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We show that mean-field rate equations for submonolayer growth cansuccessfully predict island size distributions in the pre-coalescence regime ifthe full dependence of capture numbers on both the island size and the coverageis taken into account. This is demonstrated by extensive Kinetic Monte Carlosimulations for a growth kinetics with hit and stick aggregation. A detailedanalysis of the capture numbers reveals a nonlinear dependence on the islandsize for small islands. This nonlinearity turns out to be crucial for thesuccessful prediction of the island size distribution and renders an analyticaltreatment based on a continuum limit of the mean-field rate equationsdifficult.

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