Effective cross-plane thermal conductivity of metal-dielectric multilayers at low temperatures

Heat transfer in layered metal-dielectric structures is considered theoretically based on an analytical solution of the Boltzmann transfer equation for the phonon distribution function. Taking into account the size effect, the problem of effective cross-plane thermal conductivity of structures containing two metal layers is analyzed in detail. If the thickness of the metal layers is less than the phonon mean free path, interlayer heat transfer is carried out predominantly by phonons, and the effective cross-plane thermal conductivity is determined by the reflection of phonons from the metal/dielectric interfaces. In the opposite case of thick metal layers, the effective cross-plane thermal conductivity is determined both by the thermal conductivity of the metal layers and by the thermal resistance of the dielectric layers. The results obtained are generalized to multilayer structures and superlattices.