Optical spectrum augmentation for machine learning powered spectroscopic ellipsometry

Abstract

As structures of semiconductors become more complex and finer, the importance of an accurate measurement system has emerged. Previous studies have suggested various methodologies to improve the accuracy. However, since multiple measuring instruments are used in mass production, repeatability and reproducibility are as important as the accuracy of the values produced by predictive models. In this study, we adopted a data augmentation approach that minimizes the physical difference between multiple measuring instruments by using the domain knowledge of the spectroscopic ellipsometry (SE) field. By modeling the photodetector misalignment as polynomials and taking into account random noise, we proposed stochastic polynomial wavelength calibration (s-PWC) which can improve the percentage of the gage repeatability and reproducibility (Gage R&R) value. In experiments, the proposed methodology was applied to train the nanostructure prediction model of a three-dimensional vertical NAND Flash memories with industrial data sets. The performance improvements before and after applying the method were evaluated. Gaussian noise augmentation (GNA) and polynomial wavelength calibration (PWC) methodologies devised based on previous studies were also evaluated for relative comparison. As a result of conducting the experiments under conditions similar to the actual production environment, the average value of the percentage of Gage R&R decreased from 10.23% to 6.3% when applying the proposed method, while the GNA and PWC methodologies reduced the values to 10.01% and 7.62%, respectively. There were no significant changes in the values of coefficient of determination (R2) and root mean square error (RMSE) when applying the three methods based on the data augmentation approach. In other words, applying s-PWC ensures that the predictive model produces consistent values for the same sample when it needs to infer data obtained from multiple measuring instruments, while maintaining R2 and RMSE. Future research on data augmentation techniques by modeling differences between other physical components might extend the explanations of the methodologies to improve R2 and RMSE of predictive models. We expect this study could provide guidelines for improving the performance of inferential models based on machine learning and SE in mass production environments.