Analytical selection of ideal epitaxial configurations and some speculations on the occurrence of epitaxy I. Epitaxy with rectangular interfacial atomic meshes

Abstract

Abstract This investigation has been aimed at a better understanding of epitaxy; particularly, but not exclusively, in monolayers. The description has been facilitated by the introduction of a configuration space γ, spanned by the parameters relevant to epitaxy, namely, lattice parameters, misorientation, bonding, etc. The rigid model, previously employed by Reiss (1968), has been used; first, to construct, on the basis of minimum interfacial energy, analytical criteria for ideal epitaxial configurations in γ-they are shown to be reducible to simple matching of atomic rows, i.e. one- or two-dimensional coherence; second, to show that real systems whose representative points deviate appreciably from ideality are relatively mobile; and third, that it is natural for systems, which comply with the rigid model and whose representative points in γ are close enough to ideality, to be slightly misoriented and accordingly need an additional driving force, such as is associated with coalescence, to attain perfect or near perfect epitaxy. Tables representing some simple ideal epitaxial configurations have been constructed. The conditions under which an elastic overlayer, usually a monolayer, can be strained homogeneously so as to move its representative point into coincidence with an ideal point, have been determined. A simple scale factor has been constructed to relate the energy, which can be gained from the substrate field in the rigid model to that, gained in the elastic model in a transition to coherency. The purpose of the scale factor, as well as a brief summary of the relevant influence of misfit, dislocations in energy minimization (given hare), is mainly to assist in the considerations of rhombic meshes in part, II.