Simulations of growing ordered arrays of islands on substrate steps

Abstract

The spacing of islands in systems where the diffusion of adatoms is restricted to one dimension is studied. We initially consider a point-island model on a one-dimensional lattice before moving on to a more realistic system in which two- or three-dimensional islands grow exclusively at steps on a two-dimensional substrate. Monte Carlo simulations of both of these systems have been performed, and an analytical expression giving the distribution of gaps between adjacent islands is formulated which is general with respect to the critical island size. This expression indicates that higher critical island sizes should yield more evenly spaced arrays of islands and a narrowly distributed range of island sizes, both of which are technologically desirable. These effects are studied via a simple simulation of nucleation behaviour and a new semi-analytical simulation method and the results show a distinct improvement in the evenness of size and spacing of the islands.