Self-consistent rate-equation approach to irreversible submonolayer growthin one dimension

A self-consistent rate-equation (RE) approach to irreversible submonolayer growth in one dimension is presented. Our approach is based on a set of dyn amical equations for the evolution of gaps between islands which is coupled to the island-density REs via local capture numbers and explicitly takes i nto account correlations between the size of an island and the correspondin g capture zone. In the most simple formulation, fragmentation of capture zo nes is not directly included, but accounted for through a uniform resealing , while nucleation is assumed to generate only gaps with average length. Us ing this approach, we have been able to accurately predict the scaled islan d-size, capture-number, and average-gap-size distributions in the pre-coale scence regime. Our approach also leads to a novel analytical expression for the monomer capture number sigma (1) = (4/RN(1)gamma)(1/2) where N-1 is th e monomer density, gamma is the fraction of the substrate covered by island s, and R is the ratio D/F of the diffusion rate to deposition flux which ag rees with simulations over the entire pre-coalescence regime, and implies a novel scaling behavior for the island density at low coverage, in contrast to earlier predictions. Comparisons between our RE results and kinetic Mon te Carlo simulations are presented for both point islands and extended isla nds. (C) 2001 Published by Elsevier Science B.V.