Influence of island diffusion on submonolayer epitaxial growth

Abstract

We investigate the kinetics of submonolayer epitaxial growth which is driven by a fixed flux of monomers onto a substrate. Adatoms diffuse on the surface, leading to irreversible aggregation of islands. We also account for the effective diffusion of islands, which originates from hopping processes of their constituent adatoms, on the kinetics. When the diffusivity of an island of mass k scales as ${k}^{\ensuremath{-}\ensuremath{\mu}},$ the (mean-field) Smoluchowski rate equations predicts steady behavior for $0<~\ensuremath{\mu}<1,$ with the concentration ${c}_{k}$ of islands of mass k varying as ${k}^{\ensuremath{-}(3\ensuremath{-}\ensuremath{\mu})/2}.$ For $\ensuremath{\mu}>~1,$ a quasistatic approximation of the rate equations predicts a slow continuous evolution, in which the island density increases as $(\mathrm{ln}{t)}^{\ensuremath{\mu}/2}.$ A more refined matched asymptotic expansion reveals unusual multiple-scale mass dependence for the island size distribution. Our theory also describes basic features of epitaxial growth in a more faithful model of growing circular islands. For epitaxial growth in an initial population of monomers and no external flux, a scaling approach predicts power-law island growth and a mass distribution with a behavior distinct from that of the nonzero flux system. Finally, we extend our results to one- and two-dimensional substrates. The physically relevant latter case exhibits only logarithmic corrections compared to the mean-field predictions.