Analytical results for the cluster size distribution in controlled deposition processes

This paper proposes a controlled particle deposition model for cluster growth on the substrate surface and then presents exact results for the cluster (island) size distribution. In the system, at every time step a fixed number of particles are injected into the system and immediately deposited on to the substrate surface. It investigates the cluster size distribution by employing the generalized rate equation approach. The results exhibit that the evolution behaviour of the system depends crucially on the details of the adsorption rate kernel. The cluster size distribution can take the Poisson distribution or the conventional scaling form in some cases, while it is of a quite complex form in other cases.