An Onsager reciprocity relation for ballistic phonon heat transport in anisotropic thin films of arbitrary orientation

A classic Onsager reciprocity relation for Fourier heat conduction states that the thermal conductivity tensor in bulk anisotropic solids is symmetric. However, since Fourier’s law fails in thin dielectric films due to ballistic phonon transport effects, it is natural to ask whether an analogous Onsager relation can be identified for thin films. To answer this question, we solve the Boltzmann transport equation (BTE) under the relaxation time approximation for in-plane and cross-plane heat transport in thin films with anisotropic phonon dispersion relations and scattering rates. These BTE solutions show that the effective thermal conductivity tensor of thin films is symmetric from the diffusive through the boundary scattering regime. We validate the BTE solution against previous atomistic simulations of arbitrarily aligned graphite thin films, and use published first-principles calculations to model anisotropic heat flow in black phosphorus thin films. This derivation shows how Onsager reciprocity for anisotropic heat conduction extends to the boundary scattering regime, and reduces the number of independent measurements required to characterize heat transport in anisotropic thin films.

Citation: G. Wehmeyer, A.D. Pickel, and C.Dames. PRB 98, 014304 (2018).