Reciprocal-space formulation and prediction of misfit accommodation in rigid and strained epitaxial systems

Geometrical properties form a key aspect of any description of heteroepitaxial systems in which orientation, symmetry, and lattice parameters differ. An energetically founded epitaxial criterion, which is geometric in nature, for matching at a planar interface is derived from a generalization of the Frank-van der Merwe theory and the rigid models introduced by Reiss and van der Merwe. The criterion is most naturally formulated in reciprocal space as the matching of overgrowth and substrate reciprocal lattice vectors and is visualized with a construction analogous to the Ewald construction. Structure factors are introduced and account for rigid translations and the nonprimitive nature of substrate and overgrowth surface unit cells. This article focuses on the derivation of the epitaxial criterion and its consequences as a basis of a description of epitaxial configurations, pseudomorphism, and the parameters of dislocation or misfit vernier arrays, in terms of crystallographic conventions. The strength of the description is its general nature, as it is general and applicable to any combination of crystal symmetries or mismatch and can be used to predict, or interpret, interfacial structure.