Development of a Dual/Multi-Beam Interferometric Epitaxial Layer Thickness Calculation Model Integrating FFT and Least Squares Method

Abstract

This paper proposes methods related to epitaxial layer thickness detection and inversion calculation, focusing on the exploration of epitaxial layer thickness calculation models based on the interference principle and the application of corresponding algorithms. Firstly, a specific dispersion model is adopted to fit the refractive index of the epitaxial layer, and an appropriate error metric is used to evaluate the fitting degree. Combined with Snell's law and Fresnel equations, the reflection and transmission coefficients are calculated. The optical path difference and total phase difference under variable refractive index are derived through integration, thereby establishing a thickness measurement model. Secondly, the Fast Fourier Transform (FFT) is utilized to obtain the initial thickness value. Combined with a weighted joint least squares optimization model, a specific algorithm combination is employed to invert the thickness. A resampling method is used to determine the confidence interval, ensuring a good fitting effect. Finally, the necessary conditions for multi-beam interference and the reflectivity formula are derived, and a multi-beam thickness calculation model is established. This model has a better goodness of fit and can correct the deviations of the previous model. Integrating multiple algorithms, the proposed model balances accuracy and efficiency, exhibits excellent fitting performance and strong robustness, and can accurately realize the detection of epitaxial layer thickness.