Power-law island size distributions and the Avrami model

The island size distribution in the early stages of thin-film deposition is simulated using the Avrami model and is shown to follow closely a power-law form for both two- and three-dimensional island growth. This model applies to systems where the time-averaged monomer density is constant across the substrate, as occurs for example when the mean free path of the diffusing monomers is limited. It offers a possible explanation for recently observed island size distributions which are continuously decreasing functions of size in certain systems. The distribution of nearest-neighbour separations of the islands is also considered and it is shown that this distribution can be used to distinguish between island arrays formed in the Avrami model and those of deposition-diffusion-aggregation models.