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Island size distributions in submonolayer growth: successful prediction by mean field theory with coverage dependent capture numbers

We show that mean-field rate equations for submonolayer growth can successfully predict island size distributions in the pre-coalescence regime if the full dependence of capture numbers on both the island size and the coverage is taken into account. This is demonstrated by extensive Kinetic Monte Carlo simulations for a growth kinetics with hit and stick aggregation. A detailed analysis of the capture numbers reveals a nonlinear dependence on the island size for small islands. This nonlinearity turns out to be crucial for the successful prediction of the island size distribution and renders an analytical treatment based on a continuum limit of the mean-field rate equations difficult.