Crystal Interfaces. Part II. Finite Overgrowths

A calculation of the interfacial energy between a crystalline film and a crystalline substrate of a different substance for the simple case in which the lattice parameters differ in one direction only, is presented. The results are expressed in terms of film thickness h, interfacial misfit η, interfacial bonding, and relative hardness of film and substrate. A parabolic interfacial potential has been used to investigate the effect of h showing that it is only a significant factor when either or both h and η are small. It is further shown that, in the minimum energy configuration of the system, the film is homogeneously strained. According to the calculations, a critical value of misfit ηc exists below which the film is strained to fit the substrate exactly and above which the required strain is an order of magnitude less than ηc. The misfit ηc is estimated to vary from as much as 13% for a ``soft'' monatomic layer which is tightly bound down to practically zero for thick films which are loosely bound. It is shown that the interfacial energy associated with an infinitely thick film as calculated with a Peierls-Nabarro type of interfacial force, is a useful approximation for many purposes. Approximate expressions for the strains in terms of the relevant parameters are deduced from this result.