Ordering of clusters during late-stage growth on surfaces

Abstract

The size ordering and spatial ordering of metal clusters on semiconductor surfaces has been experimentally investigated for systems in the late stages of phase separation. Specific late stage cluster growth mechanisms were achieved by suitable experimental conditions, and include (i) Ostwald ripening, (ii) coalescence, and (iii) an ``intermediate'' regime where mass conservation is only marginally violated by a relatively small deposition rate during cluster growth. The size ordering and spatial ordering of clusters were quantified by the standard deviations of the cluster size distribution and the nearest-neighbor distribution, respectively. In the Ostwald ripening regime, the size distribution is less ordered (broader) and the spatial distribution is more ordered (narrower) than is predicted by the mean-field Lifshitz-Slyozov ripening theory. In the intermediate regime, a higher degree of size ordering is observed (when compared to Ostwald ripening), but little spatial ordering with a near random spatial distribution. Finally, in the coalescence regime little size ordering and no spatial ordering are observed. These results are described using a model of local ripening, a mechanism where the ripening of an individual cluster is dominated by its nearest neighbor rather than the global growth conditions.