Abstract

We studied two bidimensional square gratings of square holes formed in photoresist layers deposited on silicon wafers, both by classical spectroscopic ellipsometry (1.5–4.5-eV spectral range) at a constant incidence angle (70.7°) and by angle-resolved Mueller polarimetry at a constant wavelength (532 nm). The grating period was 1 μm in both directions, and the nominal hole sizes were 250 and 500 nm, respectively. The ellipsometric spectra were fitted by rigorous coupled-wave analysis simulations with two adjustable parameters, the resist layer thickness and the hole size. These parameters were found to be in good agreement with independent scanning electron microscopy measurements. The experimental angle-resolved Mueller spectra were remarkably well reproduced by the simulations, showing that angle-resolved Mueller polarimetry has a great potential for grating metrology applications.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Robert, A. Mure-Ravaud, D. Lacour, “Characterization of optical diffraction gratings by use of a neural method,” J. Opt. Soc. Am. A 19, 24–32 (2002).
    [CrossRef]
  2. G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–416 (1852).
  3. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).
  4. S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).
  5. C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072–5087 (1993).
    [CrossRef]
  6. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  7. L. Li, J. Chandezon, C. Granet, J. P. Plumey, “Rigorous and efficient grating analysis method made easy for optical engineers,” Appl. Opt. 38, 304–313 (1999).
    [CrossRef]
  8. M. G. Moharam, E. B. Grann, D. A. Pommet, 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]
  9. P. Rai-Choudhury, Handbook on Microlithography, Micromachining, and Microfabrication: Microlithography (SPIE, Bellingham, Wash., 1997).
  10. E. Compain, “Conception et réalisation d’un ellipsométre de Muller achromatique fonctionnant en temps reel,” Ph.D. dissertation (Ecole Polytechnique, Palaiseau, France, 1999).
  11. E. Compain, B. Drévillon, “High-frequency modulation of the four states of polarization of light with a single phase modulator,” Rev. Sci. Instrum. 69, 1574–1580 (1998).
    [CrossRef]
  12. E. Compain, B. Drévillon, “Broadband division of amplitude polarimeter based on uncoated prisms,” Appl. Opt. 37, 5938–5944 (1998).
    [CrossRef]
  13. S. Poirier, E. Compain, B. Drévillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters and Mueller matrix ellipsometers,” Appl. Opt. 38, 3490–3502 (1999).
    [CrossRef]
  14. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997).
    [CrossRef]
  15. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
    [CrossRef]
  16. L. Li, “Formulation and comparison of two recursive matrix algorithms for mofelling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
    [CrossRef]
  17. P. Lalanne, G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
    [CrossRef]
  18. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

2002

1999

1998

E. Compain, B. Drévillon, “High-frequency modulation of the four states of polarization of light with a single phase modulator,” Rev. Sci. Instrum. 69, 1574–1580 (1998).
[CrossRef]

E. Compain, B. Drévillon, “Broadband division of amplitude polarimeter based on uncoated prisms,” Appl. Opt. 37, 5938–5944 (1998).
[CrossRef]

1997

1996

1995

1993

C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072–5087 (1993).
[CrossRef]

1986

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

1852

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–416 (1852).

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).

Chandezon, J.

Cloude, S. R.

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

Compain, E.

S. Poirier, E. Compain, B. Drévillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters and Mueller matrix ellipsometers,” Appl. Opt. 38, 3490–3502 (1999).
[CrossRef]

E. Compain, B. Drévillon, “Broadband division of amplitude polarimeter based on uncoated prisms,” Appl. Opt. 37, 5938–5944 (1998).
[CrossRef]

E. Compain, B. Drévillon, “High-frequency modulation of the four states of polarization of light with a single phase modulator,” Rev. Sci. Instrum. 69, 1574–1580 (1998).
[CrossRef]

E. Compain, “Conception et réalisation d’un ellipsométre de Muller achromatique fonctionnant en temps reel,” Ph.D. dissertation (Ecole Polytechnique, Palaiseau, France, 1999).

Drévillon, B.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

Gaylord, T. K.

Granet, C.

Grann, E. B.

Lacour, D.

Lalanne, P.

Li, L.

Moharam, M. G.

Morris, G. M.

Mure-Ravaud, A.

Petit, R.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

Plumey, J. P.

Poirier, S.

Pommet, D. A.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

Rai-Choudhury, P.

P. Rai-Choudhury, Handbook on Microlithography, Micromachining, and Microfabrication: Microlithography (SPIE, Bellingham, Wash., 1997).

Robert, S.

Stokes, G. G.

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–416 (1852).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

van der Mee, C. V. M.

C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072–5087 (1993).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

Appl. Opt.

J. Math. Phys.

C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072–5087 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Optik

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

Rev. Sci. Instrum.

E. Compain, B. Drévillon, “High-frequency modulation of the four states of polarization of light with a single phase modulator,” Rev. Sci. Instrum. 69, 1574–1580 (1998).
[CrossRef]

Trans. Cambridge Philos. Soc.

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399–416 (1852).

Other

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1989).

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

P. Rai-Choudhury, Handbook on Microlithography, Micromachining, and Microfabrication: Microlithography (SPIE, Bellingham, Wash., 1997).

E. Compain, “Conception et réalisation d’un ellipsométre de Muller achromatique fonctionnant en temps reel,” Ph.D. dissertation (Ecole Polytechnique, Palaiseau, France, 1999).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Specified structure of the grating samples. R, electron resist; Si, crystalline silicon.

Fig. 2
Fig. 2

Scanning electron microscopy images of the S250 sample. White bar lengths, 1 μm (upper image) and 200 nm (lower image).

Fig. 3
Fig. 3

Analogous to Fig. 2, for the S500 sample.

Fig. 4
Fig. 4

Resist refractive index and extinction coefficient, deduced from spectroscopic ellipsometry data.

Fig. 5
Fig. 5

Schematic of Mueller polarimeter, PSG, polarization-state generator. PSD, polarization-state detector.

Fig. 6
Fig. 6

Spectroscopic ellipsometry measurements (circles) and simulations (thick curves) for the S250 sample. Dotted curves, spectra taken on unexposed resist layer.

Fig. 7
Fig. 7

Analogous to Fig. 6, for S500 sample.

Fig. 8
Fig. 8

Angle-resolved Mueller polarimetry measurements (circles) and simulations (thick curves) for S250 sample. Thin curves, data taken on unexposed resist layer.

Fig. 9
Fig. 9

Analogous to Fig. 8, for S500 sample.

Tables (1)

Tables Icon

Table 1 Grating Parameters Derived from SEM Images and from Spectroscopic Ellipsometry Data Fits

Equations (5)

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

rp/rs=tanΨexpiΔ,
χ2=1Ni=1NΨexp-Ψthe1802+Δexp-Δthe3602,
M=τ1-cos 2Ψ00-cos 2Ψ10000sin 2Ψ cos Δ-sin 2Ψ sin Δ00sin 2Ψ sin Δsin 2Ψ cos Δ,
M33=M44, M43=-M34, M332+M342+M122=M112.
M12*=M12+M212M11, M33*=M33+M442M11, M34*=M34-M432M11.

Metrics