Diffusion-mediated nucleation and growth of islands during deposition occurs essentially irreversibly in a variety of systems. We provide a scaling theory for the full island-size distribution, both with the ratio of surface diffusion to deposition rates and with time. Scaling functions and exponents are determined by simulation and explained analytically by an unconventional rate-equation analysis. Experimental tests for theoretical predictions are discussed, including the scaling of superlattice beam profiles for diffraction studies of heteroepitaxial systems.

• Received 24 July 1992

DOI:https://doi.org/10.1103/PhysRevB.47.13891