Self-consistent Rate-equation Approach to Nucleation and Growth in Point/extended Island Models of 1-d Homoepitaxy

A self-consistent rate equation (RE) approach to submonolayer growth on a one-dimensional surface is presented. This approach explicitly takes into account the existence of gaps between clusters and can successfully predict the coverage dependence of the average densities of monomers N1, and clusters, N . It also implies an unusual dependence for the monomer-monomer capture number 1 as a function of monomer density. To obtain the island size-distribution, a second set of meaneld equations is used describing the evolution of the size-dependent capture zones and leading to explicit sizeand coverage-dependent capture numbers. The solution of this fully self-consistent RE approach is then compared with kinetic Monte Carlo results.