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(001) and Ostwald ripening for Sn and In on SI(111)) 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.