AN ARRAY OF DISLOCATIONS IN A STRAINED EPITAXIAL LAYER .1. ELASTIC ENERGY

The total energy of an array of dislocations in a strained epitaxial l ayer is composed of the self energy of the dislocations, the strain en ergy which arises from the lattice mismatch between the layer and its substrate and the interaction energy between the dislocations and the mismatch strains. The sum of the self energy and the interaction energ y represents the formation energy of the dislocations. In this study, the self energy is formulated using complex potentials. Two limiting c onditions are used to check the solution. The first is that the self e nergy of the array reduces to that for an isolated single dislocation as the dislocation spacing in the array approaches infinity. Secondly, as the layer thickness approaches infinity, the self energy reduces t o that for a dislocation wall. A negative formation energy promotes di slocation generation while a positive formation energy implies a suppr ession of dislocation generation. A critical thickness required for th e generation of an isolated dislocation is found by locating the layer thickness which corresponds to a zero value of the formation energy. The critical dislocation density at a given thickness is also determin ed.