Relaxation times of non-Fourier materials using frequency-domain thermoreflectance

Abstract

Traditional Fourier heat conduction fails to accurately describe thermal responses under rapidly varying or high-frequency heating conditions. In such scenarios, heat transfer exhibits non-Fourier behavior, where the heat flux does not instantly follow the temperature gradient. This deviation requires a more comprehensive model that incorporates relaxation times, representing the delay in the heat flux’s response to temperature changes. The relaxation time of a system is often assumed to be linked to its phonon relaxation times or other intrinsic characteristic times, but a definitive method for its characterization, and a robust theoretical framework to describe them remains an open problem. By modeling a frequency-domain thermo-reflectance (FDTR) experiment taking into account non-Fourier heat transfer, we investigate the temperature distribution in materials with diverse relaxation times, capturing transient thermal profiles. The results demonstrate high sensitivity to relaxation-time parameters in FDTR experiments and provide a practical approach for characterizing the relaxation times in non-Fourier materials.