Resumen
This review is motivated by the impact of epitaxy ? the oriented overgrowth of a thin crystalline layer (the epilayer) on a crystalline substrate ? in pursuit of perfection in crystallinity as needed in high grade technology and fundamental studies. While acceptable knowledge with respect to the thermodynamic stability and growth modes of epitaxial layers is available, need exists for a reliable, simple criterion for epitaxial growth in order to facilitate the selection of suitable materials. Frank and Van der Merwe have proposed a sufficient criterion. A clear indication of a necessary and sufficient condition has emanated from a thermodynamic theoretical study of rigid model epitaxy at fcc (111)/bcc (110) interfaces. This study has identified, as important role players: (i) the matching of atomic rows across the contact interface, (ii) the crystalline interfacial source of periodic epilayer-substrate interaction, including its Fourier representation and (iii) the magnitude of the Fourier coefficients. The objectives have been finalised by (a) the calculation of optimum Fourier coefficients and (b) the reciprocal space Fourier series description of the periodic interaction, including the structure factors as evidence of the contributions from atomic planes further away from the contact plane and the analytical formulation of the desired criterion.