Self-consistent rate-equation approach to irreversible submonolayer growth in 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 dynamical equations for the evolution of gaps between islands which is coupled to the island-density REs via local capture numbers and explicitly takes into account correlations between the size of an island and the corresponding capture zone. In the most simple formulation, fragmentation of capture zones is not directly included, but accounted for through a uniform rescaling, while nucleation is assumed to generate only gaps with average length. Using this approach, we have been able to accurately predict the scaled island-size, capture-number, and average-gap-size distributions in the pre-coalescence regime. Our approach also leads to a novel analytical expression for the monomer capture number σ1=(4/RN1γ)1/2 where N1 is the monomer density, γ is the fraction of the substrate covered by islands, and R is the ratio D/F of the diffusion rate to deposition flux which agrees 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 Monte Carlo simulations are presented for both point islands and extended islands.