The process of irreversible nucleation in multilayer growth. II. Exact results in one and two dimensions
arXiv:cond-mat/0207404 · doi:10.1103/PhysRevE.66.031606
Abstract
We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random walker in a higher-dimensional space. The spatial distribution of nucleation events is shown to differ markedly from the mean-field estimate except in the limit of very weak step-edge barriers. The nucleation rate is computed exactly, including numerical prefactors.
22 pages, 10 figures. To appear in Phys. Rev. E