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Vacuum/volume44/numbers 3/4/pages 341 to 344/1993 0042-207X/9356.00 .00P r i n t e d i n G r e a t B r i ta i n 1993 Pergamon Press Ltd

c o m p a r is o n o f T R I M a n d m o l e c u l a r d y n a m i c s inc a l c u l a t in g t h e b a c k s c a t t e r i n g y i e ld o f c a r b o ni n c i d e n t o n g r a p h i t eH B e r g s k e r , M a n n e S i e g b a h n I n s t i t u t e o f P h y s ic s , 1 0 4 0 5 S t o c k h o lm , S w e d e nand

F: Lama, B R A I N K A G , L ie c h t e n s t e inand

R Sm i th , D e p a r t m e n t o f M a t h e m a t i c a l S c ie n c e s, U n i v e r s i ty o f L o u g h b o r o u g h , L o u g h b o r o u g h ,Le ices te r sh ir e LE11 3TU, U K21nd

R Webb, Dep ar tme n t o f E lec t ron ic and E lec t r i ca l Eng inee r ing , Un ive r s i ty o f Sur rey, Gu i ld fo rd G U2 5XH , U K

This r epor t i s an a t t emp t to as ses s the va l id i ty o f t he b ina ry co l l is ions appro x ima t ion by c om par ing TR IM andmo lecu la r dynam ics in ca l cu la t ing the backsca t t e r ing o f ca rbon ions o ff a g raph i t e su r face . The TR IM ca lcu la t ionsw e r e p e r f o r m e d f o r a n a m o r p h o u s t a rg e t w i t h s m o o t h s u rf ac e . I n t h e m o l e c u l a r d y n a m i c s c a l c u la t io n s , a r e c e n t lyava i l ab le sem i -emp i r i ca l ma ny bo dy po ten t i a l by Te r so ff was used. The ca l cu la t ions w ere made fo r a pe r fec t c rys t a la t zero t empera tu re , cons i s t ing o f 1342 a toms in f ive layer s. The p rob ab i l i t y o f r e f l ec t ion w as ca l cu la t ed a s afunc t ion o f ene rgy and ang le o f i nc idence o f the p ro jec t i le . Com pared w i th the b ina ry co l l is ions ca l cu la t ions ,molec u la r dynam ics p red ic t s a s ign i f i can t ly h ighe r backsc a t t e r ing p robab i l i t y. F o r in s t ance , a t no rm a l inc idenceTR IM sho ws l e s s than one pe r cen t r e f l ec t ion in the who le ene rgy r ange up to 1 keV, w hereas in molecu la rdynam ics the r e f l ec t ion y i e ld peaks a round 20 eV wi th mo re than 40 r e f l ec t ion . The case o f a head -on co l l is ionwi th a su rface a tom a t no rm a l inc idenc e i s d i scussed in de ta il .

1 l I n t r o d u c t i o n

When an atom with energy in the eV, 10 eV or lower 100 eVrange hits a surface, it may either be implanted an d trapped, stick1:o the surface or be kinema tically reflected. Appl icatio ns whereit is essential to know the probabil ity of reflection include thefuel recycling and impu rity recycling in cont rolle d fusio n devices.]In this context it is particularly essential to know in what cir-cumstances the combination of backscattering and self-sput-tering of relevant first wall materials leads to one or mo re th anone atom being ejected per incom ing atom, since this may entailan av alanche release of impurities into the plasma. Gr aphite is afavoured wall material in todays large Tokama k experiments, but1:he plasma performance is partly degraded by so-called carbonblooms, when carbon flows into the plasma in an uncontrolled'way ~. Not only the total yield, but also the an gul ar and energy.distribution of reflected atom s is of interest in fu sion plasma:research, since it determines how far into the plasma reflectedatoms are able to penetrate before being ionized, and conse-quently restrained in their moti on by the magnetic field.

Moreover, collection of plasma ions, or of neu tral atoms pro-duced by charge exchange, on surfaces has been extensively usedto study impurity fluxes at the plasma edge in fusion exper-i[ments 2-8. The relevan t energy range in f usion research is from

l0 eV up to a few keV, and the ions or neutral atoms hit thesurface with a wide distribu tion of angles of incidence.

Finally, collection of sputtered particles on solid surfaces hasbeen used in sputt ering yield measurem ents 9. The energies in thiscase are from ~ 1 eV to a few tens ofe V an d the angle of incidenceis usually near no rmal. In these measurements as in the collectorprobe measurements in plasma devices, it is often more or lessimplicitly assumed that the reflection of heavy atoms incident onthe same or lower Z surfaces can be neglected.

Few experimental data exist on backscattering in the 1 and 10eV ranges. It has been shown that the sticking probability ofmetal ions inci dent on low Z s ubstrate s is close to u nity ~ exceptat energies below ~ 10 eV, where the reflection probability of

urani um, Rh and Nb atoms at an AI20 3 surface can be10o/ot t,~2. In an accurate relative meas urem ent it was s hownthat the reflection probability of sputtered vanadiu m, nickel andstainless steel atoms (with energy aro und 1-20 eV) o n Si, AI, Beor graphite surfaces is less tha n 4 , whereas it may exceed 10for sputtered van adi um collected on a silver surface ~3. Recentlythe energy distributions have been measured o f inert gas atomsscattered off metal surfaces with incident energies in the range10-100 eV 14.

Where solid collectors, usually graphite, have been used tocollect carbon and b oron ions in the edge plasma of Tokamaks,with energies mostly in the range 10-100 eV, there are indic ation sthat the pr obab ility of reflection may be 10-20 7,~s. In thesecases, the incide nt energy is likely to have been a dis trib utio n

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H Bergs~ ker e t a l :TRIM and molecular dynamics comparison

from a few eV to a few tens of eV and the angles of incidence afairly wide distribution but with few particles at very obliqueangles.

From a theoretical point of view, the backscattering prob-ability of a heavy ion at surfaces of lower or similar atomicmass is expected to be low, since due to kinematics it cannotbe backscattered in a single binary collision, and large anglescattering is generally suppressed. For backscattering to occur,

it is necessary to have a sequence of small angle binar y collisionswithout losing too much energy in the process, or that the energyis sufficiently low for multiple interactions to come into play. Itis well known that binary collisions calculations, such as withTRI M ' 6 , 9, result in low reflection probabil ity for ions incidenton lower or like mass surfaces 17. At energies similar to the bin dingenergy of the lattice atoms, the binary collision approximationis clearly not applicable, and it is necessary to include multipleinteractions. In a molecular dynamics calculation, Shapiro andTombrello investigated the case of copper atoms incident on acopper surface, and found no reflection at normal incidence 2.This was a calculation which was made for a zero temperaturecopper lattice and with a well-established pair potential. Pairpotentials are suitable to simulate the properties of materialswith metallic binding, but are inad equate for covalent materials.Recently, tractable empirical many body potentials have becomeavailable, which are suitable for materials like silicon and car-b o n 2 1 2 2 .

In spite of the expected shortcomings o f the bi nary collisionsapproximation at lower energies, codes like TRIM have beenwidely applied in the modelling of p lasma surface interactions infusio n plasma devices. This is because of their generality andspeed of execution. Obviously it is then important to test thevalidity of the b inary collisions approx imation, in the first placeby experiments. However, since experiments are difficult to per-form in the 10-100 eV energy range, it is also interesting tocompare T RI M predictions with calculations which include mul-

tiple interactions, and this is the purpose of the present report.We have chosen to compare TRIM and molecular dynamics incalculating the backscattering yield of carbo n atoms at a graphitesurface.

2 C a l c u l a t i o n s

For the bi nary collision calculations, a slightly modified versionof TRIM85~6 has been used. The program uses the so-calleduniver sal intera tomi c potenti al ~6. The surface is modelled b y aplanar 7.4 eV surface potential. The target atoms are distributedrandomly, and the projectile atom is subjected to b inary collisionsand to inelastic slowing down between collisions. In literature,attempts have been made to model surface roughness, e.g. byusing a sawtoo th shaped surface L or a fractal sur face 19 in TRI Mcalculations. No such refinements are made here, a perfectly fiatsurface is assumed.

For the molecular dynamics calculations, we used a pro gramwhich is a further devel opmen t of the QDY N code 23. The pr o-gram has been used previously for simulation of carbon self-sputte ring 24 25. The 'two step A' integ rati on method of r ef 26 isused. A moving atom approximation is made, such that theequatio n of motio n is integrated only for atoms which experiencea force larger than 10-' N. The target is a lattice of 1342 atomsarranged in five layers, with the projectile atom incident on the(1000) surface. Fig ure 1 shows a section of the first atomic layer.In each simulation run, 300 projectile trajectories are calculated,

o ~ I 5

~P 03

9 91

o o

79

tAP

Figure 1. A section of the graphite lattice in the molecular dynamicscalculations. Only the surface layer atoms are shown. Also indicated isthe regular grid of 300 impact points for incident atoms.

with impact point on the crystal surface distributed on a regulargrid over the shaded area in Figure 1. Calculations have beenperformed for different angles of incidence 0 from the surfacenorma l, differ ent az imutha l angles ~p : 0 ~< q~ ~< 180 and different

impact energies. As in the TRIM calculations, no account istaken of surface roughness, the target is a perfect crystal at zerotemperature. For a num ber of selected sets of input parametersthe moving atom approximation has been removed, the latticehas been heated to 2500 K or the target atoms have been ran-domly displaced according to a spherical gaussian distribution.neither of these tests has given significantly different results.

The inter atomic potential which has been used is a semi-empiri-cal man y bo dy poten tial suggested b y Terso ff 21'22. The form ofthe potential is chosen so as to reflect the fact that the bondstrength between any two atoms decreases with increasing coor-dinat ion of the two atoms to other neighbours. In all, the poten-tial has 11 adjustable parameters, which were determined fromthe cohesive energies, elastic properties and defect energies invarious carbon polytypes. The properties of diamon d and the in-plane properties o f graphite have been sho wn to be well describedby the po tentia l 22, whereas the rang e is too sh ort to mod el inter-planar bindin g in graphite.

The calculations have been performed on computers at theMann e Siegbahn Institute, mainly an Allian t FX/2824, a 31-100VAX station an d an Apollo 3500 work station. Typically a runwith 300 trajectories takes 3-24 h on a single processor on theAlliant, twice longer on the VAX station and 10 times longer onthe Apollo station.

3 R e s u l t s

Figure 2 is a comparison of the backscattering yield from TRI Mand molecular dynamics. The yield at normal incidence fromTRI M is higher than that from Eckstein and Biersack by a factortwo o r so ' 7, whereas the yield at a 45 angle of incidence is similar,and the energy dependence is similar. Fo r norma l incidence theTRI M backscattering yield is everywhere less than 1% a nd dro pssteeply below 100 eV incident energy. The backscattering yieldfrom molecular dynamics increases with decreasing energy from

50 eV, peaks ar oun d 20 eV with more tha n 40% backscatteringand drops down below 10% at still lower energy. At a 45 angleof incidence the yield from molecular dynamics falls well belowthe TRIM prediction in the range 200-1000 eV, but peaks aroun d40 eV with uni ty yield.

Figure 3 shows more in detail the backscattering yield from

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t4 Bergs~ker e t a l T R I M a n d m o l e c u l a r d y n a m i c s c o m p a r i s o n

1 . 00 ~ M o l e c u L o r / 0 ~ - 4 ~dynomics....~-,/1~_

o. o - . - . _ - - - - .

o / I . . . . - - ~ . C . ~ 0 - 4 5~0.01 / O = l 0 ~ 0~8 =~ ----~,~. MARLOVE

I I / / I II I I [

Energy (eV)

F i g u r e 2. A compar ison o f the backscatter ing yield ca lcula ted wi th TRI Mand wi th molecular dynamics . The spl ine in terpola t ion curves are toguide the eye . the p lo t ted points fo r molecular dynamics wi th polar angleof incid ence 0 = 45 are fo r azim uthal angle ~o = 0. Th e b roken linerepresents ca lcula t ions us ing M AR LO W E 28 for these inc ident angles .

m o l e c u l a r d y n a m i c s a s a f u n c t io n o f i n ci d e n t e n e rg y a n d a n g l eo f i n c id e n c e . T h e l a rg e m a j o r i t y o f t h e c a l c u l a t e d v a l u e s a r e f o r

a z i m u t h a l a n g l e ~ o = 0 , in s o m e c a s e s t h e y a r e a n a v e r a g e o fm a n y a z i m u t h a l a n g l e s. T h e d e p e n d e n c e o n t h e a z i m u t h a l a n g l ea p p e a r s t o b e w e a k . F o r i n s t a n c e , a t 2 5 e V a n d w i t h p o l a r a n g l e0 = 30 , t he y i e ld v a r i e s b e tw een 0 .25 an d 0 .32 fo r d i f f e r en ta z i m u t h a l a n g l e s .

, 1 . D i s c u s s i o n

] Fo r t h e p r e s e n t p u r p o s e t h e d i f fe r e n c e b e t w e e n t h e T R I M b a c k -s c a t t e r i n g y i e l d i n th i s w o r k a n d i n r e f 1 7 m a y b e c o n s i d e r e d a sm i n o r , I t m a y b e d u e t o t h e d i f f e r e n t i n t e r a t o m i c p o t e n t i a l o rt o d i f fe r e n t a s s u m p t i o n s f o r s u r f ac e b i n d i n g e n e r g y a n d o t h e rde t a i l s .

T h e m o s t s t r i k i n g r e s u l t is t h a t m o l e c u l a r d y n a m i c s p r e d i c t s a

h i g h b a c k s c a t t e r i n g y i e l d , e v e n a t n o r m a l i n c i d e n c e , a t e n e rg i e s

Backs cattering yield

I t.8

~ 0 6~ 0 4

oo

o ~ - - - - - - - - ~2o 4o - -0 Energy (eV/

F i g u r e 3. Backscat ter ing yie ld f rom m olecular dynamics . Calcula t ions arefor every 5 eV and every 5 in angle o f incidence, except in areas w ithzero or uni ty y ie ld , where in terpola t ion has been m ade. The yie ld a t zeroenergy has been chosen as zero .

b e l o w 1 00 e V. T h e p r e d i c t e d b a c k s c a t t e r i n g y i e l d i n t h e m o l e c u l a rd y n a m i c s c a l c u l a t i o n s i s c l e a r l y la rg e e n o u g h t o b e s i g n i f i c an t t oi m p u r i t y r e c y c l i n g i n f u s i o n d e v i ce s , a n d t o e x p e r i m e n t s w h e r ep l a s m a i o n s o r s p u t t e r e d a t o m s a r e c o l l e c t e d o n s u r f a c e s . T h i s i sp a r t i c u l a r l y t r u e a t n o n - n o r m a l i n c i d e n c e . I t s h o u l d b e k e p t i nm i n d t h a t t h e a n g l e o f i n c i d e n c e o f p l a s m a i o n s i s l i k e ly t o b et y p i c a l l y 3 0 , e v e n i f t h e m a g n e t i c f i e ld i s n o r m a l t o t h e s u r f a c e 27H o w e v e r , i t is o b v i o u s t h a t t h e c a s e o f a p e r f e c tl y f i a t s u r f a c e

d o e s n o t c o r r e s p o n d w e l l t o a r e al g r a p h i t e s u r f a c e . S i n c e m o s to f t h e r e f le c t i o n a t g r a z i n g i n c i d e n c e o c c u r s a t s p e c u l a r a n g l e i ti s l i k e l y t o b e m u c h r e d u c e d f o r a r o u g h s u r f a c e. N o t e t h a t i n r e f1 5 t h e s i g n i f ic a n t d i f f e r e n c e i n c o l l e c t i o n e f f i c i en c y w a s b e t w e e nr o u g h g r a p h i t e s u r fa c e s o n t h e o n e h a n d , a n d p o l i s h e d g r a p h i t ea n d o t h e r s u r f a c e s o n t h e o t h e r h a n d .

To u n d e r s t a n d t h e m e c h a n i s m o f b a c k s c a t t er i n g i n t h e m o d e l ,i t is n e c e s s a ry t o s t u d y s i n g l e e v e n t s i n m o r e d e t a i l. A s a n i l l u s tr a -t i v e e x a m p l e , c o n s i d e r t h e c a s e w h e r e t h e p r o j e c t i l e a t o m h i t s t h et a rg e t a t o m 9 1 ( c f. F i g u r e 1 ) in a h e a d - o n c o l l i s i o n a t n o r m a li n c id e n c e . O b v i o u s l y, i n t h e b i n a r y c o l l i s io n a p p r o x i m a t i o n t h e r ec o u l d b e n o b a c k s c a t t e r i n g i n t h is c a se , s in c e t h e p r o j e c t il e w o u l dt r a n s f e r a l l i t s e n e rg y t o t h e t a rg e t a t o m . I n t h e m o l e c u l a r d y n a m -i c s c a l c u l a t i o n s t h e s y s t e m e v o l v e s a s s h o w n i n F i g u r e s 4 a n d 5w h e r e t h e n o r m a l v e l o c i t i e s a r e p l o t t e d f o r t h e p r o j e c t i l e ( l a b e ll e d1 ) , t h e t a rg e t a t o m 9 1 , i t s n e a r e s t n e i g h b o u r 9 0 a n d t h e a t o m3 5 8 , w h i c h i s s i t u a t e d i n t h e s e c o n d g r a p h i t e p l a n e , d i r e c t l y b e l o w

x O m / s

>~

o

- 5

-5

-5

9 0

- \\

\\ A\ /

\ j ,

f -~ 91/ \ -

E = e V

:358

\

\ I\ I

i

9 0

\\

\ \

91

i / ~ \

E = 2 e V

/ \ x358 . ,

I I I I I I

0 I0 20 30 40 50

Tim e (femtoseconds)

Figure 4 . Norm al v eloci ties of the projec t i le ( labelled I ) and the targeatom s 90, 91 and 358 in the case of the projectile hitt ing ato m 91 in head-on col l i sion a t normal incidence. Ato m 90 is one of the nearesneighbours o f a tom 9 I . Atom 358 is s i tua ted in the second graphi te p landirec tly below atom 91.

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H Bergs~ker e t a l T R I M a n d m o l e c u la r d y n a m i c s c o m p a r i s o n

x 10 3m/

P t I

NN

_ I E = 8 e V3 o

\ . -~ 91

~ ~ 358~ to

J

E 6 0 e V

--, 91

I O I II 0 20 30 40 50

Time ( f emtoseconds )

Figure5. Normal ve loc i t ies of the pro jec t i le ( labe l led 1) and the ta rge ta toms 90 , 91 and 958 in the case of the pro jec t i le h i t t ing a tom 91 in ahead-on col l i s ion a t normal inc idence . Atom 90 i s one of the neares tne ighb ours of a tom 91. Atom 358 is s i tua ted in the second graphi te p lanedi rec t ly be low a to m 91.

9 1 . P o s i t i v e v e l o c i t i e s a r e d i r e c t e d i n t o t h e c r y s t a l . A t l o w e n e r g y( F i g u r e 4 ) a c o m p a r a t i v e l y l a r g e f r a c t io n o f t h e p r o j e c t il e s ' f or -w a r d m o m e n t u m is tr a n s f e r r e d t o t he n e a r e s t n e i g h b o u r s , n o t et h a t a t o m 9 0 is o n e o f t h r ee . A t 1 e V, h o w e v e r , a s u f f i ci e n t a m o u n to f t h e p r o j e c t il e e n e r g y i s d i s s ip a t e d f o r i t t o b e t r a p p e d a t t h es u r f a ce . A t 2 e V a n d a b o v e , t h e p r o j e ct i le i s b a c k s c a t t e r e d . A st h e p r o j e c t i l e e n e r g y i s i n c r e a s e d , t h e c o l l i s i o n w i t h a t o m 9 1b e c o m e s m o r e a n d m o r e l i k e a b i n a r y c o l li s io n , a n d a t 5 8 e Va l m o s t a ll f o r w a r d m o m e n t u m i s t r a n s f e r re d t o a t o m 9 1 ( F i gu r e

5 ) , b u t t h e p r o j e c t i l e i s s t i l l b a c k s c a t t e r e d , r e t a i n i n g v e r y l i t t l ee n e r g y. A b o v e 5 8 e V t h e p r o j e c ti l e o n c e a g a i n i s n o t b a c k -s c a t te r e d . T h i s e x a m p l e s h o w s t h a t t h e b i n a r y c o l l is i o n a p p r o x i -m a t i o n i s i n a d e q u a t e b e l o w 6 0 e V f o r th i s p a r t i c u l a r s y s t e m .

5 . Conc lus ionsI t h a s b e e n s h o w n h o w s i g n if i c a n t b a c k s c a t t e r i n g o f 1 0 - 5 0 e Vc a r b o n a t o m s a t n o r m a l i n c i d e n c e o n g r a p h i t e s u r f a c e s i s p r e -d i ct e d f r o m m o l e c u l a r d y n a m i c s c a l c u l a t io n s w i t h m a n y b o d yp o t e n t i a l . T h i s e f f e ct is n o t p r e d i c t e d i n c a l c u l a ti o n s b a s e d o n t h eb i n a r y c o l l i si o n s a p p r o x i m a t i o n , a n d i f i t o c c u r s f o r r e a l g r a p h i t es u r f a c e s i t m a y b e o f c o n s e q u e n c e t o i m p u r i t y r e c y c l in g i n f u s io n

e x p e r i m e n t s , a s w e ll a s t o e x p e r i m e n t s w h e r e c a r b o n i s c o l le c t e do n s u r f a c e s f o r d i a g n o s t i c p u r p o s e s . E x p e r i m e n t a l t e s t s a r e d es i r -a b l e .

A c k n o w l e d g e m e n t sT h i s w o r k h a s b e e n s u p p o r t e d b y t h e B r i t i s h S c i e n ce a n d E n g i n -e e r in g R e s e a r c h C o u n c i l ( S E R C ) a n d b y t h e S w e d i sh N a t u r a lS c i e n ce R e s e a r c h C o u n c i l ( N F R ) . T h e a u t h o r s w o u l d a l s o l ik et o th a n k t h e re f er e e, D r I v a n C h a k a r o v , f o r t h e M A R L O W Ec a l c u l a t i o n s i n c l u d e d i n F i g u r e 2 .

R e f e r e n c e s] M U l r i c k s o n ,J N u c l M a t e r,176 & 177, 44 (1990).

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