Elastic distortions of strained layers grown epitaxially in arbitrary directions

Abstract

We consider the elastic distortions which are due to lattice mismatch between epitaxial layers and substrates. The growth is assumed to take place in an arbitrary crystallographic direction. Explicit forms are obtained for the deformation of the unit cell and its two components, i.e., the angular distortions (symmetric strain) and the rigid-body rotation (antisymmetric strain). The correction factors which connect the relaxed lattice constants of the layer with observables from X-ray diffractometry are obtained in analytical forms. As shown through specific applications, the results agree with those obtained numerically in the literature.