Island size distribution with hindered aggregation

: We study the effect of hindered aggregation on the island formation processes for a one-dimensional model of epitaxial growth with arbitrary nucleus size i. In the proposed model, the attachment of monomers to islands is hindered by an aggregation barrier, e_{a}, which decreases the hopping rate of monomers to the islands. As e_{a} increases, the system exhibits a crossover between two different regimes; namely, from diffusion-limited aggregation to attachment-limited aggregation. The island size distribution, P(s), is calculated for different values of e_{a} by a self-consistent approach involving the nucleation and aggregation capture kernels. The results given by the analytical model are compared with those from kinetic Monte Carlo simulations, finding a close agreement between both sets of data for all considered values of i and e_{a}. As the aggregation barrier increases, the spatial effect of fluctuations on the density of monomers can be neglected and P(s) smoothly approximates to the limit distribution P(s)=δ_{s,i+1}. In the crossover regime the system features a complex and rich behavior, which can be explained in terms of the characteristic timescales of different microscopic processes.