The definition and calculation of interfacial energies for thin films

We provide a new definition of the interfacial energy which eliminates three physically extraneous contributions from the conventional definition: (1) the strain or stress energy due to lattice mismatch between film and substrate; (2) the surface energy of the film-vacuum interface; and, (3) the substrate surface energy contribution from substrate layers below the film layers. This new interface energy then quantifies the variation in interactions among film/substrate, film/film and substrate/substrate bonding. Using this new definition, we derive the equations for evaluation of the interfacial energy in terms of the interaction energy for any atom in each layer of the film/substrate, film/film and substrate/substrate systems. With this formulation, it is simple to determine the dependence of the interfacial energy on the film thickness using virtually any interaction potential. Using a corrected effective medium theory, we present results for a few pseudomorphic film systems containing Ni/Cu, Ni/Ag, Cu/Ag and Rh/Ag on (111) and (100) surfaces. These systems cover a wide range of lattice mismatch and alloy formation energies. The results demonstrate that the new definition of interfacial energy converges after only 3–4 film layers, regardless of the degree of lattice mismatch. We also show that the interfacial energies at (100) and (111) interfaces differ and that the interfacial energy for a given pair of materials depends on which of the materials is the film.