The strain energy density of cubic epitaxial layers

We obtain a compact exact expression for the strain energy density of a cubic epitaxial medium in the limit of linear elasticity theory. Only the result for {001} is identical to the isotropic case: the greatest departure from isotropic theory occurs for {111}. We have evaluated this difference for a large number of cubic media and have obtained an estimate of its impact on epilayer critical thickness t_c for [001] oriented growth. We suggest that it tends to lower t_c for [001] oriented growth relative to that given by isotropic theory: by 15%-30% for common semiconductors and by up to a factor of 3 for metals.