Physical Model Construction and Robust Parameter Inversion for Infrared Interferometric Spectroscopy Measurement of Silicon Carbide Epitaxial Layer Thickness

Abstract

This paper establishes a physical model and designs a robust inversion algorithm for the precise measurement of silicon carbide epitaxial layer thickness. First, under the dual-beam interference assumption, a physical dual-beam interference model for silicon carbide epitaxial layer thickness was developed. This model, based on optical path difference and phase analysis, dynamically calculates refractive index using the Sellmeier dispersion model. It quantifies beam amplitude differences through Fresnel reflection coefficients, constructing a complete total internal reflection model that satisfies energy conservation. Subsequently, a dispersion-coupled nonlinear inversion and reliability assessment scheme for epitaxial layer thickness was designed for measured spectral data. This scheme employs data preprocessing to construct a nonlinear least-squares model targeting minimization of residuals between measured and modeled reflectance. The TRF algorithm and robust loss function are then jointly optimized to determine thickness and Sellmeier parameters. Ultimately, the optimal thickness estimate was obtained. The reliability of the results was comprehensively evaluated using Bootstrap resampling, error analysis, and multi-angle consistency verification. This research provides a highly accurate and reliable measurement framework, which is crucial for quality control and process optimization in the manufacturing of high-performance silicon carbide semiconductor devices.