## Coma measurement of projection optics in lithographic tools based on relative image displacements at multiple illumination settings

Optics Express, Vol. 15, Issue 24, pp. 15878-15885 (2007)

http://dx.doi.org/10.1364/OE.15.015878

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### Abstract

In this paper, we propose a novel method for measuring the coma aberrations of lithographic projection optics based on relative image displacements at multiple illumination settings. The measurement accuracy of coma can be improved because the phase-shifting gratings are more sensitive to the aberrations than the binary gratings used in the TAMIS technique, and the impact of distortion on displacements of aerial image can be eliminated when the relative image displacements are measured. The PROLITH simulation results show that, the measurement accuracy of coma increases by more than 25% under conventional illumination, and the measurement accuracy of primary coma increases by more than 20% under annular illumination, compared with the TAMIS technique.

© 2007 Optical Society of America

## 1. Introduction

1. F. Wang, X. Wang, and M. Ma, “Measurement technique for in situ characterizing aberrations of projection optics in lithographic tools,” Appl. Opt. **45**, 6086–6093 (2006). [PubMed]

4. 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]

5. J. J. Chen, C. M. Huang, F. J. Shiu, C. S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, “The influence of coma effect on scanner overlay,” Proc. SPIE **4689**, 280–285 (2002). [CrossRef]

7. T. Saito, H. Watanabe, and Y. Okuda, “Evaluation of coma aberration in projection lens by various measurements,” Proc. SPIE **3334**, 297–308 (1998). [CrossRef]

8. 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]

9. H. Nomura and T. Sato, “Techniques for measuring aberrations in lenses used in photolithography with printed patterns,” Appl. Opt. **38**, 2800–2807 (1999). [CrossRef]

10. H. Nomura, K. Tawarayama, and T. Kohno, “Aberration measurement from specific photolithographic images: a different approach,” Appl. Opt. **39**, 1136–1147 (2000). [CrossRef]

11. J. P. Krik, G. Kunkel, and A. K. Wong, “Aberration measurement using in situ two-beam interferometry,” Proc. SPIE **4346**, 8–14 (2001). [CrossRef]

12. C. M. Garza, W. Conley, B. Roman, M. Schippers, J. Foster, J. Baselmans, K. Cummings, and D. Flagello, “Ring test aberration determination & device lithography correlation” Proc. SPIE **4346**, 36–44 (2001). [CrossRef]

13. N. R. Farrar, A. L. Smith, D. Busath, and D. Taitano, “In-situ measurement of lens aberrations,” Proc. SPIE **4000**, 18–29 (2000). [CrossRef]

14. 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]

16. F. Wang, X. Wang, M. Ma, D. Zhang, W. Shi, and J. Hu, “Coma measurement using a PSM and transmission image sensor,” Optik **117**, 21–25 (2006). [CrossRef]

## 2. Theory

*t*(

*x*),

*f*=sin

_{x}*θ*/

*λ*is the spatial frequency variables and the sinc function is defined as

_{7}, Z

_{8}, Z

_{14}, and Z

_{15}, which are the coefficients of the Zernike polynomials. The Zernike polynomials which represent the wavefront aberrations in the projection lenses can be expressed as [17]

_{7}represents third-order x-coma, Z

_{8}represents third-order y-coma, Z

_{14}represents fifth-order x-coma, and Z

_{15}represents fifth-order y-coma. When high-order coma aberrations are neglected, the aberration functions which influence the image displacements can be written as

9. H. Nomura and T. Sato, “Techniques for measuring aberrations in lenses used in photolithography with printed patterns,” Appl. Opt. **38**, 2800–2807 (1999). [CrossRef]

*ΔX*,

_{A}*ΔX*,

_{B}*ΔY*and

_{C}*ΔY*are the image displacements of marks A, B, C and D, respectively. The impact of distortion on image displacements can be eliminated by measuring the relative image displacements which can be expressed as

_{D}*ρ*=1, and the minimum image displacement caused by primary coma occurs at

*ρ*=0. The maximum relative image displacement caused by secondary coma occurs at

*ρ*=0, and the minimum image displacement caused by secondary coma occurs near

*ρ*=0.8. This is different from that of primary coma. As mentioned above, for the mark proposed in the paper which contains phase-shifting gratings, more high-order diffraction light can pass through the pupil. The diffraction spectrum has its orders positioned in the regions where large phase errors are introduced by coma, and consequently the sensitivity to relative image displacements is large.

*ΔX*(

*NA*,

*σ*) is the relative image displacement at the given NA and partial coherence setting, which can be measured by the aerial image sensor.

*S*

_{1}(

*NA*,

*σ*) and

*S*

_{2}(

*NA*,

*σ*) are sensitivities and can be expressed as

_{7}, Z

_{8}, Z

_{14}and Z

_{15}in different field positions can be determined. As can be seen from Eq. (15), when the variation ranges of the sensitivities are larger, the span of the data used for the least square fit are larger and the least square fit has higher accuracy, so the variation ranges of the sensitivities are the key factor which influences the measurement accuracy of the Zernike coefficients.

## 3. PROLITH simulation

_{max}and S

_{min}are the maximum and minimum values of sensitivity S.

_{7}for the present technique at multiple NA and partial coherence, under conventional illumination and annular illumination, respectively. Figures 2(c) and 2(d) show the sensitivities of Z

_{7}for the TAMIS technique at multiple NA and partial coherence, under conventional illumination and annular illumination, respectively. From the simulation results of sensitivities, the measurement accuracy can be estimated by Eq. (16), and the overlay accuracy of the lithographic tool is assumed to be 2nm. The simulation res ults of the sensitivities of Z

_{7}and the estimated measurement accuracy are shown in Table 1. From Fig. 2 and Table 1, the measurement accuracy of Z

_{7}increases by 25% and 21.7% under conventional illumination and annular illumination, respectively, compared with the TAMIS technique.

_{14}for the present technique at multiple NA and partial coherence, under conventional illumination and annular illumination, respectively. Figures 3(c) and 3(d) show the sensitivities of Z

_{14}for the TAMIS technique at multiple NA and partial coherence, under conventional illumination and annular illumination, respectively. The simulation results of the sensitivities of Z

_{14}and the estimated measurement accuracy are shown in Table 2. From Fig. 3 and Table 2, the measurement accuracy of Z

_{14}increases by 36.8% and 2.2% under conventional illumination and annular illumination, respectively, compared with the TAMIS technique.

_{8}and Z

_{15}equal to that of Z

_{7}and Z

_{14}, respectively.

## 4. Conclusion

## Acknowledgements

## References and links

1. | F. Wang, X. Wang, and M. Ma, “Measurement technique for in situ characterizing aberrations of projection optics in lithographic tools,” Appl. Opt. |

2. | M. Ma, X. Wang, and F. Wang, “Aberration measurement of projection optics in lithographic tools based on two-beam interference theory,” Appl. Opt. |

3. | 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 |

4. | D. G. Flagello, J. Mulkens, and C. Wagner, “Optical lithography into the millennium: sensitivity to aberrations, vibration and polarization,” Proc. SPIE |

5. | J. J. Chen, C. M. Huang, F. J. Shiu, C. S. Kuo, S. C. Fu, C. T. Ho, C. Wang, and J. H. Tsai, “The influence of coma effect on scanner overlay,” Proc. SPIE |

6. | J. Sung, M. Pitchumani, and E. G. Johnson, “Aberration measurement of photolithographic lenses by use of hybrid diffractive photomasks,” Appl. Opt. |

7. | T. Saito, H. Watanabe, and Y. Okuda, “Evaluation of coma aberration in projection lens by various measurements,” Proc. SPIE |

8. | 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. |

9. | H. Nomura and T. Sato, “Techniques for measuring aberrations in lenses used in photolithography with printed patterns,” Appl. Opt. |

10. | H. Nomura, K. Tawarayama, and T. Kohno, “Aberration measurement from specific photolithographic images: a different approach,” Appl. Opt. |

11. | J. P. Krik, G. Kunkel, and A. K. Wong, “Aberration measurement using in situ two-beam interferometry,” Proc. SPIE |

12. | C. M. Garza, W. Conley, B. Roman, M. Schippers, J. Foster, J. Baselmans, K. Cummings, and D. Flagello, “Ring test aberration determination & device lithography correlation” Proc. SPIE |

13. | N. R. Farrar, A. L. Smith, D. Busath, and D. Taitano, “In-situ measurement of lens aberrations,” Proc. SPIE |

14. | 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 |

15. | H. van der Laan and M. H. Moers, “Method of measuring aberration in an optical imaging system,” U.S. patent 6,646,729 (11 November 2003). |

16. | F. Wang, X. Wang, M. Ma, D. Zhang, W. Shi, and J. Hu, “Coma measurement using a PSM and transmission image sensor,” Optik |

17. | M. Born and E. Wolf, Principles of Optics, 7th edition, (Pergamon, 1999), chap. 9 . |

**OCIS Codes**

(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:**

Imaging Systems

**History**

Original Manuscript: July 23, 2007

Revised Manuscript: September 20, 2007

Manuscript Accepted: October 26, 2007

Published: November 15, 2007

**Citation**

Qiongyan Yuan, Xiangzhao Wang, Zicheng Qiu, Fan Wang, Mingying Ma, and Le He, "Coma measurement of projection optics in lithographic tools based on relative image displacements at multiple illumination settings," Opt. Express **15**, 15878-15885 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15878

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### References

- F. Wang, X. Wang and M. Ma, "Measurement technique for in situ characterizing aberrations of projection optics in lithographic tools," Appl. Opt. 45, 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, 8200-8208 (2006). [CrossRef] [PubMed]
- 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]
- J. J. Chen, C. M. Huang, F. J. Shiu, C. S. Kuo, S. C. Fu, C. T. Ho, C. Wang and J. H. Tsai, "The influence of coma effect on scanner overlay," Proc. SPIE 4689, 280-285 (2002). [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]
- T. Saito, H. Watanabe and Y. Okuda, "Evaluation of coma aberration in projection lens by various measurements," Proc. SPIE 3334, 297-308 (1998). [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]
- H. Nomura and T. Sato, "Techniques for measuring aberrations in lenses used in photolithography with printed patterns," Appl. Opt. 38, 2800-2807 (1999). [CrossRef]
- H. Nomura, K. Tawarayama and T. Kohno, "Aberration measurement from specific photolithographic images: a different approach," Appl. Opt. 39, 1136-1147 (2000). [CrossRef]
- J. P. Krik, G. Kunkel and A. K. Wong, "Aberration measurement using in situ two-beam interferometry," Proc. SPIE 4346, 8-14 (2001). [CrossRef]
- C. M. Garza, W. Conley, B. Roman, M. Schippers, J. Foster, J. Baselmans, K. Cummings and D. Flagello, "Ring test aberration determination & device lithography correlation" Proc. SPIE 4346, 36-44 (2001). [CrossRef]
- N. R. Farrar, A. L. Smith, D. Busath and D. Taitano, "In-situ measurement of lens aberrations," Proc. SPIE 4000, 18-29 (2000). [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]
- H. van der Laan and M. H. Moers, "Method of measuring aberration in an optical imaging system," U.S. patent 6,646,729 (11 November 2003).
- F. Wang, X. Wang, M. Ma, D. Zhang, W. Shi and J. Hu, "Coma measurement using a PSM and transmission image sensor," Optik 117, 21-25 (2006). [CrossRef]
- M. Born and E. Wolf, Principles of Optics, 7th edition, (Pergamon, 1999), Chap. 9.

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