Three-dimensional (3D) tensor-based methodology for characterizing 3D anisotropic thermal conductivity tensor

Abstract

The increasing complexity of advanced materials with anisotropic thermal properties necessitates more generic and efficient methods to determine three-dimensional (3D) anisotropic thermal conductivity tensors with up to six independent components. Current methods rely on a vector-based framework that can handle only up to four independent components, often leading to inefficiencies and inaccuracies. We introduce Three-Dimensional Spatially Resolved Lock-In Micro-Thermography (3D SR-LIT), a novel optical thermal characterization technique combining a 3D tensor-based framework with an efficient area-detection experimental system. For simple tensors (e.g., x-cut quartz, $k_{xz}=k_{yz}=0$), our method reduces uncertainty by over 50% compared to vector-based methods. For complex tensors with six independent components (e.g., AT-cut quartz), 2$\sigma$ uncertainties remain below 12% for all components. A novel adaptive mapping approach enables high-throughput data acquisition (40 s to 3 min, depending on tensor complexity), over 35 times faster than current methods, and accommodates samples with 200 nm surface roughness. Extensive numerical validation on 1000 arbitrary anisotropic tensors ranging from 1 to 1000 $W{m}^{-1}{K}^{-1}$ further validates the robustness of this methodology. This work highlights significant advancements in the thermal characterization of complex anisotropic materials.