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

In recent observations of Brownian motion of islands of adsorbed atoms and of vacancies with mean radius $R$, the cluster diffusion constant varies as $R^{-1\mathrm{}}$ and $R^{-2\mathrm{}}$. From an analytical Langevin description of the cluster's steplike boundary, we find three cases, $R^{-1\mathrm{}}$, $R^{-2\mathrm{}}$, and $R^{-3\mathrm{}}$, 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.