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 effective diffusion coefficient, the ion solubility, and the volumetric ion flux. The average cluster size in the steady-state regime is determined by the implanted species or matrix interface energy.