Abstract

The correlation between the coma sensitivity of the alternating phase-shifting mask (Alt-PSM) mark and the mark’s structure is studied based on the Hopkins theory of partially coherent imaging and positive resist optical lithography (PROLITH) simulation. It is found that an optimized Alt-PSM mark with its phase width being two-thirds its pitch has a higher sensitivity to coma than Alt-PSM marks with the same pitch and the different phase widths. The pitch of the Alt-PSM mark is also optimized by PROLITH simulation, and the structure of p=1.92λ/NA and pw=2p/3 proves to be with the highest sensitivity. The optimized Alt-PSM mark is used as a measurement mark to retrieve coma aberration from the projection optics in lithographic tools. In comparison with an ordinary Alt-PSM mark with its phase width being a half its pitch, the measurement accuracies of Z7 and Z14 apparently increase.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2007

2006

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

F. Wang, X. Wang, M. Ma, D. Zhang, W. Shi, and J. Hu, “Aberration measurement of projection optics in lithographic tools by use of an alternating phase-shifting mask,” Appl. Opt. 45, 281-287 (2006).
[CrossRef] [PubMed]

M. Ma, X. Wang, F. Wang, W. Shi, and D. Zhang, “Coma aberration measurement by lateral image displacements at different defocus positions,” Proc. SPIE 6150, 615003 (2006).
[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]

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]

2005

E. Hendrickx, A. Colina, A. V. D. Hoff, J. Finders, and G. Vandenberghe, “Image placement error: closing the gap between overlay and imaging,” J. Microlithogr. Microfabr. Microsyst. 4, 033006 (2005).
[CrossRef]

C. A. Mack, “Lithography simulation in semiconductor manufacturing,” Proc. SPIE 5645, 63-83 (2005).
[CrossRef]

C. A. Mack, “Thirty years of lithography simulation,” Proc. SPIE 5754, 1-12 (2005).
[CrossRef]

2004

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

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

P. Graupner, R. Garreis, A. Gohnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1processes at extreme high NA,” Proc. SPIE 5040, 119-130(2003).
[CrossRef]

2002

E. Hendrickx, G. Vandenberghea, and K. Ronsea, “Pattern displacement induced by lens aberrations,” Proc. SPIE 4889, 1155-1162 (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 setup and illumination pupil verification,” Proc. SPIE 4346, 394-407 (2001).
[CrossRef]

A. K. Wong, L. W. Liebmann, and A. F. Molless, “Alternating phase-shifting mask with reduced aberration sensitivity: lithography considerations,” Proc. SPIE 4346, 420-428(2001).
[CrossRef]

1999

1985

C. A. Mack, “PROLITH: a comprehensive optical lithography model,” Proc. Soc. Photo-Opt. Instrum. Eng. 538, 207-220(1985).

1965

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

1953

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

Braat, J.

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

Colina, A.

E. Hendrickx, A. Colina, A. V. D. Hoff, J. Finders, and G. Vandenberghe, “Image placement error: closing the gap between overlay and imaging,” J. Microlithogr. Microfabr. Microsyst. 4, 033006 (2005).
[CrossRef]

De Bisschop, P.

P. De Bisschop, “Evaluation of Litel's in situ interferometer (ISI) technique for measuring projection lens aberrations: an initial study,” Proc. SPIE 5040, 11-23 (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]

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]

Dirksen, P.

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

Finders, J.

E. Hendrickx, A. Colina, A. V. D. Hoff, J. Finders, and G. Vandenberghe, “Image placement error: closing the gap between overlay and imaging,” J. Microlithogr. Microfabr. Microsyst. 4, 033006 (2005).
[CrossRef]

Flagello, D.

P. Graupner, R. Garreis, A. Gohnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1processes 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. Graupner, R. Garreis, A. Gohnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1processes at extreme high NA,” Proc. SPIE 5040, 119-130(2003).
[CrossRef]

Gohnermeier, A.

P. Graupner, R. Garreis, A. Gohnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1processes at extreme high NA,” Proc. SPIE 5040, 119-130(2003).
[CrossRef]

Graupner, P.

P. Graupner, R. Garreis, A. Gohnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1processes 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]

He, L.

Heil, T.

P. Graupner, R. Garreis, A. Gohnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1processes 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]

Hendrickx, E.

E. Hendrickx, A. Colina, A. V. D. Hoff, J. Finders, and G. Vandenberghe, “Image placement error: closing the gap between overlay and imaging,” J. Microlithogr. Microfabr. Microsyst. 4, 033006 (2005).
[CrossRef]

E. Hendrickx, G. Vandenberghea, and K. Ronsea, “Pattern displacement induced by lens aberrations,” Proc. SPIE 4889, 1155-1162 (2002).
[CrossRef]

Hoff, A. V. D.

E. Hendrickx, A. Colina, A. V. D. Hoff, J. Finders, and G. Vandenberghe, “Image placement error: closing the gap between overlay and imaging,” J. Microlithogr. Microfabr. Microsyst. 4, 033006 (2005).
[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(A), 408-432 (1953).
[CrossRef]

Hu, J.

Janssen, A. J. E. M.

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

Juffermans, C.

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

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]

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]

Kwok-Kit, W. A.

W. A. Kwok-Kit, Optical Imaging in Projection Microlithography (SPIE, 2005).

Liebmann, L. W.

A. K. Wong, L. W. Liebmann, and A. F. Molless, “Alternating phase-shifting mask with reduced aberration sensitivity: lithography considerations,” Proc. SPIE 4346, 420-428(2001).
[CrossRef]

Lowisch, M.

P. Graupner, R. Garreis, A. Gohnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1processes at extreme high NA,” Proc. SPIE 5040, 119-130(2003).
[CrossRef]

Ma, M.

Mack, C. A.

C. A. Mack, “Thirty years of lithography simulation,” Proc. SPIE 5754, 1-12 (2005).
[CrossRef]

C. A. Mack, “Lithography simulation in semiconductor manufacturing,” Proc. SPIE 5645, 63-83 (2005).
[CrossRef]

C. A. Mack, “PROLITH: a comprehensive optical lithography model,” Proc. Soc. Photo-Opt. Instrum. Eng. 538, 207-220(1985).

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]

Molless, A. F.

A. K. Wong, L. W. Liebmann, and A. F. Molless, “Alternating phase-shifting mask with reduced aberration sensitivity: lithography considerations,” Proc. SPIE 4346, 420-428(2001).
[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]

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]

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.

Ronsea, K.

E. Hendrickx, G. Vandenberghea, and K. Ronsea, “Pattern displacement induced by lens aberrations,” Proc. SPIE 4889, 1155-1162 (2002).
[CrossRef]

Sato, T.

Shi, W.

F. Wang, X. Wang, M. Ma, D. Zhang, W. Shi, and J. Hu, “Aberration measurement of projection optics in lithographic tools by use of an alternating phase-shifting mask,” Appl. Opt. 45, 281-287 (2006).
[CrossRef] [PubMed]

M. Ma, X. Wang, F. Wang, W. Shi, and D. Zhang, “Coma aberration measurement by lateral image displacements at different defocus positions,” Proc. SPIE 6150, 615003 (2006).
[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]

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]

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]

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 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]

Vandenberghe, G.

E. Hendrickx, A. Colina, A. V. D. Hoff, J. Finders, and G. Vandenberghe, “Image placement error: closing the gap between overlay and imaging,” J. Microlithogr. Microfabr. Microsyst. 4, 033006 (2005).
[CrossRef]

Vandenberghea, G.

E. Hendrickx, G. Vandenberghea, and K. Ronsea, “Pattern displacement induced by lens aberrations,” Proc. SPIE 4889, 1155-1162 (2002).
[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]

Wong, A. K.

A. K. Wong, L. W. Liebmann, and A. F. Molless, “Alternating phase-shifting mask with reduced aberration sensitivity: lithography considerations,” Proc. SPIE 4346, 420-428(2001).
[CrossRef]

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 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]

Yan, Q.

Zhang, D.

M. Ma, X. Wang, F. Wang, W. Shi, and D. Zhang, “Coma aberration measurement by lateral image displacements at different defocus positions,” Proc. SPIE 6150, 615003 (2006).
[CrossRef]

F. Wang, X. Wang, M. Ma, D. Zhang, W. Shi, and J. Hu, “Aberration measurement of projection optics in lithographic tools by use of an alternating phase-shifting mask,” Appl. Opt. 45, 281-287 (2006).
[CrossRef] [PubMed]

Appl. Opt.

J. Microlithogr. Microfabr. Microsyst.

E. Hendrickx, A. Colina, A. V. D. Hoff, J. Finders, and G. Vandenberghe, “Image placement error: closing the gap between overlay and imaging,” J. Microlithogr. Microfabr. Microsyst. 4, 033006 (2005).
[CrossRef]

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

Jpn. J. Appl. Phys.

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

Opt. Express

Proc. R. Soc. A

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

Proc. Soc. Photo-Opt. Instrum. Eng.

C. A. Mack, “PROLITH: a comprehensive optical lithography model,” Proc. Soc. Photo-Opt. Instrum. Eng. 538, 207-220(1985).

Proc. SPIE

C. A. Mack, “Lithography simulation in semiconductor manufacturing,” Proc. SPIE 5645, 63-83 (2005).
[CrossRef]

C. A. Mack, “Thirty years of lithography simulation,” Proc. SPIE 5754, 1-12 (2005).
[CrossRef]

A. K. Wong, L. W. Liebmann, and A. F. Molless, “Alternating phase-shifting mask with reduced aberration sensitivity: lithography considerations,” Proc. SPIE 4346, 420-428(2001).
[CrossRef]

P. Graupner, R. Garreis, A. Gohnermeier, T. Heil, M. Lowisch, and D. Flagello, “Impact of wavefront errors on low k1processes at extreme high NA,” Proc. SPIE 5040, 119-130(2003).
[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]

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]

P. De Bisschop, “Evaluation of Litel's in situ interferometer (ISI) technique for measuring projection lens aberrations: an initial study,” Proc. SPIE 5040, 11-23 (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 setup and illumination pupil verification,” Proc. SPIE 4346, 394-407 (2001).
[CrossRef]

E. Hendrickx, G. Vandenberghea, and K. Ronsea, “Pattern displacement induced by lens aberrations,” Proc. SPIE 4889, 1155-1162 (2002).
[CrossRef]

M. Ma, X. Wang, F. Wang, W. Shi, and D. Zhang, “Coma aberration measurement by lateral image displacements at different defocus positions,” Proc. SPIE 6150, 615003 (2006).
[CrossRef]

Other

W. A. Kwok-Kit, Optical Imaging in Projection Microlithography (SPIE, 2005).

A. K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE, 2001).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

(a) IPE from the aerial image at a 0.3 threshold for an Alt-PSM mark with the pitch of 400 nm and (c) the linear relationship between IPE and the third-order x-coma Z 7 are simulated by PROLITH when only Z 7 of 0.05 λ was inputted into the aberration map. (b) IPE can be measured in two ways practically.

Fig. 2
Fig. 2

Optical lithography imaging system.

Fig. 3
Fig. 3

Diffraction patterns of different kinds of marks at the exit pupil: (a) a binary mark with 1 st-, zeroth-, and + 1 st-order diffraction light, (b) an Alt-PSM mark with ± 1 st-order diffraction light, (c) an Alt-PSM mark with ± 1 st- and ± 3 rd-order diffraction light, (d) an Alt-PSM mark with ± 1 st-, ± 3 rd-, and ± 5 th-order diffraction light.

Fig. 4
Fig. 4

Correlation between the IPE and the Alt-PSM mark’s pitch is analyzed based on Hopkins theory (solid curve) and PROLITH simulation (dashed curve). The ratio of phase width to pitch of the mark is 1 2 .

Fig. 5
Fig. 5

Diffraction patterns of Alt-PSM marks at the exit pupil. The marks have got the same pitch under the four-beam interference condition, while the phase widths of the marks are different: (a)  p w p = 1 2 and (b)  p w p = 2 3 . The ± 3 rd-order diffraction light is absent for (b).

Fig. 6
Fig. 6

Correlation between the IPE and the Alt-PSM mark’s pitch is analyzed based on Hopkins theory (solid curve) and PROLITH simulation (dashed curve). The ratio of phase width to pitch of the mark is 2 3 .

Fig. 7
Fig. 7

Structures of the Alt-PSM marks affect the marks’ sensitivity to the third-order x coma ( Z 7 ). A maximum IPE is found to correspond to a specific p w / p for each value of pitch.

Fig. 8
Fig. 8

Structures of the Alt-PSM marks affect the marks’ sensitivity to the fifth-order x coma ( Z 14 ). A minimum IPE is found to correspond to a specific p w / p for each value of pitch.

Fig. 9
Fig. 9

(a) Ordinary Alt-PSM mark with p w p = 1 2 , and (b) optimized Alt-PSM mark with p w p = 2 3 .

Fig. 10
Fig. 10

Crosstalk coefficient between Z 7 and Z 14 .

Fig. 11
Fig. 11

Some parts of background light are reduced by off-axis illumination. (a)–(e) are symmetrical illumination models, while (f) is an asymmetrical one.

Tables (1)

Tables Icon

Table 1 Variation Ranges of Sensitivities and Accuracy of Coma Measurement

Equations (15)

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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 ) = + T C C ( 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 ,
T C C ( 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 ) , where     f 2 + g 2 < 1.
Φ ( f , g ) = Z 1 + Z 2 f + Z 3 g + + Z 7 [ 3 ( f 2 + g 2 ) 2 ] f + + Z 14 [ 10 ( f 2 + g 2 ) 2 12 ( f 2 + g 2 ) + 3 ] f + .
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 x ) = i · p w p N + N δ ( f x n 2 p ) · sinc ( p w · f x ) · sin ( π p f x ) .
λ 2 ( 1 σ ) NA < p 3 λ 2 ( σ + 1 ) NA ,
O ( f x ) = C o [ δ ( f x f 0 ) δ ( f x + f 0 ) ] ,
Δ x ± 1 = i · 1 8 π f 0 · log [ T C C ( f 0 , 0 ; f 0 , 0 ) T C C ( f 0 , 0 ; f 0 , 0 ) ] .
O ( f x ± 3 ) = i · p w p sinc ( ± 3 2 · p w p ) sin ( ± 3 2 · π ) .
λ 2 ( 1 σ ) NA < p 5 λ 2 ( σ + 1 ) NA .
MA OA | S max S min | ,
Δ x i = S Z 7 · Z 7 + S Z 14 · Z 14 + C T Z 7 , Z 14 · Z 7 · Z 14 ,

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