Nucleation, adatom capture, and island size distributions: Unified scalinganalysis for submonolayer deposition - art. no. 235408

We consider the irreversible nucleation and growth of two-dimensional islan ds during submonolayer deposition in the regime of large island sizes. A qu asihydrodynamic analysis of rate equations for island densities yields an o rdinary differential equation (ODE) for the scaling function describing the island size distribution. This ODE involves the scaling function for the d ependence on island size of ''capture numbers'' describing the aggregation of diffusing adatoms. The latter is determined via a quasihydrodynamic anal ysis of rate equations for the areas of "capture zones" surrounding islands . Alternatively, a more complicated analysis yields a partial differential equation (PDE) for the scaling function describing the joint probability di stribution for island sizes and capture zone areas. Then, applying a moment analysis to this PDE, we obtain refined versions of the above ODE's, toget her with a third equation for the variance of the cell area distribution (f or islands of a given size). The key nontrivial input to the above equation s is a detailed characterization of nucleation. We analyze these equations for a general formulation of nucleation, as well as for an idealized pictur e considered previously, wherein nucleated islands have capture zones lying completely within those of existing islands.