In situ aberration measurement technique based on principal component analysis of aerial image |
Optics Express, Vol. 19, Issue 19, pp. 18080-18090 (2011)
http://dx.doi.org/10.1364/OE.19.018080
Acrobat PDF (2441 KB)
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
1. Introduction
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]
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]
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]
2. Theory
2.1 Aerial imaging model in optical lithography
- 1. Zernike space: The space constituted by Zernike coefficients.
- 2. Aerial image space: The image intensity distribution corresponding to certain Zernike coefficients combinations.
- 3. Principal component space: The statistical space constructed by principal component analysis of aerial images [17]. The transformation from principal component space to Zernike space relies on the linear transformation built by regression analysis.
2.2 Building the aerial image space
2.3 Principal component analysis
2.4 Regression matrix and Zernike aberration retrieval
3. Simulation
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]
4. Experiment
4.1 Measurement Method
21. L. Duan, J. Cheng, G. Sun, and Y. Chen, “New 0.75 NA ArF scanning lithographic tool,” Proc. SPIE 7973, 79732D (2011). [CrossRef]
4.2 Experimental Results
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]
5. Conclusion
Acknowledgments
References and links
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] |
9. | 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] |
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] |
OCIS Codes
(110.3960) Imaging systems : Microlithography
(120.3940) Instrumentation, measurement, and metrology : Metrology
(220.1010) Optical design and fabrication : Aberrations (global)
ToC Category:
Instrumentation, Measurement, and Metrology
History
Original Manuscript: July 25, 2011
Revised Manuscript: August 20, 2011
Manuscript Accepted: August 22, 2011
Published: August 30, 2011
Citation
Lifeng Duan, Xiangzhao Wang, Anatoly Y. Bourov, Bo Peng, and Peng Bu, "In situ aberration measurement technique based on principal component analysis of aerial image," Opt. Express 19, 18080-18090 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-19-18080
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References
- H. Ooki, T. Noda, and K. Matsumoto, “Aberration averaging using point spread function for scanning projection system,” Proc. SPIE4000, 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. SPIE5040, 119–130 (2003). [CrossRef]
- D. G. Flagello, J. Mulkens, and C. Wagner, “Optical lithography into the millennium: sensitivity to aberrations, vibration and polarization,” Proc. SPIE4000, 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. SPIE4346, 1379–1387 (2001). [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]
- 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]
- J. P. Kirk, “Review of photoresist-based lens evaluation methods,” Proc. SPIE4000, 2–8 (2000). [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]
- 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, M. Ma, and L. He, “Coma measurement of projection optics in lithographic tools based on relative image displacements at multiple illumination settings,” Opt. Express15(24), 15878–15885 (2007). [CrossRef] [PubMed]
- 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. SPIE5377, 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. SPIE4346, 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. SPIE6154, 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. SPIE7640, 764032, 764032-8 (2010). [CrossRef]
- 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).
- C. A. Mack, “Lithography simulation in semiconductor manufacturing,” Proc. SPIE5645, 63–83 (2005). [CrossRef]
- C. A. Mack, “Thirty years of lithography simulation,” Proc. SPIE5754, 1–12 (2004). [CrossRef]
- L. Duan, J. Cheng, G. Sun, and Y. Chen, “New 0.75 NA ArF scanning lithographic tool,” Proc. SPIE7973, 79732D (2011). [CrossRef]
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