Measuring the polarization aberration of hyper-NA lens from the vector aerial image

Currently, the deteriorated lithography imaging caused by polarization aberration is increasingly prominent. Therefore measuring the polarization aberration accurately also becomes important. However, traditional polarization aberration measurement techniques integrated with complex apparatus such as polarimetry and polarizer which result in high cost for lithography tools. An in situ measurement technique of polarization aberration in hyper numerical aperture (NA) lithographic tools from the aerial image is proposed in this paper. As the polarization aberration can be decomposed into scalar phase, apodization, retardation and diattenuation, the first two items are firstly represented by Zernike coefficients of scalar Zernike polynomials, and the last two items are represented by Zernike coefficients of orientation Zernike polynomials. Secondly, the linear relationships between the aerial image and the Zernike coefficients of these four items are established from the rigorous vector imaging theory. Finally, the polarization aberration can be easily obtained by using above relationships after the aerial images of test marks in different orientations and pitches under different illumination settings are accurately measured. In addition, the validity of linear relationships and the performance of proposed technique are clearly demonstrated by numerical simulation for an immersion projector with NA1.35. It is fully expected that the proposed technique will simple to implement and will be applicable for retrieving the polarization aberration of projector with hyper-NA.