Comprehensive characterization of contact edge roughness using elliptic Fourier descriptor

Abstract

Background: With the extreme ultraviolet lithography-driven node shrinkage, contact edge roughness (CER) analysis is becoming increasingly important as the critical dimension is directly affected by the stochastic effect. Although a polar coordinate frequency analysis was reported, it limits the comprehensive understanding of CER, which has intrinsic two-dimensional frequency information. Aim: We aim to extract and analyze two-dimensional frequency information of CER. Approach: An elliptic Fourier descriptor (EFD) was applied, which performs a Fourier transform on the x and y coordinates of the closed curve. After extracting harmonic coefficients, power spectral density (PSD) and correlation lengths were calculated. Finally, the regression with the correlation lengths and EFD coefficients for the mean radius was conducted. Results: In PSD, CER has a similar trend to line edge roughness, which gradually reduces high frequency. From the EFD method, the correlation length of the total power PSD can be analyzed for the x and y components, respectively. In addition, various curvilinear shapes can be explored, showing their applicability as a general analytical method. The XGBoost regression method obtained improved accuracy from the frequency component separation of the correlation length. Furthermore, feature importance analysis confirmed the applicability of EFD coefficients as a quantitative index for shape variation. Conclusions: From the EFD method, comprehensive characteristics of CER can be understood. With the advantages of quantitative frequency index and general applicability, it is expected to be utilized for the practical application of CER analysis.