Abstract

This paper proposes an iterative method for in situ lens aberration measurement in lithographic tools based on a quadratic aberration model (QAM) that is a natural extension of the linear model formed by taking into account interactions among individual Zernike coefficients. By introducing a generalized operator named cross triple correlation (CTC), the quadratic model can be calculated very quickly and accurately with the help of fast Fourier transform (FFT). The Zernike coefficients up to the 37th order or even higher are determined by solving an inverse problem through an iterative procedure from several through-focus aerial images of a specially designed mask pattern. The simulation work has validated the theoretical derivation and confirms that such a method is simple to implement and yields a superior quality of wavefront estimate, particularly for the case when the aberrations are relatively large. It is fully expected that this method will provide a useful practical means for the in-line monitoring of the imaging quality of lithographic tools.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
  7. T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE 5754, 1659–1669 (2004).
    [CrossRef]
  8. J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D, 61523D-10 (2006).
    [CrossRef]
  9. W. Liu, S. Y. Liu, T. T. Zhou, and L. J. Wang, “Aerial image based technique for measurement of lens aberrations up to 37th Zernike coefficient in lithographic tools under partial coherent illumination,” Opt. Express 17(21), 19278–19291 (2009).
    [CrossRef] [PubMed]
  10. W. Liu, S. Y. Liu, T. L. Shi, and Z. R. Tang, “Generalized formulations for aerial image based lens aberration metrology in lithographic tools with arbitrarily shaped illumination sources,” Opt. Express 18(19), 20096–20104 (2010).
    [CrossRef] [PubMed]
  11. H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217(1130), 408–432 (1953).
    [CrossRef]
  12. B. E. A. Saleh, “Optical bilinear transformations: general properties,” Opt. Acta (Lond.) 26, 777–799 (1979).
    [CrossRef]
  13. T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE 4691, 33–43 (2002).
    [CrossRef]
  14. D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE 3051, 672–685 (1997).
    [CrossRef]
  15. L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE 5377, 277–786 (2004).
  16. L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2004).
    [CrossRef]
  17. L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006).
    [CrossRef]
  18. R. Miyakawa, P. Naulleau, and A. Zakhor, “Iterative procedure for in situ extreme ultraviolet optical testing with an incoherent source,” J. Vac. Sci. Technol. B 27(6), 2927–2930 (2009).
    [CrossRef]
  19. R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE 7636, 76361K, 76361K-7 (2010).
    [CrossRef]
  20. S. Y. Liu, W. Liu, and T. T. Zhou, “ Fast algorithm for quadratic aberration model in optical lithography based on cross triple correlation,” J. Micro/Nanolith MEMS MOEMS 10(2), 023007 (2011).
    [CrossRef]
  21. S. Y. Liu, W. Liu, and X. F. Wu, “Fast evaluation of aberration-induced intensity distribution in partially coherent imaging systems by cross triple correlation,” Chin. Phys. Lett. 28(10), 104212 (2011).
    [CrossRef]
  22. A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE 72(7), 889–901 (1984).
    [CrossRef]
  23. K. S. Tang, K. F. Man, S. Kwong, and Q. He, “Genetic algorithms and their applications,” IEEE Signal Process. Mag. 13(6), 22–37 (1996).
    [CrossRef]
  24. D. S. Weile and E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antenn. Propag. 45(3), 343–353 (1997).
    [CrossRef]

2011 (2)

S. Y. Liu, W. Liu, and T. T. Zhou, “ Fast algorithm for quadratic aberration model in optical lithography based on cross triple correlation,” J. Micro/Nanolith MEMS MOEMS 10(2), 023007 (2011).
[CrossRef]

S. Y. Liu, W. Liu, and X. F. Wu, “Fast evaluation of aberration-induced intensity distribution in partially coherent imaging systems by cross triple correlation,” Chin. Phys. Lett. 28(10), 104212 (2011).
[CrossRef]

2010 (2)

R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE 7636, 76361K, 76361K-7 (2010).
[CrossRef]

W. Liu, S. Y. Liu, T. L. Shi, and Z. R. Tang, “Generalized formulations for aerial image based lens aberration metrology in lithographic tools with arbitrarily shaped illumination sources,” Opt. Express 18(19), 20096–20104 (2010).
[CrossRef] [PubMed]

2009 (2)

W. Liu, S. Y. Liu, T. T. Zhou, and L. J. Wang, “Aerial image based technique for measurement of lens aberrations up to 37th Zernike coefficient in lithographic tools under partial coherent illumination,” Opt. Express 17(21), 19278–19291 (2009).
[CrossRef] [PubMed]

R. Miyakawa, P. Naulleau, and A. Zakhor, “Iterative procedure for in situ extreme ultraviolet optical testing with an incoherent source,” J. Vac. Sci. Technol. B 27(6), 2927–2930 (2009).
[CrossRef]

2006 (2)

J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D, 61523D-10 (2006).
[CrossRef]

L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

2004 (3)

L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE 5377, 277–786 (2004).

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2004).
[CrossRef]

T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE 5754, 1659–1669 (2004).
[CrossRef]

2003 (1)

2002 (1)

T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE 4691, 33–43 (2002).
[CrossRef]

2001 (1)

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

2000 (1)

B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE 4000, 294–306 (2000).
[CrossRef]

1999 (1)

1997 (2)

D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE 3051, 672–685 (1997).
[CrossRef]

D. S. Weile and E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antenn. Propag. 45(3), 343–353 (1997).
[CrossRef]

1996 (1)

K. S. Tang, K. F. Man, S. Kwong, and Q. He, “Genetic algorithms and their applications,” IEEE Signal Process. Mag. 13(6), 22–37 (1996).
[CrossRef]

1984 (1)

A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE 72(7), 889–901 (1984).
[CrossRef]

1979 (1)

B. E. A. Saleh, “Optical bilinear transformations: general properties,” Opt. Acta (Lond.) 26, 777–799 (1979).
[CrossRef]

1953 (1)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217(1130), 408–432 (1953).
[CrossRef]

1934 (1)

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica 1(7-12), 689–704 (1934).
[CrossRef]

Bourov, A.

L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2004).
[CrossRef]

Cashmore, J.

L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE 5377, 277–786 (2004).

Davies, G.

D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE 3051, 672–685 (1997).
[CrossRef]

Dierichs, M.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

Flagello, D. G.

L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE 3051, 672–685 (1997).
[CrossRef]

Goldberg, K.

R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE 7636, 76361K, 76361K-7 (2010).
[CrossRef]

Hagiwara, T.

J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D, 61523D-10 (2006).
[CrossRef]

T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE 5754, 1659–1669 (2004).
[CrossRef]

He, Q.

K. S. Tang, K. F. Man, S. Kwong, and Q. He, “Genetic algorithms and their applications,” IEEE Signal Process. Mag. 13(6), 22–37 (1996).
[CrossRef]

Higashi, K.

T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE 4691, 33–43 (2002).
[CrossRef]

Hiroshi, I.

T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE 5754, 1659–1669 (2004).
[CrossRef]

Hirukawa, S.

T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE 4691, 33–43 (2002).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217(1130), 408–432 (1953).
[CrossRef]

Irihama, H.

J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D, 61523D-10 (2006).
[CrossRef]

Itani, T.

L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE 5377, 277–786 (2004).

Johnson, E. G.

Klerk, J.

D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE 3051, 672–685 (1997).
[CrossRef]

Kondo, N.

J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D, 61523D-10 (2006).
[CrossRef]

T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE 5754, 1659–1669 (2004).
[CrossRef]

Kwong, S.

K. S. Tang, K. F. Man, S. Kwong, and Q. He, “Genetic algorithms and their applications,” IEEE Signal Process. Mag. 13(6), 22–37 (1996).
[CrossRef]

Liu, S. Y.

S. Y. Liu, W. Liu, and X. F. Wu, “Fast evaluation of aberration-induced intensity distribution in partially coherent imaging systems by cross triple correlation,” Chin. Phys. Lett. 28(10), 104212 (2011).
[CrossRef]

S. Y. Liu, W. Liu, and T. T. Zhou, “ Fast algorithm for quadratic aberration model in optical lithography based on cross triple correlation,” J. Micro/Nanolith MEMS MOEMS 10(2), 023007 (2011).
[CrossRef]

W. Liu, S. Y. Liu, T. L. Shi, and Z. R. Tang, “Generalized formulations for aerial image based lens aberration metrology in lithographic tools with arbitrarily shaped illumination sources,” Opt. Express 18(19), 20096–20104 (2010).
[CrossRef] [PubMed]

W. Liu, S. Y. Liu, T. T. Zhou, and L. J. Wang, “Aerial image based technique for measurement of lens aberrations up to 37th Zernike coefficient in lithographic tools under partial coherent illumination,” Opt. Express 17(21), 19278–19291 (2009).
[CrossRef] [PubMed]

Liu, W.

S. Y. Liu, W. Liu, and T. T. Zhou, “ Fast algorithm for quadratic aberration model in optical lithography based on cross triple correlation,” J. Micro/Nanolith MEMS MOEMS 10(2), 023007 (2011).
[CrossRef]

S. Y. Liu, W. Liu, and X. F. Wu, “Fast evaluation of aberration-induced intensity distribution in partially coherent imaging systems by cross triple correlation,” Chin. Phys. Lett. 28(10), 104212 (2011).
[CrossRef]

W. Liu, S. Y. Liu, T. L. Shi, and Z. R. Tang, “Generalized formulations for aerial image based lens aberration metrology in lithographic tools with arbitrarily shaped illumination sources,” Opt. Express 18(19), 20096–20104 (2010).
[CrossRef] [PubMed]

W. Liu, S. Y. Liu, T. T. Zhou, and L. J. Wang, “Aerial image based technique for measurement of lens aberrations up to 37th Zernike coefficient in lithographic tools under partial coherent illumination,” Opt. Express 17(21), 19278–19291 (2009).
[CrossRef] [PubMed]

Lohmann, A. W.

A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE 72(7), 889–901 (1984).
[CrossRef]

Magome, N.

T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE 5754, 1659–1669 (2004).
[CrossRef]

Man, K. F.

K. S. Tang, K. F. Man, S. Kwong, and Q. He, “Genetic algorithms and their applications,” IEEE Signal Process. Mag. 13(6), 22–37 (1996).
[CrossRef]

Matsuura, S.

L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE 5377, 277–786 (2004).

McCoo, E.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

Michielssen, E.

D. S. Weile and E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antenn. Propag. 45(3), 343–353 (1997).
[CrossRef]

Miyakawa, R.

R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE 7636, 76361K, 76361K-7 (2010).
[CrossRef]

R. Miyakawa, P. Naulleau, and A. Zakhor, “Iterative procedure for in situ extreme ultraviolet optical testing with an incoherent source,” J. Vac. Sci. Technol. B 27(6), 2927–2930 (2009).
[CrossRef]

Nakashima, T.

T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE 4691, 33–43 (2002).
[CrossRef]

Naulleau, P.

R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE 7636, 76361K, 76361K-7 (2010).
[CrossRef]

R. Miyakawa, P. Naulleau, and A. Zakhor, “Iterative procedure for in situ extreme ultraviolet optical testing with an incoherent source,” J. Vac. Sci. Technol. B 27(6), 2927–2930 (2009).
[CrossRef]

Nomura, H.

Pitchumani, M.

Pongers, R.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

Reynolds, P.

L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

Rogoff, R.

D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE 3051, 672–685 (1997).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh, “Optical bilinear transformations: general properties,” Opt. Acta (Lond.) 26, 777–799 (1979).
[CrossRef]

Sato, T.

Schlief, R.

B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE 4000, 294–306 (2000).
[CrossRef]

Shi, T. L.

Smith, B. W.

L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE 5377, 277–786 (2004).

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2004).
[CrossRef]

B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE 4000, 294–306 (2000).
[CrossRef]

Stoffels, F.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

Suganaga, T.

L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE 5377, 277–786 (2004).

Sung, J.

Suzuki, K.

T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE 5754, 1659–1669 (2004).
[CrossRef]

Tang, K. S.

K. S. Tang, K. F. Man, S. Kwong, and Q. He, “Genetic algorithms and their applications,” IEEE Signal Process. Mag. 13(6), 22–37 (1996).
[CrossRef]

Tang, Z. R.

Tyminski, J. K.

J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D, 61523D-10 (2006).
[CrossRef]

van der Laan, H.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

van Greevenbroek, H.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

Vellanki, V.

L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

Wang, L. J.

Weile, D. S.

D. S. Weile and E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antenn. Propag. 45(3), 343–353 (1997).
[CrossRef]

Willekers, R.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

Wirnitzer, B.

A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE 72(7), 889–901 (1984).
[CrossRef]

Wu, X. F.

S. Y. Liu, W. Liu, and X. F. Wu, “Fast evaluation of aberration-induced intensity distribution in partially coherent imaging systems by cross triple correlation,” Chin. Phys. Lett. 28(10), 104212 (2011).
[CrossRef]

Zakhor, A.

R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE 7636, 76361K, 76361K-7 (2010).
[CrossRef]

R. Miyakawa, P. Naulleau, and A. Zakhor, “Iterative procedure for in situ extreme ultraviolet optical testing with an incoherent source,” J. Vac. Sci. Technol. B 27(6), 2927–2930 (2009).
[CrossRef]

Zavyalova, L.

L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2004).
[CrossRef]

L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE 5377, 277–786 (2004).

Zernike, F.

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica 1(7-12), 689–704 (1934).
[CrossRef]

Zhang, G.

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Figures (12)

Fig. 1
Fig. 1

Optical lithography imaging system.

Fig. 2
Fig. 2

Forward modeling and inverse problem for aberration measurement.

Fig. 3
Fig. 3

The flowchart of the aberration measurement using the CTC-based quadratic aberration model. The Zernike coefficients are extracted by the regression algorithm from the experimental through-focus aerial images.

Fig. 4
Fig. 4

Input values of aberrated wavefront for simulation.

Fig. 5
Fig. 5

The specially designed binary mask pattern for aberration measurement.

Fig. 6
Fig. 6

The linear image terms of the mask pattern shown in Fig. 5 for Z6, Z7, Z8, and Z9.

Fig. 7
Fig. 7

The quadratic image terms of the mask pattern shown in Fig. 5 for intercross between pairs of Z6, Z7, Z8, and Z9.

Fig. 8
Fig. 8

Simulation results of the mask pattern shown in Fig. 5 for the Input Aberration 1 under the input parameters: NA = 0.75, λ = 193 nm, σoutin/degree = 0.8/0.4/45°, and defocus = 0 nm.

Fig. 9
Fig. 9

Simulation result of aberration measurement for Zernike coefficients up to 37th order for the Input Aberration 1.

Fig. 10
Fig. 10

Simulation result of the measurement errors of Zernike coefficients for all the input aberrated wavefronts.

Fig. 11
Fig. 11

Agreement between the input and measured aberrated wavefronts.

Fig. 12
Fig. 12

Measurement accuracy by using the proposed quadratic model and the simplified linear model.

Equations (15)

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I(x)= O( f 1 ) O ( f 2 )TCC( f 1 , f 2 )exp[ 2πi( f 1 f 2 )x ]d f 1 d f 2 ,
TCC( f 1 , f 2 )= J(f)H(f+ f 1 ) H (f+ f 2 )df .
H(f)=P(f)exp[ ik n Z n R n (f) ],
P(f)=circ( | f | )exp[ ik W defocus (f) ],
W defocus (f)=h w defocus (f)=h[ 1N A 2 | f | 2 1 ],
I(x) I 0 (x)+ I 1 (x)+ I 2 (x)= I 0 (x)+ n Z n I lin (n) (x) + n m Z n Z m I quad (n,m) (x) ,
I 0 (x)= O( f 1 ) O ( f 2 ) T 0 ( f 1 , f 2 )exp[ 2πi( f 1 f 2 )x ]d f 1 d f 2 ,
I lin (n) (x)= O( f 1 ) O ( f 2 ) T lin (n) ( f 1 , f 2 )exp[ 2πi( f 1 f 2 )x ]d f 1 d f 2 ,
I quad (n,m) (x)= O( f 1 ) O ( f 2 ) T quad (n,m) exp[ 2πi( f 1 f 2 )x ]d f 1 d f 2 .
T 0 ( f 1 , f 2 )= C 0,0;0,0 ( f 1 , f 2 ),
T lin (n) ( f 1 , f 2 )=ik[ C n,0;0,0 ( f 1 , f 2 ) C 0,0;n,0 ( f 1 , f 2 ) ],
T quad (n,m) ( f 1 , f 2 )= 1 2 k 2 [ C n,m;0,0 ( f 1 , f 2 ) C n,0;m,0 ( f 1 , f 2 ) C m,0;n,0 ( f 1 , f 2 )+ C 0,0;n,m ( f 1 , f 2 ) ],
C k,l;m,n ( f 1 , f 2 )= J(f) { P(f+ f 1 )[ R k (f+ f 1 ) R l (f+ f 1 ) ] }{ P (f+ f 2 )[ R m (f+ f 2 ) R n (f+ f 2 ) ] }df.
CTC( f 1 , f 2 )= a(f)b(f+ f 1 )c(f+ f 2 )df ,
Z ^ =arg min Z k=1 N h | I m ( h k ) (x)T{Z} | =arg min Z k=1 N h i=1 N x j=1 N y | I m ( h k ) ( x i , y j ) I c ( h k ) ( x i , y j ) | ,

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