Theory of spatial and size scaling in strain-free island ripening

A new theory for the ripening of two-dimensional strain-free islands limited by interfacial kinetics is presented. This theory supersedes the mean-field approach by including the environmental contribution to the islands' growth law. Consequently, it accounts not only for the development of the island size distribution; it also explains the concomitant spatial ordering of the islands. The scale invariance of these properties, as observed experimentally and in Monte Carlo simulations, evolves naturally from the theory. Good agreement between the theory and simulation is found. The work is significant for nanostructure production where island spatial and size distributions are key ingredients.