Dispersion Compensation and Multi-Beam Interference Correction Algorithm for Thickness Measurement of SiC Epitaxial Layer.

To address the main challenges in thickness estimation of SiC epitaxial layers from infrared reflectance spectra, including refractive index dispersion, multi-beam interference, and spectral uncertainty, this study develops a physics-constrained inversion framework for reflectance spectrum-based analysis. For the measured spectra, Savitzky-Golay filtering is first used to suppress spectral noise, and Gaussian fitting is then employed to improve the localization of interference extrema. The Sellmeier equation is introduced to characterize refractive index dispersion, and the layer thickness is obtained together with the dispersion parameters through nonlinear least squares fitting. To account for spectra affected by higher-order internal reflections, a multi-feature confidence-based identification strategy is further constructed, and an adaptive filtering procedure is introduced for multi-beam interference correction. A Monte Carlo perturbation analysis with ±0.1% peak perturbations and Gaussian noise is additionally performed to assess the robustness of the inversion results. Using SiC datasets measured at two incident angles, the proposed framework reduces the inter-angle deviation of the thickness estimates from 1.14% to 0.08% after multi-beam correction. The results support the effectiveness and robustness of the proposed workflow for the main SiC application scenario considered in this study. In addition, silicon wafer spectra are included as a supplementary transfer test to examine whether the multi-beam identification and correction strategy can be applied beyond the SiC example, rather than as a comprehensive cross-material validation of the framework.