Anisotropic thermal conductivity tensor measurements using beam-offset frequency domain thermoreflectance (BO-FDTR) for materials lacking in-plane symmetry

Abstract

Many materials have anisotropic thermal conductivity, with diverse applications such as transistors, thermoelectrics, and laser gain media. Yet measuring the thermal conductivity tensor of such materials remains a challenge, particularly for materials lacking in-plane symmetry (i.e., transversely anisotropic materials). This paper demonstrates thermal conductivity tensor measurements for transversely anisotropic materials, by extending beam-offset frequency-domain thermoreflectance (BO-FDTR) methods which had previously been limited to transversely isotropic materials. Extensive sensitivity analysis is used to determine an appropriate range of heating frequencies and beam offsets to extract various tensor elements. This technique is demonstrated on a model transversely anisotropic material, x-cut quartz (<110> α-SiO2), by combining beam offset measurements from different sample orientations to reconstruct the full in-plane thermal conductivity tensor. The technique is also validated by measurements on two transversely isotropic materials, sapphire and highly oriented pyrolytic graphite (HOPG). The anisotropic measurements demonstrated very good self-consistency in correctly identifying isotropic directions when present, with residual anisotropy errors below 4% for sapphire and 2% for HOPG and quartz. Finally, a computational case study (simulated experiment) shows how the arbitrary in-plane thermal conductivity tensor of a fictitious material with high in-plane anisotropy can in principle be obtained from only a single sample orientation, rather than multiple orientations like the experiments on x-cut quartz.