Abstract

A linear measurement model of lithographic projection lens aberrations is studied numerically based on the Hopkins theory of partially-coherent imaging and positive resist optical lithography (PROLITH) simulation. In this linearity model, the correlation between the mark’s structure and its sensitivities to aberrations is analyzed. A method to design a mark with high sensitivity is proved and declared. By use of this method, a translational-symmetry alternating phase shifting mask (Alt-PSM) grating mark is redesigned with all of the even orders, ±3rd and ±5th order diffraction light missing. In the evaluation simulation, the measurement accuracies of aberrations prove to be enhanced apparently by use of the redesigned mark instead of the old ones.

© 2009 Optical Society of America

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2009 (1)

2008 (2)

K. Yoshimura, H. Nakano, H. Hata, N. Deguchi, M. Kobayashi, T. Ebihara, Y. Kawanobe, and T. Kanda, “Performance of the FPA-7000AS7 1.35 NA immersion exposure system for 45 nm mass production,” Proc. SPIE 6924, 69241O (2008).
[CrossRef]

J. Mulkens, J. de Klerk, M. Leenders, F. de Jong, and J. Willem Cromwijk, “Latest developments on immersion exposure systems,” Proc. SPIE 6924, 69241P (2008).
[CrossRef]

2007 (1)

T. Yoshihara, B. Takeshita, A. Shigenobu, Y. Hasegawa, Y. Ohsaki, K. Mishima, and S. Miura, “New projection optics and aberration control system for the 45 nm node,” Proc. SPIE 6520, 652022 (2007).
[CrossRef]

2006 (5)

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 (4)

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]

P. Dirksen, J. Braat, A. J. E. M. J., and C. Juffermans, “Aberration retrieval using the extended Nijboer-Zernike approach,” J. Microlith., Microfab., Microsyst. 2, 61-68 (2003).
[CrossRef]

J. Sung, M. Pitchumani, and E. G. Johnson, “Aberration measurement of photolithographic lenses by use of hybrid diffractive photomasks,” Appl. Opt. 42, 1987-1995 (2003).
[CrossRef] [PubMed]

P. Gräupner, R. Garreis, A. Göhnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1 processes at extreme high NA,” Proc. SPIE 5040, 119-130 (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 set-up and illumination pupil verification,” Proc. SPIE 4346, 394-407 (2001).
[CrossRef]

2000 (1)

1999 (1)

1995 (1)

1992 (1)

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]

Braat, J.

P. Dirksen, J. Braat, A. J. E. M. J., and C. Juffermans, “Aberration retrieval using the extended Nijboer-Zernike approach,” J. Microlith., Microfab., Microsyst. 2, 61-68 (2003).
[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]

de Jong, F.

J. Mulkens, J. de Klerk, M. Leenders, F. de Jong, and J. Willem Cromwijk, “Latest developments on immersion exposure systems,” Proc. SPIE 6924, 69241P (2008).
[CrossRef]

de Klerk, J.

J. Mulkens, J. de Klerk, M. Leenders, F. de Jong, and J. Willem Cromwijk, “Latest developments on immersion exposure systems,” Proc. SPIE 6924, 69241P (2008).
[CrossRef]

Deguchi, N.

K. Yoshimura, H. Nakano, H. Hata, N. Deguchi, M. Kobayashi, T. Ebihara, Y. Kawanobe, and T. Kanda, “Performance of the FPA-7000AS7 1.35 NA immersion exposure system for 45 nm mass production,” Proc. SPIE 6924, 69241O (2008).
[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]

Dirksen, P.

P. Dirksen, J. Braat, A. J. E. M. J., and C. Juffermans, “Aberration retrieval using the extended Nijboer-Zernike approach,” J. Microlith., Microfab., Microsyst. 2, 61-68 (2003).
[CrossRef]

Ebihara, T.

K. Yoshimura, H. Nakano, H. Hata, N. Deguchi, M. Kobayashi, T. Ebihara, Y. Kawanobe, and T. Kanda, “Performance of the FPA-7000AS7 1.35 NA immersion exposure system for 45 nm mass production,” Proc. SPIE 6924, 69241O (2008).
[CrossRef]

Flagello, D.

P. Gräupner, R. Garreis, A. Göhnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1 processes at extreme high NA,” Proc. SPIE 5040, 119-130 (2003).
[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]

Garreis, R.

P. Gräupner, R. Garreis, A. Göhnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1 processes at extreme high NA,” Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

Göhnermeier, A.

P. Gräupner, R. Garreis, A. Göhnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1 processes at extreme high NA,” Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

Gräupner, P.

P. Gräupner, R. Garreis, A. Göhnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1 processes at extreme high NA,” Proc. SPIE 5040, 119-130 (2003).
[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]

Hasegawa, Y.

T. Yoshihara, B. Takeshita, A. Shigenobu, Y. Hasegawa, Y. Ohsaki, K. Mishima, and S. Miura, “New projection optics and aberration control system for the 45 nm node,” Proc. SPIE 6520, 652022 (2007).
[CrossRef]

Hata, H.

K. Yoshimura, H. Nakano, H. Hata, N. Deguchi, M. Kobayashi, T. Ebihara, Y. Kawanobe, and T. Kanda, “Performance of the FPA-7000AS7 1.35 NA immersion exposure system for 45 nm mass production,” Proc. SPIE 6924, 69241O (2008).
[CrossRef]

Heil, T.

P. Gräupner, R. Garreis, A. Göhnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1 processes at extreme high NA,” Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

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]

Hu, J.

J., A. J. E. M.

P. Dirksen, J. Braat, A. J. E. M. J., and C. Juffermans, “Aberration retrieval using the extended Nijboer-Zernike approach,” J. Microlith., Microfab., Microsyst. 2, 61-68 (2003).
[CrossRef]

Johnson, E. G.

Juffermans, C.

P. Dirksen, J. Braat, A. J. E. M. J., and C. Juffermans, “Aberration retrieval using the extended Nijboer-Zernike approach,” J. Microlith., Microfab., Microsyst. 2, 61-68 (2003).
[CrossRef]

Kanda, T.

K. Yoshimura, H. Nakano, H. Hata, N. Deguchi, M. Kobayashi, T. Ebihara, Y. Kawanobe, and T. Kanda, “Performance of the FPA-7000AS7 1.35 NA immersion exposure system for 45 nm mass production,” Proc. SPIE 6924, 69241O (2008).
[CrossRef]

Kawanobe, Y.

K. Yoshimura, H. Nakano, H. Hata, N. Deguchi, M. Kobayashi, T. Ebihara, Y. Kawanobe, and T. Kanda, “Performance of the FPA-7000AS7 1.35 NA immersion exposure system for 45 nm mass production,” Proc. SPIE 6924, 69241O (2008).
[CrossRef]

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]

Kobayashi, M.

K. Yoshimura, H. Nakano, H. Hata, N. Deguchi, M. Kobayashi, T. Ebihara, Y. Kawanobe, and T. Kanda, “Performance of the FPA-7000AS7 1.35 NA immersion exposure system for 45 nm mass production,” Proc. SPIE 6924, 69241O (2008).
[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]

Kohno, T.

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]

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]

Leenders, M.

J. Mulkens, J. de Klerk, M. Leenders, F. de Jong, and J. Willem Cromwijk, “Latest developments on immersion exposure systems,” Proc. SPIE 6924, 69241P (2008).
[CrossRef]

Liu, L.

Lowisch, M.

P. Gräupner, R. Garreis, A. Göhnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1 processes at extreme high NA,” Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

Ma, M.

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]

Mishima, K.

T. Yoshihara, B. Takeshita, A. Shigenobu, Y. Hasegawa, Y. Ohsaki, K. Mishima, and S. Miura, “New projection optics and aberration control system for the 45 nm node,” Proc. SPIE 6520, 652022 (2007).
[CrossRef]

Miura, S.

T. Yoshihara, B. Takeshita, A. Shigenobu, Y. Hasegawa, Y. Ohsaki, K. Mishima, and S. Miura, “New projection optics and aberration control system for the 45 nm node,” Proc. SPIE 6520, 652022 (2007).
[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]

Morrison, R. L.

Mulkens, J.

J. Mulkens, J. de Klerk, M. Leenders, F. de Jong, and J. Willem Cromwijk, “Latest developments on immersion exposure systems,” Proc. SPIE 6924, 69241P (2008).
[CrossRef]

Nakano, H.

K. Yoshimura, H. Nakano, H. Hata, N. Deguchi, M. Kobayashi, T. Ebihara, Y. Kawanobe, and T. Kanda, “Performance of the FPA-7000AS7 1.35 NA immersion exposure system for 45 nm mass production,” Proc. SPIE 6924, 69241O (2008).
[CrossRef]

Nomura, H.

Ohsaki, Y.

T. Yoshihara, B. Takeshita, A. Shigenobu, Y. Hasegawa, Y. Ohsaki, K. Mishima, and S. Miura, “New projection optics and aberration control system for the 45 nm node,” Proc. SPIE 6520, 652022 (2007).
[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]

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 set-up and illumination pupil verification,” Proc. SPIE 4346, 394-407 (2001).
[CrossRef]

Qiu, Z.

Sato, T.

Shi, W.

Shigenobu, A.

T. Yoshihara, B. Takeshita, A. Shigenobu, Y. Hasegawa, Y. Ohsaki, K. Mishima, and S. Miura, “New projection optics and aberration control system for the 45 nm node,” Proc. SPIE 6520, 652022 (2007).
[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]

Socha, R. J.

R. J. Socha, “Propagation effects of partially coherent light in optical lithograplhy and inspection,” Ph.D. dissertation (University of California at Berkeley, 1997), Chap. 3

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]

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]

Takeshita, B.

T. Yoshihara, B. Takeshita, A. Shigenobu, Y. Hasegawa, Y. Ohsaki, K. Mishima, and S. Miura, “New projection optics and aberration control system for the 45 nm node,” Proc. SPIE 6520, 652022 (2007).
[CrossRef]

Tawarayama, K.

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]

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 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]

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 set-up and illumination pupil verification,” Proc. SPIE 4346, 394-407 (2001).
[CrossRef]

Willem Cromwijk, J.

J. Mulkens, J. de Klerk, M. Leenders, F. de Jong, and J. Willem Cromwijk, “Latest developments on immersion exposure systems,” Proc. SPIE 6924, 69241P (2008).
[CrossRef]

Wong, A. K.-K.

A. K. -K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005).
[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]

Yoshihara, T.

T. Yoshihara, B. Takeshita, A. Shigenobu, Y. Hasegawa, Y. Ohsaki, K. Mishima, and S. Miura, “New projection optics and aberration control system for the 45 nm node,” Proc. SPIE 6520, 652022 (2007).
[CrossRef]

Yoshimura, K.

K. Yoshimura, H. Nakano, H. Hata, N. Deguchi, M. Kobayashi, T. Ebihara, Y. Kawanobe, and T. Kanda, “Performance of the FPA-7000AS7 1.35 NA immersion exposure system for 45 nm mass production,” Proc. SPIE 6924, 69241O (2008).
[CrossRef]

Yuan, Q.

Zhang, D.

Zhou, C.

Appl. Opt. (8)

J. Microlith., Microfab., Microsyst. (1)

P. Dirksen, J. Braat, A. J. E. M. J., and C. Juffermans, “Aberration retrieval using the extended Nijboer-Zernike approach,” J. Microlith., Microfab., Microsyst. 2, 61-68 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

Proc. SPIE (9)

P. Gräupner, R. Garreis, A. Göhnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1 processes at extreme high NA,” Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

J. Mulkens, J. de Klerk, M. Leenders, F. de Jong, and J. Willem Cromwijk, “Latest developments on immersion exposure systems,” Proc. SPIE 6924, 69241P (2008).
[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. Yoshihara, B. Takeshita, A. Shigenobu, Y. Hasegawa, Y. Ohsaki, K. Mishima, and S. Miura, “New projection optics and aberration control system for the 45 nm node,” Proc. SPIE 6520, 652022 (2007).
[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]

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, J. Kougo, Y. Mizuno, H. Ooki, and M. Hamatani, “Portable phase measuring interferometer using Shack--Hartmann method,” Proc. SPIE 5038, 726-732 (2003).
[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. SPIE 4346, 394-407 (2001).
[CrossRef]

K. Yoshimura, H. Nakano, H. Hata, N. Deguchi, M. Kobayashi, T. Ebihara, Y. Kawanobe, and T. Kanda, “Performance of the FPA-7000AS7 1.35 NA immersion exposure system for 45 nm mass production,” Proc. SPIE 6924, 69241O (2008).
[CrossRef]

Other (3)

ITRS, “International technology roadmap for semiconductors, 2007 edition,” http://www.itrs.net, 1-34 (2007).

A. K. -K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005).
[CrossRef]

R. J. Socha, “Propagation effects of partially coherent light in optical lithograplhy and inspection,” Ph.D. dissertation (University of California at Berkeley, 1997), Chap. 3

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Figures (10)

Fig. 1
Fig. 1

Partially-coherent imaging scheme of the projection lens with aberrations under Kohler’s illumination.

Fig. 2
Fig. 2

Aerial images of a BIM grating mark with pitch = 2.31 λ / NA by a projection lens with (a) no aberration, (b)  0.05 λ of Coma Z 7 , (c) spherical aberration Z 9 , and (d) astigmatism Z 12 , respectively. The wavelength is 193 nm . Partial coherence σ is 0.3 and NA is 0.65.

Fig. 3
Fig. 3

(a) Coma–IPE relationship of the Alt-PSM grating mark with pitch = 0.90 and 1.15 λ / NA calculated based on Hopkins model and the PROLITH simulation. (b) Residuals of the first-degree polynomial fitting are also achieved.

Fig. 4
Fig. 4

(a) Spherical–BFS relationship of the Alt-PSM grating mark with pitch = 0.90 and 1.15 λ / NA calculated based on Hopkins model and the PROLITH simulation. (b) Residuals of the first-degree polynomial fitting are also achieved.

Fig. 5
Fig. 5

(a)  Astigmatism– BFS hv relationship of the Alt-PSM grating mark with pitch = 0.90 and 1.15 λ / NA calculated based on Hopkins model and the PROLITH simulation. (b) Residuals of the first-degree polynomial fitting are also achieved.

Fig. 6
Fig. 6

BIM grating mark with pitch of 400 nm is imaged. IPE can be obtained either by (a) measuring the shift of the center trench of the mark’s image or (b) measuring the average of the edge placement errors of outer trench edges, when threshold of the intensity is set. The best focus plane is determined by looking for (c) a best-matched CD through (d) different focus planes.

Fig. 7
Fig. 7

Correlation between coma ( Z 7 and Z 14 ) sensitivities and the Alt-PSM grating mark’s pitch.

Fig. 8
Fig. 8

Correlation between spherical aberration ( Z 9 and Z 16 ) sensitivities and the Alt-PSM grating mark’s pitch.

Fig. 9
Fig. 9

Correlation between astigmatism ( Z 12 ) sensitivities and the Alt-PSM grating mark’s pitch.

Fig. 10
Fig. 10

(a) Structure of a redesigned translation symmetry Alt-PSM grating mark with (b) its even orders, ± 3 rd and ± 5 th order diffraction light missing (b).

Tables (2)

Tables Icon

Table 1 One-Degree Polynomial Fitting Results of Coma–IPE, Spherical–BFS, and Astigmatism BFS hv Linearity Relationship

Tables Icon

Table 2 Variation Ranges of Sensitivities and Accuracy of Aberration Measurement

Equations (20)

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x o = M x o ^ λ / NA , y o = M y o ^ λ / NA , x i = x i ^ λ / NA , y i = y i ^ λ / NA , f = f ^ NA / λ , g = g ^ NA / λ ,
I ( x i , y i ) = + TCC ( f , g ; f , g ) O ( f , g ) O * ( f , g ) e i 2 π [ ( f f ) x i + ( g g ) y i ] d f d g d f d g ,
TCC ( f , g ; f , g ) = + J ( f , g ) H ( f + f , g + g ) H * ( f + f , g + g ) d f d g .
J ( f , g ) = { 1 / π σ 2 f 2 + g 2 σ 0 otherwise .
H ( f , g ) = { e i 2 π λ Φ ( f , g ) + i 2 π Δ z 1 NA 2 1 NA 2 ( f 2 + g 2 ) , f 2 + g 2 < 1 0 others ,
Φ ( f , g ) = n = 1 37 Z n R n ( f , g ) = Z 1 + Z 2 f + Z 3 g + Z 4 [ 2 ( f 2 + g 2 ) 1 ] + Z 5 ( f 2 g 2 ) + Z 7 [ 3 ( f 2 + g 2 ) 2 ] f + + Z 9 [ 6 ( f 2 + g 2 ) 2 6 ( f 2 + g 2 ) + 1 ] + + Z 12 [ 4 ( f 2 + g 2 ) 3 ] ( f 2 g 2 ) + + Z 14 [ 10 ( f 2 + g 2 ) 2 12 ( f 2 + g 2 ) + 3 ] f + + Z 16 [ 20 ( f 2 + g 2 ) 3 30 ( f 2 + g 2 ) 2 + 12 ( f 2 + g 2 ) 1 ] + .
t ( x o ) = n = + δ ( x o 2 n p ) * [ rect ( x o + p / 2 p w ) rect ( x o p / 2 p w ) ] n Z .
O ( f ) = i · p w p N + N δ ( f n 2 p ) · sinc ( p w · f ) · sin ( π p f ) .
O ( f ) = C o [ δ ( f f 0 ) δ ( f + f 0 ) ] ,
I ( x i , Δ z ) = TCC ( f 0 , 0 ; f 0 , 0 ) + TCC ( f 0 , 0 ; f 0 , 0 ) + exp ( i 4 f 0 x i ) J ( f , g ) exp ( i α ) exp ( i β ) d f d g + exp ( i 4 f 0 x i ) J ( f , g ) exp ( i α ) exp ( i β ) d f d g ,
α = 2 π Φ ( f + f 0 , g ) / λ + π Δ z [ ( f + f 0 ) 2 + g 2 ] , β = 2 π Φ ( f f 0 , g ) / λ + π Δ z [ ( f f 0 ) 2 + g 2 ] ,
I ( x i , Δ z ) = 2 C 0 2 [ J ( f , g ) cos ( α β 4 π f 0 x i ) d f d g + 1 ] .
I ( x i , Δ z = 0 ) / x i = 0 , I ( x i = 0 , Δ z ) / Δ z = 0 ,
IPE = n = 1 37 S IPE n · Z n = 1 2 λ f 0 n = 1 37 J ( f , g ) [ R n ( f + f 0 , g ) R n ( f f 0 , g ) ] d f d g J ( f , g ) d f d g · Z n ,
BFS = n = 1 37 S BFS n · Z n = 1 2 λ f 0 n = 1 37 J ( f , g ) · f · [ R n ( f + f 0 , g ) R n ( f f 0 , g ) ] d f d g J ( f , g ) f 2 d f d g · Z n .
Y i = a * X i + b + ε i .
t ( x 0 ) = w ( x 0 ) exp [ i · θ ( x 0 ) ] , where     0 x 0 1.
w ( x 0 ) = w ( x 0 1 / 2 ) , 1 / 2 x 0 1 , θ ( x 0 ) = θ ( x 0 1 / 2 ) + π .
A ( n ) = 0 1 / 2 w ( x 0 ) exp [ i · θ ( x 0 ) ] exp [ 2 π in x 0 ] [ 1 ( 1 ) n ] d x 0 = 0 , n = 3 , 5.
MA ODA | S max S min | ,

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