Size-distribution evolution of ion-beam-synthesized nanoclusters in silica

A model to describe the growth of nanoclusters in silica via ion-beam synthesis is introduced. Kinetic Monte Carlo simulations indicate that nucleation, growth, coarsening, and fragmentation occur throughout implantation, leading to a steady-state size-distribution shape that agrees with experimental observations. A set of coupled rate equations are derived and solved within a self-consistent mean-field approximation. An intermediate asymptotic scaling analysis helps to identify the important experimentally accessible parameters that control ion-beam-synthesized nanocluster size distributions. The model predicts that the shape of the as-implanted size distribution depends only on a characteristic length governed by the effective diffusivity, effective ion solubility, and the volumetric flux while the average cluster size is determined by the solute/matrix interface energy.