MD simulation of cluster formation during sputtering

Nuclear Instruments and Methods in Physics Research B 180 (2001) 222±229

www.elsevier.nl/locate/nimb

MD simulation of cluster formation during sputtering T. Muramoto, M. Okai, Y. Yamashita, K. Yorizane, Y. Yamamura

*

Department of Informatics, Okayama University of Science, Ridai-cho 1-1, Okayama 700-0005, Japan

Abstract The cluster ejection due to cluster impact on a solid surface is studied through molecular dynamics (MD) simulations. Simulations are performed for Cu cluster impacts on the Cu(1 1 1) surface for cluster energy 100 eV/atom, and for clusters of 6, 13, 28 and 55 atoms. Interatomic interactions are described by the AMLJ±EAM potential. The vibration energy spectrum is independent of the incident cluster size and energy. This comes from the fact that sputtered clusters become stable through the successive fragmentation of nascent large sputtered clusters. The vibration energy spectra for large sputtered clusters have a peak, whose energy corresponds to the melting temperature of Cu. The exponent of the power-law ®t of the abundance distribution and the total sputtering yield for the cluster impacts are higher than that for the monatomic ion impacts with the same total energy, where the exponent d is given by Yn / nd and Yn is the yield of sputtered n-atom cluster. The exponent d follows a uni®ed function of the total sputtering yield, which is a monotonic increase function, and it is nearly equal to d  )3 for larger yield. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 34.90; 36.40; 79.20R Keywords: Computer simulation; Cluster impact; Sputtering; Cluster emission

1. Introduction When a solid is bombarded by energetic ions, a number of particles emerge from the surface. It is well-known that this sputtered ¯ux may contain clusters of several or many atoms [1]. The formation of these clusters in the course of the collision processes leading to the ejection of sputtered particles represents one of the most interesting phenomena in sputtering physics. From reports of * Corresponding author. Tel.: +81-86-252-3161; fax: +81-86256-8006. E-mail addresses: [email protected], muramoto@ sp.ous.ac.jp (Y. Yamamura).

experiments and MD simulations [2±11], it has been shown that the abundance distribution of sputtered clusters can be described by a power-law function of sputtered cluster size. Cluster impacts deposit a lot of energy and particles to a localized region on the target surface, producing a very active transient state in the very small impact region of the target material. There are many interesting problems associated with cluster impact phenomena [12,13], and computer simulation is one of the most powerful methods for their investigation [14,15]. In this paper, we studied the cluster ejection due to cluster impact. MD simulations are performed for 100 eV/atom …Cu†N impacts on Cu(1 1 1) sur-

0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 4 2 1 - 9

T. Muramoto et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 222±229

faces, where N ˆ 6, 13, 28 and 55 are used. We examined the e€ect of impact cluster size and total impact energy on the abundance distribution of sputtered clusters, comparing the results with monatomic ion impacts with the same total impact energy.

2. Simulation model For the present MD simulations, we employ the hybrid AMLJ±EAM potential, which combines the embedded-atom method (EAM) potential [16,17] with the average modi®ed Lenz-Jensen (AMLJ) potential [18]. These two potentials are connected smoothly, using a cubic interpolating function between the AMLJ potential and the pair repulsive term of the EAM potential [16]. The in to 0:85r1 , terpolating distance range from 1 A where r1 is the nearest-neighbor distance of the fcc crystal. Over the corresponding range, the embedding function of the EAM potential [16] is smoothly attenuated using a cubic cut-o€ function. The cut-o€ distance rcut of the potential is set at 1:91r1 . Simulations are performed for an incident cluster energy per atom E0 of 100 eV, and incident cluster sizes N of 6, 13, 28 and 55 atoms. The incident clusters are formed by cutting out spherically from the fcc crystal lattice. The initial velocity of clusters is oriented normal to the (1 1 1) surface. The target crystals of MD simulation are formed into a hemisphere.The z-axis is oriented upside normal to the surface. The target crystal is composed of a core region r < rcore and a heatbath region r P rcore , where r is the distance from the center of the surface, and the radius of target crystal is 1.4rcore . In the present MD simulation, this radius is a function of the total incident energy, and then rcore is given by 3 =3 ˆ X0 NE0 =e; 2prcore

…1†

where X0 is the atomic volume of fcc Cu, and an empirical parameter e is set to be 1.3 eV which is determined in order to keep the core volume as small as possible and at the same to be able to neglect the e€ect of the simulation target size on

223

crater formation. The core region is treated by the standard MD calculation. The temperature of the heat-bath region is kept at 300 K using the Langevin MD method [19]. The information of sputtered clusters is stored at every time step in the MD simulation. The criteria of cluster formation of sputtered atoms are the following: We recognize the cluster as a group of linked atoms. We set the link condition Er ‡ U2 …r† < 0, where U2 is the binding energy of a Cu dimer, r is the distance between two atoms, and Er is the relative kinetic energy. The ejection of a cluster from the surface is determined by the following conditions: Rz > 2rcut ;

…2†

Vz > 0;

…3†

MVz2 =2 ‡ Usurf > 0;

…4†

where Rz is the distance between the original surface and the barycenter of a sputtered cluster, Vz is the surface normal component of the barycentric velocity of the sputtered cluster, M is the mass of the sputtered cluster, and Usurf is the potential energy between the sputtered cluster and surface atoms. 3. Results and discussions In order to study the cluster ejection due to cluster impacts, MD simulations are performed for 100 eV/atom (Cu)N impacts on a Cu(1 1 1) surface, where N ˆ 6, 13, 28 and 55 are employed. Physical quantities are averaged over 1000, 500, 200 and 100 impacts for N ˆ 6; 13; 28 and 55, respectively. The crystal-axis of incident clusters and the impact point on the surface are determined randomly for each impact. The impact region is compressed in the initial stages of cluster impact. The number densities of target atoms in the impact region are shown in Fig. 1 as a function of depth for typical time slices. The number densities are calculated for a cylindrical region of radius 0.5R0 , where R0 is the initial radius of the incident clusters. From Fig. 1, the impact of

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In Fig. 3, we show the time evolution of cluster yield Yn , which denotes the yield of sputtered Cun . Large sputtered clusters are emittedPlater than small clusters. The total yield Ytot ˆ nYn satu-

Fig. 1. Number density of target atoms in impact region as a function of depth for 100 eV/atom …Cu†N ! Cu…1 1 1†.

larger clusters appears to form higher densities (i.e., higher potential energy density) in 0.03±0.04 ps. The number of cluster atoms, which simultaneously collide with target atoms, increases with the cluster size, and larger incident clusters deposit the larger energy in a localized target region. Therefore, larger incident clusters produce higher energy density. A snapshot of the cluster impact region is displayed in Fig. 2 for 100 eV/atom …Cu†55 impact on a Cu(1 1 1) surface. In Fig. 2, there is the protuberance due to momentum transfer along the close-packed directions on the (1 1 1) surface at 0.3 ps. The momentum transfer is caused by explosion after the high-density formation which occurs at 0.03 ps. The explosion triggered by high-density produces a crater. We can observe the ejection of Cu16 from the edge of the crater. Since the edge of such craters is unstable in the early stage of crater formation, the crater formation readily results in the emission of large sputtered clusters.

Fig. 2. Snapshot of cluster impact region for 100 eV/atom …Cu†55 ! Cu…1 1 1†.

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Most of the large nascent clusters are metastable [6,11]. They fragment into small clusters and turn to be more stable clusters. From the viewpoint of stability of sputtered clusters, the internal energy of sputtered clusters is a very important factor. The total internal energy of a sputtered cluster is given by Etot ˆ Ekin ‡ Ucls , where Ucls is the total potential energy of the sputtered cluster, and Ekin is the kinetic energy of internal motion, X Ekin ˆ mi v2i =2; …5†

Fig. 3. Time evolution of cluster yield Yn and total sputtering yield Ytot for 100 eV/atom …Cu†55 ! Cu…1 1 1†. Cluster yields are given as atom yields (i.e., nYn ).

rates for t > 2 ps. After the saturation, the yield of large sputtered clusters decreases, and those of dimers and trimers increase with time. This indicates that the nascent sputtered clusters fragment. The same tendency was shown in MD simulation results of a Ar atom impact on Cu target [11]. Since the sputtered cluster yields does not change for t > 100 ps, we consider that the abundance distribution of sputtered clusters reaches the ®nal distribution at t ˆ 100 ps. The total sputtering yields per incident atom Ytot are listed in Table 1 for di€erent incident cluster sizes. It is found that yield increases with N, which is understandable because greater yields can be achieved by inducing higher energy densities in the target surface. Thus, the sputtering yield per incident atom is enhanced in high-density formation, which is one of the cluster e€ects. Table 1 Total sputtering yield per incident atom Ytot for 100 eV/atom …Cu†N ! Cu…1 1 1† N

Ytot

NYtot

6 13 28 55

0.599 0.644 0.723 0.876

3.59 8.37 20.2 48.2

mi is the mass of the ith cluster atom, and vi is the velocity in the center-of-mass system of the sputtered cluster. Moreover, Ekin is described by Ekin ˆ Erot ‡ Evib , where Evib is the energy of internal vibration, and Erot is the rotation energy of the sputtered cluster which is given as Erot ˆ L2 =2I;

…6†

where L is the total angular momentum. X Lˆ r i  m i vi ;

…7†

I is the moment of inertia which is obtained by X 2 Iˆ mi …L  ri † =L2 ; …8† where ri is the relative distance of atoms from the center of mass in a sputtered cluster. Fig. 4 shows the internal energy spectra for sputtered dimers, trimers, Cu4 and Cun …n P 5† at nascent and ®nal state, where the nascent and ®nal spectra correspond to spectra at t  2 and 100 ps, respectively. The horizontal-axis is total internal energy per cluster atom, and the vertical-axis is normalized cluster yield. From the ®gure of Cun …n P 5†, it can be seen that the high-energy part of the spectra vanishes and the low-energy part creates. This indicates that large sputtered clusters with high internal energy are decomposed into small sputtered clusters with low internal energy. In Fig. 5, a top view of trajectory of sputtered Cu atoms is shown for 100 eV/atom …Cu†55 impact on a Cu(1 1 1) surface. From Fig. 5, it is found that the moving directions of fragments di€er from that of a parent sputtered cluster. This means that the internal energy of the parent cluster is converted to barycentric energies of the fragments, and that the sum

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of internal energies of the fragments is less than the internal energy of the parent cluster. As a result, the fragments become more stable. The vibration energy spectra of sputtered clusters is shown in Fig. 6 for the cases of 100 eV/atom …Cu†55 and …Cu†13 , and 5.5 keV monatomic Cu. The horizontal-axis is vibration energy per cluster atom. In case of Cun …n P 5†, the peak energy corresponds to the melting temperature of Cu. There is no signi®cant di€erence among these three cases. Since the fragmentation is only induced by the internal state of sputtered clusters, the internal energy of the ®nal stable cluster created by fragmentation is not a€ected by the incident cluster size and energy. The abundance distribution of sputtered clusters for 100 eV/atom …Cu†55 and …Cu†13 , and 5.5 keV monatomic Cu is shown in Fig. 7. It is well known that the abundance distribution follows a power-law function which is written as

Fig. 4. Internal energy spectra of sputtered dimer, trimer, Cu4 and Cun …n P 5† for 100 eV/atom …Cu†55 ! Cu…1 1 1†. Spectra show for nascent and ®nal states.

Fig. 5. Trajectory of sputtered Cu atoms for 100 eV/atom …Cu†55 ! Cu…1 1 1†.

Fig. 6. Vibration energy spectra of sputtered dimer, trimer, Cu4 and Cun …n P 5† at ®nal state for incident particles 100 eV/atom …Cu†55 , …Cu†13 and 5.5 keV monatomic Cu.

T. Muramoto et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 222±229

Y n / nd :

Fig. 7. Abundance distribution of sputtered clusters for sputtering of Cu(1 1 1) target.

Table 2 Total binding energy (eV) of Cun clusters, as calculated by AMLJ±EAM potential, and experimental or ab initio data

AMLJ±EAM Experimental/ab initio

nˆ2

nˆ3

nˆ4

nˆ5

2.71 2.08

4.90 3.05

7.30 5.89

9.58 7.93

227

…9†

In the fragmentation process, large sputtered clusters become fragments that can fragment even further. The self-similarity of this process produces a power-law distribution. In the present simulation, it is found that the direct ejection is important than the fragmentation process for sputtered monomers. Therefore, monomer yield does not follow the power law. Moreover the AMLJ±EAM potential used in this study overestimate the binding energy of small clusters (cf. Table 2). Since the release of monomers in fragmentation is underestimated in this respect, the monomer yield will be also underestimated. From Fig. 8, we found that the exponent d of the abundance distribution increases with the incident cluster size. This property can be explained in two ways. One is the correlation between the high-energy-density formation and the incident cluster size. A large high-energy-density region emits large clusters. These large sputtered clusters and their associated fragments bring the large exponent d. The other is that the total incident energy is proportional to the incident cluster size. In the present simulation, we observed the recombi-

Fig. 8. Exponent d of power-law ®t to abundance distributions versus total sputtering yield per ion impact (i.e., NYtot ).

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nation of sputtered particles as well as the fragmentation of sputtered clusters. The probability of recombination is enhanced by an increase in the density of sputtered particles immediately above the target surface. Since the total yield per impact increases with the total incident energy, the large incident energy results in the large exponent d. A plot of exponent d versus total sputtering yield per impact is shown in Fig. 8. The simulation results in this study are plotted as solid squares, and the other symbols represent results of experiment [2±5,7±11] and MD simulation [11] for sputtered clusters due to noble gas ion impact on various solid targets. All simulation and experimental results follow a uni®ed function, which increase monotonically, and is nearly equal to )3 for larger sputtering yield. The total yield and d for 100 eV/atom …Cu†55 ; …Cu†28 and …Cu†13 are enhanced over those for 5.5, 2.8 and 1.3 keV monatomic Cu, respectively. Because the monatomic ion impact accidentally forms the high-energy-density region near the target surface while the cluster impact always forms it due to the high-density formation. The AMLJ±EAM potential used in this study overestimates the binding energy of small clusters. However, the entire property of simulation results shown in Fig. 8 agrees with that of experimental results. Therefore, the detailed property of the many-body interaction possibly comes to be less important for the exponent d of the abundance distribution due to the complexity of the fragmentation process. 4. Conclusions Sputtered cluster ejection due to cluster impact on a solid surface is studied through MD simulations. Simulations are performed for Cu cluster impacts on a Cu(1 1 1) surface, for an incident cluster energy of 100 eV/atom, and clusters of 6, 13, 28 and 55 atoms. The interatomic interaction is described by AMLJ±EAM potential. Several conclusions are derived: 1. An explosion promoted by the formation of a high-density region due to cluster impact, produce a crater. Large sputtered clusters are

2.

3.

4. 5.

emitted later than small from the edge of the crater. The sputtered clusters become stable after the successive fragmentation of nascent sputtered clusters. Then the vibration energy spectrum of sputtered clusters is independent of the incident cluster size and energy. The sputtered clusters Cun …n P 5†, have a peak, whose energy corresponds to the melting temperature of Cu. The abundance distribution of sputtered clusters is described by a power-law function Yn / nd , where Yn is the yield of sputtered natom cluster. The exponent d and the total sputtering yield for cluster impact are greater than that for monatomic ion impacts with the same total energy. The exponent d follows a uni®ed function of the total sputtering yield, which the exponent increases monotonically, and is nearly equal to d  )3 for larger yield.

Acknowledgements This work was supported by a grant of The Academic Frontier Project promoted by The Ministry of Education, Science and Culture.

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