Dynamic Scaling of the Island-Size Distribution and Percolation in a model of Sub-Monolayer Molecular Beam Epitaxy

Abstract

ABSTRACTThe results of a detailed study of the scaling and percolation behavior of the sub-Monolayer in a model of molecular beam epitaxy are presented. In our model adatoms are randomly deposited on a square lattice and then allowed to diffuse. Whenever an adatom encounters another adatom or an island, it is attached to them and becomes immobile. We have found and studied four distinct scaling regimes, corresponding to a low-coverage (nucleation) regime, intermediate-coverage regime, an aggregation regime, and coalescence and percolation regime. At low coverage the islands have a dendritic structure such as seen in Au/Ru (0001) while at higher coverages they become compact. The scaling of the cluster fractal dimension, island density, Monomer density, island size distribution, and structure factor and pair-correlation function are studied as a function of the coverage θ and the ratio R = D /F of the diffusion rate to the deposition rate.