Thermoreflectance techniques, particularly frequency-domain thermoreflectance (FDTR), play a crucial role in measuring the thermal properties of bulk and thin-film materials. These methods precisely measure thermal conductivity, specific heat capacity, and interfacial thermal conductance by analyzing the surface temperature response signals through thermoreflectance. However, the complex interplay among parameters presents challenges in data analysis, where single-variable analysis often fails to accurately capture intra-layer and inter-layer interactions. In this work, FDTR is used as a case study and the relationships between sensitivity coefficients of various parameters are systematically explored through singular value decomposition (SVD). Specifically, the SVD of sensitivity matrix S of the system's parameters is performed to identify smaller singular values and their corresponding right singular vectors, which are the basis vectors of the null space of matrix S . These vectors reveal the relationships among parameter sensitivities, thereby uncovering the most fundamental combination parameters that determine the thermoreflectance signal. This method not only clarifies the dependency relationships between variables but also determines the maximum number of parameters that can be experimentally extracted, and the parameters that must be known beforehand. To demonstrate the practical value of these combination parameters, this work conducts a detailed analysis of FDTR signals from an aluminum/sapphire sample. Unlike traditional FDTR experiments, which typically fit only the thermal conductivity and interfacial thermal conductance of the substrate, our sensitivity analysis reveals that it is possible to simultaneously determine the thermal conductivity of the metal film, substrate’s thermal conductivity, substrate’s specific heat capacity, and interfacial thermal conductance. The fitting results are consistent with reference values from the literature and measurements from other thermoreflectance techniques, thus validating the effectiveness and reliability of our method. This comprehensive analysis not only deepens the understanding of thermoreflectance phenomena but also provides strong support for the future development of thermal characterization technology and material research, showing the significant potential application of SVD in complex multi-parameter systems.
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