Analytical approach to the impact of polarization aberration on lithographic imaging

Abstract

An analytical approach to the impact of polarization aberration on lithographic imaging is proposed. The linear relationship between image placement error (IPE) of alternating phase-shifting mask (Alt-PSM) and odd aberration items of polarization aberrations, as well as that between best focus shift (BFS) of Alt-PSM and even aberration items of polarization aberrations are established by analytical equations, respectively. The validity of the linear relationships is demonstrated by numerical results. The differences and connections between scalar aberration and polarization aberration are briefly discussed based on these linear relationships.

Analytical analysis for impact of polarization aberration of projection lens on lithographic imaging quality

“…Then the IPE and BFS caused by each Pauli-Zernike coefficients are obtained from the aerial images using MATLAB. In addition, the linear fitting of IPE and BFS is performed using the standard linear model expressed as 4 PZ , 9 PZ , 16 PZ and the corresponding fitting lines under linear polarization illumination (0,1) are shown in Figure 3. The IPE and BFS of that and the corresponding fitting lines under linear polarization illumination (1,1) are shown in Compare with the corresponding ratios -2 in Eq.…”

“…By means of orientation Zernike polynomials, Johannes et al proposed an approach to quantify the retardation and diattenuation content of Jones pupils, and assessed the polarization impact on the lithographic relevant parameters without resorting to full-fledged numerical imaging simulations [7][8] . Previously, some of the authors investigated the imaging degradations caused by polarization aberration, based on Hopkins theory of partial coherent imaging 9 . However, the work didn't contain all polarization aberration components, while only referred to the Pauli pupils corresponding Pauli matrices coefficients 0 a and 1 a .…”

Challenges in coronagraph optical design

“…[1], [9]- [15] The functional form of these polarization aberrations frequently have similar patterns to the geometrical aberrations, since they arise from the geometry of surfaces and the variation of angle of incidence.…”

Polarization aberration in astronomical telescopes

“…[2]- [8] Vector extensions to diffraction theory then allow the diffraction patterns and image quality of polarization-aberrated beams to be simulated. [1], [9]- [15] The functional form of these polarization aberrations frequently have similar patterns to the geometrical aberrations, since they arise from the geometry of surfaces and the variation of angle of incidence. [11], [12], [16]- [23] 2.…”