Theory of the island and capture zone size distributions in thin film growth

The growth of islands during thin film deposition is described in terms of capture zones that determine the islands' growth rates. The evolution of the capture zones themselves is modelled as a fragmentation process when new islands nucleate, which leads to a derivation of the joint probability distribution of island and capture zone sizes. The model shows robust scaling for spontaneous nucleation where the critical island size i = 0, and only a weak time dependence for i = 1. The solutions of the model correspond well to the joint probability distributions found in thin film deposition simulations, and yield good quantitative predictions of the island and capture zone size distributions for the first time.