Abstract

We employed a grating profile measurement method, which is based on the combination of multiwavelength scatterometry and artificial neural network, to determine the critical dimensions of submicrometer-period photoresist gratings with wavy sidewall profiles. Six laser beams in three wavelengths and two orthogonal polarizations were adopted for the scatterometry measurement, and the incident angle of each beam was chosen following principles that we propose for achieving high sensitivity. We measured diffraction efficiencies of a large number of photoresist gratings made on glass substrates and high- reflectivity multilayer substrates coated with a chromium thin-film layer, and determined the grating groove parameters using a neural network model. The experimental results are statistically compared with results extracted from scanning electron micrographs. Good agreements between the indirect, neural network predicted results and the direct, scanning electron microscopy results are obtained.

© 2008 Optical Society of America

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  1. J. Garnaes, P. E. Hansen, N. Agersnap, J. Holm, F. Borsetto, and A. Kühle, “Profiles of a high-aspect-ratio grating determined by spectroscopic scatterometry and atomic-force microscopy,” Appl. Opt. 45, 3201-3212 (2006).
    [CrossRef]
  2. X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
    [CrossRef]
  3. R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys. 97, 053107 (2005).
    [CrossRef]
  4. H. Huang and F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828-836 (2004).
    [CrossRef]
  5. C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
    [CrossRef]
  6. J. Hazart, G. Grand, P. Thony, D. Hérisson, S. Garcia, and O. Lartigue, “Spectroscopic ellipsometry scatterometry: source of errors in critical dimension control,” Proc. SPIE 5041, 9-20 (2003).
  7. G. Bao, “A uniqueness theorem for an inverse problem in periodic diffractive optics,” Inverse Probl. 10, 335-340 (1994).
    [CrossRef]
  8. H. Gross and A. Rathsfeld, “Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures,” WIAS preprint No. 1164 (2006), http://www.wias-berlin.de.
  9. H. Gross, A. Rathsfeld, F. Scholze, M. Bar, and U. Dersch, “Optimal sets of measurement data for profile reconstruction in scatterometry,” Proc. SPIE 6617, 66171B (2007).
  10. R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, and D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” Proc. SPIE 1926, 60-71 (1993).
  11. I. Kallioniemi, J. Saarinen, and E. Oja, “Optical scatterometry of subwavelength diffraction gratings: neural-network approach,” Appl. Opt. 37, 5830-5835 (1998).
  12. S. Robert, A. M. Ravaud, S. Reynaud, S. Fourment, F. Carcenac, and P. Arguel, “Experimental characterization of subwavelength diffraction gratings by an inverse-scattering neural method,” J. Opt. Soc. Am. A 19, 2394-2402 (2002)
    [CrossRef]
  13. I. Kallioniemi, J. Saarinen, and E. Oja, “Characterization of diffraction gratings in a rigorous domain with optical scatterometry: hierarchical neural-network model,” Appl. Opt. 38, 5920-5930 (1999).
  14. S. Robert, A. M. Ravaud, and D. Lacour, “Characterization of optical diffraction gratings by use of a neural method,” J. Opt. Soc. Am. A 19, 24-32 (2002).
    [CrossRef]
  15. S. Robert, A. M. Ravaud, S. Thiria, M. Yacoub, and F. Badran, “Neural selection of the optimal optical signature for a rapid characterization of a submicrometer period grating,” Opt. Commun. 238, 215-228 (2004).
    [CrossRef]
  16. I. Gereige, S. Robert, G. Granet, D. Jamon, and J.-J. Rousseau, “Rapid control of submicrometer periodic structures by a neural inversion from ellipsometric measurement,” Opt. Commun. 278, 270-273 (2007).
    [CrossRef]
  17. L. Li, M. Xu, G. I. Stegeman, and C. T. Seaton, “Fabrication of photoresist masks for sub-micrometer surface relief gratings,” Proc. SPIE 835, 72-82 (1988).
  18. M. Neviere and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).
  19. S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
    [CrossRef]
  20. S. Haykin, Neural Networks--A Comprehensive Foundation, 2nd ed. (Prentice-Hall, 1999).
  21. M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989-993 (1994).
  22. S. Robert, A. Mure-Rauvaud, S. Thiria, and F. Badran, “Estimation of local error by a neural model in an inverse scattering problem,” Eur. Phys. J. Appl. Phys. 31, 71-76(2005).
    [CrossRef]

2007 (2)

H. Gross, A. Rathsfeld, F. Scholze, M. Bar, and U. Dersch, “Optimal sets of measurement data for profile reconstruction in scatterometry,” Proc. SPIE 6617, 66171B (2007).

I. Gereige, S. Robert, G. Granet, D. Jamon, and J.-J. Rousseau, “Rapid control of submicrometer periodic structures by a neural inversion from ellipsometric measurement,” Opt. Commun. 278, 270-273 (2007).
[CrossRef]

2006 (2)

H. Gross and A. Rathsfeld, “Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures,” WIAS preprint No. 1164 (2006), http://www.wias-berlin.de.

J. Garnaes, P. E. Hansen, N. Agersnap, J. Holm, F. Borsetto, and A. Kühle, “Profiles of a high-aspect-ratio grating determined by spectroscopic scatterometry and atomic-force microscopy,” Appl. Opt. 45, 3201-3212 (2006).
[CrossRef]

2005 (2)

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys. 97, 053107 (2005).
[CrossRef]

S. Robert, A. Mure-Rauvaud, S. Thiria, and F. Badran, “Estimation of local error by a neural model in an inverse scattering problem,” Eur. Phys. J. Appl. Phys. 31, 71-76(2005).
[CrossRef]

2004 (2)

H. Huang and F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828-836 (2004).
[CrossRef]

S. Robert, A. M. Ravaud, S. Thiria, M. Yacoub, and F. Badran, “Neural selection of the optimal optical signature for a rapid characterization of a submicrometer period grating,” Opt. Commun. 238, 215-228 (2004).
[CrossRef]

2003 (2)

J. Hazart, G. Grand, P. Thony, D. Hérisson, S. Garcia, and O. Lartigue, “Spectroscopic ellipsometry scatterometry: source of errors in critical dimension control,” Proc. SPIE 5041, 9-20 (2003).

M. Neviere and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

2002 (2)

2001 (1)

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

1999 (2)

1998 (1)

1995 (1)

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
[CrossRef]

1994 (2)

G. Bao, “A uniqueness theorem for an inverse problem in periodic diffractive optics,” Inverse Probl. 10, 335-340 (1994).
[CrossRef]

M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989-993 (1994).

1993 (1)

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, and D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” Proc. SPIE 1926, 60-71 (1993).

1988 (1)

L. Li, M. Xu, G. I. Stegeman, and C. T. Seaton, “Fabrication of photoresist masks for sub-micrometer surface relief gratings,” Proc. SPIE 835, 72-82 (1988).

1975 (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

Agersnap, N.

Antos, R.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys. 97, 053107 (2005).
[CrossRef]

Arguel, P.

Badran, F.

S. Robert, A. Mure-Rauvaud, S. Thiria, and F. Badran, “Estimation of local error by a neural model in an inverse scattering problem,” Eur. Phys. J. Appl. Phys. 31, 71-76(2005).
[CrossRef]

S. Robert, A. M. Ravaud, S. Thiria, M. Yacoub, and F. Badran, “Neural selection of the optimal optical signature for a rapid characterization of a submicrometer period grating,” Opt. Commun. 238, 215-228 (2004).
[CrossRef]

Bao, G.

G. Bao, “A uniqueness theorem for an inverse problem in periodic diffractive optics,” Inverse Probl. 10, 335-340 (1994).
[CrossRef]

Bao, J.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

Bar, M.

H. Gross, A. Rathsfeld, F. Scholze, M. Bar, and U. Dersch, “Optimal sets of measurement data for profile reconstruction in scatterometry,” Proc. SPIE 6617, 66171B (2007).

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

Borsetto, F.

Carcenac, F.

Dersch, U.

H. Gross, A. Rathsfeld, F. Scholze, M. Bar, and U. Dersch, “Optimal sets of measurement data for profile reconstruction in scatterometry,” Proc. SPIE 6617, 66171B (2007).

Fourment, S.

Garcia, S.

J. Hazart, G. Grand, P. Thony, D. Hérisson, S. Garcia, and O. Lartigue, “Spectroscopic ellipsometry scatterometry: source of errors in critical dimension control,” Proc. SPIE 5041, 9-20 (2003).

Garnaes, J.

Gaspar, S. M.

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, and D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” Proc. SPIE 1926, 60-71 (1993).

Gereige, I.

I. Gereige, S. Robert, G. Granet, D. Jamon, and J.-J. Rousseau, “Rapid control of submicrometer periodic structures by a neural inversion from ellipsometric measurement,” Opt. Commun. 278, 270-273 (2007).
[CrossRef]

Grand, G.

J. Hazart, G. Grand, P. Thony, D. Hérisson, S. Garcia, and O. Lartigue, “Spectroscopic ellipsometry scatterometry: source of errors in critical dimension control,” Proc. SPIE 5041, 9-20 (2003).

Granet, G.

I. Gereige, S. Robert, G. Granet, D. Jamon, and J.-J. Rousseau, “Rapid control of submicrometer periodic structures by a neural inversion from ellipsometric measurement,” Opt. Commun. 278, 270-273 (2007).
[CrossRef]

Gross, H.

H. Gross, A. Rathsfeld, F. Scholze, M. Bar, and U. Dersch, “Optimal sets of measurement data for profile reconstruction in scatterometry,” Proc. SPIE 6617, 66171B (2007).

H. Gross and A. Rathsfeld, “Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures,” WIAS preprint No. 1164 (2006), http://www.wias-berlin.de.

Hagan, M. T.

M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989-993 (1994).

Hansen, P. E.

Haykin, S.

S. Haykin, Neural Networks--A Comprehensive Foundation, 2nd ed. (Prentice-Hall, 1999).

Hazart, J.

J. Hazart, G. Grand, P. Thony, D. Hérisson, S. Garcia, and O. Lartigue, “Spectroscopic ellipsometry scatterometry: source of errors in critical dimension control,” Proc. SPIE 5041, 9-20 (2003).

Hérisson, D.

J. Hazart, G. Grand, P. Thony, D. Hérisson, S. Garcia, and O. Lartigue, “Spectroscopic ellipsometry scatterometry: source of errors in critical dimension control,” Proc. SPIE 5041, 9-20 (2003).

Holm, J.

Horie, M.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys. 97, 053107 (2005).
[CrossRef]

Huang, H.

H. Huang and F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828-836 (2004).
[CrossRef]

Hush, D. R.

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, and D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” Proc. SPIE 1926, 60-71 (1993).

Jakatdar, N.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

Jamon, D.

I. Gereige, S. Robert, G. Granet, D. Jamon, and J.-J. Rousseau, “Rapid control of submicrometer periodic structures by a neural inversion from ellipsometric measurement,” Opt. Commun. 278, 270-273 (2007).
[CrossRef]

Kallioniemi, I.

Krukar, D. M.

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, and D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” Proc. SPIE 1926, 60-71 (1993).

Krukar, R. H.

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, and D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” Proc. SPIE 1926, 60-71 (1993).

Kühle, A.

Lacour, D.

Lartigue, O.

J. Hazart, G. Grand, P. Thony, D. Hérisson, S. Garcia, and O. Lartigue, “Spectroscopic ellipsometry scatterometry: source of errors in critical dimension control,” Proc. SPIE 5041, 9-20 (2003).

Li, L.

L. Li, M. Xu, G. I. Stegeman, and C. T. Seaton, “Fabrication of photoresist masks for sub-micrometer surface relief gratings,” Proc. SPIE 835, 72-82 (1988).

McNeil, J. R.

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
[CrossRef]

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, and D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” Proc. SPIE 1926, 60-71 (1993).

Menhaj, M. B.

M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989-993 (1994).

Mistrik, J.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys. 97, 053107 (2005).
[CrossRef]

Mure-Rauvaud, A.

S. Robert, A. Mure-Rauvaud, S. Thiria, and F. Badran, “Estimation of local error by a neural model in an inverse scattering problem,” Eur. Phys. J. Appl. Phys. 31, 71-76(2005).
[CrossRef]

Murnane, M. R.

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
[CrossRef]

Naqvi, S. S. H.

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
[CrossRef]

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, and D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” Proc. SPIE 1926, 60-71 (1993).

Neviere, M.

M. Neviere and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

Niu, X.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

Ohlidal, I.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys. 97, 053107 (2005).
[CrossRef]

Oja, E.

Peng, S. T.

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

Petersen, G. A.

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, and D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” Proc. SPIE 1926, 60-71 (1993).

Pistora, J.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys. 97, 053107 (2005).
[CrossRef]

Popov, E.

M. Neviere and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

Postava, K.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys. 97, 053107 (2005).
[CrossRef]

Prins, S. L.

R. H. Krukar, S. L. Prins, D. M. Krukar, G. A. Petersen, S. M. Gaspar, J. R. McNeil, S. S. H. Naqvi, and D. R. Hush, “Using scattered light modeling for semiconductor critical dimension metrology and calibration,” Proc. SPIE 1926, 60-71 (1993).

Rathsfeld, A.

H. Gross, A. Rathsfeld, F. Scholze, M. Bar, and U. Dersch, “Optimal sets of measurement data for profile reconstruction in scatterometry,” Proc. SPIE 6617, 66171B (2007).

H. Gross and A. Rathsfeld, “Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures,” WIAS preprint No. 1164 (2006), http://www.wias-berlin.de.

Ravaud, A. M.

Raymond, C. J.

C. J. Raymond, M. R. Murnane, S. S. H. Naqvi, and J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13, 1484-1495 (1995).
[CrossRef]

Reynaud, S.

Robert, S.

I. Gereige, S. Robert, G. Granet, D. Jamon, and J.-J. Rousseau, “Rapid control of submicrometer periodic structures by a neural inversion from ellipsometric measurement,” Opt. Commun. 278, 270-273 (2007).
[CrossRef]

S. Robert, A. Mure-Rauvaud, S. Thiria, and F. Badran, “Estimation of local error by a neural model in an inverse scattering problem,” Eur. Phys. J. Appl. Phys. 31, 71-76(2005).
[CrossRef]

S. Robert, A. M. Ravaud, S. Thiria, M. Yacoub, and F. Badran, “Neural selection of the optimal optical signature for a rapid characterization of a submicrometer period grating,” Opt. Commun. 238, 215-228 (2004).
[CrossRef]

S. Robert, A. M. Ravaud, S. Reynaud, S. Fourment, F. Carcenac, and P. Arguel, “Experimental characterization of subwavelength diffraction gratings by an inverse-scattering neural method,” J. Opt. Soc. Am. A 19, 2394-2402 (2002)
[CrossRef]

S. Robert, A. M. Ravaud, and D. Lacour, “Characterization of optical diffraction gratings by use of a neural method,” J. Opt. Soc. Am. A 19, 24-32 (2002).
[CrossRef]

Rousseau, J.-J.

I. Gereige, S. Robert, G. Granet, D. Jamon, and J.-J. Rousseau, “Rapid control of submicrometer periodic structures by a neural inversion from ellipsometric measurement,” Opt. Commun. 278, 270-273 (2007).
[CrossRef]

Saarinen, J.

Scholze, F.

H. Gross, A. Rathsfeld, F. Scholze, M. Bar, and U. Dersch, “Optimal sets of measurement data for profile reconstruction in scatterometry,” Proc. SPIE 6617, 66171B (2007).

Seaton, C. T.

L. Li, M. Xu, G. I. Stegeman, and C. T. Seaton, “Fabrication of photoresist masks for sub-micrometer surface relief gratings,” Proc. SPIE 835, 72-82 (1988).

Spanos, C. J.

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

Stegeman, G. I.

L. Li, M. Xu, G. I. Stegeman, and C. T. Seaton, “Fabrication of photoresist masks for sub-micrometer surface relief gratings,” Proc. SPIE 835, 72-82 (1988).

Tamir, T.

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

Terry, F. L.

H. Huang and F. L. Terry, “Spectroscopic ellipsometry and reflectometry from gratings (scatterometry) for critical dimension measurement and in situ, real-time process monitoring,” Thin Solid Films 455, 828-836 (2004).
[CrossRef]

Thiria, S.

S. Robert, A. Mure-Rauvaud, S. Thiria, and F. Badran, “Estimation of local error by a neural model in an inverse scattering problem,” Eur. Phys. J. Appl. Phys. 31, 71-76(2005).
[CrossRef]

S. Robert, A. M. Ravaud, S. Thiria, M. Yacoub, and F. Badran, “Neural selection of the optimal optical signature for a rapid characterization of a submicrometer period grating,” Opt. Commun. 238, 215-228 (2004).
[CrossRef]

Thony, P.

J. Hazart, G. Grand, P. Thony, D. Hérisson, S. Garcia, and O. Lartigue, “Spectroscopic ellipsometry scatterometry: source of errors in critical dimension control,” Proc. SPIE 5041, 9-20 (2003).

Visnovsky, S.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys. 97, 053107 (2005).
[CrossRef]

Xu, M.

L. Li, M. Xu, G. I. Stegeman, and C. T. Seaton, “Fabrication of photoresist masks for sub-micrometer surface relief gratings,” Proc. SPIE 835, 72-82 (1988).

Yacoub, M.

S. Robert, A. M. Ravaud, S. Thiria, M. Yacoub, and F. Badran, “Neural selection of the optimal optical signature for a rapid characterization of a submicrometer period grating,” Opt. Commun. 238, 215-228 (2004).
[CrossRef]

Yamaguchi, T.

R. Antos, J. Pistora, I. Ohlidal, K. Postava, J. Mistrik, T. Yamaguchi, S. Visnovsky, and M. Horie, “Specular spectroscopic ellipsometry for the critical dimension monitoring of gratings fabricated on a thick transparent plate,” J. Appl. Phys. 97, 053107 (2005).
[CrossRef]

Appl. Opt. (3)

Eur. Phys. J. Appl. Phys. (1)

S. Robert, A. Mure-Rauvaud, S. Thiria, and F. Badran, “Estimation of local error by a neural model in an inverse scattering problem,” Eur. Phys. J. Appl. Phys. 31, 71-76(2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

IEEE Trans. Neural Netw. (1)

M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989-993 (1994).

IEEE Trans. Semicond. Manuf. (1)

X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97-111 (2001).
[CrossRef]

Inverse Probl. (1)

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[CrossRef]

J. Appl. Phys. (1)

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[CrossRef]

J. Opt. Soc. Am. A (2)

J. Vac. Sci. Technol. B (1)

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[CrossRef]

Opt. Commun. (2)

S. Robert, A. M. Ravaud, S. Thiria, M. Yacoub, and F. Badran, “Neural selection of the optimal optical signature for a rapid characterization of a submicrometer period grating,” Opt. Commun. 238, 215-228 (2004).
[CrossRef]

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[CrossRef]

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Other (3)

H. Gross and A. Rathsfeld, “Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures,” WIAS preprint No. 1164 (2006), http://www.wias-berlin.de.

M. Neviere and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, 2003).

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Figures (5)

Fig. 1
Fig. 1

SEM image of a typical photoresist grating mask studied in this work.

Fig. 2
Fig. 2

Geometric model of the wavy sidewall grating profile.

Fig. 3
Fig. 3

Sensitivity of the 1 st-order diffraction efficiencies versus grating profile parameters in different incident configurations. (a)  λ = 632.8 nm , TM polarization, h = 0.3 μm , and four different incident angles. (b)  h = 0.3 μm , φ = 20 ° , two wavelengths, and polarizations. (c)  λ = 532 nm , TM polarization, δ = 0.3 , and four different incident angles.

Fig. 4
Fig. 4

Data measured from SEM pictures and data obtained with our method in the glass-substrate case. The histograms show the absolute values of the deviations of the two sets of data.

Fig. 5
Fig. 5

Data measured from SEM pictures and data obtained with our method in the multilayer-substrate case. The histograms show the absolute values of the deviations of the two sets of data.

Tables (1)

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Table 1 Deviations of the Uncertain Quantities Considered in Theoretical Prediction

Equations (3)

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I = C 1 + C 2 cos ( 2 k y y + ϕ ) ,
k y = 2 π λ n cos θ ,
A = ( 0.1 δ + 0.0132 ± 0.005 ) d ,

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