Epitaxy on substrates with hexagonal lattice symmetry

Abstract

A general description of epitaxy between thin films and substrates of any crystal symmetry was developed from a model in which both overgrowth and substrate are initially kept rigid (Chapter 3). The overgrowth-substrate interaction is described by Fourier series, usually truncated, defined on the surface reciprocal lattice vectors of the crystal faces in the interface (Chapter 2). Energy considerations lead directly to a criterion for the existence of epitaxial configurations which occur when a pair of surface reciprocal lattice vectors of the substrate and overgrowth coincide. This criterion is analogous to the von Laue criterion and Bragg equation in diffraction theory, and has a geometrical realization related to the Ewald construction. Generalized, the formulation allows the calculation of misfit strain, (Chapter 4) and the description of interfacial structures in terms of misfit dislocation arrays or verniers (Chapter 5) - the spacing, line sense and Burgers vectors are obtained from the reciprocal lattice for an interface between crystals of the most general and diverse symmetry. The most general structures can be treated with convenient unit cells by using structure factors. Parallel to the predictions from reciprocal space, the homogeneous misfit strain (Chapter 4), the interfacial atom positions after relaxation (Chapter 5) and misfit and strain energies (both chapters) were obtained by direct numerical minimization of the total interfacial energy of a large (1105 atoms) but finite system.