Heat Transport in the Perpendicular Direction of Superlattices and Periodic Thin-Film Structures

Abstract Superlattices consisting of alternating layers of extremely thin films often demonstrate strong quantum size effects, which have been utilized to improve conventional devices and to develop new ones. The interfaces in these structures also affect their thermophysical properties through reflection and transmission of heat carriers. This work studies heat transport in the direction perpendicular to the film plane of superlattices and other periodic thin-film structures. Starting from the Boltzmann transport equation (BTE) and the first law of thermodynamics, boundary conditions based on diffuse interface scattering are established. Further treatment of the BTE leads to a set of integral equations describing the distribution of temperature gradient within each layer and thermal boundary resistance at interfaces. Numerical solution of these equations yields the temperature distribution and the thermal boundary resistance in the structure. Results show that the effective thermal conductivity of the structure in the perpendicular direction is controlled by both the size effects on heat transfer within each layer and the thermal boundary resistance between different layers. The thermal boundary resistance is no longer an intrinsic property of the interface but also depends on the layer thickness as well as the phonon mean free path. Comparison of the model predictions with available experimental data is favorable but also indicates the need for further theoretical and experimental studies.