Abstract

The extension of a spectroscopic ellipsometer that consists of a fixed polarizer, a rotating polarizer, a sample, and a fixed analyzer (PRPSE) to generalized ellipsometry to determining the generalized ellipsometric angles and the optical functions of an anisotropic medium is reported. The PRPSE configuration eliminates the polarization sensitivity of the light source. A general numerical technique has been derived to characterize the optical properties of the anisotropic material without intermediate generalized ellipsometric angles. The proposed method is experimentally verified for uniaxial mercuric iodide. The ordinary and the extraordinary refractive and absorption indices, respectively, N o = n o - ik o and N e = n e - ik e, can be extracted directly from the Fourier coefficients measured by the PRPSE on a HgI2 crystal face that contains the optical axis. The orientations of the optical axis with respect to the plane of incidence were also determined by direct analysis of the measured Fourier coefficients. Measurements were made of reflection across a spectral range of 1.5–4.13 eV at one angle of incidence (Φ = 70°) for several azimuths φ of the optical axis with respect to the plane of incidence. The generalized ellipsometric angles were obtained from numerical inversion by changes of both polarizer and analyzer azimuth angles P and A.

© 1999 Optical Society of America

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References

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  1. M. Schubert, B. Rheinländer, J. A. Woollam, B. Johs, C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial TiO2,” J. Opt. Soc. Am. A 13, 875–883 (1996).
    [CrossRef]
  2. G. E. Jellison, F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190–8198 (1997); “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184–8189 (1997).
    [CrossRef]
  3. G. E. Jellison, F. A. Modine, L. A. Boatner, “Measurement of the optical functions of uniaxial materials by two-modulator generalized ellipsometry: rutile (TiO2),” Opt. Lett. 22, 1808–1810 (1997).
    [CrossRef]
  4. G. E. Jellison, L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
    [CrossRef]
  5. T. E. Tiwald, D. W. Thompson, J. A. Woollam, W. Paulson, R. Hance, “Application of IR variable angle spectroscopic ellipsometry to the determination of free carrier concentration depth profiles,” Thin Solid Films 313–314, 661–666 (1998).
  6. D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).
  7. A. En Naciri, L. Johann, R. Kleim, M. Sieskind, M. Amann, “Spectroscopic ellipsometry of anisotropic materials: application to the optical constants of HgI2,” Appl. Opt. 38, 647–654 (1999).
    [CrossRef]
  8. R. W. Stobie, B. Rao, M. J. Dignam, “Analysis of a novel ellipsometric technique with special advantages for infrared spectroscopy,” J. Opt. Soc. Am. 65, 25–28 (1975).
    [CrossRef]
  9. S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, R. Kleim, “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313–314, 73–78 (1998).
  10. R. M. A. Azzam, N. M. Bashara, “Polarization transfer function of a biaxial system as a bilinear transformation,” J. Opt. Soc. Am. 62, 222–229 (1972).
    [CrossRef]
  11. R. M. A. Azzam, N. M. Bashara, “Application of generalized ellipsometry to anisotropic crystals,” J. Opt. Soc. Am. 64, 128–133 (1974).
    [CrossRef]
  12. D. J. De Smet, “Ellipsometry of anisotropic substrates: re-examination of a special case,” J. Appl. Phys. 76, 2571–2574 (1994).
    [CrossRef]
  13. A. Anedda, E. Grilli, M. Guzzi, F. Raga, A. Serpi, “Low temperature reflectivity and optical properties of red mercury iodide,” Solid State Commun. 39, 1121–1123 (1981).
    [CrossRef]
  14. A. K. Solanki, A. Kashyab, T. Nautiyal, S. Auluck, M. A. Khan, “Band structure and optical properties of HgI2,” Phys. Rev. B 55, 9215–9218 (1997).
    [CrossRef]
  15. B. Lecourt, “Ellipsométrie spectroscopique conventionnelle et généralisée de films moléculaires ultraminces,” Ph.D. dissertation (University of Bordeaux I, Bordeaux, France, 1998).
  16. M. I. Alonso, S. Tortosa, M. Garriga, S. Pinol, “Ellipsometric measurement of the dielectric tensor of Nd2–xCexCuO4–δ,” Phys. Rev. B 55, 3216–3220 (1997).
    [CrossRef]
  17. J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. (Oxford University, UK) 7, 308–313 (1965).
  18. P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
    [CrossRef]
  19. H. Yao, B. Johs, R. B. James, “Optical anisotropic dielectric response of mercuric iodide,” Phys. Rev. B 56, 9414–9421 (1997).
    [CrossRef]
  20. M. Sieskind, S. Nikitine, J. B. Grun, “Données nouvelles sur les spectres de réflexion et d’absorption de monocristaux d’iodure mercurique rouge perpendiculaire à l’axe optique,” J. Phys. (Paris) 20, 557–560 (1959).
  21. H. E. Merwin, International Critical Tables (McGraw-Hill, New York, 1930), Vol. 7, p. 21.
  22. J. P. Ponpon, M. Sieskind, M. Amann, A. Benz, C. Corbu, “Characterization of the HgI2 surface layer after KI etching,” Nucl. Instrum. Meth. A 380, 112–116 (1996).
    [CrossRef]
  23. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 4, p. 355.

1999 (1)

1998 (4)

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, R. Kleim, “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313–314, 73–78 (1998).

G. E. Jellison, L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
[CrossRef]

T. E. Tiwald, D. W. Thompson, J. A. Woollam, W. Paulson, R. Hance, “Application of IR variable angle spectroscopic ellipsometry to the determination of free carrier concentration depth profiles,” Thin Solid Films 313–314, 661–666 (1998).

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

1997 (5)

G. E. Jellison, F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190–8198 (1997); “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184–8189 (1997).
[CrossRef]

G. E. Jellison, F. A. Modine, L. A. Boatner, “Measurement of the optical functions of uniaxial materials by two-modulator generalized ellipsometry: rutile (TiO2),” Opt. Lett. 22, 1808–1810 (1997).
[CrossRef]

A. K. Solanki, A. Kashyab, T. Nautiyal, S. Auluck, M. A. Khan, “Band structure and optical properties of HgI2,” Phys. Rev. B 55, 9215–9218 (1997).
[CrossRef]

M. I. Alonso, S. Tortosa, M. Garriga, S. Pinol, “Ellipsometric measurement of the dielectric tensor of Nd2–xCexCuO4–δ,” Phys. Rev. B 55, 3216–3220 (1997).
[CrossRef]

H. Yao, B. Johs, R. B. James, “Optical anisotropic dielectric response of mercuric iodide,” Phys. Rev. B 56, 9414–9421 (1997).
[CrossRef]

1996 (2)

1994 (1)

D. J. De Smet, “Ellipsometry of anisotropic substrates: re-examination of a special case,” J. Appl. Phys. 76, 2571–2574 (1994).
[CrossRef]

1981 (1)

A. Anedda, E. Grilli, M. Guzzi, F. Raga, A. Serpi, “Low temperature reflectivity and optical properties of red mercury iodide,” Solid State Commun. 39, 1121–1123 (1981).
[CrossRef]

1976 (1)

P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
[CrossRef]

1975 (1)

1974 (1)

1972 (1)

1965 (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. (Oxford University, UK) 7, 308–313 (1965).

1959 (1)

M. Sieskind, S. Nikitine, J. B. Grun, “Données nouvelles sur les spectres de réflexion et d’absorption de monocristaux d’iodure mercurique rouge perpendiculaire à l’axe optique,” J. Phys. (Paris) 20, 557–560 (1959).

Alonso, M. I.

M. I. Alonso, S. Tortosa, M. Garriga, S. Pinol, “Ellipsometric measurement of the dielectric tensor of Nd2–xCexCuO4–δ,” Phys. Rev. B 55, 3216–3220 (1997).
[CrossRef]

Amann, M.

A. En Naciri, L. Johann, R. Kleim, M. Sieskind, M. Amann, “Spectroscopic ellipsometry of anisotropic materials: application to the optical constants of HgI2,” Appl. Opt. 38, 647–654 (1999).
[CrossRef]

J. P. Ponpon, M. Sieskind, M. Amann, A. Benz, C. Corbu, “Characterization of the HgI2 surface layer after KI etching,” Nucl. Instrum. Meth. A 380, 112–116 (1996).
[CrossRef]

Anedda, A.

A. Anedda, E. Grilli, M. Guzzi, F. Raga, A. Serpi, “Low temperature reflectivity and optical properties of red mercury iodide,” Solid State Commun. 39, 1121–1123 (1981).
[CrossRef]

Auluck, S.

A. K. Solanki, A. Kashyab, T. Nautiyal, S. Auluck, M. A. Khan, “Band structure and optical properties of HgI2,” Phys. Rev. B 55, 9215–9218 (1997).
[CrossRef]

Azzam, R. M. A.

Bashara, N. M.

Benz, A.

J. P. Ponpon, M. Sieskind, M. Amann, A. Benz, C. Corbu, “Characterization of the HgI2 surface layer after KI etching,” Nucl. Instrum. Meth. A 380, 112–116 (1996).
[CrossRef]

Bertucci, S.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, R. Kleim, “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313–314, 73–78 (1998).

Boatner, L. A.

G. E. Jellison, L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
[CrossRef]

G. E. Jellison, F. A. Modine, L. A. Boatner, “Measurement of the optical functions of uniaxial materials by two-modulator generalized ellipsometry: rutile (TiO2),” Opt. Lett. 22, 1808–1810 (1997).
[CrossRef]

Corbu, C.

J. P. Ponpon, M. Sieskind, M. Amann, A. Benz, C. Corbu, “Characterization of the HgI2 surface layer after KI etching,” Nucl. Instrum. Meth. A 380, 112–116 (1996).
[CrossRef]

De Smet, D. J.

D. J. De Smet, “Ellipsometry of anisotropic substrates: re-examination of a special case,” J. Appl. Phys. 76, 2571–2574 (1994).
[CrossRef]

DeVries, M. J.

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

Dignam, M. J.

El Ghemmaz, A.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, R. Kleim, “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313–314, 73–78 (1998).

En Naciri, A.

Garriga, M.

M. I. Alonso, S. Tortosa, M. Garriga, S. Pinol, “Ellipsometric measurement of the dielectric tensor of Nd2–xCexCuO4–δ,” Phys. Rev. B 55, 3216–3220 (1997).
[CrossRef]

Grilli, E.

A. Anedda, E. Grilli, M. Guzzi, F. Raga, A. Serpi, “Low temperature reflectivity and optical properties of red mercury iodide,” Solid State Commun. 39, 1121–1123 (1981).
[CrossRef]

Grun, J. B.

M. Sieskind, S. Nikitine, J. B. Grun, “Données nouvelles sur les spectres de réflexion et d’absorption de monocristaux d’iodure mercurique rouge perpendiculaire à l’axe optique,” J. Phys. (Paris) 20, 557–560 (1959).

Guzzi, M.

A. Anedda, E. Grilli, M. Guzzi, F. Raga, A. Serpi, “Low temperature reflectivity and optical properties of red mercury iodide,” Solid State Commun. 39, 1121–1123 (1981).
[CrossRef]

Hance, R.

T. E. Tiwald, D. W. Thompson, J. A. Woollam, W. Paulson, R. Hance, “Application of IR variable angle spectroscopic ellipsometry to the determination of free carrier concentration depth profiles,” Thin Solid Films 313–314, 661–666 (1998).

Hauge, P. S.

P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
[CrossRef]

Herzinger, C. M.

James, R. B.

H. Yao, B. Johs, R. B. James, “Optical anisotropic dielectric response of mercuric iodide,” Phys. Rev. B 56, 9414–9421 (1997).
[CrossRef]

Jellison, G. E.

Johann, L.

A. En Naciri, L. Johann, R. Kleim, M. Sieskind, M. Amann, “Spectroscopic ellipsometry of anisotropic materials: application to the optical constants of HgI2,” Appl. Opt. 38, 647–654 (1999).
[CrossRef]

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, R. Kleim, “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313–314, 73–78 (1998).

Johs, B.

Kashyab, A.

A. K. Solanki, A. Kashyab, T. Nautiyal, S. Auluck, M. A. Khan, “Band structure and optical properties of HgI2,” Phys. Rev. B 55, 9215–9218 (1997).
[CrossRef]

Khan, M. A.

A. K. Solanki, A. Kashyab, T. Nautiyal, S. Auluck, M. A. Khan, “Band structure and optical properties of HgI2,” Phys. Rev. B 55, 9215–9218 (1997).
[CrossRef]

Kleim, R.

A. En Naciri, L. Johann, R. Kleim, M. Sieskind, M. Amann, “Spectroscopic ellipsometry of anisotropic materials: application to the optical constants of HgI2,” Appl. Opt. 38, 647–654 (1999).
[CrossRef]

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, R. Kleim, “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313–314, 73–78 (1998).

Lecourt, B.

B. Lecourt, “Ellipsométrie spectroscopique conventionnelle et généralisée de films moléculaires ultraminces,” Ph.D. dissertation (University of Bordeaux I, Bordeaux, France, 1998).

Mead, R.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. (Oxford University, UK) 7, 308–313 (1965).

Merwin, H. E.

H. E. Merwin, International Critical Tables (McGraw-Hill, New York, 1930), Vol. 7, p. 21.

Modine, F. A.

Nautiyal, T.

A. K. Solanki, A. Kashyab, T. Nautiyal, S. Auluck, M. A. Khan, “Band structure and optical properties of HgI2,” Phys. Rev. B 55, 9215–9218 (1997).
[CrossRef]

Nelder, J. A.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. (Oxford University, UK) 7, 308–313 (1965).

Nicolas, N.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, R. Kleim, “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313–314, 73–78 (1998).

Nikitine, S.

M. Sieskind, S. Nikitine, J. B. Grun, “Données nouvelles sur les spectres de réflexion et d’absorption de monocristaux d’iodure mercurique rouge perpendiculaire à l’axe optique,” J. Phys. (Paris) 20, 557–560 (1959).

Paulson, W.

T. E. Tiwald, D. W. Thompson, J. A. Woollam, W. Paulson, R. Hance, “Application of IR variable angle spectroscopic ellipsometry to the determination of free carrier concentration depth profiles,” Thin Solid Films 313–314, 661–666 (1998).

Pawlowski, A.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, R. Kleim, “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313–314, 73–78 (1998).

Pinol, S.

M. I. Alonso, S. Tortosa, M. Garriga, S. Pinol, “Ellipsometric measurement of the dielectric tensor of Nd2–xCexCuO4–δ,” Phys. Rev. B 55, 3216–3220 (1997).
[CrossRef]

Ponpon, J. P.

J. P. Ponpon, M. Sieskind, M. Amann, A. Benz, C. Corbu, “Characterization of the HgI2 surface layer after KI etching,” Nucl. Instrum. Meth. A 380, 112–116 (1996).
[CrossRef]

Raga, F.

A. Anedda, E. Grilli, M. Guzzi, F. Raga, A. Serpi, “Low temperature reflectivity and optical properties of red mercury iodide,” Solid State Commun. 39, 1121–1123 (1981).
[CrossRef]

Rao, B.

Rheinländer, B.

Schubert, M.

Serpi, A.

A. Anedda, E. Grilli, M. Guzzi, F. Raga, A. Serpi, “Low temperature reflectivity and optical properties of red mercury iodide,” Solid State Commun. 39, 1121–1123 (1981).
[CrossRef]

Sieskind, M.

A. En Naciri, L. Johann, R. Kleim, M. Sieskind, M. Amann, “Spectroscopic ellipsometry of anisotropic materials: application to the optical constants of HgI2,” Appl. Opt. 38, 647–654 (1999).
[CrossRef]

J. P. Ponpon, M. Sieskind, M. Amann, A. Benz, C. Corbu, “Characterization of the HgI2 surface layer after KI etching,” Nucl. Instrum. Meth. A 380, 112–116 (1996).
[CrossRef]

M. Sieskind, S. Nikitine, J. B. Grun, “Données nouvelles sur les spectres de réflexion et d’absorption de monocristaux d’iodure mercurique rouge perpendiculaire à l’axe optique,” J. Phys. (Paris) 20, 557–560 (1959).

Solanki, A. K.

A. K. Solanki, A. Kashyab, T. Nautiyal, S. Auluck, M. A. Khan, “Band structure and optical properties of HgI2,” Phys. Rev. B 55, 9215–9218 (1997).
[CrossRef]

Stein, N.

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, R. Kleim, “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313–314, 73–78 (1998).

Stobie, R. W.

Thompson, D. W.

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

T. E. Tiwald, D. W. Thompson, J. A. Woollam, W. Paulson, R. Hance, “Application of IR variable angle spectroscopic ellipsometry to the determination of free carrier concentration depth profiles,” Thin Solid Films 313–314, 661–666 (1998).

Tiwald, T. E.

T. E. Tiwald, D. W. Thompson, J. A. Woollam, W. Paulson, R. Hance, “Application of IR variable angle spectroscopic ellipsometry to the determination of free carrier concentration depth profiles,” Thin Solid Films 313–314, 661–666 (1998).

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

Tortosa, S.

M. I. Alonso, S. Tortosa, M. Garriga, S. Pinol, “Ellipsometric measurement of the dielectric tensor of Nd2–xCexCuO4–δ,” Phys. Rev. B 55, 3216–3220 (1997).
[CrossRef]

Woollam, J. A.

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

T. E. Tiwald, D. W. Thompson, J. A. Woollam, W. Paulson, R. Hance, “Application of IR variable angle spectroscopic ellipsometry to the determination of free carrier concentration depth profiles,” Thin Solid Films 313–314, 661–666 (1998).

M. Schubert, B. Rheinländer, J. A. Woollam, B. Johs, C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial TiO2,” J. Opt. Soc. Am. A 13, 875–883 (1996).
[CrossRef]

Yao, H.

H. Yao, B. Johs, R. B. James, “Optical anisotropic dielectric response of mercuric iodide,” Phys. Rev. B 56, 9414–9421 (1997).
[CrossRef]

Appl. Opt. (2)

Comput. J. (Oxford University, UK) (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. (Oxford University, UK) 7, 308–313 (1965).

J. Appl. Phys. (1)

D. J. De Smet, “Ellipsometry of anisotropic substrates: re-examination of a special case,” J. Appl. Phys. 76, 2571–2574 (1994).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

J. Phys. (Paris) (1)

M. Sieskind, S. Nikitine, J. B. Grun, “Données nouvelles sur les spectres de réflexion et d’absorption de monocristaux d’iodure mercurique rouge perpendiculaire à l’axe optique,” J. Phys. (Paris) 20, 557–560 (1959).

Nucl. Instrum. Meth. A (1)

J. P. Ponpon, M. Sieskind, M. Amann, A. Benz, C. Corbu, “Characterization of the HgI2 surface layer after KI etching,” Nucl. Instrum. Meth. A 380, 112–116 (1996).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (4)

G. E. Jellison, L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
[CrossRef]

M. I. Alonso, S. Tortosa, M. Garriga, S. Pinol, “Ellipsometric measurement of the dielectric tensor of Nd2–xCexCuO4–δ,” Phys. Rev. B 55, 3216–3220 (1997).
[CrossRef]

A. K. Solanki, A. Kashyab, T. Nautiyal, S. Auluck, M. A. Khan, “Band structure and optical properties of HgI2,” Phys. Rev. B 55, 9215–9218 (1997).
[CrossRef]

H. Yao, B. Johs, R. B. James, “Optical anisotropic dielectric response of mercuric iodide,” Phys. Rev. B 56, 9414–9421 (1997).
[CrossRef]

Solid State Commun. (1)

A. Anedda, E. Grilli, M. Guzzi, F. Raga, A. Serpi, “Low temperature reflectivity and optical properties of red mercury iodide,” Solid State Commun. 39, 1121–1123 (1981).
[CrossRef]

Surf. Sci. (1)

P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
[CrossRef]

Thin Solid Films (3)

T. E. Tiwald, D. W. Thompson, J. A. Woollam, W. Paulson, R. Hance, “Application of IR variable angle spectroscopic ellipsometry to the determination of free carrier concentration depth profiles,” Thin Solid Films 313–314, 661–666 (1998).

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

S. Bertucci, A. Pawlowski, N. Nicolas, L. Johann, A. El Ghemmaz, N. Stein, R. Kleim, “Systematic errors in fixed polarizer, rotating polarizer, sample, fixed analyzer spectroscopic ellipsometry,” Thin Solid Films 313–314, 73–78 (1998).

Other (3)

B. Lecourt, “Ellipsométrie spectroscopique conventionnelle et généralisée de films moléculaires ultraminces,” Ph.D. dissertation (University of Bordeaux I, Bordeaux, France, 1998).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 4, p. 355.

H. E. Merwin, International Critical Tables (McGraw-Hill, New York, 1930), Vol. 7, p. 21.

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Figures (9)

Fig. 1
Fig. 1

Schematic of the PRPSE. PM, A, S, P t , and P.

Fig. 2
Fig. 2

Experimental data for an isotropic sample of silicon as a function of the rotation angle.

Fig. 3
Fig. 3

Determination of the orientations of the optic axis with respect to the plane of incidence. The orientation angles are expected to be independent of wavelength.

Fig. 4
Fig. 4

Measured quantities α2c, α4c, α2s, and α4s as functions of sample azimuth at a photon energy of 1.97 eV, a polarizer azimuth angle of P = 90°, an analyzer azimuth angle of A = 45°, and at an angle of incidence of Φ = 70° taken on the HgI2 face that contains the optical axis.

Fig. 5
Fig. 5

Experimental data α2c and α4c from many oblique azimuths φ. The optical axis is parallel to the HgI2 surface. The incidence angle is Φ = 70° and the azimuth angle of the polarizer is P = 0° and of the analyzer is A = 45°.

Fig. 6
Fig. 6

Experimental data α2s and α4s from many oblique azimuths φ. The optical axis is parallel to the HgI2 surface. The incidence angle is Φ = 70° and the azimuth angle of the polarizer is P = 0° and of the analyzer is A = 45°.

Fig. 7
Fig. 7

Anisotropic optical constants of HgI2 at room temperature extracted by a generalized PRPSE. The subscripts o and e indicate ordinary and extraordinary responses, respectively.

Fig. 8
Fig. 8

Experimental and calculated GE parameters tan Ψpp, tan Ψps, and tan Ψsp as functions of the wavelength for the sample azimuths φ = 39°, 120°. Excellent agreement between the theoretical and the experimental data was achieved for tan Ψpp.

Fig. 9
Fig. 9

Same as Fig. 8 but for cos Δpp, cos Δps, and cos Δsp. Note that the determination of the phase of off-diagonal parameters is extremely difficult for the PRPSE.

Tables (2)

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Table 1 Comparison of the Optical Functions of HgI2 at 2.95 eV Determined from the Fit Combining Data Measured at Selected Pairs of Sample Azimuths (ϕ1, ϕ2)

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Table 2 Ordinary no and Extraordinary ne Optical Constants at Selected Spectral Positions Compared with Results Reviewed in the Literature

Equations (31)

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Ef=MIRARsR-PtMIRPtR-PMIEi,
MI=1000, Rθ=cos θsin θ-sin θcos θ, Rs=RppRpsRspRss.
Ef=cosP-ωtR1 cos ωt+R2 sin ωt0Ei,
R1=Rpp cos A+Rsp sin A,
R2=Rps cos A+Rss sin A.
I=I0a0+a2c cos 2ωt+a2s sin 2ωt+a4c cos 4ωt+a4s sin 4ωt,
a0=2|R1|2+2|R2|2+|R1|2-|R2|2cos 2P+R¯1R2+R1R¯2sin 2P8,
a2c=|R1|2-|R2|2+|R1|2+|R2|2cos 2P4,
a2s=R¯1R2+R1R¯2+|R1|2+|R2|2sin 2P4,
a4c=|R1|2-|R2|2cos 2P-R¯1R2+R1R¯2sin 2P8,
a4s=R¯1R2+R1R¯2cos 2P+|R1|2-|R2|2sin 2P8,
Imeas=α01+α2cα0cos 2Pt+α2sα0sin 2Pt+α4cα0cos 4Pt+α4sα0sin 2Pt,
αk=Gak,  k=0, 2c, 2s, 4c, 4s.
α2c=α2cα0=a2ca0=2α+cos 2P2+α cos 2P+β sin 2P,
α2s=α2sα0=a2sa0=2β+sin 2P2+α cos 2P+β sin 2P,
α4c=α4cα0=a4ca0=α cos 2P-β sin 2P2+α cos 2P+β sin 2P,
α4s=α4sα0=a4sa0=β cos 2P+α sin 2P2+α cos 2P+β sin 2P,
α=|R1|2-|R2|2|R1|2+|R2|2,  β=R¯1R2+R1R¯2|R1|2+|R2|2.
ρpp=RppRss=tan Ψpp expiΔpp,
ρps=RpsRss=tan Ψps expiΔps,
ρsp=RspRss=tan Ψsp expiΔsp.
α=|ρpp+ρsp tan A|2-|ρps+tan A|2|ρpp+ρsp tan A|2+|ρps+tan A|2,
β=2 Reρpp+ρsp tan Aρps+tan A|ρpp+ρsp tan A|2+|ρps+tan A|2.
Rp/Rs=tan Ψ expiΔ,
tan Ψ=sgnAtan AB1+21-2 cos 2PB21/2B1-21+2 cos 2PB21/2,
cos Δ=sgnAα4s cos 2P-α4c sin 2PB12-41-2 cos 2P2B221/2,
B1=2α4c+α2c cos 2P+α2s sin 2P,
B2=α4c cos 2P+α4s sin 2P.
ρ=Rpp/Rss+Rps/Rsstan P1+Rsp/Rsstan P-1,
χ2=i=12j=12l=12α2ce-α2ccφi, Pj, Alδα2ce2+α2se-α2scφi, Pj, Alδα2se2+α4ce-α4ccφi, Pj, Alδα4ce2+α4se-α4scφi, Pj, Alδα4se2,
χ2=i=13j=12α2ce-α2ccAi, Pj; GEAδα2ce2+α2se-α2scAi, Pj; GEAδα2se2+α4ce-α4ccAi, Pj; GEAδα4ce2+α4se-α4scAi, Pj; GEAδα4se2,

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