Exact island-size distributions for submonolayer deposition: Influence of correlations between island size and separation

We determine the exact scaling form of the size distribution of islands created via homogeneous nucleation and growth during submonolayer deposition. This scaling form is shown to be controlled by the dependence on size of the propensity for islands to capture diffusing adatoms. This size dependence is determined directly from simulations. It is distinct from mean-field predictions, reflecting strong correlations between island size and separation.