Study on the early stage of thin filmgrowth in pulsed beamdeposition by kinetic Monte Carlo simulation

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1 Surface and Coatings Technology (2002) Study on the early stage of thin filmgrowth in pulsed beamdeposition by kinetic Monte Carlo simulation a, b Q.Y. Zhang *, P.K. Chu a State Key Laboratory for Materials Modification by Laser, Ion and Electron Beams, Dalian University of Technology, Dalian , PR China b Department of Physics and Materials Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, PR China Abstract In this study a pulse beam (PB) deposition model based on a square lattice is proposed and is used to simulate the process of thin filmgrowth with the kinetic Monte Carlo method. The influence of frequency and duration of pulse on the nucleation, aggregation, and morphology of thin film growth in the early stage is investigated and discussed. The simulation results show that the morphology, island-size distribution, and dynamics behavior of island growth in PB deposition are different from that in DC deposition when their average deposition rates are same. With the increase of transient deposition rate during the pulse activation, the island-size distribution and morphology lose the characteristics of the is1 model. Due to the high transient deposition rate during the pulse activation, PB deposition promotes nucleation and suppresses the growth of islands and increases the island density. The atomistic mechanism of thin film growth in pulse beam deposition is also discussed Elsevier Science B.V. All rights reserved. Keywords: Pulse beamdeposition; Kinetic Monte Carlo simulation; Thin filmgrowth 1. Introduction The growth of thin films on solid substrates has widespread applications including microelectronics, optoelectronic devices, corrosion protection, hard coatings, decoration, etc. Thin filmgrowth techniques have become very important in the development of new materials and devices. Over the years, many thin film growth techniques based on pulsed beam (PB) deposition, such as pulsed laser deposition (PLD), pulsed magnetron sputtering deposition, and plasma source ion implantation deposition, have been designed w1 5x. Pulsed beamdeposition is characterized by a non-steadystate temporal profile and a broad incident particle (atom or ion) energy distribution with a mean of a few electron volts, which is much higher than that in molecular beam epitaxy (MBE). *Corresponding author. Department of Physics, Dalian University of Technology, Dalian , PR China. Tel.: q ; fax: q address: qyzhang@dlut.edu.cn (Q.Y. Zhang). Understanding the physics of thin filmgrowth in various synthesis processes is very important both theoretically and technologically. In the early stage of thin filmgrowth, the fundamental physical processes, such as nucleation, aggregation and coalescence of islands on a two-dimensional substrate, is influenced by the factors of the growth temperature, surface energy, incident energy, and deposition rate, etc. w6 8x. In this study a pulse beamdeposition model based on a square lattice has been proposed and used to simulate the process of thin filmgrowth with kinetic Monte Carlo (MC) method. The influence of frequency and duration of pulse on the nucleation, aggregation, and morphology of thin film growth in early stage is investigated and discussed. The scaling function of island-size distribution, the dynamics behavior of island growth, and morphology of islands are presented. The role of adatomdiffusion in the pulse beamdeposition has been discussed. The simulation results are compared with that obtained with steady beam deposition. The atomistic mechanisms of thin film growth in pulse beamdeposition are also discussed in the paper /02/$ - see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S Ž

2 248 Q.Y. Zhang, P.K. Chu / Surface and Coatings Technology (2002) Fig. 1. Diagramof stable island configurations for different critical island sizes. 2. Physical modeling and simulation methods 2.1. Physical model In the studies of filmgrowth a fundamental concept named as critical island size i has been suggested, which corresponds to one less than the number of atoms in the smallest stable island w9x. The critical island size depends on the bond energies, growth temperature, and deposition rate. Fig. 1 is the diagramof the stable island configuration for different critical island sizes. In the case of is1, monomers diffuse but dimers and the adatoms with one nearest neighbors are stable. For is 2, trimers and adatoms with more than two nearest neighbors are stable and other adatoms diffuse. For is 3, tetramers are the smallest islands. In this study the critical island size is is1. To compare with the steadystate deposition or direct current (DC) deposition, such as in MBE, the kinetic energy of incident atoms is neglected. In our simulation, the pulse frequency ( f ) and the pulse duration (T p) are controlled independently, but the average deposition rates are kept at 1 monolayer per second for all the cases Simulation of diffusion process The adatomdiffusion on substrate is simulated using the kinetic MC method proposed by Voter w10x. Kinetic MC simulation is a powerful method to simulate the diffusion process and has been widespread applied in the studies of filmgrowth w11 15x. In the simulation, the substrate is a square lattice of typical size 400=400, on which incident atoms are deposited onto random sites. A periodic boundary condition is applied in the kinetic MC simulations. The hopping rate of an adatom for a specific move is determined by w10x hsnexpž yebykt. (1) 12 where ns1.0=10 Hz is the attempt frequency, EB is the height of the energy barrier that the adatomneeds to cross for that specific move, k is Boltzmann s con- y9 y12 Fig. 2. Morphologies of islands at the coverage of u s0.3, (a) DC deposition, (b) Tps10 s, (c) Tps10 s, and (d) Tps10 s, when hs Hz and f s100 Hz for pulsed beamdeposition.

3 Q.Y. Zhang, P.K. Chu / Surface and Coatings Technology (2002) Fig. 3. Island-size distribution function N (u) (s)1) for three different values of pulse duration, (a) DC deposition, (b) T s10 y9 y s, and (d) T s10 s, where hs10 Hz and f s100 Hz for pulsed beamdeposition. p s, (c) T s s p p stant, and T is the temperature. Because the hopping rate not only depends on Eb but also on T. Therefore, we only need to specify the hopping rates instead of giving each Eb and T. In this study, three hopping rates, , 10 and 10 Hz have been considered and the effects of nearest neighbor configurations on the diffusion barrier has been neglected. In the simulation, the probability of an adatomchosen to hope in a specific direction is w10x h i kis (2) 8 h j To model pulsed deposition, we define a pulse duration T p. In the case of PB deposition, atoms are deposited on the substrates only during T p. 3. Results and discussions 3.1. Island morphology Fig. 2 presents the pictures which give an overview of the typical island morphology at the coverage of us 0.3 for three different values of pulse duration (T p s y9 y =10 s, 5=10 s, and 5=10 s) when hs10 Hz and f s100 Hz, where u is coverage. For comparison, the island morphology of DC deposition is also given in the figure. As can be seen fromthe pictures, the morphologies are characterized by fractal structure, which is the typical feature for is1 model. However, the island sizes and the fractal arms in PB deposition are much smaller than that in DC deposition and the shorter the pulse duration is, the smaller the island sizes are. This is because adatomaggregation and nucleation are mainly dominated by the ratio of RsDyF, where D is the diffusion coefficient and F is the deposition rate. R is a measure of the diffusion ability of all adatoms on the substrate. The smaller the R is, the smaller the island sizes are. The deposition rate at the time of pulse activation is much higher than that in DC deposition for the same average of deposition rates in PB and in DC depositions. Therefore, the values of R considerably decrease in PB deposition. For the case of microsecond PB deposition, 7 R is of the order of 10 in the present simulation, which

4 250 Q.Y. Zhang, P.K. Chu / Surface and Coatings Technology (2002) y9 y12 Fig. 4. Scaling function of island-size distribution in Fig. 3; (a) DC deposition, (b) Tps10 s, (c) Tps10 s, and (d) Tps10 s, where 10 hs10 Hz and f s100 Hz for pulsed beamdeposition. is three orders lower than that in DC deposition. When comparing for the three cases of PB deposition, we can see that the morphology changes when the pulse duration changes frommicroseconds to nanoseconds. However, the morphology in the case of pulse duration of nanoseconds is similar to that in the case of picoseconds Island-size distribution Fig. 3 shows the island-size distribution function N s(u) (s)1) for three different values of pulse duration y9 y12 (Tps5=10 s, 5=10 s, and 5=10 s) at four different values of coverage. In the figures, we can see that the island-size distribution of the microsecond PB deposition is similar to that of DC deposition although their peak values of the island-size distribution at four different values of coverage are much smaller than that in DC deposition. With reducing the pulse duration to nanoseconds and picoseconds, however, the island-size distributions become obviously different from that in DC deposition. We can also see that PB deposition considerably increases the island density. The results imply PB deposition can promote nucleation and suppress the growth of islands. In order to reveal the dependence of island-size distribution on the pulse duration, the scaling function of island-size distribution in Fig. 3 is plotted in Fig. 4. According to the scaling theory, the scaling function of island-size distribution is defined as w16x Ž. Ž. 2 fsys sns u S yu (3) 8 sn sž u. s)1 uyn1 Ss s (4) N Ž u. N 8 s)1 s where s is island size, S is the average island size and N is the monomer density. 1 As can be seen fromfig. 4, the island-size distributions of four different values of coverage give similar scaling function although the dispersion in the cases of PB deposition is larger than that in DC deposition. The scaling functions at different pulse duration, however, show different behaviors. For microsecond PB deposi-

5 Q.Y. Zhang, P.K. Chu / Surface and Coatings Technology (2002) Fig. 5. Coverage-dependence of the island density N for different 10 pulse duration and frequency, (a) hs10 Hz and f s100 Hz for 10 y9 pulsed beamdeposition, (b) hs10 Hz and Tps10 s for pulsed beamdeposition. tion, the scaling function keeps the characters of is1 model. The peak position of the scaling function is approximately 1.0. For nanosecond PB deposition, the scaling function loses the characters of the is1 model and the peak position shifts to approximately 0.5. For picosecond PB deposition, we cannot find the peak of scaling function anymore. The scaling function in picosecond PB deposition looks like the simulation results obtained with the is0 model, where the monomers spontaneously freeze and formstable islands. In this case, the monomers are frozen during the pulse activation and the island growth is mainly dominated by the randomness of incident atoms Dynamics behavior To investigate the dynamics behavior of island growth, coverage-dependence of the island density N for different pulse duration and frequency has been calculated as shown in Fig. 5. As can be seen fromfig. 5a, growth behavior of microsecond PB deposition is similar to DC deposition. The nucleation process mainly occurs in the first pulse. The pulses followed mainly contribute to the aggregation and island coalescence. With reducing the pulse duration to nanoseconds and picoseconds, the nucleation and coalescence (the regime where island density decreasing) processes are prolonged. At the same time, the aggregation process (the regime of island density plateau) becomes short. Especially for the case of picosecond PB deposition, no obvious aggregation process can be seen. In the nucleation regimes of nanosecond and picosecond PB deposition, we can see some steps, where the island density increases sharply. This implies that there are many monomers left on the substrate after the pulse stops. These monomers nucleate and form islands in the duration between pulses. Fig. 5b shows the effect of pulse frequency on the growth behavior of islands. For f s10 Hz, the island density increases smoothly and no obvious step can be seen. This is because the atoms deposited in per pulse are 0.1 monolayers. Therefore, the island density increases to the saturation in the duration of the first pulse and there are few monomers left on the substrate. Although the island density in the case of Tps10 s, f s100 Hz is also a smooth curve, the island-size distribution and morphology, however, are very different y9 fromthat in the case of Tps10 s, f s10 Hz. For Tps10 s, f s100 Hz, the island-size distribution and morphology are similar to the results obtained in the y12 simulation of Tps10 s, f s100 Hz. Indeed, the island-size distribution and morphology in the case of y9 Tps10 s, f s1000 Hz look like the results simulated by T s10 s, f s100 Hz. p 4. Conclusions According the results and discussions, we have drawn the following conclusions: 1. The morphology, island-size distribution, and dynamics behavior of island growth in PB deposition are different fromthat in DC deposition when their average deposition rates are same. 2. With the increase of transient deposition rate during the pulse activation, the island-size distribution and morphology lose the characters of the is1 model. In the some cases, the growth behavior changes from the is1 model to the is0 model. 3. Due to the high transient deposition rate during the pulse activation, PB deposition promotes nucleation and suppresses the growth of islands. Therefore, PB deposition considerably increases the island density. Acknowledgments This work was supported by the National Natural Science Foundation of China under grant no

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