Elastic lattice deformation of semiconductor heterostructures grown on arbitrarily oriented substrate surfaces

We present a theoretical study of the lattice deformation of semiconductor epitaxial layers grown on arbitrarily oriented substrates, both with cubic symmetry. We assume a coherent (pseudomorphic) interface between the epitaxial layer and the substrate, i.e., without defects and dislocations. The elastic strain tensor components are calculated by minimization of the strain-energy density. A detailed study of the tetragonal deformation and of the shear strain is presented. We obtained no shear strain for the high-symmetry surfaces [001], [110], and [111], while for all the other surface orientations, which do not even have twofold symmetry, a shear strain was obtained with the highest value for the [113] surface. The shear strain has the opposite sign for [kk1] surfaces with respect to [11k] surfaces. In addition, the shear displacement occurs in all cases normal to the direction of highest symmetry of the interface plane.