Universality in size distributions of irreversibly grown epitaxial islands: Kinetic Monte Carlo simulations and the rate equations study

Abstract

The scaling approach to the irreversible epitaxial growth gained wide recognition due to its ability to describe with the use of a universal function the island size distributions (ISDs) corresponding to a broad range of experimental conditions. The approach, however, is operative only in the case of large average island sizes ${s}_{av}$ and large diffusion to deposition rates ratios $R$. Physically this corresponds to long deposition times and/or high temperatures. We argue that the ISDs exhibit yet another universality property which holds for much broader range of growth conditions, in particular, for low temperatures (small $R$) and small ${s}_{av}$ (short deposition times). We show that the normalized ISDs corresponding to the same ${s}_{av}$ are accurately described by the same universal distribution.