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SOME NEW DEVELOPMENTS IN THE FIELD OF AMORPHOUS SILICON SOLAR CELLS
W. Spear, R. Gibson, D. Yang, P. Lecomber, G. Müller, S. Kalbitzer
To cite this version:
W. Spear, R. Gibson, D. Yang, P. Lecomber, G. Müller, et al.. SOME NEW DEVELOPMENTS IN
THE FIELD OF AMORPHOUS SILICON SOLAR CELLS. Journal de Physique Colloques, 1981, 42
(C4), pp.C4-1143-C4-1153. �10.1051/jphyscol:19814245�. �jpa-00220877�
JOURNAL DE PHYSIQUE
ColZoque C4, suppZ&ment au nO1O, Tome 42, octobre 1981 page C4-1143
SOME NEW DEVELOPPIENTS I N THE F I E L D OF AMORPHOUS S I L I C O N SOLAR CELLS
W.E. S p e a r , R.A. Gibson, D. Yang (+), P.G.Lecomber, G. Miiller (+) and S. K a l b i t z e r (*)
University o f Dundee, U.K.
(m) Present address : Dept. o f Radio-EZectronics, University of Peking, Peking, China
(+) Mm-PZanck I n s t i t u t fiir Kemphysik, HeideZberg, F.R. G .
A b s t r a c t
.-
The p a p e r d e a l s w i t h t h e r e s u l t s from two c u r r e n t p r o j e c t s . I n t h e f i r s t , concerned w i t h m a t e r i a l s a s s e s s m e n t , s i m p l e t r a n s i e n t t e c h n i q u e s have been a p p l i e d t o p-i-n p h o t o v o l t a i c c e l l s . The measurements g i v e i n f o r m a t i o n on t h e i n t e r n a l f i e l d and on t h e t r a n s p o r t and t h e l i f e t i m e o f g e n e r a t e d h o l e s . The second p a r t of t h e p a p e r d e a l s w i t h t h e r e s u l t s o f i m p l a n t a t i o n e x p e r i m e n t s i n which t h e upper p a r t o f t h e j u n c t i o n i s formed by P - o r A l k a l i - i o n implant- a t i o n .l . I n t r o d u c t i o n .
The development o f e f f i c i e n t t h i n f i l m p h o t o v o l t a i c d e v i c e s i s o f c o n s i d e r a b l e c u r r e n t i n t e r e s t , b u t a l s o p r e s e n t s many d i f f i c u l t and c h a l l e n g i n g problems.
During t h e l a s t few y e a r s e n c o u r a g i n g p r o g r e s s h a s b e e n made i n a number o f l a b o r a t - o r i e s on amorphous (a-) S i p h o t o v o l t a i c c e l l s , b o t h of t h e S c h o t t k y b a r r i e r (MIS) and t h e p-i-n j u n c t i o n t y p e s ( 1 ) . I n t h e f o l l o w i n g we s h a l l b e concerned p r i m a r i l y w i t h t h e p h o t o v o l t a i c j u n c t i o n s . Improved e f f i c i e n c y i n t h e s e d e v i c e s h a s been a c h i e v e d by b e t t e r c e l l d e s i g n and p a r t i c u l a r l y b y t h e a t t e m p t s a t o p t i m i s i n g t h e h i g h l y doped t o p and b a c k c o n t a c t r e g i o n s .
To approach t h e d e s i r e d e c o n o m i c a l l y v i a b l e c o n v e r s i o n e f f i c i e n c y rnore c l o s e l y i t i s i n o u r view e s s e n t i a l t o advance a l o n g two main l i n e s o f development. F i r s t , t h e improvement of t h e m a t e t - i a l i t s e l f t h r o u g h a b e t t e r u n d e r s t a n d i n g of i t s e l e c t - r o n i c and t r a n s p o r t p r o p e r t i e s w i t h p a r t i c u l a r r e f e r e n c e t o t h e p h o t o v o l t a i c a p p l i c - a t i o n s and s e c o n d l y , t h e improvement and o p t i m i s a t i o n o f v a r i o u s a s p e c t s o f a-Si s o l a r c e l l t e c h n o l o g y .
I n a c c o r d a n c e w i t h t h e s e aims we s h o u l d l i k e t o d i s c u s s i n t h e f o l l o w i n g two r e l e v a n t p r o j e c t s which a r e b e i n g c a r r i e d o u t j o i n t l y by t h e groups working a t Dundee and t h e M-P-I i n H e i d e l b e r g . The f i r s t p a r t o f t h e paper i s concerned w i t h
t h e s t u d y o f t h e m a t e r i a l i t s e l f b y a p p l y i n g t r a n s i e n t t e c h n i q u e s t o t h e photo- v o l t a i c j u n c t i o n s . I n t h e second p a r t we s h a l l d i s c u s s some r e c e n t work on photo- v o l t a i c j u n c t i o n s formed by i o n i m p l a n t a t i o n .
2. T r a n s i e n t Measurements on P h o t o v o l t a i c C e l l s .
Measurements o n a-semiconductors under t r a n s i e n t e x c i t a t i o n a r e a t t r a c t i v e i n t h a t t h e y can o f t e n l e a d t o b a s i c t r a n s p o r t p a r a m e t e r s much more d i r e c t l y t h a n s t e a d y s t a t e e x p e r i m e n t s . I n t h e p a s t t h i s a p p r o a c h h a s p r o v i d e d a w e a l t h of i n f o r m a t i o n on t r a n s p o r t i n many d i s o r d e r e d m a t e r i a l s , from t h e e a r l y r e s u l t s o n a-Se ( 2 ) t o t h e s t u d y o f o r g a n i c polymers ( 3 1 , c h a l c o g e n i d e s (4) and a-Si ( 5 ) .
I n t h i s s e c t i o n we s h a l l c o n s i d e r t h e a p p l i c a t i o n o f s i m p l e t r a n s i e n t e x c i t a t i o n t e c h n i q u e s t o p h o t o v o l t a i c p-i-n c e l l s and d i s c u s s t h e i n f o r m a t i o n o b t a i n a b l e from such measurements. The approach d e s c r i b e d p r o v i d e s a u s e f u l t o o l f o r t h e a s s e s s - ment a n d comparison of p h o t o v o l t a i c c e l l p a r a m e t e r s , i n some c a s e s under o p e r a t i n g c o n d i t i o n s , a s a supplement t o c o n v e n t i o n a l s t e a d y s t a t e measurements. T r a n s i e n t t e c h n i q u e s have been used i n t h e s t u d y o f a-Si S c h o t t k y b a r r i e r c e l l s . C r a n d a l l ( 6 ) combined s t e a d y p r i m a r y p h o t o c u r r e n t and r e s p o n s e time measurements t o d e t e r m i n e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814245
C4-1144 JOURNAL DE PHYSIQUE
t h e d r i f t m o b i l i t y of t h e m a j o r i t y c a r r i e r . T i e d j e ( 7 ) and h i s c o l l e a g u e s a t t h e Exxon l a b o r a t o r i e s i n v e s t i g a t e d t h e e l e c t r o n d r i f t m o b i l i t y and deep t r a p p i n g l i f e - time i n Schottky b a r r i e r c e l l s by t i m e - o f - f l i g h t t e c h n i q u e s .
2.1 The J u n c t i o n s .
+ +
The j u n c t i o n s i n v e s t i g a t e d i n t h e f o l l o w i n g have a s t a i n l e s s s t e e l p -i-n c o n f i g u r a t i o n , w i t h t h e l i g h t i n c i d e n t on t h e n+ r e g i o n through an IT0 l a y e r . The d e v i c e i s d e p o s i t e d i n t h e glow d i s c h a r g e a t a s u b s t r a t e temperature of 2800C and t h e t h i n , h i g h l y doped p+ and n+ r e g i o n s a r e produced by t h e u s u a l gas phase doping technique ( 8 ) . The IT0 t o p c o n t a c t i s produced by e l e c t r o n beam e v a p o r a t i o n and subsequently annealed f o r 15 minutes a t 2300C i n an o x i d i s i n g atmosphere t o a t t a i n a s h e e t r e s i s t a n c e of a b o u t l O O o h m p e r s q u a r e . With a t h i c k n e s s near 500A t h e IT0 l a y e r a l s o forms a reasonably e f f e c t i v e a n t i - r e f l e c t i o n c o a t i n g ( 9 ) .
F i g . 1 r e p r e s e n t s a somewhat ' i d e a l i s e d ' band diagram of such a j u n c t i o n . Because small c a r r i e r d i f f u s i o n l e n g t h s a r e an i n h e r e n t p r o p e r t y of a-Si ( 1 0 ) ( 1 1 ) , t h e most important f e a t u r e i s t h e ' b u i l t - i n ' average d r i f t f i e l d E,, which p r o v i d e s a means of c a r r i e r t r a n s p o r t a c r o s s t h e d e v i c e . Depending on t h e d e n s i t y of s t a t e s i n t h e gap, model c a l c u l a t i o n s (12) s u g g e s t E, v a l u e s between 103 and 104 ~ c m - l .
The c h a r a c t e r i s t i c s of t h e s o l a r c e l l , such a s i t s f i l l f a c t o r and conversion e f f i c i e n c y , a r e c l o s e l y r e l a t e d t o t h e e x t e n t by which t h e i n t e r n a l f i e l d changes w i t h i l l u m i n a t i o n o r e x t e r n a l l o a d . More d e t a i l e d experimental i n f o r m a t i o n on t h e i n t e r n a l f i e l d , i t s changes w i t h d e v i c e t h i c k n e s s and i t s dependence on m a t e r i a l parameters, should t h e r e f o r e b e of c o n s i d e r a b l e v a l u e .
Cell
+ +
F i g . 1 . Model of p -i-n j u n c t i o n showing F i g . 2 . Basic c i r c u i t used i n
b u i l t i n average f i e l d E,. t r a n s i e n t experiments.
2.2 Experimental Method.
The b a s i c i d e a of t h e t r a n s i e n t experiments c o n s i s t s of u s i n g a s h o r t f l a s h of a given h t o probe t h e i n t e r n a l f i e l d a t t h e p a r t i c u l a r s t e a d y s t a t e w i t h o u t apprec- i a b l y p e r t u r b i n g t h e system. F i g . 2 shows t h e c i r c u i t . The s t a i n l e s s s t e e l bottom c o n t a c t B of t h e c e l l i s connected t o t h e load r e s i s t o r RL, t h e IT0 t o p c o n t a c t T t o a low impedance v o l t a g e box whereby a p o t e n t i a l of
+
VT can b e a p p l i e d . The c e l l can be i l l u m i n a t e d w i t h a s t e a d y l i g h t source of v a r i a b l e i n t e n s i t y . The probe f l a s h e s , about 0.4 v s l o n g , a r e produced by a s t a b l e A r spark-source r u n a t a frequency of 2-3 Hz. Most experiments were c a r r i e d o u t w i t h a b l u e o r g r e e n f i l t e r g i v i n g a b s o r p t i o n d e p t h s of about 400A and lOOOA r e s p e c t i v e l y . The f l a s h was a t t e n - uated so t h a t t h e p o t e n t i a l changes caused by t h e t r a n s i e n t e x i t a t i o n always remain- ed below 20 mV.There a r e two methods of measurement. The f i r s t c o n s i s t s of i n t e g r a t i n g t h e t r a n s i e n t c h a r g e displacement and r e q u i r e s t h a t t h e i n p u t time c o n s t a n t a c r o s s RL should b e much longer t h a n t h e time s c a l e of t h e experiment. The c o n d i t i o n i s s a t i s f i e d f o r a t y p i c a l c e l l a s long a s t h e d i f f e r e n t i a l c e l l r e s i s t a n c e RC, i n
p a r a l l e l w i t h RL, exceeds about 0 . 5 MC?. I n such an experiment, J << Jsc s o t h a t one e s s e n t i a l l y i n v e s t i g a t e s p o i n t s along t h e v o l t a g e a x i s of t h e c h a r a c t e r i s t i c . The e x t e r n a l p o t e n t i a l V a c r o s s t h e c e l l , may b e changed i n t h e following ways:
( i ) \ V B \ i n f i g . 2 can b e i n c r e a s e d by s t e a d y i l l u m i n a t i o n , ( i i ) VT can b e made pos- i t i v e o r n e g a t i v e and ( i i i ) t h e e f f e c t of i l l u m i n a t i o n can be balanced o u t , e i t h e r completely o r p a r t i a l l y , by a p o s i t i v e VT.
How w i l l t h e e x t e r n a l l y a p p l i e d p o t e n t i a f s modify t h e i n t e r n a l f i e l d ? This i s a d i f f i c u l t problem, but t o make a c o r r e l a t i o n of r e s u l t s p o s s i b l e we s h a l l assume t h a t t h e r e s u l t i n g average f i e l d E i s given by
Obviously, e q n . ( l ) i s an o v e r s i m p l i f i c a t i o n , j u s t i f i a b l e only by t h e f a c t t h a t i t l e a d s t o reasonably c o n s i s t e n t r e s u l t s , a s we s h a l l s e e i n s e c t i o n 2.4. The approx- imation i s a c c e p t a b l e a t low V , b u t could become q u i t e u n r e p r e s e n t a t i v e a s t h e i n t e r n a l f i e l d i s reduced by a n e g a t i v e V t o approach t h e f l a t band p o s i t i o n .
I n t h e second method of e x p e r i m e n t a t i o n , t h e t r a n s i e n t c u r r e n t i s d i s p l a y e d . This r e q u i r e s t h a t RL << R C , w h i c h g e n e r a l l y means a l a r g e r d e t e c t i o n s e n s i t i v i t y than f o r c h a r g e i n t e g r a t i o n . Under i l l u m i n a t i o n VB 0 and p o i n t s on t h e J - a x i s can be explored; t h e a d d i t i o n of
+
VT can now move t h e r e f e r e n c e p o i n t t o any o r i g i n i n t h e J-
V p l a n e .2.3 T r a n s i e n t P u l s e Shapes.
With t h e c e l l c o n f i g u r a t i o n i n v e s t i g a t e d h e r e ( f i g . 1 ) we a r e mainly concerned w i t h t h e e f f e c t of E on t h e t r a n s p o r t of e x c e s s h o l e s g e n e r a t e d by a b l u e o r g r e e n probe f l a s h near t h e top e l e c t r o d e . The form of t h e i n t e g r a t e d response i s shown i n f i g . 3 f o r one of t h e t h i c k e r specimens. The i n i t i a l p a r t between t = 0 and t ' fi 500 n s corresponds t o t h e p e r i o d of p h o t o - g e n e r a t i o n i n t h e h i g h f i e l d e x i s t i n g n e a r t h e n + - r e g i o n . ~ h e s i g n a l up t o t ' r e p r e s e n t s t h e charge displacements of t h e
h o l e s and of t h e e x t r a c t e d e l e c t r o n s . Beyond t ' we s e e t h e i n t e g r a t e d displacement of t h e h o l e s i n j e c t e d i n t o t h e quasi-uniform f i e l d E d e f i n e d by e q n . ( l ) .
1 I
I
Fig.3. Observed p u l s e shape f o r one of t h e t h i c k e r specimens showing i n t e g r a t e d charge v e r s u s time.
I
t'
Hole t r a n s p o r t i n a-Si h a s been i n v e s t i g a t e d by Moore (13) and by A l l a n (14) using d r i f t m o b i l i t y t e c h n i q u e s . Both a u t h o r s f i n d room temperature ph v a l u e s between 1 0 - ~ and 1 0 - ~ cm2v-ls-l and A l l a n concludes t h a t t h e t r a n s p o r t i s c o n t r o l l e d by i n t e r a c t i o n d u r i n g t r a n s i t w i t h s t a t e s near t h e maximum i n t h e d e n s i t y of s t a t e d i s t r i b u t i o n of a-Si (15). This mechanism i n t r o d u c e s d i s p e r s i o n i n t h e t r a n s i t times, without s e r i o u s l y a f f e c t i n g t h e p r o p o r t i o n a l i t y between d r i f t v e l o c i t y and f i e l d and l a r g e l y accounts f o r t h e rounded shape of t h e p u l s e i n f i g . 3 .
Although i t i s not p o s s i b l e t o d e f i n e a unique t r a n s i t time, two times t l and t 2 , can normally b e i d e n t i f i e d on t h e o s c i l l o s c o p e s c r e e n and t h e i r f i e l d dependence i n v e s t i g a t e d . t l , t h e i n t e r s e c t i o n of t h e i n i t i a l and f i n a l t a n g e n t s t o t h e p u l s e , i s r e p r e s e n t a t i v e of t h e t r a n s i t of a f a s t e r group of t h e c a r r i e r s ; t 2 , d e f i n e d by t h e merging of t h e t r a c e w i t h t h e h o r i z o n t a l r e f e r e n c e l i n e , corresponds t o t h e s l o w e s t c h a r g e displacements i n t h e d i s t r i b u t i o n . With some p r a c t i c e , t l and t 2 can b e determined d i r e c t l y from t h e o s c i l l o s c o p e s c r e e n . For c o n s i s t e n c y l t i s
C4-1146 JOURNAL DE PHYSIQUE
e s s e n t i a l t o a d j u s t t h e v e r t i c a l g a i n t o g i v e a s t a n d a r d p u l s e h e i g h t i n a l l c a s e s ; i t i s a l s o u s e f u l , p a r t i c u l a r l y f o r t h e t h i n n e r specimens, t o expand t h e time s c a l e when determining t h e p o s i t i o n of t ' .
I n t h e c u r r e n t d i s p l a y , i t i s more d i f f i c u l t t o s p o t corresponding f e a t u r e s d i r e c t l y and it t h e n becomes n e c e s s a r y to p l o t t h e p u l s e on a l o g i vs l o g t graph. This h a s been done i n t h e p r e s e n t work on a number of specimens, u s i n g a t r a n s i e n t r e c o r d e r which f e d t h e s i g n a l i n t o a l o g a r i t h m i c p l o t t e r . The r e s u l t s showed a f i e l d dependent d i s c o n t i n u i t y a t a time which was i n r e a s o n a b l e agreement w i t h t l , t h e t r a n s i t of t h e f a s t e r group of c a r r i e r s . This approach i s more time- consuming and most of t h e following r e s u l t s have been o b t a i n e d by d i r e c t o b s e r v a t i o n of t h e i n t e g r a t e d s i g n a l .
2.4 Time r e s o l v e d Wasurements and t h e i r I n t e r p r e t a t i o n .
The i n t e g r a t e d t r a n s i e n t p u l s e shapes have been i n v e s t i g a t e d i n a number of s o l a r c e l l s a s a f u n c t i o n of i l l u m i n a t i o n and a p p l i e d p o t e n t i a l s , VT, and i n t h i s s e c t i o n two examples of t h e r e s u l t s w i l l b e d i s c u s s e d . Data f o r o t h e r c e l l s a r e given i n Table 1. I f t h denotes t h e a p p r o p r i a t e t r a n s i t time a c r o s s t h e specimen f o r a group of h o l e s generated near T, t h e n
where we have used t h e approximate e x p r e s s i o n f o r t h e f i e l d given by e q n . ( l ) . A p l o t of d / t h a g a i n s t V / d should t h e r e f o r e g i v e uh a s t h e g r a d i e n t and t h e f i e l d E, a s an i n t e r c e p t on t h e n e g a t i v e V/d a x i s . On reducing t h e i n t e r n a l f i e l d by illum- i n a t i o n o r e x t e r n a l p o t e n t i a l s , a l i m i t i n g c o n d i t i o n w i l l b e approached a t which th becomes equal t o t h e l i f e time T of t h e h o l e s w i t h r e s p e c t t o t r a p p i n g i n a deep l e v e l . The measured time i n t h e d r i f t m o b i l i t y experiment should t h e n remain con- s t a n t on f u r t h e r d e c r e a s i n g t h e f i e l d . I t i s l i k e l y t h a t t h e s e t r a p p i n g c e n t r e s a r e s i t u a t e d i n t h e r e g i o n of t h e Fermi l e v e l and t h a t t h e y a r e a l s o involved i n t h e recombination p r o c e s s . The s t r i c t l y l i n e a r i n t e n s i t y dependence of Jsc g e n e r a l l y observed i n t h e s t e a d y s t a t e would b e c o n s i s t e n t w i t h such a mechanism.
Vtd
ikV cm1)
Fig.4. R e s u l t s of t r a n s i e n t e x c i t a t i o n experiments f o r c e l l A (d = 0.56 um).
F i g . 5 . R e s u l t s of t r a n s i e n t e x c i t a t i o n experiments f o r c e l l B (d = 1.15 pm).
I n f i g s . 4 and 5 we show t h e t r a n s i e n t r e s u l t s from two widely d i f f e r e n t s o l a r c e l l s , l i s t e d a s A and B i n Table 1. C e l l A i s a good d e v i c e , w i t h a reason- a b l e conversion e f f i c i e n c y and a comparatively h i g h f i l l f a c t o r . I t s t h i c k n e s s , d = 0.56 pm l i e s somewhat above t h e optimum d i n our r- v s d c o r r e l a t i o n . C e l l B on t h e o t h e r hand, i s 1.15 pm t h i c k and i t s p r o p e r t i e s a s a p h o t o v o l t a i c c e l l a r e n o t promising. What a r e t h e r e a s o n s f o r t h i s d i f f e r e n c e ?
Both f i g u r e s a r e p l o t s of d / t h v s . V/d and i n c l u d e d / t l and d / t 2 c u r v e s . P o i n t s denoted by t h e open c i r c l e s were o b t a i n e d w i t h an a p p l i e d p o t e n t i a l , i . e . V =
+
VT; t h e f u l l c i r c l e s r e f e r t o t h e c a s e i n which V = - VB i s a l t e r e d by i l l u m i n a t i o n and VT = 0. Good agreement between t h e s e two methods of c o n t r o l l i n g V h a s been found f o r most specimens. It i s encouraging t h a t i n s p i t e of t h e u n c e r t a i n t y i n determining i n d i v i d u a l t l and t 2 v a l u e s , t h e p l o t s of t h e r e s u l t s l e a d t o convincing s t r a i g h t l i n e s a s expected from eqn.(2). This a l s o s u g g e s t s t h a t eqn. ( l ) f o r E i s an a c c e p t a b l e approximation over t h e range of V used.A s d i s c u s s e d p r e v i o u s l y , t h e m o b i l i t i e s p1 and v2 t h a t can b e deduced from t h e g r a d i e n t s depend on t h e chosen r e f e r e n c e p o i n t s on t h e d i s p e r s i v e p u l s e i n f i g . 3 . I t can b e s e e n t h a t p1 v a l u e s i n Table 1 l i e somewhat above t h e range of pub- l i s h e d vh w h i l s t p2 f a l l s w e l l w i t h i n t h e range. However, i n s p i t e of t h i s d i f f - e r e n c e p1 and ~ 2 c u r v e s e x t r a p o l a t e t o t h e same v a l u e of E,, 11 kV cm-l f o r c e l l A and 4 . 8 kV cm-l f o r B .
With d e c r e a s i n g i n t e r n a l f i e l d t h e o n s e t of l i f e t i m e l i m i t a t i o n s can c l e a r l y b e seen. Two important p o i n t s have been e s t a b l i s h e d i n a l l t h e measurements:
( i ) t h e t r a n s i t i o n t o l i f e t i m e l i m i t a t i o n on t h e t l and t 2 c u r v e s o c c u r s c l o s e l y a t t h e same f i e l d v a l u e , I ~ ' l / d , f o r a given specimen, and
( i i ) w i t h i n e x p e r i m e n t a l e r r o r ~ 1E ~~ 12 ~ 2
Thus b o t h t l and t 2 c u r v e s l e a d t o i d e n t i c a l p r e d i c t i o n s f o r t h e o n s e t of l i f e t i m e l i m i t a t i o n a t a c r i t i c a l i n t e r n a l f i e l d
s o t h a t a c c o r d i n g t o e q n . ( 2 ) , u ~ T E ~ = d.
I n Table 1 p h ~ , E, a n d ( l - ~ ~ / ~ , ) v a l u e s a r e l i s t e d f o r comparison. The e q u a l i t y of t h e p r o d u c t f o r two groups of c a r r i e r s i n a d i s p e r s i v e t r a p - l i m i t e d t r a n s p o r t i s n o t unexpected,provj.ded t h e deep t r a p p i n g t r a n s i t i o n t a k e s p l a c e from t h e f r e e s t a t e .
2.5 T r a n s i e n t P u l s e Height Measurements.
F u r t h e r independent i n f o r m a t i o n on t h e b a s i c p r o p e r t i e s of t h e photovoiltaic j u n c t i o n can b e o b t a i n e d by measuring t h e i n t e g r a t e d charge displacement Q(E) ( s e e f i g . 3 ) g e n e r a t e d by t h e h i g h l y absorbed f l a s h a s a f u n c t i o n o f t h e i n t e r n a l f i e l d E = E, + Vld. The r a t i o Q/Qsat where Qsat r e p r e s e n t s t h e t o t a l e x t r a c t e d charge a s E -t m, i s g i v e n by t h e well-known Hecht-formula (16).
This r e l a t i o n i s based on a simple model i n which t h e range of t h e g e n e r a t e d h o l e s i s l i m i t e d by deep t r a p p i n g . I t should be a p p l i c a b l e t o t h e primary t r a n s i e n t photo-current observed h e r e ; t h e s m a l l e x c e s s c a r r i e r d e n s i t i e s and t h e low p u l s e r e p e t i t i o n r a t e e n s u r e t h a t any trapped s p a c e c h a r g e does n o t p e r t u r b E t o any e x t e n t . No time dependent p o l a r i s a t i o n e f f e c t s were observed i n t h e s e experiments.
As i n t h e d r i f t m o b i l i t y measurements, t h e approximation used f o r t h e i n t e r n a l f i e l d ( e q n . ( l ) ) could l e a d t o some u n c e r t a i n t y , p a r t i c u l a r l y a t low E. A more d e t a i l e d t r e a t m e n t of charge c o l l e c t i o n i n a-Si s o l a r c e l l s h a s r e c e n t l y been pub-
C4-l148 JOURNAL DE PHYSIQUE
l i s h e d by B e l l ( 1 7 ) . I t i s b a s e d o n eqn.(4) b u t c o n s i d e r s t h e c o n t r i b u t i o n of t h e o p t i c a l c a r r i e r g e n e r a t i o n t h r o u g h o u t t h e c e l l .
01L -12 -10 -8 -6 -4 -2 0 2 L 6 8 10 12
Vid ikV cm-'l
F i g . 6 . T r a n s i e n t p u l s e h e i g h t measure- F i g . 7 . T r a n s i e n t p u l s e h e i g h t measure-
ments f o r c e l l A. ments f o r c e l l B.
The e x p e r i m e n t a l p o i n t s i n f i g s . 6 and 7 r e p r e s e n t measurements o f t h e i n t e g - r a t e d p u l s e h e i g h t a s a f u n c t i o n o f V/d f o r c e l l s A and B d i s c u s s e d i n t h e p r e v i o u s s e c t i o n . Green p r o b e p u l s e s were u s e d . The s o l i d l i n e s a r e a computer f i t of eqn.14) t o t h e e x p e r i m e n t a l d a t a , which d e t e r m i n e s t h e Q/Qsat s c a l e and t h e p h ~ v a l u e . The f i t i s v e r y s a t i s f a c t o r y , g i v i n g p h ~ v a l u e s 1 . 0 X 1 0 - ~ c m ~ v - ~ and 2.7 X f o r c e l l s A and B , w h i c h s h o u l d b e compared t o 1.1 X 10-' and 2.8 X l ~ - ~ c m ~ V - l , o b t a i n e d i n d e p e n d e n t l y from t h e t i m e r e s o l v e d measurements o f ph and T i n t h e p r e v i o u s s e c t i o n .
T a b l e 1: Summary o f r e s u l t s from s t e a d y and t r a n s i e n t measurements o n a number o f p h o t o v o l t a i c c e l l s .
2.6 D i s c u s s i o n o f t h e T r a n s i e n t Measurements.
The examples p r e s e n t e d i n t h e l a s t s e c t i o n s t o g e t h e r w i t h t h e a d d i t i o n a l d a t a i n T a b l e 1 show t h a t s i m p l e t r a n s i e n t measurements on t h e p h o t o v o l t a i c d e v i c e s c a n g i v e u s e f u l a d d i t i o n a l i n f o r m a t i o n a t t h e p r e s e n t s t a g e o f development. S e v e r a l p o i n t s a r i s i n g from t h e s e e x p e r i m e n t s w i l l now b e b r i e f l y d i s c u s s e d . The f i r s t c o n c e r n s t h e volume l i m i t a t i o n imposed by t h e h o l e l i f e t i m e and h o l e d r i f t m o b i l i t y .
This i s c l e a r l y brought o u t by b o t h t h e time r e s o l v e d measurements and t h e p h ~ v a l u e s from t h e p u l s e h e i g h t a n a l y s i s , which a c c o r d i n g t o Table 1 a r e i n r e a s o n a b l e agreement. For our m a t e r i a l ph-c 2'1 0 - ~ c m ~ v - ~ , w i t h t h e l a r g e s t v a l u e of
2.8 X 1 0 - ~ c r n ~ v - ~ f o r t h e t h i c k specimen B. The r e s u l t s a r e most r e l e v a n t t o t h e p+-i-n+- IT0 c o n f i g u r a t i o n i n which an a p p r e c i a b l e f r a c t i o n of t h e g e n e r a t e d h o l e s has t o d r i f t d i s t a n c e s approaching d. The range l i m i t a t i o n accounts f o r t h e f a c t t h a t l a b o r a t o r i e s i n v e s t i g a t i n g t h i s type of c e l l have g e n e r a l l y found a f a i r l y s h a r p l y d e f i n e d optimum d e v i c e t h i c k n e s s i n e f f i c i e n c y - t h i c k n e s s c o r r e l a t i o n s . Our d a t a , e x t e n d i n g o v e r t h e l a s t two y e a r s , s u g g e s t s t h a t d 2 0 . 5 p m i s an e s s e n t i a l c o n d i t i o n f o r 11
2
5% and a s i m i l a r optimum t h i c k n e s s h a s been r e p o r t e d by t h e RCA group (1) (18).These c o n c l u s i o n s a r e d i f f i c u l t t o r e c o n c i l e w i t h t h e r e s u l t s of Mort and h i s c o l l e a g u e s a t t h e Xerox L a b o r a t o r i e s . From delayed f i e l d experiments on a-Si (19) and measurements i n t h e x e r o g r a p h i c mode (20) they o b t a i n e d a h o l e m o b i l i t y of about 8 X 1 0 - ~ c m ~ ~ - l s - ~ , w e l l w i t h i n t h e e s t a b l i s h e d range, b u t a h o l e l i f e t i m e i n e x c e s s of l ms. This g i v e s a VhT
~ o - ~ c ~ ~ v - ~
which i m p l i e s t h a t t h i c k n e s s o r range l i m i t - a t i o n s should not occur i n p r e s e n t a-Si s o l a r c e l l s . On t h e o t h e r h a n d , t h e r e c e n t work by Oda e t a 1 (21) a t t h e Tokyo I n s t i t u t e of Technology u s i n g t h e same xero- g r a p h i c technique, l e a d s t o p h ~ v a l u e s of about 4 X ~ O - ~ C ~ ~ V - ~ i n r e a s o n a b l e agree- ment w i t h o u r r e s u l t s . The reasons f o r t h e disagreement w i t h t h e Xerox d a t a a r e n o t c l e a r - t h e y could l i e i n t h e m a t e r i a l i n v e s t i g a t e d . I f t h a t were t h e c a s e , t h e n t h e wide-ranging c o n t r o l of r h by t h e p r e p a r a t i o n c o n d i t i o n s would b e a remarkable p r o p e r t y of a-Si.The p r e s e n t experiments y i e l d i n t e r e s t i n g i n f o r m a t i o n on t h e i n t e r n a l f i e l d , which i s one of t h e most important f a c t o r s a s f a r a s p h o t o v o l t a i c p r o p e r t i e s a r e concerned. Reference t o t h e Eo-column i n Table 1 shows t h a t t h e r e e x i s t s a f a i r l y convincing r e l a t i o n between E, and t h e f i l l f a c t o r and e f f i c i e n c y of t h e c e l l . Good d e v i c e s , such a s C o r D w i t h 17
2
5 % , h a v e i n t e r n a l f i e l d s of 14 o r 15 kV cm-l.The comparatively h i g h E, f o r t h e v e r y poor c e l l E seems t o b e an e x c e p t i o n . A r e l e v a n t p o i n t i s t h a t Eod l i s t e d i n Table 1 l i e s around 0.6V f o r r e a s o n a b l e c e l l s ; t h i s common p o t e n t i a l d i f f e r e n c e i s determined by t h e band p o s i t i o n s w i t h r e s p e c t t o
~f i n t h e h i g h l y doped n+ and p+ s u r f a c e r e g i o n s . With t h e known doping l i m i t a t i o n s of a-Si (8) i t appears l i k e l y t h a t E o d ~ 0 . 6 V l i e s f a i r l y c l o s e t o t h e maximum v a l u e t h a t can b e achieved under p h o t o v o l t a i c o p e r a t i o n . The r e c e n t r e s u l t s of t h e Osaka group (22) w i t h a boron-doped Si-C s u r f a c e r e g i o n a r e very encouraging and could t o some e x t e n t overcome t h e i n t e r n a l f i e l d l i m i t a t i o n .
We have seen t h a t i n c r e a s i n g t h e t h i c k n e s s of t h e c e l l reduces Eo, approximat- e l y a s l / d . On t h e o t h e r hand t h e f i e l d E,, determined from t h e o n s e t of l i f e t i m e l i m i t a t i o n , depends on b o t h V ~ and d. T I t i s u s e f u l t o c o n s i d e r t h e q u a n t i t y E,-E,, which a c c o r d i n g t o eqn.(3) can b e d i r e c t l y r e a d o f f f i g s . 4 and 5. E,-E, r e p r e s e n t s
t h e range over which t h e i n t e r n a l f i e l d can b e reduced, f o r i n s t a n c e by i n c r e a s i n g t h e e x t e r n a l load, b e f o r e l i f e t i m e l i m i t a t i o n s s e t i n and t h e photogenerated c u r r e n t begins t o d e c r e a s e r a p i d l y . E v i d e n t l y E,-E, should be r e l a t e d t o t h e f i l l f a c t o r of t h e c e l l , a s i s i n f a c t shown by t h e (Eo-E,)/Eo v a l u e s l i s t e d i n Table 1.
3. The A p p l i c a t i o n of Ion I m p l a n t a t i o n Techniques t o P h o t o v o l t a i c J u n c t i o n s . I n p a r a l l e l w i t h t h e work on gas-phase doped p h o t o v o l t a i c j u n c t i o n s we have used i o n i m p l a n t a t i o n a s an a l t e r n a t i v e approach t o t h e problem of o p t i m i s i n g t h e p r o p e r t i e s and p o t e n t i a l d i s t r i b u t i o n i n t h e r e g i o n of t h e t o p c o n t a c t of t h e c e l l . The a t t r a c t i v e f e a t u r e s of t h i s technique a r e :
( i ) i m p l a n t a t i o n i s h i g h l y c o n t r o l l a b l e and d i f f e r e n t doping p r o f i l e s can b e i n c o r p o r a t e d i n a r e p r o d u c i b l e way, and
( i i ) i m p l a n t a t i o n s can be c a r r i e d o u t a f t e r d e p o s i t i n g a b a t c h of i d e n t i c a l specimens, which h e l p s c o n s i d e r a b l y i n e s t a b l i s h i n g optimum c o n d i t i o n s f o r producing t h e t o p r e g i o n of t h e c e l l .
The e x t e n s i v e work d u r i n g t h e l a s t few y e a r s (23) (24) (25) c a r r i e d o u t j o i n t l y by t h e Dundee and M-P-I groups h a s demonstrated t h a t i o n i m p l a n t a t i o n o f f e r s i n t e r - e s t i n g new p o s s i b i l i t i e s f o r b o t h fundamental and a p p l i e d developments i n t h e a-Si
C4-1150 JOURNAL DE PHYSIQUE
f i e l d . I n t h e p r e s e n t c o n t e x t , t h e f o l l o w i n g r e s u l t s a r e r e l e v a n t : ( i ) P , B and T1 a r e t h e most e f f i c i e n t i o n s f o r n- and p- type s u b s t i t u t i o n a l doping i n a-Si
(25) and ( i i ) s t a b l e and e f f i c i e n t i n t e r s t i t i a l n- type doping i s p o s s i b l e w i t h t h e a l k a l i i o n s Na, K , Rb and CS (24).
So f a r , two s e r i e s of i m p l a n t a t i o n experiments on p h o t o v o l t a i c j u n c t i o n s have been c a r r i e d o u t under widely d i f f e r e n t c o n d i t i o n s . I n t h e f i r s t , comparatively low i o n d e n s i t i e s were used a t an i m p l a n t a t i o n d e p t h of about 1000A. S t a i n l e s s s t e e l - n+-i l a y e r s were implanted w i t h B and T l i o n s t o form t h e p- t y p e top r e g i o n of t h e j u n c t i o n . Although good s h o r t - c i r c u i t c u r r e n t s could be o b t a i n e d from t h e s e devices, t h e doping c o n d i t i o n s l i m i t e d Voc t o about 0.6V and
n
t o 3%I n t h e second group of experiments, which w i l l now be d i s c u s s e d i n some d e t a i l , shallow i m p l a n t a t i o n d e p t h s were combined w i t h implanted i o n d e n s i t i e s , N I , between 1019 and
1oZ1
cm-3 t b a c h i e v e doping c o n d i t i o n s s i m i l a r t o t h o s e i n p r e s e n t gas- doped j u n c t i o n s .3.1 Experimental D e t a i l s and I m p l a n t a t i o n P r o f i l e s .
I n t h i s work p+-i l a y e r s were d e p o s i t e d and t h e n implanted w i t h P, Na and CS i o n s t o form t h e t o p n- r e g i o n . Specimens were mounted on a r o t a t a b l e copper t a r g e t h o l d e r i n a low energy i o n a c c e l e r a t o r , s o t h a t d i f f e r e n t doses could be given d u r i n g t h e same run. A f t e r implanting a t room temperature, t h e IT0 e l e c t r o d e s were d e p o s i t e d and t h e specimens annealed a t 230012.
c- %
I t i s of i n t e r e s t t o b r i e f l y con- 40A 70A lOOA ( e ~ ) s i d e r t h e i m p l a n t a t i o n p r o f i l e s . As018
an e x a m p l e , f i g . 8 shows t y p i c a l curves f o r Na-ions i n which NI (normalised t o 1020cm-3 a t t h e maxima, r e p r e s e n t i n g -035
t h e p r o j e c t e d range), i s p l o t t e d a g a i n s tdepth below t h e s u r f a c e f o r t h r e e
---
070
e n e r g i e s used i n t h e experiments.E v i d e n t l y t h e p o s i t i o n of t h e NI max-
075
imum and t h e e x t e n t of t h e doped reg- i o n can be c l o s e l y c o n t r o l l e d by t h e energy of t h e i n c i d e n t i o n s . The pos- i t i o n of t h e Fermi l e v e l , E ~ - E ~ , with r e s p e c t t o &he extended e l e c t r o n s t a t e s has been determined from t h e previous work on Na-implanted undoped a-Si (24) and i s shown i n f i g . 8 i n r e l a t i o n t o300
t h e NI s c a l e . The d a t a can g i v e someNa-ion penetration depth ( A )
i d e a of t h e shape of t h e p o t e n t i a l p r o f i l e , i f i t i s assumed t h a t t h e NI F i g . 8 . I m p l a n t a t i o n p r o f i l e s f o r Na-ions. vs depth curves a r e a r e a s o n a b l e approx-imation t o t h e s p a t i a l d i s t r i b u t i o n of donors.
3.2 R e s u l t s and Discussion of I m p l a n t a t i o n Experiments.
The r e s u l t s of t h e Na and CS i m p l a n t a t i o n s a r e summarised i n f i g . 9 , t h o s e of t h e P i m p l a n t a t i o n s i n f i g . 1 0 . I n each s e t of diagrams V,,, Jsc, t h e f i l l f a c t o r and t h e conversion e f f i c i e n c y , a l l measured under AM1 c o n d i t i o n s , a r e p l o t t e d a g a i n s t i o n dose. The e n e r g i e s of 4, 2.5 and 1 keV used f o r t h e Na-ion i m p l a n t a t - i o n s (denoted by d i f f e r e n t symbols i n f i g . 9 ) , correspond t o t h e i m p l a n t a t i o n p r o f i l e s i n f i g . 8 w i t h maxima a t 100A, 70A and 40A r e s p e c t i v e l y .
I t can be seen t h a t a l l t h e i m p l a n t a t i o n s i n c r e a s e Voc from t h e unimplanted v a l u e i n t h e p + - i - ~ ~ ~ d e v i c e (U-I i n f i g s . 9 & 10) t o v a l u e s of 0.80V a t
NI 1 0 ~ ~ c m - ~ . The s h o r t c i r c u i t c u r r e n t a l s o i n c r e a s e s w i t h NI and reaches a max- imum around 1020cm-3 f o r Na and 3 X 1 0 ~ ' c m - ~ f o r P specimens, w i t h t h e h i g h e s t Jsc f o r t h e 4 keV CS i m p l a n t a t i o n s . The f i l l f a c t o r l i e s around 0.6 f o r a l k a l i implant- a t i o n s , b u t i s somewhat lower i n P doped specimens. The conversion e f f i c i e n c i e s reach v a l u e s around 5% f o r t h e l e s s e n e r g e t i c Na and P i o n s i n t h e dose range
N km3)
1
; 18 3 l i O 3 1i' I
(volts) + +
@---@---$- 0.8 -g---
0.6 n 100; C ~ V \
\.
-X\
0.4 Na 0 7oA 2skrv 6 \
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F i g . 9 .
-
P h o t o v o l t a i c p r o p e r t i e s o f p + - i s p e c i m e n s , i m p l a n t e d w i t h Na a n d CS i o n s , p l o t t e d a g a i n s t i o n d o s e . I o n e n e r g i e s a r e d e n o t e d by d i f f e r e n t s y m b o l s .N, [cm3)
0-6 0.4
: / - i - - - m - - ; - -
6 0.
0.2 2 .
l? 10 *O 1021 10 10 20 3 10 -3 21
NI (cm 1
F i g . 1 0 . P h o t o v o l t a i c p r o p e r t i e s o f
D+-i
s p e c i m e n s i m p l a n t e d w i t h P i o n s .JOURNAL DE PHYSIQUE
Acknowledgments. The a u t h o r s s h o u l d l i k e t o e x p r e s s t h e i r g r a t i t u d e t o S t e w a r t Kinmond and A l l y F a l c o n e r f o r p r e p a r i n g t h e specimens, and t o F r a n z Demond, Don M i t c h e l l and Hugo Steemers f o r h e l p w i t h t h e i m p l a n t a t i o n s and measurements. The
s u p p o r t of t h i s p r o j e c t by t h e EEC S o l a r Energy P r o j e c t and a Lucas R e s e a r c h F e l l o w s h i p ( f o r R.A.G.) i s g r a t e f u l l y acknowledged.
from 3 X 1 0 l ~ c m - ~ t o 1 0 ~ ~ c m - ~ . Encouraging p r e -
100 l i m i n a r y r e s u l t s have been o b t a i n e d w i t h CS
R e f e r e n c e s . CE
l%)
S e e f o r i n s t a n c e C a r l s o n , D.E., S o l a r Energy M a t e r i a l s
3
(1980) 503.S p e a r , W.E., P r o c . Phys. Soc. B E (1957) 669; i b i d
76
(1960) 826.80 F i n a l l y , we s h a l l compare t h e c o l l e c t i o n
e f f i c i e n c y o f one of t h e b e s t P- i m p l a n t e d spec- imens w i t h a comparable specimen doped from t h e g a s p h a s e .
Measurements of t h i s k i n d a r e b e i n g c a r r i e d o u t on a l l b a t c h e s of c e l l s produced i n t h e l a b - o r a t o r y ; t h e y a l l o w a u s e f u l c o n s i s t e n c y check between t h e measured J s c and t h a t o b t a i n e d by i n t e g r a t i n g o v e r t h e c o l l e c t i o n e f f i c i e n c y c u r v e .
20
c e l l , c u r v e (b)
,
g i v e s a l m o s t t h e same maximum 0 L 0 5 0 6 07 c o l l e c t i o n e f f i c i e n c y . The b l u e r e s p o n s e o f t h ehprn)
c e l l s i s a l s o s i m i l a r a n d c a n b e i n t e r p r e t e d i n t e r m s o f a 'dead l a y e r ' of a b o u t 200A a t t h e Fig.11. C o l l e c t i o n e f f i c i e n c y s u r f a c e of each c e l l .a s a f u n c t i o n o f wavelength:
( a ) g a s - p h a s e doped c e l l , ( b ) I n c o n c l u s i o n i t h a s been e s t a b l i s h e d t h a t P-implanted c e l l . i m p l a n t a t i o n w i t h a l k a l i and phosphorus i o n s i s a
v i a b l e and c o n t r o l l a b l e method of p r o d u c i n g t h e h i g h l y doped n- l a y e r i n a-Si p-i-n p h o t o v o l t a i c c e l l s . Conversion e f f i c i e n c i e s up t o 5.4% a n d c o l l e c t i o n e f f i c i e n c i e s around 80% have b e e n a c h i e v e d by t h i s tech- n i q u e which compare f a v o u r a b l y w i t h g a s - p h a s e doped j u n c t i o n s . One of t h e main problems o f p r e s e n t a-Si p-i-n c e l l s i s t h e r a p i d drop o f c o l l e c t i o n e f f i c i e n c y i n
t h e b l u e p a r t o f t h e s p e c t r u m ( s e e f i g . 1 1 ) where a growing f r a c t i o n o f t h e l i g h t i s a b s o r b e d i n t h e doped s u r f a c e r e g i o n . I t may b e p o s s i b l e t h a t w i t h t h e i m p l a n t a t i o n t e c h n i q u e a s u f f i c i e n t l y t h i n and v e r y h i g h l y doped l a y e r c o u l d b e produced t o improve t h e b l u e r e s p o n s e , w i t h o u t a f f e c t i n g t h e open c i r c u i t v o l t a g e .
-
Mort, J . , P r o c . of t h e 7 t h I n t e r n a t i o n a l Conf. o n Amorphous and L i q u i d Semi- c o n d u c t o r s , 1977,ed. W.E. S p e a r (CICL, Edinburgh) 753.
F i s c h e r , F.D., M a r s h a l l , J.M. and Owen, A.E., P h i l . Mag.
33
(1976) 261.Le Comber P.G. and S p e a r , W . E . , Phys. Rev. L e t t e r s
2
(1970) 509.C r a n d a l l , R.S., J . Non-Cryst. S o l i d s
35/36
(1980) 381.T i e d j e , T., Wronski, C.R., A b e l e s , B . and Cebulka, J . M . , SERI Amorphous S i l i c o n Workshop, San Diego 1980.
i m p l a n t a t i o n s , w i t h a 5.4% e f f i c i e n c y a t NI = 1 0 ~ ~ c m - ~ ( f i g . 9 ) .
S p e a r , W.E. and Le Comber, P.G., P h i l . Mag.
2
(1976) 935.C a r l s o n , D . E . , S m i t h , R.W., S w a r t z , G.A. a n d T r i a n o , A.R., E l e c t r o c h e m . S o c . M e e t i n g , Hollywood, F l o r i d a , 1980.
S t a e b l e r , D.L., J. Non-Cryst. S o l i d s
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(1980) 387.S n e l l , A . J . , S p e a r , W.E. and L e Comber, P.G., P h i l . Mag. B% (1981) 407.
Okamoto, H., Yamaguchi, T . a n d Hamakawa, Y . , P r o c . 1 5 t h I n t . Conf. P h y s i c s o f S e m i c o n d u c t o r s , Kyoto ( 1 9 8 0 ) , J. P h y s . S o c . J a p a n
9
(1980) 1213.Moore, A.R., A p p l . P h y s . L e t t e r s
2
(1977) 762.A l l a n , D., P h i l . Mag. B 2 (1978) 381.
Madan, A . , Le Comber, P.G. a n d S p e a r , W.E., J. Non-Cryst. S o l i d s (1976) 239.
H e c h t , K . , Z e i t s . f . P h y s i k
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(1932) 235.B e l l , R.O., Appl. P h y s . L e t t e r s
2
(1980) 9 3 6 .C a r l s o n , D . E . , P a p e r p r e s e n t e d a t t h e T r i e s t e S e m i c o n d u c t o r Symposium, 1980.
M o r t , J . , Chen, I . , T r o u p , A . , Morgan, M . , K n i g h t s , J . , a n d L u j a n , R., P h y s . Rev. L e t t e r s
5
(1980) 1348.M o r t , J . , G r a m a t i c a , S . , K n i g h t s , J.C. and L u j a n , R., S o l a r C e l l M a t e r i a l s (1981) ( i n p r e s s ) .
Oda, S . , S a i t o , Y . , S h i m i z u , I . , a n d I n o u e , E., P h i l
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Mag. ( i n ~ r e s s ) .Tawada, Y . , Nononura, S . , Yamaguchi, T . , H o t t a , S . , Okamoto, H. a n d Hamakawa,Y.
1 5 t h IEEE P h o t o v o l t a i c S p e c i a l i s t s C o n f e r e n c e , F l o r i d a ( 1 9 8 1 ) .
M u l l e r , G . , K a l b i t z e r , S . , S p q a r , W.E. a n d Le Comber, P.G., P r o c . o f t h e 7 t h I n t e r n a t i o n a l C o n f e r e n c e o n Amorphous a n d L i q u i d S e m i c o n d u c t o r s , E d i n b u r g h 1977, ed. W .E. S p e a r (CICL, U n i v e r s i t y of E d i n b u r g h ) 442.
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