Abstract

Scatterometry is a common technique for the characterization of nanostructured surfaces. With shrinking dimensions, fewer and fewer propagating diffraction orders exist, and structure roughness becomes more important. Recent investigations suggest that roughness has to be taken into account for structure reconstruction. The short wavelength of the extreme UV (EUV) is advantageous, since it provides more propagating diffraction orders as compared to UV and visible radiation and increases the sensitivity to small structural features, particularly roughness. We present a method to numerically estimate changes in measured diffraction intensities in angular resolved EUV scatterometry induced by line roughness. The model can be used to include the estimation of the roughness into the structure reconstruction algorithm.

© 2010 Optical Society of America

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  1. C. Raymond, “Overview of scatterometry applications in high volume silicon manufactoring,” AIP Conf. Proc. 788, 394–402 (2005).
  2. T. Schuster, S. Rafler, K. Frenner, and W. Osten, “Influence of line edge roughness (LER) on angular resolved and on spectroscopic scatterometry,” Proc. SPIE 7155, 71550W(2008).
    [CrossRef]
  3. T. Schuster, S. Rafler, V. Ferreras Paz, K. Frenner, and W. Osten, “Field stitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Microelectron. Eng. 86, 1029–1032 (2009).
    [CrossRef]
  4. Y. Cohen, B. Yaakobovitz, Y. Tsur, and D. Schreiner, “A novel method for pushing the limits of line edge roughness detection by scatterometry,” Proc. SPIE 6922, 692220 (2008).
    [CrossRef]
  5. P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desières, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203(2005).
    [CrossRef]
  6. C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
    [CrossRef]
  7. R. Klein, C. Laubis, R. Müller, F. Scholze, and G. Ulm, “The EUV metrology program of PTB,” Microelectron. Eng. 83, 707–709 (2006).
    [CrossRef]
  8. F. Scholze, J. Tümmler, and G. Ulm, “High-accuracy radiometry in the EUV range at the PTB soft x-ray radiometry beamline,” Metrologia 40, S224–S228 (2003).
    [CrossRef]
  9. C. Laubis, C. Buchholz, A. Fischer, S. Plöger, F. Scholz, H. Wagner, F. Scholze, and G. Ulm, “Characterization of large off-axis EUV mirrors with high accuracy reflectometry at PTB,” Proc. SPIE 6151, 61510I (2006).
    [CrossRef]
  10. F. Scholze, C. Laubis, U. Dersch, J. Pomplun, S. Burger, and F. Schmidt, “The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks,” Proc. SPIE 6617, 66171A (2007).
    [CrossRef]
  11. H. Gross, F. Scholze, A. Rathsfeld, and M. Bär, “Evaluation of measurement uncertainties in EUV scatterometry,” Proc. SPIE 7390, 73900T (2009).
    [CrossRef]
  12. J. Pomplun, S. Burger, F. Schmidt, F. Scholze, C. Laubis, and U. Dersch, “Metrology of EUV masks by EUV-scatteometry and finite element analysis,” Proc. SPIE 7028, 70280P (2008).
    [CrossRef]
  13. S. Burger, R. Klose, A. Schädle, F. Schmidt, and L. Zschiedrich, “FEM modelling of 3D photonic crystals and photonic crystal waveguides,” Proc. SPIE 5728, 164–173 (2005).
    [CrossRef]
  14. S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
    [CrossRef]
  15. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
    [CrossRef] [PubMed]
  16. J. Elschner, R. Hinder, A. Rathsfeld, and G. Schmidt, DiPoG Homepage, http://www.wias-berlin.de/software/DIPOG.
  17. H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, and A. Rathsfeld, “Mathematical modeling of indirect measurements in scatterometry,” Measurement 39, 782–794(2006).
    [CrossRef]
  18. J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze, C. Laubis, and U. Dersch, “Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters,” Proc. SPIE 6349, 63493D (2006).
    [CrossRef]
  19. F. Scholze and C. Laubis, “Use of EUV scatterometry for the characterization of line profiles and line roughness on photomasks,” in Proceedings of the 24th European Mask and Lithography Conference, U.Behringer, ed. (VDE Verlag, 2008), pp. 374–382.
  20. H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).
    [CrossRef]
  21. M. Wurm, “Über die dimensionelle Charakterisierung von Gitterstrukturen auf Fotomasken mit einem neuartigen DUV-Scatterometer,” Ph.D. dissertation (Friedrich-Schiller-Universität Jena, 2008).
  22. A. Kato and F. Scholze, “The effect of line roughness on the reconstruction of line profiles for EUV masks from EUV scatterometry,” Proc. SPIE 7636, 76362I (2010).
    [CrossRef]
  23. T. A. Germer, “Modeling the effect of line profile variation on optical critical dimension metrology,” Proc. SPIE 6518, 65180Z (2007).
    [CrossRef]
  24. K. Eidmann, M. Kühne, P. Müller, and G. D. Tsakiras, “Characterization of pinhole transmission gratings,” J. X-Ray Sci. Technol. 2, 259–273 (1990).
    [CrossRef]
  25. P. Debije, “Über den Einfluss der Wärmebewegung auf die Interferenzerscheinungen bei Röntgenstrahlen,” Verh. Dtsch. Phys. Ges. 15, 678–689 (1913).
  26. I. Waller, “Zur Frage der Einwirkung der Wärmebewegung auf die Interferenz von Röntgenstrahlen,” Z. Phys. A 17, 398–408 (1923).
    [CrossRef]
  27. H. Gross, A. Rathsfeld, F. Scholze, R. Model, and M. Bär, “Computational methods estimating uncertainties for profile reconstruction in scatterometry,” Proc. SPIE 6995, 69950T(2008).
    [CrossRef]

2010 (1)

A. Kato and F. Scholze, “The effect of line roughness on the reconstruction of line profiles for EUV masks from EUV scatterometry,” Proc. SPIE 7636, 76362I (2010).
[CrossRef]

2009 (3)

H. Gross, F. Scholze, A. Rathsfeld, and M. Bär, “Evaluation of measurement uncertainties in EUV scatterometry,” Proc. SPIE 7390, 73900T (2009).
[CrossRef]

T. Schuster, S. Rafler, V. Ferreras Paz, K. Frenner, and W. Osten, “Field stitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Microelectron. Eng. 86, 1029–1032 (2009).
[CrossRef]

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).
[CrossRef]

2008 (4)

H. Gross, A. Rathsfeld, F. Scholze, R. Model, and M. Bär, “Computational methods estimating uncertainties for profile reconstruction in scatterometry,” Proc. SPIE 6995, 69950T(2008).
[CrossRef]

Y. Cohen, B. Yaakobovitz, Y. Tsur, and D. Schreiner, “A novel method for pushing the limits of line edge roughness detection by scatterometry,” Proc. SPIE 6922, 692220 (2008).
[CrossRef]

T. Schuster, S. Rafler, K. Frenner, and W. Osten, “Influence of line edge roughness (LER) on angular resolved and on spectroscopic scatterometry,” Proc. SPIE 7155, 71550W(2008).
[CrossRef]

J. Pomplun, S. Burger, F. Schmidt, F. Scholze, C. Laubis, and U. Dersch, “Metrology of EUV masks by EUV-scatteometry and finite element analysis,” Proc. SPIE 7028, 70280P (2008).
[CrossRef]

2007 (3)

T. A. Germer, “Modeling the effect of line profile variation on optical critical dimension metrology,” Proc. SPIE 6518, 65180Z (2007).
[CrossRef]

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

F. Scholze, C. Laubis, U. Dersch, J. Pomplun, S. Burger, and F. Schmidt, “The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks,” Proc. SPIE 6617, 66171A (2007).
[CrossRef]

2006 (4)

C. Laubis, C. Buchholz, A. Fischer, S. Plöger, F. Scholz, H. Wagner, F. Scholze, and G. Ulm, “Characterization of large off-axis EUV mirrors with high accuracy reflectometry at PTB,” Proc. SPIE 6151, 61510I (2006).
[CrossRef]

R. Klein, C. Laubis, R. Müller, F. Scholze, and G. Ulm, “The EUV metrology program of PTB,” Microelectron. Eng. 83, 707–709 (2006).
[CrossRef]

H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, and A. Rathsfeld, “Mathematical modeling of indirect measurements in scatterometry,” Measurement 39, 782–794(2006).
[CrossRef]

J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze, C. Laubis, and U. Dersch, “Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters,” Proc. SPIE 6349, 63493D (2006).
[CrossRef]

2005 (5)

C. Raymond, “Overview of scatterometry applications in high volume silicon manufactoring,” AIP Conf. Proc. 788, 394–402 (2005).

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desières, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203(2005).
[CrossRef]

S. Burger, R. Klose, A. Schädle, F. Schmidt, and L. Zschiedrich, “FEM modelling of 3D photonic crystals and photonic crystal waveguides,” Proc. SPIE 5728, 164–173 (2005).
[CrossRef]

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

2003 (1)

F. Scholze, J. Tümmler, and G. Ulm, “High-accuracy radiometry in the EUV range at the PTB soft x-ray radiometry beamline,” Metrologia 40, S224–S228 (2003).
[CrossRef]

1990 (1)

K. Eidmann, M. Kühne, P. Müller, and G. D. Tsakiras, “Characterization of pinhole transmission gratings,” J. X-Ray Sci. Technol. 2, 259–273 (1990).
[CrossRef]

1923 (1)

I. Waller, “Zur Frage der Einwirkung der Wärmebewegung auf die Interferenz von Röntgenstrahlen,” Z. Phys. A 17, 398–408 (1923).
[CrossRef]

1913 (1)

P. Debije, “Über den Einfluss der Wärmebewegung auf die Interferenzerscheinungen bei Röntgenstrahlen,” Verh. Dtsch. Phys. Ges. 15, 678–689 (1913).

Bär, M.

H. Gross, F. Scholze, A. Rathsfeld, and M. Bär, “Evaluation of measurement uncertainties in EUV scatterometry,” Proc. SPIE 7390, 73900T (2009).
[CrossRef]

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).
[CrossRef]

H. Gross, A. Rathsfeld, F. Scholze, R. Model, and M. Bär, “Computational methods estimating uncertainties for profile reconstruction in scatterometry,” Proc. SPIE 6995, 69950T(2008).
[CrossRef]

H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, and A. Rathsfeld, “Mathematical modeling of indirect measurements in scatterometry,” Measurement 39, 782–794(2006).
[CrossRef]

Bodermann, B.

H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, and A. Rathsfeld, “Mathematical modeling of indirect measurements in scatterometry,” Measurement 39, 782–794(2006).
[CrossRef]

Boher, P.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desières, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203(2005).
[CrossRef]

Buchholz, C.

C. Laubis, C. Buchholz, A. Fischer, S. Plöger, F. Scholz, H. Wagner, F. Scholze, and G. Ulm, “Characterization of large off-axis EUV mirrors with high accuracy reflectometry at PTB,” Proc. SPIE 6151, 61510I (2006).
[CrossRef]

Burger, S.

J. Pomplun, S. Burger, F. Schmidt, F. Scholze, C. Laubis, and U. Dersch, “Metrology of EUV masks by EUV-scatteometry and finite element analysis,” Proc. SPIE 7028, 70280P (2008).
[CrossRef]

F. Scholze, C. Laubis, U. Dersch, J. Pomplun, S. Burger, and F. Schmidt, “The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks,” Proc. SPIE 6617, 66171A (2007).
[CrossRef]

J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze, C. Laubis, and U. Dersch, “Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters,” Proc. SPIE 6349, 63493D (2006).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Burger, R. Klose, A. Schädle, F. Schmidt, and L. Zschiedrich, “FEM modelling of 3D photonic crystals and photonic crystal waveguides,” Proc. SPIE 5728, 164–173 (2005).
[CrossRef]

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

Chaton, P.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desières, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203(2005).
[CrossRef]

Choi, K.

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

Cohen, Y.

Y. Cohen, B. Yaakobovitz, Y. Tsur, and D. Schreiner, “A novel method for pushing the limits of line edge roughness detection by scatterometry,” Proc. SPIE 6922, 692220 (2008).
[CrossRef]

Debije, P.

P. Debije, “Über den Einfluss der Wärmebewegung auf die Interferenzerscheinungen bei Röntgenstrahlen,” Verh. Dtsch. Phys. Ges. 15, 678–689 (1913).

Dersch, U.

J. Pomplun, S. Burger, F. Schmidt, F. Scholze, C. Laubis, and U. Dersch, “Metrology of EUV masks by EUV-scatteometry and finite element analysis,” Proc. SPIE 7028, 70280P (2008).
[CrossRef]

F. Scholze, C. Laubis, U. Dersch, J. Pomplun, S. Burger, and F. Schmidt, “The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks,” Proc. SPIE 6617, 66171A (2007).
[CrossRef]

J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze, C. Laubis, and U. Dersch, “Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters,” Proc. SPIE 6349, 63493D (2006).
[CrossRef]

Desières, Y.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desières, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203(2005).
[CrossRef]

Eidmann, K.

K. Eidmann, M. Kühne, P. Müller, and G. D. Tsakiras, “Characterization of pinhole transmission gratings,” J. X-Ray Sci. Technol. 2, 259–273 (1990).
[CrossRef]

Elschner, J.

J. Elschner, R. Hinder, A. Rathsfeld, and G. Schmidt, DiPoG Homepage, http://www.wias-berlin.de/software/DIPOG.

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Ferreras Paz, V.

T. Schuster, S. Rafler, V. Ferreras Paz, K. Frenner, and W. Osten, “Field stitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Microelectron. Eng. 86, 1029–1032 (2009).
[CrossRef]

Fischer, A.

C. Laubis, C. Buchholz, A. Fischer, S. Plöger, F. Scholz, H. Wagner, F. Scholze, and G. Ulm, “Characterization of large off-axis EUV mirrors with high accuracy reflectometry at PTB,” Proc. SPIE 6151, 61510I (2006).
[CrossRef]

Foucher, J.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desières, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203(2005).
[CrossRef]

Frenner, K.

T. Schuster, S. Rafler, V. Ferreras Paz, K. Frenner, and W. Osten, “Field stitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Microelectron. Eng. 86, 1029–1032 (2009).
[CrossRef]

T. Schuster, S. Rafler, K. Frenner, and W. Osten, “Influence of line edge roughness (LER) on angular resolved and on spectroscopic scatterometry,” Proc. SPIE 7155, 71550W(2008).
[CrossRef]

Gao, W.

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

Germer, T. A.

T. A. Germer, “Modeling the effect of line profile variation on optical critical dimension metrology,” Proc. SPIE 6518, 65180Z (2007).
[CrossRef]

Gross, H.

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).
[CrossRef]

H. Gross, F. Scholze, A. Rathsfeld, and M. Bär, “Evaluation of measurement uncertainties in EUV scatterometry,” Proc. SPIE 7390, 73900T (2009).
[CrossRef]

H. Gross, A. Rathsfeld, F. Scholze, R. Model, and M. Bär, “Computational methods estimating uncertainties for profile reconstruction in scatterometry,” Proc. SPIE 6995, 69950T(2008).
[CrossRef]

H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, and A. Rathsfeld, “Mathematical modeling of indirect measurements in scatterometry,” Measurement 39, 782–794(2006).
[CrossRef]

Hazart, J.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desières, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203(2005).
[CrossRef]

Hinder, R.

J. Elschner, R. Hinder, A. Rathsfeld, and G. Schmidt, DiPoG Homepage, http://www.wias-berlin.de/software/DIPOG.

Jones, R.

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

Kato, A.

A. Kato and F. Scholze, “The effect of line roughness on the reconstruction of line profiles for EUV masks from EUV scatterometry,” Proc. SPIE 7636, 76362I (2010).
[CrossRef]

Keane, D.

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

Klein, R.

R. Klein, C. Laubis, R. Müller, F. Scholze, and G. Ulm, “The EUV metrology program of PTB,” Microelectron. Eng. 83, 707–709 (2006).
[CrossRef]

Klose, R.

S. Burger, R. Klose, A. Schädle, F. Schmidt, and L. Zschiedrich, “FEM modelling of 3D photonic crystals and photonic crystal waveguides,” Proc. SPIE 5728, 164–173 (2005).
[CrossRef]

Köhle, R.

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

Koschny, T.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Kühne, M.

K. Eidmann, M. Kühne, P. Müller, and G. D. Tsakiras, “Characterization of pinhole transmission gratings,” J. X-Ray Sci. Technol. 2, 259–273 (1990).
[CrossRef]

Laubis, C.

J. Pomplun, S. Burger, F. Schmidt, F. Scholze, C. Laubis, and U. Dersch, “Metrology of EUV masks by EUV-scatteometry and finite element analysis,” Proc. SPIE 7028, 70280P (2008).
[CrossRef]

F. Scholze, C. Laubis, U. Dersch, J. Pomplun, S. Burger, and F. Schmidt, “The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks,” Proc. SPIE 6617, 66171A (2007).
[CrossRef]

R. Klein, C. Laubis, R. Müller, F. Scholze, and G. Ulm, “The EUV metrology program of PTB,” Microelectron. Eng. 83, 707–709 (2006).
[CrossRef]

C. Laubis, C. Buchholz, A. Fischer, S. Plöger, F. Scholz, H. Wagner, F. Scholze, and G. Ulm, “Characterization of large off-axis EUV mirrors with high accuracy reflectometry at PTB,” Proc. SPIE 6151, 61510I (2006).
[CrossRef]

J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze, C. Laubis, and U. Dersch, “Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters,” Proc. SPIE 6349, 63493D (2006).
[CrossRef]

F. Scholze and C. Laubis, “Use of EUV scatterometry for the characterization of line profiles and line roughness on photomasks,” in Proceedings of the 24th European Mask and Lithography Conference, U.Behringer, ed. (VDE Verlag, 2008), pp. 374–382.

Leroux, T.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desières, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203(2005).
[CrossRef]

Lin, E.

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

Linden, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

März, R.

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

Model, R.

H. Gross, A. Rathsfeld, F. Scholze, R. Model, and M. Bär, “Computational methods estimating uncertainties for profile reconstruction in scatterometry,” Proc. SPIE 6995, 69950T(2008).
[CrossRef]

H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, and A. Rathsfeld, “Mathematical modeling of indirect measurements in scatterometry,” Measurement 39, 782–794(2006).
[CrossRef]

Müller, P.

K. Eidmann, M. Kühne, P. Müller, and G. D. Tsakiras, “Characterization of pinhole transmission gratings,” J. X-Ray Sci. Technol. 2, 259–273 (1990).
[CrossRef]

Müller, R.

R. Klein, C. Laubis, R. Müller, F. Scholze, and G. Ulm, “The EUV metrology program of PTB,” Microelectron. Eng. 83, 707–709 (2006).
[CrossRef]

Nölscher, C.

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

Osten, W.

T. Schuster, S. Rafler, V. Ferreras Paz, K. Frenner, and W. Osten, “Field stitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Microelectron. Eng. 86, 1029–1032 (2009).
[CrossRef]

T. Schuster, S. Rafler, K. Frenner, and W. Osten, “Influence of line edge roughness (LER) on angular resolved and on spectroscopic scatterometry,” Proc. SPIE 7155, 71550W(2008).
[CrossRef]

Petit, J.

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desières, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203(2005).
[CrossRef]

Plöger, S.

C. Laubis, C. Buchholz, A. Fischer, S. Plöger, F. Scholz, H. Wagner, F. Scholze, and G. Ulm, “Characterization of large off-axis EUV mirrors with high accuracy reflectometry at PTB,” Proc. SPIE 6151, 61510I (2006).
[CrossRef]

Pomplun, J.

J. Pomplun, S. Burger, F. Schmidt, F. Scholze, C. Laubis, and U. Dersch, “Metrology of EUV masks by EUV-scatteometry and finite element analysis,” Proc. SPIE 7028, 70280P (2008).
[CrossRef]

F. Scholze, C. Laubis, U. Dersch, J. Pomplun, S. Burger, and F. Schmidt, “The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks,” Proc. SPIE 6617, 66171A (2007).
[CrossRef]

J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze, C. Laubis, and U. Dersch, “Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters,” Proc. SPIE 6349, 63493D (2006).
[CrossRef]

Rafler, S.

T. Schuster, S. Rafler, V. Ferreras Paz, K. Frenner, and W. Osten, “Field stitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Microelectron. Eng. 86, 1029–1032 (2009).
[CrossRef]

T. Schuster, S. Rafler, K. Frenner, and W. Osten, “Influence of line edge roughness (LER) on angular resolved and on spectroscopic scatterometry,” Proc. SPIE 7155, 71550W(2008).
[CrossRef]

Rathsfeld, A.

H. Gross, F. Scholze, A. Rathsfeld, and M. Bär, “Evaluation of measurement uncertainties in EUV scatterometry,” Proc. SPIE 7390, 73900T (2009).
[CrossRef]

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).
[CrossRef]

H. Gross, A. Rathsfeld, F. Scholze, R. Model, and M. Bär, “Computational methods estimating uncertainties for profile reconstruction in scatterometry,” Proc. SPIE 6995, 69950T(2008).
[CrossRef]

H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, and A. Rathsfeld, “Mathematical modeling of indirect measurements in scatterometry,” Measurement 39, 782–794(2006).
[CrossRef]

J. Elschner, R. Hinder, A. Rathsfeld, and G. Schmidt, DiPoG Homepage, http://www.wias-berlin.de/software/DIPOG.

Raymond, C.

C. Raymond, “Overview of scatterometry applications in high volume silicon manufactoring,” AIP Conf. Proc. 788, 394–402 (2005).

Rice, B.

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

Schädle, A.

S. Burger, R. Klose, A. Schädle, F. Schmidt, and L. Zschiedrich, “FEM modelling of 3D photonic crystals and photonic crystal waveguides,” Proc. SPIE 5728, 164–173 (2005).
[CrossRef]

Schmidt, F.

J. Pomplun, S. Burger, F. Schmidt, F. Scholze, C. Laubis, and U. Dersch, “Metrology of EUV masks by EUV-scatteometry and finite element analysis,” Proc. SPIE 7028, 70280P (2008).
[CrossRef]

F. Scholze, C. Laubis, U. Dersch, J. Pomplun, S. Burger, and F. Schmidt, “The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks,” Proc. SPIE 6617, 66171A (2007).
[CrossRef]

J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze, C. Laubis, and U. Dersch, “Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters,” Proc. SPIE 6349, 63493D (2006).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Burger, R. Klose, A. Schädle, F. Schmidt, and L. Zschiedrich, “FEM modelling of 3D photonic crystals and photonic crystal waveguides,” Proc. SPIE 5728, 164–173 (2005).
[CrossRef]

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

Schmidt, G.

J. Elschner, R. Hinder, A. Rathsfeld, and G. Schmidt, DiPoG Homepage, http://www.wias-berlin.de/software/DIPOG.

Scholz, F.

C. Laubis, C. Buchholz, A. Fischer, S. Plöger, F. Scholz, H. Wagner, F. Scholze, and G. Ulm, “Characterization of large off-axis EUV mirrors with high accuracy reflectometry at PTB,” Proc. SPIE 6151, 61510I (2006).
[CrossRef]

Scholze, F.

A. Kato and F. Scholze, “The effect of line roughness on the reconstruction of line profiles for EUV masks from EUV scatterometry,” Proc. SPIE 7636, 76362I (2010).
[CrossRef]

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).
[CrossRef]

H. Gross, F. Scholze, A. Rathsfeld, and M. Bär, “Evaluation of measurement uncertainties in EUV scatterometry,” Proc. SPIE 7390, 73900T (2009).
[CrossRef]

J. Pomplun, S. Burger, F. Schmidt, F. Scholze, C. Laubis, and U. Dersch, “Metrology of EUV masks by EUV-scatteometry and finite element analysis,” Proc. SPIE 7028, 70280P (2008).
[CrossRef]

H. Gross, A. Rathsfeld, F. Scholze, R. Model, and M. Bär, “Computational methods estimating uncertainties for profile reconstruction in scatterometry,” Proc. SPIE 6995, 69950T(2008).
[CrossRef]

F. Scholze, C. Laubis, U. Dersch, J. Pomplun, S. Burger, and F. Schmidt, “The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks,” Proc. SPIE 6617, 66171A (2007).
[CrossRef]

C. Laubis, C. Buchholz, A. Fischer, S. Plöger, F. Scholz, H. Wagner, F. Scholze, and G. Ulm, “Characterization of large off-axis EUV mirrors with high accuracy reflectometry at PTB,” Proc. SPIE 6151, 61510I (2006).
[CrossRef]

R. Klein, C. Laubis, R. Müller, F. Scholze, and G. Ulm, “The EUV metrology program of PTB,” Microelectron. Eng. 83, 707–709 (2006).
[CrossRef]

J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze, C. Laubis, and U. Dersch, “Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters,” Proc. SPIE 6349, 63493D (2006).
[CrossRef]

F. Scholze, J. Tümmler, and G. Ulm, “High-accuracy radiometry in the EUV range at the PTB soft x-ray radiometry beamline,” Metrologia 40, S224–S228 (2003).
[CrossRef]

F. Scholze and C. Laubis, “Use of EUV scatterometry for the characterization of line profiles and line roughness on photomasks,” in Proceedings of the 24th European Mask and Lithography Conference, U.Behringer, ed. (VDE Verlag, 2008), pp. 374–382.

Schreiner, D.

Y. Cohen, B. Yaakobovitz, Y. Tsur, and D. Schreiner, “A novel method for pushing the limits of line edge roughness detection by scatterometry,” Proc. SPIE 6922, 692220 (2008).
[CrossRef]

Schuster, T.

T. Schuster, S. Rafler, V. Ferreras Paz, K. Frenner, and W. Osten, “Field stitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Microelectron. Eng. 86, 1029–1032 (2009).
[CrossRef]

T. Schuster, S. Rafler, K. Frenner, and W. Osten, “Influence of line edge roughness (LER) on angular resolved and on spectroscopic scatterometry,” Proc. SPIE 7155, 71550W(2008).
[CrossRef]

Soukoulis, C. M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Thompson, G.

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

Tsakiras, G. D.

K. Eidmann, M. Kühne, P. Müller, and G. D. Tsakiras, “Characterization of pinhole transmission gratings,” J. X-Ray Sci. Technol. 2, 259–273 (1990).
[CrossRef]

Tsur, Y.

Y. Cohen, B. Yaakobovitz, Y. Tsur, and D. Schreiner, “A novel method for pushing the limits of line edge roughness detection by scatterometry,” Proc. SPIE 6922, 692220 (2008).
[CrossRef]

Tümmler, J.

F. Scholze, J. Tümmler, and G. Ulm, “High-accuracy radiometry in the EUV range at the PTB soft x-ray radiometry beamline,” Metrologia 40, S224–S228 (2003).
[CrossRef]

Ulm, G.

R. Klein, C. Laubis, R. Müller, F. Scholze, and G. Ulm, “The EUV metrology program of PTB,” Microelectron. Eng. 83, 707–709 (2006).
[CrossRef]

F. Scholze, J. Tümmler, and G. Ulm, “High-accuracy radiometry in the EUV range at the PTB soft x-ray radiometry beamline,” Metrologia 40, S224–S228 (2003).
[CrossRef]

Wagner, H.

C. Laubis, C. Buchholz, A. Fischer, S. Plöger, F. Scholz, H. Wagner, F. Scholze, and G. Ulm, “Characterization of large off-axis EUV mirrors with high accuracy reflectometry at PTB,” Proc. SPIE 6151, 61510I (2006).
[CrossRef]

Waller, I.

I. Waller, “Zur Frage der Einwirkung der Wärmebewegung auf die Interferenz von Röntgenstrahlen,” Z. Phys. A 17, 398–408 (1923).
[CrossRef]

Wang, C.

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

Wegener, M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Weigand, S.

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

Wu, W.

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

Wurm, M.

H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, and A. Rathsfeld, “Mathematical modeling of indirect measurements in scatterometry,” Measurement 39, 782–794(2006).
[CrossRef]

M. Wurm, “Über die dimensionelle Charakterisierung von Gitterstrukturen auf Fotomasken mit einem neuartigen DUV-Scatterometer,” Ph.D. dissertation (Friedrich-Schiller-Universität Jena, 2008).

Yaakobovitz, B.

Y. Cohen, B. Yaakobovitz, Y. Tsur, and D. Schreiner, “A novel method for pushing the limits of line edge roughness detection by scatterometry,” Proc. SPIE 6922, 692220 (2008).
[CrossRef]

Zhou, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Zschiedrich, L.

J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze, C. Laubis, and U. Dersch, “Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters,” Proc. SPIE 6349, 63493D (2006).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

S. Burger, R. Klose, A. Schädle, F. Schmidt, and L. Zschiedrich, “FEM modelling of 3D photonic crystals and photonic crystal waveguides,” Proc. SPIE 5728, 164–173 (2005).
[CrossRef]

J. Appl. Phys. (1)

C. Wang, R. Jones, E. Lin, W. Wu, B. Rice, K. Choi, G. Thompson, S. Weigand, and D. Keane, “Characterization of correlated line edge roughness of nanoscale line gratings using small angle x-ray scattering,” J. Appl. Phys. 102, 024901(2007).
[CrossRef]

J. X-Ray Sci. Technol. (1)

K. Eidmann, M. Kühne, P. Müller, and G. D. Tsakiras, “Characterization of pinhole transmission gratings,” J. X-Ray Sci. Technol. 2, 259–273 (1990).
[CrossRef]

Meas. Sci. Technol. (1)

H. Gross, A. Rathsfeld, F. Scholze, and M. Bär, “Profile reconstruction in extreme ultraviolet (EUV) scatterometry: modeling and uncertainty estimates,” Meas. Sci. Technol. 20, 105102 (2009).
[CrossRef]

Measurement (1)

H. Gross, R. Model, M. Bär, M. Wurm, B. Bodermann, and A. Rathsfeld, “Mathematical modeling of indirect measurements in scatterometry,” Measurement 39, 782–794(2006).
[CrossRef]

Metrologia (1)

F. Scholze, J. Tümmler, and G. Ulm, “High-accuracy radiometry in the EUV range at the PTB soft x-ray radiometry beamline,” Metrologia 40, S224–S228 (2003).
[CrossRef]

Microelectron. Eng. (2)

T. Schuster, S. Rafler, V. Ferreras Paz, K. Frenner, and W. Osten, “Field stitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry,” Microelectron. Eng. 86, 1029–1032 (2009).
[CrossRef]

R. Klein, C. Laubis, R. Müller, F. Scholze, and G. Ulm, “The EUV metrology program of PTB,” Microelectron. Eng. 83, 707–709 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, C. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95, 203901 (2005).
[CrossRef] [PubMed]

Proc. SPIE (13)

J. Pomplun, S. Burger, F. Schmidt, L. Zschiedrich, F. Scholze, C. Laubis, and U. Dersch, “Rigorous FEM-simulation of EUV-masks: influence of shape and material parameters,” Proc. SPIE 6349, 63493D (2006).
[CrossRef]

Y. Cohen, B. Yaakobovitz, Y. Tsur, and D. Schreiner, “A novel method for pushing the limits of line edge roughness detection by scatterometry,” Proc. SPIE 6922, 692220 (2008).
[CrossRef]

P. Boher, J. Petit, T. Leroux, J. Foucher, Y. Desières, J. Hazart, and P. Chaton, “Optical Fourier transform scatterometry for LER and LWR metrology,” Proc. SPIE 5752, 192–203(2005).
[CrossRef]

T. Schuster, S. Rafler, K. Frenner, and W. Osten, “Influence of line edge roughness (LER) on angular resolved and on spectroscopic scatterometry,” Proc. SPIE 7155, 71550W(2008).
[CrossRef]

C. Laubis, C. Buchholz, A. Fischer, S. Plöger, F. Scholz, H. Wagner, F. Scholze, and G. Ulm, “Characterization of large off-axis EUV mirrors with high accuracy reflectometry at PTB,” Proc. SPIE 6151, 61510I (2006).
[CrossRef]

F. Scholze, C. Laubis, U. Dersch, J. Pomplun, S. Burger, and F. Schmidt, “The influence of line edge roughness and CD uniformity on EUV scatterometry for CD characterization of EUV masks,” Proc. SPIE 6617, 66171A (2007).
[CrossRef]

H. Gross, F. Scholze, A. Rathsfeld, and M. Bär, “Evaluation of measurement uncertainties in EUV scatterometry,” Proc. SPIE 7390, 73900T (2009).
[CrossRef]

J. Pomplun, S. Burger, F. Schmidt, F. Scholze, C. Laubis, and U. Dersch, “Metrology of EUV masks by EUV-scatteometry and finite element analysis,” Proc. SPIE 7028, 70280P (2008).
[CrossRef]

S. Burger, R. Klose, A. Schädle, F. Schmidt, and L. Zschiedrich, “FEM modelling of 3D photonic crystals and photonic crystal waveguides,” Proc. SPIE 5728, 164–173 (2005).
[CrossRef]

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

A. Kato and F. Scholze, “The effect of line roughness on the reconstruction of line profiles for EUV masks from EUV scatterometry,” Proc. SPIE 7636, 76362I (2010).
[CrossRef]

T. A. Germer, “Modeling the effect of line profile variation on optical critical dimension metrology,” Proc. SPIE 6518, 65180Z (2007).
[CrossRef]

H. Gross, A. Rathsfeld, F. Scholze, R. Model, and M. Bär, “Computational methods estimating uncertainties for profile reconstruction in scatterometry,” Proc. SPIE 6995, 69950T(2008).
[CrossRef]

Verh. Dtsch. Phys. Ges. (1)

P. Debije, “Über den Einfluss der Wärmebewegung auf die Interferenzerscheinungen bei Röntgenstrahlen,” Verh. Dtsch. Phys. Ges. 15, 678–689 (1913).

Z. Phys. A (1)

I. Waller, “Zur Frage der Einwirkung der Wärmebewegung auf die Interferenz von Röntgenstrahlen,” Z. Phys. A 17, 398–408 (1923).
[CrossRef]

Other (4)

C. Raymond, “Overview of scatterometry applications in high volume silicon manufactoring,” AIP Conf. Proc. 788, 394–402 (2005).

F. Scholze and C. Laubis, “Use of EUV scatterometry for the characterization of line profiles and line roughness on photomasks,” in Proceedings of the 24th European Mask and Lithography Conference, U.Behringer, ed. (VDE Verlag, 2008), pp. 374–382.

M. Wurm, “Über die dimensionelle Charakterisierung von Gitterstrukturen auf Fotomasken mit einem neuartigen DUV-Scatterometer,” Ph.D. dissertation (Friedrich-Schiller-Universität Jena, 2008).

J. Elschner, R. Hinder, A. Rathsfeld, and G. Schmidt, DiPoG Homepage, http://www.wias-berlin.de/software/DIPOG.

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Figures (9)

Fig. 1
Fig. 1

Scheme of the absorber line profile and some of its geometric parameters. The absorber line is placed on top of a reflective multilayer.

Fig. 2
Fig. 2

Line roughness models and their cross section in the plane of incidence. Left, line edge roughness with constant pitch and CD, and random line center positions. Right, linewidth roughness with constant pitch and periodic line center positions, and random CD.

Fig. 3
Fig. 3

Fraunhofer diffraction of a reflection grating. Angle of incidence, 6 ° ; duty cycle, 1 5 ; N = 10 . Because of the chosen duty cycle, every sixth diffraction order is suppressed.

Fig. 4
Fig. 4

Disturbed diffraction pattern (bullets, undisturbed) and its standard deviation for each diffraction order. LER in the left half, LWR on the right, σ = 10 nm , N = 100 , 145 nm dark lines at 840 nm pitch.

Fig. 5
Fig. 5

Normalized standard deviation of intensity for each diffraction order: red stars, a combination of uncorrelated LER and LWR; blue circles, σ I for LER; open circles, σ I for LWR. All rms values are chosen as σ = 4 nm . N = 100 , 145 nm dark lines at 840 nm pitch.

Fig. 6
Fig. 6

Graph of Θ for LER σ values of 0, 0.05 w, and 0.1 w for the solid, dashed, and dashed–dotted curves, respectively. w = 140 nm . Double values of σ in the case of LWR.

Fig. 7
Fig. 7

Influence of surface topography on the reflectance function. For a smooth surface, shown left, radiation is incident on either reflecting or absorbing areas and the resulting reflectance function has only two values. For structures with finite height, shown right, there is a direct transition from the absorbing to the reflecting area only for the shadowed sidewall. At the opposite side, the sidewall is illuminated and, in real cases, the effective reflectance will be even lower than for the absorbing area. Thus, the reflectance function has at least three values and is no longer symmetric to the line center.

Fig. 8
Fig. 8

Optimization results. The reconstructed sidewall angle of the absorber lines is shown for different rms values.

Fig. 9
Fig. 9

Optimization results. The reconstructed geometric parameters of the absorber lines are shown for different rms values: bottom CD (dashed curve), CD at half-height (dashed–dotted curve), top CD (dotted curve), and height (solid curve).

Equations (24)

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

r ( x ) { 1 if     x [ N d 2 , N d 2 ] and j { n , , n } : | x x j | w j 2 0 otherwise } = j = n n δ ( x x j ) * rect ( x w j ) for all     x [ N d 2 , N d 2 ] .
E ( k ) F { r } ( k ) = j = n n x j w j 2 x j + w j 2 exp ( i k x ) d x = j = n n exp ( i k x j ) × { w j sin k w j 2 k w j 2 if     k 0 w j if     k = 0 .
w j = w for all     j { n , , n } ,
x j = j d for all     j { n , , n } ,
r 0 ( x ) j = n n δ ( x j d ) * rect ( x w ) for all     x [ N d 2 , N d 2 ] ,
F { r 0 } ( k ) = N w sin k w 2 k w 2 sin Nkd 2 N sin k d 2 .
I 0 ( k ) 1 ( N w ) 2 | F { r 0 } ( k ) | 2 = ( sin k w 2 k w 2 ) 2 ( sin Nkd 2 N sin k d 2 ) 2 .
x j = j d + y j for all     j { n , , n } ,
j = n n exp ( i k x j ) = 1. exp ( i k y ) j = n n exp ( i k j d ) 2. exp ( 1 2 k 2 y 2 ) sin Nkd 2 sin k d 2 = 3. exp ( 1 2 k 2 σ 2 ) sin Nkd 2 sin k d 2 ,
F { r } ( k ) = N w sin k w 2 k w 2 sin Nkd 2 N sin k d 2 exp ( σ 2 k 2 2 ) = F { r 0 } ( k ) exp ( σ 2 k 2 2 ) ,
I ( k ) = 1 ( N w ) 2 | F { r } ( k ) | 2 = I 0 ( k ) exp ( σ 2 k 2 ) .
σ F 2 ( k ) = | F { r } ( k ) | 2 | F { r } ( k ) | 2 = w 2 ( sin k w 2 k w 2 ) 2 [ | j = n n exp ( i k x j ) | 2 ( sin Nkd 2 sin k d 2 ) 2 exp ( σ 2 k 2 ) ] .
| j = n n exp ( i k x j ) | 2 = ( l = n n exp ( i k x l ) ) × m = n n exp ( i k x m ) = N + exp ( i k y ) exp ( i k y ) l = n + 1 n m = n l 1 [ exp ( i k d ( m l ) ) + exp ( i k d ( m l ) ) ] = N [ 1 exp ( σ 2 k 2 ) ] + exp ( σ 2 k 2 ) ( sin Nkd 2 sin k d 2 ) 2 .
σ F ( k ) = 2 σ N | sin k w 2 | .
σ I ( k ) = 1 ( N w ) 2 2 | F { r } ( k ) | σ F ( k ) = 4 σ w N | sin k w 2 | I ( k ) .
σ I ( k ) = 2 σ | k | N exp ( σ 2 k 2 2 ) I ( k ) for     k = 2 π m d , m Z .
w j = w + y j for all     j { n , , n } ,
I ( k ) = I 0 ( k ) exp ( σ 2 k 2 4 ) .
σ I ( k ) = 2 σ w N | cos k w 2 | I ( k ) .
σ I ( k ) = σ | k | N | cot k w 2 | exp ( σ 2 k 2 8 ) I ( k ) for     k = 2 π m d , m Z , if     sin k w 2 0.
I ( k ) = I 0 ( k ) exp [ ( σ LER 2 + 1 4 σ LWR 2 ) k 2 ] ,
σ I 2 ( k ) = σ I , LER 2 ( k ) + σ I , LWR 2 ( k ) ,
r ˜ ( x ) F 1 { F { r } } ( x ) = F 1 { F { r 0 } ( k ) exp ( σ 2 k 2 2 ) } ( x ) = r 0 ( x ) * 1 σ 2 π exp ( x 2 2 σ 2 ) = j = n n δ ( x j d ) * rect ( x w ) * 1 σ 2 π exp ( x 2 2 σ 2 ) Θ .
Θ = 1 σ 2 π rect ( x t w ) exp ( t 2 2 σ 2 ) d t = 1 2 [ erf ( 1 2 σ ( x + w 2 ) ) erf ( 1 2 σ ( x w 2 ) ) ] .

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