Theory of Nanocluster Size Distributions from Ion Beam Synthesis

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 the existence of 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 to the ion flux. The average cluster size in the steady state regime is determined by the implanted species/matrix interface energy