Articles

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

[+] Author Affiliations
Gregory R. McIntyre

University of California–Berkeley, Electronic Engineering and Computer Science Department, Berkeley, California 94720 and Advanced Micro Devices, 1 AMD Place, Sunnyvale, California 94088-3453

Jongwook Kye

Advanced Micro Devices, 1 AMD Place, Sunnyvale, California 94088-3453

Harry Levinson

Advanced Micro Devices, 1 AMD Place, Sunnyvale, California 94088-3453

Andrew R. Neureuther

University of California–Berkeley, Electronic Engineering and Computer Science Department, Berkeley, California 94720

J. Micro/Nanolith. MEMS MOEMS. 5(3), 033001 (October 06, 2006). doi:10.1117/1.2358129
History: Received November 21, 2005; Revised March 23, 2006; Accepted April 03, 2006; Published October 06, 2006
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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.

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© 2006 Society of Photo-Optical Instrumentation Engineers

Citation

Gregory R. McIntyre ; Jongwook Kye ; Harry Levinson and Andrew R. Neureuther
"Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations", J. Micro/Nanolith. MEMS MOEMS. 5(3), 033001 (October 06, 2006). ; http://dx.doi.org/10.1117/1.2358129


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