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Impact and spreading behavior of cluster atoms bombarding substrates
Applied Surface Science 256 (2009) 1395–1398
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Impact and spreading behavior of cluster atoms bombarding substrates Te-Hua Fang *, Shao-Hui Kang, Jia-Hung Liao Institute of Mechanical and Electromechanical Engineering, National Formosa University, Yunlin 632, Taiwan
A R T I C L E I N F O
A B S T R A C T
Article history: Received 24 February 2009 Received in revised form 27 August 2009 Accepted 28 August 2009 Available online 4 September 2009
The purpose of this study is to investigate the behavior of copper cluster atoms bombarding a substrate using molecule dynamics based on tight-binding second moment approximation (TB-SMA) potential. The simulated results show that a crater on the substrate surface was created by the impact of the clusters. The variations of kinetic energy of cluster bombardments can be divided into three stages. At the initial impact level, the kinetic energies of the clusters and the substrate were constant. Then, the system went into a sluggish stage of energy variation, in which the kinetic energy of the clusters reduced. In the final stage, the kinetic energy of the system became stable. The high slip vector region around the crater had a disorder damage zone. The symmetry-like cross-slip occurred beneath the top layer of the substrate along the h1 1 0i orientations. The spreading index, temperature, and potential functions that affect the bombardments are also discussed. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Molecular dynamics Spreading Cluster Bombardment Craters
1. Introduction In recent years, cluster bombardment and sputtering technology have been increasingly used for various applications in thin films, surface science, and nanotechnology [1–3]. The interaction of cluster bombardment on surfaces has achieved to etch for surface modification applications [4,5]. Deposition field techniques, such as the ionic beam sputtering (IBS) method, plasmonic fields, and molecular beam epitaxy (MBE), have potential applications in creating nanostructures on solid surfaces [6]. The contact and optical properties of the nanostructures can be controlled by the impact energy of the cluster and cluster size. The mechanism of cluster bombardment is difficult to investigate with traditional experimental methodology, but it can be easily solved by using molecular dynamics (MD) simulation. Ratner et al. [7] studied the collision between Cu dimer and Ar film and found that the dense surroundings of the Ar film could confine the Cu dimers. Bromann et al. [8] showed that Ag clusters could be deposited nondestructively on Pt substrates by using Ar buffered layers. Jime´nez-Sa´ez et al. [9] studied structural changes in Cu clusters softly landing on Au substrates at various energies and temperatures. Zang et al. [10] found that collision dynamics were dominant in the early stages of single cluster deposition. Lee et al. [11] found that cluster atoms activated copper substrate atoms through collective collisions in the impact region.
* Corresponding author. Tel.: +886 5 6315395. E-mail address: [email protected] (T.-H. Fang). 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2009.08.100
The effect of the impact energy of the cluster and cluster size on the surface and mechanical properties of the metallic nanoparticle interface is still not fully known. In this paper, the impact and spreading behavior of copper cluster atoms bombarding copper substrates were investigated. The influences of the cluster size, temperature, and potential energy on the bombardments were investigated on a nanometer-scale. 2. Molecular simulation The simulated model consisted of an impacted cluster and a Cu substrate. The Cu (1 0 0) substrate consisted of 16000 atoms perpendicular to the z-axis. The substrate, a face-centered-cubic (FCC) crystal, had dimensions of 7.24 7.24 3.62 nm. The two lowest layers of the substrate were fixed to prevent the substrate from being moved by the incident atoms during impact. The two layers above the fixed layer were called thermal layers. The velocities of atoms in these layers were rescaled at every ten time steps according to the prescribed substrate temperature. The velocities of the thermal control layer atoms were constantly adjusted by the Boltzmann distribution [12] of the prescribed substrate temperature. Other layer atoms of the substrate were Newtonian atoms. The kinetic energy of incident cluster atoms may be affected during the cluster bombardment process. Periodic boundary conditions (PBC) [12] were imposed in the x and y directions; there was no periodic boundary condition along the z direction. The incident clusters were Cu atoms and their incident velocities were calculated by the incident energy. The x and y positions of the incident atoms were assigned and the height of the
T.-H. Fang et al. / Applied Surface Science 256 (2009) 1395–1398
1396
Table 1 parameters of TB-SMA potential function for copper. Parameters
Values
r0 (A˚) A (eV) z (eV) p q
2.566 0.0855 1.2440 10.960 2.2780
incident atoms was placed at the 15-fold lattice length above the substrate surface, i.e., the distance between the substrate and cluster was 15a (lattice constant a). The impacted clusters considered in this work were composed of 32, 108, and 256 atoms after thermal relaxation. The shape of the cluster was spherical. The substrate temperatures considered were 100, 300, 600, and 1000 K. The incident angle was fixed at 08, i.e., perpendicular to the substrate surface. In this study, the tight-binding second moment approximation (TB-SMA) many-body potential function UTB(rij) [13] was chosen to simulate the interaction force of copper. In the TB-SMA model, the cohesive band energy, which is described by the second moment of the d-band density of state, and the repulsive pairwise potential energy of the Born–Mayer term [13] are summed. For an atom i, the sum can be expressed as [13]: X ri j U TB ðr i j Þ ¼ Aexp p 1 r0 j 8 9 =1=2
where rij is the separation distance between atoms i and j, j is the effective hopping integral, N is the number of atoms, and r0 is the first-neighbor distance. The values of the parameters for Cu atoms are listed in Table 1. Parameters A, q, p, and j were fitted to the experimental values of various magnitudes. The Morse potential energy UMorse(rij) is described with three parameters as: U Morse ðr i j Þ ¼ Dðe2aðri j r0 Þ 2eaðri j r0 Þ Þ
(2)
where D is the cohesive energy, a is fitted to the bulk modulus, r0 is the equilibrium distance, and rij is the separation distance between atoms i and j. For Cu–Cu atoms, values of D, a, and r0 are 0.3429 eV, 0.13588 nm1, and 0.2626 nm, respectively [14]. The Gear fiveorder predict-correct algorithm was used to calculate the position, speed, and acceleration after interaction among the microsystem atoms. To save computational time, the method also combined cell link and Verlet list to deal with the interaction among all atoms. 3. Results and discussion Fig. 1(a–c) shows the behavior of copper clusters (red for cluster atoms) impacting the substrate surface at a temperature of 300 K. Before the bombarding the substrate, the cluster consisted of 108 copper atoms at 1000 fs, as seen in Fig. 1(a). The initial kinetic energy of the cluster was about 90 eV. Fig. 1(b) shows that the hopping atoms spread and transferred to the surface at 3000 fs. Some atoms of the solid sputtered out and formed a crater after the bombardment. These snapshots show a nearly round crater on the surface. This was due to the higher diffusivity and higher lattice energy of the {1 1 1} plane system [15]. The crater formation is an important plastic deformation of cluster bombardments and collisions on the solid surface. The region near the solid surface was compressed in the [1 0 0] direction and at the same time, the atoms around the crater were relaxed. The impact cluster atoms deformed and caused decrease in kinetic energy of the cluster
Fig. 1. Snapshots of a cluster impact on a Cu (1 0 0) substrate at different instants: (a)1000 fs; (b) 3000 fs; and (c) 6500 fs (red for cluster atoms). ‘‘For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.’’
atoms then the atoms would disperse around the crater of the substrate. The shape of the crater became stable after the dislocations of the solid diffusion and structural stress relaxation, as seen at 6500 fs in Fig. 1(c). Referring to Fig. 2, the simulation shows that the variation of kinetic energy of cluster bombardment can be divided into three stages. The first stage was at the initial impact level; the kinetic energy of the cluster and substrate were constant. In the second stage, called the sluggish change area of energy, the kinetic energy of the cluster decreased, but the kinetic energy of the substrate increased. In the final stage, the kinetic energy of the substrate became stable. Before impact, both the kinetic energy of the cluster and the solid substrate were in a steady state. At the moment of bombardment, the kinetic energy of the cluster decreased but that of the substrate increased. The lag of the energy removing phenomena occurred at the substrate between 1500 and 2500 fs time levels. Then, the kinetic energy of the cluster atoms decreased, and the atoms absorbed on the solid substrate. The
T.-H. Fang et al. / Applied Surface Science 256 (2009) 1395–1398
1397
Fig. 4. Spreading index of a cluster impacts on a substrate at different temperatures as a function of time.
Fig. 2. Kinetic energy of different sized clusters impact on a substrate as a function of time.
kinetic energy transformed into deformation energy and potential energy. The energy of the substrate decreased with slight energy fluctuation, which was due to the structural dislocation relaxation. It is well known that cluster bombardment is affected by the cluster size and impacted interaction energy. The crater deformation due to dislocation slip and mechanical stress is accelerated by rapid cluster impact. Therefore, the clusters with 32, 108, and 256 atoms were investigated at 300 K in the bombardment process, as shown in Fig. 2. The results show the fluctuation of the kinetic energy of the cluster with 256 atoms. This was due to a larger cluster having a higher total kinetic energy. When a larger cluster impacted the solid substrate, a bigger contact and spreading region as well as a larger deformation of the solid were produced. The substrate obtained a larger groove.
Fig. 3. Magnitude of slip vector of impacted substrate at a time step of 2500 fs. (a) 3-D view;(b) side view.
Fig. 3 shows the magnitude distribution of slip vector beneath the impacted substrate at a time step of 2500 fs. The slip vector [16], which can be seen as another kind of strain distribution, was evaluated using the atomic position difference from the initial position to the impacted position. A larger magnitude of slip vector indicates a large displacement. For the bombardment process in Fig. 3(a), it can be seen that the high slip vector distribution was completely concentrated on the Cu atoms around the impacted ¯ crater. Moreover, the marked directions [0 1 1], [1 0 1], and ½0 1 1 all belong to the h1 1 0i family and are verified in the close-packed direction. The symmetry-like cross-slip occurred beneath the top layer of the substrate along the h1 1 0i orientations. The high slip vector region around the crater had a disorder damage zone. For the slip vector region in Fig. 3(b), the highest slip vector was concentrated around the crater; the magnitude of slip vector decreased with distance away from the crater. This is attributed to the stress relaxation after the impact process. Fig. 4 shows the relationship between the substrate temperature and the spreading index under the impacted cluster with 108 atoms. The substrate temperatures were set to 100, 300, 600, and 1000 K. The spreading index was defined as the average diffused area of the cluster on the substrate region. The spreading index was used to estimate the affected area of the cluster movement on the substrate. Higher spreading occurred on the substrate at higher temperatures. The atoms on the substrate surface with a higher temperature possessed greater kinetic energy, resulting in the atoms having greater mobility and diffusivity. The average maximum impact depths of the substrate at temperatures of 100, 300, 600, and 1000 K were about 1.68, 1.73, 1.82, and 1.86 nm, respectively. When the substrate temperature increased, the impacted depth increased slightly. This result agrees with a previous study [17] using MD based on embedded atom potentials. They found that the degree of deposition for thin film growth increased with an increase of temperature and cluster size [17]. This sputtering process of atom deposition was also observed in the simulation in [18]. They found that a higher substrate temperature resulted in higher intermixing between the incident atoms and the substrate atoms [18]. To compare the effect of the potential function, the Morse pairwise potential and TB-SMA many-body potential functions were adopted to model the atomic interactions among the Cu atoms. Unlike many-body potential functions, the Morse potential only considers the interaction between two atoms without including the simultaneous influence of their neighbor atoms. Fig. 5 shows the kinetic energy variations of the cluster atoms at different time steps. The results show that the kinetic energy of the
1398
T.-H. Fang et al. / Applied Surface Science 256 (2009) 1395–1398
began to migrate on the substrate surface and at the same time, most of the cluster atoms were embedded into the substrate. All the cluster atoms reached equilibrium after 10 ps. The relatively circular cluster configurations on the substrate at 12 ps obtained using the tight-binding and Morse potential functions are shown in Fig. 6(a) and (b), respectively. The symmetry-like slip and crossslip occurred along the (1 1 1) plane in the peripheral region of the copper substrate. However, the collision behavior of the substrate had some differences. The advantage of TB-SMA potential is better for describing copper cluster. In the case of tight-binding manybody potential simulation, the results showed more obvious dislocations and slip behavior than those in the case of Morse potential. 4. Conclusions
Fig. 5. Kinetic energy of a cluster impacts on a substrate as a function of time using Morse and tight-binding (T-B) potential models.
This paper investigated the bombardment and impact phenomena of different size clusters on a substrate at various substrate temperatures. According to the analysis, the following results were obtained: (1) The kinetic energy of the substrate decreased with slight energy fluctuation because of the structural dislocation relaxation after collision. (2) A larger fluctuation of the kinetic energy with higher mechanical stress and dislocation slip occurred when bigger clusters impacted the substrate. (3) A higher spreading occurred on the substrate at higher temperatures until 600 K. (4) The symmetry-like slip behavior occurred along the {1 1 1} in the peripheral region of the copper substrate. (5) The collision behavior of the substrate exhibited some differences between different potential functions. In the tight-binding many-body potential simulation, the results showed more obvious dislocations and slip behavior than those in the Morse two-body potential. Acknowledgements This work was partially supported by the National Science Council of Taiwan, under Grant No. NSC 95-2221-E-150-033. References [1] [2] [3] [4] [5] [6] [7] [8]
Fig. 6. Atomic configurations of a cluster impacts on a substrate using (a)TB-SMA and (b)Morse potential functions (red for cluster atoms).‘‘For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.’’
[9] [10] [11] [12]
cluster, which was simulated by the tight-binding many-body potential, decreased earlier, for the kinetic energy curves decrease at roughly the same speed. This was due to the Morse potential being a short-ranged potential. Comparing the results of Morse potential and tight-binding many-body potential, a 1% error in kinetic energy variation was observed. When the cluster penetrated the topmost substrate surface, some of the cluster atoms
[13] [14] [15] [16] [17] [18]
Z.H. Hong, S.F. Hwang, T.H. Fang, Cryst. Growth Des. 8 (2008) 949. T.H. Fang, W.J. Chang, C.M. Lin, W.C. Lien, Appl. Surf. Sci. 254 (2008) 3436. S.R. Jian, T.H. Fang, D.S. Chuu, Physica B 334 (2003) 369. M. Hou, P. Moskovkin, Appl. Surf. Sci. 226 (2004) 161. K. Meinander, K. Nordlund, J. Keinonen, Nucl. Instrum. Meth. B 242 (2006) 161. Z.H. Hong, S.F. Hwang, T.H. Fang, J. Appl. Phys. 103 (2008) 124313. M. Ratner, W. Harbich, S. Fedrigo, Phys. Rev. B 60 (1999) 11730. K. Bromann, C. Fe´lix, H. Brune, W. Harbich, R. Monot, J. Buttet, K. Kern, Science 274 (1996) 956. J.C. Jime´nez-Sa´ez, A.M.C. Pe´rez-Martı´n, J.J. Jime´nez-Rodrı´guez, Nucl. Instrum. Meth. B 249 (2006) 816. L.K. Zang, Y.X. Wang, Z.Y. Pan, L. Zhou, T.J. Liu, J. Zhu, X.M. Jiang, Surf. Sci 600 (2006) 527. R. Lee, Z. Pan, Y. Ho, Phys. Rev. B 53 (1996) 4156–4161. J.M. Haile, Molecular Dynamics Simulation: Elementary Methods, Wiley, New York, 1992. F. Cleri, V. Rosato, Phys. Rev. B 48 (1993) 22. T.H. Fang, C.I. Weng, Nanotechnology 11 (2000) 148. J. Shen, P. Ohresser, Ch.V. Mohan, M. Klaua, J. Barthel, J. Kirschner, Phys. Rev. Lett. 80 (1998) 1980. O.R. de la Fuente, J.A. Zimmerman, M.A. Gonzalez, J. de la Figuera, J.C. Hamilton, W.W. Pai, J.M. Rojo, Phys. Rev. Lett. 88 (2002) 036101. H. Chen, I. Hagiwara, T. Huang, D. Zhang, Synth. Met. 155 (2005) 652. Z.H. Hong, S.F. Hwang, T.H. Fang, Comput. Mater. Sci. 41 (2007) 70.
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Impact and spreading behavior of cluster atoms bombarding substrates Te-Hua Fang *, Shao-Hui Kang, Jia-Hung Liao Institute of Mechanical and Electromechanical Engineering, National Formosa University, Yunlin 632, Taiwan
A R T I C L E I N F O
A B S T R A C T
Article history: Received 24 February 2009 Received in revised form 27 August 2009 Accepted 28 August 2009 Available online 4 September 2009
The purpose of this study is to investigate the behavior of copper cluster atoms bombarding a substrate using molecule dynamics based on tight-binding second moment approximation (TB-SMA) potential. The simulated results show that a crater on the substrate surface was created by the impact of the clusters. The variations of kinetic energy of cluster bombardments can be divided into three stages. At the initial impact level, the kinetic energies of the clusters and the substrate were constant. Then, the system went into a sluggish stage of energy variation, in which the kinetic energy of the clusters reduced. In the final stage, the kinetic energy of the system became stable. The high slip vector region around the crater had a disorder damage zone. The symmetry-like cross-slip occurred beneath the top layer of the substrate along the h1 1 0i orientations. The spreading index, temperature, and potential functions that affect the bombardments are also discussed. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Molecular dynamics Spreading Cluster Bombardment Craters
1. Introduction In recent years, cluster bombardment and sputtering technology have been increasingly used for various applications in thin films, surface science, and nanotechnology [1–3]. The interaction of cluster bombardment on surfaces has achieved to etch for surface modification applications [4,5]. Deposition field techniques, such as the ionic beam sputtering (IBS) method, plasmonic fields, and molecular beam epitaxy (MBE), have potential applications in creating nanostructures on solid surfaces [6]. The contact and optical properties of the nanostructures can be controlled by the impact energy of the cluster and cluster size. The mechanism of cluster bombardment is difficult to investigate with traditional experimental methodology, but it can be easily solved by using molecular dynamics (MD) simulation. Ratner et al. [7] studied the collision between Cu dimer and Ar film and found that the dense surroundings of the Ar film could confine the Cu dimers. Bromann et al. [8] showed that Ag clusters could be deposited nondestructively on Pt substrates by using Ar buffered layers. Jime´nez-Sa´ez et al. [9] studied structural changes in Cu clusters softly landing on Au substrates at various energies and temperatures. Zang et al. [10] found that collision dynamics were dominant in the early stages of single cluster deposition. Lee et al. [11] found that cluster atoms activated copper substrate atoms through collective collisions in the impact region.
* Corresponding author. Tel.: +886 5 6315395. E-mail address: [email protected] (T.-H. Fang). 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2009.08.100
The effect of the impact energy of the cluster and cluster size on the surface and mechanical properties of the metallic nanoparticle interface is still not fully known. In this paper, the impact and spreading behavior of copper cluster atoms bombarding copper substrates were investigated. The influences of the cluster size, temperature, and potential energy on the bombardments were investigated on a nanometer-scale. 2. Molecular simulation The simulated model consisted of an impacted cluster and a Cu substrate. The Cu (1 0 0) substrate consisted of 16000 atoms perpendicular to the z-axis. The substrate, a face-centered-cubic (FCC) crystal, had dimensions of 7.24 7.24 3.62 nm. The two lowest layers of the substrate were fixed to prevent the substrate from being moved by the incident atoms during impact. The two layers above the fixed layer were called thermal layers. The velocities of atoms in these layers were rescaled at every ten time steps according to the prescribed substrate temperature. The velocities of the thermal control layer atoms were constantly adjusted by the Boltzmann distribution [12] of the prescribed substrate temperature. Other layer atoms of the substrate were Newtonian atoms. The kinetic energy of incident cluster atoms may be affected during the cluster bombardment process. Periodic boundary conditions (PBC) [12] were imposed in the x and y directions; there was no periodic boundary condition along the z direction. The incident clusters were Cu atoms and their incident velocities were calculated by the incident energy. The x and y positions of the incident atoms were assigned and the height of the
T.-H. Fang et al. / Applied Surface Science 256 (2009) 1395–1398
1396
Table 1 parameters of TB-SMA potential function for copper. Parameters
Values
r0 (A˚) A (eV) z (eV) p q
2.566 0.0855 1.2440 10.960 2.2780
incident atoms was placed at the 15-fold lattice length above the substrate surface, i.e., the distance between the substrate and cluster was 15a (lattice constant a). The impacted clusters considered in this work were composed of 32, 108, and 256 atoms after thermal relaxation. The shape of the cluster was spherical. The substrate temperatures considered were 100, 300, 600, and 1000 K. The incident angle was fixed at 08, i.e., perpendicular to the substrate surface. In this study, the tight-binding second moment approximation (TB-SMA) many-body potential function UTB(rij) [13] was chosen to simulate the interaction force of copper. In the TB-SMA model, the cohesive band energy, which is described by the second moment of the d-band density of state, and the repulsive pairwise potential energy of the Born–Mayer term [13] are summed. For an atom i, the sum can be expressed as [13]: X ri j U TB ðr i j Þ ¼ Aexp p 1 r0 j 8 9 =1=2
where rij is the separation distance between atoms i and j, j is the effective hopping integral, N is the number of atoms, and r0 is the first-neighbor distance. The values of the parameters for Cu atoms are listed in Table 1. Parameters A, q, p, and j were fitted to the experimental values of various magnitudes. The Morse potential energy UMorse(rij) is described with three parameters as: U Morse ðr i j Þ ¼ Dðe2aðri j r0 Þ 2eaðri j r0 Þ Þ
(2)
where D is the cohesive energy, a is fitted to the bulk modulus, r0 is the equilibrium distance, and rij is the separation distance between atoms i and j. For Cu–Cu atoms, values of D, a, and r0 are 0.3429 eV, 0.13588 nm1, and 0.2626 nm, respectively [14]. The Gear fiveorder predict-correct algorithm was used to calculate the position, speed, and acceleration after interaction among the microsystem atoms. To save computational time, the method also combined cell link and Verlet list to deal with the interaction among all atoms. 3. Results and discussion Fig. 1(a–c) shows the behavior of copper clusters (red for cluster atoms) impacting the substrate surface at a temperature of 300 K. Before the bombarding the substrate, the cluster consisted of 108 copper atoms at 1000 fs, as seen in Fig. 1(a). The initial kinetic energy of the cluster was about 90 eV. Fig. 1(b) shows that the hopping atoms spread and transferred to the surface at 3000 fs. Some atoms of the solid sputtered out and formed a crater after the bombardment. These snapshots show a nearly round crater on the surface. This was due to the higher diffusivity and higher lattice energy of the {1 1 1} plane system [15]. The crater formation is an important plastic deformation of cluster bombardments and collisions on the solid surface. The region near the solid surface was compressed in the [1 0 0] direction and at the same time, the atoms around the crater were relaxed. The impact cluster atoms deformed and caused decrease in kinetic energy of the cluster
Fig. 1. Snapshots of a cluster impact on a Cu (1 0 0) substrate at different instants: (a)1000 fs; (b) 3000 fs; and (c) 6500 fs (red for cluster atoms). ‘‘For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.’’
atoms then the atoms would disperse around the crater of the substrate. The shape of the crater became stable after the dislocations of the solid diffusion and structural stress relaxation, as seen at 6500 fs in Fig. 1(c). Referring to Fig. 2, the simulation shows that the variation of kinetic energy of cluster bombardment can be divided into three stages. The first stage was at the initial impact level; the kinetic energy of the cluster and substrate were constant. In the second stage, called the sluggish change area of energy, the kinetic energy of the cluster decreased, but the kinetic energy of the substrate increased. In the final stage, the kinetic energy of the substrate became stable. Before impact, both the kinetic energy of the cluster and the solid substrate were in a steady state. At the moment of bombardment, the kinetic energy of the cluster decreased but that of the substrate increased. The lag of the energy removing phenomena occurred at the substrate between 1500 and 2500 fs time levels. Then, the kinetic energy of the cluster atoms decreased, and the atoms absorbed on the solid substrate. The
T.-H. Fang et al. / Applied Surface Science 256 (2009) 1395–1398
1397
Fig. 4. Spreading index of a cluster impacts on a substrate at different temperatures as a function of time.
Fig. 2. Kinetic energy of different sized clusters impact on a substrate as a function of time.
kinetic energy transformed into deformation energy and potential energy. The energy of the substrate decreased with slight energy fluctuation, which was due to the structural dislocation relaxation. It is well known that cluster bombardment is affected by the cluster size and impacted interaction energy. The crater deformation due to dislocation slip and mechanical stress is accelerated by rapid cluster impact. Therefore, the clusters with 32, 108, and 256 atoms were investigated at 300 K in the bombardment process, as shown in Fig. 2. The results show the fluctuation of the kinetic energy of the cluster with 256 atoms. This was due to a larger cluster having a higher total kinetic energy. When a larger cluster impacted the solid substrate, a bigger contact and spreading region as well as a larger deformation of the solid were produced. The substrate obtained a larger groove.
Fig. 3. Magnitude of slip vector of impacted substrate at a time step of 2500 fs. (a) 3-D view;(b) side view.
Fig. 3 shows the magnitude distribution of slip vector beneath the impacted substrate at a time step of 2500 fs. The slip vector [16], which can be seen as another kind of strain distribution, was evaluated using the atomic position difference from the initial position to the impacted position. A larger magnitude of slip vector indicates a large displacement. For the bombardment process in Fig. 3(a), it can be seen that the high slip vector distribution was completely concentrated on the Cu atoms around the impacted ¯ crater. Moreover, the marked directions [0 1 1], [1 0 1], and ½0 1 1 all belong to the h1 1 0i family and are verified in the close-packed direction. The symmetry-like cross-slip occurred beneath the top layer of the substrate along the h1 1 0i orientations. The high slip vector region around the crater had a disorder damage zone. For the slip vector region in Fig. 3(b), the highest slip vector was concentrated around the crater; the magnitude of slip vector decreased with distance away from the crater. This is attributed to the stress relaxation after the impact process. Fig. 4 shows the relationship between the substrate temperature and the spreading index under the impacted cluster with 108 atoms. The substrate temperatures were set to 100, 300, 600, and 1000 K. The spreading index was defined as the average diffused area of the cluster on the substrate region. The spreading index was used to estimate the affected area of the cluster movement on the substrate. Higher spreading occurred on the substrate at higher temperatures. The atoms on the substrate surface with a higher temperature possessed greater kinetic energy, resulting in the atoms having greater mobility and diffusivity. The average maximum impact depths of the substrate at temperatures of 100, 300, 600, and 1000 K were about 1.68, 1.73, 1.82, and 1.86 nm, respectively. When the substrate temperature increased, the impacted depth increased slightly. This result agrees with a previous study [17] using MD based on embedded atom potentials. They found that the degree of deposition for thin film growth increased with an increase of temperature and cluster size [17]. This sputtering process of atom deposition was also observed in the simulation in [18]. They found that a higher substrate temperature resulted in higher intermixing between the incident atoms and the substrate atoms [18]. To compare the effect of the potential function, the Morse pairwise potential and TB-SMA many-body potential functions were adopted to model the atomic interactions among the Cu atoms. Unlike many-body potential functions, the Morse potential only considers the interaction between two atoms without including the simultaneous influence of their neighbor atoms. Fig. 5 shows the kinetic energy variations of the cluster atoms at different time steps. The results show that the kinetic energy of the
1398
T.-H. Fang et al. / Applied Surface Science 256 (2009) 1395–1398
began to migrate on the substrate surface and at the same time, most of the cluster atoms were embedded into the substrate. All the cluster atoms reached equilibrium after 10 ps. The relatively circular cluster configurations on the substrate at 12 ps obtained using the tight-binding and Morse potential functions are shown in Fig. 6(a) and (b), respectively. The symmetry-like slip and crossslip occurred along the (1 1 1) plane in the peripheral region of the copper substrate. However, the collision behavior of the substrate had some differences. The advantage of TB-SMA potential is better for describing copper cluster. In the case of tight-binding manybody potential simulation, the results showed more obvious dislocations and slip behavior than those in the case of Morse potential. 4. Conclusions
Fig. 5. Kinetic energy of a cluster impacts on a substrate as a function of time using Morse and tight-binding (T-B) potential models.
This paper investigated the bombardment and impact phenomena of different size clusters on a substrate at various substrate temperatures. According to the analysis, the following results were obtained: (1) The kinetic energy of the substrate decreased with slight energy fluctuation because of the structural dislocation relaxation after collision. (2) A larger fluctuation of the kinetic energy with higher mechanical stress and dislocation slip occurred when bigger clusters impacted the substrate. (3) A higher spreading occurred on the substrate at higher temperatures until 600 K. (4) The symmetry-like slip behavior occurred along the {1 1 1} in the peripheral region of the copper substrate. (5) The collision behavior of the substrate exhibited some differences between different potential functions. In the tight-binding many-body potential simulation, the results showed more obvious dislocations and slip behavior than those in the Morse two-body potential. Acknowledgements This work was partially supported by the National Science Council of Taiwan, under Grant No. NSC 95-2221-E-150-033. References [1] [2] [3] [4] [5] [6] [7] [8]
Fig. 6. Atomic configurations of a cluster impacts on a substrate using (a)TB-SMA and (b)Morse potential functions (red for cluster atoms).‘‘For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.’’
[9] [10] [11] [12]
cluster, which was simulated by the tight-binding many-body potential, decreased earlier, for the kinetic energy curves decrease at roughly the same speed. This was due to the Morse potential being a short-ranged potential. Comparing the results of Morse potential and tight-binding many-body potential, a 1% error in kinetic energy variation was observed. When the cluster penetrated the topmost substrate surface, some of the cluster atoms
[13] [14] [15] [16] [17] [18]
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