Surface-Thermal Modes in Simple Cubic Thin Films

Abstract
The paper reports dispersion law and polarization vectors for the modes of thermal vibration in a thin film, with special emphasis on the surface modes. The thin film is conceived as a superposition of q monatomic layers, which are (001), (110), or (111) crystallographic planes of a simple cubic lattice. The harmonic approximation for the nearest neighbors was used. The manner of treating the surface and spacelike thermal modes is suggested by a procedure used by Jelitto for spin wave modes. The surface thermal modes in thin films with symmetric surfaces are either of a symmetric (cosh), or of an antisymmetric (sinh) type. Their kind and number depend on the surface orientation and film thickness. For (001) surfaces the surface symmetric mode degenerates in a mode of constant amplitude across the film.