A model of strain relaxation in hetero-epitaxial films on compliant substrates

We propose a model for relaxing the lattice mismatch between a pseudomorphic heteroepitaxial film and its substrate, which is a thin film on a handling wafer with a relaxed twist boundary consisting of a cross-grid of screw dislocations. The model scheme predicts the generation of misfit dislocations with edge components from the initial twist boundary cross-grid of screw dislocations, without simultaneously also generating an excess of threading dislocations in the bulk of the hetero-epitaxial film. This is accomplished by the process of dislocation splitting and slip motion during which the cross-grid or mesh configuration defined initially by the boundary screw dislocations is maintained. Depending on the magnitude of the misfit strain to be relieved, the relaxation may proceed in four different stages, via the combination of a few possible splitting and slip steps, and are distinguished by the maximum strain relieved at the end of each stage. For a given twist angle phi(0) these maximum relieved strains are phi(0)/2, phi(0), 3 phi(0)/2 and 2 phi(0) respectively, at the end of each of stages I-IV. Films relaxed in each stage are characterized by a specific set of macroscopic crystallographic features that can be observed experimentally, including lattice rotation, lattice tilt, and the presence of more than one variant in some cases. For example, complete untwisting is predicted for stage IV relaxation, resulting in the disappearance of the initial twist angle between the two lattices. To relax the elastic misfit strain, extensive plastic deformation of the substrate film is involved, thus making it compliant to the hetero-epitaxial film. This thin film substrate may be cal:led the plastically compliant substrate (PCS).