Diffusion of Monolayer Adatom and Vacancy Clusters: Langevin Analysis and Monte Carlo Simulations of their Brownian Motion

Abstract

In recent observations of Brownian motion of islands of adsorbed atoms and of vacancies with mean radius $R$, the cluster diffusion constant varies as ${R}^{\ensuremath{-}1}$ and ${R}^{\ensuremath{-}2}$. From an analytical Langevin description of the cluster's steplike boundary, we find three cases, ${R}^{\ensuremath{-}1}$, ${R}^{\ensuremath{-}2}$, and ${R}^{\ensuremath{-}3}$, corresponding to the three microscopic surface mass-transport mechanisms of straight steps. We thereby provide a unified treatment of the dynamics of steps and of clusters. For corroboration, we perform Monte Carlo simulations of simple lattice gases and derive atomistic diffusion constants.