Bending of a film-substrate system by epitaxy

The curvature, strains, and stresses produced by the misfit of a film-substrate system of cubic crystals in pseudomorphic epitaxy on cubic (001) faces are found by a simple general procedure which minimizes the total elastic strain energy of the system. The film thickness is not required to be small compared to the substrate thickness, but the misfit and strain are assumed to be small so that linear elasticity theory can be used. The deviations for finite film thickness from the usual limit of negligible film thickness differ from previous work. The theory in the usual limit agrees well with a recent measurement of the bending of a system of up to seven monolayers of Ge deposited on a Si(001) surface.