Abstract

In the current optical lithography processes for semiconductor manufacturing, differently shaped illumination sources have been widely used for the need of stringent critical dimension control. This paper proposes a technique for in situ measurement of lens aberrations with generalized formulations of odd and even aberration sensitivities suitable for arbitrarily shaped illumination sources. With a set of Zernike orders, these aberration sensitivities can be treated as a set of analytical kernels which succeed in constructing a sensitivity function space. The analytical kernels reveal the physical essence of partially coherent imaging systems by taking into account the interaction between the wavefront aberration and the illumination source, and take the advantage of realizing a linear and analytical relationship between the Zernike coefficients to be measured and the measurable physical signals. A variety of mainstream illumination sources with spatially variable intensity distributions were input into the PROLITH for the simulation work, which demonstrates and confirms that the generalized formulations are suitable for measuring lens aberrations up to a high order Zernike coefficient under different types of source distributions. The technique is simple to implement and will have potential applications in the in-line monitoring of imaging quality of current lithographic tools.

© 2010 OSA

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References

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    [CrossRef]
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    [CrossRef]
  7. F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica 1(7-12), 689–704 (1934).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D (2006).
    [CrossRef]
  14. 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]
  15. W. Liu, S. Liu, T. Zhou, and L. 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]
  16. A. K. Wong, Resolution Enhancement Techniques, (SPIE Press, 2001).
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    [CrossRef]
  18. M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
    [CrossRef]
  19. A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
    [CrossRef]
  20. Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005).
    [CrossRef]
  21. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. A 217(1130), 408–432 (1953).
    [CrossRef]

2009 (6)

Z. Qiu, X. Wang, Q. Bi, Q. Yuan, B. Peng, and L. Duan, “Translational-symmetry alternating phase shifting mask grating mark used in a linear measurement model of lithographic projection lens aberrations,” Appl. Opt. 48(19), 3654–3663 (2009).
[CrossRef] [PubMed]

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]

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[CrossRef]

A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
[CrossRef]

W. Liu, S. Liu, T. Zhou, and L. 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]

2007 (1)

2006 (2)

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]

2005 (3)

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]

Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005).
[CrossRef]

2004 (1)

F. Schellenberg, “Resolution enhancement technology: The past, the present, and extensions for the future,” Proc. SPIE 5377, 1–20 (2004).
[CrossRef]

2003 (1)

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 (2)

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

H. Nomura, K. Tawarayama, and T. Kohno, “Aberration measurement from specific photolithographic images: a different approach,” Appl. Opt. 39(7), 1136–1147 (2000).
[CrossRef]

1999 (1)

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]

Adam, K.

Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005).
[CrossRef]

Bi, Q.

Bouchoms, I.

A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
[CrossRef]

Bouma, A.

A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
[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]

Degünther, M.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[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]

Duan, L.

Eisenmenger, J.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[CrossRef]

Engelen, A.

A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
[CrossRef]

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[CrossRef]

Granik, Y.

Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005).
[CrossRef]

Gronlund, K.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[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]

Hansen, S.

A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
[CrossRef]

He, L.

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]

Hopkins, H.

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

Hsu, S.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[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.

Jürgens, D.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[CrossRef]

Kazinczi, R.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[CrossRef]

Kohno, T.

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]

Liu, S.

Liu, W.

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]

Major, A.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[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]

Mulder, M.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[CrossRef]

A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
[CrossRef]

Ngai, A.

A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
[CrossRef]

Nomura, H.

Noordman, O.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[CrossRef]

Patra, M.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[CrossRef]

Peng, B.

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.

Schellenberg, F.

F. Schellenberg, “Resolution enhancement technology: The past, the present, and extensions for the future,” Proc. SPIE 5377, 1–20 (2004).
[CrossRef]

Schlief, R.

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

Streutker, G.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[CrossRef]

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 (2005).
[CrossRef]

Tawarayama, K.

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 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 Drieenhuizen, B.

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[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]

van Veen, M.

A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
[CrossRef]

Wang, F.

Wang, L.

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]

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]

Zhou, T.

Zimmermann, J.

A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
[CrossRef]

Appl. Opt. (6)

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 (2)

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 (9)

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]

F. Schellenberg, “Resolution enhancement technology: The past, the present, and extensions for the future,” Proc. SPIE 5377, 1–20 (2004).
[CrossRef]

M. Mulder, A. Engelen, O. Noordman, R. Kazinczi, G. Streutker, B. van Drieenhuizen, S. Hsu, K. Gronlund, M. Degünther, D. Jürgens, J. Eisenmenger, M. Patra, and A. Major, “Performance of a programmable illuminator for generation of freeform sources on high NA immersion systems,” Proc. SPIE 7520, 75200Y (2009).
[CrossRef]

A. Engelen, M. Mulder, I. Bouchoms, S. Hansen, A. Bouma, A. Ngai, M. van Veen, and J. Zimmermann, “Imaging solutions for the 22nm node using 1.35NA,” Proc. SPIE 7274, 72741Q (2009).
[CrossRef]

Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005).
[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]

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

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

Other (1)

A. K. Wong, Resolution Enhancement Techniques, (SPIE Press, 2001).

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Figures (8)

Fig. 1
Fig. 1

Representation of the integral region S in normalized Cartesian coordinates.

Fig. 2
Fig. 2

Characterization of analytical kernels for measuring odd aberrations under the smooth conventional illumination shown in Fig. 5.

Fig. 3
Fig. 3

Characterization of analytical kernels for measuring even aberrations under the smooth conventional illumination shown in Fig. 5.

Fig. 5
Fig. 5

Representation of mainstream types of illumination sources with different intensity distributions. The upper row: Smooth mainstream illumination sources with a Gaussian blur introduced as inputs for the simulation, including conventional, annular, dipole, and quadrupole shapes. The lower row: Top-hat mainstream illumination sources including conventional, annular, dipole, and quadrupole shapes.

Fig. 4
Fig. 4

Expansion of φ[r m , J(r c )] and D[r m , J(r c )] in the generalized sensitivity function space.

Fig. 6
Fig. 6

Correlation plots of aberration sensitivities between analytical calculation and PROLITH simulation for the four smooth sources shown in Fig. 4. (a) For odd aberration sensitivities, and (b) for even aberration sensitivities. Each of (a) and (b) totally contains 4 × 18 × 36 dots for the four input sources.

Fig. 7
Fig. 7

Comparison between the input and measured aberrated wavefronts under the smooth quadrupole illumination shown in Fig. 5.

Fig. 8
Fig. 8

Simulation results of the measurement errors of Zernike coefficients for the input aberration 1 under the smooth quadrupole illumination shown in Fig. 5.

Equations (9)

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I [ r m , J ( r c ) , h ] = 1 2 π { T C C [ 0 , r m ; J ( r c ) , h ] + T C C [ r m , 0 ; J ( r c ) , h ] } .
φ [ r m , J ( r c ) ] = k J 0 S J ( r c ) [ W o d d ( r m + r c ) W o d d ( r c ) ] d r c ,
D [ r m , J ( r c ) ] = 1 J 1 S J ( r c ) [ W e v e n ( r m + r c ) W e v e n ( r c ) ] [ w defocus ( r c ) w defocus ( r m + r c ) ] d r ,
W o d d ( r m ) = n _ o d d Z n _ o d d R n _ o d d ( r m ) ,
W e v e n ( r m ) = n _ e v e n Z n _ e v e n R n _ e v e n ( r m ) ,
φ [ r m , J ( r c ) ] = n _ o d d Z n _ o d d F n _ o d d [ r m , J ( r c ) ] ,
D [ r m , J ( r c ) ] = n _ e v e n Z n _ e v e n G n _ e v e n [ r m , J ( r c ) ] .
F n _ o d d [ r m , J ( r c ) ] = k J 0 S J ( r c ) [ R n _ o d d ( r m + r c ) R n _ o d d ( r c ) ] d r c ,
G n _ e v e n [ r m , J ( r c ) ] = 1 J 1 S J ( r c ) [ R n _ e v e n ( r m + r c ) R n _ e v e n ( r c ) ] [ w d e f o c u s ( r c ) w d e f o c u s ( r m + r c ) ] d r c .

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