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Decay mechanism of double-layer islands on close-packed surfaces: Silver on Ag(111) and copper on Cu(111)
Thin Solid Films 493 (2005) 146 – 151 www.elsevier.com/locate/tsf
Decay mechanism of double-layer islands on close-packed surfaces: Silver on Ag(111) and copper on Cu(111)B Xiu-Fang Gong a, Biao Hu a, Xi-Jing Ning a,*, Jun Zhuang b b
a Institute of Modern Physics, Fudan University, Shanghai 200433, China Department of Optic Science and Engineering, State Key Joint Laboratory for Materials Modification by Laser, Ion and Electron Beams, Fudan University, Shanghai 200433, China
Received 28 September 2004; received in revised form 17 May 2005; accepted 21 July 2005 Available online 16 August 2005
Abstract Molecular dynamics simulations are preformed to investigate the diffusion behaviors of double-layer islands on close-packed surfaces: Ag on Ag(111) and Cu on Cu(111), showing that the top layer moves mostly via concerted motions with its shape unchanged, and the top-layer atoms descend into the lower layer mainly by two-atom exchange only when they move to the verge of the lower layer. Especially, once a descent event takes place, other atoms of the top layer descend frequently at the same place in a short period. Compared to the Cu system, the dragging and the reattachment events take place much more frequently on the Ag surface and the Ag top layer shows a stronger tendency to form a compact configuration, e.g., a hexagon, by dragging one or two atoms from the lower layer, or even the Ag island can change from the initial double-layer into a three-layer structure due to upward diffusions. D 2005 Elsevier B.V. All rights reserved. PACS: 68.35.Fx; 02.70.Ns Keywords: Molecular dynamics; Surface diffusion; Silver; Copper
1. Introduction Preparation of high-performance materials relevant to quantum dots and thin films is the subject of intense current research because of their significant optical and electronic properties. Considering the practical use of such materials, we have to pay great attention to their thermal stabilities. Investigating coarsening and decay kinetics of vacancy or adatom islands is the starting point for these studies and experiments have revealed some interesting phenomena [1– 4]. Especially, a series of experimental observations and theoretical calculations indicate that the decay of a small island on top of a large one is accelerated by several orders of magnitude when it encounters the boundary of the larger i Project supported by F973_ projection of China, Contract No. 2001CB610506 and by the National Science Foundation of China, Grant Number: 10004002. * Corresponding author. E-mail address: [email protected] (X.-J. Ning).
0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.07.274
island [5 –7]. On nanometer scale, scanning microscopy can provide some information on the dynamics, but cannot identify directly single-atomic events. Diffusion barrier calculations for given atomic configurations are also helpful to understand the dynamics, but we do not know the probability of each atomic configuration emerging in realistic processes. Accordingly, real dynamic simulations are highly desirable for thoroughly understanding the island behavior. Since the so called ab initio calculations are severely limited by computing power, molecular dynamics (MD) simulation with empirical potentials is a approach to the issue. We have studied the evolution of a double-layer Cu island on Cu(111) surfaces by MD simulations [8], finding that the most probable event for atoms transport from the top layer to the lower one is two-atom exchange process taking place at the boundary of the lower island. In addition to the descending processes, upward diffusion events that atoms of the lower layer climb up to the upper layer were also observed in the simulations, which were closely
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relevant to recent investigations: an experimental study on nanocrystal formation in Al (110) homoepitaxy showed that an adatom could easily climb up at a monoatomic-layerhigh step [9], and the followed ab initio calculations of the relevant potential barriers indicated that the mechanism should be true for Al, Ag, Cu, and Pb systems [10]. In the present work, we perform MD simulations of a double-layer island evolution on fcc (111) surfaces for Cu and Ag systems, respectively, under the same simulation conditions, e.g., the initial configuration and the substrate temperature are set as the same for the two systems, which enables us to obtain the information on the differences in the two systems. In Section 2 we describe the simulation details and results, and discussions are presented in Section 3.
2. Simulation details and results The dynamical model for simulation has been elucidated in Ref. [8]. Briefly, a substrate consists of seven layers each with 10 10 atoms arranged in fcc (111) planes, on which periodic boundary conditions are imposed. The middle layer of the substrate is considered to be contacted with an imaginary thermal bath at a prescribed temperature T [8,11]. In order to obtain two simulation results at the same time, on top and bottom surfaces of the substrate we place, respectively, an island consisting of two atomic layers centered on top of each other. As shown in Fig. 1, the number of atoms in the lower and top layers is 36 and 6, respectively. A special empirical potential cited in Ref. [12] is employed to describe the interaction between atoms [12]. In our simulations, all Cu atoms and Ag atoms are initially placed in the sites of perfect crystal with a lattice constant of 0.3615 and 0.4085 nm, respectively, and the velocities of Cu and Ag atoms are assigned according to Maxwellian distribution at 600 K. Sixteen independent simulations each lasting for 4 ns are performed for Cu and Ag, respectively. The diffusion mechanism of the Cu/Ag islands on the corresponding fcc (111) surfaces at 600 K are found to be similar to the Cu islands on Cu(111) surfaces at 300 K. The shape of the lower-layer Cu/Ag island changes mainly by
Fig. 2. Snapshots of a two-atom exchange event and a jumping process on the Ag surface. (a) and (b) a top-layer atom marked with F5_ exchanging place with an atom (black ball) of the lower-layer island. (c) and (d) atom 6 jump into the lower-layer island over the step at kinks.
single atom hopping, or rotation of dimmer and trimmer at irregular peripheries [8,13]. When regular periphery forms, row shearing [8,14] occasionally takes place. The shape of the top-layer island changes more quickly and usually shows irregular peripheries. In addition to hopping, rotation and shearing mechanism at peripheries, internal row shearing can occur inside the island that is never observed for the lower layer motion [8,14]. The upper-layer island can drift by a long distance as a whole in the simulation period, which is in good agreement with the experiment observations [15 –17]. In our simulations for both the Cu and Ag systems, atom descending from the top layer into the lower one takes place when the top-layer island moves to edges of the lower-layer island. The most probable mechanism for this descent is a two-atom exchange process at straight steps, i.e., a top-layer atom pushes away a lower-layer atom and occupies its original site, shown in Fig. 2(a, b). For the Ag system, the exchange process occurs 65 and 116 times at A-type steps ({100}-faced) and B-type steps ({111}-faced), respectively,
Table 1 The numbers of two-atom exchange process, jumping process, dragging event and reattachment phenomenon
Fig. 1. Top view of the system. Two atomic layers centered on the surface of the substrate. White balls represent top-layer island atoms and black balls lower-layer island atoms.
Cu Ag
Two-atom exchange
Jumping process
Dragging event
Reattachment phenomenon
180 181
2 18
8 30
1 10
The temperature T = 600 K, and the total simulation time t tot = 4 ns.
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Fig. 3. Snapshots of a dragging event and the followed kinetics for the Ag system: an atom of the lower-layer island marked with F7_ (a) is ‘‘dragged’’ up by the top-layer island (b), (c).
while for the Cu system, the process takes place about 90 times at either A- or B-type steps. Jumping processes defined as top-layer atoms crossing the edge of the lowerlayer island take place mainly at kinks or concave corners, as shown in Fig. 2(c)Y(d), and occur at relatively low probabilities, compared with the two-atom exchange processes. The statistic results are given in Table 1. It is interesting that once a descent event occurs, the residual toplayer atoms where descent events have just occurred will descend in a short time, like a quasi-collective process. This observation is in accord with the experiment that when the top-layer island touches the step of the lower-layer island, the decay rate dramatically increases and the top-layer island frequently completely disappears. When a top-layer island lies near the center regions of the lower layer island, interlayer mass exchange is not observed in the simulations, which reflects the fact that island diffusion to the island edge is much more efficient than detachment of single atoms. We have simulated the evolution of a monolayer island and found that single atom can detach from the island, which implies that decaying of the top-layer island is also possible even if it lies in the center region of the lower island. The upward diffusion is observed for both the Cu and Ag islands. During the top-layer island wandering, one of the lower-layer atoms near the boundary may ascend onto the top-layer island, and adheres to the top-layer island (dragging event). Fig. 3(a)Y(b) shows this process, which
is similar to an inverse process of the two-atom exchange described above. It is worth noting that the dragging event occurs merely at sites where an isolated atom attaches to a smooth boundary [see Fig. 3(a)]. Reattachment phenomenon [8], as shown in Fig. 4, is also observed in the simulations. Obviously, the dragging and the reattachment events take place much more frequently on the Ag surface than on the Cu surface (seeing Table 1), making compact hexagonal clusters form easily on Ag(111) surface, as shown in Fig. 5. Different from the Cu island, the top-layer island on Ag(111) surface occasionally forms a three-dimensional (3D) cluster, such as a pyramid, due to upward diffusions. As an example, Fig. 6 illustrates one upward diffusion process, which causes the atom numbered as 2 is pushed out of the top layer and the atom 6 occupies the original site of the atom 2. This simple exchange process on Ag top layer, however, is different from the dragging event. The newly formed 3D cluster can rotate and glide on the surface. From Fig. 6(c) to (e), it rotates about 90- and eventually gets into a two-dimensional structure (Fig. 6). The whole process lasts for hundreds of picoseconds, during which the top-layer island glides by a distance of about 0.3 nm. At the end of our simulations, most of the top-layer atoms on the Cu (111) and Ag(111) surfaces have diffused completely into the lower-layer island and they locate together in one or two regions near the boundaries of the
Fig. 4. Snapshots of a reattachment process for Ag system: atom 4 descending into the lower-layer island (a) and after 10 ps ascending onto the top-layer island again (b), (c).
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Fig. 5. Compact hexagonal clusters formed on the Ag(111) surface by dragging one atom numbered as F7_ (a), or two atoms denoted as F8_ – F11_ in (b), (c), sampled from three independent simulations.
lower layer. The total numbers of atoms left on the lower island are 19 and 33 for the Cu and Ag systems, respectively. Fig. 7 shows the resultant surface structures of four independent dynamical processes, which indicates that descent of the top-layer islands is a quasi-collective process.
Fig. 6. Formation of an Ag5 cluster on Ag(111) surfaces [(a),(b),(c)] and its diffusion behavior [(c), (d), (e), (f)].
3. Discussion In our simulations, the substrate is prescribed at about 600 K, well above room temperature at which relevant experimental observations are performed [5 –7]. Comparing the results of the present simulations of the Cu system with those obtained in our previous simulations at 300 K in which the two-atom exchange, dragging and reattachment events take place 160, 4 and 2 times, respectively [8], we find no essential difference in the ratio of occurrence frequencies for various events. As stated above, the two-atom exchange process at straight steps is found to be the most probable mechanism for interlayer transport of Ag on Ag (111) and Cu on Cu (111) surfaces at 600 K. To understand the kinetic processes shown in our simulations, we computed the energy barriers for various processes with the special empirical potential by a damped trajectory method explicated in our previous work [8,18,19]. We chose and change a certain freedom according to the diffusion path, then at each fixed increment of this freedom fully relax all the other freedoms of the active atoms. For step descents by two-atom exchange process we consider different types of step edges shown in Fig. 8(a)Y(f) and the corresponding energy barriers have been summarized in Table 2. The descending barriers of atom 1 in Fig. 8(d) for the Cu system (0.74 eV) and atom 1 in Fig. 8(c) for the Ag system (0.63 eV) are in good agreement with the experimental energy barriers, 0.69 T 0.04 eV for Cu and 0.615 T 0.05 eV for Ag, respectively [20]. The energy barriers of 0.74 eV (Cu), 0.57 eV (Cu), 0.53 eV (Ag) and 0.75 eV (Ag) are consistent with 0.78 eV (Cu), 0.55 eV (Cu), 0.55 eV (Ag), and 0.74 eV (Ag), obtained by using effective medium theory, respectively (see Table 2) [21]. These enhance the conclusion that the two-atom exchange process is the most probable. For convenience, we call the two-atom exchange processes at straight steps shown in Fig. 8(e, f) and Fig. 8(c, d) as type 1 and type 2, respectively. In either of the two systems, the type 1 takes place about 110 times, while the type 2 occurs only 70 times. Obviously, the probability for the type 1 is significantly higher than that for the type 2. However, we cannot get such information from the energy
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Fig. 7. (a), (b) Shows the resultant surface structure on Ag(111) of two independent simulations after about 4 ns. (c), (d) are the resultant surface structure on Cu(111) of two independent simulations.
barriers (see Table 2). This indicates that besides the energy barriers the local atomic configurations also play an important role for the descent events. In addition, we find that the exchange process hardly occurs on the surface configurations shown in Fig. 8(a) and (b) in our MD simulations. This phenomenon can be easily understood because the corresponding energy barriers are much higher than others. In previous studies, the Arrhenius law was usually used to estimate the diffusion rate of adatoms and the decay rates of double-layer islands if the pre-exponential factor and the corresponding energy barriers were well known [5– 7]. However, the estimation without considering the specific atomic configurations on the surfaces may be rough for complicate processes. The energy barrier of the dragging event at a smooth periphery with an atom attached nearby [Fig. 3(a)] is 0.48/ 0.54 eV on the Cu (111)/Ag (111) surface. If the attached
atom is removed, the energy barrier of the dragging event increases to 0.9/0.93 eV. For the jumping process, the energy barriers of the Cu and Ag system are 1.09 and 0.98 eV, respectively, which turn into 0.61/0.74 eV in the presence of a kink [Fig. 8(g)]. These are in agreement with our MD simulations that the dragging event occurs merely at sites where an isolated atom attaches to a smooth boundary and the jumping process takes place mainly at kinks. It is worth noting that the energy barriers of the dragging events are smaller than those for the two-atom exchange processes at straight steps, which is in agreement with the results obtained from the first-principles calculations with density functional theory [10]. But our MD simulations show the probability for the exchange process is much higher than that for the dragging event. This can be understood in consideration of the fact that the dragging
Fig. 8. Various step edges for atom descents. Atom 1 or 2 is the atom we controlled.
X.-F. Gong et al. / Thin Solid Films 493 (2005) 146 – 151 Table 2 Adatom descending barriers, by two-atom exchange, corresponding to step edges illustrated in Fig. 8(a) – (f) (in eV) Figure
(a)
(a)
(b)
(b)
(c)
(d)
(e)
(f)
Descent atom
1
2
1
2
1
1
1
1
Cu Ag
0.89 0.93
0.64 0.75
1.09 1.14
0.84 0.81
0.48 0.63
0.74 0.75
0.57 0.64
0.45 0.53
events need a specific surface configuration, i.e., an atom attached to a smooth boundary [Fig. 3(a)], which forms infrequently in the dynamical processes. The energy barrier of the dragging event in the Ag system is higher than that in the Cu system, but the frequency of the dragging event is very high in the Ag system (see Table 1). A similar phenomenon appears in the exchange process: although the exchange barrier in the Ag system is significantly higher than that in the Cu system, the exchange frequency is nearly the same in the two systems. So it is very questionable to explain the decay mechanism only by comparing the energy barrier for the systems involved in many diffusion mechanisms. This gives us a hint that MD simulations are highly desired for understanding the dynamics of surface islands. In summary, the diffusion behaviors of double-layer islands on close-packed surfaces: Ag on Ag(111) and Cu on Cu(111) have been studied by molecular dynamics with a special empirical potential. Although the jumping process occurs, atoms of the top-layer islands in the two systems mostly descend by two-atom exchange processes at the straight steps and the descending process shows a quasicollective nature. In addition to descents, upward diffusion events (dragging event) take place in our simulations. Although the energy barriers of the dragging events are smaller than those for the two-atom exchange processes, the probability for the dragging event is much less than that for the exchange process, which result from that the dragging events need a specific surface configuration. The dragging and the reattachment events take place much more frequently on the Ag surfaces, which make the top layer easily form a compact island or a 3D cluster. Clearly, vast
151
MD simulations are indispensable for understanding the dynamics evolution of islands on solid surfaces.
Acknowledgments This research was supported by the 973 projection of China, contract 2001CB610506.
References [1] M.J. Rost, S.B. van Albada, J.W.M. Frenken, Phys. Rev. Lett. 86 (2001) 5938. [2] M.J. Rost, R. van Gastel, J.W.M. Frenken, Phys. Rev. Lett. 84 (2000) 1966. [3] J.B. Hannon, C. Klu¨nker, M. Gisen, H. Ibach, Phys. Rev. Lett. 79 (1997) 2506. [4] S. Kodambaka, V. Petrova, S.V. Khare, D. Gall, A. Rockett, I. Petrov, J.E. Greene, Phys. Rev. Lett. 89 (2002) 176102. [5] M. Giesen, G.S. Icking-Konert, H. Ibach, Phys. Rev. Lett. 80 (1998) 552. [6] G.S. Icking-Konert, M. Giesen, H. Ibach, Surf. Sci. 398 (1998) 37. [7] K. Morgenstern, G. Rosenfeld, G. Comsa, E. Lægsgaard, F. Besenbacher, Phys. Rev. Lett. 85 (2000) 468. [8] X.F. Gong, L. Wang, X.J. Ning, J. Zhuang, Surf. Sci. 553 (2004) 181. [9] F.B. de Mongeot, W.G. Zhu, A. Molle, R. Buzio, C. Boragno, U. Valbusa, E.G. Wang, Phys. Rev. Lett. 91 (2003) 016102-1. [10] W.G. Zhu, F.B. de Mongeot, U. Valbusa, E.G. Wang, Z.Y. Zhang, Phys. Rev. Lett. 92 (2004) 106102-1. [11] M.E. Riley, M.E. Coltrin, J. Chem. Phys. 88 (1988) 5934. [12] F. Cleri, V. Rosato, Phys. Rev., B 48 (1993) 22. [13] V. Chirita, E.P. Mu¨nger, J.E. Greene, J.E. Sundgren, Thin Solid Films 370 (2000) 179. [14] O.S. Trushin, P. Salo, M. Alatalo, T. Ala-Nissila, Surf. Sci. 482-485 (2001) 365. [15] S.C. Wang, G. Ehrlich, Phys. Rev. Lett. 79 (1997) 4234. [16] S.C. Wang, U. Ku¨rpick, G. Ehrlich, Phys. Rev. Lett. 81 (1998) 4923. [17] U. Ku¨rpick, B. Fricke, G. Ehrlich, Surf. Sci. 470 (2000) L45. [18] Q. Zhang, V. Buch, J. Chem. Phys. 92 (1990) 5004. [19] L.M. Raff, J. Chem. Phys. 95 (1991) 8901. [20] M. Giesen, H. Ibach, Surf. Sci. 464 (2000) L697. [21] K. Morgenstern, G. Rosenfeld, G. Comsa, M.R. Sørensen, B. Hammer, E. Lægsgaard, F. Besenbacher, Phys. Rev., B 63 (2001) 045412.
Decay mechanism of double-layer islands on close-packed surfaces: Silver on Ag(111) and copper on Cu(111)B Xiu-Fang Gong a, Biao Hu a, Xi-Jing Ning a,*, Jun Zhuang b b
a Institute of Modern Physics, Fudan University, Shanghai 200433, China Department of Optic Science and Engineering, State Key Joint Laboratory for Materials Modification by Laser, Ion and Electron Beams, Fudan University, Shanghai 200433, China
Received 28 September 2004; received in revised form 17 May 2005; accepted 21 July 2005 Available online 16 August 2005
Abstract Molecular dynamics simulations are preformed to investigate the diffusion behaviors of double-layer islands on close-packed surfaces: Ag on Ag(111) and Cu on Cu(111), showing that the top layer moves mostly via concerted motions with its shape unchanged, and the top-layer atoms descend into the lower layer mainly by two-atom exchange only when they move to the verge of the lower layer. Especially, once a descent event takes place, other atoms of the top layer descend frequently at the same place in a short period. Compared to the Cu system, the dragging and the reattachment events take place much more frequently on the Ag surface and the Ag top layer shows a stronger tendency to form a compact configuration, e.g., a hexagon, by dragging one or two atoms from the lower layer, or even the Ag island can change from the initial double-layer into a three-layer structure due to upward diffusions. D 2005 Elsevier B.V. All rights reserved. PACS: 68.35.Fx; 02.70.Ns Keywords: Molecular dynamics; Surface diffusion; Silver; Copper
1. Introduction Preparation of high-performance materials relevant to quantum dots and thin films is the subject of intense current research because of their significant optical and electronic properties. Considering the practical use of such materials, we have to pay great attention to their thermal stabilities. Investigating coarsening and decay kinetics of vacancy or adatom islands is the starting point for these studies and experiments have revealed some interesting phenomena [1– 4]. Especially, a series of experimental observations and theoretical calculations indicate that the decay of a small island on top of a large one is accelerated by several orders of magnitude when it encounters the boundary of the larger i Project supported by F973_ projection of China, Contract No. 2001CB610506 and by the National Science Foundation of China, Grant Number: 10004002. * Corresponding author. E-mail address: [email protected] (X.-J. Ning).
0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.07.274
island [5 –7]. On nanometer scale, scanning microscopy can provide some information on the dynamics, but cannot identify directly single-atomic events. Diffusion barrier calculations for given atomic configurations are also helpful to understand the dynamics, but we do not know the probability of each atomic configuration emerging in realistic processes. Accordingly, real dynamic simulations are highly desirable for thoroughly understanding the island behavior. Since the so called ab initio calculations are severely limited by computing power, molecular dynamics (MD) simulation with empirical potentials is a approach to the issue. We have studied the evolution of a double-layer Cu island on Cu(111) surfaces by MD simulations [8], finding that the most probable event for atoms transport from the top layer to the lower one is two-atom exchange process taking place at the boundary of the lower island. In addition to the descending processes, upward diffusion events that atoms of the lower layer climb up to the upper layer were also observed in the simulations, which were closely
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relevant to recent investigations: an experimental study on nanocrystal formation in Al (110) homoepitaxy showed that an adatom could easily climb up at a monoatomic-layerhigh step [9], and the followed ab initio calculations of the relevant potential barriers indicated that the mechanism should be true for Al, Ag, Cu, and Pb systems [10]. In the present work, we perform MD simulations of a double-layer island evolution on fcc (111) surfaces for Cu and Ag systems, respectively, under the same simulation conditions, e.g., the initial configuration and the substrate temperature are set as the same for the two systems, which enables us to obtain the information on the differences in the two systems. In Section 2 we describe the simulation details and results, and discussions are presented in Section 3.
2. Simulation details and results The dynamical model for simulation has been elucidated in Ref. [8]. Briefly, a substrate consists of seven layers each with 10 10 atoms arranged in fcc (111) planes, on which periodic boundary conditions are imposed. The middle layer of the substrate is considered to be contacted with an imaginary thermal bath at a prescribed temperature T [8,11]. In order to obtain two simulation results at the same time, on top and bottom surfaces of the substrate we place, respectively, an island consisting of two atomic layers centered on top of each other. As shown in Fig. 1, the number of atoms in the lower and top layers is 36 and 6, respectively. A special empirical potential cited in Ref. [12] is employed to describe the interaction between atoms [12]. In our simulations, all Cu atoms and Ag atoms are initially placed in the sites of perfect crystal with a lattice constant of 0.3615 and 0.4085 nm, respectively, and the velocities of Cu and Ag atoms are assigned according to Maxwellian distribution at 600 K. Sixteen independent simulations each lasting for 4 ns are performed for Cu and Ag, respectively. The diffusion mechanism of the Cu/Ag islands on the corresponding fcc (111) surfaces at 600 K are found to be similar to the Cu islands on Cu(111) surfaces at 300 K. The shape of the lower-layer Cu/Ag island changes mainly by
Fig. 2. Snapshots of a two-atom exchange event and a jumping process on the Ag surface. (a) and (b) a top-layer atom marked with F5_ exchanging place with an atom (black ball) of the lower-layer island. (c) and (d) atom 6 jump into the lower-layer island over the step at kinks.
single atom hopping, or rotation of dimmer and trimmer at irregular peripheries [8,13]. When regular periphery forms, row shearing [8,14] occasionally takes place. The shape of the top-layer island changes more quickly and usually shows irregular peripheries. In addition to hopping, rotation and shearing mechanism at peripheries, internal row shearing can occur inside the island that is never observed for the lower layer motion [8,14]. The upper-layer island can drift by a long distance as a whole in the simulation period, which is in good agreement with the experiment observations [15 –17]. In our simulations for both the Cu and Ag systems, atom descending from the top layer into the lower one takes place when the top-layer island moves to edges of the lower-layer island. The most probable mechanism for this descent is a two-atom exchange process at straight steps, i.e., a top-layer atom pushes away a lower-layer atom and occupies its original site, shown in Fig. 2(a, b). For the Ag system, the exchange process occurs 65 and 116 times at A-type steps ({100}-faced) and B-type steps ({111}-faced), respectively,
Table 1 The numbers of two-atom exchange process, jumping process, dragging event and reattachment phenomenon
Fig. 1. Top view of the system. Two atomic layers centered on the surface of the substrate. White balls represent top-layer island atoms and black balls lower-layer island atoms.
Cu Ag
Two-atom exchange
Jumping process
Dragging event
Reattachment phenomenon
180 181
2 18
8 30
1 10
The temperature T = 600 K, and the total simulation time t tot = 4 ns.
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Fig. 3. Snapshots of a dragging event and the followed kinetics for the Ag system: an atom of the lower-layer island marked with F7_ (a) is ‘‘dragged’’ up by the top-layer island (b), (c).
while for the Cu system, the process takes place about 90 times at either A- or B-type steps. Jumping processes defined as top-layer atoms crossing the edge of the lowerlayer island take place mainly at kinks or concave corners, as shown in Fig. 2(c)Y(d), and occur at relatively low probabilities, compared with the two-atom exchange processes. The statistic results are given in Table 1. It is interesting that once a descent event occurs, the residual toplayer atoms where descent events have just occurred will descend in a short time, like a quasi-collective process. This observation is in accord with the experiment that when the top-layer island touches the step of the lower-layer island, the decay rate dramatically increases and the top-layer island frequently completely disappears. When a top-layer island lies near the center regions of the lower layer island, interlayer mass exchange is not observed in the simulations, which reflects the fact that island diffusion to the island edge is much more efficient than detachment of single atoms. We have simulated the evolution of a monolayer island and found that single atom can detach from the island, which implies that decaying of the top-layer island is also possible even if it lies in the center region of the lower island. The upward diffusion is observed for both the Cu and Ag islands. During the top-layer island wandering, one of the lower-layer atoms near the boundary may ascend onto the top-layer island, and adheres to the top-layer island (dragging event). Fig. 3(a)Y(b) shows this process, which
is similar to an inverse process of the two-atom exchange described above. It is worth noting that the dragging event occurs merely at sites where an isolated atom attaches to a smooth boundary [see Fig. 3(a)]. Reattachment phenomenon [8], as shown in Fig. 4, is also observed in the simulations. Obviously, the dragging and the reattachment events take place much more frequently on the Ag surface than on the Cu surface (seeing Table 1), making compact hexagonal clusters form easily on Ag(111) surface, as shown in Fig. 5. Different from the Cu island, the top-layer island on Ag(111) surface occasionally forms a three-dimensional (3D) cluster, such as a pyramid, due to upward diffusions. As an example, Fig. 6 illustrates one upward diffusion process, which causes the atom numbered as 2 is pushed out of the top layer and the atom 6 occupies the original site of the atom 2. This simple exchange process on Ag top layer, however, is different from the dragging event. The newly formed 3D cluster can rotate and glide on the surface. From Fig. 6(c) to (e), it rotates about 90- and eventually gets into a two-dimensional structure (Fig. 6). The whole process lasts for hundreds of picoseconds, during which the top-layer island glides by a distance of about 0.3 nm. At the end of our simulations, most of the top-layer atoms on the Cu (111) and Ag(111) surfaces have diffused completely into the lower-layer island and they locate together in one or two regions near the boundaries of the
Fig. 4. Snapshots of a reattachment process for Ag system: atom 4 descending into the lower-layer island (a) and after 10 ps ascending onto the top-layer island again (b), (c).
X.-F. Gong et al. / Thin Solid Films 493 (2005) 146 – 151
149
Fig. 5. Compact hexagonal clusters formed on the Ag(111) surface by dragging one atom numbered as F7_ (a), or two atoms denoted as F8_ – F11_ in (b), (c), sampled from three independent simulations.
lower layer. The total numbers of atoms left on the lower island are 19 and 33 for the Cu and Ag systems, respectively. Fig. 7 shows the resultant surface structures of four independent dynamical processes, which indicates that descent of the top-layer islands is a quasi-collective process.
Fig. 6. Formation of an Ag5 cluster on Ag(111) surfaces [(a),(b),(c)] and its diffusion behavior [(c), (d), (e), (f)].
3. Discussion In our simulations, the substrate is prescribed at about 600 K, well above room temperature at which relevant experimental observations are performed [5 –7]. Comparing the results of the present simulations of the Cu system with those obtained in our previous simulations at 300 K in which the two-atom exchange, dragging and reattachment events take place 160, 4 and 2 times, respectively [8], we find no essential difference in the ratio of occurrence frequencies for various events. As stated above, the two-atom exchange process at straight steps is found to be the most probable mechanism for interlayer transport of Ag on Ag (111) and Cu on Cu (111) surfaces at 600 K. To understand the kinetic processes shown in our simulations, we computed the energy barriers for various processes with the special empirical potential by a damped trajectory method explicated in our previous work [8,18,19]. We chose and change a certain freedom according to the diffusion path, then at each fixed increment of this freedom fully relax all the other freedoms of the active atoms. For step descents by two-atom exchange process we consider different types of step edges shown in Fig. 8(a)Y(f) and the corresponding energy barriers have been summarized in Table 2. The descending barriers of atom 1 in Fig. 8(d) for the Cu system (0.74 eV) and atom 1 in Fig. 8(c) for the Ag system (0.63 eV) are in good agreement with the experimental energy barriers, 0.69 T 0.04 eV for Cu and 0.615 T 0.05 eV for Ag, respectively [20]. The energy barriers of 0.74 eV (Cu), 0.57 eV (Cu), 0.53 eV (Ag) and 0.75 eV (Ag) are consistent with 0.78 eV (Cu), 0.55 eV (Cu), 0.55 eV (Ag), and 0.74 eV (Ag), obtained by using effective medium theory, respectively (see Table 2) [21]. These enhance the conclusion that the two-atom exchange process is the most probable. For convenience, we call the two-atom exchange processes at straight steps shown in Fig. 8(e, f) and Fig. 8(c, d) as type 1 and type 2, respectively. In either of the two systems, the type 1 takes place about 110 times, while the type 2 occurs only 70 times. Obviously, the probability for the type 1 is significantly higher than that for the type 2. However, we cannot get such information from the energy
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Fig. 7. (a), (b) Shows the resultant surface structure on Ag(111) of two independent simulations after about 4 ns. (c), (d) are the resultant surface structure on Cu(111) of two independent simulations.
barriers (see Table 2). This indicates that besides the energy barriers the local atomic configurations also play an important role for the descent events. In addition, we find that the exchange process hardly occurs on the surface configurations shown in Fig. 8(a) and (b) in our MD simulations. This phenomenon can be easily understood because the corresponding energy barriers are much higher than others. In previous studies, the Arrhenius law was usually used to estimate the diffusion rate of adatoms and the decay rates of double-layer islands if the pre-exponential factor and the corresponding energy barriers were well known [5– 7]. However, the estimation without considering the specific atomic configurations on the surfaces may be rough for complicate processes. The energy barrier of the dragging event at a smooth periphery with an atom attached nearby [Fig. 3(a)] is 0.48/ 0.54 eV on the Cu (111)/Ag (111) surface. If the attached
atom is removed, the energy barrier of the dragging event increases to 0.9/0.93 eV. For the jumping process, the energy barriers of the Cu and Ag system are 1.09 and 0.98 eV, respectively, which turn into 0.61/0.74 eV in the presence of a kink [Fig. 8(g)]. These are in agreement with our MD simulations that the dragging event occurs merely at sites where an isolated atom attaches to a smooth boundary and the jumping process takes place mainly at kinks. It is worth noting that the energy barriers of the dragging events are smaller than those for the two-atom exchange processes at straight steps, which is in agreement with the results obtained from the first-principles calculations with density functional theory [10]. But our MD simulations show the probability for the exchange process is much higher than that for the dragging event. This can be understood in consideration of the fact that the dragging
Fig. 8. Various step edges for atom descents. Atom 1 or 2 is the atom we controlled.
X.-F. Gong et al. / Thin Solid Films 493 (2005) 146 – 151 Table 2 Adatom descending barriers, by two-atom exchange, corresponding to step edges illustrated in Fig. 8(a) – (f) (in eV) Figure
(a)
(a)
(b)
(b)
(c)
(d)
(e)
(f)
Descent atom
1
2
1
2
1
1
1
1
Cu Ag
0.89 0.93
0.64 0.75
1.09 1.14
0.84 0.81
0.48 0.63
0.74 0.75
0.57 0.64
0.45 0.53
events need a specific surface configuration, i.e., an atom attached to a smooth boundary [Fig. 3(a)], which forms infrequently in the dynamical processes. The energy barrier of the dragging event in the Ag system is higher than that in the Cu system, but the frequency of the dragging event is very high in the Ag system (see Table 1). A similar phenomenon appears in the exchange process: although the exchange barrier in the Ag system is significantly higher than that in the Cu system, the exchange frequency is nearly the same in the two systems. So it is very questionable to explain the decay mechanism only by comparing the energy barrier for the systems involved in many diffusion mechanisms. This gives us a hint that MD simulations are highly desired for understanding the dynamics of surface islands. In summary, the diffusion behaviors of double-layer islands on close-packed surfaces: Ag on Ag(111) and Cu on Cu(111) have been studied by molecular dynamics with a special empirical potential. Although the jumping process occurs, atoms of the top-layer islands in the two systems mostly descend by two-atom exchange processes at the straight steps and the descending process shows a quasicollective nature. In addition to descents, upward diffusion events (dragging event) take place in our simulations. Although the energy barriers of the dragging events are smaller than those for the two-atom exchange processes, the probability for the dragging event is much less than that for the exchange process, which result from that the dragging events need a specific surface configuration. The dragging and the reattachment events take place much more frequently on the Ag surfaces, which make the top layer easily form a compact island or a 3D cluster. Clearly, vast
151
MD simulations are indispensable for understanding the dynamics evolution of islands on solid surfaces.
Acknowledgments This research was supported by the 973 projection of China, contract 2001CB610506.
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