Achieving high-accuracy and noise-robust process window analysis through stepwise regression

SignificanceProcess window analysis (PWA) is an essential step for lithography. However, traditional PWA methods that use fixed polynomial functions to fit focus-exposure matrix (FEM) data often fail to account for variations across mask patterns and noise in critical dimension measurements. This leads to inaccurate evaluations of the process window and the optimal process conditions.AimWe propose an improved lithography PWA method by introducing stepwise regression. This method automates the selection of the most suitable model function for fitting, enabling PWA to adapt to different FEM data, thus enhancing its adaptability and accuracy.ApproachThe stepwise regression method evaluates the statistical significance of the model terms based on their p-values. Terms with unacceptable p-values are iteratively removed until all remaining terms have p-values within an acceptable range. Then, the adjusted R2 is taken into account to select the optimal model. Finally, the robustness of the method is validated by evaluation through adjusted R2 and window overlapping ratio before and after manually introducing noise to the raw data.ResultsThe stepwise regression method performed on FEM data provided an improved model with higher fitting accuracy and statistical significance. Compared with traditional methods, the proposed method also demonstrated higher noise robustness.ConclusionsThe stepwise regression method effectively enhances the accuracy and robustness of PWA, making it a valuable tool for optimizing process parameters in semiconductor manufacturing.