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COLLISION CASCADES AND SPUTTERING INDUCED BY LARGER CLUSTER IONS
P. Sigmund
To cite this version:
P. Sigmund. COLLISION CASCADES AND SPUTTERING INDUCED BY LARGER CLUSTER IONS. Journal de Physique Colloques, 1989, 50 (C2), pp.C2-175-C2-182. �10.1051/jphyscol:1989230�.
�jpa-00229428�
JOURNAL DE PHYSIQUE
Colloque C2, suppl6ment au n 0 2 , Tome 50, f6vrier 1989
COLLISION CASCADES AND SPUTTERING INDUCED BY LARGER CLUSTER IONS
Physics Division, A r g 0 ~ e National Laboratory, 9700 South Cass Avenue.
Argonne, IL 60439, U.S.A.
R e s u m e
D e s . r e c e n t s t r a v a u x e x p e r i m e n t a u x a v e c d e s i m p a c t s d e g r o s a g r e g a t s s u r d e s s u r f a c e s s o l i d e s s u g g e r e n t d e g r a n d e s d i f f 6 r e n c e s p a r r a p p o r t a u c a s u s u e l d e s r e n d e m e n t s d ' e m i s s i o n a d d i t i f s , a u s s i b i e n d a n s l e r e g i m e n u t l e a i r e q u e d a n s l e r e g i m e e l e c t r o n i q u e d u p o u v o i r d l a r r @ t . C e t a r t i c l e e s t c e n t r e s u r l e s c a s c a d e s d e c o l l i s i o n s a t o m i q u e s . E n p l u s d e s e f f e t s t r e s p r o n o n c d s d e p o i p t e d e u x p h e n o m e n e s s o n t m i 8 e n v a l e u r q u i s o n t s p e c i f i q u e s d u b o m b a r d e m e n t p a r a g r e g a t s . D e s c h o c s m u l t i p l e s d ' a t o m e s d e l ' a g r e g a t s u r l e m @ m e a t o m e c i b l e p e u v e n t c r e e r d e s a t o m e s d e r e c u l q u i o n t u n e v i t e s s e p l u s g r a n d e q u e l a v i t e s s e m a x i m u m d e r e c u l p o u v a n t @ t r e t r a n s f e r e e a u c o u r s d'un c h o c d e p r o j e c t i l e m o n o - a t o m l q u e a u n e v i t e s s e i d e n t i q u e . C e t e f f e t e s t i m p o r t a n t q u a n d l a m a s s e a t o m i q u e d ' u n a t o m e d u f a i s c e a u e s t p l u s f a i b l e q u e c e l l e d ' u n a t o m e s d e l a c i b l e M 1 << M 2 . D a n s l e c a s c o n t r a i r e . M 1 >> M Z l e s c o l l i s i o n s e n t r e l e s p a r t i c u l e s d u f a i s c e a u p e u v e n t a c c e l e r e r c e r t a i n e s d ' e n t r e e l l e s e t e n r a l e n t i r d ' a u t r e s . Q u e l q u e s c o n s e q u e n c e s s o n t i n d i q u e e s . D e s r e m a r q u e s s u r l e p o u v o i r d ' a r r e t n u c l e a i r e d e g r o s a g r e g a t s e t l e " s p u t t e r i n g " e l e c t r o n i q u e p a r b o m b a r d e m e n t d ' a g r e g a t s s o n t d o n n e e s e n c o n c l u s i o n .
Abstract
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Recent experimental work on larger cluster impact on solid surfaces suggests large deviations from the standard case of additive sputter yields both in the nuclear and electronic stopping regime. The paper concentrates on elastic collision cascades. In addition to very pronounced spike effects, two phenomena are pointed out that are specific to cluster bombardment. Multiple hits of cluster atoms on one and the same target atom may result in recoil atoms that move faster than the maximum recoil speed for monomer bombardment at the same projectile speed.This effect is important when the atomic mass of a beam atom is less than that of a target atom, MI << M2. In the opposite case, MI >> M2,
collisions between beam particles may accelerate some beam particles and slow down others. Some consequences are mentioned. Remarks on the nuclear stopping power of larger clusters and on electronic sputtering by cluster bombardment conclude the paper.
1
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INTRODUCTIONCluster bombardment of solid surfaces is an upcoming field 11-131. Motivations for studies reach from the needs of surface analysis and biomolecular mass spectrometry to surface modification of materials that are of interest in microengineering and space research.
Existing experimental facilities provide water clusters of
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25-150 molecules in the energy range of 1-10 keV per molecule 13-51, hydrogen clusters of up to60 atoms with a total energy of 600 keV 16-81, C02 clusters of unspecified size accelerated to 155 kV 191, covalent as well as ionic clusters of total energies in the lower keV range 1101, small hydrocarbon clusters in the MeV range 1111, and A1 clusters accelerated up to a few kV 1121.
These experimental possibilities cover very different physical situations. At the highest velocities 16-8.111, energy dissipation of penetrating clusters andlor cluster fragments is predominantly electronic, and damage and sputtering
(l)~r~onne Fellow 1988-89 on leave from Odense University, 5230 Odense M, Denmark.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989230
C2-176 JOURNAL
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PHYSIQUEeffects observed on insulators are likely to be electronic. At lower energies, clusters may still be expected to penetrate
--
although highly fragmented--
but dissipate their energy predominantly via recoil cascades 13-5,9/. When the energy per atom reaches the lower eV range, clusters may still initiate
collision cascades although only a minor fraction of the constituents may penetrate 110,121. At even lower velocities, phenomena may be observed that are not unlike those seen after macro- and micro-meteorite bombardment /2,14-161.
This brief survey will emphasize some phenomena that are unique to cluster bombardment in the sense that they will not be seen in monomer bombardment at conventional current densities. There will be little specific reference to existing experimental results, but mainly penetrating clusters in the nuclear stopping region will be considered.
2
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THE STANDARD CASEAs a reference standard, take the case where a cluster dissociates right at the surface and all its constituent atoms penetrate independently without mutual interference. This case may be realized in knock-on sputtering of a metallic target by a small cluster of light ions at not too low energy. say 10-100 keV.
The standard case will manifest itself such that neither the penetration profile nor the sputter yield per cluster atom nor the damage per cluster atom depend on n, the number of atoms per cluster, provided that the comparison is made at constant velocity.
Experiments on cluster bombardment are more often performed at constant energy per cluster, say E. Then, assuming the standard case, the sputter yield Yn for a homonuclear cluster containing n atoms is
Yn
(E) =n Y1
( E l n ) .For a small, high-energy proton cluster 161 bombarding a metal, one expects Y1 (E) a E - ~ by Rutherford's law 1171 and hence Yn a n2. Conversely, if Y1 (El)
a
E, which is the case at much lower energies 1171, Yn becomesindependent of n. Evidently, care is indicated in this type of comparison: An n2 dependence of the sputter yield per cluster need by no means be indicative of a nonlinear effect, unless the comparison is done at constant velocity.
From the point of view of ion penetration and collision physics, this standard case does not offer many challenges. However, a target bombarded by cluster ions does differ from a.target bombarded by an equivalent beam of cluster fragments or individual atoms. Most of all, craters may be expected to form more easily, hence the surface morphology may develop differently; the primary damage state will be more compact; bubbles and precipitates may form at low fluences where one would not look for such phenomena otherwise.
Whether or not one deals with the standard case may well depend on the type of phenomenon observed. The total sputter yield per cluster atom is notorically sensitive to n, even for very small clusters 118,191, while the energy
reflection coefficient (or sputter efficiency), being a small effect governed by high-energy recoils and reflected projectile particles 1201, may be expected to be less sensitive to cluster size.
It may be necessary to include the charge balance in considerations of whether or not one deals with the standard case. A cluster ion typically contains more electrons than an equivalent beam of atomic ions. These additional electrons may contribute to the measured secondary electron yield 121,221.
3. Elastic-Collision Spikes
It has long been known that a high concentration of deposited energy per volume causes deviations from the standard linear cascade theory of energy dissipation 1231. This shows up in enhanced sputter yields of heavy targets bombarded by heavy atomic ions 117,181 and, more convincingly, for bombardment with dimers and trimers /18,19/.
The range of energy deposited per volume achievable in larger-cluster
bombardment reaches far beyond that for dimers and trimers. Estimates have been performed for water clusters 131 that indicate energies
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100 eV per target atom in the core of the track. These numbers are based on the assumption ofindependent continuous slowing down of the constituent atoms of the cluster, the latter being smeared out to a monolayer circular disk. Details of the
calculation may be questioned. The neglect of angular scattering and recoil transport may overestimate the deposition density in particular in deeper layers, yet approximating the cluster as a disk rather than a sphere has the opposite tendency. Moreover. "evaporation" of atoms at the high temperatures quoted above cannot be an activated process. All this does not- affect the main point that a cluster of
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100 water molecules of a total energy of 300 keV must generate more dramatic spike phenomena than any atomic ion at a similar energy.Observed sputter yields of up to lo5 atoms per bombarding cluster provide ample evidence 141.
From a theoretical point of view, cluster bombardment provides an experimental tool to realize three-dimensional energy deposition profiles gained from standard penetration theory 1241. The latter constitute an average over many bombarding particles, and considerable labor has been invested to arrive at feasible statements about the average energy deposition volume of individual cascades 125-271. In cluster bombardment, the initial assumption of many bombarding atomic particles is realized with a relative fluctuation n-lI2.
Hence,
that
problem has been largely eliminated.The basic assumption of a randomized elastic-collision spike may be expected to be realized to a higher degree in bombardment with large water clusters than for dimers or trimers of heavy ions because of substantial angular scattering of oxygen atoms, in particular for heavy targets like gold or tantalum 141 where projectiles scatter frequently and lose their energy in small bits.
There is no unanimous agreement on the detailed mechanism of enhanced sputtering from an elastic-collision spike 1281, where evaporation 129.41 and shockwaves 130,311 have been proposed as the main alternatives, and gas flow for the special case of condensed inert gas targets 1321. The relative merits of these models may be of minor significance in the present connection.
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MULTIPLE HITSConsider a cluster containing n atoms of mass M1 hitting a target consisting of atoms with mass M2, and assume for a moment that M1 << M2. Evidently, a target atom C recoiling from a collision with a beam atom A moves slowly enough to have a chance to be hit by another beam atom B (Fig. la). If ~712 is a pertinent cross section for such a collision, the average number u2 of hits on a target atom, caused by atoms of one cluster, is given by
provided that the target atom lies within the trajectory of the cluster, where N1 is the number density of atoms in the cluster and
La,
the average length of a straight line going through the cluster. For a spherical cluster with a radius R,Equation (2) is most readily found by viewing the interaction from a coordinate system in which the cluster is at rest (Fig. lb). The simplifying assumption of
M1 << M2 enters in several ways: It justifies the straight line trajectory in
Fig. 2b as well as the neglect of the dependence on target speed in 012.
The net result of a multiple hit is a recoil energy exceeding that achievable by monomer bombardment at the same velocity. In fact, multiple hits can lead to an energy transfer from the projectile to the target as long as the speed of the
JOURNAL
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PHYSIQUEANL-P-19.316
Fig. 1
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Target particle C hit by several beam atoms A, B... The size of the circles reflects the mass of the atoms. a) Seen from the laboratory frame of reference. b) Seen from a frame moving with the cluster.beam particle exceeds that of the target particle. Hence, an upper limit on the energy E2 of a target atom is given by
where El is the energy per beam atom, and E and M the total energy and mass of the cluster, respectively. Evidently, Eq. (4) is only relevant for clusters with M > M2, otherwise E2 < E.
In practice, Eq. (2) will be of interest for collisions leading to significant energy transfer which, at the same time, are infrequent. Hence, except for very large clusters, double hits may be the most prominent feature to show up in such experiments, resulting in a moderate increase of the maximum energy of a target atom by somewhat less than a factor of two beyond the familiar limit 7 El, with
7
= 4MlM2 (Mi+
M ~ ) - ~ .Even such a moderate enhancement may cause a significant increase of damage production and sputtering, in particular under conditions where monomer bombardment would be just about below the pertinent threshold.
5
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COLLIDING BEAM PARTICLES;Consider now the reverse case of a cluster of heavy atoms hitting a target of light ones. M1 >> M2 (Fig. 2a). Again, it is convenient to view the penetration from a system moving along with the projectile. In this frame, let a target atom C hit a beam atom A (Fig. 2b). A will receive a recoil velocity while C will be scattered away. The heavy beam atom A has a larger cross section for collision with other beam atoms than the light target atom. Hence, the most likely subsequent event is a collision between A and another beam atom B (Fig.
2c). As shown in the graph, B may have a velocity component in the positive
Fig. 2
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C o l l i s i o n s between beam atoms A and B , i n i t i a t e d by an i n t e r a c t i o n between beam atom A and t a r g e t atom C. The s i z e of t h e c i r c l e s r e f l e c t s t h e mass of t h e atoms. a ) I n i t i a l c o n f i g u r a t i o n seen from t h e l a b o r a t o r y frame of r e f e r e n c e . b ) A c o l l i d i n g w i t h C, seen from a frame moving w i t h t h e c l u s t e r . C ) A c o l l i d i n g w i t h B , same frame a s i n b ) .beam d i r e c t i o n . Hence, i n t h e l a b o r a t o r y frame. B has been a c c e l e r a t e d t o above t h e i n i t i a l beam v e l o c i t y . A t t h e same time, A has been d e f l e c t e d toward t h e d i r e c t i o n opposing t h e beam, i . e . . it may have slowed i n t h e l a b o r a t o r y system.
A s i g n i f i c a n t f r a c t i o n of a c c e l e r a t e d beam p a r t i c l e s has been found by computer s i m u l a t i o n of argon c l u s t e r s bombarding carbon t a r g e t s , and t h i s f e a t u r e was a s c r i b e d t o n o n l i n e a r e f f e c t s i n t h e c o l l i s i o n cascade 1131. While t h e r e i s l i t t l e doubt about t h e importance of n o n l i n e a r e f f e c t s i n t h i s type of cascade, t h e very occurrence of a c c e l e r a t e d beam p a r t i c l e s i s an e n t i r e l y l i n e a r e f f e c t a s i s e v i d e n t from Fig. 2b. The only d i f f e r e n c e from t h e conventional scheme i s t h e f a c t t h a t t h e l i n e a r cascade propagates i n t h e p r o j e c t i l e r a t h e r t h a n i n t h e t a r g e t l
Accelerated beam p a r t i c l e s may open up new r e a c t i o n channels, i n p a r t i c u l a r w i t h regard t o e l e c t r o n i c e x c i t a t i o n and e l e c t r o n emission, a s w e l l a s enhanced damage production and s p u t t e r i n g n e a r t h r e s h o l d .
Note t h a t f o r every a c c e l e r a t e d beam p a r t i c l e t h e r e i s another one t h a t has s u f f e r e d enhanced stopping. Thus, c o l l i s i o n s between beam p a r t i c l e s a f f e c t p r i m a r i l y t h e s t r a g g l i n g r a t h e r t h a n t h e stopping power. Heavy atomic i o n s h i t t i n g a l i g h t t a r g e t have t y p i c a l l y a r a t h e r narrow range p r o f i l e 1331. This p r o f i l e w i l l be spread i n case of c l u s t e r bombardment by c o l l i s i o n s between beam p a r t i c l e s , t h u s allowing some beam atoms t o come t o r e s t v e r y c l o s e t o t h e s u r f a c e . The o b s e r v a t i o n of Cs i o n s i n a low-fluence SIMS s i g n a l i n i t i a t e d by c l u s t e r s c o n t a i n i n g Cs 1101 may be r e l a t e d t o t h i s phenomenon.
JOURNAL DE PHYSIQUE
6
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QUANTITATIVE ESTIMATES?The range of validity of conventional transport theory 1171 must be considerably narrower in describing cluster bombardment than for monomer bombardment. At the same time, the range of applicability of continuum descriptions 12.3.29-321 is enhanced. Phenomena involving hard collisions such as those sketched in the previous sections should, however, be accessible to transport theory.
Computer simulation is an obvious alternative, yet, many existing simulation codes do not readily adapt to cluster bombardment. Standard Monte Carlo and binary collision lattice simulation codes do not contain a clock; this feature appears important in case of nearly simultaneous bombardment by several projectiles.
Standard molecular dynamics codes readily allow for cluster bombardment but may run into capacity problems when simulating bombardments with clusters of high total energies such as several hundreds of keV.
Feasible compromises are molecular dynamics codes with a narrow cutoff
radius 1341 or a binary collision code with a built-in clock 1131. In a recent comparison between different types of simulation codes 1351, molecular dynamics and binary collision lattice codes turned up to have more in common with each other than accepted conventionally, while Monte Carlo codes showed a less coherent behavior.
It is thus quite feasible to describe the collisional phase with a binary collision code
--
as was done in Ref. 1131--
while the relaxation toequilibrium of a target implanted with a high concentration of impurities, and thus an estimate of a penetration profile in absolute length units, must invoke properties that are beyond the scope of a binary collision simulation.
7
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STOPPING POWER OF A CLUSTERThe question of whether the stopping power per atom of a cluster is higher or lower than that of a monomer appears interesting and important 121. Only effects due to elastic nuclear collisions are considered here.
A target atom hit by a projectile atom tends to move away from the track of the cluster, and hence might leave the track before being hit by another beam particle (Fig. 2b). This paving-the-way effect tends to decrease the effective stopping power of the beam. A similar effect has been analyzed recently on very small collision systems 1361. The effect on the stopping power turned out small there, but the systems analyzed were too small to justify implications on larger cluster penetration. At any rate, paving-the-way should be most pronounced for
MI >> M2. This shows up clearly in simulations of argon on carbon 1131 where
the mean penetration depth was found to increase by more than a factor of four when the cluster size increased from n = 1 to 200.
For M1 << M2, recoil velocities are too small to allow recoil atoms to escape from the track. It appears unlikely that multiple hits have a pronounced effect on the stopping power.
For distant collisions, the momentum transferred to a target atom by the atoms from a cluster may in principle show a positive interference effect resulting in an enhanced energy loss. This effect is expected to cancel for large clusters where the cluster diameter is larger than the pertinent impact parameters contributing to nuclear stopping.
In Ref. 121, specific geometries were pointed out leading to an increased collisional energy loss. If, e.g., the trajectory of a target particle in Fig. lb goes between a "ring" of 2-4 projectile atoms, the simultaneity of the collisions increases the transferred momentum and hence the energy loss per projectile atom 1361. However, the opposite case of a target atom passing by a number of atoms on one side, and hence greater deflection, increased collision distance and smaller momentum transfer per beam particle, would seem
statistically more significant. This phase space argument would seem to favor smaller stopping powers.
8
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ELECTRONIC SPUTTERINGIn a series of very promising experiments 16-81. empirical scaling rules have been found which clearly demonstrate that the emission of positive and negative ions from CsI and a biomolecular target induced by hydrogen clusters in the electronic stopping regime (v
"
vo = e2/h) does not go under the standard case.The interpretation is complicated due to the fact that negative and positive ions seem to obey different scaling relations, and that the significance of the electronic stopping power in determining erosion yields is subject to debate.
Estimates of dimer stopping powers are involved in the analysis 1381, the validity of which is not ascertained for targets that do not contain free electrons and for clusters with a radius significantly larger than the Bohr adiabatic radius, the latter being quite small at the rather low projectile velocities. The major point of uncertainty in the analysis is the lack of an unambiguous description of the laws governing the erosion of these targets by monomer bombardment. Cluster bombardment might well elucidate some aspects of this process. However, the velocity range around v
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vo may well be the most complex one to tackle.ACKNOWLEDGEMENTS
I should like to thank Professor Y. LeBeyec for his kind invitation to devote some thought to the problem of sputtering by cluster ions and Drs. A. Belkacem, R. J. Beuhler. L. Friedman, P.R.W. Henkes, R.E. Johnson, E.A. Schweikert and J.P. Thomas for informative discussions. This work was supported by the U. S. Department of Energy, Office of Basic Energy Sciences, under Contract W-31-109-ENG-38.
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