Abstract

Mueller matrix imaging polarimeter (MMIP) can be used to measure the polarization aberration (PA) of a lithographic projector in the form of the Mueller pupil, while the Jones pupil is required for lithographic imaging simulations, projection lens design and PA evaluation. In this paper, a Jones pupil measurement method of lithographic projection lens is proposed. The measurement device of the method is the same as an MMIP, but a new polarimetric measurement equation is derived to solve the Jones pupil directly from the Kronecker product of the Jones matrix and the measured intensities. Two new polarimeter configurations with the minimum condition number are designed to further improve the accuracy in the presence of error sources. The performance of the method is evaluated by measurement errors of a typical Jones pupil in the presence of error sources. Comparisons between the proposed method and the conventional method, in which the Jones pupil is converted from the Mueller pupil measured by MMIP, are given. The results validate that the measurement accuracy of the Jones pupil is significantly improved without increasing the complexity of existing measurement systems.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
  4. H. Nomura and I. Higashikawa, “Mueller matrix polarimetry for immersion lithography tools with a polarization monitoring system at the wafer plane,” Proc. SPIE 7520, 752012 (2009).
    [Crossref]
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    [Crossref]
  6. L. Li, Y. Li, Q. Chi, K. Liu, X. Zhang, and J. Li, “Optimized imaging polarimeter for measuring polarization properties of hyper number aperture lithography tools,” Proc. SPIE 9282, 928232 (2014).
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    [Crossref]
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2014 (1)

L. Li, Y. Li, Q. Chi, K. Liu, X. Zhang, and J. Li, “Optimized imaging polarimeter for measuring polarization properties of hyper number aperture lithography tools,” Proc. SPIE 9282, 928232 (2014).
[Crossref]

2012 (1)

2010 (1)

H. Nomura and I. Higashikawa, “In-situ Mueller matrix polarimetry of projection lenses for 193-nm lithography,” Proc. SPIE 7640, 76400Q (2010).
[Crossref]

2009 (3)

J. Ruoff and M. Totzeck, “Orientation Zernike polynomials: a useful way to describe the polarization effects of optical imaging systems,” J. Micro. Nanolithogr. MEMS MOEMS 8(3), 031404 (2009).
[Crossref]

T. Fujii, K. Muramatsu, N. Matsuo, Y. Ohmura, and M. Sawada, “True polarization characteristics of hyper-NA optics excluding impact of measurement system,” Proc. SPIE 7274, 72743K (2009).
[Crossref]

H. Nomura and I. Higashikawa, “Mueller matrix polarimetry for immersion lithography tools with a polarization monitoring system at the wafer plane,” Proc. SPIE 7520, 752012 (2009).
[Crossref]

2008 (3)

2007 (2)

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

T. Fujii, Y. Kudo, Y. Ohmura, K. Suzuki, J. Kogo, Y. Mizuno, N. Kita, and M. Sawada, “Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group,” Proc. SPIE 6520, 65204W (2007).
[Crossref]

2006 (2)

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, “Polarization aberration analysis in optical lithography systems,” Proc. SPIE 6154, 61540E (2006).
[Crossref]

G. R. McIntyre, J.-W. Kye, H. J. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Micro. Nanolithogr. MEMS MOEMS 5(3), 033001 (2006).
[Crossref]

2005 (1)

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

1997 (1)

S. N. Savenkov and V. V. Marienko, “The method of extraction of the Mueller-Jones part out of experimental Mueller matrix,” Proc. SPIE 2982, 226–231 (1997).
[Crossref]

1995 (1)

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34(6), 1558–1568 (1995).
[Crossref]

1994 (1)

1988 (1)

1985 (1)

J. J. Gil and E. Bernabeu, “A depolarization criterion in mueller matrices,” J. Opt. Soc. Am. 32(3), 259–261 (1985).

1982 (1)

R. Simon, “The connection between mueller and jones matrices of polarization optics,” Opt. Commun. 42(5), 293–297 (1982).
[Crossref]

Anderson, D. G. M.

Azzam, R. M. A.

Barakat, R.

Bernabeu, E.

J. J. Gil and E. Bernabeu, “A depolarization criterion in mueller matrices,” J. Opt. Soc. Am. 32(3), 259–261 (1985).

Chi, Q.

L. Li, Y. Li, Q. Chi, K. Liu, X. Zhang, and J. Li, “Optimized imaging polarimeter for measuring polarization properties of hyper number aperture lithography tools,” Proc. SPIE 9282, 928232 (2014).
[Crossref]

Chipman, R. A.

Dittmann, O.

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

Elminyawi, I. M.

Elsaba, A. M.

Flagello, D.

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

Fujii, T.

T. Fujii, K. Muramatsu, N. Matsuo, Y. Ohmura, and M. Sawada, “True polarization characteristics of hyper-NA optics excluding impact of measurement system,” Proc. SPIE 7274, 72743K (2009).
[Crossref]

T. Fujii, J. Kogo, K. Suzuki, and M. Sawada, “Polarization characteristics of state-of-art lithography optics reconstructed from on-body measurement,” Proc. SPIE 6924, 69240Z (2008).
[Crossref]

T. Fujii, Y. Kudo, Y. Ohmura, K. Suzuki, J. Kogo, Y. Mizuno, N. Kita, and M. Sawada, “Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group,” Proc. SPIE 6520, 65204W (2007).
[Crossref]

Geh, B.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Gil, J. J.

J. J. Gil and E. Bernabeu, “A depolarization criterion in mueller matrices,” J. Opt. Soc. Am. 32(3), 259–261 (1985).

Gohnermeier, A.

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

Graupner, P.

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

Gräupner, P.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Heil, T.

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

Hempelmann, U.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Higashikawa, I.

H. Nomura and I. Higashikawa, “In-situ Mueller matrix polarimetry of projection lenses for 193-nm lithography,” Proc. SPIE 7640, 76400Q (2010).
[Crossref]

H. Nomura and I. Higashikawa, “Mueller matrix polarimetry for immersion lithography tools with a polarization monitoring system at the wafer plane,” Proc. SPIE 7520, 752012 (2009).
[Crossref]

Kamenov, V.

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

Kaneko, M.

Kita, N.

T. Fujii, Y. Kudo, Y. Ohmura, K. Suzuki, J. Kogo, Y. Mizuno, N. Kita, and M. Sawada, “Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group,” Proc. SPIE 6520, 65204W (2007).
[Crossref]

Kogo, J.

T. Fujii, J. Kogo, K. Suzuki, and M. Sawada, “Polarization characteristics of state-of-art lithography optics reconstructed from on-body measurement,” Proc. SPIE 6924, 69240Z (2008).
[Crossref]

T. Fujii, Y. Kudo, Y. Ohmura, K. Suzuki, J. Kogo, Y. Mizuno, N. Kita, and M. Sawada, “Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group,” Proc. SPIE 6520, 65204W (2007).
[Crossref]

Krahmer, D.

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

Kudo, Y.

T. Fujii, Y. Kudo, Y. Ohmura, K. Suzuki, J. Kogo, Y. Mizuno, N. Kita, and M. Sawada, “Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group,” Proc. SPIE 6520, 65204W (2007).
[Crossref]

Kye, J.

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, “Polarization aberration analysis in optical lithography systems,” Proc. SPIE 6154, 61540E (2006).
[Crossref]

Kye, J.-W.

G. R. McIntyre, J.-W. Kye, H. J. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Micro. Nanolithogr. MEMS MOEMS 5(3), 033001 (2006).
[Crossref]

Layden, D.

Lee, C. C.

Levinson, H. J.

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, “Polarization aberration analysis in optical lithography systems,” Proc. SPIE 6154, 61540E (2006).
[Crossref]

G. R. McIntyre, J.-W. Kye, H. J. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Micro. Nanolithogr. MEMS MOEMS 5(3), 033001 (2006).
[Crossref]

Li, J.

L. Li, Y. Li, Q. Chi, K. Liu, X. Zhang, and J. Li, “Optimized imaging polarimeter for measuring polarization properties of hyper number aperture lithography tools,” Proc. SPIE 9282, 928232 (2014).
[Crossref]

Li, L.

L. Li, Y. Li, Q. Chi, K. Liu, X. Zhang, and J. Li, “Optimized imaging polarimeter for measuring polarization properties of hyper number aperture lithography tools,” Proc. SPIE 9282, 928232 (2014).
[Crossref]

Li, Y.

L. Li, Y. Li, Q. Chi, K. Liu, X. Zhang, and J. Li, “Optimized imaging polarimeter for measuring polarization properties of hyper number aperture lithography tools,” Proc. SPIE 9282, 928232 (2014).
[Crossref]

Liao, B. H.

Liu, K.

L. Li, Y. Li, Q. Chi, K. Liu, X. Zhang, and J. Li, “Optimized imaging polarimeter for measuring polarization properties of hyper number aperture lithography tools,” Proc. SPIE 9282, 928232 (2014).
[Crossref]

Liu, M. C.

Marienko, V. V.

S. N. Savenkov and V. V. Marienko, “The method of extraction of the Mueller-Jones part out of experimental Mueller matrix,” Proc. SPIE 2982, 226–231 (1997).
[Crossref]

Matsuo, N.

T. Fujii, K. Muramatsu, N. Matsuo, Y. Ohmura, and M. Sawada, “True polarization characteristics of hyper-NA optics excluding impact of measurement system,” Proc. SPIE 7274, 72743K (2009).
[Crossref]

McIntyre, G.

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, “Polarization aberration analysis in optical lithography systems,” Proc. SPIE 6154, 61540E (2006).
[Crossref]

McIntyre, G. R.

G. R. McIntyre, J.-W. Kye, H. J. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Micro. Nanolithogr. MEMS MOEMS 5(3), 033001 (2006).
[Crossref]

Mengel, M.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Mizuno, Y.

T. Fujii, Y. Kudo, Y. Ohmura, K. Suzuki, J. Kogo, Y. Mizuno, N. Kita, and M. Sawada, “Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group,” Proc. SPIE 6520, 65204W (2007).
[Crossref]

Muramatsu, K.

T. Fujii, K. Muramatsu, N. Matsuo, Y. Ohmura, and M. Sawada, “True polarization characteristics of hyper-NA optics excluding impact of measurement system,” Proc. SPIE 7274, 72743K (2009).
[Crossref]

Nakahira, K.

Neureuther, A. R.

G. R. McIntyre, J.-W. Kye, H. J. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Micro. Nanolithogr. MEMS MOEMS 5(3), 033001 (2006).
[Crossref]

Nomura, H.

H. Nomura and I. Higashikawa, “In-situ Mueller matrix polarimetry of projection lenses for 193-nm lithography,” Proc. SPIE 7640, 76400Q (2010).
[Crossref]

H. Nomura and I. Higashikawa, “Mueller matrix polarimetry for immersion lithography tools with a polarization monitoring system at the wafer plane,” Proc. SPIE 7520, 752012 (2009).
[Crossref]

Norihiro, Y.

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, “Polarization aberration analysis in optical lithography systems,” Proc. SPIE 6154, 61540E (2006).
[Crossref]

Ohmura, Y.

T. Fujii, K. Muramatsu, N. Matsuo, Y. Ohmura, and M. Sawada, “True polarization characteristics of hyper-NA optics excluding impact of measurement system,” Proc. SPIE 7274, 72743K (2009).
[Crossref]

T. Fujii, Y. Kudo, Y. Ohmura, K. Suzuki, J. Kogo, Y. Mizuno, N. Kita, and M. Sawada, “Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group,” Proc. SPIE 6520, 65204W (2007).
[Crossref]

Pezzaniti, J. L.

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34(6), 1558–1568 (1995).
[Crossref]

Ruoff, B.

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

Ruoff, J.

J. Ruoff and M. Totzeck, “Orientation Zernike polynomials: a useful way to describe the polarization effects of optical imaging systems,” J. Micro. Nanolithogr. MEMS MOEMS 8(3), 031404 (2009).
[Crossref]

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Savenkov, S. N.

S. N. Savenkov and V. V. Marienko, “The method of extraction of the Mueller-Jones part out of experimental Mueller matrix,” Proc. SPIE 2982, 226–231 (1997).
[Crossref]

Sawada, M.

T. Fujii, K. Muramatsu, N. Matsuo, Y. Ohmura, and M. Sawada, “True polarization characteristics of hyper-NA optics excluding impact of measurement system,” Proc. SPIE 7274, 72743K (2009).
[Crossref]

T. Fujii, J. Kogo, K. Suzuki, and M. Sawada, “Polarization characteristics of state-of-art lithography optics reconstructed from on-body measurement,” Proc. SPIE 6924, 69240Z (2008).
[Crossref]

T. Fujii, Y. Kudo, Y. Ohmura, K. Suzuki, J. Kogo, Y. Mizuno, N. Kita, and M. Sawada, “Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group,” Proc. SPIE 6520, 65204W (2007).
[Crossref]

Schmitt-Weaver, E.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Simon, R.

R. Simon, “The connection between mueller and jones matrices of polarization optics,” Opt. Commun. 42(5), 293–297 (1982).
[Crossref]

Suzuki, K.

T. Fujii, J. Kogo, K. Suzuki, and M. Sawada, “Polarization characteristics of state-of-art lithography optics reconstructed from on-body measurement,” Proc. SPIE 6924, 69240Z (2008).
[Crossref]

T. Fujii, Y. Kudo, Y. Ohmura, K. Suzuki, J. Kogo, Y. Mizuno, N. Kita, and M. Sawada, “Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group,” Proc. SPIE 6520, 65204W (2007).
[Crossref]

Takano, Y.

Totzeck, M.

J. Ruoff and M. Totzeck, “Orientation Zernike polynomials: a useful way to describe the polarization effects of optical imaging systems,” J. Micro. Nanolithogr. MEMS MOEMS 8(3), 031404 (2009).
[Crossref]

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

Twietmeyer, K. M.

Vitkin, I. A.

Wood, M. F. G.

Zhang, X.

L. Li, Y. Li, Q. Chi, K. Liu, X. Zhang, and J. Li, “Optimized imaging polarimeter for measuring polarization properties of hyper number aperture lithography tools,” Proc. SPIE 9282, 928232 (2014).
[Crossref]

Zimmermann, J.

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Appl. Opt. (1)

J. Micro. Nanolithogr. MEMS MOEMS (2)

G. R. McIntyre, J.-W. Kye, H. J. Levinson, and A. R. Neureuther, “Polarization aberrations in hyper-numerical-aperture projection printing: a comparison of various representations,” J. Micro. Nanolithogr. MEMS MOEMS 5(3), 033001 (2006).
[Crossref]

J. Ruoff and M. Totzeck, “Orientation Zernike polynomials: a useful way to describe the polarization effects of optical imaging systems,” J. Micro. Nanolithogr. MEMS MOEMS 8(3), 031404 (2009).
[Crossref]

J. Opt. Soc. Am. (1)

J. J. Gil and E. Bernabeu, “A depolarization criterion in mueller matrices,” J. Opt. Soc. Am. 32(3), 259–261 (1985).

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

R. Simon, “The connection between mueller and jones matrices of polarization optics,” Opt. Commun. 42(5), 293–297 (1982).
[Crossref]

Opt. Eng. (1)

J. L. Pezzaniti and R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34(6), 1558–1568 (1995).
[Crossref]

Opt. Express (2)

Proc. SPIE (10)

M. Totzeck, P. Graupner, T. Heil, A. Gohnermeier, O. Dittmann, D. Krahmer, V. Kamenov, B. Ruoff, and D. Flagello, “How to describe polarization influence on imaging,” Proc. SPIE 5754, 57540 (2005).
[Crossref]

S. N. Savenkov and V. V. Marienko, “The method of extraction of the Mueller-Jones part out of experimental Mueller matrix,” Proc. SPIE 2982, 226–231 (1997).
[Crossref]

H. Nomura and I. Higashikawa, “Mueller matrix polarimetry for immersion lithography tools with a polarization monitoring system at the wafer plane,” Proc. SPIE 7520, 752012 (2009).
[Crossref]

H. Nomura and I. Higashikawa, “In-situ Mueller matrix polarimetry of projection lenses for 193-nm lithography,” Proc. SPIE 7640, 76400Q (2010).
[Crossref]

L. Li, Y. Li, Q. Chi, K. Liu, X. Zhang, and J. Li, “Optimized imaging polarimeter for measuring polarization properties of hyper number aperture lithography tools,” Proc. SPIE 9282, 928232 (2014).
[Crossref]

T. Fujii, J. Kogo, K. Suzuki, and M. Sawada, “Polarization characteristics of state-of-art lithography optics reconstructed from on-body measurement,” Proc. SPIE 6924, 69240Z (2008).
[Crossref]

T. Fujii, K. Muramatsu, N. Matsuo, Y. Ohmura, and M. Sawada, “True polarization characteristics of hyper-NA optics excluding impact of measurement system,” Proc. SPIE 7274, 72743K (2009).
[Crossref]

T. Fujii, Y. Kudo, Y. Ohmura, K. Suzuki, J. Kogo, Y. Mizuno, N. Kita, and M. Sawada, “Polarization properties of state-of-art lithography optics represented by first canonical coordinate of Lie group,” Proc. SPIE 6520, 65204W (2007).
[Crossref]

J. Kye, G. McIntyre, Y. Norihiro, and H. J. Levinson, “Polarization aberration analysis in optical lithography systems,” Proc. SPIE 6154, 61540E (2006).
[Crossref]

B. Geh, J. Ruoff, J. Zimmermann, P. Gräupner, M. Totzeck, M. Mengel, U. Hempelmann, and E. Schmitt-Weaver, “The impact of projection lens polarization properties on lithographic process at hyper-NA,” Proc. SPIE 6520, 65200F (2007).
[Crossref]

Other (2)

G. Strang, Introduction to linear algebra, 4th ed. (Wellesley-Cambridge, 2009), Chap. 9.

D. Juergens, “Projection exposure method, system and objective,” U.S. patent US9036129 (2015).

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Figures (13)

Fig. 1
Fig. 1 Approximate polar decomposition of Jones matrix. A Jones matrix can be approximated decomposed into the product of a scalar transmission factor, a scalar phase factor and three matrices representing a linear polarizer, a rotator and a linear retarder.
Fig. 2
Fig. 2 Pupil maps of the first 18 OZP terms. The maps are arranged according to the M-symmetric properties and are indexed by the Fringe labeling scheme. The colors in these maps represent the maximum changes of transmittance or phase, and the axes indicate the orientations with the maximum transmittance or advanced phase, which are invariant after 180° rotation.
Fig. 3
Fig. 3 Schematic of the Jones pupil metrology system for lithographic projection objectives. P1 and Q1 compose the polarization generator to generate specific incident polarization state, and the exiting polarized state after PO are analyzed by the analyzer composed of Q2 and P2.
Fig. 4
Fig. 4 Typical Platonic solids inscribed inside the Poincaré sphere: (a) Tetrahedron; (b) octahedron; (c) cube; (d) octahedron and cube.
Fig. 5
Fig. 5 Trajectories on the Poincaré sphere of a polarization-state-generator composed of a rotating quarter-wave plate and a fixed polarizer. Rotation angles of polarizer θ are 0° and 45°.
Fig. 6
Fig. 6 Condition number distribution of the polarization generator matrix, with the angular increment of polarizer Δθ and that of quarter-wave plate Δϕ ranging from 0° to 90°. A nonlinear and inversed color scale is used to focus on the minimal (red) condition numbers.
Fig. 7
Fig. 7 Typical m × n polarization states on the Poincaré sphere: (a) 3 × 3 and (b) 4 × 4. Each case corresponds to a discretely rotating polarizer with m equally spaced angles and quarter-wave plate with n equally spaced angles.
Fig. 8
Fig. 8 Condition number distribution of coefficient matrix for conventional dual-rotating-retarder configurations, with the angular increments of two quarter-wave plates Δϕ1 and Δϕ2 ranging from 0° to 90°. Red color indicates desired low values.
Fig. 9
Fig. 9 Comparison of condition number distribution of two dual-rotating configurations: (a) the conventional configuration and (b) the improved configuration. A nonlinear and inversed color scale is used to focus on the minimal (red) condition numbers.
Fig. 10
Fig. 10 Jones pupil extracted from a catadioptric projection lens for a 1.35 NA immersion scanner [21]: (a) schematic of the projection lens; (b) three field points selected from the 26 × 5.5mm image field; (c) diattenuation and (d) retardance pupil of field point F1.
Fig. 11
Fig. 11 Components of the tested Jones pupil: (a) diattenuation pupil and (b) its OZP coefficients; (c) retardance pupil and (d) its OZP coefficients. The colors in D and R pupil represent the maximum changes of transmittance and phase, and the axes in the pupil are bright axes and fast axes, respectively. Blue bars in figures of OZP coefficients represent + jth OZP coefficients, while red bars represent -jth coefficients.
Fig. 12
Fig. 12 Measured Jones pupil on the exit pupil grid by our method: (a) diattenuation pupil and (b) retardance pupil. The coordinates are normalized spatial frequencies ranged from −1 to 1.
Fig. 13
Fig. 13 Errors of the measured Jones pupil: (a) errors of diattenuation amplitude (maximum transmittance deviation); (b) errors of OZP coefficients for diattenuation; (c) errors of retardance amplitude (maximum phase shift) and (d) errors of OZP coefficients for retardance.

Tables (5)

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Table 1 Different types of polarimeter configurations

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Table 2 Comparison between the existing and optimized configurations

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Table 3 Basic error sources in Jones pupil polarimetry

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Table 4 Measurement errors of the conventional and proposed method

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Table 5 Measurement errors of the existing and optimized configurations by the proposed method

Equations (44)

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Jt e iΦ J pol (d,θ) J rot (α) J ret (ϕ,β).
J pol (d,θ)= J rot (θ)[ 1+d 0 0 1d ] J rot (θ),
J rot (α)=[ cosα sinα sinα cosα ],
J ret (ϕ,β)= J rot (β)[ e -iϕ 0 0 e iϕ ] J rot (β).
J pol =I+ j c j O Z j ,
J ret Ii j c j O Z j ,
O Z j =O Z n,ε m (r,φ)= R n m (r) O ε m (φ),
R n m (r)= s=0 (n| m |)/2 (1) s (ns)! s!( n+m 2 s)!( nm 2 s)! r n2s ,
O 0 m (φ)=[ cosmφ sinmφ sinmφ cosmφ ], O 1 m (φ)=[ sinmφ cosmφ cosmφ sinmφ ].
E= P 2 ( θ 2 ) Q 2 ( ϕ 2 )J Q 1 ( ϕ 1 ) P 1 ( θ 1 ) E 0 ,
I( θ 1 , θ 2 , ϕ 1 , ϕ 2 )= E 0 * P 1 ( θ 1 ) * Q 1 ( ϕ 1 ) * J * Q 2 ( ϕ 2 ) * P 2 ( θ 2 ) * P 2 ( θ 2 ) Q 2 ( ϕ 2 )J Q 1 ( ϕ 1 ) P 1 ( θ 1 ) E 0 ,
M( θ 2 , ϕ 2 )= Q 2 ( ϕ 2 ) * P 2 ( θ 2 ) * P 2 ( θ 2 ) Q 2 ( ϕ 2 ),
U( θ 1 , ϕ 1 )= Q 1 ( ϕ 1 ) P 1 ( θ 1 ) E 0 ,
I( θ 1 , θ 2 , ϕ 1 , ϕ 2 )=U ( θ 1 , ϕ 1 ) * J * M( θ 2 , ϕ 2 )JU( θ 1 , ϕ 1 ).
X=vec( J * J)=vec( [ J xx J xx ¯ J xy J xx ¯ J xx J yx ¯ J xy J yx ¯ J yx J xx ¯ J yy J xx ¯ J yx J yx ¯ J yy J yx ¯ J xx J xy ¯ J xy J xy ¯ J xx J yy ¯ J xy J yy ¯ J yx J xy ¯ J yy J xy ¯ J yx J yy ¯ J yy J yy ¯ ] ),
K( θ 1 , θ 2 , ϕ 1 , ϕ 2 )=U ( θ 1 , ϕ 1 ) * M( θ 2 , ϕ 2 )U( θ 1 , ϕ 1 ),
AB=[ a 11 B a 1n B a m1 B a mn B ],
I( θ 1 , θ 2 , ϕ 1 , ϕ 2 )=vec (K ( θ 1 , θ 2 , ϕ 1 , ϕ 2 ) T ) T X,
C=[ K 1,1 K 1,2 K 1,m K 2,1 K 2,2 K 2,m K n,1 K n,2 K n,m ],
I=CX,
X= ( C * C ) 1 C * I,
J xx = X 1 J xy = X 3 ¯ / J xx J yx = X 9 ¯ / J xx J yy = X 11 ¯ / J xx .
trace( M T M)=4 M 11 2 .
J xx = 1 2 M 11 + M 12 + M 21 + M 22 J xy = 1 2 M 11 M 12 + M 21 M 22 ( M 13 + M 23 ) 2 + ( M 14 + M 24 ) 2 [ ( M 13 + M 23 )i( M 14 + M 24 ) ] J yx = 1 2 M 11 + M 12 M 21 M 22 ( M 31 + M 32 ) 2 + ( M 41 + M 42 ) 2 [ ( M 31 + M 32 )+i( M 41 + M 42 ) ] J yy = 1 2 M 11 M 12 M 21 + M 22 ( M 33 + M 44 ) 2 + ( M 43 M 34 ) 2 [ ( M 33 + M 44 )+i( M 43 M 34 ) ] .
ΔX= S true ΔIorΔ X a = i ( S true ) a,i Δ I i ,
Δ X a Δ X b = i,j ( S true ) a,i ( S true ) b,j Δ I i Δ I j ,
Δ X a 2 = i ( S true ) a,i 2 σ i 2 .
ΔX=ΔS I true or Δ X a = i Δ S a,i ( I true ) i
ΔS= ( C true * C true ) 1 ( Δ C * ( Δ C * C true + C true * ΔC ) ( C true * C true ) 1 C true * )
Δ X a Δ X b = i,j Δ S a,i Δ S b,j ( I true ) i ( I true ) j .
A = sup x0 Ax x ,
ΔX S true ΔI and I true C true X true ,
κ(A)= A A + .
ΔX X true κ( C true ) ΔI I true and ΔX X true κ( C true ) ΔS S true ,
G v ( θ 1 , ϕ 1 )= Q 1 ( ϕ 1 ) P v1 ( θ 1 )= Q 1 ( ϕ 1 )[ cos( θ 1 ) sin( θ 1 ) ].
A v ( θ 2 , ϕ 2 )= Q 2 ( ϕ 2 ) * P v2 ( θ 2 )= Q 2 ( ϕ 2 ) * [ cos( θ 2 ) sin( θ 2 ) ].
K( θ 1 , θ 2 , ϕ 1 , ϕ 2 )= G v ( θ 1 , ϕ 1 ) * A v ( θ 2 , ϕ 2 ) A v ( θ 2 , ϕ 2 ) * G v ( θ 1 , ϕ 1 ).
G=[ vec ( ( G v ( θ 11 , ϕ 11 ) G v ( θ 11 , ϕ 11 ) * ) T ) T vec ( ( G v ( θ 12 , ϕ 12 ) G v ( θ 12 , ϕ 12 ) * ) T ) T vec ( ( G v ( θ 1m , ϕ 1m ) G v ( θ 1m , ϕ 1m ) * ) T ) T ],
A=[ vec ( ( A v ( θ 21 , ϕ 21 ) A v ( θ 21 , ϕ 21 ) * ) T ) T vec ( ( A v ( θ 22 , ϕ 22 ) A v ( θ 22 , ϕ 22 ) * ) T ) T vec ( ( A v ( θ 2n , ϕ 2n ) A v ( θ 2n , ϕ 2n ) * ) T ) T ].
κ(C)=κ(A)*κ(G),
Δθ=k* 180 ° /m, m>2, k=1, 2, 3, ... , (m1)/2 Δϕ=l* 90 ° /n, n>1, l=1, 2, 3, ... , n1
Δ θ 1 =k* 180 ° /m, m>2, k=1, 2, 3, ... , (m1)/2 Δ θ 2 =l* 180 ° /n, n>2, l=1, 2, 3, ... , (n1)/2 Δ ϕ 1 =r* 90 ° /p, p>3, r=1, 2, 3, ... , p1 Δ ϕ 2 =s* 90 ° /p, p>3, s=1, 2, 3, ... , p1 rs r+sp ,
P=R(θΔθ)[ e i(δ/2) 0 0 η e i(δ/2) ]R(θ+Δθ),
Q=R(θΔθ)[ e i( π/4+δ/2 ) 0 0 ( 1η ) e i( π/4+δ/2 ) ]R(θ+Δθ),

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