Excess stress and the stability of strained heterostructures

Abstract
We derive stability criteria for arbitrary strained heterostructures. The criteria are based on evaluating the excess stress as a continuous function of position within a structure for the two well-known Matthews–Blakeslee [J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974)] dislocation mechanisms for strain relief by plastic flow. If the excess stress for either mechanism exceeds zero anywhere within the structure, then the structure is unstable or metastable to strain relief by that mechanism.