COMPUTER SIMULATION OF METAL-SEMICONDUCTOR AND SEMICONDUCTOR-SEMICONDUCTOR INTERFACES

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COMPUTER SIMULATION OF METAL-SEMICONDUCTOR AND SEMICONDUCTOR-SEMICONDUCTOR

INTERFACES

C. Matthai, P. Ashu

To cite this version:

C. Matthai, P. Ashu. COMPUTER SIMULATION OF METAL-SEMICONDUCTOR AND

SEMICONDUCTOR-SEMICONDUCTOR INTERFACES. Journal de Physique Colloques, 1990, 51

(C1), pp.C1-873-C1-878. �10.1051/jphyscol:19901137�. �jpa-00230048�

COMPUTER SIMULATION OF METAL-SEMICONDUCTOR AND SEMICONDUCTOR-SEMICONDUCTOR INTERFACES

C.C. MATTHAI and P. ASHU

Department of Physics, University of Wales, College of Cardiff, GB-Cardiff

CFI 3 T H , Great-Britain

Bbstract

-

A S i - G e i n t e r a t o m i c p o t e n t i a l w a s u s e d t o c a l c u l a t e t h e e n e r g y d i f f e r e n c e b e t * e e n s t r a i n e d a n d u n s t r a i n e d Ge l a y e r s on S i ( 0 0 1 ) s u b s t r a t e s a s a f u n c t i o n o f t h e n u m b e r o f l a y e r s . From t h i s we e s t i m a t e t h e c r i t i c a l t h i c k n e s s f o r d i s l o c a t i o n n u c l e a t i o n t o b e l e s s t h a n 1 2 l a y e r s . T h e embedded a t o m m e t h o d w a s u s e d t o c o n s t r u c t e m b e d d i n g f u n c t i o n s a n d p a i r i n t e r a c t i o n s f o r b u l k N i a n d

Nisi2.

T h i s a p p r o a c h w a s t h e n u s e d t o c a l c u l a t e t h e e n e r g y o f t h e N i S i 2 / S i ( l l l ) i n t e r f a c e f r o m w h i c h we f i n d t h a t t h e i n t e r f a c e i n t e r p l a n a r s e p a r a t i o n i n t h e T y p e B c a s e is less t h a n t h a t f o r T y p e A .

1 - INTRODUCTION

R e c e n t l y t h e r e h a s b e e n g r e a t i n t e r e s t i n d e v e l o p i n g s i m p l e m o d e l i n t e r a t o m i c p o t e n t i a l s w h i c h c a n b e u s e d i n t h e s t u d y o f c o m p l e x s y s t e m s . A l t h o u g h m o s t of s u c h w o r k h a s c o n c e n t r a t e d o n e l e m e n t a l s y s t e m s , t h e r e h a v e b e e n some a t t e m p t s t o c o n s t r u c t p o t e n t i a l s f o r u s e i n s y s t e m s w i t h m o r e t h a n o n e k i n d o f a t o m a s i n a l l o y s / l / a n d c o m p o u n d s 2 T h e a t o m i c s t r u c t u r e a t s e m i c o n d u c t o r i n t e r f a c e s p l a y s a v e r y i m p o r t a n t r o l e i n d e t e r m i n i n g t h e p a r a m e t e r s i n f l u e n c i n g t h e e l e c t r i c a l p r o p e r t i e s o f d e v i c e s . T h e S c h o t t k y B a r r i e r h e i g h t (SBH) a t e p i t a x i a l s i l i c i d e - s i l i c o n i n t e r f a c e s h a s b e e n shown t o b e v e r y d e p e n d e n t on t h e i n t e r f a c e i n t e r p l a n a r s e p a r a t i o n /3/ a n d t h e a t o m i c c o o r d i n a t i o n o f t h e m e t a l a t o m a t t h e i n t e r f a c e / 4 / . A t s e m i c o n d u c t o r - s e m i c o n d u c t o r

i n t e r f a c e s , c h a n g e s i n t h e a t o m i c p o s i t i o n s a t t h e i n t e r f a c e c a n l e a d t o s u b s t a n t i a l c h a n g e s i n t h e b a n d o f f s e t s . I t is t h e r e f o r e c l e a r t h a t b e f o r e s u c h q u a n t i t i e s a r e d e t e r m i n e d , a k n o w l e d g e o f t h e a t o m i c g e o m e t r y w o u l d b e v e r y a d v a n t a g e o u s .

W i t h t h e a d v e n t o f m o d e r n c r y s t a l g r o w t h t e c h n i q u e s l i k e MBE, i t h a s become p o s s i b l e t o g r o w l a t t i c e m a t c h e d ' s u p e r l a t t i c e s a n d a l s o s t r a i n e d l a y e r s u p e r l a t t i c e s . I n t h e l a t t e r c a s e t h e l a t t i c e m i s m a t c h r e s u l t s i n t h e f o r m a t i o n o f m i s f i t d i s l o c a t i o n s when t h e s t r a i n e n e r g y b e c o m e s l a r g e . O n c e a p p r o p r i a t e i n t e r a t o m i c p o t e n t i a l s a r e a v a i l a b l e i t b e c o m e s p o s s i b l e t o p e r f o r m a c o m p u t e r s i m u l a t i o n o f t h e g r o w t h p r o c e s s w h i c h w o u l d y i e l d n o t j u s t c r i t i c a l t h i c k n e s s f o r d i s l o c a t i o n n u c l e a t i o n b u t much i n f o r m a t i o n on t h e n a t u r e a n d e v o l u t i o n o f i n t e r f a c i a l s t r u c t u r e .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19901137

Cl-874 COLLOQUE DE PHYSIQUE

I n t h i s p a p e r we r e p o r t on t h e u s e o f p r e v i o u s l y c o n s t r u c t e d S i - G e p o t e n t i a l s /5/ t o d e t e r m i n e t h e a f o r e m e n t i o n e d c r i t i c a l t h i c k n e s s . We h a v e a l s o c o n s t r u c t e d N i - S i i n t e r a c t i o n f u n c t i o n s w h i c h h a v e b e e n u s e d t o s t u d y t h e r e l a x a t i o n a t t h e N i s i 2 - S i i n t e r f a c e .

2

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SILICON-GERMANIUM INTERFACE

T h e r e h a s b e e n c o n s i d e r a b l e i n t e r e s t i n t h e s t u d y o f s t r a i n i n m i s m a t c h e d e p i t a x i a l l a y e r s . H o s t o f t h e m o d e l s c a l c u l a t e t h e c r i t i c a l t h i c k n e s s ( h c ) u t i l i z i n g e n e r g y o r f o r c e b a l a n c e w i t h i n t h e f r a m e w o r k o f e l a s t i c i t y t h e o r y /6/. I n m o s t c a s e s t h e v a l u e o f hc t h u s d e t e r m i n e d i s h i g h e r t h a n t h a t f o u n d e x p e r i m e n t a l l y a n d t h i s h a s u s u a l l y b e e n t h o u g h t t o b e t h e r e s u l t o f a n i n a d e q u a t e k n o w l e d g e o f t h e n a t u r e a n d e v o l u t i o n o f t h e d i s l o c a t i o n c o n c e r n e d . C o m p u t e r s i m u l a t i o n o f s u c h s y s t e m s w o u l d g r e a t l y b e n e f i t i n t h e u n d e r s t a n d i n g o f t h e s e f a c t o r s . Of c o u r s e , t h e r e s u l t s o f s i m u l a t i o n w o u l d o n l y b e a s g o o d a s t h e d e s c r i p t i o n f o r t h e t o t a l e n e r g y . I t is i m p e r a t i v e t h a t s u c h s t u d i e s e m p l o y a n e n e r g y d e s c r i p t i o n t h a t c o r r e c t l y p r e d i c t s t h e e l a s t i c b e h a v i o u r o f s i m i l a r s y s t e m s .

I n r e c e n t y e a r s e m p i r i c a l i n t e r a t o m i c p o t e n t i a l s h a v e b e e n shown t o b e u s e f u l i n t h e s t u d y o f s u r f a c e r e c o n s t r u c t i o n s i n s i l i c o n . S t i l l i n g e r a n d Weber (SW) / 7 / c o n s t r u c t e d a t w o b o d y p l u s t h r e e b o d y p o t e n t i a l f o r s i l i c o n w h i c h m i n i m i s e d t h e e n e r g y f o r t h e d i a m o n d s t r u c t u r e . T h e t w o p a r t s o f t h e p o t e n t i a l c a n b e t h o u g h t o f a s e x t e n s i o n s t o t h e b o n d s t r e t c h a n d b o n d b e n d i n g f o r c e s o f t h e K e a t i n g m o d e l . D i n g a n d A n d e r s o n /8/ c o n s t r u c t e d p o t e n t i a l s o f t h e s a m e f o r m t o d e s c r i b e t h e c o n d e n s e d p h a s e s o f g e r m a n i u m . F o l l o w i n g t h e s u g g e s t i o n b y A b e l l / Q / t h a t a t o m i c c o o r d i n a t i o n s were a n i m p o r t a n t f a c t o r t h a t n e e d e d t o b e c o n s i d e r e d . v a r i o u s p o t e n t i a l s w e r e p r o p o s e d f o r s i l i c o n , t h e m o s t s i g n i f i c a n t b e i n g t h a t o f T e r s o f f / 1 0 / . R e c e n t l y , T e r s o f f / l l / h a s p r o p o s e d a g e n e r a l i z a t i o n o f h i s e a r l i e r m o d e l f o r S i t o d e s c r i b e t h e S i - G e a n d S i - C s y s t e m s . T h e e l a s t i c p r o p e r t i e s o f t h e l a t t e r s y s t e m a p p e a r t o b e v e r y w e l l d e s c r i b e d . We a l s o p r o p o s e d /5/ a g e n e r a l i z a t i o n o f t h e SW S i p o t e n t i a l w h i c h c o u l d b e u s e d f o r t h e S i - G e s y s t e m . T h i s w a s f o u n d t o g i v e t h e r e l a x a t i o n s i n t h e ( S i ) n ( G e ) n ( 0 0 1 ) s u p e r l a t t i c e s t r u c t u r e i n g o o d a g r e e m e n t w i t h a b i n i t i o t o t a l e n e r g y c a l c u l a t i o n s / 1 2 / . A l t h o u g h a f u l l s i m u l a t i o n s t u d y o f Ge g r o w t h on S i is b e y o n d o u r p r e s e n t c a p a b i l i t i e s , we p r e s e n t a p r e l i m i n a r y s t u d y o f c r i t i c a l t h i c k n e s s i n t h e S i - G e s y s t e m b y u s i n g a n e n e r g y b a l a n c e c r i t e r i o n f o r e s t i m a t i n g h = . A c r y s t a l b l o c k w i t h Ge a t o m s s t r a i n e d o n t o a S i ( 0 0 1 ) s u b s t r a t e w a s c o n s t r u c t e d a n d t h e e n e r g y m i n i m i s e d b y t h e m e t h o d o f m o l e c u l a r d y n a m i c s / 2 / . A d i s l o c a t i o n w a s t h e n i n t r o d u c e d a n d t h e new minimum e n e r g y d e t e r m i p e d . T h e c a l c u l a t i o n s w e r e d o n e f o r a n e d g e d i s l o c a t i o n w i t h b

=

i [ l l O ] c e n t e r e d a t t h e i n t e r f a c e a n d a t t h r e e l a y e r s a b o v e t h e i n t e r f a c e . A 6 0 ' g l i s s i l e d i s l o c a t i o n o n t h e { 1 1 1 ) p l a n e w a s a l s o c o n s i d e r e d . T h e c a l c u l a t i o n s w e r e p e r f o r m e d f o r t h e SW t y p e p o t e n t i a l m e n t i o n e d a b o v e a n d f o r a K e a t i n g p o t e n t i a l w i t h t h e p a r a m e t e r s f i t t e d t o r e p r o d u c e t h e a b i n i t i o d e t e r m i n e d r e l a x a t i o n s i n ( S i ) n ( G e ) n s u p e r l a t t i c e s . T h e d i f f e r e n c e i n e n e r g y o f t h e s t r a i n e d s y s t e m , E=, a n d t h e s y s t e m w i t h t h e e d g e d i s l o c a t i o n c e n t e r e d a t t h e i n t e r f a c e , E,, f o r v a r y i n g number o f Ge l a y e r s is shown i n f i g u r e 2 .

t h e i n t e r f a c e

GERMANIUM THICKNESS/A

F i g 2 . T h e e n e r g y d i f f e r e n c e (Ed - E=) p l o t t e d a s a f u n c t , i o n o f t h e number o f Ge l a y e r s f o r t h e SW p o t e n t i a l ( f u l l l i n e ) a n d t h e K e a t i n g p o t e n t i a l ( b r o k e n l i n e ) .

Cl-876 COLLOQUE DE PHYSIQUE

From t h e f i g u r e we e s t i m a t e hc t o b e a b o u t 1 2 a n d 1 5 l a y e r s f o r t h e SW a n d K e a t i n g p o t e n t i a l s r e s p e c t i v e l y . T h i s is t h e n a n u p p e r l i m i t o f t h e c r i t i c a l t h i c k n e s s . F o r t h e 6 0 ' d i s l o c a t i o n , h c w a s f o u n d t o b e l e s s t h a n 1 0 l a y e r s . T h i s is i n g o o d a g r e e m e n t w i t h t h e m o d e l c a l c u l a t i o n s .

3

-

N i S i 2 / S i ( l l l ) INTERFACE

Nisi2

^{i s} o f f l u o r i t e s t r u c t u r e a n d i s a l m o s t l a t t i c e m a t c h e d t o t h e S i ( 1 1 1 ) s u r f a c e . I t h a s b e e n shown t h a t when N i is d e p o s i t e d on S i ( 1 1 1 ) a t a t e m p e r a t u r e b e t w e e n 300C a n d 450C, s u b s e q u e n t a n n e a l i n g r e s u l t s i n t h e f o r m a t i o n o f

Nisiz

a t t h e i n t e r f a c e . However t h e s i l i c i d e c a n f o r m i n e i t h e r o f t w o d i f f e r e n t o r i e n t a t i o n s c a l l e d T y p e A a n d T y p e B . ( S e e f i g u r e 3 )

T u n g / 1 3 / f o u n d t h a t t h e SBH f o r t y p e B i n t e r f a c e w a s l e s s t h a n t h a t f o r t h e t y p e A b y a b o u t 0 . 1 4 e V . R e c e n t c a l c u l a t i o n s s u g g e s t t h a t t h e SBH is v e r y d e p e n d e n t on t h e i n t e r f a c e i n t e r l a y e r s e p a r a t i o n . R e e s a n d M a t t h a i /3/, u s i n g t h e X - r a y s t a n d i n g wave r e s u l t s o f V l i e g e t a 1 / 1 4 / h a v e shown a r e d u c t i o n i n t h e SBH w i t h d e c r e a s e d s e p a r a t i o n o f a m a g n i t u d e c o n s i s t e n t w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n . A more r e c e n t e x p e r i m e n t / 1 5 / h a s f o u n d t h e i n t e r l a y e r s e p a r a t i o n a t t h e t y p e A i n t e r f a c e i s s m a l l e r t h a n f o r t h e t y p e B c a s e , i n c o n t r a d i c t i o n w i t h t h e r e s u l t s o f V l i e g e t a l . I n t h i s s t u d y we h a v e c a l c u l a t e d t h e i n t e r l a y e r s e p a r a t i o n , f o r t h e two c a s e s u s i n g a n embedded a t o m t y p e a p p r o a c h .

We h a v e u s e d t h e embedded a t o m m e t h o d / l / a s a b a s i s f o r d e s c r i b i n g t h e i n t e r a c t i o n s i n b u l k N i a n d t h i s w a s t h e n u s e d , i n c o n j u n c t i o n w i t h t h e T e r s o f f p o t e n t i a l f o r m f o r S i , t o d e s c r i b e b u l k

Nisi2

a n d t h e N i s i 2 - S i i n t e r f a c e s t r u c t u r e s . F o r t h e e m b e d d i n g f u n c t i o n we h a v e c h o s e n t o u s e t h e s q u a r e r o o t f o r m a s i n t h e F i n n i s - S i n c l a i r Model / 1 6 / . T h e t o t a l e n e r g y f o r b u l k N i is t h u s

w h e r e pi = Z @ ( r i j ) j

T h e f u n c t i o n s V ( r ) a n d @ ( r ) w e r e t a k e n a s e x p o n e n t i a l l y d e c a y i n g f u n c t i o n s

T h e f o u r p a r a m e t e r s w e r e d e t e r m i n e d b y f i t t i n g t h e c o h e s i v e e n e r g y , v a c a n c y f o r m a t i o n e n e r g y , t h e e q u i l i b r i u m s e p a r a t i o n a n d t h e C a u c h y d i s c r e p a n c y .

T h e S i - S i i n t e r a c t i o n e n e r g y i s g i v e n b y

w h e r e V ( r ) = Asexp(-Xsr) + Bs e x p ( - p s r ) . b s

bs i s a m e a s u r e o f t h e bond o r d e r a n d t h e c o n s t a n t s a r e a s t a b u l a t e d b y T e r s o f f / 1 0 / .

a t o m s i n t h e '

Nisiz

a n d S i r e g i o n s a t t h e i n t e r f a c e . T h e N i a t o m s a r e d e n o t e d b y o p e n c i r c l e s a n d t h e S i a t o m s b y f u l l c i r c l e s .

T h e N i - S i i n t e r a c t i o n w a s t a k e n t o h a v e t h e s a m e f o r m a s t h e N i - N i i n t e r a c t i o n .

T h u s ,

a n d 9( r ) = a e x p (/JN,r)

w i t h Ans hNS = (XN + h S ) / 2 , pNS= ( p N + P,)/2

a n d CNs

= c

T h e p a r a m e t e r

P

a n d a w e r e f i t t e d t o r e p r o d u c e t h e e x p o n e n t i a l c o h e s i v e e n e r g y a n d e q u i l i b r i u m l a t t i c e s p a c i n g f o r b u l k

Nisiz.

A l l t h e i n t e r a c t i o n s w e r e a s s u m e d t o h o l d o n l y f o r n e a r e s t n e i g h b o u r s .

T a b l e 1

V a l u e s o f t h e c o n s t a n t s a p p e a r i n g i n t h e i n t e r a c t i o n e n e r g y

A ( e v ) C ( e v ) A(A) P ( A ) a I?

N i - V i 2 5 . 0 4 - 5 . 9 9 1 . 8 0 8 0 . 9 8 0

- -

N i - S i 2 8 5 9 1 - 2 3 . 8 9 2 . 5 2 4 1 . 1 5 3 0 . 5 1 . 7 T h e e n e r g i e s o f t h e t y p e A a n d t y p e B N i s i 2 - S i w e r e t h e n m i n i m i s e d

-

a n d i t was f o u n d t h a t t h e t y p e A i n t e r f a c e u n d e r g o e s n e g l i g i b l e r e l a x a t i o n c o m p a r e d w i t h a r e d u c t i o n o f 0 . 1 A i n z f o r t y p e B . T h i s is i n e x c e l l e n t a g r e e m e n t w i t h t h e r e s u l t s o f V l i e g e t a1 of 0 . 0 4 A a n d O . l l A r e s p e c t i v e l y .

COLLOQUE DE PHYSIQUE

4 - CONCLUSION

We have that it is possible to construct interatomic potentials Por compound systems starting from elemental interatomic potentials with geometric averages yielding the appropriate constants. Potentials thus constructed for Si-Ge were used to estimate the critical thickness for Ge layers on Si(OO1) substrates. Nisiz was treated in a similar fashion to elemental Ni with geometric means giving the relevant constants. It was found necessary to introduce parameters,a and

P ,

to account for the dissimilarity between the elements. Energy minimization of the Nisi2-Si(ll1) interface showed that more relaxation takes place in type B than in type A.

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