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A Fokker-Planck equation is used to model the coarsening of surface nanostructure arrays. Metastable states are identified which are associated with a narrow size distribution and a coverage dependent mean island size. This is a general feature linked to nanostructures which, as a function of island size, are associated with a minimum in formation energy per atom and a positive chemical potential gradient. This has important implications for the self-organization of quantum dots.

We present a linear stability analysis of ultradense arrays of coherently strained islands against Ostwald ripening. Surprisingly, short-range elastic interactions are found to overcome the destabilizing contribution of surface energy, leading to a metastable array of quantum dots. Simulations of Ostwald ripening kinetics directly verify the existence of this metastable regime and confirm the nature of the most unstable mode for subcritical island coverage.

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