Simulations of growing ordered arrays of islands on substrate steps

The spacing of islands in systems where the diffusion of adatoms is restric ted 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 i n which two- or three-dimensional islands grow exclusively at steps on a tw o-dimensional substrate. Monte Carlo simulations of both of these systems h ave 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 narro wly distributed range of island sizes, both of which are technologically de sirable. These effects are studied via a simple simulation of nucleation be haviour and a new semi-analytical simulation method and the results show a distinct improvement in the evenness of size and spacing of the islands.