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Submitted on 1 Jan 1983
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CHARACTERIZATION OF STRESS FIELD AND ELECTRIC ACTIVITY OF DISLOCATIONS IN
SEMICONDUCTORS
A. Haydar, A. Coret
To cite this version:
A. Haydar, A. Coret. CHARACTERIZATION OF STRESS FIELD AND ELECTRIC ACTIVITY
OF DISLOCATIONS IN SEMICONDUCTORS. Journal de Physique Colloques, 1983, 44 (C4), pp.C4-
169-C4-181. �10.1051/jphyscol:1983421�. �jpa-00223040�
JOURNAL DE PHYSIQUE
Colloque C4, supplément au n°9, Tome 44, septembre 1983 page C4-169
CHARACTERIZATION OF STRESS FIELD AND ELECTRIC ACTIVITY OF DISLOCATIONS IN SEMICONDUCTORS
A. Haydar and A. Coret
Ldboratoire de Speotrosoopie et d'Optique du Corps Solide (assooig au C.N.R.S.
n°2S2), 5, rue de I'Universtte, 67000 Strasbourg, France
Résumé - Les mesures optiques et photoélectriques peuvent être utilisées pour caractériser les dislocations dans les semiconducteurs. Nous avons ainsi interprété la biréfringence et la photoconductivité excitonique de cristaux de CU2O : les raaxima anisotropes de photocourant sont dus à la dissociation des excitons par des champs électriques internes provenant d'arrangements de dislocations du type empilement.
Le rôle des dislocations peut être envisagé de la même manière dans d'autres composés semiconducteurs : CuCl et CuBr en particulier.
Abstract - Optical and photoelectrical measurements can be used to characte- rize dislocations in semiconductors. Birefringence and excitonic photocon- ductivity in CU2O crystals are interpreted : anisotropic photocurrent maxima are due to dissociation of excitons by internal electric fields resulting from specific arrangements of dislocations of pile-up type. The role of dislocations can be interpreted in the same way in other semiconducting compounds : CuCl and CuBr in particular.
INTRODUCTION
It is well established that electronic energy levels in crystals depend on the nature of atoms in the crystal and its symmetry. Dislocations, as linear struc- ture defects, can then affect local intrinsic electronic states in semiconductors by their stress or electric fields which change the symmetry of the crystal.
Excitons1, as intrinsic elementary excitation of non metallic solids, are very sensitive to imperfections or impurities in the crystal. They are affected by perturbations such as electric, stress (internal or external) and magnetic fields.
The study of external perturbation effects on excitons is necessary to understand the nature of internal ones. These effects are studied in many materials [CU2O, CuX
(X = Cl, Br, I ) , II-VI, III-V, Si, Ge . . .] l.
The two particle nature (electron and hole) of excitons lead to different properties from material to another. Excitons, as neutral quasi-particles, cannot contribute, at low excitation densities, to photoconductivity at low temperature
(4 K) without interaction with imperfections or impurities in the crystal. The photoconductivity measurements constitute then a very sensitive tool to study the effects of dislocations on excitons2. Such effects were also observed by light scattering, reflexion and luminescence spectra of excitons3'1*. The comparison with the effects of external perturbation is very useful to characterize dislocations.
On the other hand, elastobirefringence revealed to be a good technique to characterize stress field of slip-bands5'6 or individual dislocations in semicon- ductors . Dark-field-illumination based on light scattering was also used to visua- lize dislocations . In contrast with electron microscopy technique which is necessary to study detailed structure of dislocations, these optical methods are nondestructive and permit real structure investigations.
More complete informations are available by associating birefringence and excitonic photoconductivity measurements. We discuss here the results obtained in
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983421
C4-170 JOURNAL DE PHYSIQUE
Cu20 c r y s t a l s . W e p r e s e n t t h e n e x c i t o n i c p h o t o c o n d u c t i v i t y s p e c t r a i n CuCl, C u m w h i c h show s i m i l a r b e h a v i o u r as i n Cu20.
I . BIREFRINGENCE AND STRUCTURAL DEFECTS I N C u 2 0 - CRYSTALS
R e c e n t l y , we h a v e s t u d i e d t h e b i r e f r i n g e n c e i n d i f f e r e n t k i n d s o f Cu20 c r y s t a l s G . W e s u m m a r i z e h e r e t h e p r i n c i p a l r e s u l t s .
I n a s grown c r y s t a l s , b i r e f r i n g e n t r e g i o n s a r e g e n e r a l l y l o c a l i z e d n e a r p r e c i p i t a t i o n s , c a l l e d " t e r a t o i d e s " . T h e s e b i r e f r i n g e n t r e g i o n s d e p e n d o n - t h e d i r e c t i o n o f o b s e r v a t i o n : t h e y a r e c r o s s s h a p e d i n [loo] a n d [010] when _001] i s the d i r e c t i o n o f o b s e r v a t i o n a s . s h o w n i n f i g u r e 1. P r i n c i p a l a x i s o f t h e c r y s t a l i n t h e s e b i r e f r i n g e n t r e g i o n s a r e L100] a n d 1010]. E t c h p i t s r e v e a l p a r t i c u l a r a r r a n - g e m e n t s o f d i s l o c a t i o n s " p i l e - u p s " i n b i r e f r i n g e n t r e g i o n s a s shown i n f i g u r e 2 .
F i g u r e 1 . C r o s s s h a p e d b i r e f r i n g e n t r e g i o n s on a n as-grown c r y s t a l o f Cu2O.
F i g u r e 2 . ~ t c h p i t s on a [OOI] f a c e of: a n as-qrown c r y s t a l o f cu O . 2
T h e s e " p i l e - u p s " a r e f o r m e d i n c r y s t a l l o g r a p h i c p l a n s o f t h e t y p e ( 1 0 0 ) d u r i n g c r y s t a l s g r o w t h . The same b i r e f r i n g e n c e was a l s o o b s e r v e d i n p i l e - u p s r e g i o n s i n the a b s e n c e o f " t e r a t o i d e s " .
U s i n g a q u a r t e r wave p l a t e 6 , we h a v e shown t h a t the s l o w p r i n c i p a l a x i s o f t h e c r y s t a l i n b i r e f r i n g e n t r e g i o n s a r e p a r a l l e l t o " p i l e - u p s " i n t h e s e r e g i o n s i . e . p a r a l l e l t o B u r g e r s v e c t o r o f d i s l o c a t i o n s .
On t h e o t h e r h a n d , p l a s t i c d e f o r m a t i o n a n d e l e c t r o n m i c r o s c o p y i n v e s t i g a - t i o n ~ ~ ~ ' ~ show t h a t t h e m a j o r i t y o f d i s l o c a t i o n s a r e o f e d g e t y p e w i t h B u r g e r s v e c t o r [ l g o ] . Two e q u i v a l e n t g l i d e s y s t e m s ( 1 0 0 ) [010] a n d ( 0 1 0 ) [ l o o ] a r e a c t i v e i n p l a s t i c d e f o r m a t i o n a t h i g h t e m p e r a t u r e (% 700°C) when t h e a p p l i e d s t r e s s i s i n
[110] d i r e c t i o n . I n s u c h d e f o r m e d c r y s t a l s , s i m i l a r b i r e f r i n g e n c e w i t h c r o s s s h a p e d s l i p r e g i o n s i n [ l o o ] a n d [010] d i r e c t i o n s i s o b s e r v e d ( s e e f i g u r e 3 ) . U s i n g a q u a r t e r wave p l a t e , w e a l s o show t h a t t h e s l o w p r i n c i p a l a x i s o f t h e c r y s t a l i n b i r e f r i n g e n t r e g i o n s a r e p e r p e n d i c u l a r t o cross b a r s . I t was c o n c l u d e d t h a t " p i l e -
u p s " a r e formed i n b i r e f r i n g e n t r e g i o n s by p l a s t i c d e f o r m a t i o n . T h e s e " p i l e - u p s "
a r e p e r p e n d i c u l a r t o c r o s s b a r s a s i l l u s t r a t e d s c h e m a t i c a l l y i n f i g u r e 8 .
d
l
Applied stress during plastic deFormat~on<I 10)
t
F i g u r e 3. B i r e f r i n g e n c e o f a d e f o r m e d F i g u r e 4 . A r r a n g e m e n t o f d i s l o c a t i o n i n c r y s t a l o f Cu20 b y a n u n i a x i a l s t r e s s c r o s s b a r r e g i o n s .
a l o n g [110] d i r e c t i o n .
11. EXCITONS I N Cu70 CRYSTAL -
2up;ous o x i d e c r y s t a l l i z e s i n c u b i c s y s t e m w i t h non s y m o r p h i c symmetry g r o u p 0
.
I n the v i s i b l e s p e c t r u m , a l l o w e d a n d f o r b i d d e n e x c i t o n i c t r a n s i t i o n s e x i s t . h ~ h e y a r e known a s y e l l o w , g r e e n , b l u e a n d v i o l e t s e r i e s r e f e r e d t o t h e r e g i o n o f v i s i b l e s p e c t r u m w h e r e t h e y t a k e p l a c e 1 7 .The symmetry p r o p e r t i e s o f p o s s i b l e o p t i c a l t r a n s i t i o n w e r e s t u d i e d i n s u c h
C4-172 JOURNAL
DE
PHYSIQUEc r y s t a l 1 3 1 1 4 . The f i r s t e x c i t o n i c s t a t e i n Cu20 c r y s t a l , c a l l e d (ISJ) corresponds t o an o p t i c a l quadrupolar t r a n s i t i o n a t 6098i. Experimental s t u d i e s l Q show t h a t i t h a s t h e symmetry
~f
which i s t h r e e f o l d d e g e n e r a t e . Because of t h e quadrupolar n a t u r e , t h e corresponding o p t i c a l a b s o r p t i o n depends on t h e d i r e c t i o n and p o l a r i z a - t i o n of l i g h t w i t h r e s p e c t t o c r y s t a l l o g r a p h i c d i r e c t i o n s :- + q / / Cd : i s o t r o p i c a b s o r p t i o n - + q / / C, : i s o t r o p i c a b s o r p t i o n
.I
- + q // C2 : a n i s o t r o p i c a b s o r p t i o n
I
/ / C4 t h e a b s o r p t i o n t a k e p l a c e .\ 2
// C 2 no a b s o r p t i o n . + + -where q and e is t h e wave v e c t o r and p o l a r i z a t i o n of l i g h t r e s p e c t i v e l y .
We choose t o s t u d y t h e p h o t o c o n d u c t i v i t y corresponding t o t h i s e x c i t o n i c t r a n s i t i o n because o f i t s low a b s o r p t i o n c o e f f i c i e n t (2. 1 cm-l) and h i g h binding energy of t h e corresponding q u a s i - p a r t i c l e (?. 0,14 eV). I t f o l l o w s t h a t thermal i o n i z a t i o n a t low temperature ( 4 K ) and s u r f a c e e f f e c t can be n e g l e c t e d .
On t h e o t h e r hand, t h e e f f e c t s of e x t e r n a l p e r t u r b a t i o n s ( e l e ~ t r i c ~ l - ~ ~ and s t r e s s l 4 r 2 4 - 2 7 ) on t h e (ISJ) e x c i t o n i c t r a n s i t i o n were a l r e a d y s t u d i e d .
When t h e c r y s t a l i s p e r t u r b e d by e l e c t r i c f i e l d , t h e f o l l o w i n g e f f e c t s a r e
expected1 :
-
Broadening and displacement t o s m a l l e r e n e r g i e s of t h e a b s o r p t i o n l i n e . - S p l i t t i n g and i g n i t i o n of some forbidden components f o r c e r t a i n p o l a r i z a -t i o n of l i g h t .
The experimental i n ~ e s t i g a t i o n s ~ ~ show t h e broadening, t h e displacement and t h e i g n i t i o n of t h e a b s o r p t i o n l i n e . No s p l i t t i n g was observed even f o r a p p l i e d e l e c t r i c f i e l d of 150 KV/cm.
When t h e c r y s t a l i s p e r t u r b e d by s t r e s s , one e x p e c t broadening and s l i t t i n g 25,!?6 of t h e a b s o r p t i o n l i n e 1 ' which i s i n agreement with experimental r e s u l t s
.
Non-l i n e a r e f f e c t i s observed a t high a p p l i e d s t r e s s z 7 .
I t should be mentioned t h a t t h e fundamental d i f f e r e n c e between t h e s e two p e r t u r b a t i o n s i s t h a t t h e e l e c t r i c f i e l d does n o t conserve t h e p a r i t y of e l e c t r o n i c s t a t e s , t h e r e f o r e one observe t h e i g n i t i o n of t h e a b s o r p t i o n ( i . e . d i p o l a r c h a r a c t e r of t h e o p t i c a l t r a n s i t i o n ) i n normally f o r b i d d e n d i r e c t i o n s , which i s n o t t h e c a s e under a p p l i e d s t r e s s . Also, displacement of t h e a b s o r p t i o n l i n e t o s m a l l e r e n e r g i e s is observed o n l y with a p p l i e d e l e c t r i c f i e l d .
We have i n v e s t i g a t e d t h e p h o t o c o n d u c t i v i t y i n as-grown c r y s t a l corresponding t o t h e ISJ e x c i t o n i c t r a n s i t i o n i n t h e p a r t i c u l a r arrangement 3//[110] where t h e a b s o r p t i o n i s a n i s o t r o p i c i n t h e absence of e l e c t r i c p e r t u r b a t i o n . The experimental arrangements were d e s c r i b e d elsewhere2 3 0 . F i g u r e s 5 a ) b ) show t h e p h o t o c u r r e n t and t r a n s m i s s i o n s p e c t r a i n t h e r e g i o n of ISJ e x c i t o n i c t r a n s i t i o n a t low temperature
( 4 . 2 K ) . I k o d i f f e r e n t p o l a r i z a t i o n s of l i g h t were c o n s i d e r e d : Q//[001] and
$// [ITO] where t h e following p o i n t should be n o t i c e d :
i - I s o t r o p i c p h o t o c u r r e n t which corresponds t o a n i s o t r o p i c a b s o r p t i o n . ii
-
S p e c t r a l width of p h o t o c u r r e n t response i s h i g h e r than t h a t ofa b s o r p t i o n l i n e i n allowed d i r e c t i o n :// [001]
.
iii
-
P h o t o c u r r e n t minima which corresponds t o t h e a b s o r p t i o n l i n e i n t h e allowed d i r e c t i o n . The asymmetric shape of t h e p h o t o c u r r e n t response i n d i c a t e s i t s displacement t o lower e n e r g i e s r e l a t i v e t o t h e a b s o r p t i o n l i n e .We o b t a i n t h i s shape i n most of t h e c a s e s . However o t h e r shapes a r e avai- l a b l e depending on t h e a p p l i e d p o t e n t i a l , on t h e sample, on t h e p o i n t of t h e sample
- - -
i (A)
- - - - - - - - - - - - - - - - - 34d9-
Figure 5 . P h o t o c u r r e n t i n t h e ISJ a b s o r p t i o n l i n e f o r two p o l a r i z a t i o n s a1 ://[lT0]
,
b) ://[001]. Transmission is drawn i n i n t e r r u p t e d l i n e .which i s i r r a d i a t e d . F i g u r e 6 summarizes t h r e e t y p e s of response curves :
a ) The maximum of p h o t o c u r r e n t is i n t h e e x a c t p o s i t i o n of t h e l i n e .
b) The maximum of p h o t o c u r r e n t i s on t h e low energy s i d e of t h e l i n e and t h e minimum a t hvo.
C ) The maximum o f p h o t o c u r r e n t i s on t h e high energy s i d e of t h e l i n e and t h e
minimum a l s o a t hvo.
F i g u r e 6. Types of p h o t o c u r r e n t response curve i n t h e ISJ e x c i t o n i c l i n e of C u 2 0 .
The p h o t o c u r r e n t i n t h e forbidden d i r e c t i o n e / / [ l i o ] i n d i c a t e s t h a t e x c i t o n i c a b s o r p t i o n had taken p l a c e b u t , it i s t o o small t o be d e t e c t a b l e by t r a n s m i s s i o n measurement. This can o n l y happen under e l e c t r i c f i e l d p e r t u r b a t i o n i 4 e 2
-
Applied p o t e n t i a l b e i n g very s m a l l ( 2 . 5 V/crn) t o p e r t u r b e t h e c r y s t a l , i t f o l l o w s t h a t e x c i t o n i c a b s o r p t i o n f o r e / / [ l ~ ~ ] i s due t o p e r t u r b e d r e g i o n s by i n t e r n a l e l e c t r i c f i e l d s.
JOURNAL DE PHYSIQUE
I s o t r o p i c e x c i t o n i c p h o t o c o n d u c t i v i t y and a n i s o t r o p i c a b s o r p t i o n i n d i c a t e s inhanogeWouS e f f i c i e n c y o f e x c i t o n s i n p h o t o c o n d u c t i v i t y a t low t e m p e r a t u r e : o n l y e x c i t o n s which a r e c r e a t e d i n r e g i o n s p e r t u r b e d by i n t e r n a l e l e c t r i c f i e l d s c a n c o n t r i b u t e t o t h e c r e a t i o n o f p h o t o c a r r i e r s .
T h i s i n d i c a t e s a l s o t h a t i g n i t i o n o f e x c i t o n i c a b s o r p t i o n i n p e r t u r b e d r e g i o n s o c c u r s o n l y i n t h e p o l a r i z a t i o n
$//[lie].
Comparison w i t h t h e e f f e c t o f e x t e r n a l e l e c t r i c f i e l d on e x c i t o n i c a b s o r p t i o n i n s i m i l a r e x p e r i m e n t a l condi- t i o n ~ ~ ~ i n d i c a t e s t h a t i n t e r n a l e l e c t r i c f i e l d i n p e r t u r b e d r e g i o n s s h o u l d b e i n C4 d i r e c t i o n s . I t was shown i n t h i s c a s e 2 3 t h a t the a b s o r p t i o n + i n t h e f o r b i d d e n d i r e c t i o n3//[li0]
becomes e q u a l t o t h a t i n a l l o w e d d i r e c t i o n e//[001] f o r a p p l i e d e l e c t r i c f i e l d o f a b o u t 30 KV/cm. I t f o l l o w s t h a t i n t e r n a l e l e c t r i c f i e l d i n photo- c o n d u c t i v e r e g i o n s is o f the same o r d e r .The inhomogenous e f f i c i e n c y of e x c i t o n s i n p h o t o c o n d u c t i v i t y i s c o n f i r m e d a l s o by t h e s h a p e o f t h e p h o t o c u r r e n t r e s p o n s e c u v r e which c o r r e s p o n d s t o e x c i t o n i c a b s o r p t i o n i n non p e r t u r b e d r e g i o n s f o r "allowed" d i r e c t i o n if//[001]. The s h a p e o f p h o t o c u r r e n t r e s p o n s e c o u l d b e e x p l a i n e d by a s i m p l i f i e d model2 :
Suppose t h a t vo and vp a r e t h e f r e q u e n c i e s a t which e x c i t o n i c a b s o r p t i o n t a k e p l a c e i n i m p e r t u r b e d and p e r t u r b e d r e g i o n s r e s p e c t i v e l y . I t s h o u l d b e remember t h a t vp < V o f o r e l e c t r i c f i e l d p e r t u r b a t i o n . The a b s o r p t i o n c o e f f i c i e n t c o r r e s p o n d i n g t o ISJ e x c i t o n i c t r a n s i t i o n c o u l d b e c o n s i d e r e d a s a G a u s s i a n w i t h r e s p e c t t o t h e f r e q u e n c y :
and we s u p p o s e t h a t i t h a s t h e same s h a p e i n p e r t u r b e d r e g i o n s :
where :
Ko(v) { K ~ ( v ) : 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 i n u n p e r t u r b e d { p e r t u r b e d ) r e g i o n s .
K o max {Kp max} : 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 v ( v } i n u n p e r t u r b e d { p e r t u r b e d } r e g i o n s . 0 P
Avo {Av
1
: i s t h e w i d t h o f a b s o r p t i o n l i n e a t-
maxP i n
u n p e r t u r b e d { p e r t u r b e d ) r e g i o n s .
L e t us c o n s i d e r a l l p e r t u r b e d r e g i o n s a s a f i c t i v e one w i t h w i d t h X i n t h e m i d d l e o f t h e c r y s t a l a l o n g t h e d i r e c t i o n o f t h e i n c i d e n t l i g h t ( s e e f i g u r & 7 ) . The number of a b s o r b e d p h o t o n s b y u n i t t i m e i n this f i c t i v e r e t i o n i s :
N = N { l - e x p (-K X
) I
P P P
where :
N = N e x p (-K X ) 0 0
N : i s t h e number o f i n c i d e n t p h o t o n s on t h e c r y s t a l by u n i t t i m e . Xo : i s t h e d e p t h of f i c t i v e p e r t u r b e d r e g i o n s ( s e e f i g u r e 7 ) .
F o r s m a l l a b s o r p t i o n c o e f f i c i e n t and s m a l l t h i c k n e s s of t h e c r y s t a l , which is s a t i s f i e d i n o u r c a s e , one c a n w r i t e :
e x p (-K X 1 = 1 - K X
0 0 0 0
e x p (-K X ) = 1 - K X
P P P P
E q u a t i o n ( 3 ) t a k e s t h e n t h e f o l l o w i n g form :
F i g u r e 7 . A b s o r p t i o n p r o c e s s i n a s i m p l i f i e d model o f inhomogeneous c r y s t a l
.
2 ( v - v ) 2 N = N K
P 0 P max P o max o
2 ( v - v ) 2 e x p
[-{--&-I
1n2]
P
The p h o t o c u r r e n t i s p r o p o r t i o n a l t o t h e number of e x c i t o n s c r e a t e d i n p e r t u r . b e d r e g i o n s i . e . t o t h e number o f a b s o r b e d photons N i n t h e s e r e g i o n s .
F i g u r e 8 shows t h e p h o t o c u r r e n t r e s p o n s e o b t a i n e d by e q u a t i o n ( 7 ) which h a s t h e same form a s i n f i g u r e 5. We h a v e c o n s i d e r e d N K X a s u n i t y and
o p max p
F i g u r e 8. C a l c u l a t e d r e s p o n s e c u r v e of the p h o t o c u r r e n t I n t h e 1s
e x c i t o n i c l i n e . J
C4-176 JOURNAL DE PHYSIQUE
vo = 16399.5
cl,
v = 16399,2 cm-l, Avo = 1 cm-l, Avp = 3 an-', K, ma, = 5 cm-l, Xo = 0.1 cm. Av = 3 cm -1 corresponds t o r e g i o n s p e r t u r b e d by an e l e c t r i c f i e l d of about 30 K V / m '23.
According t o t h e e x i s t e n c e o f l o c a l i z e d e l e c t r i c f i e l d s we have p u t i n e v i - d e n c e , t h e s e shapes a r e very w e l l i n t e r p r e t e d :
Case a ) : The l o c a l i z e d e l e c t r i c f i e l d s a r e t o o weak t o g i v e r i s e t o a s h i f t of t h e l i n e b u t high enough t o d r i f t t h e e x c i t o n s towards r e t i o n s where t h e y can d i s s o c i a t e .
Case b) : The LEF a r e high enough t o g i v e r i s e t o a s h i f t . We know t h a t a continuous e l e c t r i c E i e l d induces a d e c r e a s e of t h e gap and a s h i f t of t h e l i n e s i n the low energy s i d e o f t h e spectrum. A minimum should o c c u r a t hvo which corresponds t o t h e formation of e x c i t o n s i n region of t h e c r y s t a l where no LEF e x i s t s .
Case c) : A s h i f t of t h e p h o t o c u r r e n t maximum towards high energy could b e induced by e l e c t r i c f i e l d g r a d i e n t . The quadrupolar c h a r a c t e r of t h e l i n e g l v e r i s e t o s p e c i f i c i n t e r a c t i o n w i t h t h e g r a d i e n t of e l e c t r i c f i e l d s which can e x p l a i n t h e s h i f t .
I n f a c t , one should know t h e e x a c t d i s t r i b u t i o n of p e r t u r b e d r e g i o n s t o have q u a n t i t a t i v e i n t e r p r e t a t i o n o f e x c i t o n i c p h o t o c u r r e n t response. We supposed t h a t t h e s e r e g i o n s a r e e s s e n t i a l l y t h e b i r e f r i n g e n t ones where an e l e c t r i c f i e l d could be formed by d i s l o c a t i o n s i n " p i l e - u p s " . This i s i n agreement with p h o t o c o n d u c t i v i t y measurements by o p t i c a l scanning i n p l a s t i c a l l y deformed c r y s t a l s 2 1 3 2 .
B,
EZ~i_t2~l~-~h?_t2_~0!!dU_CLi_~i-t~-b~-_0~_ti_C~1~~~a"!!&!!_g
We have i n v e s t i g a t e d t h e e x c i t o n i c p h o t o c o n d u c t i v i t y p o i n t by p o i n t i n p l a s - t i c a l l y deformed c r y s t a l s because t h e b i r e f r i n g e n t r e g i o n s a r e more l o c a l i z e d , which p e r m i t us t o compare p h o t o c u r r e n t response i n d i f f e r e n t r e g i o n s . Experimental s e t - u p was d e s c r i b e d elsewhere2 3 2 . I n t h e s e experiments, we have 4//[0011 where no a n i s o t r o p i c e f f e c t i n ISJ e x c i t o n i c a b s o r p t i o n i s e x p e c t e d y i t h o u t e l e c t r i c
f i e l d l 4 p 2 : . The c r y s t a l w a s scanned a t wavelength h = 6098 A which corresponds t o ISJ e x c i t o n i c a b s o r p t i o n .
Figure 9 shows t h e b i r e f r i n g e n c e ( a ) , t h e e x c i t o n i c p h o t o c u r r e n t response f o r two p o l a r i z a t i o n s , 8//[100] (b) and 2//[010] ( c ) i n 5 % deformed c r y s t a l . Black r e g i o n s i n ( b ) and ( c ) correspond t o a maximum of e x c i t o n i c p h o t o c o n d u c t i v i t y
F i g u r e 9. B i r e f r i n g e n c e ( a ) and scanned p h o t o c o n d u c t i v i t y a t 6098 A 0
( b and c ) of a deformec? c r v s t a l . Axes of c r y s t a l a r e given In ( b ) .
r e l a t i v e t o o t h e r r e g i o n s . White round r e g i o n s correspond t o e l e c t r i c c o n t a c t on t h e s e m i - t r a n s p a r e n t e l e c t r o d e on t h e s u r f a c e of t h e c r y s t a l .
One c a n s e e t h a t e x c i t o n i c p h o t o c o n d u c t i v i t y maxima correspond t o b i r e f r i n - g e n t c r o s s b a r s which a r e p e r p e n d i c u l a r t o t h e p o l a r i z a t i o n of i n c i d e n t l i g h t . I t should b e mentioned t h a t homogeneous p h o t o c u r r e n t d i s t r i b u t i o n i s o b t a i n e d when t h e c r y s t a l i s scanned a t wavelength o u t s i d e t h e e x c i t o n i c a b s o r p t i o n 2 . These r e s u l t s confirm t h e inhomogeneous model of e x c i t o n i c p h o t o c o n d u c t i v i t y .
The a n i s o t r o p i c p h o t o c u r r e n t maxima i n b i r e f r i n g e n t r e g i o n s could b e i n t e r - p r e t e d by a n i s o t r o p i c e x c i t o n i c a b s o r p t i o n i n t h e s e r e g i o n s because of i n t e r n a l e l e c t r i c f i e l d p e r t u r b a t i o n . We have shown t h a t i n t e r n a l e l e c t r i c f i e l d i n p e r t u r b e d r e g i o n s should be i n C4 d i r e c t i o n s (§ A ) . We e x p e c t t h e n t h e e x i s t e n c e of i n t e r n a l e l e c t r i c f i e l d p e r p e n d ~ c u l a r t o "pile-ups" i n b i r e f r i n g e n t r e g i o n s a s r e p r e s e n t e d s c h e m a t i c a l l y i n f i g u r e 10.
F i g u r e 10. R e l a t i v e e f f i c i e n c y of t h e p h o t o c o n d u c t i v i t y a t 6098 A according t o t h e d i r e c t i o n of p o l a r i z a t i o n v e c t o r w i t h r e s p e c t of t h e p o s i t i o n of p i l e - u p s i n t h e c r o s s b a r s of b i r e f r i n g e n c e . Case a ) corresponds t o a maximum of p h o t o c u r r e n t .
On t h e o t h e r hand, i g n i t i o n of e x c i t o n i c a b s o r p t i o n is expected t h e o r e t i - c a l l y and observed e x p e r i m e n t a l l y 2 3 when 6//c4 -t
3,
and f, is p a r a l l e l t o a n o t h e r C4 d i r e c t i o n , only f o r l i g h t p o l a r i z a t i o n '& L%.
T h i s i g n i t i o n i s r e p r e s e n t e d sche- m a t i c a l l y on f i g u r e 9 a ) and can e x p l a i n t h e a n i s o t r o p i c e x c i t o n i c photoconducti- v i t y .I n f a c t , p i l e - u p s could be considered a s charged p l a n s with s u r f a c e charge d e n s i t y p . A t a d i s t a n c e g r e a t e r t h a n t h a t between two a d j a c e n t d i s l o c a t i o n s i n t h e p i l e - u p , t h e induced e l e c t r i c f i e l d p e r p e n d i c u l a r t o t h e p i l e - u p i s given by :
where :
e : i s t h e vacuum p e r m i t i v i t y .
E : i s t h e d i e l e c t r i c c o n s t a n t of t h e c r y s t a l .
To e v a l u a t e charge d e n s i t y , one s h o u l d know t h e e x a c t s t r u c t u r e of d i s l o c a - t i o n s i n p i l e - u p s which i s n o t a v a i l a b l e i n Cu20.
C4-178 JOURNAL DE PHYSIQUE
111. DISLOCATIONS AND EXCITONIC PHOTOCONDUCTIVITY I N OTHER COMPOUNDS AND CONCLUSION
T h i s a n a l y s i s c a n b e a p p l i e d t o o t h e r compounds a l r e a d y s t u d i e d t e n y e a r s a g o 3 3 1 3 ~ . Minima o f p h o t o c u r r e n t i n t h e I S l i n e s i n CuCl a n d CuBr ( s e e f i g u r e s 11 a n d 1 2 ) w e r e i n t e r p r e t e d i n t e r m s o f s u r f a c e e f f e c t s : t h e r e c o m b i n a t i o n r a t e o f
F i g u r e 1 1 . P h o t o c o n d u c t i v i t y s p e c t r u m o f a c r y s t a l o f CuCl a t 4 K . Minima a t 3 8 7 0 . 5 a n d 3787 c o r r e s p o n d t o t h e p o s i t i o n o f v
v l d a b s o r p t i o n l i n e s r e s p e c t i v e l y . I f and
F i g u r e 1 2 . P h o t o c o n d u c t i v i t y s p e c t r u m o f a C U B ~ c r y s t a l a t 4 K f o r two d i f f e r e n t a p p l i e d p o t e n t i a l s : a ) E = 2 0 v/cm, b) E = 2 kV/cm.
carriers was b e l i e v e d t o i n c r e a s e n e a r t h e s u r f a c e . The s c h e m e s o f f i g u r e 13 show how the maxima o f p h o t o c u r r e n t a r e s h i f t e d a c c o r d i n g t o t h e a b s o r p t i o n l i n e s . P o s i t i o n o f l i n e s i n a n e n e r g y s c a l e a r e v.+ I f , v l d - f o r CuC1, v T d a n d v i f f o r CuBr.
Figure 13. Schematic r e p r e s e n t a t i o n of t h e r e l a t i v e p o s i t i o n s of t h e a b s o r p t i o n l i n e s and maxima of p h o t o c u r r e n t of 1S e x c i t o n s i n CuCl and CuBr
.
f and d a r e r e p o r t e d t o two e x c i t o n s e r i e s r e l a t e d t o t h e degeneracy of t h e valence band of t h e two compounds. + o r - i n d i c a t e s how t h e resonance l i n e i s s h i f t e d by t h e a p p l i c a t i o n of an e l e c t r i c f i e l d : towards high and low energy r e s - p e c t i v e l y .
I t is c l e a r t h a t t h e maximum of p h o t o c u r r e n t i s s h i f t e d i n t h e same way a s t h e a b s o r p t i o n l i n e under a p p l i c a t i o n o f an e l e c t r i c f i e l d . According t o t h e dipo- l a r n a t u r e of t h e o p t i c a l t r a n s i t i o n s , no e f f e c t of an e l e c t r i c f i e l d q r a d i e n t i s t o b e expected. Furthermore, a l l t h e experiments on r e f e r e n c e a r e made a t low tempe- r a t u r e (2) 4 K) where t h e thermal d i s s o c i a t i o n of e x c i t o n s i s n e g l i g i b l e .
I t r e s u l t s t h a t t h e work we have done on Cu20 p e r m i t s a g e n e r a l i z a t i o n of t h e p h y s i c a l i n t e r p r e t a t i o n of e x c i t o n d i s s o c i a t i o n i n e l e c t r i c f i e l d s t o a t l e a s t two o t h e r compounds. I n t h i s l a t e r c a s e (CuC1, CuBr),we have no proof of t h e d i r e c t r o l e of d i s l o c a t i o n s : s u r f a c e e l e c t r i c f i e l d s can a l s o work i n the e x c i t o n d i s s o - c i a t i o n p r o c e s s . However, t h e r e c e n t d a t a on CdS by Vyvenko e t a l . ' show t h a t t h e o p t i c a l s p e c t r a of e x c i t o n s a r e s h i f t e d n e a r d i s l o c a t i o n s l i p bands. Less r e c e n t d a t a 3 5 have shown t h a t t h e e x i s t e n c e of minima of p h o t o c u r r e n t i n t h e e x c i t o n l i n e s i s a q u i t e g e n e r a l phenomenon ( e s p e c i a l l y i n CdS) although i r r e p r o d u c i b l e .
We have now an ensemble of experimental d a t a which p u t i n evidence t h e c l o s e r e l a t i o n between e x c i t o n s and s t r u c t u r a l d e f e c t s . We have s e e n t h a t a good know- ledge of t h e o p t i c a l p r o p e r t i e s of a given c r y s t a l can h e l p i n t h e c h a r a c t e r i z a t i o n of t h e s e d e f e c t s .
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