Unraveling intrinsic relationship of thermal properties in thermoreflectance experiments

Abstract

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 temperature-dependent reflectivity changes in materials. 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. This paper uses FDTR as a case study and systematically explores the relationships between sensitivity coefficients of various parameters through Singular Value Decomposition (SVD). Specifically, the sensitivity matrix <b><i>S</i></b> of the system's parameters is subjected to SVD to identify smaller singular values and their corresponding right singular vectors, which are the basis vectors of the null space of matrix <b><i>S</i></b> . These vectors reveal the relationships among parameter sensitivities, and by contradiction, these relationships reveal the most fundamental combined parameters that determine the thermoreflectance signal. This approach not only clarifies the dependencies among variables but also identifies the maximum number of parameters that can be experimentally extracted, as well as the parameters that must be known beforehand. To demonstrate the practical value of these combined parameters, this study conducts a detailed analysis of FDTR signals from an aluminum/sapphire sample. Unlike traditional FDTR experiments, which typically fit only substrate thermal conductivity and interfacial thermal conductance, our sensitivity analysis reveals that it is possible to simultaneously determine the thermal conductivity of the metal film, substrate thermal conductivity, substrate specific heat capacity, and interfacial thermal conductance. The fitting results are consistent with reference values from the literature and measurements from other thermoreflectance techniques, validating the effectiveness and reliability of our method. This comprehensive analysis not only deepens the understanding of thermoreflectance phenomena but also provides robust support for advancements in thermal characterization technology and material research, showcasing the significant potential of applying SVD in complex multi-parameter systems.