The size dependence of equilibrium elastic strain in finite epitaxial islands

Abstract

The equilibrium elastic strain in epitaxial islands of small size is shown to have a sawtooth dependence on island width by minimizing the systems energy as calculated from a periodic interaction potential between substrate and overgrowth. Such a sawtooth variation is consistent with Vincent's observations and idea that a given misfit between island and substrate may not be entirely accommodated by an integral number of identical misfit dislocations, and hence, the remaining misfit, which depends in part on island width, will be accommodated by residual elastic strain. The present calculations of mechanical equilibrium support these ideas and further reveal that in some cases misfit dislocations may over compensate for the misfit, thereby introducing an elastic strain of opposite sign to that normally expected. Other results of the calculations are in agreement with earlier theoretical and experimental observations.