Determination of Silicon Carbide Epitaxial Layer Thickness Based on Genetic Algorithm and Transfer Matrix Model

Abstract

This paper focuses on determining the thickness of silicon carbide epitaxial layers using infrared interferometry. A mathematical model was established based on the principle of double-beam interference, incorporating Snell’s Law and the Pythagorean theorem to calculate the optical path difference between two reflected beams (from the epitaxial layer surface and the substrate interface). The phase difference was linked to the interference order, and conditions for constructive and destructive interference were analyzed to derive the fundamental thickness model. The Sellmeier dispersion model was introduced to account for the wavelength-dependent refractive index influenced by doping concentration. For experimental verification, the reflectance spectra were preprocessed to remove noise and convert wavenumbers into wavelengths. Extreme interference points were identified, and thickness was optimized globally using genetic algorithms in MATLAB, minimizing the least-squares error between modeled and measured reflectance. Reliability was confirmed through residual analysis and consistency across incidence angles. The impact of multi-beam interference was analyzed by comparing its characteristics with double-beam interference and identifying necessary conditions (e.g., high reflectivity and phase stability). The coefficient of variation in wavenumber spacing was used to multi-beam effects. For silicon wafers, the transfer matrix model and genetic algorithms were employed to calculate optimized thickness, accounting for multi-beam interference. This work provides a robust framework for high-accuracy, nondestructive thickness measurement of epitaxial layers.