My Modeling Nanocluster Formation During Ion Beam Synthesis
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My Modeling Nanocluster Formation During Ion Beam Synthesis Chun-Wei Yuan, 1,2 Diana O. Yi, 1,2 Ian D. Sharp, 3 Swanee J. Shin, 1,2 Christopher Y. Liao, 1,2 Julian Guzman, 1,2 Joel W. Ager III, 2 Eugene E. Haller1,2 and Daryl C. Chrzan1,2 1 Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, U.S.A 2 Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 947201760, U.S.A. 3 Walter Schottky Institut, Technische Universität München, Am Coulombwall 3, 85748 Garching, Germany ABSTRACT Ion beam synthesis of nanoclusters is studied via both kinetic Monte Carlo simulations and the self-consistent mean-field solution to a set of coupled rate equations. Both approaches predict a steady-state shape for the cluster size distribution that depends only on a characteristic length determined by the ratio of the effective diffusion coefficient times the effective solubility to the ion flux. The average cluster size in the steady state regime is determined by the implanted species/matrix interface energy. INTRODUCTION Ion beam synthesis (IBS) is a technologically important method to synthesize nanocrystals within a solid matrix. The technique involves embedding one or more strongly-segregating species into a suitable matrix through the implantation of energetic ions. During implantation, the ions move about and encounter other implanted ions, leading to cluster nucleation. The clusters may then grow/evaporate via adsorption/desorption of single atoms. The description thus far resembles a 3-D analogue of 2-D submonolayer epitaxial nucleation, growth and coarsening [1-8]. IBS, however, differs from classical nucleation and growth problems in one important respect: During IBS, cluster growth is often interrupted by ion damage. The deposition of ions fragments the clusters, leads to inverse Ostwald ripening [9], and ultimately limits cluster sizes. The basic understanding of IBS has been exploited to fabricate interesting nanostructures and alter cluster size distributions [9–16]. But unlike submonolayer epitaxy [2-8] and low dose semiconductor doping via implantation that are extensively studied and understood [17–19], no detailed, comprehensive, quantitative theory of IBS has been developed. In this study, kinetic Monte Carlo (KMC) simulations, and the mean-field self-consistent solution to a set of coupled rate equations are developed to model cluster size distribution evolution during implantation. It is shown that the two key parameters governing the asimplanted size distribution for a given material are the characteristic length, L = (Dn∞ / F)1/2 , where F is the volumetric flux and n∞ is the ion’s solubility, and γ the interface energy between the implanted species and the matrix. THEORY
The employed KMC simulations include five fundamental processes: 1) implantation into an amorphous silica matrix at a rate F , 2) the off-lattice random walk of implanted atoms, represented by a diffusion coefficient D (the hop distance is chosen to be 5 Å), 3) the
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