Abstract

Determining the period of a grating generating multiple diffraction orders from the data of diffraction angle measurement is not an easy task, mainly because of positioning error. We propose a novel technique, i.e., numerically adjusting the specimen position, to solve the problem. The procedure alone would reduce the amount of uncertainty by two orders of magnitude.

© 2014 Optical Society of America

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References

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  1. I. Misumi, S. Gonda, O. Sato, Q. Huang, and T. Kurosawa, “Nanometric lateral scales as CRM candidates for AFM, SEM and optical diffractometer,” J. Phys. 13, 206–215 (2005).
  2. H. U. Danzebrink, L. Koenders, G. B. Picotto, A. Lassila, S. H. Wang, and P. Klapetek, “Final report on EUROMET.L-S15.a (EURONET Project 925): intercomparison on step height standards and 1D gratings,” Metrologia 47, 04006 (2010).
    [CrossRef]
  3. D. Sharma, R. Sharma, S. Dua, and V. N. Ojha, “Pitch measurements of 1D/2D gratings using optical profiler and comparison with SEN/AFM,” in AdMet 2012 (Metrology Society of India, 2012), paper NM 003.
  4. X. Chen and L. Koenders, “A novel pitch evaluation of one-dimensional gratings based on a cross-correlation filter,” Meas. Sci. Technol. 25, 044007 (2014).
    [CrossRef]
  5. J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.
  6. S. S. H. Naqvi, S. Gaspar, K. Hickman, K. Bishop, and J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
    [CrossRef]
  7. F. Meli, R. Thalmann, and P. Blattner, “High precision pitch calibration of gratings using laser diffractometry,” in Proceedings of the First International Conference on Precision Engineering and Nanotechnology, Vol. 2, 31May–4 June 1999, pp. 252–255.
  8. V. I. Korotkov, S. A. Pulkin, A. L. Vitushkin, and L. F. Vitushkin, “Laser interferometric diffractometry for measurements of diffraction grating spacing,” Appl. Opt. 35, 4782–4786 (1996).
    [CrossRef]
  9. T. H. Yoon, C. I. Eom, M. S. Chung, and H. J. Kong, “Diffractometric methods for absolute measurement of diffraction-grating spacings,” Opt. Lett. 24, 107–109 (1999).
    [CrossRef]
  10. J. R. Taylor, An Introduction to Error Analysis (University Science Books, 1982).

2014 (1)

X. Chen and L. Koenders, “A novel pitch evaluation of one-dimensional gratings based on a cross-correlation filter,” Meas. Sci. Technol. 25, 044007 (2014).
[CrossRef]

2010 (1)

H. U. Danzebrink, L. Koenders, G. B. Picotto, A. Lassila, S. H. Wang, and P. Klapetek, “Final report on EUROMET.L-S15.a (EURONET Project 925): intercomparison on step height standards and 1D gratings,” Metrologia 47, 04006 (2010).
[CrossRef]

2005 (1)

I. Misumi, S. Gonda, O. Sato, Q. Huang, and T. Kurosawa, “Nanometric lateral scales as CRM candidates for AFM, SEM and optical diffractometer,” J. Phys. 13, 206–215 (2005).

1999 (1)

1996 (1)

1992 (1)

Bishop, K.

Blattner, P.

F. Meli, R. Thalmann, and P. Blattner, “High precision pitch calibration of gratings using laser diffractometry,” in Proceedings of the First International Conference on Precision Engineering and Nanotechnology, Vol. 2, 31May–4 June 1999, pp. 252–255.

Chen, X.

X. Chen and L. Koenders, “A novel pitch evaluation of one-dimensional gratings based on a cross-correlation filter,” Meas. Sci. Technol. 25, 044007 (2014).
[CrossRef]

Chung, M. S.

Danzebrink, H. U.

H. U. Danzebrink, L. Koenders, G. B. Picotto, A. Lassila, S. H. Wang, and P. Klapetek, “Final report on EUROMET.L-S15.a (EURONET Project 925): intercomparison on step height standards and 1D gratings,” Metrologia 47, 04006 (2010).
[CrossRef]

Dua, S.

D. Sharma, R. Sharma, S. Dua, and V. N. Ojha, “Pitch measurements of 1D/2D gratings using optical profiler and comparison with SEN/AFM,” in AdMet 2012 (Metrology Society of India, 2012), paper NM 003.

Eom, C. I.

Gaspar, S.

Gonda, S.

I. Misumi, S. Gonda, O. Sato, Q. Huang, and T. Kurosawa, “Nanometric lateral scales as CRM candidates for AFM, SEM and optical diffractometer,” J. Phys. 13, 206–215 (2005).

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Hickman, K.

Huang, Q.

I. Misumi, S. Gonda, O. Sato, Q. Huang, and T. Kurosawa, “Nanometric lateral scales as CRM candidates for AFM, SEM and optical diffractometer,” J. Phys. 13, 206–215 (2005).

Kitta, J.

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Klapetek, P.

H. U. Danzebrink, L. Koenders, G. B. Picotto, A. Lassila, S. H. Wang, and P. Klapetek, “Final report on EUROMET.L-S15.a (EURONET Project 925): intercomparison on step height standards and 1D gratings,” Metrologia 47, 04006 (2010).
[CrossRef]

Koenders, L.

X. Chen and L. Koenders, “A novel pitch evaluation of one-dimensional gratings based on a cross-correlation filter,” Meas. Sci. Technol. 25, 044007 (2014).
[CrossRef]

H. U. Danzebrink, L. Koenders, G. B. Picotto, A. Lassila, S. H. Wang, and P. Klapetek, “Final report on EUROMET.L-S15.a (EURONET Project 925): intercomparison on step height standards and 1D gratings,” Metrologia 47, 04006 (2010).
[CrossRef]

Kong, H. J.

Korotkov, V. I.

Kurosawa, T.

I. Misumi, S. Gonda, O. Sato, Q. Huang, and T. Kurosawa, “Nanometric lateral scales as CRM candidates for AFM, SEM and optical diffractometer,” J. Phys. 13, 206–215 (2005).

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Lassila, A.

H. U. Danzebrink, L. Koenders, G. B. Picotto, A. Lassila, S. H. Wang, and P. Klapetek, “Final report on EUROMET.L-S15.a (EURONET Project 925): intercomparison on step height standards and 1D gratings,” Metrologia 47, 04006 (2010).
[CrossRef]

McNeil, J. R.

Meli, F.

F. Meli, R. Thalmann, and P. Blattner, “High precision pitch calibration of gratings using laser diffractometry,” in Proceedings of the First International Conference on Precision Engineering and Nanotechnology, Vol. 2, 31May–4 June 1999, pp. 252–255.

Mine, H.

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Misumi, I.

I. Misumi, S. Gonda, O. Sato, Q. Huang, and T. Kurosawa, “Nanometric lateral scales as CRM candidates for AFM, SEM and optical diffractometer,” J. Phys. 13, 206–215 (2005).

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Mizuno, T.

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Nakayama, Y.

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Naqvi, S. S. H.

Ojha, V. N.

D. Sharma, R. Sharma, S. Dua, and V. N. Ojha, “Pitch measurements of 1D/2D gratings using optical profiler and comparison with SEN/AFM,” in AdMet 2012 (Metrology Society of India, 2012), paper NM 003.

Picotto, G. B.

H. U. Danzebrink, L. Koenders, G. B. Picotto, A. Lassila, S. H. Wang, and P. Klapetek, “Final report on EUROMET.L-S15.a (EURONET Project 925): intercomparison on step height standards and 1D gratings,” Metrologia 47, 04006 (2010).
[CrossRef]

Pulkin, S. A.

Sasada, K.

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Sato, O.

I. Misumi, S. Gonda, O. Sato, Q. Huang, and T. Kurosawa, “Nanometric lateral scales as CRM candidates for AFM, SEM and optical diffractometer,” J. Phys. 13, 206–215 (2005).

Sharma, D.

D. Sharma, R. Sharma, S. Dua, and V. N. Ojha, “Pitch measurements of 1D/2D gratings using optical profiler and comparison with SEN/AFM,” in AdMet 2012 (Metrology Society of India, 2012), paper NM 003.

Sharma, R.

D. Sharma, R. Sharma, S. Dua, and V. N. Ojha, “Pitch measurements of 1D/2D gratings using optical profiler and comparison with SEN/AFM,” in AdMet 2012 (Metrology Society of India, 2012), paper NM 003.

Takatsuji, T.

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Taylor, J. R.

J. R. Taylor, An Introduction to Error Analysis (University Science Books, 1982).

Thalmann, R.

F. Meli, R. Thalmann, and P. Blattner, “High precision pitch calibration of gratings using laser diffractometry,” in Proceedings of the First International Conference on Precision Engineering and Nanotechnology, Vol. 2, 31May–4 June 1999, pp. 252–255.

Vitushkin, A. L.

Vitushkin, L. F.

Wang, S. H.

H. U. Danzebrink, L. Koenders, G. B. Picotto, A. Lassila, S. H. Wang, and P. Klapetek, “Final report on EUROMET.L-S15.a (EURONET Project 925): intercomparison on step height standards and 1D gratings,” Metrologia 47, 04006 (2010).
[CrossRef]

Yoneda, S.

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Yoon, T. H.

Yoshizaki, K.

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

Appl. Opt. (2)

J. Phys. (1)

I. Misumi, S. Gonda, O. Sato, Q. Huang, and T. Kurosawa, “Nanometric lateral scales as CRM candidates for AFM, SEM and optical diffractometer,” J. Phys. 13, 206–215 (2005).

Meas. Sci. Technol. (1)

X. Chen and L. Koenders, “A novel pitch evaluation of one-dimensional gratings based on a cross-correlation filter,” Meas. Sci. Technol. 25, 044007 (2014).
[CrossRef]

Metrologia (1)

H. U. Danzebrink, L. Koenders, G. B. Picotto, A. Lassila, S. H. Wang, and P. Klapetek, “Final report on EUROMET.L-S15.a (EURONET Project 925): intercomparison on step height standards and 1D gratings,” Metrologia 47, 04006 (2010).
[CrossRef]

Opt. Lett. (1)

Other (4)

D. Sharma, R. Sharma, S. Dua, and V. N. Ojha, “Pitch measurements of 1D/2D gratings using optical profiler and comparison with SEN/AFM,” in AdMet 2012 (Metrology Society of India, 2012), paper NM 003.

J. Kitta, H. Mine, S. Gonda, K. Yoshizaki, I. Misumi, T. Takatsuji, T. Kurosawa, Y. Nakayama, K. Sasada, S. Yoneda, and T. Mizuno, “Development of a 100-nm pitch calibration system with a DUV laser diffractometer,” in Proceedings of Second International Symposium on Standard Materials and Metrology for Nanotechnology, Tokyo, Japan, 25–26 May2006.

F. Meli, R. Thalmann, and P. Blattner, “High precision pitch calibration of gratings using laser diffractometry,” in Proceedings of the First International Conference on Precision Engineering and Nanotechnology, Vol. 2, 31May–4 June 1999, pp. 252–255.

J. R. Taylor, An Introduction to Error Analysis (University Science Books, 1982).

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Figures (5)

Fig. 1.
Fig. 1.

Methods of measuring a diffraction angle. θ=0 is assumed as an example. Thick red lines denote light paths. (a) Direct. (b) Indirect.

Fig. 2.
Fig. 2.

Schematic detail of angular error. D, detector; thick solid red lines, actual path; thick broken red lines, presumed but incorrect path.

Fig. 3.
Fig. 3.

Simplified geometry of Fig. 2.

Fig. 4.
Fig. 4.

Numerical search of a.

Fig. 5.
Fig. 5.

Effect of numerical displacement correction. Gray, raw data; black, after correction.

Tables (1)

Tables Icon

Table 1. Summary of Measurements

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

sinθmsinθ=mλ/nd,
Δd=|dθm|Δθm=|mλncosθmsin2θm|Δθm.
tanθm=s/l.
Δd=(dlΔl)2+(dsΔs)2,
dl=mλncos2θmlsinθm,
ds=mλncos3θmlsin2θm.
l2=[(Δl)2sin2θm+(Δs)2cos2θm]cos2θm/(Δθm)2.
bcsin(θmθm)=Lsin(θ+θm),
ctan(θ+θm)=a,
tan(θ+θm)=[a+Lsin(θ+θm)]/[b+Lcos(θ+θm)].
tan2θ=[a+Lsin(θ+θ0)]/[b+Lcos(θ+θ0)].
ct=(dmaxdmin)/(dmax+dmin),

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