The energy of an array of dislocations: Implications for strain relaxation in semiconductor heterostructures

Abstract

An exact closed-form formula is given for the energy of an array of dislocations, arranged periodically on the interface between an epitaxial layer and its substrate, when these are modelled as elastically isotropic with the same elastic constants. In the course of the formulation, the exact equivalence of equilibrium theories originating in the work of Frank and van der Merwe and of Matthews and Blakeslee is established. The new formula allows the exact assessment of arrays of dislocations in equilibrium, for layers thicker than critical. This demonstrates that previous approximations may be seriously in error.