Computer simulation of sputtering

Computer simulation of sputtering

Volume 32A, number 5 PHYSICS LETTERS COMPUTER SIMULATION OF 1U August 1970 SPUTTERING D. OSTRY and R. J. MacDONALD Department of P h y s i c s...

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Volume 32A, number 5

PHYSICS LETTERS

COMPUTER

SIMULATION

OF

1U

August 1970

SPUTTERING

D. OSTRY and R. J. MacDONALD Department of P h y s i c s . School o f General Studzes, Australian National Un~uers~ty. Canberra A. C. T. Received 16 June 1970

A brief descriptmn of the preliminary results of the computer s,mulation of the sputtering of single crystals of Ge with 1 keV Ar + ions is presented. The simulation reproduces experimental ejection patterns very well. Focussing events are not observed to contmbute to the electron pattern. All sputtered atoms are the result of collisions similar to those described m previous slmulatmn expemments on Cu.

The f i r s t r e p o r t s of c o m p u t e r s i m u l a t i o n of s p u t t e r i n g a p p e a r e d s o m e y e a r s ago [1] and the r e s u l t s w e r e r a t h e r r a d i c a l in that they s u g g e s t e d that the contribution of f o c u s s e d c o l l i s m n s e q u e n c e s to the s p u t t e r e d atom e j e c t i o n p a t t e r n was n e g l i g i b l e . Since then the published r e s u l t s h a v e been c r i t i c i s e d [2] and defended [3]. While we c o n c e d e that s p u t t e r i n g s i m u l a t i o n does not take account of d a m a g e and c o n s i d e r s only an i d e a l l a t t i c e , we b e l i e v e they do give s o m e i n d i cation of the c o l l i s i o n s l e a d i n g to s p u t t e r e d a t o m e l e c t i o n . C o m p u t e r s i m u l a t i o n has been applied to the s p u t t e r i n g of g e r m a n i u m s i n g l e c r y s t a l s and the r e s u l t s a g r e e e x t r e m e l y w e l l with the e x p e r i m e n t a l r e s u l t s published r e c e n t l y [4]. Full d e t a i l s of the computation p r o c e d u r e will be p u b l i s h ed in the n e a r future. In b m e i the s t a n d a r d t ech n i q u e of s o l v i n g the equatton oi m o t i o n in a n u m b e r of s u c c e s s i v e s m a l l t i m e i n t e r v a l s is used to c a l c u l a t e the position and v e l o c i t y of the a t o m s in the model. T h e b a s i c c r y s t a l block is about 200-250 a t o m s but a s h e l l m o d e l is used to r e d u c e c o m p u t in g t i m e . In this m o d e l , only a t o m s in a s m a l l i n n e r s h e l l a r e i n i t i a l l y c o n s i d e r e d and a s the c a s c a d e builds up the s h e l l s i z e i n c r e a s e s to take into account m o r e a t o m s . A fifth o r d e r n u m e r i c a l i n t e g r a t i o n is used i n v o l v i n g a ' p r e d i c t o r - c o r r e c t o r ' t e c h nique which k e e p s a continual check on the q u a d r a t u r e e r r o r . T h e l a t t e r is n e v e r allowed to e x c e e d a p r e - s p e c i f i e d v a lu e of usually 0.03%. The r e s u l t a n t e r r o r in total e n e r g y at the end of the run is l e s s than 0.5%. T he i n t e r a t o m i c p o t e n t i a l is a B o r n - M a y e r p o t e n t i a l with the A b r a h a m s o n c o n s t a n t s , m a t c h e d to a M o r s e p o t e n t i a l such that the i n t e r a c t i o n at the e q u i l i b r i u m d i s t a n c e is z e r o and

the potential p r e d i c t s c o r r e c t v a l u e s of s o m e e l a s t i c co n st an t s and the s u b l i m a t i o n en er g y . One run was p e r f o r m e d using the H a r r i s o n co n st an t s [3] and although the shape of the e j e c tion p a t t e r n did not change, t h e r e was a n o t i c e able d i f f e r e n c e in c o n t r a s t between the spots and background. This o b s e r v a t i o n has not been e x p l o r e d any f u r t h e r . I m p a c t points w e r e chosen at r a n d o m to c o v e r a r e p r e s e n t a t i v e a r e a of the unit c e l l of the s u r face. Suitable r o t a t i o n and r e f l e c t i o n would c o v e r the whole unit cell. Two s u r f a c e s t r u c t u r e s w e r e c o n s i d e r e d , n a m e l y the i d eal (100) Ge s u r l a c e and a s h g h t l y modified f o r m of the r e c o n s t r u c t e d (100) Ge s u r f a c e s u g g e s t e d by the low e n e r g y e l e c t r o n d i f f r a c t i o n e x p e r i m e n t s of L a n d e r and M o r r i s o n [5]. A step function s u r f a c e binding e n e r g y was used r a t h e r than the p r o b a bility type function d e s c r i b e d by H a r r i s o n [1]. T h e r e is so l i t t l e known about the b e h a v i o u r of the s u r f a c e binding e n e r g y under the d y n am i c conditions found in t h e s e e x p e r i m e n t s that we b e l i e v e both types of binding e n e r g y to be a r t i f i ci al . A g r e e m e n t with e x p e r i m e n t was c l o s e s t when binding e n e r g i e s of 1-2 eV w e r e used. T h i s is s i m i l a r to the v a l u e s given by H a r r i s o n f o r Cu. Th e s i m u l a t e d e j e c t i o n p a t t e r n f r o m a (100) 1deal Ge s u r f a c e b o m b a r d e d with 1 keV A r + ions is shown in fig. 1. Th e p a t t e r n should be c o m p a r e d with those shown in ref. [4], when the c r y s t a l t e m p e r a t u r e is above the t r a n s i t i o n t e m p e r a t u r e f o r an n eal i n g of the ion induced d i s o r d e r . Th e a g r e e m e n t is e x c e l l e n t with both s i m u l a t i o n and e x p e r i m e n t giving spots along the (111> d i r e c t i o n and a s q u a r e background o r i e n t e d with r e s p e c t to the i n t e r s e c t i o n of (100) p l a n e s

303

PHYSICS

Volume 32A n u m b e r 5

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Fig 1. Ejection pattern obtained on a flat plate collector when the sputtering of Ge(100) is mmulated. Ar* energy 1 keV, binding energy 2 eV. w i t h t h e s u r f a c e of t h e c r y s t a l . T h e p a t t e r n in h g . 1 i n c l u d e s e j e c t i o n up to a n g l e s of ~ = arctan 3 from the surface normal. The experim e n t a l r e s u l t s d o n o t i n c l u d e m u c h b e y o n d ~? = a r c t a n 1.5. T h e e j e c h o n p a t t e r n f r o m t h e r e c o n s t r u c t e d s u r f a c e i s v e r y s i m i l a r to t h a t i n f i g . 1, e x c e p t t h a t t h e s p o t s a r e m o r e d i f f u s e a n d contrast between spots and background conseq u e n t l y l e s s t h a n t h a t m fig. 1. The most important results come Irom analy s i s of t h e t r a j e c t o r i e s r e s u l t i n g in s p u t t e r e d a t o m e j e c t i o n . W e s u g g e s t e d in r e f . [4] t h a t t h e r e m i g h t p o s s i b l y b e a {111} f o c u s m n g in Ge. W e c a n f i n d no e v i d e n c e of s u c h a n e v e n t m t h e mmulation. All the ejectmns result from collis t u n s v e r y s i m i l a r to t h o s e d e s c r i b e d b y H a r r i son. The most common event we have observed s o f a r i n v o l v e s t h e s t r u c k a t o m on t h e G e s u r face burrowing under a surface neighbour and so

304

LETTERS

10 August 1970

p r o d u c i n g e j e c h o n . S o m e e v i d e n c e of c o r r e l a t e d colhslons propagating into the bulk lattice has been observed and more will be said about this m a later pubhcahon. Almost all sputtered a t o m s a r e t h e r e s u l t of t h e f i r s t c o l l i s i o n of t h e p r i m a r y ion m t h e l a t t i c e . T h e e j e c t i o n p a t t e r n s e e m s to b e b e s t d e s c r i b e d a s t h e r e s u l t of a p e r i o d i c d i s t r i b u t i o n of a t o m s a r o u n d a p o i n t f r o m w h i c h a t o m s a r e e j e c t e d in a r a n d o m f a s h i o n . T h i s p o i n t i s t h e p o i n t of i m p a c t of t h e i n c i d e n t ion. T h e s e c o n c l u s i o n s do n o t a g r e e w i t h t h o s e of N e l s o n a n d Von J a n n [6], w h o h a v e u s e d a s l m u l a h o n t e c h n i q u e to e v a l u a t e t h e c o n t r i b u t i o n of f o c u s s e d c o l l i s i o n s e q u e n c e s to t h e s p u t t e r e d atom ejection pattern• Their model assumed a collision occurred deep within the lattice and t h e y o b s e r v e d t h e c o r r e l a t i o n e f f e c t s of f o c u s s e d s e q u e n c e s in t h e c o l h s i o n p r o p a g a t i n g t o w a r d s t h e s u r f a c e . T h i s i s s i m i l a r to t h e o b s e r v a t i o n by Harrmon; he observed focussing events propa g a t i n g i n t o t h e c r y s t a l b u t t h a t t h e y t o o k no p a r t in t h e e j e c t i o n e v e n t s . O n l y w h e n o n e s i m u l a t e s sputtering by including the ion interacting with t h e s u r f a c e d o e s o n e o b s e r v e t h e i n d e p e n d e n c e of the ejechon pattern from focussed collision sequences.

References [1] D E. Harrison, N.S. Levy, J. P. Johnson and H. M. Effron, J. Appl. Phys. 39 (1968) 3742. [2] M . T . R o b m s o n , J Appl. Phys. 40 (1969) 2670. [3] D . E . H a r r l s o n , J. Appl. Phys 40 (1969) 3870 [4] R J.MacDonald, Phil. Mag. 21 (1970) 519. [5] J J Lander and J. Morrlson. J. Appl. Phys. 34 {1963) 1403. [6] R. S. Nelson and R. Von Jann, Can. J. Phys. 46 (1968) 747.