Self-consistent rate-equation approach to transitions in critical island size in metal (100) and metal (111) homoepitaxy

Abstract

A self-consistent rate-equation approach to the study of transitions in the critical island size $i$ in submonolayer growth from $i=1$ to $i=2$ and from $i=1$ to $i=3,$ corresponding to homoepitaxial growth on metal (111) and (100) surfaces, is presented. In contrast to previous standard rate-equation results, the average island density and monomer density are well predicted along with the transition temperature from $i=1$ to a higher critical island size. It is shown that the method's implicit short-range correlations between attachment/detachment rates, together with a careful estimate of the escape rates for small clusters, are important factors for a good agreement with the kinetic Monte Carlo simulation results.