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SPIN EFFECTS IN ELECTRON TRANSITIONS VIA DISLOCATION STATES IN SILICON
T. Figielski
To cite this version:
T. Figielski. SPIN EFFECTS IN ELECTRON TRANSITIONS VIA DISLOCATION STATES IN SILICON. Journal de Physique Colloques, 1979, 40 (C6), pp.C6-95-C6-100.
�10.1051/jphyscol:1979620�. �jpa-00219036�
JOURNAL DE PHYSIQUE Colloque CF, suppl6ment au n06, t a e 40, j u i n 1979, page CF-95
S P I N EFFECTS I N ELECTRON T R A N S I T I O N S V I A D I S L O C A T I O N STATES I N S I L I C O N T. F i g i e l s k i
I n s t i t u t e o f Physics, Polish Academy o f Sciences, A Z . ~ o t n i k h u 32/46, 02-668 Varsaw, Poland
Resume.- Nous d i s c u t o n s , dans ce p a p i e r , l e s r e s u l t a t s experimentaux concernant l a recombinaison d@- pendante du s p i n des p o r t e u r s de charge a i n s i que de l e u r g e n e r a t i o n s u r l e s d i s l o c a t i o n s dans l e s i l i c i u m . Nous proposons un modele t h e o r i q u e t e n a n t compte d ' u n e i n t e r a c t i o n d'echange e n t r e e l e c - t r o n s pendants v o i s i n s . Ce modele t i e n t compte d ' u n e p a r t de l a grande a m p l i t u d e de c e t e f f e t e t d ' a u t r e p a r t de l a v a r i a t i o n en f o n c t i o n de l a temperature.
A b s t r a c t . - E x p e r i m e n t a l r e s u l t s c o n c e r n i n g spin-dependent r e c o m b i n a t i o n and g e n e r a t i o n o f charge c a r - r i e r s a t d i s l o c a t i o n s i n s i l i c o n a r e discussed. A t h e o r e t i c a l model t a k i n g i n t o a c c o u n t an exchange i n t e r a c t i o n between n e i g h b o u r i n g d a n g l i n g e l e c t r o n s i s c o n s i d e r e d . I t i s shown t h a t t h i s model can account f o r b o t h t h e l a r g e mangitude o f t h e e f f e c t and i t s temperature v a r i a t i o n .
Spin-dependent e f f e c t s o f f e r a p o w e r f u l t o o l f o r s t u d y i n g t h e n a t u r e o f d i s l o c a t i o n e l e c t r o n s t a - t e s i n semiconductors. I n t h i s a r t i c l e t h e c u r r e n t s t a t u s o f a knowledge on spin-dependent e l e c t r o n t r a n s i t i o n s ( r e c o m b i n a t i o n and g e n e r a t i o n ) o c c u r r i n g v i a d i s l o c a t i o n s i n s i l i c o n i s surveyed. The p l a n o f t h i s paper i s t h e f o l l o w i n g . A b r i e f h i s t o r y o f t h e development o f t h i s r e s e a r c h and i t s methods i s sketched f i r s t , t h e n t h e e x p e r i m e n t a l f a c t s c o l l e c t e d h i t h e r t o a r e p r e s e n t e d . Next a t h e o r e t i c a l model i s proposed a s s u r i n g t h e b e s t e x p l a n a t i o n o f t h e expe- r i m e n t a l r e s u l t s . The a r t i c l e i s c l o s e d w i t h some g e n e r a l comments upon t h e s u b j e c t under c o n s i d e r a - t i o n .
1. Development o f r e s e a r c h . - Spin-dependent p h o t o - c o n d u c t i v i t y ( S D ~ ) was observed f i r s t by L e p i n e and P r e j e a n /1/ i n s i l i c o n c o n t a i n i n g r e c o m b i n a t i o n cen- t r e s o f unknown o r i g i n . An a t t e m p t t o a t t r i b u t e t h o s e c e n t r e s t o s u r f a c e s t a t e s was n e x t made by L e p i n e /2/ who has t r i e d a l s o t o a c c o u n t f o r t h e u n e x p e c t e d l y l a r g e magnitude o f t h i s e f f e c t .
A f t e r t h e d i s c o v e r y by Alexander e t a1
.
/3/o f an EPR s i g n a l o r i g i n a t i n g f r o m d i s l o c a t i o n s i n S i i t seemed r e a s o n a b l e t o l o o k f o r spin-dependent r e - c o m b i n a t i o n a t d i s l o c a t i o n s . ~ o s i h s k i /4/ was t h e f i r s t who c o n s c i o u s l y searched f o r t h a t e f f e c t i n p l a s t i c a l l y deformed s i l i c o n and succeeded i n f i n - d i n g i t . He has c o l l e c t e d a g r e a t amount o f i n f o r - m a t i o n c o n c e r n i n g t h i s phenomenon /5-8/ and has proposed a r e a s o n a b l e e x p l a n a t i o n f o r i t . Indepen- d e n t l y G r a z h u l i s e t a l . /9/ observed t h e s p i n - dependent e f f e c t i n d i s l o c a t e d S i a t h e l i u m tempe- r a t u r e s b u t t h e y a t t r i b u t e d i t t o a change i n c a r r i e r m o b i l i t y . T h i s i n t e r p r e t a t i o n was l a t e r changed i n
f a v o u r o f t h e SDP e f f e c t / l o / . Makosa /11/ has exa- mined how does SDP s i g n a l v a r i e s under d i f f e r e n t h e a t t r e a t m e n t c o n d i t i o n s . ~ o s i h s k i and S z k i e l k o /12/ have i n v e s t i g a t e d a l s o t h e i n f l u e n c e o f e l e c t r o n i r r a d i a t i o n on SDP i n p l a s t i c a l l y deformed S i . The experiments done by Neubert and h i s coworkers /13/
have b r o u g h t some new r e s u l t s a l t h o u g h t h e p o i n t o f view o f t h e s e a u t h o r s h a r d l y can be accepted. Recent- l y t h e complementary e f f e c t o f spin-dependent gene- r a t i o n a t d i s l o c a t i o n s was f o u n d b y S z k i e l k o /14/.
2. E x p e r i m e n t a l methods.- The most c o n v e n i e n t method o f s t u d y i n g SDP i s t o f o l l o w t h e d i f f e r e n c e between t h e p h o t o c o n d u c t i v i t y observed under EPR c o n d i t i o n s and a p a r t f r o m t h e resonance, i . e . a t two d i f f e r e n t s p i n p o l a r i z a t i o n s o f t h e e l e c t r o n system. Because t h e e f f e c t i s r e l a t i v e l y s m a l l t h e m o d u l a t i o n t e c h n i - que has t o be used.
The most common f o r m o f m o d u l a t i o n employed t o s t u d y o f SDP i s t h e m o d u l a t i o n o f t h e microwave power ( b a s i c method). U n f o r t u n a t e l y i t a l l o w s us o n l y t o r e c o r d t h e i n t e g r a l f o r m o f t h e s i g n a l . I n o r d e r t o r e v e a l t h e s t r u c t u r e o f t h e r e s o n a n t l i n e i t i s much b e t t e r t o r e c o r d d i r e c t l y t h e d e r i v a t i v e o f t h e s i - g n a l . The m o d u l a t i o n o f t h e sweeping magnetic f i e l d , as i n t h e c o n v e n t i o n a l EPR t e c h n i q u e , u s u a l l y cannot be a p p l i e d h e r e because o f t h e a p p e a r i n g o f a s t r o n g magnetoresistance s i g n a l
.
O n l y recent1.y Neubert /13/was succeeded i n o b t a i n i n g t h e SDP spectrum u s i n g v e r y s l i g h t magnetic f i e l d m o d u l a t i o n . A l t e r n a t i v e l y t h e f r e q u e n c y m o d u l a t i o n can be employed w h i c h p r o - duce no m a g n e t o r e s i s t a n c e s i g n a l / 5 / . Another p o s s i - b i l i t y i s t o a p p l y a c o n t a c t l e s s method i n which t h e change i n Q - f a c t o r o f t h e c a v i t y c o n t a i n i n g t h e sam- p l e i s observed under resonance c o n d i t i o n s / 5 / . The
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979620
C6-96 JCURNAL DE PHYSIQUE
main f e a t u r e s o f v a r i o u s methods a r e surveyed i n t a b l e I.
Table I
The experimental set-up o f the basic method i s shown i n f i g u r e 1. The sample i s placed i n t o a micro- wave c a v i t y and i s subjected t o steady i l l u m i n a t i o n i n c r e a s i n g i t s c o n d u c t i v i t y by AU. When sweeping t h e magnetic f i e l d over the EPR r e g i o n a resonant decrea- se i n p h o t o c o n d u c t i v i t y 6 0 i s observed ( F i g . 2 ) . The r a t i o do/ho i s c a l l e d t h e r e l a t i v e SDP s i g n a l .
A serious l i m i t a t i o n o f the basic SDP t e c h n i - que i s the appearance o f an off-resonance background s i g n a l . I t appears simultaneously w i t h t h e resonant one a t t h e frequency of microwave power modulation.
The amplitude o f t h e background s i g n a l increases w i t h l o w e r i n g temperature almost p r o p o r t i o n a l l y t o ,the square o f t h e c a r r i e r m o b i l i t y ( F i g . 3 ) . The
o r i g i n o f t h i s d i s t u r b i n g e f f e c t has been explained
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F i g . 1 : Sample c o n f i g u r a t i o n under experimental con- d i t i o n s .
WHAT IS MEASURED
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F i g . 2 : SDP
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resonant decrease o f p h o t o c o n d u c t i v i t y under EPR c o n d i t i o n s .3. Experimental r e s u l t s . - The SDP s i g n a l appears i n p l a s t i c a l l y deformed s i l i c o n samples ( b o t h n and p type) o n l y whereas i t i s n o t observed i n t h e samples subjected t o t h e same heat treatment as t h e previous ones b u t n o t deformed. Contrary t o EPR r e s u l t s /16/
t h e SDP s i g n a l i s almost independent o f t h e tempera- t u r e o f sample deformation w i t h i n t h e range 740
-
920°C ( f l o a t i n g zone s i l i c o n ) /11/ and i s a l s o obser- ved on t h e samples deformed a t 700°C and 1000°C /13/.
The SDP s i g n a l was measured w i t h i n the tempe- r a t u r e range from 350 K down t o 80 K /4,6,7,8/ and a l s o a t helium temperatures /9/. I t d i s p l a y s a h a l f - w i d t h o f l i n e o f about 6 Oe independently o f t h e temperature. The g - f a c t o r o f the l i n e i s 2.004 w i t h IN
p-n JUNCTION
-
by F i g i e l s k i and Kurek / 1 5 / as being due t o t h e no e s s e n t i a l anisotropy. This value corresponds t o ,,detection,, of the magnetic vector of the microwave the p o s i t i o n o f t h e " c e n t r a l
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1 ines observed i n the b y t h e semiconductor sample. Due t o maqnetoresis- EPR spectrum o f deformed s i l i c o n /17, 18/. No p e r i - tance e f f e c t t h e sample behave as a magnetical ly pheral l i n e s l i k e those obseri/ed by ~ c h r n i d t e t a l .l i n e a r device.
/ l a /
have been revealed i n t h e SDP spectrum d e s p i t esome e f f o r t s made i n o r d e r t o f i n d them.
T. F i g i e l s k i
F i g . 3 : Temperature dependence o f the background s i g n a l /6/.
F i g . 4 : R e l a t i v e p b o t o c o n d u c t i v i t y Au/u and r e l a - t i v e resonant decrease o f p h o t o c o n d u c t i v i t y 6u/o vs.
temperature / 7 / .
Some p r o p e r t i e s o f t h e SDP s i g n a l t o g e t h e r w i t h those o f the usual p h o t o c o n d u c t i v i t y are shown i n f i g u r e s 4 and 5. I t may be concluded t h a t SDP behaves q u i t e s i m i 1 a r l y t o t h e off-resonance photoconducti- v i t y which i n t u r n can be described by t h e b a r r i e r model o f recombination a t d i s l o c a t i o n s /19/. So w i t h i n the whole temperature range o f experiments
the recombination r a t e i s l i m i t e d by the c a p t u r i n g o f m a j o r i t y charge c a r r i e r s . M i n o r i t y c a r r i e r s are trapped i n the d i s l o c a t i o n s and p r a c t i c a l l y do n o t c o n t r i b u t e t o p h o t o c o n d u c t i v i t y .
light intensity (orb. units)
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F i g . 5 : R e l a t i v e p h o t o c o n d u c t i v i t y A d a and r e l a t i v e resonant decrease o f p h o t o c o n d u c t i v i t y 6o/a vs.
i l l u m i n a t i o n l e v e l / 8 / .
Most o f t h e measurements o f SDP has.been per- formed on samples deformed by bending which c o n t a i - ned no more than l o 7 d i s l o c a t i o n s per cm2. This den- s i t y i s u s u a l l y t o o small t o be detected i n standard EPR measurements. Therefore a s p e c i a l e f f o r t wasmade i n o u r l a b o r a t o r y by ~ o s i Aski t o observe b o t h EPR and SDP s i g n a l s on the same samples. This t a s k has been s u c c e s s f u l l y c a r r i e d o u t w i t h t h e h e l p o f t h e Cologne g r o u p o f p r o f . Alexander who s u p p l i e d us w i t h h i g h l y d i s l o c a t e d samples deformed by compression.
Using t h e methods a l l o w i n g one t o r e c o r d t h e d e r i v a t i v e o f t h e s i g n a l one c o u l d r e v e a l a c e r t a i n s t r u c t u r e o f SDP l i n e , s i m i l a r as t h a t observed i n EPR. Neubert e t a1 ./13/ were able t o decompose t h e i r s i g n a l s by a computer program i n t o t h r e e l i n e s w i t h t h e f o l l o w i n g g - f a c t o r s : 2.001, 2.004 and 2.009.
The amplitude o f c e n t r a l l i n e was always t h e s t r o n - gest, b u t the r a t i o o f the t h r e e components v a r i e d independently from each o t h e r f o r d i f f e r e n t samples.
As p o i n t e d o u t by those authors these resonance li- nes, observed a l s o i n EPR, do not.seem t o be sensi- t i v e t o c r y s t a l l o g r a p h i c o r i e n t a t i o n and have r a t h e r a u n i v e r s a l character.
The e f f e c t o f a f t e r - d e f o r m a t i o n annealing on SDP was s t u d i e d by Makosa /11/. Although these i n - v e s t i g a t i o n s a r e n o t completed y e t some o f h i s r e - s u l t s have t o be mentioned here. Deformed samples were subjected t o subsequent c y c l e s o f heat t r e a t - ment a t 800°C i n n i t r o g e n gas. The s i g n a l amplitude was recorded a f t e r each h a l f - h o u r c y c l e w i t h no e s s e n t i a l change i n i t s amplitude. However, a f t e r several h e a t i n g c y c l e s a new l i n e ( g = 2.009 ?) w i t h
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o p p o s i t e s i g n t o t h e main o r i g i n a l l i n e appears. T h i s l i n e wasobserved o n l y below t h e temperature o f 170 K.
No s a t i s f a c t o r y e x p l a n a t i o n o f t h i s e f f e c t can be o f f e r e d a t t h e moment.
The r e s u l t s o f 10 MeV e l e c t r o n i r r a d i a t i o n o f deformed s i l i c o n /12/ seem t o i n d i c a t e t h e o p e n i n g o f a c o m p e t i t i v e channel o f s p i n - i n d e p e n d e n t recom- b i n a t i o n .
The most s t r i k i n g f e a t u r e o f t h e normal SDP s i g n a l i s i t s unexpected l a r g e a m p l i t u d e . I t i s con- v e n i e n t t o e x t r a p o l a t e t h e magnitude o f t h e observed s i g n a l t o i n f i n i t e microwave power i . e . t o t h e case o f f u l l r a n d o m i z a t i o n o f t h e s p i n system. T h i s e x t r a - p o l a t e d s i g n a l i s about two o r d e r s o f magnitude l a r - g e r t h a n t h e maximum s i g n a l p r e d i c t e d by a s i m p l e model f o r n o n i n t e r a c t i n g paramagnetic r e c o m b i n a t i o n c e n t r e s / 2 / . That i s t h e most i m p o r t a n t r e s u l t which needs an e x p l a n a t i o n f i r s t o f a l l .
R e c e n t l y S z k i e l k o /14/ d i s c o v e r e d t h a t a r e s o - n a n t i n c r e a s e i n t h e r e v e r s e c u r r e n t f l o w i n g t h r o u g h p-n j u n c t i o n made on deformed s i l i c o n appears under EPR c o n d i t i o n s ( F i g . 6 ) . As f o l l o w s f r o m an a n a l y s i s o f t h e shape of t h e I - V c h a r a c t e r i s t i c s and i n accor- dance w i t h commonly accepted o p i n i o n t h e c u r r e n t i n t h a t case i s m a i n l y due t o c a r r i e r s generated i n t h e space charge r e g i o n o f t h e p-n j u n c t i o n . Thus t h e r e i s a new e f f e c t : t h e spin-dependent g e n e r a t i o n a t d i s l o c a t i o n s .
e RESONANT SIGNAL .2=105 a .- REVERSE CURRENT
BIAS VOLTAGE (VOLTS)
F i g . 6 : R e l a t i v e r e s o n a n t i n c r e a s e i n r e v e r s e c u r - r e n t and r e v e r s e c u r r e n t f l o w i n g t h r o u g h p-n j u n c - t i o n vs.' b i a s v o l t a g e /14/.
4,Theoretical model.- An i m p o r t a n t c o n c l u s i o n may be drawn f r o m t h e ' d e t a i l e d correspondence between t h e SDP and p h o t o c o n d u c t i v i t y observed i n e x p e r i m e n t s : r e c o m b i n a t i o n i n deformed samples i s f u l l y c o n t r o l l e d by paramagnetic c e n t r e s c r e a t e d ' b y p l a s t i c deforma- t i o n . Presumably t h e s e c e n t r e s a r e d a n g l i n g bonds i n d i s l o c a t i o n core. A p o s s i b l e c o n t r i b u t i o n o f p o i n t d e f e c t s , i n t r o d u c e d i n t o t h e c r y s t a l d u r i n g i t s de-
f o r m a t i o n , t o SDP e f f e c t has t o be r a t h e r excluded i n t h e l i g h t o f r e c e n t r e s u l t s o b t a i n e d on t h e sam- p l e s s u b j e c t e d t o a n n e a l i n g o r e l e c t r o n bombardment.
The d e t e r m i n a t i o n b o t h o f t h e a t o m i c and t h e e l e c t r o n i c s t r u c t u r e o f d i s l o c a t i o n c o r e s i s a com- p l i c a t e d problem which i s n o t s a t i s f a c t o r i l y s o l v e d t i l l t o d a y /19/. Thus t h e o n l y way o f d i s c u s s i n g t h e SDP i s t o do t h i s as g e n e r a l l y as p o s s i b l e w i t h o u t r e f e r r i n g t o any p a r t i c u l a r s t r u c t u r e o f d i s -
l o c a t i o n e l e c t r o n s t a t e s . I n p r i n c i p l e one can d i s - t i n g u i s h between t h r e e p a r t i c u l a r cases which a r e s p e c i f i e d below a c c o r d i n g t o a d e c r e a s i n g o v e r l a p o f t h e a d j a c e n t d a n g l i n g e l e c t r o n o r b i t a l s : t h e h a l f f i l l e d energy band, t h e two band Mott-Hubbard system, and i s o l a t e d c e n t r e s h a v i n g t h r e e charge s t a t e s and d e s c r i b e d b y two d i s c r e t e energy l e v e l s . F o r t h e sake o f convenience t h e f i r s t case w i l l be adopted f o r t h e d i s c u s s i o n o f SDP a l t h o u g h t h e two o t h e r s ' l e a d t o e s s e n t i a l l y t h e same r e s u l t s .
I t i s assumed t h a t t h e s p i n o f t h e r e c o m b i n i n g charge c a r r i e r i s conserved i n t h e process o f i t s c a p t u r e b y a d i s l o c a t i o n . Thus a c c o r d i n g t o t h e P a u l i e x c l u s i o n p r i n c i p l e t h o s e e l e c t r o n t r a n s i t i o n s w h i c h a r e shown i n f i g u r e 7 a r e t h e o n l y ones p o s s i b l e . The f i g u r e i s sketched f o r n - t y p e m a t e r i a l when one may n e g l e c t t h e t r a n s i t i o n s o f h o l e s which a r e b e i n g t r a p p e d by t h e d i s l o c a t i o n s . I n t h e s t e a d y s t a t e t h e r e i s assumed t o be an e q u i l i b r i u m i n s i d e each o f t h e e l e c t r o n s p i n systems.
F o r a h a l f f i l l e d energy band i n t e r m e d i a t i n g i n t h e r e c o m b i n a t i o n p r o c e s s one o b t a i n s f r o m s i m p l e s t a t i s t i c s t h e f o l l o w i n g approximate e x p r e s s i o n f o r t h e n e t c a p t u r e r a t e o f an e l e c t r o n
R = Ro ( 1
-
pP), ( 1 )where Ro i s t h e c a p t u r e r a t e f o r z e r o s p i n p o l a r i z a - t i o n , P and p a r e t h e degrees o f s p i n p o l a r i z a t i o n o f d i s l o c a t i o n e l e c t r o n s and o f c o n d u c t i o n e l e c t r o n s r e s p e c t i v e l y .
Randomization o f ( a t l e a s t ) one o f t h e two s p i n systems causes a change i n R
GR = RopP, ( 2 )
and t h i s i m p l i e s t h e r e l a t i v e change o f s t e a d y s t a t e p h o t o c o n d u c t i v i t y equal t o
60 -
- - -
A 0 pP ( 3 )
J u s t t h e same c o n c l u s i o n r e s u l t s f r o m L e p i n e s model / 2 / f o r r e c o m b i n a t i o n o c c u r r i n g t h r o u g h an i n t e r m e - d i a t e s i n g l e t s t a t e o f a c e n t r e .
The f o r m u l a ( 3 ) i s v a l i d a l s o f o r t h e case o f t h e b a r r i e r model o f r e c o m b i n a t i o n . T h i s f o r m u l a p r e d i c t s f o r t h e systems o f i s o l a t e d s p i n s an e f f e c t w h i c h i s a t l e a s t two o r d e r s o f magnitude l o w e r t h a n t h a t
T. Figielski C6-99
observed i n experiments. I t has been proposed by w i t h r e s p e c t t o t h e magnetic f i e l d , one o b t a i n s t h e Wosihski /6/ t h a t an exchange i n t e r a c t i o n between spin p o l a r i z a t i o n P o f t h e system. The expression l o c a l i z e d spins on d i s l o c a t i o n s can account f o r t h e f o r P / 7 / i s t o o complex t o be discussed a n a l y t i c a l l y .
l a r g e value o f SDP. Hence i t i s presented here i n the form o f a diagram
f o r a p a r t i c u l a r value o f 8 = J/2kT and d i f f e r e n t numbers o f coupled spins i n a chain, m ( F i g . 9 ) .
F i g . 8 : L i n e a r c h a i n of spins along d i s l o c a t i o n s .
F i g . 7 : D e n s i t i e s o f s t a t e s under a p p l i e d magnetic f i e l d and p o s s i b l e e l e c t r o n t r a n s i t i o n s .
As a t e n t a t i v e model t h e case o f t h e 6O0-dis-
l o c a t i o n o f t h e s h u f f l e s e t i s considered. The dan- sp~B/kT
-
g l i n g e l e c t r o n o r b i t a l s a r e spaced along t h a t d i s l o - Fig. : Polarization degree of a linear chai,n of c a t i o n a t distances o f 3.82
a
and they dangle perpen- exchange coupled spins v s - reduced magnetic f i e l d d i c u l a r l y t o t h e d i s l o c a t i o n a x i s . I t i s assumed i n /13/.c a l c u l a t i o n s t h a t those o r b i t a l s a r e described by atomic sp3 hybrids. I n t h a t approximation the exchan- ge i n t e g r a l J between two neighbouring s t a t e s has been computed by ~ o s i h s k i /6/. He has obtained a p o s i t i v e value o f J = 85 meV. This c a l c u l a t i o n may seem t o be n o t very r e a l i s t i c . However i t shows t h a t ferromagnetic type i n t e r a c t i o n between l o c a l i z e d spins on d i s l o c a t i o n may e x i s t and be s u f f i c i e n t l y s t r o n g t o enhance e s s e n t i a l l y magnetic p o l a r i z a t i o n o f the system.
The d i s l o c a t i o n i s t r e a t e d here as l i n e a r c h a i n of p e r i o d i c a l l y arranged S=7 1 spins. The cou- p l i n g energy between t h e n e a r e s t neighbours can be approxiniated by the I s i n g form
-
~ J S : S ~ + ~ . Jogs, kinks, i n ~ p u r i t i e s o r e l e c t r o n s and holes accepted a t the d i s l o c a t i o n break up the c h a i n i n t o separate segments (Fig. 8 ) .With pure I s i n g i n t e r a c t i o n the p a r t i t i o n f u n c t i o n of a f i n i t e c h a i n o f s p i n s i n a magnetic f i e l d may be c a l c u l a t e d e x a c t l y . T h i s has been done by Opechowski and Bryan whose t h e o r y i s adopted here f o r e x p l a i n i n g SDP i n deformed c r y s t a l s . By d i f f e r e n t i a t i n g t h e l o - g a r i t h m o f t h e p a r t i t i o n f u n c t i o n taken from /20/
Using equation ( 3 ) c o r r e c t e d f o r t h e a c t u a l microwa- ve power, and P c a l c u l a t e d according t o the theory o f Opechowski and Bryan w i t h the value o f J = 85 meV, one o b t a i n s the t h e o r e t i c a l dependence o f 6o/Ao on temperature. The o n l y f r e e parameter i s then t h e number o f exchange coupled spins i n a chain. The b e s t f i t between t h e theory and experiment i s obtained p u t t i n g m = 20 which i s a reasonable value. The r e - s u l t o f t h a t f i t t i n g i s shown i n f i g u r e 10.
Recently a q u i t e new t h e o r e t i c a l approach t o t h e problem o f spin-dependent e f f e c t s has been pro- posed by Kaplan e t a l . /21/. I t does n o t account, however, f o r t h e temperature v a r i a t i o n o f SDP-signal amp1 i tude observed i n deformed samples.
5. Remarks.- I t i s very i m p o r t a n t f o r t h e conception o f d i s l o c a t i o n recombination s t a t e s i n semi conductors t o decide i f t h e model discussed here i s c o r r e c t o r n o t . Thus some c r u c i a l experiments have t o be done.
One o f them may c o n s i s t i n f o l l o w i n g t h e v a r i a t i o n o f t h e SDP s i g n a l w i t h h y d r o s t a t i c pressure. The exchange i n t e r a c t i o n as being s t r o n g l y s e n s i t i v e t o t h e distances between neighbouring spins would be v a r i e d much under pressure.
JOURNAL DE PHYSIQUE
F i g . 10 : R e l a t i v e spin-dependent p h o t o c o n d u c t i v i t y vs. r e c i p r o c a l temperature. S o l i d l i n e : experiment, d o t t e d 1 in e : theory /7/.
A d r a s t i c d i f f e r e n c e between t h e dependences o f t h e SDP- and EPR-signals on deformation tempera- t u r e needs some comnents. I n p r i n c i p l e t h e r e i s no discrepancy i n t h e r e s u l t s o f these two methods. The r e l a t i v e SDP s i g n a l does n o t depend on t h e number o f paramagnetic centres, as f a r as they a r e the o n l y centres o f recombination, whereas the EPR s i g n a l does depend on i t .
The e f f e c t o f spin-dependent generation can- riot be explainecl i n a s i m i l a r way as spin-dependent r e c o r ~ i o i n a t i o r ~ and nerds a more s o p h i s t i c a t e d theory.
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