Abstract

This paper proposes a technique for in situ measurement of lens aberrations up to the 37th Zernike coefficient in lithographic tools under partial coherent illumination. The technique requires the acquisition and analysis of aerial image intensities of a set of 36 binary gratings with different pitches and orientations. By simplifying the theoretical derivation of the optical imaging under partial coherent illumination, two linear models are proposed in a compact expression with two matrixes, which can be easily obtained in advance by numerical calculation instead of by lithographic simulators, and then used to determine the Zernike coefficients of odd aberration and even aberration respectively. The simulation work conducted by PROLITH has validated the theoretical derivation and confirms that such a technique yields a superior quality of wavefront estimate with an accuracy of Zernike coefficients on the order of 0.1mλs (λ = 193nm) and an accuracy of wavefronts on the order of mλs, due to further considering the influence of the partial coherence factor on pupil sampling. It is fully expected that this technique will simple to implement and will provide a useful practical means for the in-line monitoring of imaging quality of lithographic tools under partial coherent illumination.

©2009 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Iterative method for in situ measurement of lens aberrations in lithographic tools using CTC-based quadratic aberration model

Shiyuan Liu, Shuang Xu, Xiaofei Wu, and Wei Liu
Opt. Express 20(13) 14272-14283 (2012)

Wavefront aberration measurement method for a hyper-NA lithographic projection lens based on principal component analysis of an aerial image

Boer Zhu, Xiangzhao Wang, Sikun Li, Guanyong Yan, Lina Shen, and Lifeng Duan
Appl. Opt. 55(12) 3192-3198 (2016)

References

  • View by:
  • |
  • |
  • |

  1. B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE 4000, 294–306 (2000).
    [Crossref]
  2. 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]
  3. F. Wang, X. Wang, and M. Ma, “Measurement technique for in situ characterizing aberrations of projection optics in lithographic tools,” Appl. Opt. 45(24), 6086–6093 (2006).
    [PubMed]
  4. 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]
  5. F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica 1(7-12), 689–704 (1934).
    [Crossref]
  6. M. Born, and E. Wolf, Principles of Optics, 7th edition, (Pergamon, 1999), chap. 9.
  7. M. Ma, X. Wang, and F. Wang, “Aberration measurement of projection optics in lithographic tools based on two-beam interference theory,” Appl. Opt. 45(32), 8200–8208 (2006).
    [Crossref] [PubMed]
  8. L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2005).
    [Crossref]
  9. M. van de Kerkhof, W. de Boeij, H. Kok, M. Silova, J. Baselmans, and M. Hemerik, “Full optical column characterization of DUV lithographic projection tools,” Proc. SPIE 5377, 1960–1970 (2004).
    [Crossref]
  10. T. Fujii, K. Suzuki, Y. Mizuno, and N. Kita, “Integrated projecting optics tester for inspection of immersion ArF scanner,” Proc. SPIE 6152, 615237 (2006).
    [Crossref]
  11. T. Fujii, J. Kougo, Y. Mizuno, H. Ooki, and M. Hamatani, “Portable phase measuring interferometer using Shack-Hartmann method,” Proc. SPIE 5038, 726–732 (2003).
    [Crossref]
  12. Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberrations of projection optics with hyper-NA,” Proc. SPIE 6154, 615424 (2006).
    [Crossref]
  13. 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 setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
    [Crossref]
  14. Q. Yuan, X. Wang, Z. Qiu, F. Wang, M. Ma, and L. He, “Coma measurement of projection optics in lithographic tools based on relative image displacements at multiple illumination settings,” Opt. Express 15(24), 15878–15885 (2007).
    [Crossref] [PubMed]
  15. Z. Qiu, X. Wang, Q. Yuan, and F. Wang, “Coma measurement by use of an alternating phase-shifting mask mark with a specific phase width,” Appl. Opt. 48(2), 261–269 (2009).
    [Crossref] [PubMed]
  16. Q. Yuan, X. Wang, Z. Qiu, F. Wang, and M. Ma, “Even aberration measurement of lithographic projection system based on optimized phase-shifting marks,” Microelectron. Eng. 86(1), 78–82 (2009).
    [Crossref]
  17. J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D (2006).
    [Crossref]
  18. T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE 5754, 1659–1669 (2005).
    [Crossref]
  19. H. Hopkins, “Canonical coordinates in geometrical and diffraction image theory,” Jpn. J. Appl. Phys. 4, 31–35 (1965).
  20. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. A 217(1130), 408–432 (1953).
    [Crossref]
  21. T. Nakashima, S. D. Slonaker, T. Kudo, and S. Hirukawa, “Evaluation of Zernike sensitivity method for CD distribution,” Proc. SPIE 5040, 1600–1610 (2003).
    [Crossref]

2009 (2)

Z. Qiu, X. Wang, Q. Yuan, and F. Wang, “Coma measurement by use of an alternating phase-shifting mask mark with a specific phase width,” Appl. Opt. 48(2), 261–269 (2009).
[Crossref] [PubMed]

Q. Yuan, X. Wang, Z. Qiu, F. Wang, and M. Ma, “Even aberration measurement of lithographic projection system based on optimized phase-shifting marks,” Microelectron. Eng. 86(1), 78–82 (2009).
[Crossref]

2007 (1)

2006 (5)

Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberrations of projection optics with hyper-NA,” Proc. SPIE 6154, 615424 (2006).
[Crossref]

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

F. Wang, X. Wang, and M. Ma, “Measurement technique for in situ characterizing aberrations of projection optics in lithographic tools,” Appl. Opt. 45(24), 6086–6093 (2006).
[PubMed]

M. Ma, X. Wang, and F. Wang, “Aberration measurement of projection optics in lithographic tools based on two-beam interference theory,” Appl. Opt. 45(32), 8200–8208 (2006).
[Crossref] [PubMed]

T. Fujii, K. Suzuki, Y. Mizuno, and N. Kita, “Integrated projecting optics tester for inspection of immersion ArF scanner,” Proc. SPIE 6152, 615237 (2006).
[Crossref]

2005 (2)

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2005).
[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 (2005).
[Crossref]

2004 (1)

M. van de Kerkhof, W. de Boeij, H. Kok, M. Silova, J. Baselmans, and M. Hemerik, “Full optical column characterization of DUV lithographic projection tools,” Proc. SPIE 5377, 1960–1970 (2004).
[Crossref]

2003 (3)

T. Fujii, J. Kougo, Y. Mizuno, H. Ooki, and M. Hamatani, “Portable phase measuring interferometer using Shack-Hartmann method,” Proc. SPIE 5038, 726–732 (2003).
[Crossref]

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]

T. Nakashima, S. D. Slonaker, T. Kudo, and S. Hirukawa, “Evaluation of Zernike sensitivity method for CD distribution,” Proc. SPIE 5040, 1600–1610 (2003).
[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 setup 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)

1965 (1)

H. Hopkins, “Canonical coordinates in geometrical and diffraction image theory,” Jpn. J. Appl. Phys. 4, 31–35 (1965).

1953 (1)

H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. 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]

Ando, M.

Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberrations of projection optics with hyper-NA,” Proc. SPIE 6154, 615424 (2006).
[Crossref]

Baselmans, J.

M. van de Kerkhof, W. de Boeij, H. Kok, M. Silova, J. Baselmans, and M. Hemerik, “Full optical column characterization of DUV lithographic projection tools,” Proc. SPIE 5377, 1960–1970 (2004).
[Crossref]

Bourov, A.

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2005).
[Crossref]

de Boeij, W.

M. van de Kerkhof, W. de Boeij, H. Kok, M. Silova, J. Baselmans, and M. Hemerik, “Full optical column characterization of DUV lithographic projection tools,” Proc. SPIE 5377, 1960–1970 (2004).
[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 setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[Crossref]

Fujii, T.

T. Fujii, K. Suzuki, Y. Mizuno, and N. Kita, “Integrated projecting optics tester for inspection of immersion ArF scanner,” Proc. SPIE 6152, 615237 (2006).
[Crossref]

T. Fujii, J. Kougo, Y. Mizuno, H. Ooki, and M. Hamatani, “Portable phase measuring interferometer using Shack-Hartmann method,” Proc. SPIE 5038, 726–732 (2003).
[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 (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 (2005).
[Crossref]

Hamatani, M.

T. Fujii, J. Kougo, Y. Mizuno, H. Ooki, and M. Hamatani, “Portable phase measuring interferometer using Shack-Hartmann method,” Proc. SPIE 5038, 726–732 (2003).
[Crossref]

He, L.

Hemerik, M.

M. van de Kerkhof, W. de Boeij, H. Kok, M. Silova, J. Baselmans, and M. Hemerik, “Full optical column characterization of DUV lithographic projection tools,” Proc. SPIE 5377, 1960–1970 (2004).
[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 (2005).
[Crossref]

Hirukawa, S.

T. Nakashima, S. D. Slonaker, T. Kudo, and S. Hirukawa, “Evaluation of Zernike sensitivity method for CD distribution,” Proc. SPIE 5040, 1600–1610 (2003).
[Crossref]

Hopkins, H.

H. Hopkins, “Canonical coordinates in geometrical and diffraction image theory,” Jpn. J. Appl. Phys. 4, 31–35 (1965).

H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. 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 (2006).
[Crossref]

Johnson, E. G.

Kita, N.

T. Fujii, K. Suzuki, Y. Mizuno, and N. Kita, “Integrated projecting optics tester for inspection of immersion ArF scanner,” Proc. SPIE 6152, 615237 (2006).
[Crossref]

Koga, S.

Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberrations of projection optics with hyper-NA,” Proc. SPIE 6154, 615424 (2006).
[Crossref]

Kok, H.

M. van de Kerkhof, W. de Boeij, H. Kok, M. Silova, J. Baselmans, and M. Hemerik, “Full optical column characterization of DUV lithographic projection tools,” Proc. SPIE 5377, 1960–1970 (2004).
[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 (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 (2005).
[Crossref]

Kougo, J.

T. Fujii, J. Kougo, Y. Mizuno, H. Ooki, and M. Hamatani, “Portable phase measuring interferometer using Shack-Hartmann method,” Proc. SPIE 5038, 726–732 (2003).
[Crossref]

Kudo, T.

T. Nakashima, S. D. Slonaker, T. Kudo, and S. Hirukawa, “Evaluation of Zernike sensitivity method for CD distribution,” Proc. SPIE 5040, 1600–1610 (2003).
[Crossref]

Ma, M.

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 (2005).
[Crossref]

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 setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[Crossref]

Mizuno, Y.

T. Fujii, K. Suzuki, Y. Mizuno, and N. Kita, “Integrated projecting optics tester for inspection of immersion ArF scanner,” Proc. SPIE 6152, 615237 (2006).
[Crossref]

T. Fujii, J. Kougo, Y. Mizuno, H. Ooki, and M. Hamatani, “Portable phase measuring interferometer using Shack-Hartmann method,” Proc. SPIE 5038, 726–732 (2003).
[Crossref]

Mori, T.

Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberrations of projection optics with hyper-NA,” Proc. SPIE 6154, 615424 (2006).
[Crossref]

Nakashima, T.

T. Nakashima, S. D. Slonaker, T. Kudo, and S. Hirukawa, “Evaluation of Zernike sensitivity method for CD distribution,” Proc. SPIE 5040, 1600–1610 (2003).
[Crossref]

Nomura, H.

Ohsaki, Y.

Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberrations of projection optics with hyper-NA,” Proc. SPIE 6154, 615424 (2006).
[Crossref]

Ooki, H.

T. Fujii, J. Kougo, Y. Mizuno, H. Ooki, and M. Hamatani, “Portable phase measuring interferometer using Shack-Hartmann method,” Proc. SPIE 5038, 726–732 (2003).
[Crossref]

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 setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[Crossref]

Qiu, Z.

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]

Shiode, Y.

Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberrations of projection optics with hyper-NA,” Proc. SPIE 6154, 615424 (2006).
[Crossref]

Silova, M.

M. van de Kerkhof, W. de Boeij, H. Kok, M. Silova, J. Baselmans, and M. Hemerik, “Full optical column characterization of DUV lithographic projection tools,” Proc. SPIE 5377, 1960–1970 (2004).
[Crossref]

Slonaker, S. D.

T. Nakashima, S. D. Slonaker, T. Kudo, and S. Hirukawa, “Evaluation of Zernike sensitivity method for CD distribution,” Proc. SPIE 5040, 1600–1610 (2003).
[Crossref]

Smith, B. W.

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2005).
[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 setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[Crossref]

Sung, J.

Suzuki, K.

T. Fujii, K. Suzuki, Y. Mizuno, and N. Kita, “Integrated projecting optics tester for inspection of immersion ArF scanner,” Proc. SPIE 6152, 615237 (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 (2005).
[Crossref]

Tezuka, T.

Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberrations of projection optics with hyper-NA,” Proc. SPIE 6154, 615424 (2006).
[Crossref]

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 (2006).
[Crossref]

van de Kerkhof, M.

M. van de Kerkhof, W. de Boeij, H. Kok, M. Silova, J. Baselmans, and M. Hemerik, “Full optical column characterization of DUV lithographic projection tools,” Proc. SPIE 5377, 1960–1970 (2004).
[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 setup 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 setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[Crossref]

Wang, F.

Wang, X.

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 setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[Crossref]

Yamamoto, K.

Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberrations of projection optics with hyper-NA,” Proc. SPIE 6154, 615424 (2006).
[Crossref]

Yuan, Q.

Zavyalova, L.

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2005).
[Crossref]

Zernike, F.

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

Appl. Opt. (5)

Jpn. J. Appl. Phys. (1)

H. Hopkins, “Canonical coordinates in geometrical and diffraction image theory,” Jpn. J. Appl. Phys. 4, 31–35 (1965).

Microelectron. Eng. (1)

Q. Yuan, X. Wang, Z. Qiu, F. Wang, and M. Ma, “Even aberration measurement of lithographic projection system based on optimized phase-shifting marks,” Microelectron. Eng. 86(1), 78–82 (2009).
[Crossref]

Opt. Express (1)

Physica (1)

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

Proc. R. Soc. A (1)

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

Proc. SPIE (10)

T. Nakashima, S. D. Slonaker, T. Kudo, and S. Hirukawa, “Evaluation of Zernike sensitivity method for CD distribution,” Proc. SPIE 5040, 1600–1610 (2003).
[Crossref]

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

J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D (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 (2005).
[Crossref]

L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2005).
[Crossref]

M. van de Kerkhof, W. de Boeij, H. Kok, M. Silova, J. Baselmans, and M. Hemerik, “Full optical column characterization of DUV lithographic projection tools,” Proc. SPIE 5377, 1960–1970 (2004).
[Crossref]

T. Fujii, K. Suzuki, Y. Mizuno, and N. Kita, “Integrated projecting optics tester for inspection of immersion ArF scanner,” Proc. SPIE 6152, 615237 (2006).
[Crossref]

T. Fujii, J. Kougo, Y. Mizuno, H. Ooki, and M. Hamatani, “Portable phase measuring interferometer using Shack-Hartmann method,” Proc. SPIE 5038, 726–732 (2003).
[Crossref]

Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberrations of projection optics with hyper-NA,” Proc. SPIE 6154, 615424 (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 setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[Crossref]

Other (1)

M. Born, and E. Wolf, Principles of Optics, 7th edition, (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 Imaging of a binary grating object in a lithographic tool.
Fig. 2
Fig. 2 The impact of aberrations on imaging.
Fig. 3
Fig. 3 Representation of the integral region S(σ).
Fig. 4
Fig. 4 Estimate of aberration errors with lateral metrology error of 1nm and axial metrology error of 5nm.
Fig. 5
Fig. 5 Input values of aberrated wavefront for simulation.
Fig. 6
Fig. 6 Correlation plots between simulated and calculated shifts for all the input aberrated wavefronts under σ = 0.31. (a) Plot of predicted phase shifts versus simulated phase shifts. (b) Plot of predicted axial shifts versus simulated axial shifts. Each of (a) and (b) contains 180 dots corresponding to 5 sets of 36 linear equations.
Fig. 7
Fig. 7 Simulation result of Z37 AIS technique at multiple partial coherences for the Input Aberration 1.
Fig. 8
Fig. 8 Simulation result of the proposed technique at partial coherence 0.31 for the Input Aberration 1.
Fig. 9
Fig. 9 Simulation result of the measurement errors of Zernike coefficients for all the input aberrated wavefronts.
Fig. 10
Fig. 10 Agreement between the input and measured aberrated wavefronts.
Fig. 11
Fig. 11 Different representation of the Input Aberration 5.
Fig. 12
Fig. 12 Measured results of Zernike coefficients up to different orders.

Equations (39)

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

O(ρ)=12sinc(ρ2ρm)l=+δ(ρlρm),   lZ,
I(ρm,θm,σ,h)=12π[TCC(0,0;αm,βm;σ,h)+TCC(αm,βm;0,0;σ,h)],
αm=ρmcosθm,   βm=ρmsinθm.
TCC(f,g;f,g;σ,h)=+J(fc,gc,σ)H(f+fc,g+gc,h)H(f+fc,g+gc,h)dfcdgc.
J(fc,gc,σ)=1πσ2circ(fc2+gc2σ).
H(f,g,h)=exp[jkW(f,g,h)]circ(f2+g2),
W(f,g,h)=Wlens(f,g)+Wdefocus(f,g,h),
Wlens(f,g)=Wodd(f,g)+Weven(f,g),
Wdefocus(f,g,h)=hwdefocus(f,g)=h[1NA2(f2+g2)1],
φ(ρm,θm,σ,h)=arctan(Im[I(ρm,θm,σ,h)]Re[I(ρm,θm,σ,h)]),
|I(ρm,θm,σ,h)|=Re2[I(ρm,θm,σ,h)]+Im2[I(ρm,θm,σ,h)].
Re[I(ρm,θm,σ,h)]=1(πσ)2S(σ)cos{k[Wodd(αm+fc,βm+gc)Wodd(fc,gc)]}                                                                         ×cos{k[Weven(αm+fc,βm+gc)Weven(fc,gc)                           ,                                                                         +hwdefocus(αm+fc,βm+gc)hwdefocus(fc,gc)]}dfcdgc
Im[I(ρm,θm,σ,h)]=1(πσ)2S(σ)sin{k[Wodd(αm+fc,βm+gc)Wodd(fc,gc)]}                                                                         ×cos{k[Weven(αm+fc,βm+gc)Weven(fc,gc)                             ,                                                                         +hwdefocus(αm+fc,βm+gc)hwdefocus(fc,gc)]}dfcdgc
W(f,g,h)~0,cos[kW(f,g,h)]~1,tan[kW(f,g,h)]~sin[kW(f,g,h)]~kW(f,g,h).
φ(ρm,θm,σ)=kS(σ)[Wodd(αm+fc,βm+gc)Wodd(fc,gc)]dfcdgc.
|I(ρm,θm,σ,h)|h=0.
D(ρm,θm,σ)=S(σ)[Weven(αm+fc,βm+gc)Weven(fc,gc)]   ×[wdefocus(fc,gc)wdefocus(αm+fc,βm+gc)]dfcdgcS(σ)[wdefocus(fc,gc)wdefocus(αm+fc,βm+gc)]2dfcdgc.
φ(ρm,θm,σ)=n_oddZn_oddFn_odd(ρm,θm,σ),
D(ρm,θm,σ)=n_evenZn_evenGn_even(ρm,θm,σ),
Fn_odd(ρm,θm,σ)=kS(σ)[Rn_odd(αm+fc,βm+gc)Rn_odd(fc,gc)]dfcdgc,
Gn_even(ρm,θm,σ)=S(σ)[Rn_even(αm+fc,βm+gc)Rn_even(fc,gc)]×[wdefocus(fc,gc)wdefocus(αm+fc,βm+gc)]dfcdgcS(σ)[wdefocus(fc,gc)wdefocus(αm+fc,βm+gc)]2dfcdgc.
[φ(ρ1,θ1,σ)φ(ρ2,θ2,σ)φ(ρ36,θ36,σ)]=[F2(ρ1,θ1,σ)F3(ρ1,θ1,σ)F35(ρ1,θ1,σ)F2(ρ2,θ2,σ)F3(ρ2,θ2,σ)F35(ρ2,θ2,σ)F2(ρ36,θ36,σ)F3(ρ36,θ36,σ)F35(ρ36,θ36,σ)][Z2Z3Z35],
[D(ρ1,θ1,σ)D(ρ2,θ2,σ)D(ρ36,θ36,σ)]=[G4(ρ1,θ1,σ)G5(ρ1,θ1,σ)G37(ρ1,θ1,σ)G4(ρ2,θ2,σ)G5(ρ2,θ2,σ)G37(ρ2,θ2,σ)G4(ρ36,θ36,σ)G5(ρ36,θ36,σ)G37(ρ36,θ36,σ)][Z4Z5Z37].
Φ=FZodd,
D=GZeven,
ΔΦ=FΔZodd,
ΔD=GΔZeven,
Δφm=2πTmΔx,
cos{k[Wodd(αm+fc,βm+gc)Wodd(fc,gc)]}1,
cos{k[Weven(αm+fc,βm+gc)Weven(fc,gc)]}1,
arctan{kS(σ)[Wodd(αm+fc,βm+gc)Wodd(fc,gc)]dfcdgc}kS(σ)[Wodd(αm+fc,βm+gc)Wodd(fc,gc)]dfcdgc,
sin{k[Wodd(αm+fc,βm+gc)Wodd(fc,gc)]}k[Wodd(αm+fc,βm+gc)Wodd(fc,gc)].
φ(ρm,θm,σ)=kS(σ)[Wodd(αm+fc,βm+gc)Wodd(fc,gc)]dfcdgc.
sin{k[Wodd(αm+fc,βm+gc)Wodd(fc,gc)]}0,
sin{k[Weven(αm+fc,βm+gc)Weven(fc,gc)+hwdefocus(αm+fc,βm+gc)hwdefocus(fc,gc)]}k[Weven(αm+fc,βm+gc)Weven(fc,gc)+hwdefocus(αm+fc,βm+gc)hwdefocus(fc,gc)]   .
|I(ρm,θm,σ,h)|=1(πσ)2S(σ)cos{k[Weven(αm+fc,βm+gc)Weven(fc,gc)                                                               +hwdefocus(αm+fc,βm+gc)hwdefocus(fc,gc)]}dfcdgc.
|I(ρm,θm,σ,h)|h=k(πσ)2S(σ)sin{k[Weven(αm+fc,βm+gc)Weven(fc,gc)                                                                      +hwdefocus(αm+fc,βm+gc)hwdefocus(fc,gc)]}                                                                       ×[wdefocus(αm+fc,βm+gc)wdefocus(fc,gc)]dfcdgc=0.
S(σ)[Weven(αm+fc,βm+gc)Weven(fc,gc)+hwdefocus(αm+fc,βm+gc)hwdefocus(fc,gc)]   ×[wdefocus(αm+fc,βm+gc)wdefocus(fc,gc)]dfcdgc=0.
D(ρm,θm,σ)=S(σ)[Weven(αm+fc,βm+gc)Weven(fc,gc)]   ×[wdefocus(fc,gc)wdefocus(αm+fc,βm+gc)]dfcdgcS(σ)[wdefocus(fc,gc)wdefocus(αm+fc,βm+gc)]2dfcdgc.

Metrics