Epitaxial strain and epitaxial bending

The relation between the curvatures of an epitaxial film-substrate system and the epitaxial strain in the him is generalized to an arbitrary substrate surface of an arbitrary crystal structure. The determination of elastic constants of epitaxial film material from curvature measurements is compared with the determination from bulk perpendicular strain measurements by quantitative low-energy electron diffraction. Minimization of the elastic strain energy of the curved system as a function of an assumed single isotropic curvature leads to a particularly simple formula for the single curvature. The single curvature is proportional to an elastic constant which is simply the strain energy for unit in-plane epitaxial strain and is also proportional to the misfit strain and the ratio of film to substrate thickness. However, in general the curvature is anisotropic and a procedure for calculating the principal curvatures and their orientation is described and applied. The single curvature is shown to be close to the arithmetic average of the principle curvatures.