International Journal of Applied Mathematics and Machine LearningAuthor's: Yanlin Sun, Xingda Cheng, Wenkang Xu, Qirui Xiao, Li Li and Jianqiang Gao
Pages: [1] - [30]
Received Date: December 29, 2025
Submitted by:
DOI: http://dx.doi.org/10.18642/ijamml_7100122333
To address the challenge of non-destructive measurement of silicon carbide (SiC) and silicon (Si) epitaxial layer thickness, this paper proposes a high-precision measurement method based on the infrared interference principle and the non-linear least squares method. First, a mathematical model based on single-beam interference theory is established, in which the Sellmeier equation is utilized to correct refractive index dispersion to iteratively solve the SiC data, achieving a goodness of fit (R2) exceeding 0.99. Second, addressing the multi-beam interference characteristics of silicon materials, an improved model based on the Airy Function is constructed, resulting in a Root Mean Square Error (RMSE) of less than 0.01. Finally, the moving average method is introduced for data preprocessing, which effectively eliminates random noise and significantly enhances the robustness of the model.
infrared interference, non-linear least squares method, airy function, epitaxial layer thickness.
