Late stage cluster growth: spatial correlations and ordering on surfaces

The widely accepted models for late stage clustering, the Lifshitz-Slyozov-Wagner theory for Ostwald ripening and the self-similar Monte Carlo simulations by Family and Meakin for coalescence growth, are consistent with random spatial distributions of the clustered phase. Several detailed investigations have revealed that cluster-cluster interactions have to be further considered. Only one of these studies lead to predictions of spatial ordering when long-range repulsive forces were included. In this paper we investigate nearest neighbor cluster distance distributions for both late stage growth processes (coalescence for Ga on GaAs(0 0 1) and Ostwald ripening for Sn and In on Si(1 1 1)) and correlate the results with experimental and theoretical results for the cluster-cluster interaction in these systems. Non-random spatial distributions are found for ripening even at rather low areal cluster densities, indicating that (i) cluster-cluster interactions play a major role in the morphological evolution of ripening structures at much smaller areal fractions than previously assumed and (ii) the Gibbs-Thomson effect, in combination with a diffusion controlled exchange of matter between clusters, is sufficient as a driving force to obtain partially ordered structures.