ELECTRONIC STRUCTURE OF AMORPHOUS SiOx

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ELECTRONIC STRUCTURE OF AMORPHOUS SiOx

E. Martínez, F. Ynduráin

To cite this version:

E. Martínez, F. Ynduráin. ELECTRONIC STRUCTURE OF AMORPHOUS SiOx. Journal de

Physique Colloques, 1981, 42 (C4), pp.C4-1021-C4-1024. �10.1051/jphyscol:19814223�. �jpa-00220853�

CoZZoque

suppldment au nolO, Tome

octobre 1981

ELECTRONIC STRUCTURE OF AMORPHOUS SiO,

E. ~ a r t i n e z and F. ~ n d u r 6 i n

Departamento de ~ i s i c a Fundamental, Universidad ~ut6noma de Madrid, Canto BZanco, Madrid

Spain

Abstract.-The e l e c t r o n i c s t r u c t u r e of amorphous SiO, ( 0 ,< X 6 2) i s s t u d i e d i n o r d e r t o c h a r a c t e r i s e t h e d i s t r i b u t i o n of S i and 0 atoms i n t h e a l l o y . Our r e s u l t s a r e i n e x c e l l e n t agreement w i t h p h o t o e m i s s i o n d a t a a s w e l l a s w i t h o p t i c a l a b s o r p t i o n measurements. Our c a l c u l a t i o n s i n d i c a t e t h a t t h e r e i s no s h o r t - r a n g e o r d e r such a s (Si04)ySil-y and t h e d i s t r i b u t i o n of s i l i c o n and oxygen atoms i s random w i t h no oxygen-oxygen bonds, t h e Si-0-Si bond a n g l e f o r SiO b e i n g s m a l l e r (%12O0) t h a n f o r Si02 (144O). The n o n - l i n e a r v a r i a t i o n of t h e SiO, gap w i t h c o n c e n t r a - t i o n i s r e l a t e d t o t h e b r e a k i n g of S i c h a i n s i n t h e a l l o y . The i m p l i c a - t i o n s of o u r r e s u l t s on t h e e l e c t r o n i c p r o p e r t i e s of t h e S i / S i 0 2 i n t e r - f a c e a r e a l s o d i s c u s s e d .

We have performed a t h e o r e t i c a l s t u d y of t h e e l e c t r o n i c s t r u c t u r e of amorphous SiO,. Although t h e s t u d y of SiOx i s v e r y i n t e r e s t i n g by i t s e l f , o u r f i n a l g o a l i s t o s t u d y t h e i n t e r f a c e Si-SiOz where a n amorphous t r a n s i t i o n r e g i o n of SiO, i s formed (1)

.

The main q u e s t i o n s we want t o answer i n t h i s work a r e : ( i ) Which i s t h e l o c a l bonding i n a-SiO,?

( i i ) Which a r e t h e bonding s t a t i s t i c s of SiOx ( i . e . random-bonding model o r mix- t u r e model)?

( i i i ) Which i s t h e a t o m i c s t r u c t u r e of t h e a l l o y and i n p a r t i c u l a r which i s t h e bond a n g l e Si-0-Si?

( i v ) What i s t h e e l e c t r o n i c s t r u c t u r e a t t h e Si-Si02 i n t e r f a c e when t h e r e i s a t r a n s i t i o n r e g i o n between S i and SiO

2?

To d e s c r i b e t h e e l e c t r o n i c s t r u c t u r e of SiO, we h a v e used a t i g h t - b i n d - i n g h a m i l t o n i a n which i n c l u d e s t h e 3s and 3p o r b i t a l s of S i and t h e 2s and 2p o r b i - t a l s of 0. I n t h e c a s e of t h e S i - S i bond we t a k e i n t o a c c o u n t a l l p o s s i b l e i n t e r a c - t i o n s between t h e o r b i t a l s i n n e a r e s t - n e i g h b o u r atoms whereas i n t h e Si-0 bond o n l y a - l i k e i n t e r a c t i o n s a r e t a k e n . T h i s h a m i l t o n i a n g i v e s a v e r y good d e s c r i p t i o n of t h e e l e c t r o n i c s t r u c t u r e of b o t h a-Si (2) and a-Si02 ( 3 ) .

We now d i s c u s s s e p a r a t e l y t h e f o u r p o i n t s mentioned above.

( i ) To s i m u l a t e t h e s t r u c t u r e of SiO, we assume t h e f o l l o w i n g :

a ) The sp3 h y b r i d i s a t i o n of t h e S i atom i s k e p t i r r e s p e c t i v e of t h e k i n d of t h e i r n e a r e s t - n e i g h b o u r atoms. T h i s i s s u p p o r t e d by t h e f a c t t h a t e l e c t r o n d i f f r a c t i o n measurements f o r a-SiO, ( 0 6 X g 2 ) f i l m s (4) i n d i c a t e t e t r a h e d r a l coor- d i n a t i o n of t h e S i atoms.

b) No oxygen-oxygen bonds a r e a l l o w e d i n t h e s t r u c t u r e .

c ) The c o n t i n u o u s random network of atoms forms a Bethe l a t t i c e w i t h no

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814223

C4-1022 JOURNAL DE PHYSIQUE

c l o s e d r i n g s o f bonds. The c a l c u l a t i o n f o l l o w s t h e c l u s t e r - B e t h e l a t t i c e model p r o c e d u r e ( 5 ) . i i ) I n o r d e r t o d e t e r m i n e t h e bonding s t a t i s - t i c s of a-SiOxwe have s t u d i e d t h e v a r i a t i o n of t h e o p t i c a l a b s o r p t i o n w i t h c o n c e n t r a t i o n . R e s u l t s of o u r c a l c u l a t i o n s of t h e e n e r g y gap (Eg) f o r a random d i s t r i b u t i o n of atoms a l o n g w i t h t h e e x p e r i m e n t a l r e s u l t s ( 6 ) a r e shown i n F i g u r e 1. We i n t e r p r e t t h e a b r u p t change of Eg a t X = 1 . 4 a s b e i n g r e l a t e d t o t h e p e r c o l a t i o n t h r e s h o l d ( 7 ) . It c a n b e shown (3) t h a t f o r e n e r g i e s n e a r t h e S i gap t h e SiOx s t r u c t u r e i s e q u i v a l e n t t o t h e two n o n - i n t e r a c t i n g s t r u c - t u r e s ; one formed by S i and t h e o t h e r one by S i - 0 ( s e e F i g u r e 2 ) . It c a n a l s o b e shown (3) t h a t a s l o n g a s t h e r e a r e i n f i n i t e ( l o n g enough) S i c h a i n s i n t h e a l l o y t h e t o p of t h e v a l e n c e band i s t h e same a s i n a-Si. I f t h e d i s t r i b u t i o n i s random t h e d i s a p p e a r a n c e of i n - f i n i t e S i c h a i n s (which i s r e l a t e d t o t h e p e r - c o l a t i o n t h r e s h o l d ) t a k e s p l a c e a t x c = 1 . 3 3 i n good agreement w i t h e x p e r i m e n t s . One c a n a l s o c a l c u l a t e t h e p e r c o l a t i o n t h r e s h o l d f o r d i s t r i - b u t i o n o t h e r t h a n random. I n p a r t i c u l a r i f SiO, i s l i k e Siy(SiOq)l-y X, = 1 . 7 7 and i f i t i s a s i n ( S i - S i 4 ) y ( S i 0 4 ) l - y t h e n x c = 1 . 8 7 i n

1 0 0.5 1.0 1.5 2.O

F i g . 1: V a r i a t i o n of t h e o p t i c a l gap of

a-SiO, v s c o n c e n t r a t i o z X. Block s q u a r e s Oxygen c o n c e n t r a t i o n i n d i c a t e t h e o r e t i c a l r e s u l t s and t h e s t a r s

i n d i c a t e e x p e r i m e n t a l d a t a ( r e f . 6 ) . The t h e o r e t i c a l r e s u l t s h a v e been s h i f t e d i n energy f o r a b e t t e r comparison w i t h e x p e r i - ments.

F i g . 2: Two-dimensional s i m u l a t i o n of t h e d e c o u p l i n g of t h e a-SiO, network. ( a ) a-SiO, network. (b) S i - l i k e network and ( c ) Si02- l i k e network. Open and b l o c k c i r c l e s i n d i c a t e oxygen and s i l i c o n atoms r e s p e c t i v e l y .

t i o n h a s a s t r o n g tendency t o b e random s i n c e t h e m i x t u r e d i s t r i b u t i o n ( 8 ) g i v e s a n X much h i g h e r t h a n t h a t experimen- t a l l ? o b s e r v e d .

i i i ) The o p t i c a l a d s o r p t i o n i s i n d e e d i n d e p e n d e n t o f t h e Si-0-Si bond a n g l e 8 , t h e r e f o r e i n o r d e r t o g a i n some i n s i g h t i n t o t h e s t r u c t u r e of SiOx we h a v e looked a t p h o t o e m i s s i o n measurements of SiO ( 9 ) . I n F i g u r e 3 ( a ) we h a v e shown t h e photo- e m i s s i o n s p e c t r u m of SiO and i n F i g u r e s 3(b) and 3 ( c ) o u r c a l c u l a t e d d e n s i t i e s of s t a t e f o r a random d i s t r i b u t i o n and f o r 8 = 144" ( a s i n a - q u a r t z ) and 8=125"

r e s p e c t i v e l y . We g e t a good agreement between t h e o r y and e x p e r i m e n t s f o r 0 = 1 2 5 " i n agreement w i t h c h e m i c a l s h i f t a n a l y s i s (10) a t t h e Si-SiO i n t e r f a c e . The double-peak s t r u c t u r e 0% t h e c a l c u - l a t e d d e n s i t y of s t a t e s a t 2. -2 eV is due t o t h e a b s e n c e of 0-0 and ppn i n t e r a c - t i o n s i n t h e Si-0 bond i n t h e h a m i l t o n - i a n .

i v ) I11 o r d e r t o s t u d y t h e e f f e c t of t h e p r e s e n c e of a n amorphous l a y e r a t t h e Si-SiO2 i n t e r f a c e , we h a v e c a l c u l a t e d t h e d e n s i t y of s t a t e s when t h e r e is a l a y e r o f SiOOe5 between S i and S i 0 2 ( s e e F i g u r e 4 ) . I n o u r c a l c u l a t i o n , t h e Si-0-Si

ENERGY [ e V )

F i g . 3: E l e c t r o n i c s t r u c t u r e of SiO.

( a ) E x p e r i m e n t a l UPS d a t a ( r e f . 9 ) . b) C a l g u l a t e d d e n s i t y of s t a t e s f o r

6

.

.

Energy tevl

T.. r i g 4: L o c a l d e n s i t y of s t a t e s a t a s i l i c o n atom i n t h e SiOo.5 l a y e r d e s c r i b e d i n t h e t e x t between S i and S i 0 2 . E i n d i c a t e s t h e t o p of t h e S i v a l e n c e band. v

C4-1024 JOURNAL DE PHYSIQUE

bond a n g l e a t t h e i n t e r f a c e is 1 2 5 9 u r r e s u l t s o u r shown i n F i g u r e 4. The m a i n e f f e c t o f t h e p r e s e n c e o f t h e i n t e r f a c e SiOo.5 l a y e r is t o i n d u c e l o c a l i s e d s t a t e s a t t h e S i g a p 0 . 1 eV a b o v e t h e t o p of t h e s i l i c o n v a l e n c e b a n d .

Acknowledgements.- P a r t o f t h i s work was s u p p o r t e d by t h e U.S.-Spain F r i e n d s h i p C o o p e r a t i v e T r e a t y , Complementary Agreement No. 3.

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