Molecular dynamics simulations of low energy ion sputtering of copper nano-dimensional clusters on graphite substrates

Nuclear Instruments and Methods in Physics Research B 227 (2005) 261–270 www.elsevier.com/locate/nimb

Molecular dynamics simulations of low energy ion sputtering of copper nano-dimensional clusters on graphite substrates G.V. Kornich a

a,*

, G. Betz

b,*

, V. Zaporojtchenko c, A.I. Bazhin d, F. Faupel

c

Computational Mathematics Department, Zaporozhye National Technical University, Jhukovski Street 64, 69063 Zaporozhye, Ukraine b Institut fu¨r Allgemeine Physik, Technische Universita¨t Wien, Wiedner Hauptstr. 8-10, A-1040 Wien, Austria c Technische Fakulta¨t, Christian-Albrechts-Universita¨t, Kaiserstr. 2, 24143 Kiel, Germany d Physics Department, Donetsk National University, Universitetskaja Str. 24, 83055 Donetsk, Ukraine Received 8 June 2004; received in revised form 18 August 2004

Abstract Molecular dynamics simulations have been performed of sputtering of copper clusters, which consisted of 13, 39, 75 and 195 Cu atoms, on a (0 0 0 1) graphite surface by 200 eV Ar ions. The role of multiple Ar–Cu and Ar–C interactions in the polar distributions of backscattered Ar ions was investigated. Yields, energy and angular distributions of sputtered cluster atoms were examined. The azimuthal angular distribution of sputtered Cu atoms exhibit periodic maxima every 60°. The polar angular distributions of sputtered Cu atoms have maxima in directions parallel to the substrate surface for all clusters. The obtained sputtering yields are for a surface with a single Cu cluster deposited. A solution to the problem of comparing the sputtering yield for such a single surface cluster with the yield from a surface with a given cluster coverage is presented. Ó 2004 Elsevier B.V. All rights reserved. PACS: 34.50.Dy Keywords: Sputtering; Cluster; Molecular dynamics

1. Introduction

* Corresponding authors. Tel.: +43 15880113440; fax: +43 15880113499. E-mail addresses: [email protected] (G.V. Kornich), [email protected] (G. Betz).

Binary systems of metal nano-dimensional clusters on metal and carbon-based substrates [1–9] are of considerable technological interest in the field of heterogenous catalysis, new materials for electronic devices, thin film growth, epitaxy and

0168-583X/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.08.018

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the fabrication of nanostructured materials. A number of computer simulations of such cluster/ substrate systems have been performed during the last decade for carbon systems [10–13], deposition of metal clusters [14–18], sputtering of metal and non-metal surfaces initiated by energetic clusters [19–23], as well as cluster [24] and molecular fragment [25] sputtering mechanisms. So far no detailed simulations of sputtering of nanodimensional clusters on a substrate have been performed. Especially the interplay of substrate and cluster in ion scattering, the angular and energy distributions of sputtered atoms from such a binary system under ion bombardment as well as the sputtering yield values have not been investigated, but can be studied within the framework of classical molecular dynamics (MD) [26]. The present investigations are devoted to MD simulations of low energy ion backscattering from and sputtering of binary systems, consisting of copper nano-dimensional clusters of different sizes on a (0 0 0 1) graphite surface. We analyzed the penetration depth of implanted ions as well as the polar angular and energy distributions of backscattered bombarding ions. Furthermore for sputtered Cu cluster atoms angular (azimuthal and polar) and energy distributions were obtained. The relevant mechanisms are discussed for Ar ion backscattering from the clusters and sputtering of Cu cluster atoms on graphite substrates. The results for the copper–graphite systems are compared to the MD calculated sputtering yield of a pure Cu (1 0 0) surface and are used to estimate effective sputtering yields for such Cu clusters on graphite systems.

2. Model Simulations were performed for Cu clusters consisting of 13, 39, 75 and 195 Cu atoms on (0 0 0 1) graphite substrates, which consisted of 1584, 2288, 3000 and 5880 carbon atoms, respectively. Additionally, a cluster with 27 Cu atoms on a graphite substrate with 1920 carbon atoms was used for sputtering yield estimations. Carbon atoms were arranged in two layers with an inter˚ and a nearest neighbor dislayer distance of 3.35 A

˚ between carbon atoms in the layer. tance of 1.46 A The Tersoff potential [27] with a cut-off radius ðCÞ ˚ splined to the Ziegler–Biersack– of Rcf ¼ 2:1 A, Littmark potential [28], was applied to the C–C interactions. A tight binding many body potential, directly connected to the Born–Mayer potenðCuÞ ˚ tial [29,30] with a cut-off radius of Rcf ¼ 5:5 A, was used for the Cu–Cu interatomic interactions. C–Cu interactions were simulated using a Lennard–Jones potential [31]. Different parameter estimates exist in the literature for the C–Cu Lennard–Jones potential [32–34]. We have used the values given by Dorfman et al. [32] and ðCu–CÞ ˚ The C–Cu potential was splined Rcf ¼ 3:75 A. to the Ziegler–Biersack–Littmark potential. Trajectories of particles were calculated in accordance to NewtonÕs equations of motion using the Verlet algorithm [26]. The variable time step for the integration of the equations of motion was in all cases less than 4 fs. Conservation of energy was in all cases better than 1%. Every ion impact was calculated for 2 ps. The initial copper clusters were also obtained from molecular dynamics calculations. Copper lattice fragments of the appropriate size were heated to 1700 K at a heating velocity of 0.25°/ps. At 1700 K the fragments were allowed to relax freely during 104 ps. Afterwards clusters were cooled at the same velocity to 0 K in accordance to an algorithm, suggested in [19]. The obtained copper clusters exhibit a lattice structure similar to the structure of free model nickel clusters obtained in [35]. For the preparation of the cluster/substrate systems these copper clusters were located close to the C surfaces in the range of, at least, a few Cu–C pair interactions. Then the relaxation of the cluster/substrate system was calculated for 20–40 ps, depending on cluster size. The final kinetic energies of Cu atoms in the binary system after relaxation were less than 0.02 eV/atom. The substrate graphite (0 0 0 1) atomic planes were allowed to relax freely only in the lateral directions during this relaxation process, to avoid distortions of the graphite structure [36]. An energy dissipation layer [37] as well as periodic boundary conditions [26] were put at all lateral borders of the carbon substrates. Calculations were performed for 200 eV Ar ions, impinging normally to the substrate surface.

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3. Results and discussion

(13 Cu)

0.6 Probability

(39 Cu) (75 Cu)

0.4

(195 Cu)

0.2

(a) Ion energy loss/range (eV)

Ion impact points were chosen by random numbers. Impact points far away from the cluster will lead to no sputtering or no ion–Cu interaction. Therefore in each investigation 2000 ion impacts were finally selected, for which the energy of, at least, one Ar–Cu pair interaction was larger than 37 eV. It was found previously [36] that with this criterion more than 99% of all randomly over the whole surface chosen impacts are taken into account, which will lead to sputtering of a Cu cluster atom. Cluster atoms were identified as sputtered particles, if after 2 ps they are no longer interacting with the remaining Cu cluster, independent, if such an atom hits the substrate and is deposited or reflected.

0

120 (13 Cu) (39 Cu)

80

(75 Cu) (195 Cu)

40

0 1

3.1. Depth distribution of Ar ions and their energy loss The depth distributions of Ar ions, which have come to rest inside the Cu cluster or the C substrate after 2 ps are presented in Fig. 1(a). Back˚ scattered ions, which are located more than 5 A above the top of the surface cluster after 2 ps are also shown (range 1). The probability for an ion to be reflected is always larger than 50% and increases only insignificantly with cluster size. Almost no impinging Ar ions remain in the Cu clusters (range 2) after 2 ps in agreement with MD results of Ar ion bombardment of a Cu (1 0 0) crystal for the same potential [38]. Thus essentially all ions, which did not scatter, end up in the substrate. For the 13 Cu atom cluster a rather large part of ions comes to rest in the first substrate layer as compared to larger clusters. A possible explanation is the small size of this Cu cluster. Penetration of ions into the second layer and below the substrate is again only weakly cluster size dependent. Depth distributions of the mean energy loss of a bombarding Ar ion are presented in Fig. 1(b). The values in range 1 indicate the reflected energy. It is found, that Ar ions deposit in average about half of their impact energy in the surface copper clusters. Backscattered Ar ions take away 10–20%

263

(b)

2

3 Ranges

4

5

Fig. 1. Reflection and depth distribution of (a) bombarding Ar ions; (b) mean Ar ion elastic energy loss for 200 eV Ar ion bombardment after 2 ps. Ranges: 1 – backscattered ions; 2 – copper clusters; 3 – the first atomic layer of the graphite substrate; 4 – the second atomic layer of the graphite substrate; 5 – ions penetrating below the bottom of the substrate.

of the impact energy. In the substrate the energy loss decreases with depth and amounts to less then half of the total energy, independent on cluster size. 3.2. Polar angular distributions of backscattered Ar ions and their energies The obtained polar distributions (number of backscattered ions per unit solid angle/total number of impacts) of backscattered Ar ions are presented in Fig. 2. A particle being reflected back or into a direction parallel to the surface has a polar angle of 0° or 90°, respectively. For all cluster sizes the backscattering probability shows a pronounced maximum in the region from 50° to 80°. The corresponding polar angle mean energy distributions of backscattered Ar ions (total backscattered energy per unit solid angle/number of backscattered ions per unit solid angle) are presented in Fig. 3. Results in Fig. 3 show that the

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0.25 (13 Cu) (39 Cu)

0.2

(75 Cu)

Probability

(195 Cu)

0.15

0.1

0.05

0

0

20

40 60 80 Polar angle, degrees

100

Fig. 2. Polar angular distributions of backscattering probabilities for Ar ion bombardment at 200 eV of copper cluster– graphite substrate targets. The smoothing curves are drawn to guide the eye.

100 lone Cu atom (13 Cu) (39 Cu) (75 Cu) (195 Cu) (13 Cu) approx.

Energy, eV

80

60

(39 Cu) approx. (75 Cu) approx. (195 Cu) approx.

40

20

0 0

20

40 60 80 Polar angle, degrees

100

Fig. 3. Polar angular distributions of the mean energy of backscattered Ar ions. The smoothing curves are drawn to guide the eye. The dashed line is an analytical calculation of the angular energy distribution of scattered Ar ions for interaction with a single Cu atom.

distribution has two maxima for all clusters except the smallest one (13 atoms). For all clusters a maximum in the reflected energy per particle is ob-

served at 90–100° (parallel to the surface), which can be understood in terms of a simple binary collision with a Cu cluster atom (dotted line in Fig. 3, with a maximum at 90°). A few particles are also reflected with angles larger than 90° and exhibit high energies. The explanation is the finite size of the C target and the fact that for Ar and Cu atoms no periodic boundary conditions are applied. Thus an Ar ion scattered from the Cu cluster at an angle slightly larger than 90° might not hit the substrate. A second peak in Fig. 3 exists around 70° for all larger clusters. This peak is attributed to a sequence of Ar–Cu collisions, which is unlikely for the small 13 atom Cu cluster. Multiple Ar–Cu collisions in a large surface cluster allow to keep more ion energy as compared to one Ar–Cu collision as in a 13 atom Cu cluster, if they lead to the same total deflection. Indeed the mean energy in the peak at about 70° is about twice as high as we would expect from a simple binary collision leading into the same direction. In addition another effect will contribute. Ar ions undergoing a sequence of a few collisions and being scattered in a direction almost parallel but directed towards the surface (polar angles more than 90°) retain higher energies as from a single Ar–Cu collision. Due to their glancing incidence towards the surface they will undergo mirror scattering with little energy loss and contribute to the large angle high energy peak. Particles being reflected in the range of polar angles between 0° and 45° have a low mean energy. Such an ion will be reflected back from the cluster and transfer most of its energy to a cluster atom in a near head on collision (dotted line in Fig. 3). In principle a second possibility exists: the ion is slightly deflected from the cluster and then reflected back from the substrate and transfer most of its energy to the substrate in a near head on collision. However, as Ar is heavier than C, this process cannot occur. A weakly deflected Ar ion will penetrate into the substrate. Only at low energies a simultaneous collective interaction with a few substrate atoms will take place, which can lead to reflection. Additional simulations of the interaction of Ar ions with pure graphite agree with experimental results [39], where the existence of a penetration threshold energy of 43.5 eV was

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observed for Ar ions impinging normal to the (0 0 0 1) plane of highly oriented pyrolythic graphite. On the other hand an ion deflected by 90° or more from the Cu cluster will carry still a substantial amount of energy. It will hit the substrate under a near glancing angle and therefore be reflected with most of its energy and neither penetrate nor damage the substrate. It will contribute to the high energy peak around 70° in Fig. 3. 3.3. Sputtering of Cu cluster atoms The statistics of sputtered atoms for all simulated clusters shows that a pronounced difference in the emission probability exists between internal and external cluster atoms. Internal cluster atoms and interface internal Cu atoms (internal atoms with respect to the Cu–C system and at the Cu–C interface) have low sputtering probabilities. For example, the central atom in the 13 atom Cu cluster has a sputtering probability of less than 0.005 as compared to approximately 0.1 for external atoms. Practically all copper atoms in the 39 atoms Cu cluster, which have sputtering probabilities less than 0.0025, are internal atoms along h1 1 0 0i directions (see white color atoms in Fig. 4). Atoms, which have the largest sputtering prob-

265

abilities (for example, more than 0.03 in a 39 atom Cu cluster), are located usually in the upper external part of the cluster and, particularly, at lateral sides (see below). The most transparent azimuthal directions in the 39, 75 and 195 atom surface clusters are formed by atomic sequences, which consist of 3– 6 Cu atoms and are oriented along h1 1 0 0i directions (see Fig. 4). This agrees with MD simulations [18], where Pt clusters on a (0 0 0 1) graphite surface showed hexagonal close packed atomic structures under the influence of the substrate. Border Cu atoms of atomic sequences oriented in h1 1 0 0i directions, also have large sputtering probabilities, preferentially to directions, which are close to the h1 1 0 0i axis. These atoms play a dominant role in the formation of quasi-periodical azimuthal distributions of sputtered Cu atoms (see Section 3.4). Sputtered dimers, trimers and even larger copper particles also were identified in the calculations. The contribution of small clusters to the sputtering yield is shown in Table 1. Approximately 8–20% of sputtered Cu atoms are in the form of polyatomic particles. Cu2 dimers form the largest part of sputtered material among multi-atomic sputtered particles. Table 1 shows that the contribution of sputtered Cu2 dimers increases with the size of the surface Cu cluster. The simulations also indicate that multi-atomic Cu particles are formed preferentially from external cluster atoms. Sputtering of carbon atoms was not investigated in this work, because the sputtering probabilities were too low to obtain statistically relevant results. Cu–C dimers as well as larger sputtered particles, which include simultaneously C and Cu atoms, were not observed.

Table 1 Probability for a Cu atom to be sputtered as a single atom or as part of a dimer or trimer Clusters Fig. 4. Initial position of a 39 atom Cu cluster on a graphite substrate. White spheres are Cu atoms, which have sputtering probabilities of less than 0.0025. Dark-grey spheres are external Cu atoms. Light-grey spheres are substrate carbon atoms.

Cun

13 Cu

39 Cu

75 Cu

195 Cu

Cu1 Cu2 Cu3

0.911 0.084 0.005

0.863 0.114 0.017

0.801 0.161 0.023

0.785 0.192 0.017

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3.4. Angular distributions of sputtered Cu atoms Polar angular distributions of sputtered Cu atoms are presented in Fig. 5. The results show that the distributions are similar for all cluster sizes and have a maximum emission probability at polar angles of 80–95°. It means that the largest number of particles are sputtered in directions parallel to the substrate surface independently from cluster size. Sputtering in directions normal to the substrate surface and for angle up to 60° is very low. Polar angles of sputtered Cu atoms of more than 90° can occur due to the restricted size of our C substrate (path 4 in Fig. 6). Particles which are deposited on the substrate (path 2 in Fig. 6) have been taken into account as sputtered particles

Fig. 5. Polar angular distributions of sputtered Cu atoms from 13 atom Cu, 39 atom Cu, 75 atom Cu and 195 atom Cu clusters. The line indicates the directions parallel to the graphite substrate.

if they are sufficiently far away from the cluster (see Section 2). Reflected particles (path 3 in Fig. 6) were also taken into account in the sputtering yield. Energy polar angular distributions (total energy of sputtered particles into every degree/ number of impacts) are similar to the polar distributions of atoms. Azimuthal angular distributions of sputtering probability of Cu atoms for all cluster sizes are presented in Fig. 7(a)–(d). Two different distributions are shown in Fig. 7: sputtering to all polar angles (curve 1) and to polar angles less than 90° (curve 2). Six maxima of sputtering probability with an azimuthal interval of 60° can be seen in both cases, which coincide with the most transparent h1 1 0 0i directions of the 39 atom, 75 atom and 195 atom Cu clusters. A transparent h1 1 0 0i direction of atomic structure is shown in Fig. 4 for the 39 atom Cu cluster. In the case of the 13 atom Cu cluster (see Fig. 7(a)) this periodicity in the sputtering probability does not arise, due to the insufficient number of atoms in the cluster and therefore the absence of oriented atomic sequences in the cluster. Comparison of curves 1 and 2 in Fig. 7 shows that this six-maxima form of the azimuthal distribution of sputtered atoms is less pronounced if we take only sputtered atoms into account, which are emitted with a polar angle less than 90°. From this we can conclude that mostly atoms sputtered in a direction parallel to the surface exhibit this azimuthal structure with six maxima. Analysis of the sputtered Cu atoms shows that surface border atoms of atomic sequences in h1 1 0 0i directions create the largest contributions to the azimuthal maxima of the sputtering probability. 3.5. Energy distributions of sputtered Cu atoms

1 3

4

2

Fig. 6. Possible events after a particle is sputtered.

Energy distributions of sputtered Cu atoms for different azimuthal directions are presented in Fig. 8(a)–(c) for 39 atom, 75 atom and 195 atom Cu clusters, respectively. The energy spectrum of Cu atoms sputtered into azimuthal directions within the peaks in Fig. 7 exhibit clearly a much broader energy distribution, which is peaked at higher energies than for atoms sputtered into other directions. This peculiarity of the energy spectra indicates the

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267

(a) (a)

(b)

(b)

(c)

(c)

(d) Fig. 7. Azimuthal angular distributions of sputtering probabilities of Cu atoms from (a) 13 atom, (b) 39 atom, (c) 75 atom and (d) 195 atom Cu surface clusters: 1 – total polar angular range; 2 – polar angles smaller than 90°.

importance of non-focused low energy random collisions in non-peak ranges of the azimuthal sputtering distribution (see also Section 3.3). Total energy distributions of sputtered Cu atoms exhibit a weak tendency that the maxima

Fig. 8. Energy distributions of sputtered Cu atoms from (a) the 39, (b) the 75 and (c) the 195 atom Cu clusters. Curve 1 refers to atoms sputtered into an azimuthal direction within the peaks of the azimuthal distribution of Fig. 7 and curve 2 to atoms sputtered into directions outside the peaks.

of the energy distributions shift to higher energies with increasing cluster size. This agrees qualitatively with the increase of the sublimation energy Usub of clusters with size (see Table 2). 3.6. Sputtering yields Values of sputtering yields for the different surface clusters are presented in Fig. 9 for two polar

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Table 2 Energetic and geometrical characteristics of surface clusters Cluster characteristics

13 Cu

27 Cu

39 Cu

75 Cu

195 Cu

Usub (eV) ns ln (nm) reff (nm2)

2.57 3 0.37 0.112

2.65 14 0.30 0.241

2.75 18 0.35 0.310

2.93 19 0.48 0.452

3.08 32 0.64 0.887

Usub is the sublimation energy without taking into account the Cu–C interactions. ns is the numbers of Cu atoms at the cluster–substrate interface (bottom layer of clusters). ln is the distance of the cluster center of mass from the substrate surface. reff is the effective cross-section for sputtering.

0.03

2.5 0.02

2 1.5

0.01

1 1 2 3

0.5 0

Parameter Q, nm

Sputtering yields, atoms/ion

3

13

27

39

75

195

0

Numbers of atoms in clusters Fig. 9. Sputtering yields of Cu atoms and Q parameter for 13 atom, 27 atom, 39 atom, 75 atom and 195 atom Cu surface clusters at 200 eV Ar ion bombardment normally to the (0 0 0 1) graphite substrate surface; (1) are sputtering yields for the polar angular range 0–90°; (2) are total sputtering yields to all polar angles; (3) are values of the Q parameter. The dotted line indicates the sputtering yield of a (1 0 0) Cu crystal surface at 200 eV Ar ion bombardment normal to the surface in the framework of our MD model [38] at a target temperature of 300 K (500 ion impacts).

angular ranges: less than 90° (curve 1) and all polar angles (total yield, curve 2). The sputtering yield for a 27 atom Cu surface cluster was also calculated to give a more precise presentation of the yield dependency from cluster size. Atoms are considered to be sputtered, if after 2 ps they are no

longer interacting with the remaining Cu cluster, independently if such an atom hits the substrate and is deposited or reflected. The number of cluster atoms at the cluster–substrate interface ns and the height of the center of mass of a cluster above the substrate ln for the different clusters are given in Table 2. If a cluster sits on the surface very flat (large ns and small ln) a large amount of the ion energy originally deposited in the cluster will be transferred quickly to the substrate and not be available to sputtering. If ln is large and in addition ns the number of atoms at the cluster–substrate interface is small most of the ion energy will remain inside the cluster and contribute to sputtering. No efficient collisional energy transfer to the substrate will take place. Therefore the sputtering yield should scale with Q = ln/ns. This parameter Q is also presented in Fig. 9. In both cases (curves 1 and 2 in Fig. 9) as well as for Q we observe a minimum in the sputtering yield for the 39 atom Cu cluster. This is connected with a more effective impact energy transfer to the substrate for the 39 atom Cu cluster as for other clusters. Only three atoms effectively interact with the substrate in the 13 atom Cu cluster, while 14 Cu atoms (see Table 2) directly interact with the substrate in 39 atom Cu cluster. In addition ln is actually smaller for the 39 atom Cu cluster. Finally, the total sputtering yield of 27 atom Cu cluster is noticeably smaller as compared to the total sputtering yield of 13 atom Cu cluster as well as smaller than the total sputtering yield of 75 atom Cu cluster, that does not contradict to the minimal value of the sputtering yield of 39 atom Cu cluster among simulated ones (see Fig. 9). ln of the 75 atom Cu cluster is larger than for the 39 atom Cu cluster, but the number of interface Cu atoms is almost the same, therefore we can expect a larger sputtering yield. This scaling of the yield with Q will however break down for sufficiently large cluster, as for them the energy deposited at or near the interface is no longer relevant for the sputtering yield. The figure indicates that this is probably already the case for cluster of 200 atoms and more. For the 13 atom Cu cluster we would expect a much higher yield from the Q parameter (Q = 0.123 nm) as actually observed. However, this cluster exhibits a quite different

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atomic structure as compared to other model clusters and probably for such a small cluster total destruction of the cluster is quite likely (predicted high sputtering yield). However, atoms are more likely to be sputtered and deposited directly below the original cluster at the surface and not counted as sputtered atoms. For comparison in Fig. 9 also the yield for a flat (1 0 0) copper crystal under 200 eV normal Ar ion bombardment with the same atomic potential [29,30] is shown. Sputtering yields for an experiment where the C surface has a certain known cluster coverage, can be easily deduced from the present results. The effective cross-sections reff for sputtering are listed in Table 2. This is the area each cluster presents to the incoming ion flux, in which sputtering has been observed based on the 37 eV criterion (see Section 2). For impact points outside this area no sputtering of Cu atoms was observed and also no reflection for the bombarding ions was observed, because of the large mass Ar ion as compared to the C atom mass. However, inside this area the reflection coefficient is around 60%. Thus if c is the number of clusters/cm2 the observed Cu sputtering yield in an experiment should be Yexp = reffcYcl, with Ycl the yield for one cluster as shown in Fig. 9. On the other hand, if the yield is measured the surface coverage c in number of clusters/cm2 can be deduced. In addition, the measurement of the flux of backscattered Ar particles can be used as a tool of semi-quantitative estimation of coverage of graphite surfaces by copper clusters due to the absence of any noticeable ion back scattering at normal impacts of 200 eV Ar ions on pure graphite surface (see Section 3.2). Results in Fig. 1(a) show that the backscattering coefficients for 200 eV Ar ions are all around k = 0.6 for all simulated clusters. Thus the surface coverage csurf (fraction of surface area covered by clusters) can be obtained from the experimental backscattering coefficient csurf = (Ireflk)/Iin (Iin flux of bombarding ions and Irefl flux of reflected ions) and the coverage c in number of clusters/cm2 will be c = csurf/reff. These considerations assume that the clusters are well apart from each other, i.e. a low surface coverage, as otherwise redeposition of sputtered atoms on neighboring clusters will occur.

269

Thus, the present work allows a self-consistent comparison of experimental and simulated results for binary clusters–substrate systems with no strong variations of sizes of surface clusters and low substrate coverage by clusters, where the clusters are well apart. 4. Conclusions Molecular dynamics simulations of sputtering were performed for 200 eV Ar ions bombarding nano-dimensional copper clusters on a (0 0 0 1) surface of a graphite substrate. The results show a pronounced influence of the graphite substrate on the yield and angular distribution of sputtered Cu atoms as well as on angular and energy distributions of backscattered Ar ions. The atomic structure of surface clusters is modified by the substrate. The azimuthal angular distributions of sputtered atoms exhibit six maxima, which reflect the internal atomic structure of the clusters on a (0 0 0 1) graphite substrate. The influence of the substrate on the cluster atomic structure is supported by recent calculations [40] for Cu clusters on a Cu substrate. In this case the azimuthal angular distributions of sputtered atoms exhibit four maxima, which reflect the internal atomic structure of the clusters on a (1 0 0) Cu substrate. The polar angular distribution of sputtered Cu atoms has a maximum into directions parallel to the substrate. Backscattered ions are to a large part, after being deflected from the cluster, finally reflected from the substrate. In such a process they loose less energy compared to a direct reflection from the cluster into the same direction. From the obtained results sputtering yields can be deduced for a surface with a given cluster coverage. In addition, we found that from a measurement of backscattered Ar particles and the calculated backscattering coefficient the cluster surface coverage can be determined, provided the surface coverage is low. Acknowledgements One author (G.V.K.) profoundly gratitudes to the Technische Universita¨t Wien and the Christian-Albrechts-Universita¨t in Kiel for financial

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