High-Precision Inversion Algorithm and Full-Spectrum Optimization for Silicon Carbide Epitaxial Layer Thickness Based on Single-Reflection Interference Model

Abstract

To address measurement errors in infrared interferometry caused by neglecting complex optical effects during epitaxial layer thickness determination, this study focuses on modeling and optimization for silicon carbide (SiC) epitaxial layer thickness inversion. First, utilizing Snell's law, the optical path difference formula, and interference conditions, a two-beam interference model based on single reflection was derived. This established the relationship between epitaxial layer thickness d and wavelength "λ", refractive index n, and incident angle "θ", accounting for the functional relationship n=f(C, "λ" ) where refractive index n varies with dopant carrier concentration C and wavelength "λ" . Second, based on this interference model and incorporating multi-band reflectance spectral data, a high-precision thickness inversion algorithm was designed. The core of this algorithm lies in achieving precise characterization of refractive index variation with wavelength (dispersion) through Nth-order polynomial fitting, while introducing an incident angle correction. Key optimization steps include adopting the Fresnel coefficient method to uniformly describe s/p polarization and naturally incorporating the influence of half-wave loss on the position of interference maxima. Ultimately, high-precision thickness inversion was achieved by constructing a nonlinear least-squares optimization objective function E(d, "θ" ) based on full-spectrum reflectance. Numerical results demonstrate that this optimized model reduces thickness calculation errors by approximately 15% when accounting for wavelength dependence and incident angle correction.