Temperature dependence of anisotropic thermal conductivity tensor of bulk black phosphorus

Abstract

To date, the intrinsic thermal conductivity tensor of bulk black phosphorus (BP), an important 2D material, is still unknown, since recent studies focus on BP flakes not on bulk BP. Here we report the anisotropic thermal conductivity tensor of bulk BP, for temperature range 80 - 300 K. Our measurements are similar to prior measurements on submicron BP flakes along zigzag and armchair axes, but are >25% higher in the through-plane axis, suggesting that phonon mean-free-paths are substantially longer in the through-plane direction. We find that despite the anisotropy in thermal conductivity, phonons are predominantly scattered by the same Umklapp processes in all directions. We also find that the phonon relaxation time is rather isotropic in the basal planes, but is highly anisotropic in the through-plane direction. Our work advances fundamental knowledge of anisotropic scattering of phonons in BP and is an important benchmark for future studies on thermal properties of BP nanostructures.