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The atomic sputtering from {111} surfaces of fcc metals
270
Nuclear
The atqrnic sputtering from
(
Instruments
and Methods
in Physics
Research
B53 (1991) 270-278 North-Holland
111) surfaces of fee metals
W. Eckstein Max-Planck-Insiitut
ftir Plasmaphysik, E URA TOM association, W-8046 Garching, Germany
M. Hou Universitt! Libre de Bruxelles, CP234, Bd. du Triomphe, B-1050 Brussels, Belgium Received
23 August
1990
New sputtering mechanisms are identified by means of computer simulation with the MARLOWE code, which give rise to the most pronounced structures in the angular distributions of ejection from a { 111) gold surface. The influence of surface scattering of ejected recoils and of the trajectory refraction by the surface binding forces is identified. This allows the relation between the structure of the sputtering angular patterns and the anisotropies in the distribution of the directions of motion of cascade atoms to be emphasized. Transient focusing processses in the cascade development are found responsible for the major structures in the
sputtering angular distributions. These distributions are strongly dependent on the sputtering energy. It is suggested that this prediction can be checked by energy- and angular-resolvedsputtering measurements.
1. Introduction Atomic collision cascades generated by energetic particles in solids are short lifetime events. As a consequence, the direct observation of the atomic motion and instantaneous spatial configurations is not possible. The only method to gather detailed information about the evolution of collision cascades in a material is computer experiments. However, these are based on atomic interaction models whose range of applicability may differ from one material to another and may also be dependent on the interaction energies involved. Therefore, they need to be checked empirically. Since this is not directly possible on the basis of the collision cascade development, related measurable processes have to be used instead. One of the few direct dynamic consequences of atomic collision cascades in solids which can be studied experimentally in details is sputtering. Atomic collision cascades were recognized as a possible origin of sputtering a long time ago [l]. A brief historical overview of collisional sputtering theories is given in ref. [2]. Numerous experimental studies of sputtering were performed since its discovery [3], in continuously improved conditions. Reviews are presented in ref. [4]. Hence, computer simulation models can be checked and adjusted by quantitative comparison to experimental sputtering data [5-81. The relation between sputtering simulation and collision cascades can be established, but is not straightforward, because of the role played by the surface. 0168-583X/91/$03.50
0 1991 - Elsevier Science
Publishers
The quantities related to atomic sputtering that are the most currently measured and calculated are sputtering yields, energy and angular distributions. Analytical collision cascade theories usually make use of a random target model [9-121 and allow reasonable predictions of sputtering yields for a wide range of systems, on the basis of a linearized Boltzmann transport equation [12]. The parameter which represents the major limit to the sputtering yield from metals is the surface binding energy and yield studies only provide moderate information about the development of collision cascades. The relation between the atomic sputtering energy distribution and the kinetic energy distribution of atoms moving in the cascades could be established [13]. It presents a maximum related to the value of the surface binding energy and a high energy tail with a close to inverse quadratic dependence on the energy. The latter is typical of energy distributions as predicted for atomic collision cascades in random materials (131. Recent computer simulations in the binary collision approximation allowed a more accurate analysis and suggests this tail to be decreasing as E-‘13 with energy [6,7]. More detailed information about the atomic motion in collision cascades may be expected in angular distributions of sputtered atoms from single crystals, which also display a more complex structure. Indeed, the sputtering from single crystals is known to display preferential directions [14], often rather close to low-index crystallographic directions intersecting the surface. These anisotropies are assumed to have their origin in
B.V. (North-Holland)
W. Eckstein, M. Hou / Computer simulation of {II I}-surface sputtering random cascades [15,16]. This suggests a cascade development model which is dominantly random but from which directional effects - called focusing effects originate from the lattice structure. By random cascade, it is meant that the collision sequences undergone by the moving atoms are considered as stochastic chains. This implies the target structure to be of negligible influence. It should be noticed that such a model does not imply the isotropy of the final rest configuration of the cascades, which structure is known to be correlated to the momentum direction of the high-energy moving atoms at the very first steps of the cascade development [17]. Final atomic rest configurations are not considered in the presented work. Their study is presented elsewhere [17-191. Aspects of the random cascade model are discussed in ref. [20] on the basis of computer simulations in the binary collision approximation. It was found that the lattice structure in single- and polycrystals acts as a strong rigid mechanical constraint. Consequently, most of the cascade atoms have their motion driven by the crystal structure. It was also found that channelling and focusing chains were not sufficient to account for the whole anisotropic character of the momentum direction distributions in the cascades, which is energy dependent. Insofar the atomic sputtering can be considered as a consequence of the atomic motion in collision cascades, the relation between sputtering angular distributions and momentum direction distributions in the developing cascades should be possible. It is our purpose to emphasize this relation on the basis of computer simulations in the binary collision approximation, compared with experimental measurements [21]. The discussion is based on the case of the irradiation of a gold (111) surface by Xe atoms with 600 eV incident kinetic energy. In such conditions, the elastic energy transfers represent the dominant energy-loss mechanism.
2. The simulation model The MARLOWE computer simulation code [22] was used for the present calculations. It is based on the binary collision approximation. 2.1. The impact and energy parameters Between collisions, particles are assumed to move along their asymptotic trajectories. Provision is made for an approximate treatment of quasi-simultaneous collisions [23]. A zero binding energy is used for the gold atoms to their lattice sites. A small binding energy is however assumed for replacement collisions (0.2 eV) in order to correct for the many body nature of such
211
events [24]. This approach was discussed in detail on the basis of comparison with classical dynamics calculations. As shown in [24], the mean energy loss along replacement sequences is systematically underestimated because, in the binary collision approximation, the dynamics of the interaction between successive atoms in a row is not handled properly. To our knowledge, no information about the magnitude of this underestimate is available in the case of gold and the choice of 0.2 eV, although expected of the right order of magnitude, is somewhat arbitrary. The energy dissipation through binary collisions proceeds until the kinetic energy of the moving particles falls below a preset cutoff value, 3.78 eV, which is also used as an energy displacement threshold and as the magnitude of the surface binding energy, assumed with planar symmetry. Only the contribution of collisions with an impact parameter smaller then 0.62a, (where a, = 4.076 A is the length of a lattice cell edge) is considered. Inelastic energy loss is assumed to be equally shared between local and nonlocal electron excitations, according to Oen and Robinson [25] and Lindhard [26] respectively. 2.2. The cascade scheduling Time is not a currently available cascade characteristic in binary collision models. Real time is used for the simulation of sputtering of silver by bismuth atoms and of carbon by very large argon clusters [27]. It was also introduced in MARLOWE for the study of Auger emission [28] in an approximate way which range of applicability is limited to the high energy part of the cascades. The MARLOWE code is in the process of being redesigned in order to allow for the simulation of fully time-driven events and already was used in slowingdown and cascade studies [29,30]. In the present version of the Marlowe code (version 12.0), after each collision step, the fastest atom is selected as the next projectile to be followed, until all cascade particles have their kinetic energy below the cutoff value. Deviations from this model are anticipated to influence sputtering significantly in case of the occurrence of strong nonlinear effects, which only can be handled properly with a time-driven cascade scheduling procedure. The present work focuses on the angular distribution of sputtering from a (111) surface and its relation to the velocity direction distribution of moving atoms in the cascade. This requires a careful modelling and analysis of the ejection process. 2.3. The potential
and the surface binding energy
Atomic collisions are governed by the pairwise Moliere potential [31] and the screening length for the homonuclear gold pair is a parameter. Firsov screening distances [32] are assumed to be valid for rare gas atoms
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W. Eckstein, M. Hou / Computer simulation of {II I}-surface sputtering
and these for heteronuclear pairs (Xe-Au) are estimated as harmonic means of the screening lengths for the homonuclear pairs [33]. The choice of the Au-Au screening length is discussed below. The same sputtering model is used as in our preceding work [5,34,35]. An atom which aims to escape from a planar surface has to overcome two balancing effects: i) the scattering from close neighbouring surface atoms which tends to feed its trajectory toward the surface normal and ii) a refraction toward the surface imposed by the surface binding energy. The former effect is obviously potential dependent while the latter depends on the magnitude of the surface binding energy. Both have a significant effect on the angular distribution of sputtering, as discussed in ref. [34,35] and shown below. In ref. [35], the same case study as considered in the present work was used in order to find the best adjustment of the potential parameter and the surface binding energy, in order to match the simulation results from a static lattice to those sputtering angular distributions obtained experimentally in the same incident conditions at 15 K. The choice of the cohesive energy for gold (3.78 eV [36]) was found reasonable in conjunction with the Moliere potential used with a screening length of 0.0752 A for a gold homonuclear interacting pair. This value is the same as that suggested in ref. [22] and deduced by matching the Moliere potential to the Born-Mayer potential at the first neighbor distance. The parameters for this latter model potential were obtained from equilibrium crystal data [13]. 2.4. The influence of the model parameters
on the sputter-
ing pattern
It was found in ref. [35] that the major feature of the sputtering angular distribution from a (111) gold surface irradiated with 600 eV Xe atoms is an intense six-fold symmetrical spot pattern. The six spots are centered around a direction making an angle of about 32” with the surface normal. We were unable to find a couple of potential and surface binding parameters, significantly distinct from those presently used and which allows the reproduction of the experimental data as well. This six-fold geometry does not match that of low index directions intersecting the surface plane ((loo), (110) and (111) directions intersecting the surface make angles of 54.74O, 35.26 o and 70.53” with the surface normal, respectively). The same symmetrical pattern was, however found experimentally, over a wide range of incident energies, incident masses and target temperatures [21]. On the other hand, as far as the sputtering direction distribution is concerned, it was found that modifying the strength of the potential or the magnitude of the binding energy had no other significant effect other than modifying the spot positions and shapes in direc-
tions parallel to the (110) planes normal to the surface. The effect is the same for each spot. The occurrence of the six-fold symmetrical spot pattern is thus not much dependent on the surface ejection model. It has its origin in the cascade development close to the surface.
3. The origin of sputtering in preferential directions The angular distributions of sputtering from single crystals are commonly analyzed in terms of two different mechanisms related to focusing along close-packed directions [15] and the flux distribution from a random cascade through the surface lattice [16]. These mechanisms were suggested to have the same origin [34] and were used as a basis to discuss the sputtering direction distributions from various surfaces of materials with various common structures [37]. The sputtering simulations presented in ref [34] indeed illustrate the important role of replacement sequences on the ejection from {loo} and { llO} surfaces from fee crystals and their contribution could be quantified. Such a quantification is also presented for the Xe-Au (100) system in ref. [24]. The balance between surface scattering of sputtered recoils and surface refraction by the binding force was emphasized. Owing to the energy dispersion in replacement sequences, the surface refraction has the effect to bent the ejection directions at various angles with the result of the occurrence of streaks in the sputtering patterns. This was a first illustration that particles ejected by a focusing chain mechanism does not only contribute to sputtering spots. The situation is even more complex in the case of the ejection from a (111) surface and the following description will show that the known stable focusing processes are not responsible for the six-fold symmetrical spot pattern obtained in the present simulations. It was shown in ref. [20] that momentum distributions in collision cascades are not isotropic. Prior to discussing the relation between the anisotropy of momentum distributions and sputtering patterns, a description of the energy dependence of sputtering patterns is given. Since about 90% of the sputtering originates from the surface plane [38], its understanding requires the knowledge of the atomic momentum distribution in the close vicinity of the surface as well as the effect of surface scattering and refraction. In order to follow the sputtering process, the momentum distributions in the close vicinity of the surface plane are compared at successive steps of the ejection process, as a function of the kinetic energy. Three situations are compared. The first is the momentum distribution of atoms moving in the vicinity of the surface plane in the half space including the vacuum and limited at a distance of half a planar spacing beneath the surface. Secondly, distributions are con-
W. Eckstein, M. Hou / Computer simulation of (I I I}-surface
strutted as in the first situation but they are restricted to atoms which fulfill the conditions to overcome the surface energy barrier. In the third situation, the refraction of the trajectories in the vacuum is taken into account. In such a way, the sputtering angular distribution of atoms ejected with different kinetic energies is displayed. The energy dependence of the sputtering angular distributions is studied with the same method as the
sputtering
273
momentum direction distributions in refs. [20] and [39]. The angular distributions are recorded for all particles entering a prespecified kinetic energy interval. Consecutive intervals are taken as (E,/2”, E,/2”+‘), where E,, is the primary energy, for increasing integer values of n until the cutoff energy is reached. The distributions are represented in the form of contour-line plots of equal intensities. The number of contour lines is limited to 20. Their equidistance corresponds to 5% of the maximal
(4
1
E -0 4: csl z =:
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1.0
0.6
0.8
1.0
cos P.COSINE of POLAR ANGLE b)
-"I0
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
cosp, COSINE of POLAR ANGLE Fig. 1. (a) Loci of the directions parallel to the most compact crystallographic planes. Their intersections represent the close packed directions in the lattice, that are labelled in the figure. o o 0: loci of directions parallel to (100) planes, AAA: loci of directions parallel to (110) planes, + + + loci of directions parallel to the (111) planes, n : (100) directions, 0: (110) directions, l : (111) directions, A: (112) directions and v: (221) directions. (b) A pattern as in (a) is superimposed on a contour plot in order to illustrate how the latter can be analyzed in detail. The energy of the moving atoms lies between 9.75 and 19.5 eV. The focusing in close packed directions can be noticed, as well as in open directions. These are easily identified as close to (221) directions. The two-dimensional focusing parallel to { 110) planes is visible too. The equidistance of the 20 adjacent contour lines is 5% of the maximum intensity.
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W. Eckstein, M. Hou / Computer simulation of {Ill}-surface
display of contour plots to a range of 120° azimuthal angle from a (110) surface direction. As the kinetic energy of the moving atoms dissipates, momentum starts to turn toward the surface when the kinetic energy gets below 150 eV, as shown in fig. 2 a for atoms moving in the vicinity of the surface. However, trajectories toward the vacuum are still directed rather close to the surface and surface scattering is not sufficient to help to overcome the surface energy barrier. At energies below 75 eV, a large fraction of momentum is found to be turned back toward the surface. This however only concerns atoms coming from the bulk, located just beneath the surface plane and that do not retain enough energy after crossing the surface in order to be sputtered. Sputtering starts to be significant at lower energy, and a substantial contribution is found below about 40 eV. Surface effects on the angular distributions can be seen in fig. 3. Indeed, surface recoils prevent the ejection of atoms in directions close to the surface. At this energy, a three-fold sputtering spot pattern occurs, which is not much influenced by the the refraction effect. The spot-splitting configuration subsequent to surface crossing (cos fl= -0.8) should be noticed. The structure in the sputtering distribution is due to atoms fed into low-constraint open directions. The major spots are oriented around (221) and (124) directions, close to the backward surface normal directions. Reference is made to crystallo-
intensity. The distributions are two-dimensional; one axis is the azimuthal angle with respect to a surface (110) direction, the other is the cosine of the angle p between the momentum direction and the inward surface normal. In such a representation, the direction distributions are constructed at constant solid angle (the resolution chosen here is limited to 4.2 x 10e3 sr). The contour lines are determined by means of a linear interpolation technique such that they would join boxes in the direction distributions with equal number of counts. The relation between momentum anisotropy and crystal structure as the energy dissipates can be analyzed in detail by a comparison of the contour plots with the low-index crystallographic directions and the loci of the directions parallel to the major low-index crystallographic planes. These are given in fig. la and an example of superposition on a contour plot is given in fig. lb for the momentum direction distributions in the whole cascades. From this latter figure, the correlation between the directions of atomic motion and the lattice structure obviously appears to dominate the cascade development. The complex structure in the backward directions (cos p < -0.6) is of particular interest for sputtering insofar as it also occurs in the close vicinity of the surface. In what follows, advantage is taken from the threefold symmetry of the (111) surface in order to present the figures in a compact way by limiting the
600 eV Xe- Au (1111 at NORMAL
cos p. COSINE
sputtering
INCIDENCE
of POLAR
,150 eV-=E-=300eV
ANGLE
Fig. 2. (a) Contour-line plots representing the angular distributions of atoms moving in the cascades generated by 600 eV Xe atoms incident on a Au (111) surface, in a layer from half an interplanar spacing beneath the surface plane to the vacuum. The abscissae represent the cosine of the polar angle, p, with respect to the inward surface normal and the ordinates represent the azimuth, +, with respect to a (110) surface direction. The plots are drawn for all particles whose kinetic energy gets lower than 300 eV but remain above 150 eV. The equidistance of the 20 adjacent contour lines is 5 percent of the maximum intensity. (b) Same as in (a) but among the atoms moving toward the vacuum, only those which fulfill the ejection conditions are taken into account. (c) Same as in (b), after surface refraction.
W. Eckstein, M. Hou / Computer simulation of (III}-surface
600eVXe
-Au
(Ill)
at NORMAL
cos p. COSINE
sputtering
275
INClDENCE,19eV
of POLAR
ANGLE
Fig. 3. Same as fig. 2 for cascade atoms which energy falls below 37.5 eV but remains above 19 eV. The surface binding energy has to be subtracted from these values in order to obtain the energy interval of the corresponding sputtered atoms.
threefold symmetric pattern is induced as exemplified in fig. 4 for particles sputtered with energies between 4.75 and 9.5 eV. The major six-fold pattern in the flux distribution, giving rise to sputtering is here the result of a combination of (112) and (221) focusing processes. These are the lowest-energy important contributions observed and they overwhelm the higher energy (221) and (124) ejection. The effect is reinforced at the lowest energies considered (down to 3.78 ev). As a result, the
directions only in order to identify the spots in the figures. At lower energy, around 20 eV, the pattern is dominated by (112) and (221) ejection. The additional contribution of ejection close to (124) directions only represents a minor contribution to the structure of the (221) spots. Focusing close to (124) directions is a short range effect and is specific to some energy interval. As the energy dissipates further, an additional graphic
600eV Xe -Au
-3 0
-08
-06
(Ill)
-04
at NORMAL INCIDENCE,4.75eV-=E-=9.5eV
-02
cos p, COSINE
0
02
of POLAR
04
06
08
1.0
ANGLE
Fig. 4. Same as fig. 3 for cascade atoms which energy falls below 9.5 eV but remains above 4.75 eV. This is an energy interval just below that considered in fig. lb. The differences in the momentum direction distributions in both cases are not significantly distinct.
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W. Ecksiein, M. Hou / Computer simulation of {I 1 l]-surface sputtering
whole sputtering pattern is dominated by the major six-fold pattern resulting from (112) and (221) focusing. It thus turns out that the interpretation of the anisotropy in sputtering angular distributions from (111) gold surfaces is rather complex since, depending on the ejection energy, the origin of the contributions to the same spots is different. Insofar as sputtering is dominated by low energy ejection, the major contribution to the spot pattern originates from (112) and (221) short range focusing, The contribution of (110) replacement sequences is found to be small. At this point, It can be anticipated that energy and angular resolved experiments might confirm the contribution of the focusing processes predicted here. Indeed, the predicted transition between three- and six-fold symmetric patterns as decreasing energies are analyzed should be observable experimentally.
4. Discussion Since the volume of an individual cascade has a finite size, the low-energy recoil density can be quite high. Hence, collisions between moving atoms become increasingly probable as the energy per atom decreases; such interactions are not properly modelled in the present version of the binary collision approximation. Also, at low energies, the distance of closest approach in a binary collision can be as large as a significant fraction of the atomic spacing, with the result that real trajectories may significantly deviate from the asymptotic motion. Although an approximate correction is provided in the MARLOWE program in the cases of such low energy events, the influence on sputtering estimates is difficult to anticipate. To our knowledge, no quantified measure of these two approximations on sputtering calculations exists, so that the only way to check the validity of the model is empirical. Qualitative and quantitative comparisons of simulated sputtering yields [5,34] as well as angular [34,35] and energy [5] distributions with experiment were made and are partially commented above. These comparisons performed for various systems and various incident conditions indicate that computer simulations with the present binary collision model allow fairly good predictions of the experimental data. This suggests that the binary collision approximation is reasonably valid for the description of cascade events in the energy regimes considered in the present work. As spot patterns are concerned, the LehmannSigmund-Nelson-Thompson mechanism [15,16,34] suggests ejection in close packed directions, which must be corrected for the surface scattering and refraction effects. This picture of sputtering in preferential directions was found useful in the case of { lOO} and { 110)
surface planes [34]. Ejection mechanisms from (111) surfaces are different and illustrate different collision cascade features. The efficiency of replacement sequence production is the highest in (110) directions and therefore, in principle, they could contribute to three of the six spots in the sputtering angular distribution from the (111) surface. Fig. lb shows that momentum direction distributions can be strongly peaked in these directions (cos /I = -0.82), but also that they may be surrounded by pairs of satellites stretching along (110) planes intersecting the surface. Fig. 3a shows that at energies between 19 and 37.5 eY, the contribution of (110) replacement sequences is possible in principle ( $J = 270 o ) but figs. 3b and 3c indicate that, when reaching the surface, the energy lost in the last collision is too large to allow ejection. At lower energies, fig. 4 shows that atoms ejected in the three-fold symmetrical directions close to (110) (cos /? = -0.82) are originated from the satellites displayed in fig. lb in the polar direction at cos /3 = -0.94. Figs. 3a and 4a show that the peaks in the velocity direction distributions before ejection are close enough to the surface normal that the surface scattering after the exit from the surface plane is negligible. Therefore, the only significant surface effect on the sputtering pattern is the refraction as seen by comparing figs. 3b and 4b to figs. 3c and 4c respectively. This makes the establishment of the relation between sputtering preferential directions and preferential directions of motion in the cascades simpler than in the case of (100) and (IlO} surfaces. It was found in ref. [20] that as a cascade develops, not only stable uniaxial focusing processes appear, but that transient one- and two-dimensional anisotropies occur, which may even dominate the contribution of replacement sequences. As a result, the momentum direction distribution in the cascades remain strongly anisotropic, whatever the kinetic energy of the atoms is. These energy dependent distributions are dominated by i) the effect of the symmetrical balancing forces transverse to (110) planes and which tend to confine the atomic motion inside them and ii) the existence of rather open solid angles in the crystal structure which allow the motion of atoms close to high index crystallographic directions over distances significantly larger than the first neighbor distance. The sputtering patterns obtained in the present simulations are typical of both processes. Indeed, fig. lb illustrates how the symmetrical configuration of atoms around { 110) planes acts to confine the directions of motion in them. A detailed analysis of the cascade evolution, as performed in ref. [20], shows that all satellite spots around the (110) directions are transient, align with the (110) planes and their direction is slightly energy dependent. These satellites were
W. Eckstein,
M. Hou / Computer simulation
found to originate from low energy unstable trajectories into (110) axial channels. In fig. lb they are close to (221) directions. When such directions intersect the surface, they give rise to a spot in the sputtering pattern and this is the origin of the preferential directions seen in fig. 4 and +=30”, 150° and 270”. The three other spots obviously have another origin which is not associated with (110) directions. These are close to (112) directions and the different contributions observed in figs. 3 and 4 all correspond to solid angles in which the crystal structure allows almost free motion over about 10 A. As in the experiments, the simulation sputtering direction pattern appears to be dominated by a six-fold structure which is the superposition of two three-fold spot patterns. They result from distinct transient focusing mechanisms in the collision cascades. A comparison between figs. 3c and 4c suggests that this prediction could be checked by an angular and energy resolved experiment. Strong uncorrelated displacements of the atoms from their lattice sites were found to prevent the two-dimensional (110) focusing and to stimulate the confinement of trajectories between (111) planes, which are the most compact [20]. This two-dimensional focusing process is also unstable and tends to vanish at the very low energies since, locally, the forces transverse to the { 111) planes are not balancing. Thermal displacements destabilize (110) focusing chains and the dominant focusing mechanism becomes short range in the available open solid angles. This represents an alternative mechanism for the preferential sputtering close to (221) directions. Here again, energy and angular resolved measurements in combination with computer simulations may help to determine the temperature range at which transient (110) focusing dominates and that for which the role of (111) planes is the most important in the cascade development and the sputtering ejection directions distributions. 5. Conclusion The present work illustrates how angular distributions of atomic sputtering is related to the anisotropic character of the cascade development in single crystals. The case of a (111) gold single crystal sputtered by 600 eV xenon atoms allows us to suggest new sputtering mechanisms in preferential directions which are energy dependent. It is consequently predicted that sputtering direction distributions recorded at different energies should display well pronounced and distinct features. An experimental verification of this prediction would confirm the occurrence of transient focusing mechanisms and would thus contribute to better characterize the role of the lattice constraint on the development of atomic collision cascades in solids.
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[34] M. Hou and W. Eckstein, Nucl. Instr. and Meth. B13 (1986) 324. [35] W. Eckstein and M. Hou, Nucl. Instr. and Meth. B31 (1988) 386. [36] M. Matsunami, S. Miyagawa, K. Morita and R. Shimizu, IPPJ-AM-14 (Institute of Plasma Physics, Nagoya University, Nagoya, Japan, 1980); R. Hultgren, J.P. De&, D.T. Hawkins, M. Gleiser, K.K. Kelley and D.D. Wagman, Selected Values of the Thermodynamic Properties of the Elements (Am. Sot. Metals Park, Ohio, U.S.A., 1973).
sputtering
[37] Y. Yamamura and W. Takeuchi, Nucl. Instr. and Meth. B29 (1987) 461. [38] P. Sigmund, M.T. Robinson, M.I. Baskes, M. Hautala, F.Z. Cui, W. Eckstein, Y. Yamamura, S. Hosaka, T. Ishitani, V.I. Shul’ga, D.E. Harrison, Jr., I.R. Charkov, D.S. Karpuzov, E. Kawatoh and R. Shimizu, S. Valkealahti, R. Nieminen, G. Betz and W. Husinsky, M.H. Shapiro, M. Vicanek and H.M. Urbassek, Nucl. Instr. and Meth. B36 (1989) 110. [39] M. Hou and W. Eckstein, IPP-report 9/65 (1988).
Nuclear
The atqrnic sputtering from
(
Instruments
and Methods
in Physics
Research
B53 (1991) 270-278 North-Holland
111) surfaces of fee metals
W. Eckstein Max-Planck-Insiitut
ftir Plasmaphysik, E URA TOM association, W-8046 Garching, Germany
M. Hou Universitt! Libre de Bruxelles, CP234, Bd. du Triomphe, B-1050 Brussels, Belgium Received
23 August
1990
New sputtering mechanisms are identified by means of computer simulation with the MARLOWE code, which give rise to the most pronounced structures in the angular distributions of ejection from a { 111) gold surface. The influence of surface scattering of ejected recoils and of the trajectory refraction by the surface binding forces is identified. This allows the relation between the structure of the sputtering angular patterns and the anisotropies in the distribution of the directions of motion of cascade atoms to be emphasized. Transient focusing processses in the cascade development are found responsible for the major structures in the
sputtering angular distributions. These distributions are strongly dependent on the sputtering energy. It is suggested that this prediction can be checked by energy- and angular-resolvedsputtering measurements.
1. Introduction Atomic collision cascades generated by energetic particles in solids are short lifetime events. As a consequence, the direct observation of the atomic motion and instantaneous spatial configurations is not possible. The only method to gather detailed information about the evolution of collision cascades in a material is computer experiments. However, these are based on atomic interaction models whose range of applicability may differ from one material to another and may also be dependent on the interaction energies involved. Therefore, they need to be checked empirically. Since this is not directly possible on the basis of the collision cascade development, related measurable processes have to be used instead. One of the few direct dynamic consequences of atomic collision cascades in solids which can be studied experimentally in details is sputtering. Atomic collision cascades were recognized as a possible origin of sputtering a long time ago [l]. A brief historical overview of collisional sputtering theories is given in ref. [2]. Numerous experimental studies of sputtering were performed since its discovery [3], in continuously improved conditions. Reviews are presented in ref. [4]. Hence, computer simulation models can be checked and adjusted by quantitative comparison to experimental sputtering data [5-81. The relation between sputtering simulation and collision cascades can be established, but is not straightforward, because of the role played by the surface. 0168-583X/91/$03.50
0 1991 - Elsevier Science
Publishers
The quantities related to atomic sputtering that are the most currently measured and calculated are sputtering yields, energy and angular distributions. Analytical collision cascade theories usually make use of a random target model [9-121 and allow reasonable predictions of sputtering yields for a wide range of systems, on the basis of a linearized Boltzmann transport equation [12]. The parameter which represents the major limit to the sputtering yield from metals is the surface binding energy and yield studies only provide moderate information about the development of collision cascades. The relation between the atomic sputtering energy distribution and the kinetic energy distribution of atoms moving in the cascades could be established [13]. It presents a maximum related to the value of the surface binding energy and a high energy tail with a close to inverse quadratic dependence on the energy. The latter is typical of energy distributions as predicted for atomic collision cascades in random materials (131. Recent computer simulations in the binary collision approximation allowed a more accurate analysis and suggests this tail to be decreasing as E-‘13 with energy [6,7]. More detailed information about the atomic motion in collision cascades may be expected in angular distributions of sputtered atoms from single crystals, which also display a more complex structure. Indeed, the sputtering from single crystals is known to display preferential directions [14], often rather close to low-index crystallographic directions intersecting the surface. These anisotropies are assumed to have their origin in
B.V. (North-Holland)
W. Eckstein, M. Hou / Computer simulation of {II I}-surface sputtering random cascades [15,16]. This suggests a cascade development model which is dominantly random but from which directional effects - called focusing effects originate from the lattice structure. By random cascade, it is meant that the collision sequences undergone by the moving atoms are considered as stochastic chains. This implies the target structure to be of negligible influence. It should be noticed that such a model does not imply the isotropy of the final rest configuration of the cascades, which structure is known to be correlated to the momentum direction of the high-energy moving atoms at the very first steps of the cascade development [17]. Final atomic rest configurations are not considered in the presented work. Their study is presented elsewhere [17-191. Aspects of the random cascade model are discussed in ref. [20] on the basis of computer simulations in the binary collision approximation. It was found that the lattice structure in single- and polycrystals acts as a strong rigid mechanical constraint. Consequently, most of the cascade atoms have their motion driven by the crystal structure. It was also found that channelling and focusing chains were not sufficient to account for the whole anisotropic character of the momentum direction distributions in the cascades, which is energy dependent. Insofar the atomic sputtering can be considered as a consequence of the atomic motion in collision cascades, the relation between sputtering angular distributions and momentum direction distributions in the developing cascades should be possible. It is our purpose to emphasize this relation on the basis of computer simulations in the binary collision approximation, compared with experimental measurements [21]. The discussion is based on the case of the irradiation of a gold (111) surface by Xe atoms with 600 eV incident kinetic energy. In such conditions, the elastic energy transfers represent the dominant energy-loss mechanism.
2. The simulation model The MARLOWE computer simulation code [22] was used for the present calculations. It is based on the binary collision approximation. 2.1. The impact and energy parameters Between collisions, particles are assumed to move along their asymptotic trajectories. Provision is made for an approximate treatment of quasi-simultaneous collisions [23]. A zero binding energy is used for the gold atoms to their lattice sites. A small binding energy is however assumed for replacement collisions (0.2 eV) in order to correct for the many body nature of such
211
events [24]. This approach was discussed in detail on the basis of comparison with classical dynamics calculations. As shown in [24], the mean energy loss along replacement sequences is systematically underestimated because, in the binary collision approximation, the dynamics of the interaction between successive atoms in a row is not handled properly. To our knowledge, no information about the magnitude of this underestimate is available in the case of gold and the choice of 0.2 eV, although expected of the right order of magnitude, is somewhat arbitrary. The energy dissipation through binary collisions proceeds until the kinetic energy of the moving particles falls below a preset cutoff value, 3.78 eV, which is also used as an energy displacement threshold and as the magnitude of the surface binding energy, assumed with planar symmetry. Only the contribution of collisions with an impact parameter smaller then 0.62a, (where a, = 4.076 A is the length of a lattice cell edge) is considered. Inelastic energy loss is assumed to be equally shared between local and nonlocal electron excitations, according to Oen and Robinson [25] and Lindhard [26] respectively. 2.2. The cascade scheduling Time is not a currently available cascade characteristic in binary collision models. Real time is used for the simulation of sputtering of silver by bismuth atoms and of carbon by very large argon clusters [27]. It was also introduced in MARLOWE for the study of Auger emission [28] in an approximate way which range of applicability is limited to the high energy part of the cascades. The MARLOWE code is in the process of being redesigned in order to allow for the simulation of fully time-driven events and already was used in slowingdown and cascade studies [29,30]. In the present version of the Marlowe code (version 12.0), after each collision step, the fastest atom is selected as the next projectile to be followed, until all cascade particles have their kinetic energy below the cutoff value. Deviations from this model are anticipated to influence sputtering significantly in case of the occurrence of strong nonlinear effects, which only can be handled properly with a time-driven cascade scheduling procedure. The present work focuses on the angular distribution of sputtering from a (111) surface and its relation to the velocity direction distribution of moving atoms in the cascade. This requires a careful modelling and analysis of the ejection process. 2.3. The potential
and the surface binding energy
Atomic collisions are governed by the pairwise Moliere potential [31] and the screening length for the homonuclear gold pair is a parameter. Firsov screening distances [32] are assumed to be valid for rare gas atoms
212
W. Eckstein, M. Hou / Computer simulation of {II I}-surface sputtering
and these for heteronuclear pairs (Xe-Au) are estimated as harmonic means of the screening lengths for the homonuclear pairs [33]. The choice of the Au-Au screening length is discussed below. The same sputtering model is used as in our preceding work [5,34,35]. An atom which aims to escape from a planar surface has to overcome two balancing effects: i) the scattering from close neighbouring surface atoms which tends to feed its trajectory toward the surface normal and ii) a refraction toward the surface imposed by the surface binding energy. The former effect is obviously potential dependent while the latter depends on the magnitude of the surface binding energy. Both have a significant effect on the angular distribution of sputtering, as discussed in ref. [34,35] and shown below. In ref. [35], the same case study as considered in the present work was used in order to find the best adjustment of the potential parameter and the surface binding energy, in order to match the simulation results from a static lattice to those sputtering angular distributions obtained experimentally in the same incident conditions at 15 K. The choice of the cohesive energy for gold (3.78 eV [36]) was found reasonable in conjunction with the Moliere potential used with a screening length of 0.0752 A for a gold homonuclear interacting pair. This value is the same as that suggested in ref. [22] and deduced by matching the Moliere potential to the Born-Mayer potential at the first neighbor distance. The parameters for this latter model potential were obtained from equilibrium crystal data [13]. 2.4. The influence of the model parameters
on the sputter-
ing pattern
It was found in ref. [35] that the major feature of the sputtering angular distribution from a (111) gold surface irradiated with 600 eV Xe atoms is an intense six-fold symmetrical spot pattern. The six spots are centered around a direction making an angle of about 32” with the surface normal. We were unable to find a couple of potential and surface binding parameters, significantly distinct from those presently used and which allows the reproduction of the experimental data as well. This six-fold geometry does not match that of low index directions intersecting the surface plane ((loo), (110) and (111) directions intersecting the surface make angles of 54.74O, 35.26 o and 70.53” with the surface normal, respectively). The same symmetrical pattern was, however found experimentally, over a wide range of incident energies, incident masses and target temperatures [21]. On the other hand, as far as the sputtering direction distribution is concerned, it was found that modifying the strength of the potential or the magnitude of the binding energy had no other significant effect other than modifying the spot positions and shapes in direc-
tions parallel to the (110) planes normal to the surface. The effect is the same for each spot. The occurrence of the six-fold symmetrical spot pattern is thus not much dependent on the surface ejection model. It has its origin in the cascade development close to the surface.
3. The origin of sputtering in preferential directions The angular distributions of sputtering from single crystals are commonly analyzed in terms of two different mechanisms related to focusing along close-packed directions [15] and the flux distribution from a random cascade through the surface lattice [16]. These mechanisms were suggested to have the same origin [34] and were used as a basis to discuss the sputtering direction distributions from various surfaces of materials with various common structures [37]. The sputtering simulations presented in ref [34] indeed illustrate the important role of replacement sequences on the ejection from {loo} and { llO} surfaces from fee crystals and their contribution could be quantified. Such a quantification is also presented for the Xe-Au (100) system in ref. [24]. The balance between surface scattering of sputtered recoils and surface refraction by the binding force was emphasized. Owing to the energy dispersion in replacement sequences, the surface refraction has the effect to bent the ejection directions at various angles with the result of the occurrence of streaks in the sputtering patterns. This was a first illustration that particles ejected by a focusing chain mechanism does not only contribute to sputtering spots. The situation is even more complex in the case of the ejection from a (111) surface and the following description will show that the known stable focusing processes are not responsible for the six-fold symmetrical spot pattern obtained in the present simulations. It was shown in ref. [20] that momentum distributions in collision cascades are not isotropic. Prior to discussing the relation between the anisotropy of momentum distributions and sputtering patterns, a description of the energy dependence of sputtering patterns is given. Since about 90% of the sputtering originates from the surface plane [38], its understanding requires the knowledge of the atomic momentum distribution in the close vicinity of the surface as well as the effect of surface scattering and refraction. In order to follow the sputtering process, the momentum distributions in the close vicinity of the surface plane are compared at successive steps of the ejection process, as a function of the kinetic energy. Three situations are compared. The first is the momentum distribution of atoms moving in the vicinity of the surface plane in the half space including the vacuum and limited at a distance of half a planar spacing beneath the surface. Secondly, distributions are con-
W. Eckstein, M. Hou / Computer simulation of (I I I}-surface
strutted as in the first situation but they are restricted to atoms which fulfill the conditions to overcome the surface energy barrier. In the third situation, the refraction of the trajectories in the vacuum is taken into account. In such a way, the sputtering angular distribution of atoms ejected with different kinetic energies is displayed. The energy dependence of the sputtering angular distributions is studied with the same method as the
sputtering
273
momentum direction distributions in refs. [20] and [39]. The angular distributions are recorded for all particles entering a prespecified kinetic energy interval. Consecutive intervals are taken as (E,/2”, E,/2”+‘), where E,, is the primary energy, for increasing integer values of n until the cutoff energy is reached. The distributions are represented in the form of contour-line plots of equal intensities. The number of contour lines is limited to 20. Their equidistance corresponds to 5% of the maximal
(4
1
E -0 4: csl z =:
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1.0
0.6
0.8
1.0
cos P.COSINE of POLAR ANGLE b)
-"I0
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
cosp, COSINE of POLAR ANGLE Fig. 1. (a) Loci of the directions parallel to the most compact crystallographic planes. Their intersections represent the close packed directions in the lattice, that are labelled in the figure. o o 0: loci of directions parallel to (100) planes, AAA: loci of directions parallel to (110) planes, + + + loci of directions parallel to the (111) planes, n : (100) directions, 0: (110) directions, l : (111) directions, A: (112) directions and v: (221) directions. (b) A pattern as in (a) is superimposed on a contour plot in order to illustrate how the latter can be analyzed in detail. The energy of the moving atoms lies between 9.75 and 19.5 eV. The focusing in close packed directions can be noticed, as well as in open directions. These are easily identified as close to (221) directions. The two-dimensional focusing parallel to { 110) planes is visible too. The equidistance of the 20 adjacent contour lines is 5% of the maximum intensity.
214
W. Eckstein, M. Hou / Computer simulation of {Ill}-surface
display of contour plots to a range of 120° azimuthal angle from a (110) surface direction. As the kinetic energy of the moving atoms dissipates, momentum starts to turn toward the surface when the kinetic energy gets below 150 eV, as shown in fig. 2 a for atoms moving in the vicinity of the surface. However, trajectories toward the vacuum are still directed rather close to the surface and surface scattering is not sufficient to help to overcome the surface energy barrier. At energies below 75 eV, a large fraction of momentum is found to be turned back toward the surface. This however only concerns atoms coming from the bulk, located just beneath the surface plane and that do not retain enough energy after crossing the surface in order to be sputtered. Sputtering starts to be significant at lower energy, and a substantial contribution is found below about 40 eV. Surface effects on the angular distributions can be seen in fig. 3. Indeed, surface recoils prevent the ejection of atoms in directions close to the surface. At this energy, a three-fold sputtering spot pattern occurs, which is not much influenced by the the refraction effect. The spot-splitting configuration subsequent to surface crossing (cos fl= -0.8) should be noticed. The structure in the sputtering distribution is due to atoms fed into low-constraint open directions. The major spots are oriented around (221) and (124) directions, close to the backward surface normal directions. Reference is made to crystallo-
intensity. The distributions are two-dimensional; one axis is the azimuthal angle with respect to a surface (110) direction, the other is the cosine of the angle p between the momentum direction and the inward surface normal. In such a representation, the direction distributions are constructed at constant solid angle (the resolution chosen here is limited to 4.2 x 10e3 sr). The contour lines are determined by means of a linear interpolation technique such that they would join boxes in the direction distributions with equal number of counts. The relation between momentum anisotropy and crystal structure as the energy dissipates can be analyzed in detail by a comparison of the contour plots with the low-index crystallographic directions and the loci of the directions parallel to the major low-index crystallographic planes. These are given in fig. la and an example of superposition on a contour plot is given in fig. lb for the momentum direction distributions in the whole cascades. From this latter figure, the correlation between the directions of atomic motion and the lattice structure obviously appears to dominate the cascade development. The complex structure in the backward directions (cos p < -0.6) is of particular interest for sputtering insofar as it also occurs in the close vicinity of the surface. In what follows, advantage is taken from the threefold symmetry of the (111) surface in order to present the figures in a compact way by limiting the
600 eV Xe- Au (1111 at NORMAL
cos p. COSINE
sputtering
INCIDENCE
of POLAR
,150 eV-=E-=300eV
ANGLE
Fig. 2. (a) Contour-line plots representing the angular distributions of atoms moving in the cascades generated by 600 eV Xe atoms incident on a Au (111) surface, in a layer from half an interplanar spacing beneath the surface plane to the vacuum. The abscissae represent the cosine of the polar angle, p, with respect to the inward surface normal and the ordinates represent the azimuth, +, with respect to a (110) surface direction. The plots are drawn for all particles whose kinetic energy gets lower than 300 eV but remain above 150 eV. The equidistance of the 20 adjacent contour lines is 5 percent of the maximum intensity. (b) Same as in (a) but among the atoms moving toward the vacuum, only those which fulfill the ejection conditions are taken into account. (c) Same as in (b), after surface refraction.
W. Eckstein, M. Hou / Computer simulation of (III}-surface
600eVXe
-Au
(Ill)
at NORMAL
cos p. COSINE
sputtering
275
INClDENCE,19eV
of POLAR
ANGLE
Fig. 3. Same as fig. 2 for cascade atoms which energy falls below 37.5 eV but remains above 19 eV. The surface binding energy has to be subtracted from these values in order to obtain the energy interval of the corresponding sputtered atoms.
threefold symmetric pattern is induced as exemplified in fig. 4 for particles sputtered with energies between 4.75 and 9.5 eV. The major six-fold pattern in the flux distribution, giving rise to sputtering is here the result of a combination of (112) and (221) focusing processes. These are the lowest-energy important contributions observed and they overwhelm the higher energy (221) and (124) ejection. The effect is reinforced at the lowest energies considered (down to 3.78 ev). As a result, the
directions only in order to identify the spots in the figures. At lower energy, around 20 eV, the pattern is dominated by (112) and (221) ejection. The additional contribution of ejection close to (124) directions only represents a minor contribution to the structure of the (221) spots. Focusing close to (124) directions is a short range effect and is specific to some energy interval. As the energy dissipates further, an additional graphic
600eV Xe -Au
-3 0
-08
-06
(Ill)
-04
at NORMAL INCIDENCE,4.75eV-=E-=9.5eV
-02
cos p, COSINE
0
02
of POLAR
04
06
08
1.0
ANGLE
Fig. 4. Same as fig. 3 for cascade atoms which energy falls below 9.5 eV but remains above 4.75 eV. This is an energy interval just below that considered in fig. lb. The differences in the momentum direction distributions in both cases are not significantly distinct.
216
W. Ecksiein, M. Hou / Computer simulation of {I 1 l]-surface sputtering
whole sputtering pattern is dominated by the major six-fold pattern resulting from (112) and (221) focusing. It thus turns out that the interpretation of the anisotropy in sputtering angular distributions from (111) gold surfaces is rather complex since, depending on the ejection energy, the origin of the contributions to the same spots is different. Insofar as sputtering is dominated by low energy ejection, the major contribution to the spot pattern originates from (112) and (221) short range focusing, The contribution of (110) replacement sequences is found to be small. At this point, It can be anticipated that energy and angular resolved experiments might confirm the contribution of the focusing processes predicted here. Indeed, the predicted transition between three- and six-fold symmetric patterns as decreasing energies are analyzed should be observable experimentally.
4. Discussion Since the volume of an individual cascade has a finite size, the low-energy recoil density can be quite high. Hence, collisions between moving atoms become increasingly probable as the energy per atom decreases; such interactions are not properly modelled in the present version of the binary collision approximation. Also, at low energies, the distance of closest approach in a binary collision can be as large as a significant fraction of the atomic spacing, with the result that real trajectories may significantly deviate from the asymptotic motion. Although an approximate correction is provided in the MARLOWE program in the cases of such low energy events, the influence on sputtering estimates is difficult to anticipate. To our knowledge, no quantified measure of these two approximations on sputtering calculations exists, so that the only way to check the validity of the model is empirical. Qualitative and quantitative comparisons of simulated sputtering yields [5,34] as well as angular [34,35] and energy [5] distributions with experiment were made and are partially commented above. These comparisons performed for various systems and various incident conditions indicate that computer simulations with the present binary collision model allow fairly good predictions of the experimental data. This suggests that the binary collision approximation is reasonably valid for the description of cascade events in the energy regimes considered in the present work. As spot patterns are concerned, the LehmannSigmund-Nelson-Thompson mechanism [15,16,34] suggests ejection in close packed directions, which must be corrected for the surface scattering and refraction effects. This picture of sputtering in preferential directions was found useful in the case of { lOO} and { 110)
surface planes [34]. Ejection mechanisms from (111) surfaces are different and illustrate different collision cascade features. The efficiency of replacement sequence production is the highest in (110) directions and therefore, in principle, they could contribute to three of the six spots in the sputtering angular distribution from the (111) surface. Fig. lb shows that momentum direction distributions can be strongly peaked in these directions (cos /I = -0.82), but also that they may be surrounded by pairs of satellites stretching along (110) planes intersecting the surface. Fig. 3a shows that at energies between 19 and 37.5 eY, the contribution of (110) replacement sequences is possible in principle ( $J = 270 o ) but figs. 3b and 3c indicate that, when reaching the surface, the energy lost in the last collision is too large to allow ejection. At lower energies, fig. 4 shows that atoms ejected in the three-fold symmetrical directions close to (110) (cos /? = -0.82) are originated from the satellites displayed in fig. lb in the polar direction at cos /3 = -0.94. Figs. 3a and 4a show that the peaks in the velocity direction distributions before ejection are close enough to the surface normal that the surface scattering after the exit from the surface plane is negligible. Therefore, the only significant surface effect on the sputtering pattern is the refraction as seen by comparing figs. 3b and 4b to figs. 3c and 4c respectively. This makes the establishment of the relation between sputtering preferential directions and preferential directions of motion in the cascades simpler than in the case of (100) and (IlO} surfaces. It was found in ref. [20] that as a cascade develops, not only stable uniaxial focusing processes appear, but that transient one- and two-dimensional anisotropies occur, which may even dominate the contribution of replacement sequences. As a result, the momentum direction distribution in the cascades remain strongly anisotropic, whatever the kinetic energy of the atoms is. These energy dependent distributions are dominated by i) the effect of the symmetrical balancing forces transverse to (110) planes and which tend to confine the atomic motion inside them and ii) the existence of rather open solid angles in the crystal structure which allow the motion of atoms close to high index crystallographic directions over distances significantly larger than the first neighbor distance. The sputtering patterns obtained in the present simulations are typical of both processes. Indeed, fig. lb illustrates how the symmetrical configuration of atoms around { 110) planes acts to confine the directions of motion in them. A detailed analysis of the cascade evolution, as performed in ref. [20], shows that all satellite spots around the (110) directions are transient, align with the (110) planes and their direction is slightly energy dependent. These satellites were
W. Eckstein,
M. Hou / Computer simulation
found to originate from low energy unstable trajectories into (110) axial channels. In fig. lb they are close to (221) directions. When such directions intersect the surface, they give rise to a spot in the sputtering pattern and this is the origin of the preferential directions seen in fig. 4 and +=30”, 150° and 270”. The three other spots obviously have another origin which is not associated with (110) directions. These are close to (112) directions and the different contributions observed in figs. 3 and 4 all correspond to solid angles in which the crystal structure allows almost free motion over about 10 A. As in the experiments, the simulation sputtering direction pattern appears to be dominated by a six-fold structure which is the superposition of two three-fold spot patterns. They result from distinct transient focusing mechanisms in the collision cascades. A comparison between figs. 3c and 4c suggests that this prediction could be checked by an angular and energy resolved experiment. Strong uncorrelated displacements of the atoms from their lattice sites were found to prevent the two-dimensional (110) focusing and to stimulate the confinement of trajectories between (111) planes, which are the most compact [20]. This two-dimensional focusing process is also unstable and tends to vanish at the very low energies since, locally, the forces transverse to the { 111) planes are not balancing. Thermal displacements destabilize (110) focusing chains and the dominant focusing mechanism becomes short range in the available open solid angles. This represents an alternative mechanism for the preferential sputtering close to (221) directions. Here again, energy and angular resolved measurements in combination with computer simulations may help to determine the temperature range at which transient (110) focusing dominates and that for which the role of (111) planes is the most important in the cascade development and the sputtering ejection directions distributions. 5. Conclusion The present work illustrates how angular distributions of atomic sputtering is related to the anisotropic character of the cascade development in single crystals. The case of a (111) gold single crystal sputtered by 600 eV xenon atoms allows us to suggest new sputtering mechanisms in preferential directions which are energy dependent. It is consequently predicted that sputtering direction distributions recorded at different energies should display well pronounced and distinct features. An experimental verification of this prediction would confirm the occurrence of transient focusing mechanisms and would thus contribute to better characterize the role of the lattice constraint on the development of atomic collision cascades in solids.
of {l II}-surface
sputtering
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