The strain energy densities of hexagonal and tetragonal epitaxial media

Motivated by the burgeoning interest in the epitaxial growth of hexagonal and tetragonal semiconductors, we report expressions for the strain energy density for the high symmetry directions in these crystal systems. In addition, we have calculated the behaviour of the strain energy density as a function of epilayer surface normal orientation for the following systems: GaN on 6H-SiC, GaN on AIN, AIN on 6H-SiC and CuInSe2 on GaAs. For the first three cases, we suggest that substrate orientations not yet investigated may improve film quality as they will serve to reduce the strain energy density by approximately 30%, 17% and 65%, respectively, relative to the commonly employed (001) substrate orientation.