SHADOWING EFFECTS OBSERVED IN SLOW IONS BACKSCATTERING ON A METALLIC CRYSTAL : EXPERIMENTS AND SIMULATIONS

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SHADOWING EFFECTS OBSERVED IN SLOW IONS BACKSCATTERING ON A METALLIC CRYSTAL :

EXPERIMENTS AND SIMULATIONS

C. Coudray

To cite this version:

C. Coudray. SHADOWING EFFECTS OBSERVED IN SLOW IONS BACKSCATTERING ON A

METALLIC CRYSTAL : EXPERIMENTS AND SIMULATIONS. Journal de Physique Colloques,

1984, 45 (C2), pp.C2-133-C2-137. �10.1051/jphyscol:1984230�. �jpa-00223943�

JOURNAL DE PHYSIQUE

Colloque C2, supplément au n°2, Tome 45, février 1984 page C2-133

SHADOWING EFFECTS O B S E R V E D IN SLOW IONS B A C K S C A T T E R I N G ON A M E T A L L I C C R Y S T A L : E X P E R I M E N T S A N D S I M U L A T I O N S

C. Coudray

Laboratoire de Physique des Solides, Université Paris-Sud, Bât. 510, 91405 Orsay, France

Résumé - Un calcul numérique a permis de simuler des expériences de rétrodiffusion d'ions lents mettant en évidence d'importants effets d'ombrage. Ce papier en présen- te les résultats, et analyse l'origine possible des désaccords avec l'expérience.

Abstract - A numerical simulation of slow ions backscattering experiments involving important shadowing effects has been performed. In this paper, the results of this computation are given, and the possible reasons of their discrepancies with expe- riments are discussed.

I - THE EXPERIMENTS.

20 +

A fixed beam of mass-filtered Ne ions of low energy (1 to 10 keV) strikes a (100)Cu surface with a 45° oblique incidence. Amongst the backscattered 20fj

+ • j

those which satisfy the two following conditions are collected : i) the deviation of their final moment from the surface normal does not exceed 1° ; ii) their energy

ED E D

belongs to the pass-band [E„ , En + — ] , En being the binary collision energy The crystal is rotated in its surface plane, and the signal intensity I R is recor- ded as a function of >•$, ^ being the angle between the normal to the fixed plane of incidence and a direction tied to the crystal, the <100> direction for instance.

The variations of I R are shown in Fig. 1, for different primary beam energies.

Fig. 1

Experimental result : evolu- tion of the variations of the backscattered ions 20jj

+ inten sities with the incident ener- gy.

9y?]lt§tiye_study. Only the values of ^ comprise between - TT/3 and + TT/3 are shown in"FTgT"I"But~the periodic structures of the curves (with a period of ir/2),as well as their symmetries with respect to each entire multiple of IT/4 (see for instance Ref.(l)), are already apparent in this figure. These characteristics are obviously due to the crystal symmetries.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984230

C2-134 JOURNAL DE PHYSIQUE

Now t h e c o l l e c t i o n c o n d i t i o n s l i m i t t o t h e f i r s t two l a y e r s atoms t h e p o s s i b l e p a r t - ners o f a backscattered ion. I n f i r s t approximation, t h e f i r s t l a y e r atoms c o n t r i - b u t i o n i s i s o t r o p i c , t h e p r o x i m i t y e f f e c t s remaining always very small a t t h e s t u d i e d energies. So t h e v a r i a t i o n s o f I R are due t o t h e second l a y e r atoms c o l l i s i o n s . Each c r y s t a l atom deviates t h e i n c i d e n t t r a j e c t o r i e s i n such a way t h a t i t hides a whole r e g i o n o f t h e space t o t h e i n c i d e n t beam. T h i s r e g i o n (see F i g . 2 ) has t h e geome- t r i c a l shape o f a cone, t h e a x i s o f which being t h e p a r a l l e l t o t h e i n c i d e n t beam oassing through t h e atom. During t h e c r y s t a l r o t a t i o n , each second l a y e r atom des- c r i b e s a c i r c l e which successively crosses t h e f o u r shadow cones o f i t s neighbouring f i r s t la y e r atoms : f o r qA ~ ' Q B , f o r instance, i t i s n o t seen by t h e i n c i d e n t p a r t i c l e s . Then, a1 t e r n a t i v e l y ) ightened and shadowed, i t g i v e s r i s e t o t h e "crene- l a t e d " s t r u c t u r e s o f Fig. 1

Fig. 2

\ . (a, Crystal surface.

@ Flxed ~nc~dent direction ( a ) intersection of the

-a o • first layer atom shadow

0

I st layer atom cone with the second

layer plane.

2 nd layer atom . (8) characteristic area.

Flxed

o (b) The two atoms model.

crystal rotation 1

U'1 ,

Furthermore, a p r e c i s e c a l c u l a t i o n ( 2 ) shows t h a t d i f f e r e n t i n c i d e n t t r a j e c t o r i e s are c r o s s i n g themselves a t t h e edge o f t h e shadow cone, l e a d i n g t o a compression o f t h e i n c i d e n t beam i n t h i s r e g i o n - t h e "wedge-focusing" e f f e c t -,which e x p l a i n s the two peaks observed on each s i d e o f t h e "crenels".

However, t h i s two atoms model cannot e x p l a i n t h e experimental curves i n a complete way, and a c r y s t a l s i m u l a t i o n has t o be undertaken.

I 1 - THE COMPUTATIONS.

The-chmen-pmgyt-m. To simulate t h e c r y s t a l and i t s i n t e r a c t i o n s w i t h t h e i n c i d e n t

p a r t i c l e s , we have chosen t h e program MARLOWE, which works i n t h e frame o f C l a s s i c a l

Hechanics. The i n t e r a c t i o n s between p a r t i c l e s are computed as t h e r e s u l t o f b i n a r y

c o l l i s i o n s , w i t h an approximate procedure a l l o w i n g t o take i n t o account t h e s i m u l t a -

neous a c t i o n o f up t o 10 c r y s t a l atoms. Another approximation c o n s i s t s i n r e p l a c i n g

each t r a j e c t o r y by i t s asymptots i n t h e Laboratory system.

We have checked t h e v a l i d i t y o f these approximations i n some p a r t i c u l a r cases by an exact numerical Runge-Kutta i n t e g r a t i o n o f t h e equations o f motion, and shown t h a t MARLOWE leads t o s a t i s f a c t o r y r e s u l t s i n t h e c o n d i t i o n s o f our b a c k s c a t t e r i n g problem.

I_he-jngrg~jgnp-_of-_o!r-sjm!1~tjg~. Our simula i o n reproduces t h e general geometry o f t h e experiment, i.e. a f i x e d 45' o b l i q u e beam, a Cu monocrystal r o t a t i n g i n i t s (100) surface plane, and a normal c o l l e c t i o n . The d e t e c t i o n cone as w e l l as t h e energy window ( c o n d i t i o n s i ) and i i ) o f 5 I ) a r e a l s o e x a c t l y simulated.

However, t h e f o l l o w i n g s i m p l i f y i n g assumptions h o l d :

a) t h e i n c i d e n t beam i s p e r f e c t l y p a r a l l e l and monokinetic, b) t h e c r y s t a l , made up o f 6 3 ~ u atoms only, i s p e r f e c t ,

c ) n e i t h e r t h e i n e l a s t i c losses, n o r t h e n e u t r a l i z a t i o n , a r e taken i n t o account.

Ihg-tgchnj~s-of-_our-_computg;jgfi,An usual computation w i t h MARLOWE would c o n s i s t i n chosing on t h e c r y s t a l s u r f a c e an area which, due t o t h e c r y s t a l symmetries, surnma- r i z e s the whole surface, and i n bombarding randomly t h i s " c h a r a c t e r i s t i c area"

( c f . Fig. 2a 6). However, independently o f any energy consideration, t h e p r o b a b i l i t y f o r an i o n t o be backscattered w i t h a f i n a l v e l o c i t y belonging t o the d e t e c t i o n cone i s so low - from t o f o r i n c i d e n t energies v a r y i n g from 1 t o 10 keV - t h a t such a s i m u l a t i o n cannot be undertaken.

Nevertheless, t o be backscattered w i t h a s u i t a b l e f i n a l moment d i r e c t i o n , an i o n must have h i t t h e c r y s t a l surface on a p r e c i s e small f r a c t i o n o f t h e c h a r a c t e r i s t i c area. I f furthermore, i t s f i n a l energy i s comprise between two l i m i t s , t h i s f r a c t i o n i s s t i l l reduced. Now, f o r each value o f q , IR i s p r o p o r t i o n a l t o the r e s u l t i n g

"impact area". These impact areas were obtained by t h e method o f t r i a l and e r r o r w i t h t h e h e l p o f a subroutine added t o MARLOWE.

Result?. The computations were done w i t h a M o l i e r e p o t e n t i a l . The screening l e n g t h associated t o t h e Ne-Cu i n t e r a c t i o n s , t h e o n l y i n t e r a c t i o n s o f i n t e r e s t i n t h i s problem, was chosen as t h e harmonic mean o f t h e Ne-Ne and o f t h e Cu-Cu screening lengthes, t h e f i r s t one having t h e F i r s o v value, t h e second one, as suggested by Robinson ( 3 ) , being equal t o 0.0738 1. Then t h e r e s u l t s o f t h e s i m u l a t i o n are shown i n Fig. 3 .

I 1 1 - DISCUSSION

A t t h e h i g h e s t energy, t h e agreement between experiment and s i m u l a t i o n i s f a i r l y good. When t h e energy i s lowered, important s i m i l a r i t i e s remain between t h e two s e t s o f curves, b u t discrepancies do appear. F o r instance, t h e decrease o f t h e shadow cone s i z e w i t h i n c r e a s i n g energies, o r t h e wedge-focusing e f f e c t can be observed i n both s e r i e s o f diagrams, although no q u a n t i t a t i v e agreement holds between them. Furthermore, t h e computations l e a d t o a r a t i o second t o f i r s t l a y e r which i s a decreasing f u n c t i o n o f t h e i n c i d e n t energy, when t h e experimental curves show t h e o p p o s i t e tendancy. As t o t h e v a r i a t i o n s o f IR, they appear t o be very more abrupt i n t h e s i m u l a t i o n s than i n t h e experiments.

Rather than i n t h e p o t e n t i a l choice, which cannot a f f e c t i n a s u b s t a n t i a l way t h e major trends o f t h e r e s u l t s o f t h e simulations, t h e o r i g i n o f these discrepancies must be looked f o r i n t h e d i v e r s e s i m p l i f i c a t i o n s i n c l u d e d i n t h e computations.

L e t us t r y t o d i s e n t a n g l e t h e e f f e c t s o f each o f them, by g a t h e r i n g those which p r e c i s e l y g i v e r i s e t o t h e same k i n d o f consequence.

The i m p r e c i s i o n on t h e l o c a t i o n o f t h e atoms due t o t h e thermal v i b r a t i o n s leads t o

a r e l a t e d i m p r e c i s i o n on t h e impact areas, and then on the values o f IR. The Cu

second i s o t o p e gives r i s e t o a second b i n a r y peak, b u t t h i s peak i s n o t comprise

between t h e l i m i t s o f t h e chosen pass-band, and i t s o n l y consequence i s a constant

lowering o f IR, independently o f Q. Besides, a smoothing o f t h e experimental s t r u c -

JOURNAL DE PHYSIQUE

Fig. 3

Result of the simulation : variations of the backscattered intensity IR at various incident energies E. As a matter of comparison, the experimental result is drawn at 9500 eV : cvrve (b).

t u r e s r e s u l t s from t h e s u p e r p o s i t i o n o f t h e 6 3 ~ u and o f t h e s l i g h t l y wider 6 5 ~ u shadow cones. A s i m i l a r , although very s m a l l e r e f f e c t , would be t h e r e s u l t o f a s u p e r f i c i a l r e l a x a t i o n , t h e second l a y e r atom remaining then hidden a s h o r t e r time.

So a general smoothing o f t h e curves, as w e l l as a b l u r r i n g o f t h e peaks, a r e t o be expected from a computation t a k i n g i n t o account these t h r e e phenomena. As t o t h e abrupt v a r i a t i o n s o f F i g . 3, t h e y a r e e a s i l y accounted f o r by t h e f a c t t h a t , i n t h e s i m u l a t i o n o f a p e r f e c t c r y s t a l , according t o t h e values o f q , t h e second l a y e r as a whole c o n t r i b u t e s , o r not, t o t h e backscattered i n t e n s i t y .

The e v o l u t i o n o f t h e c o n t r a s t second t o f i r s t l a y e r i n t h e s i m u l a t i o n s may e a s i l y be a t t r i b u t e d t o t h e f o c u s i n g e f f e c t o f t h e r i n g o f t h e f o u r f i r s t l a y e r atoms met by an e x i t i n g p a r t i c l e a f t e r a second l a y e r c o l l i s i o n ( c f . Fig. 2a). The simultaneous r e p u l s i o n o f t h e r i n g atoms b r i n g s t h e f i n a l moment o f t h e p a r t i c l e nearer t o t h e normal d i r e c t i o n , and then a l l o w s t o i n c l u d e i n t h e c o l l e c t i o n p a r t i - c l e s which otherwise would have escaped t o i t . T h i s e f f e c t increases w i t h lowering energies, t h e p a r t i c l e s becoming slower and slower. On t h e contrary, i f one o f t h e r i n g atom i s missing, t h e moment o f t h e e x i t i n g p a r t i c l e i s d e v i a t e d towards t h e vacancy, and t h e f o c u s i n g e f f e c t may become a defocusing e f f e c t , according t o t h e d i r e c t i o n o f t h e p a r t i c l e v e l o c i t y . T h i s e f f e c t may concern the p a r t i c l e s backscat- t e r e d on each o f t h e f o u r second l a y e r atoms surrounding t h e vacancy ; so f o r a r a t e o f vacancies standing around 25

i n t h e f i r s t l a y e r , almost t h e whole o f t h e second l a y e r i s a f f e c t e d . Another consequence o f a f i r s t l a y e r vacancy i s t o b r i n g t o l i g h t i t s u n d e r l y i n g t h i r d l a y e r atom, which then replaces a second l a y e r atom. However, t h i s atom may be hidden when a t r u e second l a y e r atom would be seen, f o r i n s t a n c e f o r values o f v near 45", i t may be shadowed by a f i r s t l a y e r neigh- bouring atom. T h i s c o u l d e x p l a i n t h e " h o l e " observed i n t h i s r e g i o n . i n t h e 9500 eV experimental curve (2).

The i n e l a s t i c losses and t h e n e u t r a l i z a t i o n may a l s o a f f e c t the r e l a t i v e c o n t r i b u -

t i o n s o f t h e f i r s t two l a y e r s , as we1 1 as t h e p r e c i s e s t r u c t u r e s of these c o n t r i -

butions. Both o f them a r e expected t o depend on t h e path o f t h e p a r t i c l e , and then on the k i n d o f c o l l i s i o n s i t has experimented (5,6). As t o a p o s s i b l e r e d u c t i o n i n t h e b i n a r y peak energy due t o i n e l a s t i c losses (7), i t cannot a f f e c t t h e angular dependence o f IR.

The l a s t s i m p l i f i c a t i o n concerns t h e angular divergence (about l o ) and t h e energy d i s p e r s i o n (10-15 eV) o f t h e i n c i d e n t beam, which have been neglected i n t h e computations. T h e i r e f f e c t s , which o b v i o u s l y increase when t h e ions energy i s lowered, would be worth t o be evaluated. A p r e l i m i n a r y c a l u l a t i o n seems t o show t h a t t h e same angular d i s p e r s i o n e x e r t s a more important i n f l u e n c e on t h e data i f i t takes p l a c e i n t h e i n c i d e n t beam than i n t h e f i n a l one. Complementary studies, experimental as w e l l as computational, would then be o f prime i n t e r e s t .

I V - CONCLUSION

The r e s u l t s presented here c o n s t i t u t e a necessary f i r s t step o f a more complete study, which would have t o t a k e i n t o account i s o t o p i c e f f e c t s , a p o s s i b l e neutra- l i z a t i o n , some k i n d o f ion-induced d i s o r d e r , and t o i n c l u d e a b e t t e r s i m u l a t i o n o f t h e incidence c o n d i t i o n s . Such a study would considerably improve our knowledge o f s u p e r f i c i a l e f f e c t s i n b a c k s c a t t e r i n g experiments.

Many evdLgktening d i n c u n n i o ~ n wLth MWLC Behnheh and Geokge~ Sdodzian have &owed t k i n watrk. I t LA a p l e a ~ u k e t o thank both 06 them dot R h d &Liendly coUabalzat.ion.

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