A fully self-consistent rate-equation approach to irreversible submonolayer growth is presented. This approach explicitly takes into account the correlation between the size of an island and the corresponding average capture zone. It is shown that this leads to capture numbers which depend explicitly on the island-size, and excellent agreement with experimental and Monte Carlo results is found for this size-dependence. Consequently, the predictions for the island-size distributions are in very good agreement with Monte Carlo simulation results over the whole range of coverages in the pre-coalescence regime.
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