Estimating depth-directional thermal conductivity profiles using neural network with dropout in frequency-domain thermoreflectance

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Non-contact and non-destructive methods are essential for accurately determining the thermophysical properties necessary for the optimal thermal design of semiconductor devices and for assessing the properties of materials with varying crystallinity across their thickness. Among these methods, frequency-domain thermoreflectance (FDTR) stands out as an effective technique for evaluating the thermal characteristics of nano/microscale specimens. FDTR varies the thermal penetration depth by modifying the heating frequency, enabling a detailed analysis of the thermophysical properties at different depths. This study introduces a machine learning approach that employs FDTR to examine the thermal conductivity profile along the depth of a specimen. A neural network model incorporating dropout techniques was adapted to estimate the posterior probability distribution of depth-wise thermal conductivity. Analytical databases for both uniform and non-uniform thermal conductivity profiles were generated, and the machine learning model was trained using these databases. The effectiveness of the predictive model was confirmed through assessments of both uniform and non-uniform thermal conductivity profiles, achieving a coefficient of determination between 0.96 and 0.99. For uniform thermal conductivity, the method attained mean absolute percentage errors of 1.362% for thermal conductivity and 3.466% for thermal boundary conductance (compared to actual values in the analytically calculated database). In cases of non-uniform thermal conductivity, the prediction accuracy decreased, particularly near the sample's surface, primarily due to the limited availability of machine learning data at higher heating frequencies.