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.