e f f e c t , b u t it a l s o p r e d i c t s t h e dependence on Ho.A model o f r e s o n a n t h e a t i n g of t h e exchange r e s e r v o i r o f D-centers s p i n s s t e m and l o c a l i s e d d i s l o c a t i o n phonons were proposed i n
11 3,147. But t h e s e models a l s o g i v e s t h e dependence on Ho.
The o n l y model which p r e d i c t s ( a t t h e f i r s t a p p r o x i m a t i o n ) no depen- dence on Ho i s one proposed by Kaplan, Solomon and Mott 115) f o r SDR i n amorphous S i .
It u s e s q u i t e a u n i v e r s a l i d e a of r e c o m b i n a t i o n v i a i n t e r m e d i a t e l o c a - l i s e d p a i r s t a t e t o t h e f i n a l s t a t e w i t h S = 0 . Examples of such r e c o m b i n a t i o n i n v o l v i n g p a i r s a r e e x i t o n o r d o n o r - a c c e p t o r recombi- n a t i o n .
L e t ' s t r y now t o u s e t h i s i d e a and t o change t h e o r i g i n a l model 1 1 5 1 t a k i n g i n t o account what we know a b o u t D-centers.
Let U S suppose t h a t D-centers c o r r e s p o n d s t o one-dimensional c h a i n s of DDB N-spins l o n g . Holes can be t r a p e d t o band 1 ( f i g . 1 ) and e l e c t r o n s
-
t o band 2.F i g . 6:
The dependence of SDR-signal on l i g h t i n t e n s i t y . T = 1 . 4 K , Ho = 0 . 3 3 T .
F o l l o w i n g t h e e x p l a n a t i o n p r o p o s e d i n 1161 f o r microwave conduc- t i v i t y o b s e r v e d a t low t e m p e r a t u r e s i n d i s l o c a t e d S i a n d G e , w e s h o u l d s u g g e s t t h a t t r a p p e d e l e c t r o n and h o l e can move a l o n g t h e c h a i n and t h e f i n a l r e c o m b i n a t i o n would t a k e p l a c e when t h e y r e a c h t h e same DDB.
But t h i s l a s t p r o c e s s i s n o t i n t e r e s t i n g f o r u s a t t h e moment b e c a u s e s t a t e s 1 , 2 a r e v e r y d e e p and t h e r m a l a c t i v a t i o n o f c a p t u r e d c a r r i e r back t o Ec o r E, i s n o t p o s s i b l e a t T
<
100 K . L e t u s s u g g e s t now t h a t t h e e l e c t r o n s c a n b e t r a ~ p 2 t o band 1 m a i n l y from some s h a l l o w s t a t e s Ecd ( f i g . 1 ) where t h e y c a n b e t r a m t o from c o n d u c t i o n band Ec. I t i s q u i t e r e a s o n a b l e t o assume t h a t s t a t e s Ecd a r e due t o t h e d e f o r m a t i o n p o t e n t i a l o f t h e d i s l o c a t i o n . The e l e c t r o n i n E c d - s t a t e c a n be e x c i t e d back t o Ec o r b e trapre2 t o DDB (band 1 ) . I n t h e l a s t c a s e t h e f i n a l s t a t e i s assumed t o have s p i n S = 0 a n d t h e t o t a l s p i n c o n s e r v a t i o n r u l e assumed t o b e o b s e r v e d i n t h i s p r o c e s s .Then t h e p r o b a b i l i t y f o r t r a n s i t i c n Ecd
-
El i s Wc = Wo WS, whereWS i s t h e p r o b a b i l i t y f o r p a i r e l e c t r o n i n Ecd
-
DDB t o be i n s i n g l e t s t a t e S = 0 , a v e r a g e d f o r a l l DDB i n g i v e n c h a l n . I f Ho # 0 , t h e DDB s p i n s r o t a t e s a r o u n d Ho n o t w i t h t h e same f r e q u e n c i e a s Ecd e l e c t r o n s p i n . ~f y (gDDB-
g e ) H~>>
( T * ) -1,
we c a n u s ews
= I / 4 (l-p,pDDB) Wp(PDDB),
where p = c o s 0 , and O i s a n g l e between Ho and s p l n ,Wp(PDDB) i s p r o b a b i l i t y t o h a v e c h a i n w i t h g i v e n a v e r a g e v a l u e PDDB.
However, it i s n o t v e r y e a s y t o c a l c u l a t e \ap e x a c t l y , b u t f o r e x t i m a - t i o n s w e u s e d a s i m p l e f o r m u l a :
P = ( N + - N - ) / N , assuming pHo/kT
<<
1 and N>>
1 .I f n ( p c , P D D B ) i s t h e number o f E e d - e l e c t r o n s w i t h g i v e n pe, t r a p e d t o Ecd n e a r DDB-chain w i t h g i v e n PDDB, t h e n , i n e q u i l i b r i u m :
C4-350 JOURNAL DE PHYSIQUE
where G
-
i s g e n e r a t i o n r a t e , WD - p r o b a b i l i t y o f e l e c t r o n a c t i v a t i o n from Ecd t o Ec, WE-
p r o b a b i l i t y f o r PDDB t o be changed by HF-field o r by s p i n - l a t t i c e r e l a x a t i o n .t h e n t h e r e c o m b i n a t i o n r a t e i s
+
1R = 1 / 4 Wo n(pcIPDDB) (1-pCPDDB) dpC dPDDB ( 1 )
-1 and
+I
t * = I/G n (pC lPDDB) dpC dPDDB -1
So, SDR depends on p a r a m e t e r s b = WD/Wo, A = ( t l , W o ) -1 and N a t
T
<
4 K we know p a r a m e t e r s t * and T I and t h e o n l y f r e e a r e N and Wo.F i g . 6 p r e s e n t s t h e e x p e r i m e n t a l d a t a , o b t a i n e d a t d i f f e r e n t l i g h t i n t e n s i t y s and c a l c u l a t e d t h e o r e t i c a l dependence f o r N = 8 and Wo 63 s e c - 1 .
A s t o t h e dependence on t e m p e r a t u r e , we d o n ' t know t h e e x a c t depen- dence Wo and WD on T. Experimental d a t a f o r r l a r e a v a i l a b l e o n l y f o r
T
<
6 K and T>
20 K b u t we can u s e some rough e x t r a p o l a t i o n w i t h i n6 K t o 20 K r a n g e . S o l i d l i n e s i n f i g . 5 shows r e s u l t o f c o v p u t e r ' s c a l c u l a t i o n f o r A6/6 and r * o b t a i n e d under t h e assumption t h a t N 8 ,
W o - 6 3 + 1 . 5 - 1 0 exp(-E*/kT) 5 and
WD 25
+
2-
10' e x p ( - E * / ~ T ) , E: where E* a 0.01 eV.S e v e r a l p o i n t s s h o u l d b e made now.
1. We n e g l e c t e d a l l p o s s i b l e exchange i n t e r a c t i o n s . F o r example, i f some weak exchange i n t e r a c t i o n H,-DDB between E c d - e l e c t r o n and DDB e x i s t and Hc-DDB
>
hy(gDDB-
gc) H?, we w i l l be a b l e t o u s e a d i r e c t i o n o f E c d - e l e c t r o n s p i n a s a x l s and t h e r e f o r e u s e o n l y one i n t e g r a t i o n i n (1) and ( 2 ).
The r e s u l t w i l l b e q u a l i t a t i v e l y s i m i l a r , b u t t h e v a l u e A6/6 being l a r g e r we s h o u l d t a k e N 1 20 i n s t e a d of N = 8 .2. A s t h e A6/6 i s a l m o s t i n v e r s e l y p r o p o r t i o n a l t o N , t h e o b t a i n e d v a l u e N = 8 d o e s n ' t mean t h e a v e r a g e l e n g t h o f c h a i n s .
I f we, f o r example, have Gaussian d i s t r i b u t i o n of DDB-chains l e n g t h s w i t h d i s p e r s i o n AN/N
=
0 . 6-
3, t h e n N w i l l be 16 not 8 .3 . L e t ' s e s t i m a t e t h e d i s t a n c e between DDB-chains. Assuming t h e d i s t a n c e between DDB w i t h i n c h a i n a* t o b e 4
-
108
we can c a l c u - l a t e t h e d i p o l e - d i p o l e i n t e r a c t i o n a s Hdd'
u B / ( a * ) j=
10-
100 Oe.S i n c e t h e r e a l w i d t h of s p i n - p a c k e t s from ESR d a t a i s 0 . 5
-
1 Oe, W e s h o u l d s u g g e s t t h e e x i s t a n c e of exchange i n t e r a c t i o n Hc and from AH"
~ 3Hc .<
~1 0 Oe we have Hc 2 200-
2000 Oe. S i n c e t h e e f f e c t i v e i n t e r a c t i o n between c h a i n s I,-, must b e weaker t h e ex- p e r i m e n t a l v a l u e f o r TYf, we can w r i t e :T h a t means t h a t t h e d i s t a n c e f r o m c h a i n t o c h a i n s h o u l d be i a r g e r t h e n r o
=
70 W. The r e a s o n f o r e x i s t a n c e s u c h g a p s w i t h o u t s p i n s a l o n g t h e d i s l o c a t i o n may b e t h e same a s f o r d i s a p p e a r a n c e D- c e n t e r s a f t e r a n n e a l i n g a t T>
700 OC. A s i t was p r o p o s e d i n 1171 it may be some k i n d o f c o r e r e c o n s t r u c t i o n .4 . What i s t h e r e a s o n f o r a s t r o n g i n f l u e n c e o f l i g h t on t h e D-cen- t e r s s p i n - l a t t i c e r e l a x a t i o n t i m e t , o b s e r v e d ? The s i m p l e s t mecha- nism t o which on c a n a t t e m p t t o a t t r i b u t e i t i s a exchange i n t e r - a c t i o n b e t w e e n DDB a n d f r e e c a r r i e r s . Then:
w h e r e TDDBl Tc a r e s p i n t e m p e r a t u r e f o r DDB a n d e l e c t r o n s , n , NDDB a r e c o n c e n t r a t i o n s o f e l e c t r o n s a n d DDB,
tyDDB
a n drqc
a r eo r i g i n a l s p i n - l a t t i c e r e l a x a t i o n t i m e s f o r DDB a n d e l e c t r o n s , U i s e x c h a n g e p r o b a b i l i t y .
T h e r e f o r e
The g e n e r a t i o n r a t e G c a n b e e s t i m a t e d f r o m t h e l i g h t i n t e n s i t y u s e d , a n d tQc z s e c a c c o r d i n g t o ( 1 8 ) . But t o f i t o u r d a t a u s i n g t h i s f o r m u l a we n e e d t h e n v a l u e t o b e by s e v e r a l o r d e r s l a r g e , t h a n i t c a n b e e s t i m a t e d by c o n d u c t i v i t y . The p o s s i b l e way t o remove t h i s d i s c r e p a n c y i s t o t a k e i n t o a c c o u n t t h e d e f o r - m a t i o n p o t e n t i a l i n t h e d i s l o c a t i o n c o r e v i c i n i t y , w h i c h c a n l e a d t o t h e much h i g h e r l o c a l c o n c e n t r a t i o n o f c a r r i e r s .
R e f e r e n c e s
(
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JETP,3,
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71 LEPINE D . , ~ h y s . Rev. B ,5
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( 1 975)
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W O S I N K S I T . , F I G I E L S K I T . , P h y s . S t a t . S o l . (b)
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40
( 1 9 7 9 ) , 1 0 7KAPLAN D . , SOLOMON I . , MOTT N . F . , J . d e P h y s i q u e - L e t t e r s ,
2
( 1 9 7 8 )
,
L - 5 1O S I P J A N Y u . A . , C r y s t a l R e s e a r c h and T e c h n o l o g y ,
16
( 1 9 8 1 ) , 2 4 7 ZOLOTUKHIN M.N., KVEDER V . V . , O S I P J A N Y u . A . , S O V . P h y s .-
J E T P I 5 4 ( 1 9 8 1 ) , 1 6 0-
E L L I O T R . J . 1 P h y s . R e v . ( 1 9 5 4 ) I 2 6 6
