Size Effect on the Thermal Conductivity of High-T_c Thin-Film Superconductors

Using the kinetic theory approximation and reported data, this study shows that at low temperatures, the phonon mean free path in polycrystalline ceramic YBa₂Cu₃O₇ can be of the order of the thickness of thin-film superconductors. In this case, boundary scattering reduces the thermal conductivity with decreasing film thickness. A simple method accounts for the size effect on conduction in thin films. This analysis rests solely on geometric arguments and does not consider the effect of grain boundaries. For conduction along the film, this model approximates well an analytical solution of the Boltzmann transport equation, and is in good agreement with experimental data for thin lead films. The model is also employed to analyze the size effect on conduction across the film and the influence of anisotropy.