Screw misfit dislocations in soft substrates of epitaxial heterostructures

We derive compact analytical formulae for the elastic field induced by an anti-plane mismatch deformation in a heterostructure with different elastic moduli of the constituents. Unlike previous studies, we consider the possibility that the misfit dislocations may appear in the substrate, not in the epilayer. We show that this situation can be realized in heterostructures where the substrate is softer than the epilayer. In order to avoid cumbersome calculations, we consider screw misfit dislocations. The misfit dislocations emerge with zero density away from the interface in the body of the substrate when the epilayer reaches its critical thickness. Thus the epilayer remains free from dislocations if it is grown on a softer substrate. This property, which was recently observed experimentally, may find numerous applications in electronics, where epilayers are widely used as active elements.