Critical thickness condition for a strained compliant substrate/epitaxial film system

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. (C) 1996 American Institute of Physics.