Strain interactions between dislocation arrays in epitaxial Si _x Ge_1-x /Si heterostructures

Lattice disregistry that exists in epitaxial overgrowths is often accommodated by interfacial dislocation arrays. The transition between strain accommodation by uniform interfacial shear and by interfacial dislocations is fairly sharp and thought to be controlled by energy minimization considerations. In this paper we demonstrate an extension of the Frank-van der Merwe approach by incorporating the continuum methodology of Eshelby to the analysis of strain interactions between arrays of interfacial dislocations in a bi-layered epitaxial film. Numerical examples are given for a Si/Si _x Ge_1-x /Si heterostructure. The importance of such an analysis to the study of defect propagation through strained layer superlattices is briefly discussed.