LATE-STAGE CLUSTER GROWTH - SPATIAL CORRELATIONS AND ORDERING ON SURFACES

The widely accepted models for late stage clustering, the Lifshitz-Sly ozov-Wagner theory for Ostwald ripening and the self-similar Monte Car lo simulations by Family and Meakin for coalescence growth, are consis tent with random spatial distributions of the clustered phase. Several detailed investigations have revealed that cluster-cluster interactio ns have to be further considered. Only one of these studies lead to pr edictions of spatial ordering when long-range repulsive forces were in cluded. In this paper we investigate nearest neighbor cluster distance distributions for both late stage growth processes (coalescence for G a on GaAs(001) and Ostwald ripening for Sn and In on SI(111)) and corr elate the results with experimental and theoretical results for the cl uster-cluster interaction in these systems. Non-random spatial distrib utions are found for ripening even at rather low areal cluster densiti es, 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 ef fect, in combination with a diffusion controlled exchange of matter be tween clusters, is sufficient as a driving force to obtain partially o rdered structures.