A phenomenological theory of the thermal conductivity of thin films

A phenomenological theory is presented for the lattice thermal conductivity of thin plates (or films) in a contact with another material (e.g. a thin plate covered by an oxide film, a thin film evaporated on a substrate, etc.). In such heterogeneous systems, it is necessary to consider — besides reflections — the exchange of phonons between the phases of which the system is composed. Boundary conditions are formulated for the phonon distribution functions. It is shown that the surrounding material (or the substrate) can exert considerable influence upon the effective thermal conductivity of the plate (film).In conclusion, the authors express their sincere gratitude to . Bárta for valuable discussions on the subject of this paper.