A critical thickness condition for a strained compliant substrate/epitaxial film system

Abstract

The physical system under study is a single crystal film grown epitaxially on a substrate of comparable thickness which is constrained to remain flat. In general, the layers are strained due to a mismatch in lattice parameter between the film and substrate materials. The free energy change of the system due to formation of strain-relaxing interface misfit dislocations is estimated, and the discriminating case of zero energy change leads to a critical thickness condition on mismatch strain, film thickness, substrate thickness, and crystallographic slip orientation which is necessary for the spontaneous formation of such dislocations. The condition obtained generalizes the Matthews–Blakeslee (MB) criterion for a thin film on a thick substrate to the case of a complaint substrate/epitaxial film system, and it reduces to the MB criterion when either the film or substrate is relatively thick.