Solving Strategy for Silicon Carbide Epitaxial Layer Thickness Based on Nonlinear Least Squares Method

Silicon Carbide (SiC) is a pivotal semiconductor material for next-generation high-power and high-frequency electronics, where precise measurement of its epitaxial layer thickness is crucial. This paper presents a robust method for de-termining this thickness using infrared interference and a nonlinear least squares optimization framework. We first establish a dual-beam interference model based on the Fresnel equa-tions and Snell's law, deriving reflectivity as a function of thickness and wave-length. The Drude model is incorporated to account for the refractive index dis-persion influenced by carrier concentration. For thickness inversion, experi-mental reflectivity data from SiC wafers is processed by excluding the anoma-lous "reststrahlen band" (700-1000 cm⁻¹). A hybrid algorithm combining dif-ferential evolution for global initial guess generation and nonlinear least squares for local refinement is implemented, yielding a thickness of 7.921 μm with a high goodness-of-fit (R² ≈ 0.94). Furthermore, we analyze multi-beam interference, deriving its necessary condi-tions: high interface reflectivity, sufficient coherence length, and layer stability. An adaptive hybrid interference model is developed, dynamically applying dual or multi-beam theory based on local optical conditions. Applied to silicon wafer data, it identifies multi-beam regions and calculates a thickness of 3.765 μm. Re-evaluating the SiC data with this model and a region-weighted strategy to mitigate multi-beam effects in the 399.7-666.3 cm⁻¹ band yields an optimized thickness of 7.049 μm. This work provides a reliable and adaptable framework for high-precision thickness characterization in semiconductor engineering.