Abstract

We propose a novel in situ aberration measurement technique for lithographic projection lens by use of aerial image based on principal component analysis (AMAI-PCA). The aerial image space, principal component space and Zernike space are introduced to create a transformation model between aerial images and Zernike coefficients. First the aberration-induced aerial images of measurement marks are simulated to form an aerial image space with a statistical Box–Behnken design pattern. The aerial image space is then represented by their principal components based on principal component analysis. The principal component coefficients of the aerial images are finally connected with Zernike coefficients by a regression matrix through regression analysis. Therefore in situ aberration measurement can be achieved based on the regression matrix and the principal component coefficients of the detected aerial images. The measurement performance of the proposed AMAI-PCA technique is demonstrated superior compared to that of the conventional TAMIS technique by using a lithographic simulator tool (Prolith). We also tested the actual performance of AMAI-PCA technique on a prototype wafer exposure tool. The testing results show our proposed technique can rapidly measure the aberrations up to high-order Zernike polynomial term with 1σ repeatability of 0.5nm to 2.3nm depending on the aberration type and range.

© 2011 OSA

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References

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  1. H. Ooki, T. Noda, and K. Matsumoto, “Aberration averaging using point spread function for scanning projection system,” Proc. SPIE 4000, 551–558 (2000).
    [CrossRef]
  2. P. Graeupner, R. Garreis, A. Goehnermeiter, 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]
  3. D. G. Flagello, J. Mulkens, and C. Wagner, “Optical lithography into the millennium: sensitivity to aberrations, vibration and polarization,” Proc. SPIE 4000, 172–183 (2000).
    [CrossRef]
  4. M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (2001).
    [CrossRef]
  5. 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]
  6. 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]
  7. J. P. Kirk, “Review of photoresist-based lens evaluation methods,” Proc. SPIE 4000, 2–8 (2000).
    [CrossRef]
  8. B. Peng, X. Wang, Z. Qiu, Q. Yuan, and Y. Cao, “Aberration-induced intensity imbalance of alternating phase-shifting mask in lithographic imaging,” Opt. Lett. 35(9), 1404–1406 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  10. 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]
  11. L. V. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. S. Cashmore, “In-situ aberration monitoring using phase wheel targets,” Proc. SPIE 5377, 172–184 (2004).
    [CrossRef]
  12. 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]
  13. Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberration of projection optics with hyper-NA,” Proc. SPIE 6154, 615424, 615424-10 (2006).
    [CrossRef]
  14. A. Y. Bourov, L. Li, Z. Yang, F. Wang, and L. Duan, “Aerial image model and application to aberration measurement,” Proc. SPIE 7640, 764032, 764032-8 (2010).
    [CrossRef]
  15. KLA-Tencor, Software package Prolith v8.0.3.
  16. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
  17. H. George, Dunteman, Principal Components Analysis (SAGE, Newbury Park, London, 1989).
  18. J. Timothy, Robinson, Box–Behnken Designs. Encyclopedia of Statistics in Quality and Reliability (Wiley, 2008).
  19. C. A. Mack, “Lithography simulation in semiconductor manufacturing,” Proc. SPIE 5645, 63–83 (2005).
    [CrossRef]
  20. C. A. Mack, “Thirty years of lithography simulation,” Proc. SPIE 5754, 1–12 (2004).
    [CrossRef]
  21. L. Duan, J. Cheng, G. Sun, and Y. Chen, “New 0.75 NA ArF scanning lithographic tool,” Proc. SPIE 7973, 79732D (2011).
    [CrossRef]

2011 (1)

L. Duan, J. Cheng, G. Sun, and Y. Chen, “New 0.75 NA ArF scanning lithographic tool,” Proc. SPIE 7973, 79732D (2011).
[CrossRef]

2010 (2)

A. Y. Bourov, L. Li, Z. Yang, F. Wang, and L. Duan, “Aerial image model and application to aberration measurement,” Proc. SPIE 7640, 764032, 764032-8 (2010).
[CrossRef]

B. Peng, X. Wang, Z. Qiu, Q. Yuan, and Y. Cao, “Aberration-induced intensity imbalance of alternating phase-shifting mask in lithographic imaging,” Opt. Lett. 35(9), 1404–1406 (2010).
[CrossRef] [PubMed]

2009 (1)

2007 (1)

2006 (3)

2005 (1)

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

2004 (2)

C. A. Mack, “Thirty years of lithography simulation,” Proc. SPIE 5754, 1–12 (2004).
[CrossRef]

L. V. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. S. Cashmore, “In-situ aberration monitoring using phase wheel targets,” Proc. SPIE 5377, 172–184 (2004).
[CrossRef]

2003 (1)

P. Graeupner, R. Garreis, A. Goehnermeiter, 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 (2)

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (2001).
[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]

2000 (3)

H. Ooki, T. Noda, and K. Matsumoto, “Aberration averaging using point spread function for scanning projection system,” Proc. SPIE 4000, 551–558 (2000).
[CrossRef]

D. G. Flagello, J. Mulkens, and C. Wagner, “Optical lithography into the millennium: sensitivity to aberrations, vibration and polarization,” Proc. SPIE 4000, 172–183 (2000).
[CrossRef]

J. P. Kirk, “Review of photoresist-based lens evaluation methods,” Proc. SPIE 4000, 2–8 (2000).
[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 aberration of projection optics with hyper-NA,” Proc. SPIE 6154, 615424, 615424-10 (2006).
[CrossRef]

Beaudry, N.

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (2001).
[CrossRef]

Bechtz, A.

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (2001).
[CrossRef]

Bourov, A. Y.

A. Y. Bourov, L. Li, Z. Yang, F. Wang, and L. Duan, “Aerial image model and application to aberration measurement,” Proc. SPIE 7640, 764032, 764032-8 (2010).
[CrossRef]

Cao, Y.

Cashmore, J. S.

L. V. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. S. Cashmore, “In-situ aberration monitoring using phase wheel targets,” Proc. SPIE 5377, 172–184 (2004).
[CrossRef]

Chen, Y.

L. Duan, J. Cheng, G. Sun, and Y. Chen, “New 0.75 NA ArF scanning lithographic tool,” Proc. SPIE 7973, 79732D (2011).
[CrossRef]

Cheng, J.

L. Duan, J. Cheng, G. Sun, and Y. Chen, “New 0.75 NA ArF scanning lithographic tool,” Proc. SPIE 7973, 79732D (2011).
[CrossRef]

Cummings, K. D.

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (2001).
[CrossRef]

de Boeij, W.

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (2001).
[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]

Duan, L.

L. Duan, J. Cheng, G. Sun, and Y. Chen, “New 0.75 NA ArF scanning lithographic tool,” Proc. SPIE 7973, 79732D (2011).
[CrossRef]

A. Y. Bourov, L. Li, Z. Yang, F. Wang, and L. Duan, “Aerial image model and application to aberration measurement,” Proc. SPIE 7640, 764032, 764032-8 (2010).
[CrossRef]

Flagello, D.

P. Graeupner, R. Garreis, A. Goehnermeiter, 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]

Flagello, D. G.

D. G. Flagello, J. Mulkens, and C. Wagner, “Optical lithography into the millennium: sensitivity to aberrations, vibration and polarization,” Proc. SPIE 4000, 172–183 (2000).
[CrossRef]

Garreis, R.

P. Graeupner, R. Garreis, A. Goehnermeiter, 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]

Goehnermeiter, A.

P. Graeupner, R. Garreis, A. Goehnermeiter, 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]

Graeupner, P.

P. Graeupner, R. Garreis, A. Goehnermeiter, 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]

He, L.

Heil, T.

P. Graeupner, R. Garreis, A. Goehnermeiter, 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]

Itani, T.

L. V. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. S. Cashmore, “In-situ aberration monitoring using phase wheel targets,” Proc. SPIE 5377, 172–184 (2004).
[CrossRef]

Kirk, J. P.

J. P. Kirk, “Review of photoresist-based lens evaluation methods,” Proc. SPIE 4000, 2–8 (2000).
[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 aberration of projection optics with hyper-NA,” Proc. SPIE 6154, 615424, 615424-10 (2006).
[CrossRef]

Li, L.

A. Y. Bourov, L. Li, Z. Yang, F. Wang, and L. Duan, “Aerial image model and application to aberration measurement,” Proc. SPIE 7640, 764032, 764032-8 (2010).
[CrossRef]

Lowisch, M.

P. Graeupner, R. Garreis, A. Goehnermeiter, 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.

Mack, C. A.

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 (2004).
[CrossRef]

Matsumoto, K.

H. Ooki, T. Noda, and K. Matsumoto, “Aberration averaging using point spread function for scanning projection system,” Proc. SPIE 4000, 551–558 (2000).
[CrossRef]

Matsuura, S.

L. V. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. S. Cashmore, “In-situ aberration monitoring using phase wheel targets,” Proc. SPIE 5377, 172–184 (2004).
[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 set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

Moers, M.

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (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 aberration of projection optics with hyper-NA,” Proc. SPIE 6154, 615424, 615424-10 (2006).
[CrossRef]

Mulkens, J.

D. G. Flagello, J. Mulkens, and C. Wagner, “Optical lithography into the millennium: sensitivity to aberrations, vibration and polarization,” Proc. SPIE 4000, 172–183 (2000).
[CrossRef]

Noda, T.

H. Ooki, T. Noda, and K. Matsumoto, “Aberration averaging using point spread function for scanning projection system,” Proc. SPIE 4000, 551–558 (2000).
[CrossRef]

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 aberration of projection optics with hyper-NA,” Proc. SPIE 6154, 615424, 615424-10 (2006).
[CrossRef]

Ooki, H.

H. Ooki, T. Noda, and K. Matsumoto, “Aberration averaging using point spread function for scanning projection system,” Proc. SPIE 4000, 551–558 (2000).
[CrossRef]

Peng, B.

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.

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 aberration of projection optics with hyper-NA,” Proc. SPIE 6154, 615424, 615424-10 (2006).
[CrossRef]

Smith, B. W.

L. V. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. S. Cashmore, “In-situ aberration monitoring using phase wheel targets,” Proc. SPIE 5377, 172–184 (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 set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

Suganaga, T.

L. V. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. S. Cashmore, “In-situ aberration monitoring using phase wheel targets,” Proc. SPIE 5377, 172–184 (2004).
[CrossRef]

Sun, G.

L. Duan, J. Cheng, G. Sun, and Y. Chen, “New 0.75 NA ArF scanning lithographic tool,” Proc. SPIE 7973, 79732D (2011).
[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 aberration of projection optics with hyper-NA,” Proc. SPIE 6154, 615424, 615424-10 (2006).
[CrossRef]

van der Laan, H.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration set-up and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).
[CrossRef]

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (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]

van Zwol, A.

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (2001).
[CrossRef]

Wagner, C.

D. G. Flagello, J. Mulkens, and C. Wagner, “Optical lithography into the millennium: sensitivity to aberrations, vibration and polarization,” Proc. SPIE 4000, 172–183 (2000).
[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]

Willekersa, R.

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (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 aberration of projection optics with hyper-NA,” Proc. SPIE 6154, 615424, 615424-10 (2006).
[CrossRef]

Yang, Z.

A. Y. Bourov, L. Li, Z. Yang, F. Wang, and L. Duan, “Aerial image model and application to aberration measurement,” Proc. SPIE 7640, 764032, 764032-8 (2010).
[CrossRef]

Yuan, Q.

Zavyalova, L. V.

L. V. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. S. Cashmore, “In-situ aberration monitoring using phase wheel targets,” Proc. SPIE 5377, 172–184 (2004).
[CrossRef]

Zellenrath, M.

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (2001).
[CrossRef]

Appl. Opt. (3)

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (12)

L. V. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. S. Cashmore, “In-situ aberration monitoring using phase wheel targets,” Proc. SPIE 5377, 172–184 (2004).
[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]

Y. Ohsaki, T. Mori, S. Koga, M. Ando, K. Yamamoto, T. Tezuka, and Y. Shiode, “A new on-machine measurement system to measure wavefront aberration of projection optics with hyper-NA,” Proc. SPIE 6154, 615424, 615424-10 (2006).
[CrossRef]

A. Y. Bourov, L. Li, Z. Yang, F. Wang, and L. Duan, “Aerial image model and application to aberration measurement,” Proc. SPIE 7640, 764032, 764032-8 (2010).
[CrossRef]

J. P. Kirk, “Review of photoresist-based lens evaluation methods,” Proc. SPIE 4000, 2–8 (2000).
[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 (2004).
[CrossRef]

L. Duan, J. Cheng, G. Sun, and Y. Chen, “New 0.75 NA ArF scanning lithographic tool,” Proc. SPIE 7973, 79732D (2011).
[CrossRef]

H. Ooki, T. Noda, and K. Matsumoto, “Aberration averaging using point spread function for scanning projection system,” Proc. SPIE 4000, 551–558 (2000).
[CrossRef]

P. Graeupner, R. Garreis, A. Goehnermeiter, 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]

D. G. Flagello, J. Mulkens, and C. Wagner, “Optical lithography into the millennium: sensitivity to aberrations, vibration and polarization,” Proc. SPIE 4000, 172–183 (2000).
[CrossRef]

M. Moers, H. van der Laan, M. Zellenrath, W. de Boeij, N. Beaudry, K. D. Cummings, A. van Zwol, A. Bechtz, and R. Willekersa, “Application of the aberration ring test (ARTEMISTM) to determine lens quality and predict its lithographic performance,” Proc. SPIE 4346, 1379–1387 (2001).
[CrossRef]

Other (4)

KLA-Tencor, Software package Prolith v8.0.3.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).

H. George, Dunteman, Principal Components Analysis (SAGE, Newbury Park, London, 1989).

J. Timothy, Robinson, Box–Behnken Designs. Encyclopedia of Statistics in Quality and Reliability (Wiley, 2008).

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of a projection lithography system.

Fig. 2
Fig. 2

Comparison of aerial images without and with coma for 250nm isolated space (at wafer level). (a) Ideal aerial image and (b) asymmetric aerial image with 20nm coma. The simulation was performed at 0.75NA. and 0.65 partial coherence factor.

Fig. 3
Fig. 3

The transformation relation among three kinds of parameter spaces in AMAI-PCA technique.

Fig. 4
Fig. 4

Schematic illustration of a three dimensional Box-Behnken design.

Fig. 5
Fig. 5

Illustration of principal component analysis of an aerial image. (a) The original aerial image, (b) the residual of the aerial image (a) subtracted by the sum of the first 5 PCs multiplied by their coefficients, (c) the root mean square(RMS) of the residual vs. PC number.(When PC number is 0, it corresponds to the RMS of original image).

Fig. 6
Fig. 6

The measurement mark for the comparison between TAMIS and AMAI-PCA.

Fig. 7
Fig. 7

The comparison of Zernike aberration simulated measurement accuracy with TAMIS and AMAI-PCA technique with the aberration within the range of −10nm to 10nm. The left figure shows the Zernike retrieval accuracy with TAMIS, and the right figure shows that with AMAI-PCA.

Fig. 8
Fig. 8

The comparison of Zernike aberration simulated measurement accuracy with TAMIS and AMAI-PCA technique with aberration within the range of −20nm to 20nm. The left figure shows the Zernike retrieval accuracy with TAMIS, and the right figure shows that with AMAI-PCA.

Fig. 9
Fig. 9

Illustration of the aerial image sensor structure in SSA600/10.

Fig. 10
Fig. 10

Repeatability (1σ) of Z5, Z7, Z8, Z9, Z14, Z15 and Z16 measurments. The measurement repeatability for the same Zernike aberration term varies along different field point due to the aberration variation across the exposure field.

Fig. 11
Fig. 11

Z7 variation across the exposure field for four wavelength settings.

Tables (1)

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Table 1 Simulation settings

Equations (8)

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I ( x i , y i ) = + T C C ( f ' , g ' ; f " , g " ) O ( f ' , g ' ) O * ( f " , g " ) exp { j 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 c , g c ) H ( f ' + f c , g ' + g c ) H * ( f " + f c , g " + g c ) d f c d g c
J ( f c , g c ) = { 1 π σ 2 f 2 + g 2 σ 2 0 e l s e .
H ( f , g ) = H 0 ( f , g ) exp ( j 2 π λ W ( f , g ) ) f 2 + g 2 < 1
W ( f , g ) = n = 1 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 6 2 f g + Z 7 [ 3 ( f 2 + g 2 ) 2 ] f + Z 8 [ 3 ( f 2 + g 2 ) 2 ] g + Z 9 [ 6 ( f 2 + g 2 ) 2 6 ( f 2 + g 2 ) + 1 ] +
A I ( x , z ; Z ) = α = 1 t P C α ( x , z ) V α ( Z )
A I = [ P C 1 P C 2 P C m ] [ V 1 V 2 V m ] + E T
[ V 1 V 2 V m ] = [ R M 1 R M 2 R M m ] Z + E R

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