Influence of island diffusion on submonolayer epitaxial growth

We investigate the kinetics of submonolayer epitaxial growth which is drive n by a fixed flux of monomers onto a substrate. Adatoms diffuse on the surf ace, leading to irreversible aggregation of islands. We also account for th e effective diffusion of islands, which originates from hopping processes o f their constituent adatoms, on the kinetics. When the diffusivity of an is land of mass k scales as k(-mu), the (mean-field) Smoluchowski rate equatio ns predicts steady behavior for 0 less than or equal to mu < 1, with the co ncentration ck of islands of mass k varying as k(-(3-mu)/2). For mu greater than or equal to 1, a quasistatic approximation of the rate equations pred icts a slow continuous evolution, in which the island density increases as (In t)(mu/2). A more refined matched asymptotic expansion reveals unusual m ultiple-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 isl and growth and a mass distribution with a behavior distinct from that of th e nonzero flux system. Finally, we extend our results to one- and two-dimen sional substrates. The physically relevant latter case exhibits only logari thmic corrections compared to the mean-field predictions. [S0163-1829(99)09 223-1].