Machine Learning-Enabled Fast and Accurate Inversion of Thermal Properties at the Micro- and Nanoscale via Optical Metrology

Escalating power densities in monolithic three-dimensional (M3D) integrated circuits (ICs) and heterogeneous integration (HI) technologies intensify hot spots in upper tiers and dense interconnects, demanding precise, scale-aware thermal characterization to unlock effective thermal management strategies. Micro- and nanoscale optical metrologies, including frequency- and time-domain thermoreflectance (FDTR and TDTR), transient thermoreflectance (TTR), and laser-based Ångström method, meet this need by linking measured surface signals to subsurface properties through physics-based forward models. Yet the corresponding inverse problems present different mathematical hurdles. For example, FDTR, TDTR, and TTR inversions are nonlinear, so the least-squares fits can converge to local minima. In contrast, the Ångström inversion is linear, yet least-squares estimates are susceptible to noise-driven variance amplification. Such limitations have motivated machine learning (ML) approaches that deliver comparable or improved accuracy, enhance physical fidelity, and simultaneously accelerate inversion. For each optical metrology, this review formulates the forward and inverse problems, examines the limitations of conventional inversions, surveys ML inversion frameworks and benchmarks, and outlines open challenges and future research directions.