Modelling of cluster emission from metal surfaces under ion impact

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1 /rsta FirstCite e-publishing Modelling of cluster emission from metal surfaces under ion impact By G. Betz and W. Husinsky Institut für Allgemeine Physik, Technische Universität Wien, Wiedner Hauptstrasse 8 10, 1040 Wien, Austria (betz@iap.tuwien.ac.at) Using the molecular-dynamics technique, cluster emission for 5 kev Ar bombardment of a Cu (111) surface has been investigated using a many-body (tight binding) potential for the Cu Cu interaction. The calculations allow us to analyse the basic processes underlying cluster emission. It is found that two distinct processes can be distinguished which lead to cluster emission under energetic ion bombardment. The first process causes the emission of small clusters, which are emitted by a collective motion during the development of the collision cascade within the first picosecond after impact. Thus, emission times of such clusters agree with the emission times of atoms in sputtering. Such a process can be envisioned if, for example, a few layers below the surface, an energetic recoil causes the development of a subcascade. Energy transferred by this event to the surface is strongly directional and can lead to the simultaneous emission of a group of neighbouring surface atoms, which in some cases will remain bounded and form a cluster after emission. Typically, clusters emitted by this mechanism consist of atoms, which are neighbouring in the target and are almost exclusively surface atoms, similar to all sputtered atoms. Emission of large clusters (cluster sizes of 10 or more atoms), as observed experimentally, is a puzzling phenomenon. From our calculations we conclude that the emission of such large clusters does not occur during the collisional phase of sputtering, but happens much later (5 10 ps after ion impact). Emission can occur for spike events, where all the energy of the impinging ion is deposited locally in a small volume near to the surface, and the sputtering yield is 3 5 times the average yield. Such events are rare, but we have found a few cases in our calculations where stable clusters consisting of more than 20 atoms were emitted. Melting of the spike volume occurs, and the high temperatures and pressures produced can cause emission of large fragments during the thermal phase. The composition of such large clusters is quite different from that of small clusters. They consist of atoms from different layers and the constituents are also generally not next-neighbour atoms. This change in origin of the cluster atoms reflects the mixing and diffusion processes occurring in the melted zone before emission. The calculations indicate that hydrodynamical phenomena might play a role in the emission of large fragments. Additional calculations, where the energy was distributed thermally in a three-dimensional volume One contribution of 11 to a Theme Sputtering: past, present and future. W. R. Grove 150th Anniversary Issue. Phil. Trans. R. Soc. Lond. A 1 c 2003 The Royal Society

2 04TA1403/2 G. Betz and W. Husinsky under the surface for 500 fs, give very similar results, even in such cases where the kinetic phase of the collision-cascade development was absent. Keywords: sputtering; ion bombardment; cluster emission; computer simulation; molecular dynamics 1. Introduction If a metal target is bombarded with inert-gas ions having energies in the kev range, it is well known that not only does the sputtered flux consist of monatomic target particles, but, depending on the experimental conditions, a certain fraction of the emitted flux will consist of neutral and ionized clusters. While sputtering of atoms can be understood as a consequence of the intersection of the collision cascade with the surface, set into motion by the bombarding ion, the explanation for cluster emission is still an open question. In particular, the observation of large clusters that consist of up to several tens of atoms (Wucher & Wahl 1996; Urbassek & Hofer 1993; Coon et al. 1993a; Staudt et al. 2000) is still under discussion. In addition, the contribution of (neutral) clusters to the total sputtered flux is unclear and estimates range from ca. 2% up to some 10% for metals (Urbassek & Hofer 1993; Staudt et al. 2000; Betz & Husinsky 1995). The yield of clusters decreases strongly with cluster size, typically the yield of clusters with size N + 1 is lower by one order of magnitude than for size N, but there is good evidence that large clusters are relatively more abundant and that the relative yield of clusters shows a power-law dependence on the number N of atoms in the cluster (Y (N) N δ ) (Urbassek & Hofer 1993; Coon et al. 1993a; Staudt et al. 2000). Originally, information on the yield and energy distribution of clusters came mainly from cluster ions. For cluster ions, a general tendency that the maxima and the width of their energy distributions shift to lower energies with increasing cluster size (Dennis & MacDonald 1972; Staudenmaier 1972, 1973) was observed. For the high-energy tail of the distributions, an E n dependence was observed, with n typically increasing with cluster size (Staudenmaier 1972; Makarenko et al. 1991). For example, Staudenmaier (1972) found, for 150 kev ion bombardment of W, n = 0.5 for ions, n = 3 for dimer ions and n = 4 for trimer ions. An n value between 0.5 and 1.5, as observed for ions (Staudenmaier 1972; Dennis & MacDonald 1972; Oechsner & Reichert 1966), indicates that ions are predominantly energetic particles compared with atoms (n = 2), but cluster ions are less energetic than atoms. Preferred emission of cluster ions from single crystals into low-index lattice directions was observed in a manner similar to that for neutral clusters (Hofer & Gnaser 1987; Holland et al. 1980). Those clusters which are emitted in an ionized state or are post-ionized by electrons or lasers, are observed in secondary-ion mass spectrometry (SIMS) and related techniques. More recently, the use of lasers, especially the possibility of multi-photon ionization (MPI) in combination with the time-of-flight technique, has considerably increased our knowledge of neutral clusters sputtered from metal targets. Both energy distributions and cluster yields were obtained for different metal targets (Coon et al. 1991, 1993a, b; Wucher et al. 1993; Husinsky et al. 1993; Wahl & Wucher 1994). For kev ion bombardment of Ag and Cu, energy distributions were obtained for cluster sizes up to n = 7 and n = 6, respectively (Coon et al. 1993b; Wahl & Wucher 1994).

3 Cluster emission from metal surfaces under ion impact 04TA1403/3 Staudt et al. (2000) observed cluster sizes up to n = 60 and confirmed the power-law dependence of the cluster yield on cluster size (Y (N) N δ ) observed before. Theoretical modelling of cluster emission from metals is based on the work by Können et al. (1974) and Gerhard (1975), as well as later extensions and modifications (Haring et al. 1987; Hoogerbrugge & Kistemaker 1987a, b; Snowdon & Haring 1987). For the energy distributions, these models predict an E 3N+1 behaviour for a cluster consisting of N atoms, i.e. E 2, E 5 or E 8 for atoms, dimers or trimers, respectively. However, the experiments using MPI (Coon et al. 1991, 1993a, b; Wucher et al. 1993; Husinsky et al. 1993) indicate that the energy distribution of clusters falls off with E much more slowly than predicted, and appears to be better characterized by an E 3 or E 4 decay for clusters up to size 7. For dimer emission, essentially two models exist. The so-called single-collision model (de Jonge et al. 1987; Sigmund et al. 1986; Oechsner et al. 1978) assumes that preformed molecules, like adsorbed gas molecules, exist on the surface, and it is in general not applicable to modelling cluster emission from metal targets. The other model is the so-called double-emission model, also referred to as the recombination model, atomic combination model or statistical model (Können et al. 1974; Gerhard 1975; Haring et al. 1987; Hoogerbrugge & Kistemaker 1987a, b). This is applicable to metal targets and will be discussed further together with the calculation from molecular-dynamics (MD) calculations. The MD technique is ideally suited to studying the fundamental processes of ion bombardment, for times up to about one picosecond, in which the impinging particle transfers its energy to the target atoms leading to disorder (mixing) at and near the surface and to particle emission (sputtering). Many features of the sputtering process, such as energy distributions, angular distributions, depth of origin of sputtered particles, cluster emission or mixing inside the crystal, can be investigated with such MD calculations. Information on cluster emission by MD computer simulations started with the work of Harrison & Delaplain (1976). Such MD simulations, using modern many-body potentials (Foiles et al. 1986), have given additional insight into the cluster-emission process and sufficient statistics has been achieved to give representative results for dimers emitted from metals (Wucher & Garrison 1992a; Karetta & Urbassek 1992; Betz et al. 1994). The use of many-body potentials is very important in cluster-emission studies from metals, since the metallic bond cannot be described in terms of pairwise binding potentials. Agreement with experimental results with respect to measured energy distributions, especially with respect to the behaviour at high emission energies of dimers and trimers, has been claimed (Wucher & Garrison 1992a, 1996; Karetta & Urbassek 1992; Betz et al. 1994). In such simulations it was clearly shown that, under kev ion bombardment, sputtered dimers originate predominantly from next-neighbour sites, indicating a true double-collision mechanism being responsible for the majority of dimers formed (Karetta & Urbassek 1992; Betz et al. 1994). The so-called push-andstick mechanism (Bitensky et al. 1992) gives only a minor contribution to the dimer flux. The emission of larger clusters, especially of those with cluster sizes of n>10, as observed experimentally, remained a puzzling phenomenon and could not be understood by statistical models. Because emission of a large cluster is a very infrequent event in sputtering, many thousand impacts have to be simulated to find a few larger clusters 5 10 atoms in size. In order to obtain statistics on even larger clusters, we

4 04TA1403/4 G. Betz and W. Husinsky would need the calculation of so many impacts that the CPU time would become prohibitively large. In the following, MD calculations will be presented for kev ion bombardment of Cu, performed during an extensive study of cluster emission (Betz & Husinsky 1995, 2000; Colla et al. 1998) over a number of years. An attempt is made to give a picture of this process, based on the simulations, including results on the emission of large clusters consisting a few tens of atoms. In presenting the results of these MD calculations on cluster emission we will distinguish between emission of small (n <10) and large (n >10) clusters to elaborate on the two processes, which lead to cluster emission from metal targets under energetic ion bombardment. This division is to some degree artificial. As there is a continuous transition from the processes leading to small-cluster emission to those leading to large-cluster emission, however, it will help to extract the two different processes. The typical time-scale during which particle emission (sputtering) takes place is of the order of one picosecond or less. After one picosecond, the average energy of the atoms in the collision cascade is below the surface binding energy, preventing further emission of atoms, as can clearly be seen in MD simulations of the sputtering process (Betz & Husinsky 1995). We will show that, during the time the collision cascade exists and atoms are sputtered, only small clusters are emitted. In addition, we have observed the emission of large clusters in rare cases, but this occurs much later than the main set of sputtered particles and small clusters typically after 5 ps or more due to thermal processes. 2. Computer experiment set-up Ion bombardment of a Cu (111) surface by up to 5 kev Ar ions at normal incidence has been investigated by MD simulations. A many-body (tight-binding) potential for the Cu Cu interaction (Gades & Urbassek 1992) was used, which was splined to the high-energy Ziegler Biersack Littmark (ZBL) potential (Ziegler et al. 1985) and a purely repulsive ZBL potential was taken for the Ar Cu interaction. Some of the earlier calculations used a Born Mayer potential instead of the ZBL potential. However, the qualitative conclusions were not influenced by the choice of the potential, as was verified in later calculations, with this more realistic potential combination. Additional details of the potentials used and the MD code are given in Betz & Husinsky (1995), Colla et al. (1998) and in the following sections for specific calculations. As is typical for MD calculations of sputtering, they were done in the limit of zero fluence, i.e. each ion impact was on an ideal undisturbed single-crystal surface. 3. Small clusters (n <10) Most results presented are from a calculation of 6100 ion impacts for 5 kev Ar on Cu (111) (Betz & Husinsky 1995). For all calculations, the crystal consisted of 6174 atoms (17 17 LU and 9 layers deep, 1 LU = nm). For each ion impact, the development of the collision cascade has been followed up to 1 ps, which is much longer than the typical sputter time. No periodic boundary conditions were used. Even for such a large crystal there are impact points, especially at 5 kev, for which the cascade is not fully contained within the crystal. However, we have tested that

5 Cluster emission from metal surfaces under ion impact 04TA1403/5 Table 1. Composition of the sputtered flux for 5 kev Ar bombardment of a Cu (111) surface after 100 ps (5000 impacts, total sputter yield 17) cluster sputtered clusters sputtered cluster cluster size cluster yield size (number) (% of all sputtered atoms) (cluster/impact) transmission sputtering for those cascades will not influence the results for backward sputtering from the surface, as compared with an infinitely thick target. Emitted clusters might be highly excited and decay into smaller subunits by unimolecular decomposition (even the total energy of the original cluster is negative in the centre-of-mass system). To identify sputtered clusters, we did not use a total energy criterion in the centre-of-mass system to check their stability, as was done in early simulations (Harrison & Delaplain 1976; Garrison et al. 1978) and criticized (Andersen 1987). Such a criterion is correct for dimers, but not for larger clusters (as has been pointed out by Wucher & Garrison) due to decomposition of excited clusters into smaller subunits (unimolecular decomposition) (Wucher & Garrison 1992b). In a separate calculation we followed all sputtered particles for another 100 or 200 ps. A cluster was than identified by the simple criterion of finding groups of atoms that were interacting with each other (with separations less than the cut-off radius of the potential used). No further decomposition of clusters was detected after 100 ps and all results presented are for a final calculation time of 100 ps. In table 1, the composition of the sputtered flux and the cluster yields for a set of 5000 impacts of 5 kev Ar ions on Cu after 100 ps are presented. The largest cluster observed was of size 8. Statistical information for cluster sizes up to n = 6 could be obtained from this and additional calculations. The high relative yields of clusters found are at first glance surprising. However, a contribution of 32.3% of atoms from the dimer to the total flux actually only means an atom/dimer ratio of 3.6 or a total dimer yield of 2.7. We are dealing with a high-yield (Cu (111)) surface. In comparison, experimental results for polycrystalline Ag at 5 kev by Franzreb et al. (1991) report an Ag 2 /Ag yield ratio of or a Ag 2 yield of 0.88 assuming a total sputtering yield of 8 for polycrystalline Ag (average over experimental data points from Andersen & Bay (1981)). From the well-known fact that the dimer yield scales with Ytot 2 (Gerhard 1975; Gnaser & Oechsner 1991) we can extrapolate the Ag dimer yield for a total sputtering yield of 17, resulting in a value of 4.0. Thus, the obtained value of 2.7 in our MD calculations is actually rather low in comparison, if one bears in mind that we are dealing with a high-yield surface. Figure 1 shows the dependence of the relative yield on the cluster size. As can also be seen in computer simulations, we find the experimentally observed power-law dependence of the cluster yield on cluster size N: Y (N) = const. N δ (Urbassek

6 04TA1403/6 G. Betz and W. Husinsky 10 0 calculation power law 10 1 relative yield 10 2 n cluster size n Figure 1. Calculated cluster abundance distribution for Cu n clusters sputtered by 5 kev Ar impact from Cu (111) after the fragmentation of metastable clusters. & Hofer 1993; Coon et al. 1993a; Staudt et al. 2000). For the high-yield Cu (111) surface, the value of δ = 4.5 is also in reasonable agreement with experimental results, if one takes into account that δ scales with the total sputtering yield (Wucher 1993; Coon et al. 1994) in experiments. Due to this high value of δ, we obtain a contribution of 40 50% of clusters to the total sputtered atom flux as shown in table 1. In agreement with calculations at lower energies (Betz et al. 1994), and with analytical theories and experiments (Falcone & Sigmund 1981; Vicanek et al. 1989; Burnett et al. 1988), we observe that the dominant contribution to the sputtered flux is from first-layer atoms. About 92% of all sputtered atoms are from the first layer, 5.1% are from the second, 1.3% are from the third and 1.4% are from deeper layers. With respect to cluster emission, it is interesting to note that atoms from deeper layers (n >2) contribute significantly more to sputtered single atoms than to clusters. About 60 70% of all clusters with n > 3 are exclusively from firstlayer atoms. This supports and confirms previous evidence that sputtered dimers and larger clusters originate predominantly from next-neighbour sites at the surface, indicating that a true double-collision mechanism is responsible for the majority of dimers formed (Karetta & Urbassek 1992; Betz et al. 1994). The so-called pushand-stick mechanism (Bitensky et al. 1992) gives only a minor contribution to the dimer flux. Indeed, ca. 60% of all dimers are formed by next-neighbour atoms and, in addition, a substantial number of dimers not formed from next neighbours can be traced back to the decomposition of larger clusters. At an energy of 5 kev, essentially all impact points lead to at least single-atom sputtering and most impact points lead to the emission of at least one dimer. Impact points leading to the emission of larger clusters are randomly distributed over the minimum-impact zone defined by the crystal symmetry indicating no region of predominant cluster emission. Looking at the frequency distributions for the emission of the total number of sputtered particles, events could be identified, where up to

7 Cluster emission from metal surfaces under ion impact 04TA1403/7 D (a) (b) U Figure 2. (a) In the double collision mechanism mechanisms for dimer emission, two (neighbouring) atoms receive, simultaneously, almost parallel momenta, leading to their emission. A dimer is emitted if the sum of the relative kinetic energies of the two emitted atoms are less than the dissociation energy D of the dimer formed. (b) Evidence from computer simulations indicates an emission mechanism for large clusters, in which, due to correlated motion in the collision cascade, a group of neighbouring atoms on the surface receive, simultaneously, near-parallel momenta, leading to the emission of a group of bonded atoms (cluster). 60 particles were emitted in total. However, cluster emission was found to be only weakly correlated with high-yield events and clusters up to size 6 could also be identified with total emission yields below 20. For 5 kev Ar on Cu, most sputtered atoms are emitted within fs after the primary particle impinges on the surface. A clear correlation was observed: the emission time of clusters (defined as the average emission time of the individual atoms) increases with cluster size, and reached ca. 900 fs for cluster size 6. This indicates that cluster emission is a late and therefore low-energy event in the development of the collision cascade. A large number of the emitted clusters of size n>2 are exclusively from first-layer atoms. Moreover, they are also, to a high degree, connected, i.e. they form groups of next-neighbour atoms. In those clusters containing second layer atoms, these are also always next neighbours to surface cluster atoms. Analysis of the data shows that between 60 and 70% of all clusters with size n = 3 8 consist of connected atoms. These data still lead to an underestimation of the situation at the time of emission, as decomposition of clusters will occur after emission during the 100 ps of calculation time. The main mechanism of cluster emission from metals discussed in the literature is the so-called double-collision mechanism (recombination model, atomic combination, statistical model) (see figure 2a), which is based on the fact that, for metals and semiconductors, the dissociation energy D of a dimer is typically smaller than the surface binding energy (sublimation energy) U b and, if enough centre-of-mass energy is transferred to a dimer, its internal energy is usually so high that it will not survive the emission from the solid intact. No preformed molecules exist. In the doublecollision mechanism, dimers or larger clusters are formed from independently ejected atoms, if they are emitted close enough in time and space and their relative kinetic energies are less than the binding energy of the dimer (cluster) (Können et al. 1974; Gerhard 1975; Haring et al. 1987; Hoogerbrugge & Kistemaker 1987a). Note that a dimer cannot form far from the surface but only close to it, where the dimer still

8 04TA1403/8 G. Betz and W. Husinsky yield (arb. units) Cu Cu 2 Cu 3 Cu 4 Cu thick full lines from MD thin full line: 1/E 2 dashed line: 1/E energy (ev) Figure 3. Energy distributions (flux) of Cu atoms and Cu clusters up to Cu 5 (data points) sputtered with 3.9 kev Ar ions (Coon et al. 1993a) are compared with MD simulation results for atoms, dimers, trimers, quatromers and pentomers for 5 kev Ar ions on Cu (111). The MD cluster yields have been normalized to the experimental results. Asymptotic distributions (thin lines) for 1/E 2 and 1/E 3 are also shown. feels the forces of surface atoms, to carry off the recombination energy. The model can be extended in a straightforward manner to multimer emission. Theoretical treatments are based on the following assumptions. (i) Sputtering of individual atoms occurs according to the linear cascade theory with uncorrelated momenta. Provided that their momenta and trajectories are sufficiently close to each other, the atoms can form a dimer or multimer on leaving the surface. (ii) The dimer/multimer potential is suddenly turned on for particles leaving the surface. Based on such statistical considerations, predictions of the dependence of the yield on the ion energy, on the energy distribution, on rotational and vibrational excitation and on their angular distribution have been made (Können et al. 1974, 1975; Gerhard 1975; Haring et al. 1987; Hoogerbrugge & Kistemaker 1987a; Snowdon 1985). The models predict that the high-energy tail of the energy distribution of a cluster should fall off as E 3N+1 for a cluster consisting of N atoms, i.e. E 5 for dimers and E 8 for trimers as compared with E 2 for atoms (Können et al. 1974, 1975; Hoogerbrugge & Kistemaker 1987a; Snowdon 1985). Experimental results can be and are typically fitted with a modified Sigmund Thompson distribution of the form E Φ(E)dE = (E + U b ) n+1, in which n and U b are fitting parameters, and the high-energy behaviour E n is compared with the model predictions.

9 Cluster emission from metal surfaces under ion impact 04TA1403/9 Experimentally, using lasers (MPI), problems can arise due fragmentation of the cluster (Staudt et al. 2000; Wucher et al. 1993; Husinsky et al. 1993) in the highdensity laser beam, necessary for MPI. In addition, low yields for large clusters make the measurements of the high-energy tail of the energy distribution difficult, and the claimed agreement with the model predictions is sometimes doubtful. Just as one example, figure 3 presents experimental energy distributions (Coon et al. 1993a) for 3.9 kev Ar bombardment of polycrystalline Cu for clusters up to size 6 and, as comparison, the energy distributions obtained from the MD calculations at 5 kev for Cu (111) (Betz & Husinsky 1995). The MD cluster yields have been normalized to the experimental data, as no absolute yield data were obtained in the experiments, and also the MD cluster yields are considerably larger than the experimental estimates for a polycrystalline target. Asymptotic distributions for 1/E 2 and 1/E 3 are also shown and we will leave it open, what the final asymptotic behaviour of energy distributions from the experiments and the MD calculations are. For a thorough discussion the reader is referred to the original papers (Coon et al. 1993a; Betz & Husinsky 1995). Nevertheless, from the calculations a picture evolves how one can understand the processes leading to emission of medium-sized clusters (2 <n<10), which should be extremely rare from statistical considerations, on which the theoretical models for cluster emission are based. As was shown before, clusters are predominantly composed from first-layer atoms, which are neighbouring atoms. This suggests that, due to correlated motion in the collision cascade, a group of neighbouring atoms on the surface receives, simultaneously, near-parallel and equally large momenta, leading to the emission of a group of bonded atoms (a cluster), as shown schematically in figure 2b. Such correlated processes are not considered in any statistical model, and therefore such models cannot account for the high yields of large clusters or predict their correct energy distributions. Further evidence for such correlated emission processes by model calculations is given in Betz & Husinsky (1995). Evidence is presented to suggest that a low-energy sputtered particle has an increased probability that its neighbour atoms are also sputtered, which means that the emission is strongly correlated. Such correlated motion in the collision cascade towards the surface can result in the emission of a group of neighbouring atoms located at the surface. Such a process can be envisioned if, for example, a few layers below the surface an energetic recoil causes the development of a subcascade, as demonstrated in figure 4 for the emission of a cluster of size 6. Energy transferred by this event towards the surface is strongly directional and can lead to the simultaneous emission of a group of neighbouring surface atoms, which in some cases will remain bonded and form a cluster after emission, if the conditions of simultaneous emission and nearly parallel momenta are fulfilled. Thus, correlated processes not considered in any statistical model account for the high yields of medium-sized clusters. We assume that at least for clusters of sizes n>3, the outward expansion of the target surface due to the internally deposited energy in the cascade is responsible for the highly correlated momentum transfer causing cluster emission. Thus, the main characteristics for the emission of small-to-medium-sized clusters as found from MD calculations are as follows. (i) Single-atom sputtering occurs essentially during the first few picoseconds after ion impact. This is also true for the emission of small clusters. However, it is

10 04TA1403/10 G. Betz and W. Husinsky (a) (b) (c) (d) (e) Figure 4. Emission of a small cluster. The 5 kev Ar ion-impact point on the Cu (111) surface is indicated by the arrow. The six red surface atoms, which are neighbouring atoms (a connected group of atoms) will be sputtered together, forming a cluster of size 6. (a) The situation 60 fs after ion impact. Sputtering has started only around the impact point. (b) The situation 120 fs after ion impact. As can be seen, there are now two distinct surface regions where sputtering has started. One area is near the ion-impact point, the other is near the six red atoms. Analysis of the cascade shows that it develops underneath the impact point, but, in addition, a subcascade is forming below the surface, where the six red atoms are located. This subcascade is responsible for the second group of sputtered atoms. (c) Close-up view after 150 fs. The subcascade causes the surface to bulge upward. The six red surface atoms receive similar momenta from this process and are uplifted from the surface. (d) After 210 fs, the cluster starts to leave the surface. (e) After 570 fs these six atoms have formed a cluster of size 6 which no longer interacts with the surface. Nearby surface atoms, which have received more energy, have already left the surface. The cluster did not decay, at least up to the end of our post-evaluation (100 ps). It should be noted that, in most cases of cluster emission, the group of connected atoms originally emitted will reduce in size due to unimolecular decomposition. found that the average emission time for a cluster of size n increases with n and approaches 1 ps for large clusters of size n>6. (ii) About 92% of the sputtered flux is from the surface layer. For clusters, the contribution of surface atoms is even more pronounced. In addition, in most cases cluster atoms belong to a connected group of atoms, i.e. they form a group of next-neighbour atoms (see figure 4). This suggests a high correlation

11 Cluster emission from metal surfaces under ion impact 04TA1403/11 in the emission of individual atoms. In this way, atoms in a group receive similar momenta leading to their emission as a cluster. (iii) Uplifting of the surface due to internally deposited energy (for example, in a subcascade) is responsible for the correlated motion of atoms away from the surface. (iv) From such calculations, in agreement with experimental findings, yields and energy distributions of small emitted clusters (clusters size up to n = 6) have been obtained. 4. Large clusters (n >10) Emission of large clusters, consisting of atoms and more, as observed experimentally, is an even more puzzling phenomenon. In all calculations up to 1 ps discussed earlier, no emission of clusters larger than size 8 were observed. As noted in 3, the emission time is correlated with cluster size. Thus, one should expect emission of large clusters at times greater than one picosecond. By selecting likely candidates, i.e. impact points leading to a high yield and increasing the calculation time, a few large clusters could be found. Emission was typically after 5 10 ps. Taking high-sputter-yield events, where the yield is 3 5 times the average yield, means selecting impact points where the major part of the energy is deposited close to the surface, creating a dense collision cascade. From such calculations we conclude (Betz & Husinsky 2000) that the emission of such large clusters does not occur during the collisional phase of sputtering, but happens much later (5 10 ps after particle impact), during the thermal phase of the cascade. Emission will occur for spike events, where all the energy of the impinging ion is deposited locally into a small volume near the surface. In this way, events were found where stable clusters consisting of more than 20 atoms were emitted. Melting of the spike volume occurs and the high temperatures and pressures produced can cause emission of large fragments during the thermal phase. Thus, an event leading to the emission of a large cluster can be described in the following way. It is a high-sputter-yield impact, where a spike is formed near to and intersecting the surface, and local melting occurs. The temperature of target atoms was calculated in the usual manner by assuming equipartition between potential and kinetic energy (Urbassek 1997). To check the validity of the temperature concept, we analysed the velocity distribution of the atoms in the centre of the spike after 1 ps. It agrees well with a Maxwell Boltzmann distribution with an equivalent temperature of about twice the melting temperature of Cu (cf. figure 5). Thus, the spike region is a molten zone, which starts to shrink after ca. 2 ps due to heat conduction to the surrounding crystal. Protrusions are formed at the surface (figure 5b). Only after 5 ps, when most of the spike region has re-solidified, except for the still hot asperities, are two clusters seen leaving the surface from such protrusions (figure 5c). Figure 6 is a total view of the same impact after 5 ps. It shows that there is a delay of a few picoseconds between cascade-induced emission of atoms and small clusters and the late, thermally induced, emission processes of large clusters. For the event shown in figure 5, the clusters consist of 13 and 27 atoms, respectively. Analysis shows, for all such large clusters emitted after a few picoseconds, that the atoms forming the cluster are no longer dominantly surface atoms, but come from

12 04TA1403/12 G. Betz and W. Husinsky (a) (b) (c) Figure 5. Emission of large clusters for a 5 kev Ar ion impact on a Cu (111) surface. The different colours and grey levels of the atoms indicate their temperature (grey, T<T melt (1300 K) with black for T close to T melt ; blue, T melt <T <2T melt ; green, 2T melt <T <3T melt ; red, T>3T melt ). The figure parts show cross-sections through the crystal. (a) After 1 ps, cascade sputtering is terminated. Most sputtered atoms are far away from the target and are no longer visible in the figure. Sputtered atoms are all very hot (black, T > 3T melt ), as can be seen for those atoms still visible. A molten spike region has formed below the ion-impact point. (b) After 4 ps the spike region has strongly decreased in size due to cooling. Only asperities at the surface remain hot, due to the limited heat transfer to the bulk of the crystal. (c) After 6 ps a cluster of size 13 is emitted from such an asperity. Actually two clusters, of sizes 13 and 27, respectively, leave the surface after 5 6 ps. After 10 ps the temperature of the crystal has decreased below the melting point everywhere. 1 ps cluster 13 5 ps cluster 27 Figure 6. View of the crystal in figure 5 after 5 ps. The circles indicate typical distances of sputtered surface atoms, which have been sputtered 1 ps or 5 ps after ion impact, respectively. Note that the area between the 1 ps and 5 ps circles is empty, indicating no sputtering between 1 and 5 ps.

13 Cluster emission from metal surfaces under ion impact 04TA1403/13 different layers of the target. Indeed only 11 atoms of the cluster of size 27 are surface atoms and atoms from up to the sixth layer are contained in the cluster. The atoms of a cluster come from different layers but still from a local neighbourhood, indicating mixing processes in the melt. After 100 ps, the cluster of size 13 has lost two atoms and finally has size 11, and the cluster with 27 atoms has lost a dimer and two atoms, now forming a stable cluster of size 23. Thus, the composition of such large clusters is quite different from that of small clusters. Large clusters consist of atoms from different layers and the constituents are also generally not next-neighbour atoms, but are generally from the same neighbourhood. This change in origin of the cluster atoms reflects the mixing and diffusion processes occurring in the molten zone before emission. The calculations indicate that thermal phenomena play a role in the emission of large fragments. Emission of large clusters can be summarized as follows. (i) Large clusters are emitted after 5 10 ps during the thermal part of the cascade evolution: much later than the majority of sputtered atoms and small clusters. (ii) Large clusters are formed from atoms of the same neighbourhood, but no longer from surface atoms. (iii) Thermal processes in the molten zone of the spike are responsible for cluster emission. Using MD simulation, we can explore artificial systems (i.e. those non-existent in nature). In the present context, it is particularly interesting to investigate a pseudo- Cu material in which the cohesive energy E b has been halved with respect to that of natural Cu. Since the total sputter yield is roughly inversely proportional to the surface binding energy and hence the cohesive energy we can expect strong increases in the yield and cluster abundance. Indeed, in calculations, such a weak pseudo- Cu has about twice the sputtering yield of Cu and a correspondingly lower melting point. For such a material the emission of large clusters becomes a very frequent event indeed (Colla et al. 1998). An example for a 5 kev impact after 5 and 10 ps, where large clusters are formed, is shown in figure 7. To simulate these dramatic sputter events, it proved necessary to increase the size of the target crystallite to around atoms. While after 5 ps this pronounced probability of forming large clusters is quite evident for pseudo-cu, cluster emission up to 1 ps is quite similar to regular Cu. This indicates that the early emission processes are to a high degree collisional processes. 5. Model for large clusters To test the influence of the collisional part of the cascade, additional MD simulations were performed in which the kinetic energy of the bombarding ion was distributed thermally in a three-dimensional volume under the surface. Therefore, in this case, no impinging ion was present, and no collision cascades could form. The addition of thermal energy was done during 0.5 ps, which is the typical time-scale for the evolution of a collision cascade. The size of the cylindrical volume, where the thermal energy has been added, was of the order of the dimension of a dense collision cascade. It was 2 nm in any lateral radial direction around the centre of the crystal

14 04TA1403/14 G. Betz and W. Husinsky 0 fs 50 fs 100 fs 150 fs 200 fs 250 fs 500 fs 1 ps 1.5 ps 2 ps 5 ps 3 ps 6.5 ps 4 ps 8.5 ps Figure 7. For a large-yield event in artificial Cu, in which the cohesive energy has been halved with respect to that of natural Cu, large-cluster emission occurs at times that are large compared with the typical emission time of sputtered atoms. The figure shows a sequence of snapshots up to 8.5 ps. The colour coding indicates temperature and is the same as in figure 5. Large-cluster emission occurs after ca. 5 ps and emission stops and temperatures are below the melting point for t = 10 ps. Not the whole crystal is shown in the figure. surface, 2 nm deep and contained ca atoms. In these calculations, the crystal was coupled to a heat bath at 300 K and periodic boundary conditions were used as in Betz & Husinsky (1995).

15 Cluster emission from metal surfaces under ion impact 04TA1403/15 (a) (b) (c) Figure 8. 4 kev of energy is assumed to have been deposited as thermal energy within 500 fs in a Cu (111) crystal in a cylindrical volume (radius 2 nm, depth 2 nm) bordering the surface. The maximum temperature in the heated volume was 5000 K at the end of thermal energy deposition. Typically in such calculations, the emission of one or two large clusters is observed. Different layers of the crystal are drawn in different grey levels, indicating that clusters are composed of atoms from different layers. View of the crystal after (a) 3 ps; (b) 8 ps; (c) 15 ps. emission of large fragments cold crystal hot region pressure pressure heat conduction (a) (b) (c) Figure 9. Model for the emission of large clusters. (a) The bombarding ion creates a dense cascade (spike) near the surface. A hot molten region is formed (after 1 ps). This hot region (a few thousand kelvins) exerts pressure to all sides as it tries to expand. At all sides except the surface this pressure is counteracted by the crystal. (b) This leads to a collective motion of the hot surface parts away from the surface. At the same time, heat conduction towards the cold bulk leads to cooling of those parts of the molten zone in contact with the crystal. The surface area and especially the asperities formed remain hottest and maintain their momentum away from the surface. (c) Due to the imparted collective motion, large clusters are emitted after a few picoseconds. The impinging ion serves only as the provider of sufficient energy to create a hot molten volume intersecting the surface. While for energy depositions below 3 kev no emission at all was observed, for higher energies (4 kev and above) the emission of one or two large clusters after 5 10 ps was always found to take place, as shown in figure 8. Thus, large-cluster emission on a similar time-scale to that for sputtering can be induced thermally. The collisional part of the cascade is not necessary: only the amount of energy delivered and the time during which the energy is deposited are important. After thermal energy deposition, typically much larger clusters are emitted than under ion bombardment at the same deposited energy. We assume that this is due to the more homogenous energy deposition compared with ion bombardment. From these considerations, we propose the model for the emission of large clusters, as outlined in figure 9; it assumes that the process is essentially of a thermal

16 04TA1403/16 G. Betz and W. Husinsky and hydrodynamical nature. A rapidly heated volume intersecting the surface will start to expand in the direction towards the surface as the only possible direction for expansion and can lead to the emission of large fragments. Such processes are also most likely to be responsible for the extreme sputtering yields observed experimentally for kev Au cluster bombardment of Au (Andersen et al. 1998), as very dense cascades due to cascade overlapping are obtained under cluster bombardment. 6. Conclusions Cluster emission has not been well understood for many years. MD modelling of these processes has given us clues as to what is causing the emission of small clusters as well as large clusters. Small clusters are predominantly emitted in the collisional phase of the sputter process (for times up to 1 ps) or due to fragmentation of large cluster. Large clusters are emitted well after the collision cascade is thermalized, and can be understood in terms of thermal and hydrodynamic processes. Thus, in a way, the old picture of sputtering as a thermal process has returned, at least for some special effects in the emission process. References Andersen, H. H Computer simulations of atomic collisions in solids with a special emphasis on sputtering. Nucl. Instrum. Meth. Phys. Res. B 18, Andersen, H. H. & Bay, H. L Sputtering yield measurements. In Sputtering by particle bombardment I (ed. R. Behrisch). Topics in Applied Physics, vol. 52, pp Springer. Andersen, H. H., Brunelle, A., Della-Negra, S., Depauw, J., Jacquet, D., Le Beyec, Y., Chaumont, J. & Bernas, H Giant metal sputtering yields induced by kev/atom gold clusters. Phys. Rev. Lett. 80, Betz, G. & Husinsky, W Molecular dynamics study of cluster emission in sputtering. Nucl. Instrum. Meth. Phys. Res. B 102, Betz, G. & Husinsky, W Modelling of cluster emission from metal surfaces due to ion impact. In Secondary ion mass spectrometry, SIMS XII (ed. A. Benninghoven, P. Bertrand, H.-N. Migeon & H. W. Werner), pp Elsevier. Betz, G., Kirchner, R., Husinsky, W., Rüdenauer, F. & Urbassek, H. M Molecular dynamics study of sputtering of Cu (111) under Ar ion bombardment. Rad. Eff. Def. Solids 130/131, Bitensky, I. S., Parilis, E. S. & Wojciechowski, I. A Push-and-stick mechanism for charged and excited small cluster emission under ion bombardment. Nucl. Instrum. Meth. Phys. Res. B 67, Burnett, J. W., Biersack, J. P., Gruen, D. M., Jørgensen, B., Krauss, A. R., Pellin, M. J., Schweitzer, E. L., Yates Jr, J. T. & Young, C. E Depth of origin of sputtered atoms: experimental and theoretical study of Cu/Ru(0001). J. Vac. Sci. Technol. A 6, Colla, T. J., Urbassek, H. M., Wucher, A., Staudt, C., Heinrich, R., Garrison, B. J., Dandachi, C. & Betz, G Experiment and simulation of cluster emission from 5 kev Ar Cu. Nucl. Instrum. Meth. Phys. Res. B 143, Coon, S. R., Calaway, W. F., Burnett, J. W., Pellin, M. J., Gruen, D. M., Spiegel, D. R. & White, J. M Yields and kinetic energy distributions of sputtered neutral copper clusters. Surf. Sci. 259, Coon, S. R., Calaway, W. F., Pellin, M. J. & White, J. M. 1993a New findings on the sputtering of neutral metal clusters. Surf. Sci. 298,

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