Scaling functions for island-size distributions

Island-size distributions for submonolayer epitaxy are obtained by solving mean-field rate equations in the limit that the ratio of the adatom diffusion rate to the deposition rate becomes infinite. We determine the necessary and sufficient conditions for the existence of a scaling solution and show that it is determined by the growth rates of islands. Distributions are calculated for several standard models and the pertinence of our results to real epitaxial systems is discussed.