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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE4000, 294–306 (2000).
    [CrossRef]
  2. H. Nomura and T. Sato, “Techniques for measuring aberrations in lenses used in photolithography with printed patterns,” Appl. Opt.38(13), 2800–2807 (1999).
    [CrossRef] [PubMed]
  3. J. Sung, M. Pitchumani, and E. G. Johnson, “Aberration measurement of photolithographic lenses by use of hybrid diffractive photomasks,” Appl. Opt.42(11), 1987–1995 (2003).
    [CrossRef] [PubMed]
  4. F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica1(7-12), 689–704 (1934).
    [CrossRef]
  5. M. Born and E. Wolf, Principles of Optics, 7th Ed. (Pergamon, 1999), chap. 9.
  6. 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. SPIE4346, 394–407 (2001).
    [CrossRef]
  7. T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE5754, 1659–1669 (2004).
    [CrossRef]
  8. J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE6152, 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. Express17(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. Express18(19), 20096–20104 (2010).
    [CrossRef] [PubMed]
  11. H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A217(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. SPIE4691, 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. SPIE3051, 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. SPIE5377, 277–786 (2004).
  16. L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE5754, 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. SPIE6154, 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. B27(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. SPIE7636, 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 MOEMS10(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. IEEE72(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

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 MOEMS10(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

R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE7636, 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. Express18(19), 20096–20104 (2010).
[CrossRef] [PubMed]

2009

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. Express17(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. B27(6), 2927–2930 (2009).
[CrossRef]

2006

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. SPIE6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE6152, 61523D, 61523D-10 (2006).
[CrossRef]

2004

L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE5377, 277–786 (2004).

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE5754, 1728–1737 (2004).
[CrossRef]

T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE5754, 1659–1669 (2004).
[CrossRef]

2003

2002

T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE4691, 33–43 (2002).
[CrossRef]

2001

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. SPIE4346, 394–407 (2001).
[CrossRef]

2000

B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE4000, 294–306 (2000).
[CrossRef]

1999

1997

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

D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE3051, 672–685 (1997).
[CrossRef]

1996

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

A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE72(7), 889–901 (1984).
[CrossRef]

1979

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

1953

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A217(1130), 408–432 (1953).
[CrossRef]

1934

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica1(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. SPIE6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE5754, 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. SPIE5377, 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. SPIE3051, 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. SPIE4346, 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. SPIE6154, 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. SPIE3051, 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. SPIE7636, 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. SPIE6152, 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. SPIE5754, 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. SPIE4691, 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. SPIE5754, 1659–1669 (2004).
[CrossRef]

Hirukawa, S.

T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE4691, 33–43 (2002).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A217(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. SPIE6152, 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. SPIE5377, 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. SPIE3051, 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. SPIE6152, 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. SPIE5754, 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 MOEMS10(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. Express18(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. Express17(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 MOEMS10(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. Express18(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. Express17(21), 19278–19291 (2009).
[CrossRef] [PubMed]

Lohmann, A. W.

A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE72(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. SPIE5754, 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. SPIE5377, 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. SPIE4346, 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. SPIE7636, 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. B27(6), 2927–2930 (2009).
[CrossRef]

Nakashima, T.

T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE4691, 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. SPIE7636, 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. B27(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. SPIE4346, 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. SPIE6154, 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. SPIE3051, 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. SPIE4000, 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. SPIE6154, 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. SPIE5377, 277–786 (2004).

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE5754, 1728–1737 (2004).
[CrossRef]

B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE4000, 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. SPIE4346, 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. SPIE5377, 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. SPIE5754, 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. SPIE6152, 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. SPIE4346, 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. SPIE4346, 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. SPIE6154, 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. SPIE4346, 394–407 (2001).
[CrossRef]

Wirnitzer, B.

A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE72(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. SPIE7636, 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. B27(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. SPIE6154, 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. SPIE5377, 277–786 (2004).

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE5754, 1728–1737 (2004).
[CrossRef]

Zernike, F.

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica1(7-12), 689–704 (1934).
[CrossRef]

Zhang, 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. SPIE6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

Zhou, T. T.

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 MOEMS10(2), 023007 (2011).
[CrossRef]

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. Express17(21), 19278–19291 (2009).
[CrossRef] [PubMed]

Appl. Opt.

Chin. Phys. Lett.

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]

IEEE Signal Process. Mag.

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]

IEEE Trans. Antenn. Propag.

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

J. Micro/Nanolith MEMS MOEMS

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 MOEMS10(2), 023007 (2011).
[CrossRef]

J. Vac. Sci. Technol. B

R. Miyakawa, P. Naulleau, and A. Zakhor, “Iterative procedure for in situ extreme ultraviolet optical testing with an incoherent source,” J. Vac. Sci. Technol. B27(6), 2927–2930 (2009).
[CrossRef]

Opt. Acta (Lond.)

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

Opt. Express

Physica

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica1(7-12), 689–704 (1934).
[CrossRef]

Proc. IEEE

A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE72(7), 889–901 (1984).
[CrossRef]

Proc. R. Soc. London, Ser. A

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A217(1130), 408–432 (1953).
[CrossRef]

Proc. SPIE

R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE7636, 76361K, 76361K-7 (2010).
[CrossRef]

T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE4691, 33–43 (2002).
[CrossRef]

D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE3051, 672–685 (1997).
[CrossRef]

L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE5377, 277–786 (2004).

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE5754, 1728–1737 (2004).
[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. SPIE6154, 61540Y, 61540Y-9 (2006).
[CrossRef]

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. SPIE4346, 394–407 (2001).
[CrossRef]

T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE5754, 1659–1669 (2004).
[CrossRef]

J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE6152, 61523D, 61523D-10 (2006).
[CrossRef]

B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE4000, 294–306 (2000).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics, 7th Ed. (Pergamon, 1999), chap. 9.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

Equations on this page are rendered with MathJax. Learn more.

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 ) | ,

Metrics