Beam-offset thermoreflectance with Bayesian optimization to measure the anisotropic thermal properties of semiconductor superlattices

The directional nature of heat conduction in semiconductor superlattices—marked by significant differences between in-plane and cross-plane pathways—poses substantial challenges for precise thermal property assessment. Conventional frequency-domain thermoreflectance (FDTR) techniques, while proficient at evaluating cross-plane thermal conductivity, suffer from restricted capability in resolving in-plane transport due to inherent phase-delay constraints and inadequate lateral resolution. In this investigation, we overcome these limitations through a hybrid analytical framework that integrates a non-contact Beam-offset Frequency-Domain Thermoreflectance (BO-FDTR) setup with a neural network initialization, a Gaussian Process Regression, and Bayesian Optimization (GPR-BO) technique. The enabling innovation is our inversion engine: neural networks provide instantaneous initial parameter estimates that seed a GPR-BO scheme, performing rigorous probabilistic inference to deliver final thermal conductivity values with 95 % credible intervals. This hybrid framework preserves the statistical rigor of Bayesian inversion while exploiting the computational efficiency of neural networks for accelerated experimental guidance. This method reduces estimation inaccuracies, attaining measurement uncertainties under 1 % to 2 % at 95 % confidence intervals. The technique demonstrates improved performance, furnishing a structured protocol for AlAs/GaAs superlattice (period thickness 52 nm) that delivers thermal conductivity values of 14.7 (cross-plane) and 37.4 W m−1 K−1 (in-plane). Our findings confirm that the neural-network-initialized GPR-BO protocol, applied to frequency sweeps with varied beam-offset locations, delivers superior measurement precision that exceeds conventional single-variable methods—validating the robustness of our thermal assessment across both geometric arrangements.