CRITICAL THICKNESS CONDITION FOR A STRAINED COMPLIANT SUBSTRATE EPITAXIAL FILM SYSTEM/

The physical system under study is a single crystal film grown epitaxi ally on a substrate of comparable thickness which is constrained to re main flat. In general, the layers are strained due to a mismatch in la ttice parameter between the film and substrate materials. The free ene rgy 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 str ain, film thickness, substrate thickness, and crystallographic slip or ientation which is necessary for the spontaneous formation of such dis locations. The condition obtained generalizes the Matthews-Blakeslee ( MB) criterion for a thin film on a thick substrate to the case of a co mplaint substrate/epitaxial film system, and it reduces to the MB crit erion when either the film or substrate is relatively thick. (C) 1996 American Institute of Physics.