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 diffusi on race 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 ca lculated for several standard models and the pertinence of our results to r eal epitaxial systems is discussed.