PROGRESSIVE MODELING FOR SILICON CARBIDE EPITAXIAL LAYER THICKNESS MEASUREMENT: FROM DUAL-BEAM THEORY TO MULTI-BEAM INTERFERENCE CORRECTION

Abstract

Combining infrared reflection interferometry with experimental validation, this paper presents a layered structural modeling and inversion approach for measuring the thickness of silicon carbide (SiC) epitaxial layers. To overcome the challenges in directly acquiring critical parameters during measurement, an analytical relationship between the epitaxial layer thickness and the wavenumber, incident angle, refractive index, and interference order is established. This framework integrates geometric optics, Snell’s law, and the Fresnel equations within a dual-beam interferometry context. To handle the discrete and non-uniformly sampled nature of the measured reflectance spectra, the optimal interpolation method is selected based on cross-validation and the root mean square error (RMSE) criterion. Refractive index inversion is subsequently conducted via a golden section search, while the Brent method is employed to accurately locate interference extrema, enabling stable thickness inversion at incident angles of 10° and 15°. Furthermore, recognizing that multi-beam interference (MBI) typically dominates in practical experiments, this study investigates the coherent superposition of multiple reflected beams. A necessary condition for significant MBI (R²→1) is derived, and a comprehensive MBI model—incorporating complex amplitude reflection coefficients and phase correction terms—is developed. This research provides a robust theoretical and mathematical foundation for the high-precision, non-destructive measurement of SiC epitaxial layer thickness.