Stability of an hexagonal array of coherently strained conical islands against Ostwald ripening

We present a linear stability analysis of an hexagonal array of coherently strained islands against the exchange of material between islands. Surprisingly, ultra-dense arrays are found to be metastable due to the short-range stabilizing effect of elastic interactions which overcome the destabilizing contribution of surface energy. Mean-field simulations are used to investigate the ripening kinetics of local volume defects in arrays which are found to equilibrate through island volume oscillations. Simulations of global perturbations directly verify the existence of the metastable regime and confirm the nature of the most unstable mode as derived from the stability analysis for sub-critical island coverage.