A molecular dynamics study of Cu dimer sputtering mechanisms

Nuclear Instruments North-Holland

and Methods

in Physics Research

B 84 (1994) 453-464

NIOMI B

Beam Interactions with Materials&Atoms

A molecular dynamics study of Cu dimer sputtering mechanisms

+

M.H. Shapiro a,b,* and T.A. Tombrello a ’ Division of Physics, Mathematics, and Astronomy, California

Institute of Technology, Pasadena, CA 91125, USA b Department of Physics, California State University, Fullerton, CA 92634, USA Received

22 February

1993 and in revised

form 14 October

1993

Molecular dynamics simulations were used to investigate the mechanisms responsible for the sputtering of dimers from Cu(100) were carried out using both a and Cu(ll1) surfaces following bombardment by normally incident, 5 keV Ar + ions. Simulations pair-potential and a many-body, embedded-atom potential to describe the Cu-Cu interaction. Computer animation techniques which allowed visual inspection of individual dimer trajectories were used to identify the mechanisms responsible for dimer ejection. In the pair-potential simulations dimers accounted for about 5% of the sputtering yield from both the (100) and (111) surfaces, while in the embedded-atom simulations dimers accounted for approximately 2% of the yield from the (100) and (111)

surfaces. Three mechanisms were found to be responsible for the bulk of the dimer ejection events. Direct ejection of intact dimers and recombination in or near the surface were the most prevalent mechanisms observed. Less frequent, but still significant numbers of “push-stick” events were also seen. The simulations suggest that the sputtering of dimers is the result of competing mechanisms that take place preferentially towards the later phase of collision cascades that produce relatively large numbers of sputtered atoms.

1. Introduction Numerous experimental, theoretical, and simulation studies of the sputtering of small neutral metal clusters have been carried out in the past two decades. Recent reviews [l-6] provide extensive references to this literature. Early theoretical models were developed in the papers by Benninghoven and Miiller [7], Gerhard [S], and Konnen, Tip, and de Vries [9,10]. Many additions and refinements to these early models have been presented [3,11-191; however, essentially all the theoretical models for dimer ejection can be divided into two broad classifications depending on the number of collisions by cascade atoms that are required to sputter the dimer. In the multiple collision class of mechanisms each atom of the dimer receives a momentum transfer from one or more cascade atoms, while in the single collision class of mechanisms only a single momentum transfer from a cascade atom occurs. Multiple collision mechanisms can sputter dimers directly from the surface (direct emission) if two nearby atoms are struck at essentially the same time by cascade atoms, and each of the pair are given initial

* Corresponding author, tel. +l 714 773 3884, fax +1 714 449 5810. + Supported in part by NSF Grant DMR90-11230 at Caltech, and by NSF Grant DMR90-02532 at CSUF. 0168-583X/94/$07.00 0 1994 - Elsevier SSDZ 0168-583X(93)E0714-R

Science

momenta that leave them in a state where their total internal energy is negative. Multiple collisions also can cause dimers to be formed by association (also termed “recombination” in the literature). In this case two atoms, which were not originally bound to each other, collide in or near the surface to form the dimer. Some energy loss mechanism must be present if a stable dimer is to be formed; however, several channels for such losses usually are available. Two different single collision mechanisms can cause the sputtering of a dimer from a metal surface. In the first case (also referred to as direct emission), one of the atoms of the pair is struck by a cascade atom with enough energy being transferred to the pair to eject it but not to break the bond between the pair. Another single collision mechanism recently has been proposed by Bitensky et al. [18]. In this case, a cascade atom collides with an atom at the surface. Provided that energy can be transferred to nearby atoms, it is possible for both atoms to eject from the surface in a bound state. This has been called the “push-stick” mechanism by Bitensky et al. Because dimers (and larger clusters) most often are sputtered from fully developed collision cascades that yield a large total number of sputtered atoms, molecular dynamics (MD) techniques have been favored by investigators attempting computer simulations of dimer ejection processes. Much early work in this area was carried out by Harrison, Jr. and his associates [20-291.

B.V. All rights reserved

454

M.H. Shapiro, T.A. Tombrello /Nucl. Instr. and Meth. in Phys. Res. B 84 (1994) 453-464

Generally, low bombarding energies (< 1 keV) and relatively small targets ( < 400 atoms) were used in the simulations. The interactions between target atoms were described by semi-empirical pair-potentials Born-Mayer or Moliere repulsive potentials splined to attractive Morse wells. The use of pair-potentials created a problem for the study of dimer ejection, because of differences between the depth of the attractive well needed to fit the bulk parameters of the target material and the depth needed to produce the correct binding for the free dimer. For example, the typical Morse potential depth needed for bulk Cu is about 0.5 eV, while the binding energy for the Cu-Cu dimer is 2.1 eV [30]. In the pair-potential simulations it was not possible to accomplish the transition from the bulk material to the free dimer smoothly. Nevertheless, the early simulations provided valuable information about dimer formation processes. At low energy it was found that a relatively small subset of collision sequences would lead to dimer formation, and that “recombination” mechanisms seemed to dominate [25]. Recent MD simulations of dimer ejection [30-331 have used many-body, embedded-atom potentials to describe the interaction between target atoms. If properly chosen, such potentials can fit both the bulk properties of the target material and the properties of the free dimer with reasonable accuracy, and the transition from the bulk to the free dimer is smooth. Wucher and Garrison carried out MD simulations of Ag dimer ejection following bombardment with 1 keV Ar+ ions [30,31], and found good agreement with experimental data for the dimer yield and translational kinetic energy spectrum. Karetta and Urbassek carried out MD simulations of Cu dimer ejection following 0.3 and 1 keV Cu bombardment [33] using an embedded-atom potential for Cu. At the lowest bombarding energy they found that a relatively high fraction of the sputtered atoms were bound in dimers (N 30%). This dropped to u 20% at the higher bombarding energy. Experimental measurements of the properties of neutral dimers (and neutral small clusters) sputtered from metal surfaces have been carried out with increasing frequency in recent years owing to the availability of improved postionization techniques [34-461. Neutral dimer yields from the Ar-Cu system have been reported at a number of bombarding energies between 0.09 and 8.0 keV [34-36,39-451. At the lowest bombarding energies the observed ratio of dimers to monomers (Y/Y,) typically is about 0.03. This increases to as much as 0.19 at 8 keV [42]. However, there is considerable variability in the experimental data. For example, Brizzolara and Cooper report Y,/Y, values that range from 0.08 to 0.15 for bombarding energies from 0.2 to 0.6 keV [41], while Gnaser and Oechsner [45] report values ranging from about 0.05 to about 0.12 in the same energy range. At 5 keV bom-

barding energy Gnaser and Hofer [39] report a Yz/Y, value of approximately 0.42, while Coon et al. [43] report a value of slightly greater than 0.01 at 3.6 keV bombarding energy. The wide variations in reported Y,/Y, values probably can be attributed to a number of experimental problems that arise in this type of measurement. For example, many measurements were taken at only a single emission angle (usually along the surface normal). Our simulation results (see below) suggest that dimers tend to be preferentially ejected in the forward direction compared to monomers. Thus, measurements in the direction of the surface normal would tend to overestimate the Y,/Y, value. Likewise, if the postionization technique employed tends to ionize dimers more efficiently than monomers, then the ratio also will be overestimated. On the other hand, if the postionization techniques causes some dimers to dissociate, then the ratio will be underestimated. In any event, it probably is safe to assume that the dimerto-monomer ratio for Cu is somewhere between 1 and 15% for a bombarding energy of 5 keV. Several investigators have attempted to infer dimer (and cluster) emission mechanisms from the behavior of Y,/Y, values vs bombarding energy and consequently total sputtering yield, or from the translational energy distributions of monomers, dimers, and trimers. Statistical or “recombination” models generally predict a linear dependence of Y,/Y, on total yield, and this has been observed in a number of cases [41,42,44,45]. However, Coon et al. [43] note that multiple collision models in general should produce such behavior. They also report that multiple collision models are in qualitative agreement with their data, but specific predictions of these models for dimer and trimer translational kinetic energy distributions do not agree well with their observations. (In fact, they were unable to find any single model of dimer ejection that could fully explain their data.) Likewise, Franzreb et al. [46] observe deviations from the statistical model in the emission of silver dimers, but not in the emission of trimers or tetramers. In the simulations reported here, we have attempted to identify specific dimer ejection mechanisms by visual inspection of individual dimer sputtering events. Our results suggest that, at least at higher bombarding energies, the dimer emission process is complicated; and, they suggest that at least three competing processes are present simultaneously.

2. Simulation model 2.1. Pair-potential

simulations

A modified version of the multiple-interaction, molecular dynamics code SPUT2 code [47] was used

M.H. Shapiro, T.A. Tombrello/Nucl. Table 1 Pair-potential parameters Molike: 03r/B +o.J~~-‘.~‘/B +o le-6r/B Kj = (A /rX0.35er < ra Cubic spline: ra 4 r < rb vj = Co + C1r + C2r2 + C3r3, Morse: rb < r < r, Kj = De[e-2P(r-rd - 2e-Zfi(r-rd], K, =0,

Instr. and Meth. in Phys. Res. B 84 (1994) 453-464

I,

r 2 rc Interaction

Parameter

Ar-Cu

a

cu-cu 9689.3

6012.6

A [eV A]

[Al ra [Al Co[evl C, [eV/h

0.09603

0.1035

B

1.50 567.341

2.50

- 760.405

C, [eV/A*]

339.923

C, [eV/A3]

- 50.5911

rb [A] 0, [evl

1.988 0.37

P G-9 re [Al rc [A

2.866

a The Ar-Cu simulations.

1.359

5.250 Moliire

potential

was also

used for the EAM

for the pair-potential simulations reported in this paper. This code uses a low-order predictor-corrector method with an adaptive time-step algorithm to integrate the classical equations of motion for the incident ion (Ar+) and for the atoms (Cu) located at the lattice sites of an ideal crystallite. SPUT2 also employs neighbor-list logic [48] to reduce computation time. The net force on an atom (or the incident ion) is obtained from the superposition of two-body forces between the atom and its neighbors. For these simulations the Cu-Cu interaction was represented by a repulsive Moliere potential joined to an attractive Morse well with a cubic spline. The potential parameters (see Table 1) were chosen to fit the bulk properties of copper. This results in a potential depth ( _ 0.4 eV) that is considerably shallower than that needed to fit the free Cu dimer (2.1 eV), and an equilibrium radius (2.87 ;i> that is somewhat larger than that needed to fit the free dimer data (2.22 A) [49]. These pair-potential parameters were used for both copper atoms in the target region, and for those which escaped the target region. Our reasons for doing this were twofold. First, we did not wish to introduce discontinuities by arbitrarily switching potentials as atoms escaped the surface. Second, recent work by Wucher and Garrison [30] suggested that a large fraction of emitted dimers are ejected with high internal energies. Thus, the use of a

455

small value for the dimer binding energy should still yield a relatively large number of dimers, while providing a useful test of the sensitivity of our results to changes in potential parameters. The SPUT2 code was modified to check for the emission of clusters at the end of each sputtering event. Pairs of sputtered atoms were considered bound if their internal energy, Ere, + v(r), was negative. Larger assemblies of atoms were assumed to form clusters if there was one or more bonds between each pair of atoms that satisfied the same condition, Because the cut-off time for each trajectory was set at 500 fs, it is likely that many of the larger clusters observed in the simulation probably were not stable against unimolecular decomposition [32]. However, the total yield of clusters with n r 3 seen in these simulations was small enough that our results would not be affected greatly by this effect. One thousand impacts on a six-layer Cu (100) target with 675 atoms, and 500 impacts on a six-layer Cu (111) target with 824 atoms were simulated with the SPUT2 code. Information about sputtered clusters including the starting locations of the atoms in the target, the internal energy of all pairs of atoms in the cluster, and the target impact location of the incident ion responsible for the sputtering event were written to files during the simulations. Events that produced valid dimers, i.e. those not including any atom(s) from the edges or sides of the target and having a negative internal energy, were recomputed individually with a version of the SPUT2 code that saved the positions of each of the dimer atoms at each time step to a separate file. This file then was displayed with a standard three-dimensional graphical display code to provide an animated display of the trajectories of the atoms forming the dimer. In most cases by viewing this display, it was possible to determine the mechanism by which the individual dimer formed. For example, many “recombination” events could be clearly identified because one atom of the pair started well before the other and left the target region before the second atom caught up with it. Likewise, “ejection intact” events often were obvious because both atoms started essentially at the same time and followed parallel trajectories out of the target. “Push-stick” events were somewhat more difficult to identify because collisions took place with other atoms besides the one that was struck and ejected. For some events a clear distinction between mechanisms was not possible. 2.2. EAM simulations A new code, SPUT3, was written to carry out simulations with many-body, embedded-atom method potentials to describe the interaction between Cu atoms. In the embedded-atom method [SO,%] the potential

M.H. Shapiro, T.A. Tombrello /Nucl. In&. and Meth. in Phys. Res. B 84 (1994) 453-464

456

energy of the ith atom in the lattice is written as ,?Zi= F[pi] + f& + j’p( rij), where F is the “embedding function”, pi is the total electron density at the position of the ith atom due to other atoms in the lattice, and q(rij) is a pair-potential describing the repulsive part of the interaction. The total electron density at atom i in the EAM is approximated by the sum of spherically averaged charge densities from the surrounding atoms, i.e. pi = Zj+i~atomic(rij). We have used the empirically-determined Cu embedding function of Foiles, Baskes, and Daw [52] and charge densities obtained from the Roothaan-Hartree-Fock wave functions of Clementi and Roetti [53] in our calculations. To increase the speed of computation, a fifthorder polynomial of the form u0rm3 + utr-’ + u2r-i + us + u4r + u5r2 was fitted to the expression for Patomic obtained from ref. [53]. Likewise, the embedding function F[pi] obtained from ref. [52] was replaced with fifth-order polynomials of the form be + b,pi + b& + b3pf + b,pf + b,p!. In order to obtain high quality fits over the entire range of pi, it was found necessary to use three distinct polynomials of this form. The results of these fitting procedures are shown in Figs. 1 and 2, and the corresponding fitting parameters are given in Table 2. The empirical EAM potential for copper in ref. [52] was obtained by fitting properties of the metal at densities close to equilibrium. As a result, it is not sufficiently repulsive at small interatomic distances to account properly for the hard collisions that occur early in some collision cascades initiated by keV ions. Since at the small interatomic distances associated with hard collisions, the two-body component of the interac-

0.02

0 *i

0.0 I

c\z *”

0.0 L 2.0

3.0

4.0

5.0

6.0

r (A) Fig. 1. Fifth-order polynomial fit to the atomic charge density (in atomic units) for Cu (from ref. [53]). The function patomic has been plotted as a solid line, and the polynomial fit as a dotted line; however, the differences between the function and the polynomial fit are so small that they cannot be distinguished at the scale of this figure. The coefficients of the polynomial are given in Table 2.

-4 -

-8 -

-12

I 0

I

0.1

0.2

Ptotal Fig. 2. Fifth-order polynomial fits to the embedding function for Cu (from ref. [52]). Charge densities are in atomic units. The function F has been plotted as a solid line, and the polynomial fits as dotted lines; however, the differences between the function and the polynomial fits are so small that it is difficult to distinguish them at the scale of this figure. The coefficients of the polynomials and their ranges are given in Table 2.

tion potential will dominate, we modified the EAM potential of ref. [52] by connecting the EAM effective dimer potential to a repulsive Moliere core with a cubic spline. In order to obtain a smooth effective two-body potential, a constant 17 eV was subtract%d from the standard Moliere potential for r < 1.45 A. This modified Moliere potential then was connected to the EAM dimer potenJia1 with a cubic spline in the region 1.45 I r I 1.55 A. Beyond 1.55 A the unmodified EAM potential was used. This procedure for handling hard collisions differs from that used in a previous EAM simulation of sputtering from the Ar-Cu system by our group [54]. The ejected-atom energy distributions and polar-angle distributions produced by the EAM potential used in the present simulations are considerably more realistic than those obtained in ref. 1541. Our new procedure for handling hard collisions leaves the EAM potential of ref. [32] essentially unmodified in the charge density region that is important for determining the effective Cu dimer potential. This is useful because the EAM dimer potential is a very good approximation to the Cu dimer potential obtained from experiment. In Fig. 3 the EAM effective dimer potential is compared with a Morse potential that has been fitted to the experimental ground-state binding energy, vibrational frequency, and equilibrium separation of the Cu dimer [49]. The EAM effective dimer potential has an equilibrium radius that is almost identical to that of the experimental dimer potential. Its depth is approximately 10% greater, and its range is about 20% less than the experimental dimer

M.H. Shapiro, T.A. Tombrello/Nucl. Instr. and Meth. in Phys.Res. B 84 (1994) 453-464

451

Table 2 Cu EAM fitting parameters Charge density: patomic(rij)= aOrw3+ a1rm2 + a2F1 + a3 + a4r + a5r2 a, [electrons]

0.08888982236

aI [electrons/A]

0.07005612552

a2 [electrons/i*]

0.01306470204

a3 [electrons/i31 a4 [electrons/A41

- 0.03338396922

a5 [electrons/~5]

- 0.0006769380998

0.008847557008

Embedding function: F(pi) = b, + b,p, + b,p; + b,p? + b,p; + b5p;

pz 5 0.0045 b, [eVl

0.0045 < pi 5 0.0083

0.0 - 326.7786255 23065.82617 176.1127930 1.033064127 0.00550667429

b, b, b, b, bs

- 0.3976599872 - 132.7479858 - 1.545039296 - 0.01423106436 - 0.0001221462735 -0.0000010233878

potential. These small deviations should have no major effect on our results. The same test for the emission of clusters that was used in the modified SPUT2 code was aiso used in SPUT3. The total sputtering yields observed with the EAM code were roughly half those found with the two-body code. To achieve comparable statistics in the number of observed dimers, it was necessary to calculate trajectories for 4000 impacts on the Cu(100) face and 2000 impacts on the Cu(ll1) face with the EAM code. Six-layer targets also were used with the EAM code to ensure that the electron density calculations in the collision cascade were not significantly affected by

I

1.5

I

I

2.5

I

I

3.5

I

I

4.5

I

88

5.5

r (Al

Fig. 3. The effective Cu-dimer potential derived from the EAM potential is shown as a solid line. A Morse potential fitted to the experimental Cu-dimer data from ref. [49] is shown as a dotted line.

p, > 0.0083

- 0.6358204484 - 109.8931580 714.5303955 - 3292.178223 4810.807129 2896.340576

the finite size of the target. As with the two-body code, sputtering events that produced valid dimers were recomputed to produce position vs time data for each atom in the dimer, and animated displays were viewed individually to determine the specific ejection mechanism.

3. Simulation results 3.1. yields, energy-, angle-, and ejected-atoms/impactdistributions

For comparison with experimental data and previous simulation work, we present in this section our simulation results for 1) monomer, dimer, and trimer yields; 2) translational kinetic energy distributions for all sputtered atoms and for sputtered dimers; 3) internal energy distributions for sputtered dimers; 4) polar angle distributions for all sputtered atoms and for sputtered dimers; and 5) ejected-atoms/ impact distributions [55] for impacts that produced no dimers or larger clusters and for impacts that produced at least one dimer or larger cluster. Yields obtained in these simulations are summarized in Table 3. The EAM total sputtering yields are only about 40 to 50% of the pair-potential total yields. The pair-potential results are within 15% of the absolute yields observed experimentally [56,57] for 5 keV Ar+ on the Cu(100) and Cu(ll1) faces, which are 4.1 and 9.5 respectively. The EAM results are too low by a factor of - 2. The experimental ratio of Yc,,oII/ Ycuom~ is 2.32. Both our pair-potential value (2.74) and

M.H. Shapiro, T.A. Tombrello /Nucl.

4.58

Instr. and Meth. in Phys. Res. B 84 (1994) 453-464

Table 3 Sputtering yields y total Pair-potential (100) 3.54 (111) 9.69 EAM (100) 1.84 (111) 3.79

YI

yz

r,

y2 /

3.33 9.09

0.093 0.256

0.007 0.024

0.028 0.028

0.0021 0.0026

1.80 3.71

0.0165 0.038

0.001 0.002

0.009 0.010

0.0006 0.0005

Yl

y3 /

Yl

our EAM value (2.06) for this ratio are in reasonably good agreement with the experimental ratio. The averaged EAM dimer-to-monomer number ratio is 0.0097, while the average pair-potential dimerto-monomer number ratio is 0.028. These results are quite close to the Y,/Y, ratio observed by Coon et al. [43]. They are considerably lower, however, than the other experimental values reported in the keV bom-

I

barding energy range (0.42 and 0.18, respectively) [39,42]. Trimer yields and trimer-to-monomer number ratios are also presented in Table 3. We find that the relative yields of monomers, dimers, and trimers from the EAM and pair-potential simulations separately can be fit quite well by power-law dependences on the number of atoms in the cluster (Y,,, = n-6.8 and Ypair = n-5.4). Coon et al. have found experimentally that Y = n-7.9 for Cu, clusters with n I 20 [58]. They argue that this power-law yield dependence is inconsistent with collision-cascade models. However, our simulations show that collision-cascade cluster ejection mechanisms are consistent with a power-law yield dependence, at least for small clusters. The pair-potential and EAM kinetic energy distributions for all sputtered atoms from the Cu(100) and Cu(ll1) faces are shown in Figs. 4a and 4b, respectively. The peaks in the EAM distributions are shifted to slightly higher energies by about 2 eV compared to the pair-potential distributions. The EAM distributions

““7

““‘I

(b) Cu(ll1)

.. ,.,., ‘00

$

2500

‘500

z 0 2

2 -0

m

s

I

g

i.2

‘Ooo 500 0 2000

\

z

G 0

b

2000

% @

‘O

3 ::

z 5

k

‘00

-e

‘600

-

i.5

“E 1200

2

z’

'0

II

b.’

:w

I

‘0

Fig. 4. Simulated kinetic energy distributions of all sputtered atoms from (a) the Cu(100) and (b) the Cu(ll1) surfaces. The distributions computed with the EAM potential are shown as solid lines. The distributions computed with the pair-potential are shown with dots. The EAM distributions have been norto have

the same total yields distributions.

I’.“.-C..2 ..,’ \ ,% ,:a \ Q...............” i.. >a. ? \ \

_

‘00

Energy (eV)

malized

\

(a) cu(100)

..=

.,,..,..’

...,.,.’

i.

as the pair-potential

Polar Angle (deg) Fig. 5. Simulated polar angle distributions of all sputtered atoms from (a) the Cu(100) and (b) the Cu(ll1) surfaces. The distributions computed with the EAM potential are shown as solid lines. The distributions computed with the pair potential are shown as dotted lines. The EAM distributions have been normalized to have the same total area as the pair-potential distributions.

M.H. Shapiro, T.A. Tombrello /Nucl. Instr. and Meth. in Phys. Res. B 84 (1994) 453-464

also are slightly broader than the pair-potential distributions in the energy range up to about 30 eV. However, the EAh4 kinetic energy distributions obtained in the present simulations do not exhibit the very broad low-energy behavior seen in the earlier Ar-Cu EAM simulations of Lo et al. [54]. There is more difference between the pair-potential and EAM polar-angle distributions for all sputtered atoms from the Cu(100) and Cu(ll1) faces. In both cases (cf. Figs. 5a and 5b) the pair-potential polar-angle distributions are narrower than the EAM distributions. The differences between the pair-potential and EAM energy and polar-angle distributions observed in the present simulations are similar to those observed in previous sputtering simulations [59]. Translational kinetic energy distributions for dimers ejected from the C&11) surface obtained from the pair-potential and EAM simulations are shown in Figs. 6a and 6b, respectively. Both distributions peak at higher energies than the corresponding distributions for all sputtered atoms (which are dominated by monomers). The EAM energy distribution extends to somewhat higher energies than the pair-potential distribution. Because of the poor statistics in both distri-

(b) Cdlll) EAM potential!

(a) Cu(ll1) Pair-potential

III II. I I.1 IO

I . 100

Energy (eV) Fig. 6. Simulated translational kinetic energy distributions for dimers sputtered from the Cu(ll1) surface computed (a) with the pair potential and (b) with the EAM potential.

459

(b) Cdlll)

IO

t

l-4 (a) Cu(100)

I: -2.5

G.0

-1.5

-1.0

-0.5

0.0

Energy (eV)

Fig. 7. Simulated internal energy distributions for dimers sputtered from (a) the Cu(100) surface and from (b) the Cu(ll1) surface with the EAM potential.

butions, comparisons with experimental data can be made only qualitatively. However, the shift to higher energies of the peaks in the dimer energy distributions is more consistent with the data obtained by Coon et al. [41] at 3.6 keV than with that obtained by Brizzolara and Cooper [39] at 1 keV. The internal energy distributions calculated in the EAM simulations for dimers ejected from the Cu(100) and Cu(ll1) faces are shown in Figs. 7a and 7h, respectively. It can be seen from these distributions that the majority of dimers are ejected in highly excited states. This observation is consistent with the results obtained by Wucher and Garrison for the Ar-Ag system [30,31], which showed that silver dimers were ejected with very high effective rotational and vibrational temperatures. Polar-angle distributions of dimers sputtered from the Cu(ll1) face are shown in Figs. 8a (pair-potential) and 8b (EAh4). In both cases the polar-angle distribu^ . tions for the sputtered dimers are more forward peaked than those for all sputtered atoms. The EAM polar-angle distribution for the dimers (Fig. 8b) is significantly more forward peaked than the comparable distribution for all sputtered atoms (Fig. 5b). Since EAh4 simula-

460

M.H. Shapiro, T.A. Tombrello/Nucl. In&r. and Meth. in Phys.Res. B 84 (1994) 453-464 I

I

I

3.2. Specific ejection mechanisms and starting locations for ejected dimer atoms

I

(b) Cu(l11) EAM-potential

The trajectories of the atoms comprising valid sputtered dimers were examined using a three-dimensional graphical display program. This program allowed us to observe the trajectories from different viewing angles and at adjustable rates of temporal development. Dimer ejection events were classified into three groups “recombination”, “ejection intact”, or “push-stick” when the mode of formation was obvious from inspection of the event. (Recombination events were identified by observing that the two atoms forming the dimer started moving at different times, and that one of the atoms ejected from the target before the other. For ejection intact events both atoms started their motion essentially simultaneously, and both atoms left the surface at essentially the same time. Push-stick events were identified by an obvious collision between a mov-

(a) Cu(ll1) Pair-potential

0

IO

20

30

Polar

40

50

60

70

80

90

IO

Angle (deg) 5

Fig. 8. Simulated polar-angle distributions for dimers sputtered from the Cu(ll1) surface computed with (a) the pair potential and (b) the EAM potential.

0 300

tions are believed to produce substantially more realistic angular distributions than pair-potential simulations [59], this result would suggest that measurements of Y,/Y, at very forward angles are likely to overestimate this ratio. Ejected atoms per impact distributions are shown in Figs. 9a-9d for events which yielded no dimers from the Cu(100) and Cu(ll1) faces (Figs. 9a and SC), and for events which yielded one or more dimers from the same faces (Figs. 9b and 9d). The distributions shown were obtained from the EAh4 simulations. Similar results were found in the pair-potential simulations. As can be seen in these figures, dimers most frequently are associated with events that produce large numbers of sputtered atoms. The bulk of the dimers are ejected in events where the total number of sputtered atoms is 6 or more, while the bulk of the events that did not yield dimers had fewer than 6 sputtered atoms. Thus, sputtered dimers often are associated with events that cause significant disruption of the surface. This would suggest that analytical models for dimer ejection that employ idealized models of the surface (such as a planar surface boundary or a fixed surface binding energy) are likely to be inadequate to explain the experimental observations.

Y 5 & L 0

200 100

k

0 IO

-E 2

5

Cu(100) Dimers I

0

III!

I

(a) Cu( 100) No Dimers

400 200 0

0

Number

Ill,,. IO

I 20

of Ejected

30

40

Atoms/Incident

50

Ion

Fig. 9. Distributions of the number of sputtered atoms per incident ion computed with the EAM potential. (a) Events in which no dimers were sputtered

from the Cu(100) surface.

(b)

Events in which one or more dimers were sputtered from the Cu(100) surface. (c) Events in which no dimers were sputtered from the Cu(ll1) surface. (d) Events in which one or more dimers were sputtered from the Cu(ll1) surface.

M. H. Shapiro, TA. Tombrello / Nucl. I&r.

ing target atom and a stationary one, followed by the ejection of the pair.) In a few cases the mode of dimer formation was not obvious after viewing the event, and these were tabulated in a fourth category. All of the valid dimers ejected from the Cu(100) surface in both the pair-potential and EAM simulations were examined in this manner. It was not possible because of time constraints to examine visually all the valid dimers ejected from the Cu(ll1) surface in the pair-potential simulation. Instead subsets of events comparable in number to the Cu(100) cases were examined. Typical dimer trajectories from the Cu(100) surface are shown in Figs. lOa-lOc, and similar trajectories from the Cu(ll1) surface are shown in Figs. lla-llc. All of these trajectories were computed in the EAM

21

1

,((,,,.

.J’

,_.... .I’

..A

461

and Meth. in Phys. Res. B 84 (1994) 453-464

(cl “ejection-intact”

(b) “Dush-stick”

i6-

14 12 IO 8

Cc)

-Y

“ejection-intact”

(a) “recombination”

,,_... ___..i ._

,,.__A

Y(A) (b) “Dush-stick”

(a) ‘recombination”

-6-5

-4-3

-2-l

Lffd3X(A)

0’

YUi, Fig. 10. Typical trajectories computed with the EAM potential for dimers ejected from the Cu(100) surface. The front surfaces of the targets, shown with dotted lines, are located in the X-Z plane. Ejected atoms move to the left in the figure. In (a) a first-layer atom started first and sputtered first, while a second first-layer atom caught up with the first one above the surface to form the dimer by the “recombination” mechanism. In (b) a second-layer atom started first, then struck a first-layer atom. The pair then ejected to form the dimer by the “push-stick” mechanism. In (c) two second-nearestneighbor atoms ejected simultaneously. Vibrational motion of the dimer pair can be seen in all three figures. Rotational motion is also seen in event (a).

Fig. 11. Typical trajectories computed with the EAM potential for dimers ejected from the Cu(ll1) surface (same orientation as in Fig. 10). In (a) a first-layer atom started and ejected first. A second first-layer atom caught up with the first atom above the surface to form the dimer by the “recombination” mechanism. In (b) a second-layer atom started first, hit a first-layer atom, and both ejected to form the dimer by the “push-stick” mechanism. In (c) two nearest-neighbor atoms in the first-layer of the target were ejected simultaneously. Rotational motion of the dimer is visible in (c).

simulations. In a number of cases vibrational or rotational motion of the dimer could be observed when viewing the trajectories produced in the EAM simulations. Generally, the pair-potential trajectories did not exhibit as pronounced vibrational or rotational motion as was seen for the EAM trajectories. This, of course, is a direct consequence of the fact that the EAM dimer potential is much deeper than the pair dimer potential, which allows a greater range of internal excitation to occur in the EAM case without the dimer breaking up. The frequencies with which specific dimer ejection mechanisms occurred in the simulations are summarized in Table 4. Approximately 35% of the ejected dimers from both the C&100) and Cu(ll1) surfaces were observed to form via “recombination”. “Ejection intact” was observed for approximately 40% of the dimers ejected from the Cu(100) surface and approximately 50% of those ejected from the Cu(ll1) surface. The “push-stick” mechanism was observed less fre-

462

M.H. Shapiro, T.A. Tombrello/Nucl.

Table 4 Dimer ejection

In.&. and Meth. in Phys. Res. B 84 (1994) 453-464

mechanisms Recombination

[%I

Ejection

intact [%I

Push-stick

[%I

Other

a [%I

CuwnI) Pair-pot. EAM Cu(lll)

28 40

43 38

21 17

8 5

Pair-pot. EAM

31 36

56 42

8 18

5 4

a Includes

all events not assigned

to the first three categories.

quently - accounting for approximately 20% of the dimers ejected from the Cu(100) surface and approximately 15% of those ejected from the Cu(ll1) surface. Owing to the small number of dimer events that could be examined visually, the statistical uncertainties in the percentages listed in Table 4 are of the order of 15 to 20%. Thus, there would appear to be no statistically significant differences in the relative frequency of ejection mechanisms for the (100) and (111) surfaces; nor, is there a statistically significant difference between the ejection mechanism results from the pair-potential and the EAM simulations. In Table 5 we have summarized data relating to the original locations of the atoms that formed ejected dimers in our simulations. More than half of the atoms that formed dimers from both the Cu(100) and Cu(ll1) faces originally were first nearest-neighbors. The number of second nearest-neighbors forming sputtered dimers was higher from the (100) face than the (111) face (- 30% vs - 3%). In the EAM simulations 30% or more of the ejected dimers were formed from atoms that originally were further apart than third nearestneighbors, while in the pair-potential simulations this number was only - 15%.

Table 5 Initial locations

cuUK0 Pair-pot. EAM Cu(ll1) Pair-pot. EAM

cuwMI) Pair-pot. EAM Cu(ll1) Pair-pot. EAM

of dimer

atoms. All values

These results are not consistent with the pair-potential simulations of Winograd et al. [21] for 0.6 keV Ar ions bombarding Cu nor with the EAM simulations of Karetta and Urbassek [33] for 0.3 keV Cu ions bombarding Cu(lOO), in which most of the ejected dimers were found to originate from second nearest-neighbors. However, they are reasonably consistent with the observations of Karetta and Urbassek [33] for the case of 1 keV Cu bombarding Cu(lOO), where it was found that 52% of the dimers were formed from first nearest-neighbors and 26% were formed from second nearest-neighbors. More than - 97% of all dimers included at least one atom that originally was in the first layer of the target (see Table 5). Approximately 75% of the dimers ejected from the Cu(100) surface and about 88% of the dimers ejected from the Cu(ll1) surface were formed from two atoms that originally were in the first layer. These results are somewhat different from the simulations at 0.3 keV [33], 0.6 keV [21], and 1.0 keV [33] bombarding energy, where most dimers (90% or more) were found to be formed from first layer atoms. It is an indication, that at 5.0 keV bombarding energy the collision cascades are more fully developed and the

in percent

lst-NN

2nd-NN

3rd-NN

> 3rd-NN

54 48

31 28

0 0

14 25

80 55

3 3

0 0

17 42

lst-layer lst-layer

2nd-layer 2nd-layer

3rd-layer 3rd-layer

lst-layer 2nd-layer

2nd-layer 3rd-layer

lst-layer 3rd-layer

76 75

3 3

0 0

20 20

0 0

1 2

90 86

0 1

0 0

10 10

0 0

0 3

M.H. Shapiro, T.A. Tombrello /Nucl. Instr. and Meth. in Phys. Rex B 84 (1994) 453-464

resulting surface disruption, particularly for the (100) surface, is greater than at the lower bombarding energies. While we have not investigated the behavior of sputtered clusters with n 2 3 in great detail, clusters as large as n = 4 were observed in these simulations. In most cases the sputtered clusters with n r 3 were formed from atoms that initially were dose neighbors in the target.

4. Discussion We can make the following conclusions based on our simulations regarding the sputtering of metal dimers following bombar~ent with keV ions: First, the ratio of sputtered dimers to monomers appears to be of the order of a few percent at most. Our values for Y/Y, (0.028 (pair) and 0.0097 (EAM)) are in good agreement with the experimental results of Coon et al. [43]. Second, the translational kinetic energy distributions for sputtered dimers peak at higher energies by about 1 to 2 eV than the monomer energy distributions. This also agrees well with the experimental results of Coon et al. Third, the polar-angle distributions of sputtered dimers are predicted to be significantly more forward peaked than those of the monomers. This implies that e~erimental measurements of Y,/Y, at a single ejection angle may be unrepresentative. Fourth, dimers preferentially are sputtered from cascades that yield a large total number of sputtered atoms. Fifth, dimers generally are sputtered in highly excited states. Sixth, at these bombarding energies the dimer ejection process is complex, and at least three competing ejection mechanisms appear to be present simultaneously. Finally, we note that while the E/&i MD simulations generally are believed to produce more realistic trajectories than pair-potential MD simulations, no major differences in our conclusions would have been drawn from the pair-potential results alone.

Acknowledgements The authors thank Barbara Garrison and Klaus Franzreb for helpful conversations. We also thank them and Andreas Wucher for providing copies of their work prior to publication.

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463

[33 H.M. Urbassek, ibid., p. 587.

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