Abstract

We present a specialized scatterometry method to measure the groove profiles of highly asymmetric triangular gratings. Compared with the conventional scatterometry working in a specular way, this method utilizes diffraction spectra of the reflected ±1st orders and is good at measuring this kind of asymmetric grating with a higher sensitivity. In our work, diffraction efficiency angular spectra at a single wavelength are measured and passed on to a parameter optimization process to retrieve three profile defining parameters. Final results are compared with the ones from an atomic force microscope and discrepancies are discussed and explained.

© 2014 Optical Society of America

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References

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  1. M. C. Hutley, Diffraction Gratings (Academic, 1982).
  2. Y. Aoyagi and S. Namba, “Blazed ion-etched holographic gratings,” Opt. Acta 23, 701–707 (1976).
    [CrossRef]
  3. C. J. Raymond, “Scatterometry for semiconductor metrology,” in Handbook of Silicon Semiconductor Metrology, A. C. Diebold, ed. (Marcel Dekker, 2001), pp. 477–514.
  4. 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]
  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. B. K. Minhas, S. A. Coulombe, S. S. H. Naqvi, and J. R. McNeil, “Ellipsometric scatterometry for the metrology of sub-0.1-μm-linewidth structures,” Appl. Opt. 37, 5112–5115 (1998).
    [CrossRef]
  7. X. Niu, N. Jakatdar, J. Bao, and C. J. Spanos, “Specular spectroscopic scatterometry,” IEEE Trans. Semicond. Manuf. 14, 97–111 (2001).
    [CrossRef]
  8. T. Novikova, A. De Martino, S. B. Hatit, and B. Drévillon, “Application of Mueller polarimetry in conical diffraction for critical dimension measurements in microelectronics,” Appl. Opt. 45, 3688–3697 (2006).
    [CrossRef]
  9. 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]
  10. P. Vincent and M. Nevière, “The reciprocity theorem for corrugated surfaces used in conical diffraction mountings,” Opt. Acta 26, 889–898 (1979).
    [CrossRef]
  11. 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]
  12. L. F. Johnson, “Evolution of grating profiles under ion-beam erosion,” Appl. Opt. 18, 2559–2574 (1979).
    [CrossRef]
  13. M. Bass, C. M. DeCusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. IV.
  14. S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech. 23, 123–133 (1975).
    [CrossRef]
  15. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  16. Ph. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
    [CrossRef]
  17. G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).
    [CrossRef]
  18. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
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  19. E. W. Cheney and D. R. Kincaid, Numerical Mathematics and Computing (Brooks/Cole, 2012).
  20. T. Germer, H. Patrick, R. Silver, and B. Bunday, “Developing an uncertainty analysis for optical scatterometry,” Proc. SPIE 7272, 72720T (2009).
    [CrossRef]
  21. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).
  22. D. W. Marquardt, “An algorithm for the least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
    [CrossRef]
  23. J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980).
    [CrossRef]
  24. L. Li, J. Chandezon, G. Granet, and J. P. Plumey, “Rigorous and efficient grating-analysis method made easy for optical engineers,” Appl. Opt. 38, 304–313 (1999).
    [CrossRef]
  25. A. D. Rakić, “Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum,” Appl. Opt. 34, 4755–4767 (1995).
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  27. J. Ganguly, R. N. Bhattacharya, and S. Chakraborty, “Convolution effect in the determination of compositional profiles and diffusion coefficients by microprobe step scans,” Am. Mineral. 73, 901–909 (1988).
  28. J. S. Villarrubia, “Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation,” J. Res. Natl. Inst. Stand. Technol. 102, 425–454 (1997).
    [CrossRef]

2009 (1)

T. Germer, H. Patrick, R. Silver, and B. Bunday, “Developing an uncertainty analysis for optical scatterometry,” Proc. SPIE 7272, 72720T (2009).
[CrossRef]

2006 (2)

2005 (1)

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]

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 (1)

1998 (1)

1997 (1)

J. S. Villarrubia, “Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation,” J. Res. Natl. Inst. Stand. Technol. 102, 425–454 (1997).
[CrossRef]

1996 (3)

1995 (3)

1992 (1)

1988 (1)

J. Ganguly, R. N. Bhattacharya, and S. Chakraborty, “Convolution effect in the determination of compositional profiles and diffusion coefficients by microprobe step scans,” Am. Mineral. 73, 901–909 (1988).

1984 (1)

1980 (1)

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980).
[CrossRef]

1979 (2)

L. F. Johnson, “Evolution of grating profiles under ion-beam erosion,” Appl. Opt. 18, 2559–2574 (1979).
[CrossRef]

P. Vincent and M. Nevière, “The reciprocity theorem for corrugated surfaces used in conical diffraction mountings,” Opt. Acta 26, 889–898 (1979).
[CrossRef]

1976 (1)

Y. Aoyagi and S. Namba, “Blazed ion-etched holographic gratings,” Opt. Acta 23, 701–707 (1976).
[CrossRef]

1975 (1)

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

1963 (1)

D. W. Marquardt, “An algorithm for the least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

1944 (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

Agersnap, N.

Aoyagi, Y.

Y. Aoyagi and S. Namba, “Blazed ion-etched holographic gratings,” Opt. Acta 23, 701–707 (1976).
[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]

Bass, M.

M. Bass, C. M. DeCusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. IV.

Bertoni, H. L.

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

Bhattacharya, R. N.

J. Ganguly, R. N. Bhattacharya, and S. Chakraborty, “Convolution effect in the determination of compositional profiles and diffusion coefficients by microprobe step scans,” Am. Mineral. 73, 901–909 (1988).

Bishop, K.

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]

Borsetto, F.

Bunday, B.

T. Germer, H. Patrick, R. Silver, and B. Bunday, “Developing an uncertainty analysis for optical scatterometry,” Proc. SPIE 7272, 72720T (2009).
[CrossRef]

Chakraborty, S.

J. Ganguly, R. N. Bhattacharya, and S. Chakraborty, “Convolution effect in the determination of compositional profiles and diffusion coefficients by microprobe step scans,” Am. Mineral. 73, 901–909 (1988).

Chandezon, J.

L. Li, J. Chandezon, G. Granet, and J. P. Plumey, “Rigorous and efficient grating-analysis method made easy for optical engineers,” Appl. Opt. 38, 304–313 (1999).
[CrossRef]

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980).
[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]

Cheney, E. W.

E. W. Cheney and D. R. Kincaid, Numerical Mathematics and Computing (Brooks/Cole, 2012).

Coulombe, S. A.

De Martino, A.

DeCusatis, C. M.

M. Bass, C. M. DeCusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. IV.

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]

Dodge, M. J.

Drévillon, B.

Enoch, J. M.

M. Bass, C. M. DeCusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. IV.

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]

Ganguly, J.

J. Ganguly, R. N. Bhattacharya, and S. Chakraborty, “Convolution effect in the determination of compositional profiles and diffusion coefficients by microprobe step scans,” Am. Mineral. 73, 901–909 (1988).

Garnaes, J.

Gaspar, S.

Gaylord, T. K.

Germer, T.

T. Germer, H. Patrick, R. Silver, and B. Bunday, “Developing an uncertainty analysis for optical scatterometry,” Proc. SPIE 7272, 72720T (2009).
[CrossRef]

Granet, G.

Grann, E. B.

Guizal, B.

Hansen, P. E.

Hatit, S. B.

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]

Hickman, K.

Holm, J.

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, 1982).

Jakatdar, N.

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

Johnson, L. F.

Kincaid, D. R.

E. W. Cheney and D. R. Kincaid, Numerical Mathematics and Computing (Brooks/Cole, 2012).

Kühle, A.

Lakshminarayanan, V.

M. Bass, C. M. DeCusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. IV.

Lalanne, Ph.

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]

Levenberg, K.

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

Li, G.

M. Bass, C. M. DeCusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. IV.

Li, L.

MacDonald, C.

M. Bass, C. M. DeCusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. IV.

Mahajan, V. N.

M. Bass, C. M. DeCusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. IV.

Marquardt, D. W.

D. W. Marquardt, “An algorithm for the least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Maystre, D.

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980).
[CrossRef]

McNeil, J. R.

Minhas, B. K.

Moharam, M. G.

Morris, G. M.

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]

Namba, S.

Y. Aoyagi and S. Namba, “Blazed ion-etched holographic gratings,” Opt. Acta 23, 701–707 (1976).
[CrossRef]

Naqvi, S. S. H.

Nevière, M.

P. Vincent and M. Nevière, “The reciprocity theorem for corrugated surfaces used in conical diffraction mountings,” Opt. Acta 26, 889–898 (1979).
[CrossRef]

Niu, X.

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

Novikova, T.

Patrick, H.

T. Germer, H. Patrick, R. Silver, and B. Bunday, “Developing an uncertainty analysis for optical scatterometry,” Proc. SPIE 7272, 72720T (2009).
[CrossRef]

Peng, S. T.

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

Plumey, J. P.

Pommet, D. A.

Rakic, A. D.

Raoult, G.

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980).
[CrossRef]

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]

C. J. Raymond, “Scatterometry for semiconductor metrology,” in Handbook of Silicon Semiconductor Metrology, A. C. Diebold, ed. (Marcel Dekker, 2001), pp. 477–514.

Silver, R.

T. Germer, H. Patrick, R. Silver, and B. Bunday, “Developing an uncertainty analysis for optical scatterometry,” Proc. SPIE 7272, 72720T (2009).
[CrossRef]

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]

Tamir, T.

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

Van Stryland, E.

M. Bass, C. M. DeCusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. IV.

Villarrubia, J. S.

J. S. Villarrubia, “Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation,” J. Res. Natl. Inst. Stand. Technol. 102, 425–454 (1997).
[CrossRef]

Vincent, P.

P. Vincent and M. Nevière, “The reciprocity theorem for corrugated surfaces used in conical diffraction mountings,” Opt. Acta 26, 889–898 (1979).
[CrossRef]

Am. Mineral. (1)

J. Ganguly, R. N. Bhattacharya, and S. Chakraborty, “Convolution effect in the determination of compositional profiles and diffusion coefficients by microprobe step scans,” Am. Mineral. 73, 901–909 (1988).

Appl. Opt. (8)

IEEE Trans. Microw. Theory Tech. (1)

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

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]

J. Opt. (1)

J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Res. Natl. Inst. Stand. Technol. (1)

J. S. Villarrubia, “Algorithms for scanned probe microscope image simulation, surface reconstruction, and tip estimation,” J. Res. Natl. Inst. Stand. Technol. 102, 425–454 (1997).
[CrossRef]

J. Vac. Sci. Technol. B (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]

Opt. Acta (2)

Y. Aoyagi and S. Namba, “Blazed ion-etched holographic gratings,” Opt. Acta 23, 701–707 (1976).
[CrossRef]

P. Vincent and M. Nevière, “The reciprocity theorem for corrugated surfaces used in conical diffraction mountings,” Opt. Acta 26, 889–898 (1979).
[CrossRef]

Proc. SPIE (2)

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. Germer, H. Patrick, R. Silver, and B. Bunday, “Developing an uncertainty analysis for optical scatterometry,” Proc. SPIE 7272, 72720T (2009).
[CrossRef]

Q. Appl. Math. (1)

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).

SIAM J. Appl. Math. (1)

D. W. Marquardt, “An algorithm for the least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Other (4)

E. W. Cheney and D. R. Kincaid, Numerical Mathematics and Computing (Brooks/Cole, 2012).

M. Bass, C. M. DeCusatis, J. M. Enoch, V. Lakshminarayanan, G. Li, C. MacDonald, V. N. Mahajan, and E. Van Stryland, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Vol. IV.

C. J. Raymond, “Scatterometry for semiconductor metrology,” in Handbook of Silicon Semiconductor Metrology, A. C. Diebold, ed. (Marcel Dekker, 2001), pp. 477–514.

M. C. Hutley, Diffraction Gratings (Academic, 1982).

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Figures (12)

Fig. 1.
Fig. 1.

Characterization of the grating groove profile. (a) SEM observation of a typical etched grating before cleaning. (b) The coordinate system Oxy is established at the middle of BC.

Fig. 2.
Fig. 2.

Schematic of a classical grating mounting.

Fig. 3.
Fig. 3.

Comparison of R0 and R1 in diffraction efficiency angular spectra. Multiple curves in each subfigure correspond to variations of αl from 10° to 20°, with dotted lines for αl=10°. ns, αr and fc are set to 1.46958, 60° and 0.2, respectively.

Fig. 4.
Fig. 4.

Comparison of R0 and R1 in contour plots and condition numbers. In (a) and (b) the solid lines and dashed lines are for R0 at θ=40° and θ=60°, respectively. In (c) and (d) the solid lines correspond to R+1 at θ=40° and the dashed ones for R1 at θ=40°. For each subfigure the bold dot (15,60) is observed and condition number κ in 2-norm is calculated. ns and fc are set to 1.46958 and 0.2, respectively.

Fig. 5.
Fig. 5.

Influence of profile asymmetry to R1 in the form of condition number and retrieving uncertainty. Both results are calculated with R+1 at θ=40° and R1 at θ=40°. The uncertainties of αl and αr are supposed only from the error of the measurand with a relative uncertainty of 1%.

Fig. 6.
Fig. 6.

Schematic of a numerical retrieving process using the parameter optimization method.

Fig. 7.
Fig. 7.

Sketch of the experimental configuration for measuring the angular spectra of the diffraction efficiency.

Fig. 8.
Fig. 8.

Measurement result of grating sample #1.

Fig. 9.
Fig. 9.

Comparison of retrieved and AFM measured results for all of the fourteen measurements.

Fig. 10.
Fig. 10.

Similarity measurements of all of the grating samples.

Fig. 11.
Fig. 11.

Comparison of evaluated dispersion spectra corresponding to retrieved and AFM measured results.

Fig. 12.
Fig. 12.

Schematic of a specific 2D case. Scanning direction is supposed along the grating vector.

Tables (1)

Tables Icon

Table 1. Profile Parameters of Retrieval and AFM Measurements for all of the Grating Samples

Equations (5)

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

G=(Gαl1Gαr1Gαl2Gαr2),
χ2=i=1N[ηiexpη(xi,a0,b)]2,
S1=1i=1N(piqi)2i=1Npi2+i=1Nqi2,
S2=1i=1N|piqi|i=1N|pi|+i=1N|qi|,
S3=i=1N(pip¯)(qiq¯)i=1N(pip¯)2i=1N(qiq¯)2,

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