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Journal of Micro/Nanolithography, MEMS, and MOEMS

Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations
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Paper Abstract

Various representations of polarization aberrations are described and compared for optical lithography. Polarization aberrations, which are potentially important with hyper-numerical-aperture tools, are a complicated phenomena that refer to induced polarization-dependent wavefront distortions as light propagates through an imaging system. Pupil representations based on the following concepts are discussed: the physical polarization properties, the Mueller matrix, the Jones matrix, and the Jones matrix decomposed into a Pauli spin matrix basis. Although each has its own advantages and disadvantages, it is concluded that the Jones matrix representation decomposed into a Pauli spin matrix basis offers the most useful format for the lithographer due to its compact notation, physically intuitive interpretation, ability to be implemented into standard imaging equations, and its usefulness as an input into a lithographic simulator. Depending on the assumptions that can be made, the pupil specification consists of three to eight independent functions, where a normalization constant is calculated to ensure a physically realizable pupil. An example is shown to illustrate the usefulness of this strategy. Additionally, a simple metric for lens polarization quality based on this representation is proposed.

Paper Details

Date Published: 1 July 2006
PDF: 13 pages
J. Micro/Nanolith. MEMS MOEMS 5(3) 033001 doi: 10.1117/1.2358129
Published in: Journal of Micro/Nanolithography, MEMS, and MOEMS Volume 5, Issue 3
Show Author Affiliations
Gregory R. McIntyre, IBM Corp. (United States)
Jong-Wook Kye, Advanced Micro Devices, Inc. (United States)
Harry J. Levinson, Advanced Micro Devices, Inc. (United States)
Andrew R. Neureuther, Univ. of California/Berkeley (United States)

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