Strains in epitaxial films: The general case

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Abstract
A procedure is given for the calculation of the complete strain tensor of a film in pseudomorphic or coherent epitaxy on an arbitrary substrate. In the general case the misfit between the film and substrate determines three in-plane strain components. The elastic equations of the film then determine the three out-of-plane components. Quantitative low-energy electron diffraction can find the structure of bulk layers of a metal film; hence strain analysis can use the measured structure to obtain information about the elastic constants of the material of the film. The procedure is applied to two examples of observed general pseudomorphic epitaxy and to one example of possible general pseudomorphic epitaxy from a list of closely matched bcc and fcc surfaces. The concept of an epitaxial line, which plots the geometry of a film under strain as the substrate is changed in scale, is generalized to an arbitrary pair of film-substrate surfaces.