Fast thermal aberration model for lithographic projection lenses.

A novel fast thermal aberration model for lithographic projection lenses is proposed. In the model, optical intensity calculation is simplified by using pupil intensity mapping, and simplified formulas for temperature calculation are derived to realize fast simulation of thermal aberration. The simulation results using the proposed model are compared with that of experiments carried out on a commercial lithography tool. The R-square of the simulation is better than 0.99 and the simulation time is about 10 minutes. Experiments and simulations show that the model is capable of predicting the thermal aberration or the variation trend of the thermal aberration of lithographic projection lenses fast and accurately. The model is applicable in projection lens design, evaluating degree of production risk posed by thermal aberration, etc.

General analytical expressions for the impact of polarization aberration on lithographic imaging under linearly polarized illumination.

With the shrinking of the critical dimension, the impact of polarization aberration on lithographic imaging becomes increasingly prominent. In this paper, the linear relationships between the image placement error and odd Pauli-Zernike polarization aberrations, as well as those between the best focus shift and even Pauli-Zernike polarization aberrations, are established by analyzing the imaging of the alternating phase-shifting mask. The relational expressions of the polarization aberration sensitivities (PAS) and the polarization angle of illumination are obtained based on these linear relationships. Then the expressions for the zero-value points and extremum points of the PAS are derived, and the impact of the polarization angle of illumination on the PAS is analyzed. The derived analytical expressions match the simulation results well; these can be used to analyze the detrimental impact of polarization aberration on lithographic imaging and provide a theoretical basis for exploring polarization aberration measurement and control techniques.

Wavefront aberration measurement method for a hyper-NA lithographic projection lens based on principal component analysis of an aerial image.

A wavefront aberration measurement method for a hyper-NA lithographic projection lens by use of an aerial image based on principal component analysis is proposed. Aerial images of the hyper-NA lithographic projection lens are expressed accurately by using polarized light and a vector imaging model, as well as by considering the polarization properties. As a result, the wavefront aberrations of the hyper-NA lithographic projection lens are measured accurately. The lithographic simulator PROLITH is used to validate the accuracies of the wavefront aberration measurement and analyze the impact of the polarization rotation of illumination on the accuracy of the wavefront aberration measurement, as well as the degree of polarized light and the sample interval of aerial images. The result shows that the proposed method can retrieve 33 terms of Zernike coefficients (Z5-Z37) with a maximum error of less than 0.00085λ.