Rate-equation approach to island size distributions and capture numbers in submonolayer irreversible growth

We present a quantitative rate-equation approach to irreversible submonolayer growth on a two-dimensional substrate. Our method explicitly takes into account the existence of a denuded (``capture'') zone around every island and the correlations between the size of an island and the corresponding average capture zone. The evolution of the capture-zone distributions is described by a set of Voronoi-area evolution equations, which are coupled to the usual rate equations for the island densities through local rates of monomer capture. The combined set of equations leads to a fully self-consistent calculation of the size- and coverage-dependent capture numbers. The resulting predictions for the average capture-zone and capture-number distributions are in excellent agreement with experimental results and Monte Carlo simulations. As a result, the corresponding scaled island size distributions and their dependence on coverage and deposition rate are also accurately predicted in the precoalescence regime.