Iterative method for in situ measurement of lens aberrations in lithographic tools using CTC-based quadratic aberration model |
Optics Express, Vol. 20, Issue 13, pp. 14272-14283 (2012)
http://dx.doi.org/10.1364/OE.20.014272
Acrobat PDF (1072 KB)
Abstract
This paper proposes an iterative method for in situ lens aberration measurement in lithographic tools based on a quadratic aberration model (QAM) that is a natural extension of the linear model formed by taking into account interactions among individual Zernike coefficients. By introducing a generalized operator named cross triple correlation (CTC), the quadratic model can be calculated very quickly and accurately with the help of fast Fourier transform (FFT). The Zernike coefficients up to the 37th order or even higher are determined by solving an inverse problem through an iterative procedure from several through-focus aerial images of a specially designed mask pattern. The simulation work has validated the theoretical derivation and confirms that such a method is simple to implement and yields a superior quality of wavefront estimate, particularly for the case when the aberrations are relatively large. It is fully expected that this method will provide a useful practical means for the in-line monitoring of the imaging quality of lithographic tools.
© 2012 OSA
1. Introduction
1. B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE 4000, 294–306 (2000). [CrossRef]
3. J. Sung, M. Pitchumani, and E. G. Johnson, “Aberration measurement of photolithographic lenses by use of hybrid diffractive photomasks,” Appl. Opt. 42(11), 1987–1995 (2003). [CrossRef] [PubMed]
4. F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica 1(7-12), 689–704 (1934). [CrossRef]
6. 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]
7. T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE 5754, 1659–1669 (2004). [CrossRef]
8. J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D, 61523D-10 (2006). [CrossRef]
9. W. Liu, S. Y. Liu, T. T. Zhou, and L. J. 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] [PubMed]
10. W. Liu, S. Y. Liu, T. L. Shi, and Z. R. Tang, “Generalized formulations for aerial image based lens aberration metrology in lithographic tools with arbitrarily shaped illumination sources,” Opt. Express 18(19), 20096–20104 (2010). [CrossRef] [PubMed]
11. H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217(1130), 408–432 (1953). [CrossRef]
12. B. E. A. Saleh, “Optical bilinear transformations: general properties,” Opt. Acta (Lond.) 26, 777–799 (1979). [CrossRef]
13. T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE 4691, 33–43 (2002). [CrossRef]
14. D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE 3051, 672–685 (1997). [CrossRef]
17. L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006). [CrossRef]
18. R. Miyakawa, P. Naulleau, and A. Zakhor, “Iterative procedure for in situ extreme ultraviolet optical testing with an incoherent source,” J. Vac. Sci. Technol. B 27(6), 2927–2930 (2009). [CrossRef]
19. R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE 7636, 76361K, 76361K-7 (2010). [CrossRef]
20. S. Y. Liu, W. Liu, and T. T. Zhou, “ Fast algorithm for quadratic aberration model in optical lithography based on cross triple correlation,” J. Micro/Nanolith MEMS MOEMS 10(2), 023007 (2011). [CrossRef]
21. S. Y. Liu, W. Liu, and X. F. Wu, “Fast evaluation of aberration-induced intensity distribution in partially coherent imaging systems by cross triple correlation,” Chin. Phys. Lett. 28(10), 104212 (2011). [CrossRef]
2. Theory
2.1 The quadratic aberration model based on cross triple correlation
11. H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217(1130), 408–432 (1953). [CrossRef]
20. S. Y. Liu, W. Liu, and T. T. Zhou, “ Fast algorithm for quadratic aberration model in optical lithography based on cross triple correlation,” J. Micro/Nanolith MEMS MOEMS 10(2), 023007 (2011). [CrossRef]
22. A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE 72(7), 889–901 (1984). [CrossRef]
20. S. Y. Liu, W. Liu, and T. T. Zhou, “ Fast algorithm for quadratic aberration model in optical lithography based on cross triple correlation,” J. Micro/Nanolith MEMS MOEMS 10(2), 023007 (2011). [CrossRef]
2.2 The iterative method for aberration measurement
23. K. S. Tang, K. F. Man, S. Kwong, and Q. He, “Genetic algorithms and their applications,” IEEE Signal Process. Mag. 13(6), 22–37 (1996). [CrossRef]
24. D. S. Weile and E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antenn. Propag. 45(3), 343–353 (1997). [CrossRef]
3. Simulation
3.1 Simulation parameters
17. L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006). [CrossRef]
3.2 Aerial image calculations by the CTC-based quadratic aberration model
20. S. Y. Liu, W. Liu, and T. T. Zhou, “ Fast algorithm for quadratic aberration model in optical lithography based on cross triple correlation,” J. Micro/Nanolith MEMS MOEMS 10(2), 023007 (2011). [CrossRef]
21. S. Y. Liu, W. Liu, and X. F. Wu, “Fast evaluation of aberration-induced intensity distribution in partially coherent imaging systems by cross triple correlation,” Chin. Phys. Lett. 28(10), 104212 (2011). [CrossRef]
3.3 Aberration measurement by the proposed iterative method
3.4 Comparison to the linear model method
9. W. Liu, S. Y. Liu, T. T. Zhou, and L. J. 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] [PubMed]
10. W. Liu, S. Y. Liu, T. L. Shi, and Z. R. Tang, “Generalized formulations for aerial image based lens aberration metrology in lithographic tools with arbitrarily shaped illumination sources,” Opt. Express 18(19), 20096–20104 (2010). [CrossRef] [PubMed]
4. Conclusion and future work
Acknowledgments
References and links
1. | B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE 4000, 294–306 (2000). [CrossRef] |
2. | H. Nomura and T. Sato, “Techniques for measuring aberrations in lenses used in photolithography with printed patterns,” Appl. Opt. 38(13), 2800–2807 (1999). [CrossRef] [PubMed] |
3. | J. Sung, M. Pitchumani, and E. G. Johnson, “Aberration measurement of photolithographic lenses by use of hybrid diffractive photomasks,” Appl. Opt. 42(11), 1987–1995 (2003). [CrossRef] [PubMed] |
4. | F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica 1(7-12), 689–704 (1934). [CrossRef] |
5. | M. Born and E. Wolf, Principles of Optics, 7th Ed. (Pergamon, 1999), chap. 9. |
6. | 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] |
7. | T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE 5754, 1659–1669 (2004). [CrossRef] |
8. | J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE 6152, 61523D, 61523D-10 (2006). [CrossRef] |
9. | W. Liu, S. Y. Liu, T. T. Zhou, and L. J. 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] [PubMed] |
10. | W. Liu, S. Y. Liu, T. L. Shi, and Z. R. Tang, “Generalized formulations for aerial image based lens aberration metrology in lithographic tools with arbitrarily shaped illumination sources,” Opt. Express 18(19), 20096–20104 (2010). [CrossRef] [PubMed] |
11. | H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217(1130), 408–432 (1953). [CrossRef] |
12. | B. E. A. Saleh, “Optical bilinear transformations: general properties,” Opt. Acta (Lond.) 26, 777–799 (1979). [CrossRef] |
13. | T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE 4691, 33–43 (2002). [CrossRef] |
14. | D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE 3051, 672–685 (1997). [CrossRef] |
15. | L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE 5377, 277–786 (2004). |
16. | L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE 5754, 1728–1737 (2004). [CrossRef] |
17. | L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE 6154, 61540Y, 61540Y-9 (2006). [CrossRef] |
18. | R. Miyakawa, P. Naulleau, and A. Zakhor, “Iterative procedure for in situ extreme ultraviolet optical testing with an incoherent source,” J. Vac. Sci. Technol. B 27(6), 2927–2930 (2009). [CrossRef] |
19. | R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE 7636, 76361K, 76361K-7 (2010). [CrossRef] |
20. | S. Y. Liu, W. Liu, and T. T. Zhou, “ Fast algorithm for quadratic aberration model in optical lithography based on cross triple correlation,” J. Micro/Nanolith MEMS MOEMS 10(2), 023007 (2011). [CrossRef] |
21. | S. Y. Liu, W. Liu, and X. F. Wu, “Fast evaluation of aberration-induced intensity distribution in partially coherent imaging systems by cross triple correlation,” Chin. Phys. Lett. 28(10), 104212 (2011). [CrossRef] |
22. | A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE 72(7), 889–901 (1984). [CrossRef] |
23. | K. S. Tang, K. F. Man, S. Kwong, and Q. He, “Genetic algorithms and their applications,” IEEE Signal Process. Mag. 13(6), 22–37 (1996). [CrossRef] |
24. | D. S. Weile and E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antenn. Propag. 45(3), 343–353 (1997). [CrossRef] |
OCIS Codes
(110.4980) Imaging systems : Partial coherence in imaging
(110.5220) Imaging systems : Photolithography
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(220.1010) Optical design and fabrication : Aberrations (global)
ToC Category:
Instrumentation, Measurement, and Metrology
History
Original Manuscript: April 16, 2012
Revised Manuscript: May 31, 2012
Manuscript Accepted: May 31, 2012
Published: June 12, 2012
Citation
Shiyuan Liu, Shuang Xu, Xiaofei Wu, and Wei Liu, "Iterative method for in situ measurement of lens aberrations in lithographic tools using CTC-based quadratic aberration model," Opt. Express 20, 14272-14283 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-14272
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References
- B. W. Smith and R. Schlief, “Understanding lens aberration and influences to lithographic imaging,” Proc. SPIE4000, 294–306 (2000). [CrossRef]
- H. Nomura and T. Sato, “Techniques for measuring aberrations in lenses used in photolithography with printed patterns,” Appl. Opt.38(13), 2800–2807 (1999). [CrossRef] [PubMed]
- J. Sung, M. Pitchumani, and E. G. Johnson, “Aberration measurement of photolithographic lenses by use of hybrid diffractive photomasks,” Appl. Opt.42(11), 1987–1995 (2003). [CrossRef] [PubMed]
- F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten form, der Phasenkontrastmethode,” Physica1(7-12), 689–704 (1934). [CrossRef]
- M. Born and E. Wolf, Principles of Optics, 7th Ed. (Pergamon, 1999), chap. 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 set-up and illumination pupil verification,” Proc. SPIE4346, 394–407 (2001). [CrossRef]
- T. Hagiwara, N. Kondo, I. Hiroshi, K. Suzuki, and N. Magome, “Development of aerial image based aberration measurement technique,” Proc. SPIE5754, 1659–1669 (2004). [CrossRef]
- J. K. Tyminski, T. Hagiwara, N. Kondo, and H. Irihama, “Aerial image sensor: in-situ scanner aberration monitor,” Proc. SPIE6152, 61523D, 61523D-10 (2006). [CrossRef]
- W. Liu, S. Y. Liu, T. T. Zhou, and L. J. Wang, “Aerial image based technique for measurement of lens aberrations up to 37th Zernike coefficient in lithographic tools under partial coherent illumination,” Opt. Express17(21), 19278–19291 (2009). [CrossRef] [PubMed]
- W. Liu, S. Y. Liu, T. L. Shi, and Z. R. Tang, “Generalized formulations for aerial image based lens aberration metrology in lithographic tools with arbitrarily shaped illumination sources,” Opt. Express18(19), 20096–20104 (2010). [CrossRef] [PubMed]
- H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A217(1130), 408–432 (1953). [CrossRef]
- B. E. A. Saleh, “Optical bilinear transformations: general properties,” Opt. Acta (Lond.)26, 777–799 (1979). [CrossRef]
- T. Nakashima, K. Higashi, and S. Hirukawa, “Impact of Zernike cross term on line width control,” Proc. SPIE4691, 33–43 (2002). [CrossRef]
- D. G. Flagello, J. Klerk, G. Davies, and R. Rogoff, “Towards a comprehensive control of full-field image quality in optical photolithography,” Proc. SPIE3051, 672–685 (1997). [CrossRef]
- L. Zavyalova, B. W. Smith, T. Suganaga, S. Matsuura, T. Itani, and J. Cashmore, “In-situ aberration monitoring using pahse wheel targets,” Proc. SPIE5377, 277–786 (2004).
- L. Zavyalova, A. Bourov, and B. W. Smith, “Automated aberration extraction using phase wheel targets,” Proc. SPIE5754, 1728–1737 (2004). [CrossRef]
- L. Zavyalova, B. W. Smith, A. Bourov, G. Zhang, V. Vellanki, P. Reynolds, and D. G. Flagello, “Practical approach to full-field wavefront aberration measurement using phase wheel targets,” Proc. SPIE6154, 61540Y, 61540Y-9 (2006). [CrossRef]
- R. Miyakawa, P. Naulleau, and A. Zakhor, “Iterative procedure for in situ extreme ultraviolet optical testing with an incoherent source,” J. Vac. Sci. Technol. B27(6), 2927–2930 (2009). [CrossRef]
- R. Miyakawa, P. Naulleau, A. Zakhor, and K. Goldberg, “Iterative procedure for in situ optical testing with an incoherent source,” Proc. SPIE7636, 76361K, 76361K-7 (2010). [CrossRef]
- S. Y. Liu, W. Liu, and T. T. Zhou, “ Fast algorithm for quadratic aberration model in optical lithography based on cross triple correlation,” J. Micro/Nanolith MEMS MOEMS10(2), 023007 (2011). [CrossRef]
- S. Y. Liu, W. Liu, and X. F. Wu, “Fast evaluation of aberration-induced intensity distribution in partially coherent imaging systems by cross triple correlation,” Chin. Phys. Lett.28(10), 104212 (2011). [CrossRef]
- A. W. Lohmann and B. Wirnitzer, “Triple correlations,” Proc. IEEE72(7), 889–901 (1984). [CrossRef]
- K. S. Tang, K. F. Man, S. Kwong, and Q. He, “Genetic algorithms and their applications,” IEEE Signal Process. Mag.13(6), 22–37 (1996). [CrossRef]
- D. S. Weile and E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: a review,” IEEE Trans. Antenn. Propag.45(3), 343–353 (1997). [CrossRef]
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