Simultaneous measurement of in-plane and through-plane thermal conductivity using beam-offset frequency domain thermoreflectance

Abstract

Transient thermoreflectance (TTR) techniques are ubiquitous methods for measuring thermal conductivity of bulk materials and thin-films. Both through-plane thermal conductivity k⊥ and in-plane thermal conductivity k∥ should be independently measured in transversely anisotropic materials. When these properties are measured using conventional TTR techniques, the accuracy of the k∥ measurement is dependent on the accuracy of measuring k∥ and vice versa. This is especially problematic for thin-films measurements as uncertainty in k⊥ (∼5%) can propagate and grow for uncertainty in k∥. In this paper, we present a method for the simultaneous measurement of k⊥ and k∥ using beam-offset frequency domain thermoreflectance (FDTR) with robust uncertainty estimation. The conventional diffusive heat transfer solution is analyzed to show that offset and heating frequency can independently control the sensitivity to directional thermal conductivity and extract values for k∥ and k⊥. Numerical uncertainty analyses demonstrate that sweeping both heating frequency and beam offset results in a reduction of measurement uncertainty. This modified measurement technique is demonstrated on crystalline alumina (c-Al2O3), amorphous alumina (a-Al2O3), quartz, fused silica, and highly oriented pyrolytic graphite.