Abstract
This article describes an approach to the heteroepitaxy of lattice mismatched semiconductors, that we call nanoheteroepitaxy. The theory developed here shows that the 3D stress relief mechanisms that are active when an epilayer is nucleated as an array of nanoscale islands on a compliant patterned substrate, will significantly reduce the strain energy in the epilayer and extend the critical thickness dramatically. Calculations show that with the scale of patterning that is achievable with advanced lithography (10–100 nm) we can eliminate mismatch dislocations from heterojunctions that are mismatched by as much as 4.2%.