Interference effects and space-charge-limited conduction in amorphous silicon devices

SPACE-CHARGE-LIMITED

CONDUCTION IN AMORPHOUS

SILICON DEVICES

SPACE-CHARGE-LIMITED

CONDUCTION IN AMORPHOUS

SILICON DEVICES

Proefschrift

Ter verkrijging van de graad van doctor in de

technische wetenschappen aan de

Technische Hogeschool Delft, op gezag van

de Rector Magnificus, prof. ir. B.P.Th. Veltman,

in het openbaar te verdedigen ten overstaan van

het College van dekanen op 27 september 1983,

te 14.00 uur

B I B L I O T H E E K T U Delft P 2128 4012

door

Willem den Boer

natuurkundig ingenieur

geboren te Dordrecht

it mum li n li li li li mui! urn ut» mm m m iron urn win l i ¡11 ui it l p li li li mm i f i n m n H J I i j P i ! ! ™ II I II II li II II II ill ill I Hill i l l II I III II II II Mill 11 III II i n

: B I, i; |P.

: 8. IIII lllil • it'll I I I « it ft li I

III I I I

I

1. GENERAL INTRODUCTION 1 1.1. H i s t o r i c a l background 1 1.2. Some p r o p e r t i e s of a-Si:H 2 1.2.1. E l e c t r i c a l p r o p e r t i e s 3 1.2.2. O p t i c a l p r o p e r t i e s 6 1.3. Scope of t h i s t h e s i s 7 References 10

2. GLOW DISCHARGE PRODUCTION OF A-SI:H FILMS 12

2.1. I n t r o d u c t i o n 12 2.2. The d e p o s i t i o n apparatus 13 2.3. D e p o s i t i o n parameters and t h e i r i n f l u e n c e on f i l m p r o p e r t i e s 14 2.4. Other d e p o s i t i o n methods 16 References 17

3. INTERFERENCE EFFECTS IN A-SI:H SOLAR CELLS 19

3.1. I n t r o d u c t i o n 19 3.2. A b s o r p t i o n c o e f f i c i e n t measurements 20 3.3. Computer s i m u l a t i o n o f o p t i c a l behaviour o f s o l a r c e l l s 22 3.3.1. A b s o r p t i o n i n the a-Si:H f i l m 26 3.3.2. O p t i m i z a t i o n o f a n t i r e f l e c t i o n c o a t i n g s 30 3.3.3. A b s o r p t i o n p r o f i l e s 31 3.4. C o l l e c t i o n e f f i c i e n c y measurements 34 3.5. C o n c l u s i o n s 36 References 38

4.1. I n t r o d u c t i o n 40 4.2. Theory o f o n e - c a r r i e r SCL c u r r e n t s 45 4.3. G r a p h i c a l a n a l y s i s o f c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s 50 4.4. Sample p r e p a r a t i o n 53 4.5. E x p e r i m e n t a l setup 55 4.6. P r o p e r t i e s o f the n+- c o n t a c t 57 4.7. C u r r e n t - v o l t a g e measurements 59 4.8. D e n s i t i e s o f l o c a l i z e d s t a t e s 64 4.9. E r r o r d i s c u s s i o n and comparison w i t h o t h e r t e c h n i q u e s 69 4.10. E f f e c t o f i l l u m i n a t i o n on SCL c u r r e n t s 72 4.11. T r a n s i e n t c u r r e n t s i n n+- i - n+ d e v i c e s 76 4.11.1. Response t o a v o l t a g e r e d u c t i o n 77 4.11.2. Response t o a v o l t a g e i n c r e a s e 84 4.11.3. AC c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s 87 4.12.Observation o f t h r e s h o l d s w i t c h i n g i n n+- i - n+ d e v i c e s 91 4.13.Conclusions 96 References 98 SUMMARY IO4 SAMENVATTING 107 ACKNOWLEDGEMENTS H O

1. GENERAL INTRODUCTION

1 , 1 , H I S T O R I C A L BACKGROUND

Amorphous s i l i c o n was l o n g c o n s i d e r e d i n t e r e s t i n g from o n l y an academic p o i n t o f v i e w . F i l m s p r e p a r e d by c o n v e n t i o n a l methods such as vacuum e v a p o r a t i o n and s p u t t e r i n g have a h i g h d e n s i t y o f l o c a l i z e d s t a t e s i n t h e gap and a r e c o n s e q u e n t l y n o t s u i t a b l e f o r e l e c t r o n i c d e v i c e s . The i n t r o d u c t i o n o f t h e glow d i s c h a r g e d e p o s i t i o n t e c h n i q u e by C h i t t i c k e t a l . [ 1 . 1 ] i n 1969 marked t h e t u r n i n g p o i n t . I n t h i s t e c h n i q u e s i l a n e gas i s decomposed i n a glow d i s c h a r g e and an amorphous s i l i c o n f i l m i s d e p o s i t e d on s u b s t r a t e s h e l d a t a t e m p e r a t u r e o f 250 t o 300 °C. Glow d i s c h a r g e d e c o m p o s i t i o n o f s i l a n e y i e l d s f i l m s w i t h a h i g h p h o t o c o n d u c t i v i t y and a low d e n s i t y o f gap s t a t e s , as r e p o r t e d b y Spear e t a l . [ 1 . 2 ] - [ l . 3] i n t h e p e r i o d 1970 t o 1975.

The s u c c e s s o f t h e glow d i s c h a r g e t e c h n i q u e i s due t o t h e i n c o r p o r a t i o n o f h y d r o g e n (about 10 a t o m i c p e r c e n t ) i n t h e s i l i c o n f i l m . Hydrogen s a t u r a t e s d a n g l i n g bonds i n t h e amorphous network and c o n s e q u e n t l y l o w e r s t h e d e n s i t y o f gap s t a t e s .

An i m p o r t a n t b r e a k t h r o u g h o c c u r r e d i n 1975 when S p e a r e t a l . [ 1 . 4 ] showed t h a t t h e c o n d u c t i v i t y o f h y d r o g e n a t e d amorphous s i l i c o n ( a - S i : H ) c a n be m o d i f i e d by as much as s i x o r d e r s o f m a g n i t u d e by n - t y p e and p - t y p e d o p i n g . I n 1976

C a r l s o n and W r o n s k i [1.5] r e p o r t e d t h e f i r s t a - S i : H s o l a r c e l l w i t h a p - i - n c o n f i g u r a t i o n . S i n c e t h e n many l a b o r a t o r i e s have e n t e r e d t h e f i e l d and s o l a r c e l l e f f i c i e n c i e s g r e a t e r t h a n 10 % have been a c h i e v e d [ 1 . 6 ] . The f i e l d e f f e c t t e c h n i q u e , w h i c h was used f o r t h e d e t e r m i n a t i o n o f t h e d e n s i t y o f l o c a l i z e d s t a t e s i n t h e e a r l y y e a r s , l e d t o t h e development o f a - S i : H f i e l d - e f f e c t t r a n s i s t o r s s u i t a b l e f o r d r i v i n g l i q u i d c r y s t a l d i s p l a y s i n 1979 [ 1 . 7 ] .

The glow d i s c h a r g e t e c h n i q u e i s i n e x p e n s i v e and can e a s i l y be u p s c a l e d f o r l a r g e a r e a d e p o s i t i o n . The d e p o s i t i o n t e m p e r a t u r e below 300 °C p e r m i t s t h e use o f low c o s t s u b s t r a t e s . T h e r e f o r e , a - S i : H i s e s p e c i a l l y i n t e r e s t i n g f o r a p p l i c a t i o n s i n w h i c h t h e use o f s i n g l e - c r y s t a l s i l i c o n w a f e r s i s n o t a t t r a c t i v e b e c a u s e o f t h e i r h i g h c o s t and l i m i t e d s i z e . Such a p p l i c a t i o n s i n c l u d e s o l a r c e l l s [1.8] and l a r g e a r e a a r r a y s o f t h i n f i l m t r a n s i s t o r s f o r m a t r i x a d d r e s s i n g o f f l a t p a n e l d i s p l a y s [ 1 . 9 ] . In a d d i t i o n , a - S i : H has s p e c i a l f e a t u r e s w h i c h makes i t s u i t a b l e f o r o t h e r a p p l i c a t i o n s . The h i g h r e s i s t i v i t y and h i g h p h o t o c o n d u c t i v i t y have l e d t o i t s use as an e l e c t r o p h o t o g r a p h i c r e c e p t o r [ 1 . 1 0 ] and as a p h o t o c o n d u c t o r i n v i d i c o n s [ 1 . 1 1 ] . These a p p l i c a t i o n s r e a c h e d t h e i n d u s t r i a l s t a g e o r were i n an advanced s t a g e o f d e v e l o p m e n t i n t h e e a r l y 1980's. 1 , 2 . SOME P R O P E R T I E S OF A - S I : H F i l m s o b t a i n e d by t h e p l a s m a d e c o m p o s i t i o n o f s i l a n e a t about 300 °C a r e i n g e n e r a l amorphous, as e v i d e n c e d by X - r a y and e l e c t r o n d i f f r a c t i o n s t u d i e s [ 1 . 1 2 ] . Under s p e c i a l c o n d i t i o n s (see c h a p t e r I I ) m i c r o c r y s t a l l i n e f i l m s w i t h

c r y s t a l l i t e s i z e s o f t h e o r d e r o f 5 ran a r e o b t a i n e d . As a r e s u l t o f t h e amorphous s t r u c t u r e t h e f i l m p r o p e r t i e s a r e homogeneous i n t h e p l a n e o f t h e f i l m , i n c o n t r a s t w i t h p o l y c r y s t a l l i n e f i l m s i n w h i c h t r a n s p o r t p a r a m e t e r s a t and n e a r g r a i n b o u n d a r i e s a r e d i f f e r e n t f r o m t h o s e i n t h e r e s t o f t h e f i l m .

The p r o p e r t i e s o f a - S i : H can be m o d i f i e d i n a wide r a n g e by c h a n g i n g t h e d e p o s i t i o n c o n d i t i o n s . In g e n e r a l , t h e o p t i m a l c o n d i t i o n s w i l l be d i f f e r e n t f o r d i f f e r e n t a p p l i c a t i o n s . I n s e v e r a l r e v i e w s [ 1 . 1 3 ] - [ 1 . 1 6 ] t h e p r o p e r t i e s o f a - S i : H f i l m s have been e x t e n s i v e l y d e s c r i b e d . In t h e f o l l o w i n g s u b s e c t i o n s some a s p e c t s w i l l be c o n s i d e r e d , w i t h emphasis on d i f f e r e n c e s between c r y s t a l l i n e s i l i c o n and a - S i : H . 1 . 2 , 1 . E L E C T R I C A L P R O P E R T I E S An amorphous s e m i c o n d u c t o r i s c h a r a c t e r i z e d by a s i g n i f i c a n t d e n s i t y o f s t a t e s i n t h e gap, i n p a r t i c u l a r n e a r t h e v a l e n c e and c o n d u c t i o n band. T h e r e a r e no s h a r p l y d e f i n e d band edges; Ec and a r e d e f i n e d as t h e e n e r g y

l e v e l s w h i c h s e p a r a t e l o c a l i z e d s t a t e s from n o n - l o c a l i z e d s t a t e s ( e x t e n d e d s t a t e s ) (see a l s o s e c t i o n 4 . 1 ) . A t Ec and Ey. t h e m o b i l i t y d r o p s s e v e r a l o r d e r s o f m a g n i t u d e . T h e r e f o r e , t h e e n e r g y r e g i o n between Ec and Ev i s c a l l e d t h e m o b i l i t y gap. The c o n d u c t i v i t y o o f undoped a - S i : H f i l m s d e p o s i t e d a t 250-300 °C l i e s i n t h e range f r o m 1 0- 6 t o 1 0 "1 0( f i c m )- 1. A p l o t o f I n a v s . l / T , t h e r e c i p r o c a l a b s o l u t e t e m p e r a t u r e , y i e l d s a s t r a i g h t l i n e , w h i c h i n d i c a t e s t h a t ' t h e dominant c o n d u c t i o n mechanism i s v i a c a r r i e r s i n t h e e x t e n d e d s t a t e s . In vacuum e v a p o r a t e d and s p u t t e r e d f i l m s ,

on t h e o t h e r hand, t h e dominant mechanism i s h o p p i n g t h r o u g h l o c a l i z e d s t a t e s . From t h e s l o p e o f I n a v s . l / T t h e c o n d u c t i v i t y a c t i v a t i o n e n e r g y E i s deduced, w h i c h r a n g e s a from 0.75 t o 0.5 eV f o r undoped a - S i : H f i l m s . B o t h t h e a c t i v a t i o n e n e r g y and t h e c o n d u c t i v i t y a r e v e r y s e n s i t i v e t o t h e d e p o s i t i o n c o n d i t i o n s and, t h e r e f o r e , d i f f i c u l t t o c o n t r o l a c c u r a t e l y . Undoped f i l m s a r e s l i g h t l y n - t y p e . Because o f t h e h i g h r e s i s t i v i t y o f undoped a - S i : H t h e d i e l e c t r i c r e l a x a t i o n t i m e , i . e . t h e p r o d u c t o f r e s i s t i v i t y and p e r m i t t i v i t y , i s l a r g e r t h a n t h e m i n o r i t y c a r r i e r l i f e t i m e . Hence, a - S i : H i s a r e l a x a t i o n s e m i c o n d u c t o r [1.17] i n s t e a d o f a l i f e t i m e s e m i c o n d u c t o r s u c h as s i n g l e - c r y s t a l s i l i c o n . T h i s i m p l i e s t h a t a f t e r l o c a l i n j e c t i o n o f m i n o r i t y c a r r i e r s e q u i l i b r i u m i s r e s t o r e d by r e d u c t i o n o f t h e l o c a l m a j o r i t y c a r r i e r c o n c e n t r a t i o n t h r o u g h r e c o m b i n a t i o n and by s u b s e q u e n t d i e l e c t r i c r e l a x a t i o n . In a l i f e t i m e s e m i c o n d u c t o r t h e sequence i s c a r r i e d o u t i n r e v e r s e . Q u a n t i t i e s s u c h as l i f e t i m e and m o b i l i t y , w h i c h a r e used t o s p e c i f y s i n g l e - c r y s t a l s e m i c o n d u c t o r s , have a more c o m p l i c a t e d meaning i n amorphous s e m i c o n d u c t o r s due t o t h e p r e s e n c e o f t r a p s , w h i c h a r e c o n t i n u o u s l y d i s t r i b u t e d i n e n e r g y . The c o n c e p t o f l i f e t i m e i s n o t w e l l d e f i n e d i n a - S i : H . In t h e f i r s t p l a c e t h e m a j o r i t y c a r r i e r l i f e t i m e i s n o t e q u a l t o t h e m i n o r i t y c a r r i e r l i f e t i m e , b e c a u s e t h e f r e e c a r r i e r d e n s i t i e s a r e much s m a l l e r t h a n t h e d e n s i t y o f s t a t e s i n t h e gap. S e c o n d l y , t h e l i f e t i m e s depend s t r o n g l y on t h e i n j e c t i o n l e v e l . F o r example, when a - S i : H i s i l l u m i n a t e d , t h e gap s t a t e s a c t i n g as r e c o m b i n a t i o n c e n t r e s l i e a p p r o x i m a t e l y between t h e h o l e q u a s i - F e r m i l e v e l E and t h e e l e c t r o n q u a s i - F e r m i l e v e l E„ [ 1 . 1 8 ] . When t h e Fn

i l l u m i n a t i o n l e v e l i s i n c r e a s e d , E„ and E„ a r e f u r t h e r Fp Fn

s e p a r a t e d and t h e d e n s i t y o f r e c o m b i n a t i o n c e n t r e s i n c r e a s e s . Hence, t h e c a r r i e r l i f e t i m e s d e c r e a s e .

The c o n c e p t o f m o b i l i t y i s a l s o more c o m p l i c a t e d i n a - S i : H t h a n i n s i n g l e - c r y s t a l s i l i c o n . A d i s t i n c t i o n h a s t o be made between t h e f r e e c a r r i e r m o b i l i t y ( o r e x t e n d e d s t a t e m o b i l i t y ) yQ and t h e d r i f t m o b i l i t y u ^ . These a r e n o t e q u a l

due t o t h e h i g h d e n s i t y o f t r a p s . The f r e e c a r r i e r m o b i l i t y has n o t been measured d i r e c t l y , b u t c a n be deduced f r o m c o n d u c t i v i t y measurements [ 1 . 1 3 ] . F o r b o t h e l e c t r o n s and h o l e s v a l u e s i n t h e r a n g e 1-10 c m2/ V s e c have been r e p o r t e d [ 1 . 1 3 ] - [ 1 . 1 4 ] . However, t h e r e i s no c o n s e n s u s a b o u t t h e i r v a l u e . R e v e r s e r e c o v e r y measurements on p - i - n d i o d e s have b e e n i n t e r p r e t e d as g i v i n g e v i d e n c e f o r a f r e e e l e c t r o n m o b i l i t y o f 100 c m2/ V s e c [ 1 . 1 9 ] . The d r i f t m o b i l i t y i s s e v e r a l o r d e r s o f m a g n i t u d e s m a l l e r t h a n \iQ and, f o r e l e c t r o n s , g i v e n b y y ^ = yon/n^_, where n i s t h e f r e e e l e c t r o n d e n s i t y and n^_ t h e d e n s i t y o f t r a p p e d e l e c t r o n s . F o r h o l e s an a n a l o g u e e q u a t i o n h o l d s . The d r i f t m o b i l i t y can, i n p r i n c i p l e , be deduced f r o m a c o n v e n t i o n a l t i m e - o f - f l i g h t e x p e r i m e n t and v a l u e s o f ( 2 - 5 ) x l 0- 2 c m2/ V s e c f o r e l e c t r o n s and ( 5 - 6 ) x l 0- l t c m2/ V s e c f o r h o l e s have b e e n r e p o r t e d [ 1 . 2 0 ] . One h a s t o be c a r e f u l w i t h t h e i n t e r p r e t a t i o n o f t i m e - o f - f l i g h t d a t a , s i n c e t r a n s p o r t i n many amorphous s e m i c o n d u c t o r s i s d i s p e r s i v e , even a t room t e m p e r a t u r e [ 1 . 2 1 ] . D i s p e r s i v e t r a n s p o r t i s due t o t h e i m m o b i l i z a t i o n o f c h a r g e c a r r i e r s f o r t i m e p e r i o d s t h a t e x t e n d a l l t h e way up t o t h e t i m e s c a l e o f t h e measurement. I n a - S i : H t h e i m m o b i l i z a t i o n o f c h a r g e c a r r i e r s i s a r e s u l t o f m u l t i p l e t r a p p i n g i n gap s t a t e s and l e a d s t o a n o n l i n e a r dependence o f t h e t r a n s i t t i m e on e l e c t r o d e s p a c i n g and e l e c t r i c f i e l d i n a t i m e - o f - f l i g h t e x p e r i m e n t [ 1 . 2 1 ] . I n s u c h an e x p e r i m e n t c h a r g e i s i n j e c t e d i n t h e c o n d u c t i o n band ( o r v a l e n c e band) and i t t a k e s some t i m e b e f o r e t h e e q u i l i b r i u m between f r e e and t r a p p e d c h a r g e i s e s t a b l i s h e d . T h i s i m p l i e s t h a t t h e r a t i o n/n£ d e c r e a s e s

d e c r e a s i n g f u n c t i o n o f t i m e .

The c o n d u c t i v i t y change i n a - S i : H upon d o p i n g w i t h i m p u r i t i e s such as p h o s p h o r u s and b o r o n can e x c e e d s i x o r d e r s o f magnitude, even t h o u g h n o t a l l i m p u r i t i e s a r e s u b s t i t u t i o n a l l y i n c o r p o r a t e d and f o u r f o l d c o o r d i n a t e d . In b o t h s i n g l e - c r y s t a l s i l i c o n and a - S i : H p r a c t i c a l l y a l l donor and a c c e p t o r atoms a r e i o n i z e d a t room t e m p e r a t u r e , b u t t h e mechanisms r e s p o n s i b l e f o r t h e c o n d u c t i v i t y change a r e d i f f e r e n t i n t h e two m a t e r i a l s . I n c r y s t a l l i n e s i l i c o n a l m o s t a l l e x t r a c a r r i e r s due t o i m p u r i t i e s c o n t r i b u t e t o t h e c o n d u c t i o n , so t h a t t h e f r e e c a r r i e r d e n s i t y i s p r a c t i c a l l y e q u a l t o t h e i m p u r i t y c o n c e n t r a t i o n . I n a - S i : H t h e e x t r a c a r r i e r s condense i n deep t r a p s . The r e s u l t i n g s h i f t o f t h e F e r m i l e v e l i s r e s p o n s i b l e f o r t h e c o n d u c t i v i t y change. A low d e n s i t y o f s t a t e s n e a r midgap i s r e q u i r e d t o o b t a i n e f f i c i e n t d o p i n g .

1 . 2 . 2 . O P T I C A L P R O P E R T I E S

The o p t i c a l a b s o r p t i o n s p e c t r u m o f a - S i : H e x h i b i t s an a b s o r p t i o n edge a t an e n e r g y w h i c h c o r r e s p o n d s t o t h e s o - c a l l e d o p t i c a l gap (see s e c t i o n 3.2). The o p t i c a l gap i s a p p r o x i m a t e l y e q u a l t o t h e m o b i l i t y gap. F o r h i g h e r p h o t o n e n e r g i e 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 i n c r e a s e s and i s d e t e r m i n e d m a i n l y by b a n d - t o - b a n d a b s o r p t i o n . The o p t i c a l gap o f a - S i : H i s about 1.7 eV f o r f i l m s d e p o s i t e d a t 275 and i n c r e a s e s w i t h i n c r e a s i n g h y d r o g e n c o n t e n t [ 1 . 1 5 ] . The h y d r o g e n c o n t e n t becomes l a r g e r a t l o w e r d e p o s i t i o n t e m p e r a t u r e s . F o r p h o t o n e n e r g i e s below t h e o p t i c a l gap ( i n t h e i n f r a r e d r e g i o n ) a i s s m a l l (< 1 03 c m- 1) and d e t e r m i n e d

by t r a n s i t i o n s t o and from gap s t a t e s . I n t h e f a r i n f r a r e d r e g i o n peaks o c c u r i n t h e a b s o r p t i o n s p e c t r u m w h i c h a r e due

t o t h e v i b r a t i o n a l a b s o r p t i o n a t s i t e s c o n t a i n i n g one,two o r t h r e e H atoms: S i H , S i H2 and S i H3 [ 1 . 2 2 ] . They p r o v i d e

i n f o r m a t i o n on t h e s t r u c t u r e and h y d r o g e n c o n t e n t o f a - S i : H . Due t o t h e l a c k o f l o n g r a n g e o r d e r t h e momentum v e c t o r c a n n o t be used as a quantum number i n a - S i : H . T h i s i m p l i e s t h a t d i r e c t o p t i c a l t r a n s i t i o n s w i t h o u t i n v o l v i n g a phonon a r e p o s s i b l e , i n c o n t r a s t w i t h s i n g l e - c r y s t a l s i l i c o n , w h i c h has an i n d i r e c t gap, so t h a t d i r e c t o p t i c a l t r a n s i t i o n s have a s m a l l p r o b a b i l i t y [ 1 . 2 3 ] . As a r e s u l t t h e a b s o r p t i o n c o e f f i c i e n t o f a - S i : H i s a b o u t one o r d e r o f m a g n i t u d e l a r g e r i n t h e v i s i b l e range t h a n t h a t o f c r y s t a l l i n e s i l i c o n (see s e c t i o n 3.2). T h i s h i g h a b s o r p t i o n c o e f f i c i e n t i s e s s e n t i a l f o r t h e a p p l i c a t i o n o f a - S i : H i n s o l a r c e l l s . 1 , 3 , S C O P E OF T H I S T H E S I S T h i s t h e s i s c o n s i s t s o f two p a r t s , w h i c h a r e b o t h aimed a t t h e o p t i m i z a t i o n o f amorphous s i l i c o n s o l a r c e l l s . A f t e r t h e d e s c r i p t i o n o f t h e f i l m p r e p a r a t i o n method i n c h a p t e r I I t h e o p t i c a l b e h a v i o u r o f t h e c e l l s i s s t u d i e d i n t h e f i r s t p a r t ( c h a p t e r I I I ) . The p u r p o s e i s t o a b s o r b a maximal f r a c t i o n o f t h e i n c i d e n t l i g h t i n t h e a c t i v e s e m i c o n d u c t o r l a y e r o f t h e c e l l . S i n c e a t h i n f i l m s o l a r c e l l i s a m u l t i l a y e r s t r u c t u r e i n w h i c h i n t e r f e r e n c e e f f e c t s o c c u r , t h i s i s n o t a t r i v i a l p r o b l e m and i s d i f f i c u l t t o t r e a t a n a l y t i c a l l y . T h e r e f o r e , one has t o r e s o r t t o computer c a l c u l a t i o n s t o d e t e r m i n e t h e optimum c e l l p a r a m e t e r s . I t w i l l be shown t h a t i n t e r f e r e n c e e f f e c t s can be e x p l o i t e d t o

improve t h e e f f i c i e n c y o f t h e c e l l and t h a t optimum t h i c k n e s s e s e x i s t f o r t h e a - S i : H l a y e r . T h i s w i l l be i l l u s t r a t e d w i t h s p e c t r a l r e s p o n s e measurements on S c h o t t k y d i o d e s o l a r c e l l s . F o r a g i v e n s o l a r c e l l c o n f i g u r a t i o n t h e

t h i c k n e s s and r e f r a c t i v e i n d e x o f t h e optimum a n t i - r e f l e c t i o n c o a t i n g w i l l be c a l c u l a t e d . I t w i l l a l s o be shown t h a t due t o i n t e r f e r e n c e t h e v a r i a t i o n i n t h e e l e c t r o n - h o l e p a i r g e n e r a t i o n r a t e w i t h d i s t a n c e from t h e f r o n t c o n t a c t i s n o t e x p o n e n t i a l . O p t i c a l o p t i m i z a t i o n i s t h e f i r s t s t e p towards t h e improvement o f c e l l e f f i c i e n c y , b u t has r e c e i v e d r e l a t i v e l y l i t t l e a t t e n t i o n i n l i t e r a t u r e . I t can be t r e a t e d more o r l e s s s e p a r a t e l y from t h e s e c o n d e q u a l l y i m p o r t a n t o p t i m i z a t i o n s t e p , i n w h i c h t h e p r o b l e m i s t o c o l l e c t a maximal f r a c t i o n o f t h e l i g h t - g e n e r a t e d e l e c t r o n s and h o l e s a t t h e c o n t a c t s . T h i s f r a c t i o n depends on t h e r e c o m b i n a t i o n r a t e and on t h e e l e c t r i c - f i e l d d i s t r i b u t i o n i n t h e c e l l . The e f f e c t o f t h e b u i l t - i n e l e c t r i c f i e l d i s much more i m p o r t a n t i n a - S i : H s o l a r c e l l s t h a n i n s i n g l e c r y s t a l s i l i c o n c e l l s , s i n c e m i n o r i t y c a r r i e r s have t o r e l y m a i n l y on d r i f t t o be c o l l e c t e d b e c a u s e o f t h e i r s h o r t d i f f u s i o n l e n g t h . B o t h r e c o m b i n a t i o n r a t e and e l e c t r i c - f i e l d d i s t r i b u t i o n i n t h e c e l l a r e s t r o n g l y d e p e n d e n t on t h e gap d e n s i t y o f s t a t e s .

In t h e second p a r t o f t h i s t h e s i s ( c h a p t e r IV) a method b a s e d on s p a c e - c h a r g e - l i m i t e d c u r r e n t measurements i s o u t l i n e d t o d e t e r m i n e t h e midgap d e n s i t y o f s t a t e s i n a - S i : H . The s p a c e - c h a r g e - l i m i t e d c u r r e n t i s measured i n + + n - l - n sandwich d e v i c e s o f a - S i : H . T h i s method y i e l d s t h e b u l k d e n s i t y o f s t a t e s i n c o n t r a s t t o t h e p r e v i o u s l y u s e d f i e l d - e f f e c t t e c h n i q u e i n w h i c h i n t e r f a c e s t a t e s a t t h e s e m i c o n d u c t o r - i n s u l a t o r i n t e r f a c e can p l a y a dominant r o l e . D u r i n g t h e s t u d y o f e l e c t r i c a l c o n d u c t i o n i n n+- i - n+ sandwich d e v i c e s o t h e r i n t e r e s t i n g phenomena were

o b s e r v e d . T r a n s i e n t c u r r e n t s on a t i m e s c a l e o f s e c o n d s t o m i n u t e s can o c c u r a f t e r a change i n t h e a p p l i e d b i a s . These phenomena a r e due t o t h e l o n g t h e r m a l r e l e a s e t i m e s o f e l e c t r o n s t r a p p e d i n deep t r a p s . A f t e r a v o l t a g e r e d u c t i o n

t h e s t o r e d e x c e s s c h a r g e i n t h e sample forms a p o t e n t i a l b a r r i e r and r e d u c e s t h e c u r r e n t . T h i s t r a n s i e n t b e h a v i o u r i-s r e s p o n s i b l e f o r t h e s t r o n g l y enhanced n o n l i n e a r i t y o f t h e c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s under AC ( a l t e r n a t i n g c u r r e n t ) c o n d i t i o n s . A model w i l l be d e s c r i b e d t o e x p l a i n t h e t r a n s i e n t c u r r e n t s . I n t h i c k e r n+- i - n+ d e v i c e s (> 2 um) t h r e s h o l d s w i t c h i n g i s o b s e r v e d a f t e r an i n i t i a l f o r m i n g p r o c e s s . Some p r o p e r t i e s o f t h e s e t h r e s h o l d s w i t c h e s w i l l be d e s c r i b e d .

R E F E R E N C E S

[ 1 . 1 ] . R.C. C h i t t i c k , J.H. A l e x a n d e r and H.F. S t e r l i n g , "The p r e p a r a t i o n and p r o p e r t i e s o f amorphous s i l i c o n " , J . E l e c t r o c h e m . S o c . 116, 77 (1969) [ 1 . 2 ] . W.E. Spear and P.G. LeComber, " I n v e s t i g a t i o n o f

t h e l o c a l i s e d s t a t e d i s t r i b u t i o n i n amorphous S i f i l m s " , J . N o n - C r y s t . S o l i d s 8-10, 727 (1972)

[ 1 . 3 ] . R . J . L o v e l a n d , W.E. Spear and A. A l - S h a r b a t y , " P h o t o c o n d u c t i v i t y and a b s o r p t i o n i n amorphous S i " , J . N o n - C r y s t . S o l i d s 13, 55 (1973)

[ 1 . 4 ] . W.E. Spear and P.G. LeComber, " S u b s t i t u t i o n a l d o p i n g o f amorphous s i l i c o n " . S o l i d S t a t e Comm. 17, 1193 (1975)

[ 1 . 5 ] . D.E. C a r l s o n and C R . W r o n s k i , "Amorphous s i l i c o n s o l a r c e l l " , A p p l . Phys. L e t t . 28, 671 (1976) [ 1 . 6 ] . A. C a t a l a n o , R.V. d ' A i e l l o , J . D r e s n e r , B.

Faughnan, A. F i r e s t e r , J . Kane, H. Schade, Z.E. Smith, G. S w a r t z and A. T r i a n o , " A t t a i n m e n t o f 10 % c o n v e r s i o n e f f i c i e n c y i n amorphous s i l i c o n s o l a r c e l l s " , P r o c . 1 6 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 Conf., San D i e g o , September 1982

[ 1 . 7 ] . P.G. LeComber, W.E. Spear and A. G h a i t h , " A m o r p h o u s - s i l i c o n f i e l d - e f f e c t d e v i c e and p o s s i b l e a p p l i c a t i o n " , E l e c t r o n . L e t t . 15, 179 (1979) [ 1 . 8 ] . Y. Hamakawa, "Recent advances i n amorphous s i l i c o n

s o l a r c e l l s " , S o l a r E n e r g y Mat. 8, 101 (1982)

[ 1 . 9 ] . M. F u k a i and S. Nagata, Amorphous S e m i c o n d u c t o r T e c h n o l o g i e s and D e v i c e s , e d . Y. Hamakawa, N o r t h - H o l l a n d , Amsterdam (1982), p . 199

[ 1 . 1 0 ] . T. Kawamura and N. Yamamoto, Amorphous S e m i c o n d u c t o r T e c h n o l o g i e s and D e v i c e s , e d . Y. Hamakawa, N o r t h - H o l l a n d , Amsterdam (1982), p. 311 [ 1 . 1 1 ] . T. H i r a i and E . Maruyama, Amorphous S e m i c o n d u c t o r

T e c h n o l o g i e s and D e v i c e s , e d . Y. Hamakawa, N o r t h - H o l l a n d , Amsterdam (1982), p . 264

F i t z g e r a l d , " E l e c t r o n i c p r o p e r t i e s o f m i c r o c r y s t a l l i n e s i l i c o n f i l m s p r e p a r e d i n a glow d i s c h a r g e p l a s m a " , J . de P h y s i q u e 42, C4-257 (1981) [ 1 . 1 3 ] . H. F r i t z s c h e , " C h a r a c t e r i z a t i o n o f glow d i s c h a r g e d e p o s i t e d a - S i : H " , S o l a r E n e r g y Mat. 3, 447 (1980) [ 1 . 1 4 ] . W.E. S p e a r , "Doped amorphous s e m i c o n d u c t o r s " , Adv.

i n Phys. 26, 811 (1977)

[ 1 . 1 5 ] . D.E. C a r l s o n and C.R. W r o n s k i , Amorphous S e m i c o n d u c t o r s , e d . M.H. B r o d s k y , S p r i n g e r - V e r l a g , B e r l i n (1979), c h a p t e r 10

[ 1 . 1 6 ] . P.G. LeComber and W.E. S p e a r , Amorphous S e m i c o n d u c t o r s , e d . M.H. B r o d s k y , S p r i n g e r - V e r l a g , B e r l i n (1979), c h a p t e r 9

[ 1 . 1 7 ] . G.H. D o h l e r and H. Heyszenau, " C o n d u c t i o n i n t h e r e l a x a t i o n r e g i m e " , Phys. Rev. B12, 641 (1975) [ 1 . 1 8 ] . A. Rose, C o n c e p t s i n P h o t o c o n d u c t i v i t y and A l l i e d

P r o b l e m s , W i l e y and Sons, New Y o r k (1963)

[ 1 . 1 9 ] . M. S i l v e r , N.C. G i l e s , E . Snow, M.P. Shaw, V. C a n n e l l a and D. A d l e r , "Study o f t h e e l e c t r o n i c s t r u c t u r e o f amorphous s i l i c o n u s i n g r e v e r s e - r e c o v e r y t e c h n i q u e s " , A p p l . Phys. L e t t . 41, 935 (1982)

[ 1 . 2 0 ] . A.R. Moore, " E l e c t r o n and h o l e d r i f t m o b i l i t y i n amorphous s i l i c o n " , A p p l . Phys. L e t t . 31, 762

(1977)

[ 1 . 2 1 ] . T. T i e d j e and A. Rose, "A p h y s i c a l i n t e r p r e t a t i o n o f d i s p e r s i v e t r a n s p o r t i n d i s o r d e r e d s e m i c o n d u c t o r s " , S o l i d S t a t e Comm. 37, 49 (1981) [ 1 . 2 2 ] . G. L u c o v s k y and T.M. Hayes, Amorphous

S e m i c o n d u c t o r s , e d . M.H. B r o d s k y , S p r i n g e r - V e r l a g , B e r l i n (1979), c h a p t e r 8

[ 1 . 2 3 ] . N.F. Mott and E.A. D a v i s , E l e c t r o n i c P r o c e s s e s i n N o n c r y s t a l l i n e M a t e r i a l s , C l a r e n d o n P r e s s , O x f o r d

2. GLOW DISCHARGE PRODUCTION OF

A-SI:H FILMS

2 , 1 . I N T R O D U C T I O N

H y d r o g e n a t e d amorphous s i l i c o n f i l m s were o r i g i n a l l y p r e p a r e d m a i n l y by glow d i s c h a r g e d e c o m p o s i t i o n o f s i l a n e i n

systems i n w h i c h t h e r a d i o f r e q u e n t ( r f ) power was i n d u c t i v e l y c o u p l e d . To o b t a i n f i l m s w i t h b e t t e r u n i f o r m i t y and l a r g e r a r e a most l a b o r a t o r i e s a r e now u s i n g c a p a c i t i v e c o u p l i n g i n p a r a l l e l p l a t e r e a c t o r s . DC glow d i s c h a r g e s a r e a l s o b e i n g u s e d . The p l a s m a c h e m i s t r y o f t h e d e c o m p o s i t i o n p r o c e s s i s e x t r e m e l y c o m p l i c a t e d and n o t y e t w e l l u n d e r s t o o d . However, t h e r a p i d development o f p l a s m a d e p o s i t e d s i l i c o n n i t r i d e and s i l i c o n d i o x i d e i n i n t e g r a t e d c i r c u i t t e c h n o l o g y h a s a i d e d i n g a i n i n g a b e t t e r u n d e r s t a n d i n g o f plasma p r o c e s s e s . Mass s p e c t r o m e t r y [ 2 . 1 ] and o p t i c a l e m i s s i o n s p e c t r o s c o p y [ 2 . 2 ] a r e used f o r p l a s m a d i a g n o s t i c s o f t h e s i l a n e glow d i s c h a r g e . N-type and p - t y p e f i l m s a r e o b t a i n e d by m i x i n g s i l a n e w i t h s m a l l amounts o f d o p i n g g a s e s s u c h as p h o s p h i n e ( P H 3 )

and d i b o r a n e ( I ^ H g ) . Gas phase d o p i n g opens up t h e p o s s i b i l i t y t o grow an a r b i t r a r y number o f doped and undoped l a y e r s w i t h an a r b i t r a r y sequence and t h i c k n e s s . T h i s p o s s i b i l i t y h a s l e d t o e l e c t r o n i c d e v i c e s s u c h as p - n - d i o d e s , p - i - n - d i o d e s , n - i - n d e v i c e s and m u l t i j u n c t i o n s o l a r c e l l s . Plasma d e c o m p o s i t i o n o f s i l a n e i s a v e r s a t i l e p r o c e s s . By a d d i n g g a s e s s u c h as methane (CH,), ammonia (NH, ) o r

germane (GeH^) mixed a l l o y s a r e o b t a i n e d w i t h band gaps v a r y i n g from 1.1 t o 5.2 eV [ 2 . 3 ] . D e p o s i t i o n o f s u c c e s s i v e l a y e r s w i t h d i f f e r e n t band gaps can be used f o r h e t e r o j u n c t i o n and tandem-type s o l a r c e l l s [ 2 . 3 ] , w h i c h can y i e l d h i g h e r c o n v e r s i o n e f f i c i e n c i e s t h a n s i n g l e - b a n d - g a p c e l l s . F o r example, t h e use o f p - t y p e a - S i C : H w i t h a l a r g e band gap o f 2.2 eV as a window l a y e r i n p - i - n s o l a r c e l l s has i n c r e a s e d t h e c o n v e r s i o n e f f i c i e n c y from 5.7 t o 8 % [ 2 . 3 ] . 2 . 2 . T H E D E P O S I T I O N A P P A R A T U S The a p p a r a t u s used f o r t h e d e p o s i t i o n o f a - S i : H f i l m s i s s c h e m a t i c a l l y d e p i c t e d i n f i g u r e 2.1. The r e a c t i o n chamber i s a q u a r t z o r p y r e x g l a s s t u b e w i t h a r e c t a n g u l a r c r o s s - s e c t i o n (3x7 cm). The f l o w r a t e o f t h e s i l a n e gas ( S i H ^ ) i s c o n t r o l l e d by an e l e c t r o n i c mass f l o w c o n t r o l l e r . A r o t a r y pump m a i n t a i n s t h e p r e s s u r e i n t h e r e a c t o r a t 0.1 t o 1 mbar. The glow d i s c h a r g e o c c u r s between two p a r a l l e l e l e c t r o d e s . The upper e l e c t r o d e i s c o n n e c t e d t o t h e 13.56 MHz r a d i o - f r e q u e n t ( r f ) power g e n e r a t o r . S u b s t r a t e s a r e p l a c e d on t h e l o w e r grounded e l e c t r o d e , w h i c h i s h e a t e d by a r a d i a n t s o u r c e . A t h e r m o c o u p l e s e n s o r w i t h a c o n t r o l u n i t i s used f o r c l o s e d - l o o p t e m p e r a t u r e c o n t r o l i n t h e r a n g e 50-350 °C. M i x t u r e s o f 1 % p h o s p h i n e (PJ^) i n s i l a n e and 1 % d i b o r a n e (I^Hg) i n s i l a n e a r e used t o d e p o s i t doped l a y e r s .

13.56 MHz RF generator matching box plasma t.c. Mass flow controller radiant y heating Pirani pressure gauge rotary pump SiH, 1% P H3 in S i H4 temperature control unit t.c. = thermocouple

Figure 2.1. Schematic representation of glow discharge deposition apparatus used for growth of a-Si:H films.

2 . 3 , D E P O S I T I O N P A R A M E T E R S AND T H E I R I N F L U E N C E ON F I L M P R O P E R T I E S

The p r o p e r t i e s o f glow d i s c h a r g e a - S i : H f i l m s depend on t h e d e p o s i t i o n p a r a m e t e r s such as s u b s t r a t e t e m p e r a t u r e , r f power l e v e l , gas f l o w r a t e , p r e s s u r e , s u b s t r a t e b i a s and d e g r e e o f d i l u t i o n o f s i l a n e i n a c a r r i e r g a s . F r i t z s c h e

[ 2 . 4 ] h a s r e v i e w e d t h e i r i n f l u e n c e on f i l m p r o p e r t i e s .

F i l m s w i t h a h i g h e l e c t r o n i c q u a l i t y a r e o b t a i n e d w i t h s u b s t r a t e t e m p e r a t u r e s Ts i n t h e range 250-325 °C. A t l o w e r

and h i g h e r Tg t h e d e n s i t y o f gap s t a t e s i n c r e a s e s ( s e e s e c t i o n 4.8). To s u s t a i n t h e glow d i s c h a r g e p r e s s u r e s i n t h e r a n g e 0.1-1 mbar a r e u s e d . F o r p r e s s u r e s h i g h e r t h a n 1 mbar p o l y m e r i z a t i o n o f s i l a n e i n t h e d i s c h a r g e o c c u r s , e s p e c i a l l y a t h i g h r f power l e v e l s . P o l y m e r i z a t i o n r e s u l t s i n c o n t a m i n a t i o n o f t h e r e a c t o r w i t h p o l y s i l a n e p a r t i c l e s and c a n l e a d t o p i n h o l e s i n t h e f i l m s .

The r f power d e n s i t y s h o u l d be k e p t low, j u s t s u f f i c i e n t t o s u s t a i n t h e glow d i s c h a r g e . H i g h r f power l e v e l s l e a d t o s t r o n g i o n bombardment o f t h e g r o w i n g f i l m , w h i c h t e n d s t o i n c r e a s e t h e number o f d e f e c t s such as m i c r o v o i d s .

The d e p o s i t i o n r a t e depends on t h e c o m b i n a t i o n o f gas f l o w r a t e , p r e s s u r e and r f power d e n s i t y . The h i g h e s t q u a l i t y f i l m s a r e o b t a i n e d w i t h low growth r a t e s

(< 0.5 nm/sec). Undoped f i l m s f o r t h i s t h e s i s were grown i n p u r e s i l a n e . When S i H ^ i s d i l u t e d i n a c a r r i e r g a s , t h e d e p o s i t i o n r a t e a l s o depends on t h e d e g r e e o f d i l u t i o n . S t r o n g d i l u t i o n o f s i l a n e i n h y d r o g e n y i e l d s m i c r o c r y s t a l l i n e f i l m s [ 2 . 5 ] - [ 2 . 6 ] w i t h c r y s t a l l i t e s i z e s o f t h e o r d e r o f 5 nm. In t a b l e 2.1 t h e s t a n d a r d d e p o s i t i o n c o n d i t i o n s a r e shown; u n l e s s o t h e r w i s e m e n t i o n e d t h e s e c o n d i t i o n s were used f o r t h e f i l m s on w h i c h t h i s t h e s i s r e p o r t s . T a b l e 2.1. S t a n d a r d d e p o s i t i o n c o n d i t i o n s S u b s t r a t e t e m p e r a t u r e 275 °C r f power d e n s i t y 50-150 mW/cm2 S i l a n e f l o w r a t e 50-100 cm3/min P r e s s u r e 0.3-0.5 mbar D e p o s i t i o n r a t e 0.3-0.6 nm/sec

2 , 4 . OTHER D E P O S I T I O N METHODS H y d r o g e n a t e d amorphous s i l i c o n f i l m s can a l s o be o b t a i n e d by o t h e r methods, i n c l u d i n g r e a c t i v e s p u t t e r i n g i n a p a r t i a l p r e s s u r e o f h y d r o g e n [ 2 . 7 ] , homogeneous c h e m i c a l v a p o u r d e p o s i t i o n (CVD) [ 2 . 8 ] , CVD o f d i s i l a n e [2.9] and p o s t h y d r o g e n a t i o n o f CVD f i l m s [ 2 . 1 0 ] . CVD f i l m s have some a d v a n t a g e s o v e r p l a s m a - d e p o s i t e d f i l m s . S p u t t e r e d and glow d i s c h a r g e f i l m s a r e s u b j e c t e d t o i o n bombardment d u r i n g growth, w h i c h may l e a d t o m i c r o v o i d s where h y d r o g e n can c l u s t e r . T h i s p r o b l e m does n o t o c c u r i n CVD, i n w h i c h f i l m s a r e d e p o s i t e d by p y r o l i t i c d e c o m p o s i t i o n o f t h e g a s . Amorphous s i l i c o n f i l m s grown by c o n v e n t i o n a l CVD o f m o n o s i l a n e ( S i H4) a t 600-700 °C c o n t a i n a n e g l i g i b l e

amount o f h y d r o g e n and, c o n s e q u e n t l y , have a low e l e c t r o n i c q u a l i t y . However, when d i s i l a n e (Si2Hg) i s used a t Tg=400-500 °C, h i g h - q u a l i t y f i l m s c o n t a i n i n g 3-4 % h y d r o g e n

a r e o b t a i n e d [ 2 . 1 1 ] .

In homogeneous CVD t h e s u b s t r a t e i s h e l d a t a much l o w e r t e m p e r a t u r e (30-300 °C) t h a n t h e r e a c t o r chamber and gas ( 6 0 0 - 7 0 0 ° C ) . Homogeneous CVD f i l m s have a l s o good e l e c t r o n i c p r o p e r t i e s . In p a r t i c u l a r , f i l m s d e p o s i t e d a t o Tg=30 C e x h i b i t i n t e r e s t i n g p r o p e r t i e s , such as a low s p i n d e n s i t y and h i g h l y e f f i c i e n t v i s i b l e p h o t o l u m i n e s c e n c e e x c e e d i n g t h a t o f c o m m e r c i a l l i g h t - e m i t t i n g d i o d e s [ 2 . 1 2 ] . O t h e r d a n g l i n g bond t e r m i n a t o r s t h a n h y d r o g e n have a l s o been i n c o r p o r a t e d i n amorphous s i l i c o n . Glow d i s c h a r g e d e c o m p o s i t i o n o f m i x t u r e s o f s i l i c o n t e t r a f l u o r i d e ( S i F ^ ) and h y d r o g e n y i e l d mixed a - S i : F : H a l l o y s w i t h good s e m i c o n d u c t i n g p r o p e r t i e s [ 2 . 1 3 ] . These f i l m s have t h e a d v a n t a g e t h a t l i g h t - i n d u c e d changes, w h i c h a r e f r e q u e n t l y o b s e r v e d i n a - S i : H (see s e c t i o n 4 . 1 0 ) , a r e n e g l i g i b l e [ 2 . 1 4 ] .

R E F E R E N C E S

[ 2 . 1 ] . G. T u r b a n , Y. C a t h e r i n e and B. G r o l l e a u , "Mass s p e c t r o m e t r y o f a s i l a n e glow d i s c h a r g e d u r i n g p l a s m a d e p o s i t i o n o f a - S i : H f i l m s " . T h i n S o l i d F i l m s 67, 309 (1980)

[ 2 . 2 ] . T. Hamasaki, M. H i r o s e and Y. Osaka, "Plasma d i a g n o s t i c d u r i n g t h e growth o f a - S i : H " , J . de P h y s i q u e 42, C4-807 (1981)

[ 2 . 3 ] . Y. Hamakawa, "Recent a d v a n c e s i n amorphous s i l i c o n s o l a r c e l l s " , S o l a r E n e r g y Mat. 8, 101 (1982)

[ 2 . 4 ] . H. F r i t z s c h e , " C h a r a c t e r i z a t i o n o f glow d i s c h a r g e d e p o s i t e d a - S i : H " , S o l a r E n e r g y Mat. 3, 447 (1980) [ 2 . 5 ] . T. Hamasaki, H. K u r a t a , M. H i r o s e and Y. Osaka,

"Low-temperature c r y s t a l l i z a t i o n o f doped a - S i : H a l l o y s " , A p p l . Phys. L e t t . 37, 1084 (1980)

[ 2 . 6 ] . W.E. S p e a r , G. W i l l e k e , P.G. LeComber and A.G. F i t z g e r a l d , " E l e c t r o n i c p r o p e r t i e s o f m i c r o c r y s t a l l i n e s i l i c o n f i l m s p r e p a r e d i n a glow d i s c h a r g e p l a s m a " , J . de P h y s i q u e 42, C4-257

(1981)

[ 2 . 7 ] . W. P a u l , A . J . L e w i s , G.A.N. C o n n e l l and T.D. Moustakas, "Doping, S c h o t t k y b a r r i e r and p-n j u n c t i o n f o r m a t i o n i n amorphous germanium and s i l i c o n by r f s p u t t e r i n g " . S o l i d S t a t e Comm. 20, 969 (1976)

[ 2 . 8 ] . B.A. S c o t t , J.A. Reimer, R.M. P l e c e n i k , E.E. S i m o n y i and W. R e u t e r , "Low d e f e c t d e n s i t y amorphous h y d r o g e n a t e d s i l i c o n p r e p a r e d by homogeneous c h e m i c a l v a p o u r d e p o s i t i o n " , A p p l . Phys. L e t t . 40, 973 (1982) [ 2 . 9 ] . S. Gau, B.R. W e i n b e r g e r , M. A k h t a r , Z. K i s s and A.G. M c D i a r m i d , " P r e p a r a t i o n o f amorphous s i l i c o n f i l m s by c h e m i c a l v a p o u r d e p o s i t i o n from h i g h e r s i l a n e s " , A p p l . P h y s . L e t t . 41, 1146 (1982) [ 2 . 1 0 ] . N. S z y d l o , D. K a p l a n and R. P o i r i e r , " P o s t - h y d r o g e n a t i o n o f CVD amorphous s i l i c o n : a p r o m i s i n g p r e p a r a t i o n p r o c e s s f o r s o l a r c e l l s " , P r o c . 3 r d E.C. P h o t o v o l t a i c S o l a r E n e r g y C o n f . ,

Cannes, O c t o b e r 1980, R e i d e l , D o r d r e c h t , p. 317 [ 2 . 1 1 ] . M. A k h t a r , V.L. D a l a i , K.R. Ramaprasad, S. Gau

and J.A. Cambridge, " E l e c t r o n i c and o p t i c a l p r o p e r t i e s o f amorphous S i : H f i l m s d e p o s i t e d by c h e m i c a l vapour d e p o s i t i o n " , A p p l . Phys. L e t t . 41, 1146 (1982)

[ 2 . 1 2 ] . D.J. W o l f o r d , B.A. S c o t t , J.A. Reimer and J.A. B r a d l e y , " E f f i c i e n t v i s i b l e l u m i n e s c e n c e from h y d r o g e n a t e d amorphous s i l i c o n " , P r o c . 16th I n t . Conf. on t h e P h y s i c s o f S e m i c o n d u c t o r s , M o n t p e l l i e r , 1982

[ 2 . 1 3 ] . A. Madan, S.R. O v s h i n s k y and E. Benn, " E l e c t r i c a l and o p t i c a l p r o p e r t i e s o f amorphous S i : F : H a l l o y s " , P h i l . Mag. B, 40, 259 (1979) [ 2 . 1 4 ] . Y. Kuwano, M. O h n i s h i , H. N i s h i w a k i , S. Tsuda and H. S h i b u y a , " P r o p e r t i e s o f amorphous S i : F : H f i l m and i t s p h o t o v o l t a i c c h a r a c t e r i s t i c s " , J a p . J . A p p l . P h y s . 20, 157 (1981)

Prometheusplein 1 2600 MG D e l f t V e r l e n g i n g : 015-2784510 I n f o r m a t i e : 015-2785678 * L O O P B O N V O O R B O E K A A N V R A G E N Aangevraagd op: 25 J u n i 1999 T i j d : 1428 U i t e r l i j k terugbezorgen op (stempel datum):

Documentgegevens ( a u t e u r / t i t e l )

Boer, Willem den.: INTERFERENCE EFFECTS AND

SPACE-CHARGE-LIMITED CONDUCTION IN AMORPHOUS SILICON

Plaatsnummer(s) Exemplaarnummer(s) - 21284012 CBmg (cB) 877506

Opmerkingen:

Uw aanvraag wordt n i e t gehonoreerd ivm.

O Afwezig O A l l e e n t e r inzage O U h e e f t t e v e e l boeken O Openstaande boete O Overig n l .

Note: Gebruikers-ID: 110657 Categorie: 03 R. Schuitema Fac. ITS-ECTM, LB 1.480 Mekelweg 4 2628 CD D e l f t Rasbak: 9 B e z o r g l o k a t i e : CBmg (cB)

3. INTERFERENCE EFFECTS IN A-SI:H

SOLAR CELLS

3 , 1 , I N T R O D U C T I O N

The improvement o f amorphous s i l i c o n s o l a r c e l l s t o e f f i c i e n c i e s h i g h e r t h a n 8 % [3.1] has b e e n m a i n l y due t o t h e o p t i m i z a t i o n o f t h e undoped m a t e r i a l and t h e p+ and

n+ c o n t a c t l a y e r s . R e l a t i v e l y l i t t l e a t t e n t i o n has b e e n p a i d t o t h e o p t i c a l o p t i m i z a t i o n o f t h e d e v i c e . T h i s o p t i m i z a t i o n can be a c h i e v e d by u s i n g o p t i m i z e d a n t i r e f l e c t i o n c o a t i n g s and h i g h l y r e f l e c t i v e back c o n t a c t s , so t h a t a maximal number o f s o l a r p h o t o n s i s a b s o r b e d i n t h e a c t i v e s e m i c o n d u c t o r l a y e r . S i n c e t h e a c t i v e l a y e r i s o n l y a few w a v e l e n g t h s t h i c k (0.3-1 ym), i n t e r f e r e n c e e f f e c t s w i l l o c c u r i n c e l l s w i t h a r e f l e c t i v e b a c k c o n t a c t f o r w e a k l y a b s o r b e d l i g h t . These e f f e c t s can be used t o improve t h e e f f i c i e n c y . S e v e r a l a u t h o r s have r e p o r t e d i n t e r f e r e n c e p e a k s i n t h e s p e c t r a l r e s p o n s e o f a - S i : H s o l a r c e l l s [ 3 . 2 ] - [ 3 . 7 ] , b u t no s y s t e m a t i c s t u d y has been c a r r i e d o u t on t h e v a r i o u s i n t e r f e r e n c e e f f e c t s . S i n c e a n a l y t i c a l t r e a t m e n t o f t h e a b s o r p t i o n i n m u l t i l a y e r s y s t e m s r e s u l t s i n e x t r e m e l y c o m p l i c a t e d f o r m u l a e , t h e c e l l s were s i m u l a t e d on computer by u s i n g t h e r e f r a c t i v e i n d i c e s o f r e a l m a t e r i a l s [ 3 . 8 ] - [ 3 . 9 ] . The c a l c u l a t i o n s a r e r e s t r i c t e d t o t h e o p t i c a l b e h a v i o u r o f t h e c e l l s . An e l a b o r a t e computer model o f a - S i : H s o l a r c e l l s w h i c h i n c l u d e s t h e i r e l e c t r o n i c b e h a v i o u r has been p u b l i s h e d by S w a r t z [ 3 . 1 0 ] . S w a r t z , however, does n o t t a k e i n t o a c c o u n t m u l t i p l e r e f l e c t i o n s i n t h e s e m i c o n d u c t o r l a y e r . In s e c t i o n 3.2 r e s u l t s o f measurements t o d e t e r m i n e t h e

o p t i c a l c o n s t a n t s o f a - S i : H w i l l be p r e s e n t e d . These r e s u l t s were used i n t h e computer c a l c u l a t i o n s . The p r o c e d u r e f o r c a l c u l a t i n g t h e o p t i c a l b e h a v i o u r o f t h i n f i l m s o l a r c e l l s i s o u t l i n e d i n s e c t i o n 3.3. T h i s p r o c e d u r e i s a p p l i e d t o a - S i : H S c h o t t k y d i o d e s o l a r c e l l s t o c a l c u l a t e t h e a b s o r p t i o n o f monochromatic l i g h t and t h e s o l a r s p e c t r u m i n t h e a - S i : H f i l m . The a b s o r p t i o n p r o f i l e s i n t h e s e m i c o n d u c t o r l a y e r w i l l a l s o be computed. F o r a s p e c i f i c c e l l t h e t h i c k n e s s and r e f r a c t i v e i n d e x o f t h e o p t i m a l a n t i r e f l e c t i o n c o a t i n g a r e c a l c u l a t e d . C o l l e c t i o n e f f i c i e n c y measurements w h i c h p r o v e t h e e x i s t e n c e o f i n t e r f e r e n c e e f f e c t s a r e p r e s e n t e d i n s e c t i o n 3.4. 3 . 2 . A B S O R P T I O N C O E F F I C I E N T MEASUREMENTS The o p t i c a l b e h a v i o u r o f a m a t e r i a l i s d e t e r m i n e d by i t s complex r e f r a c t i v e i n d e x N ( M = n ( M - j k ( M • n ( M and - k ( A ) a r e t h e r e a l and i m a g i n a r y p a r t s o f N ( A ) , r e s p e c t i v e l y . k ( A ) i s r e l a t e d t o 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 ( A ) by k ( A )=a ( A ) X/4TT . F o r p a r t i a l l y t r a n s p a r e n t t h i n f i l m s n ( A ) and ct ( A ) can be deduced from t r a n s m i t t a n c e and r e f l e c t a n c e measurements [ 3 . 3 , 3 . 1 1 ] . We used a - S i : H f i l m s w i t h t h i c k n e s s e s r a n g i n g from 0.1 t o 2.5 ym d e p o s i t e d on q u a r t z and g l a s s s u b s t r a t e s . The t r a n s m i t t a n c e was measured w i t h a Pye Unicam SP8-250 s p e c t r o p h o t o m e t e r . S i n c e no r e f l e c t a n c e u n i t was a v a i l a b l e on t h i s i n s t r u m e n t , we c o u l d n o t s i m u l t a n e o u s l y d e t e r m i n e

n ( A )

o t ( A ) .

f i l m s d e p o s i t e d a t s i m i l a r c o n d i t i o n s . ot ( A ) i s d e t e r m i n e d from t h e s e d a t a and t h e t r a n s m i t t a n c e measurements.

In f i g u r e 3.1 a ( M i s shown. The d a t a o f Z a n z u c c h i e t a l . [ 3 . 1 2 ] a r e i n good agreement w i t h t h e s e r e s u l t s , as

i n d i c a t e d i n t h e f i g u r e . F o r c o m p a r i s o n t h e a b s o r p t i o n c o e f f i c i e n t o f c r y s t a l l i n e s i l i c o n i s a l s o shown [ 3 . 1 3 ] . In t h e p h o t o n e n e r g y range where t h e s o l a r s p e c t r u m i s maximal, t h e 01 o f a - S i : H i s a b o u t one o r d e r o f magnitude h i g h e r t h a n t h a t o f c r y s t a l l i n e s i l i c o n .

Wavelength (u.m)

102 I 1 1 1 ' 1

1 2 3 4

photon energy (eV)

Figure 3,1. Optical absorption coefficient of undoped a-Si:H films. For comparison the absorption coefficient of crystalline silicon is also shown.

3 , 3 , COMPUTER S I M U L A T I O N OF O P T I C A L B E H A V I O U R OF SOLAR C E L L S

The m u l t i l a y e r c o n f i g u r a t i o n s w h i c h c o n s t i t u t e a - S i : H s o l a r c e l l s have been s i m u l a t e d on computer. F i g u r e 3.2 shows such a m u l t i l a y e r s t r u c t u r e w i t h m l a y e r s . E a c h l a y e r i i s c h a r a c t e r i z e d by i t s complex r e f r a c t i v e i n d e x Ni= n ^ - j ki < Monochromatic l i g h t i s i n c i d e n t p e r p e n d i c u l a r t o I N C I D E N T R A D I A T I O N Ni = nrjki 1 Z l ; z2 Ni = ni- j ki N = n - j k m m m i-1 ^m-l H ( z ,) = 1 H" ( z ,) = 0 mK m- 1 ' mmvv m-1' m-1 '

Figure 3.2. Multilayer configuration simulating a thin film solar cell.

the i n t e r f a c e s between t h e l a y e r s a l o n g t h e p o s i t i v e z - d i r e c t i o n . The i n t e r f a c e s a r e assumed t o be p e r f e c t l y p l a n p a r a l l e l , so t h a t i n c o h e r e n t r e f l e c t i o n s a r e a b s e n t . They a r e l o c a t e d a t z ^ , Z 2 » * • • » • • •zm - l » s o t ^ a t d.=z.-z. ..is t h e t h i c k n e s s o f t h e i - t h l a y e r . C a l c u l a t i o n s 1 1 l - l can be b a s e d e i t h e r on t h e m a g n e t i c f i e l d a m p l i t u d e o r on the e l e c t r i c f i e l d a m p l i t u d e . The m a g n e t i c f i e l d a m p l i t u d e H(z) i s , a r b i t r a r i l y , c h o s e n . H ^ ( z ) and H ^ ( z ) a r e waves p r o p a g a t i n g i n t h e p o s i t i v e and t h e n e g a t i v e z - d i r e c t i o n , r e s p e c t i v e l y , i n t h e i - t h l a y e r . F o r monochromatic l i g h t i n c i d e n t from t h e t o p i n f i g u r e 3.2 H^(z) and H ^ ( z ) a r e s u b s e q u e n t l y c a l c u l a t e d a t b o t h s i d e s o f e a c h i n t e r f a c e s t a r t i n g from t h e b o t t o m [ 3 . 1 4 ] . The s t a r t i n g v a l u e s a r e H _ ( z „ ,)=0 and H * ( z „ ,)=1. A l l q u a n t i t i e s f i n a l l y o b t a i n e d , m m-1 m m-1 ^ J s u c h as r e f l e c t i o n and a b s o r p t i o n , w i l l be n o r m a l i z e d t o t h e i n c i d e n t f l u x d e n s i t y a t t h e end o f t h e c a l c u l a t i o n s . The r e l a t i o n s h i p between H^(z^) and H7 + i / (zi )a t b o t h s i d e s o f t h e i - t h i n t e r f a c e i s g i v e n by t h e t r a n s f e r m a t r i x (3.1) where

[

— ] ~ P

"

l

The r e l a t i o n s h i p between H^(z^) and H^(z^_^) i s g i v e n b y t h e t r a n s f e r m a t r i x t T . ( d ' ) ] :

where L -> 0 exp ( y . d . )J (3.4) Here Y ^ i s t h e p r o p a g a t i o n c o e f f i c i e n t i n t h e i - t h medium: 27rN± Y i = j ~ (3.5)

The e n e r g y f l u x d e n s i t i e s I ^ ( z ) and IJ ( Z ) f o r waves i n the p o s i t i v e and t h e n e g a t i v e z - d i r e c t i o n , r e s p e c t i v e l y , a r e :

I*(z) = \ R e ( Zi) |H+(Z) I 2 (3.6)

I ^ ( z ) = \ R e ( Zi) | H ~ ( Z ) I 2 (3.7)

i s t h e impedance o f t h e i - t h medium and i s r e l a t e d t o t h e impedance ZQ o f vacuum (ZQ=377ft) by Z Z, = — (3.8) N . l The n e t e n e r g y f l u x d e n s i t y I ^ ( z ) i n t h e p o s i t i v e z - d i r e c t i o n i s I±( z ) = I+(z) - I ~ ( z ) + J±( z ) (3.9) where J . ( z ) i s an i n t e r f e r e n c e t e r m : i J±( z ) = - Im(Zi) Im{H+(z)H~* (z) } (3.10)

The r e f l e c t a n c e R o f t h e m u l t i l a y e r c o n f i g u r a t i o n i s g i v e n by

(3.11)

+

Medium 1 ( a i r ) i s assumed t o be l o s s f r e e , so I j and 1^ a r e i n d e p e n d e n t o f z. The f r a c t i o n a l a b s o r p t i o n A^ i n t h e i - t h medium n o r m a l i z e d t o t h e i n c i d e n t f l u x i s : K z . J - i ( z , ) Ai = =—=— (3.12) Tl Assuming a quantum e f f i c i e n c y o f u n i t y we d e f i n e a n o r m a l i z e d < i - t h medium: n o r m a l i z e d e l e c t r o n - h o l e p a i r g e n e r a t i o n r a t e G ^ ( z ) i n t h e 1 where d l dz = - R e ( Zi) R e ( Y±) J I H+ ( z) I 2 + IH (z) |2} + 2 l m ( zi) T m ( yi) Re | H+ (z) H~* (z) } (3.14)

F o r a i r mass one (AMI) i l l u m i n a t i o n t h e f r a c t i o n a l a b s o r p t i o n A^0^3''" o f p h o t o n s i n t h e i - t h medium i s g i v e n b y

Ai °tal = jAi U ) " t o t a l d X (3.15)

t o t a l p h o t o n f l u x o f a r e l e v a n t p a r t o f t h e s p e c t r u m o v e r w h i c h we i n t e g r a t e . The g e n e r a t i o n r a t e under AMI

• i •. „total . . . i l l u m i n a t i o n G^ ( z ) i s w r i t t e n a s : = J G1( Z , ; _ t o t a l , . j „ , ,, s ( \ ) i ( z) " IG i ( z ' A ) p î a l d A <3-1 6> 3 . 3 . 1 . A B S O R P T I O N I N T H E A - S I : H F I L M

The computer model h a s been a p p l i e d t o S c h o t t k y d i o d e a - S i : H s o l a r c e l l s as shown i n t h e i n s e t o f f i g u r e 3.3. The back c o n t a c t i s e i t h e r molybdenum (low r e f l e c t i v e ) o r s i l v e r

( h i g h l y r e f l e c t i v e ) . The t r a n s p a r e n t S c h o t t k y m e t a l c o n t a c t i s 7.5 nm g o l d . Data f o r t h e r e f r a c t i v e i n d i c e s o f t h e m e t a l s were t a k e n from r e f . [ 3 . 1 5 ] . F i g u r e 3.3 shows t h e c a l c u l a t e d a b s o r p t i o n v e r s u s A i n t h e a - S i : H f i l m f o r a c e l l o f 0.35 urn t h i c k n e s s and e i t h e r a s i l v e r o r a molybdenum back c o n t a c t . The c e l l w i t h t h e s i l v e r b a c k c o n t a c t e x h i b i t s an i n t e r f e r e n c e peak i n t h e l o n g w a v e l e n g t h r e g i o n . F o r s h o r t w a v e l e n g t h l i g h t b o t h c u r v e s c o i n c i d e , s i n c e t h i s i s c o m p l e t e l y a b s o r b e d b e f o r e r e a c h i n g t h e b a c k c o n t a c t . When an a n t i r e f l e c t i o n ( a . r . ) c o a t i n g w i t h r e f r a c t i v e i n d e x n=2 and t h i c k n e s s d=45 nm i s added, t h e a b s o r p t i o n i n t h e a - S i : H l a y e r i s a l m o s t d o u b l e d , as i l l u s t r a t e d i n f i g u r e 3.4. When t h e t h i c k n e s s o f t h e a - S i : H f i l m i s changed, t h e i n t e r f e r e n c e peak s h i f t s on t h e w a v e l e n g t h s c a l e and c a n become l e s s e f f e c t i v e when i n t e g r a t e d o v e r t h e s o l a r s p e c t r u m . T h i s i s shown i n f i g u r e 3.5 where t h e AMI i n t e g r a t e d a b s o r p t i o n o f a c e l l w i t h a . r . c o a t i n g i s p l o t t e d as a f u n c t i o n o f a - S i : H f i l m t h i c k n e s s t . The

i n t e g r a t i o n i s p e r f o r m e d o v e r t h e w a v e l e n g t h r e g i o n 400-800 nm, s i n c e t h e c o n t r i b u t i o n o f l o n g e r w a v e l e n g t h p h o t o n s t o t h e p h o t o c u r r e n t i s n e g l i g i b l e . R e l a t i v e maxima o c c u r a t t=0.18, 0.27, 0.35, 0.43, 0.51, 0.60 and 0.69 ym. The p o s i t i o n o f t h e s e maxima depends m a i n l y on t h e r e a l p a r t o f t h e r e f r a c t i v e i n d e x n ( X ) . F o r d i f f e r e n t f i l m d e p o s i t i o n c o n d i t i o n s n(X) m i g h t be s l i g h t l y d i f f e r e n t from t h e v a l u e s used i n t h e c a l c u l a t i o n s , w h i c h r e s u l t s i n a s m a l l s h i f t o f t h e maxima. F o r a molybdenum back c o n t a c t t h e i n c r e a s e i n /AMI i n t e g r a t e d a b s o r p t i o n w i t h t h i c k n e s s i s monotonous. The

100 7.S nm Au 0.35 u.m a - S i : H back c o n t a c t 80 Mo b a c k contact C r ( 2 n m ) - A g back c o n t a c t 60 O Q-O X) nj 0 ¿00 500 600 700 w a v e l e n g t h (nm)

Figure 3.3. Calculated spectral absorption in a~Si;H film for cell shown in the inset.

a b s o r p t i o n i n a 0.35 ym s i l v e r back c o n t a c t c e l l i s c o n s i d e r a b l y l a r g e r t h a n i n a 0.4 ym c e l l and i s a l m o s t e q u a l t o t h e /AMI a b s o r p t i o n i n a 0.55 ym c e l l . From t h e e l e c t r o n i c p o i n t o f v i e w a 0.35 ym c e l l i s p r e f e r a b l e t o a 0.55 ym c e l l , b e c a u s e t h e r a t i o o f d r i f t l e n g t h t o c e l l t h i c k n e s s i s h i g h e r , so t h a t r e c o m b i n a t i o n i s r e d u c e d . In p r a c t i c a l c e l l s an n+- l a y e r i s r e q u i r e d t o o b t a i n an

ohmic back c o n t a c t . T h i s l a y e r c a n be i n t r o d u c e d as a dead l a y e r i n t h e computer program. E l e c t r o n - h o l e p a i r s g e n e r a t e d i n t h i s l a y e r do n o t c o n t r i b u t e t o t h e

WAVELENGTH (nm)

Figure 3.4. Calculated spectral absorption in a-Si:H film for cell shown in the inset.

p h o t o c u r r e n t , b e c a u s e t h e r e c o m b i n a t i o n t i m e i s v e r y s h o r t i n h i g h l y doped l a y e r s . The n - l a y e r w i l l n o t s i g n i f i c a n t l y a f f e c t t h e r e s u l t s , s i n c e i t s t h i c k n e s s (5 t o 10 nm) i s s m a l l compared t o t h e undoped l a y e r t h i c k n e s s . The model can be a d a p t e d f o r p - i - n c e l l s by i n t r o d u c i n g t h e p+- l a y e r as a dead l a y e r as w e l l . p+- l a y e r s have a l a r g e r a b s o r p t i o n c o e f f i c i e n t t h a n undoped f i l m s and c o n s e q u e n t l y t h e o p t i c a l b e h a v i o u r o f p - i - n c e l l s w i l l be d i f f e r e n t , e s p e c i a l l y f o r c e l l s i l l u m i n a t e d t h r o u g h t h e p+- l a y e r . IF 0-01 $ m < Ü 0.5 -• Mo back c o n t a c t A g b a c k c o n t a c t 0.1 0.2 0.3 0.4 0.5

A-Si:H FILM THICKNESS (urn)

0.6

Figure 3.5. Total absorption integrated over the solar spectrum as a function of a-Si:H film thickness.

3 . 3 . 2 . O P T I M I Z A T I O N OF A N T I R E F L E C T I O N C O A T I N G S

F o r a g i v e n s o l a r c e l l c o n f i g u r a t i o n t h e optimum r e f r a c t i v e i n d e x n and t h i c k n e s s d f o r an a . r . c o a t i n g a r e found by c a l c u l a t i n g t h e AMI i n t e g r a t e d a b s o r p t i o n i n t h e a - S i : H f i l m f o r a range o f v a l u e s o f n and d. T h i s i s shown i n t a b l e 3.1« A i s i n t h i s c a s e n o r m a l i z e d t o t h e optimum v a l u e . F o r t h e s i l v e r b a c k c o n t a c t c e l l w i t h t=0.35 um t h e optimum v a l u e s a r e n=2.3 and d=40 run. The c o m b i n a t i o n s f o r w h i c h t h e AMI i n t e g r a t e d a b s o r p t i o n i s l e s s t h a n 1% below t h e maximimum a r e u n d e r l i n e d . They l i e i n a r a n g e f o r w h i c h t h e p r o d u c t o f n and d i s a p p r o x i m a t e l y c o n s t a n t . T h i s shows t h a t a b r o a d r a n g e o f r e f r a c t i v e i n d i c e s a r e s u i t a b l e , p r o v i d e d t h e t h i c k n e s s i s a p p r o p r i a t e l y c h o s e n . T a b l e 3.1. AMI i n t e g r a t e d a b s o r p t i o n as a f u n c t i o n o f r e f r a c t i v e i n d e x and t h i c k n e s s o f a . r . c o a t i n g \ . n d (nrajN. 2.0 2.1 2.2 2.3 2.4 2.5 2.6 32 0.886 0.985 0.989 35 0.913 0.981 0.995 0.990 37 0.956 0.977 0.992 0.997 0.969 40 0.976 0.992 1 0.998 43 0.989 0.998 0.998 0.989 45 0.993 0.998 0.993 0.979 47 0.984 0.995 0.995 0.985 0.965 0.937 0.904 50 0.988 0.992 0.985 0.966 0.941 0.907 0.868