An Epitaxial Layer Thickness Inversion Framework Based on Cauchy Dispersion and Multiple-Beam Interference Models

Abstract

For measuring the thickness of epitaxial layers under infrared reflectance spectroscopy conditions, this paper proposes a thickness inversion method that integrates spectral preprocessing, interferometric model identification, and iterative optimization of dispersion parameters. First, the Savitzky–Golay filter is applied to suppress high-frequency noise while preserving the extrema characteristics of the interference fringes. Based on this, a dual-beam interference thickness calculation model is established, and the Cauchy dispersion model is introduced to describe the variation of refractive index with wavelength. Nonlinear least squares and damped iteration are then used to achieve a simultaneous estimation of the refractive index parameters and thickness. Furthermore, by combining interface reflectance and coherence length criteria to identify multi-beam interference conditions, a corresponding thickness correction model was established to mitigate the impact of higher-order reflections on the inversion results. Experimental results show that, after correction for multi-beam interference, the thicknesses obtained under 10° and 15° incidence conditions are 8.463 μm and 8.532 μm, respectively, demonstrating good consistency. This method can adapt to different incidence conditions and material dispersion characteristics, providing a highly versatile computational approach for measuring the thickness of thin films and epitaxial layers based on infrared interferometric spectroscopy.