Simulation and theory of island nucleation, growth, and coalescence on stepped substrates

We present a theoretical model of island growth on substrate steps which is of potential importance in the development of low-dimensional structures. Monte Carlo simulations have been performed in which randomly deposited monomers diffuse on a stepped substrate, and aggregate to form islands on the steps. The islands grow by monomer capture, so that adjacent islands eventually coalesce to form clusters, and ultimately a single continuous cluster will cover each step. The simulations are analyzed using models for each phase of the film's evolution. The models successfully reproduce the variation of the monomer, island, and cluster densities, and predict the points at which saturation of the island density and complete coverage of the step are achieved. Our models also allow us to understand which processes are most important in determining the behavior of these systems, and will be of interest to the experimental community involved in the development of nanoscale structures.