Identifiability of the three-dimensional anisotropic thermal-conductivity tensor in thermoreflectance measurements: Single-orientation limits and full-tensor recover

RESUMO

Materials with full anisotropic thermal conductivity tensors are widely used in advanced applications, creating a need for dedicated characterization. Such tensors contain six independent components: three diagonal conductivities and three non-zero off-diagonal couplings. However, whether thermoreflectance measurements on a single crystalline orientation can uniquely determine an arbitrary tensor remains unclear. Here, we show that every fully anisotropic thermal-conductivity tensor admits a Schur-equivalent tensor with zero cross-plane couplings ($k_{xz}=k_{yz}=0$). The two tensors produce identical surface thermal responses, and this equivalence persists as frequency, delay time, beam geometry, and spatial offset vary. We further demonstrate that parameter-identifiability assessments based on heuristic interpretations of sensitivity trends or singular-value decomposition (SVD) of the sensitivity matrix cannot, by themselves, rule out globally equivalent solutions in fully anisotropic systems. Combining systematic analysis with numerical validation, we provide guidance on selecting signals and measurement orientations for full-tensor characterization. Specifically, measurements at three mutually orthogonal crystallographic orientations provide complementary information for full-tensor recovery. These findings clarify the limits of single-surface measurements and establish a systematic approach to characterizing fully anisotropic thermal-conductivity tensors.