Analytical analysis of the impact of polarization aberration of projection fens on lithographic imaging

摘要

In high-numerical aperture (NA) and hyper-NA lithography systems, the polarization aberration of the projection lens leads to imaging degradations. Typically, commercial simulators, which usually entail relatively higher computing cost and lack sufficient theoretical support, are used to explore the relationship. Analytical analysis of the impact of polarization aberration of the projection lens on the aerial image is performed. In the analysis process, an alternating phase-shift mask is used, and different components of the linear polarized illumination light vector are considered. The analytical expressions of image placement error (IPE) and best focus shift (BFS) caused by polarization aberration are derived from the intensity of the aerial image. The linear relationships between IPE and odd Pauli-Zemike polarization aberrations as well as that between BFS and even Pauli-Zernike polarization aberrations are established. Moreover, the polarization aberration sensitivities are given and compared when different components of the linear polarized illumination light vector are adopted. All derived expressions match simulation results well and can be used to understand more fully the detrimental impact of polarization aberration on lithographic imaging. The accuracy of the linear relationships is assessed by the least square method.