Machine learning reconstruction of depth-dependent thermal conductivity profile from pump–probe thermoreflectance signals

Characterizing spatially varying thermal conductivities is significant to unveil the structure–property relation for a wide range of thermal functional materials such as chemical-vapor-deposited (CVD) diamonds, ion-irradiated materials, nuclear materials under radiation, and battery electrode materials. Although the development of thermal property microscopy based on time/frequency-domain thermoreflectance (TDTR/FDTR) enabled in-plane scanning of a thermal conductivity profile, measuring depth-dependent profiles remains challenging. This work proposed a machine-learning-based reconstruction method for extracting depth-dependent thermal conductivity K ( z ) directly from pump–probe phase signals. We demonstrated that the simple supervised-learning algorithm kernel ridge regression can reconstruct K ( z ) without requiring pre-knowledge about the functional form of the profile. The reconstruction method can not only accurately reproduce typical K ( z ) distributions such as the exponential profile of CVD diamonds and the Gaussian profile of ion-irradiated materials but also complex profiles artificially constructed by superimposing Gaussian, exponential, polynomial, and logarithmic functions. In addition to FDTR, the method also shows excellent performance of reconstructing K ( z ) of ion-irradiated semiconductors from TDTR signals. This work demonstrates that combining machine learning with pump–probe thermoreflectance is an effective way for depth-dependent thermal property mapping.