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 and R^-2. From an analytical Langevin description of the cluster's steplike boundary, we find three cases, R^-1, R^-2, and R^-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.