Abstract

We report for the first time on the application of generalized ellipsometry at far-infrared wavelengths (wave numbers from 150 cm-1 to 600 cm-1) for measurement of the anisotropic dielectric response of doped polar semiconductors in layered structures within an external magnetic field. Upon determination of normalized Mueller matrix elements and subsequent derivation of the normalized complex Jones reflection matrix r of an n-type doped GaAs substrate covered by a highly resistive GaAs layer, the spectral dependence of the room-temperature magneto-optic dielectric function tensor of n-type GaAs with free-electron concentration of 1.6×1018 cm-3 at the magnetic field strength of 2.3 T is obtained on a wavelength-by-wavelength basis. These data are in excellent agreement with values predicted by the Drude model. From the magneto-optic generalized ellipsometry measurements of the layered structure, the free-carrier concentration, their optical mobility, the effective-mass parameters, and the sign of the charge carriers can be determined independently, which will be demonstrated. We propose magneto-optic generalized ellipsometry as a novel approach for exploration of free-carrier parameters in complex organic or inorganic semiconducting material heterostructures, regardless of the anisotropic properties of the individual constituents.

© 2003 Optical Society of America

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  1. The effective-mass concept addressed here descends from the similarity with the Newton force equation (acceleration of a body with mass m) and the acceleration experienced by a Bloch electron due to an external force. The inverse tensor obtained thereby depends on the curvature of the plots of electron energetic states versus electron momentum, which is diagonal by a suitable choice of axes. Different experiments require different concepts, resulting in definition of the effective conductivity mass, the density-of-states effective mass, the Hall effective mass, or the cyclotron effective mass, all of which are not discussed here. For the material investigated here (GaAs), the response of the zinc-blended, Γ-point conduction band (single-species, i.e., single-valley) Bloch electrons studied at infrared wavelengths is on a time scale much smaller than the average time between scattering events of the free electrons. One may also refer to the effective mass here as an (infrared) optical effective mass. See also Refs. 2 and 3.
  2. C. M. Wolfe, N. Holonyak, G. E. Stillmann, Physical Properties of Semiconductors (Prentice-Hall, Englewood Cliffs, N.J., 1989).
  3. C. R. Pidgeon, “Free carrier optical properties of semiconductors,” in Handbook of Semiconductors, M. Balkanski, ed. (North-Holland, Amsterdam, 1980), Vol. 2, pp. 223–228.
  4. P. Drude, The Theory of Optics, translated from German by C. R. Mann, R. A. Millikan (Longmans, Green, New York, 1902).
  5. H. Raether, Surface Polaritons (Springer, Berlin, 1988).
  6. A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie, Berlin, 1992).
  7. J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Theory of magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455–1458 (1972).
    [Crossref]
  8. J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Interaction of surface magnetoplasmons and surface optical phonons in polar semiconductors,” Surf. Sci. 34, 73–80 (1973).
    [Crossref]
  9. A. Hartstein, E. Burstein, J. J. Brion, R. F. Wallis, “Surface polaritons on semi-infinite anisotropic media,” Surf. Sci. 34, 81–89 (1973).
    [Crossref]
  10. R. F. Wallis, J. J. Brion, E. Burstein, A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9, 3424–3437 (1974).
    [Crossref]
  11. M. Schubert, “Infrared ellipsometry on III-V semiconductor layer structures,” Habilitationsschrift (Universität Leipzig, Leipzig, Germany), available at http://www.uni-leipzig.de/∼hlp/ellipsometrie .
  12. G. B. Wright, B. Lax, “Magnetoreflection experiments in intermetallics,” J. Appl. Phys. 32, 2113–2117 (1961).
    [Crossref]
  13. M. Cardona, “Electron effective masses of InAs and GaAs as a function of temperature and doping,” Phys. Rev. 121, 752–758 (1961).
    [Crossref]
  14. Restrictions apply to highly conductive layers that are optically thick, such as highly doped semiconductor substrates, or metal films several hundreds of nanometers thick. As long as the layer with high free-carrier concentration is passing electromagnetic radiation on to the next constituent, the ellipsometric parameters will contain information about the buried layers.
  15. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1984).
  16. D. E. Aspnes, “The accurate determination of optical properties by ellipsometry,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1998), Vol. I, pp. 89–112.
  17. R. M. A. Azzam, N. M. Bashara, “Generalized ellipsometry for surfaces with directional preference: application to diffraction gratings,” J. Opt. Soc. Am. 62, 1521–1523 (1972).
    [Crossref]
  18. M. Schubert, B. Rheinländer, B. Johs, C. M. Herzinger, J. A. Woollam, “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]
  19. G. E. Jellison, L. A. Boatner, “Optical functions of uniaxial ZnO determined by generalized ellipsometry,” Phys. Rev. B 58, 3586–3589 (1998).
    [Crossref]
  20. D. W. Thompson, M. J. De Vries, 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).
    [Crossref]
  21. M. Schubert, T. E. Tiwald, J. A. Woollam, “Explicit solutions for the optical properties of arbitrary magneto-optic materials in generalized ellipsometry,” Appl. Opt. 38, 177–187 (1999).
    [Crossref]
  22. M. Schubert, C. M. Herzinger, “Ellipsometry on anisotropic materials: Bragg conditions and phonons in dielectric helical thin films,” Phys. Status Solidi A 188, 1563–1575 (2001).
    [Crossref]
  23. M. Schubert, W. Dollase, “Generalized ellipsometry for biaxial absorbing minerals: determination of crystal orientation and optical constants from Sb2S3,” Opt. Lett. 27, 2073–2075 (2002).
    [Crossref]
  24. M. Schubert, “Theory and application of generalized ellipsometry,” in Handbook of Ellipsometry, G. E. Irene, H. W. Tompkins, eds. (to be published).
  25. M. Schubert, B. Rheinländer, B. Johs, J. A. Woollam, “Application of generalized ellipsometry to complex optical systems,” in Polarimetry and Ellipsometry, M. Pluta, T. R. Wolinsky, eds., Proc. SPIE3094, 255–265 (1997).
    [Crossref]
  26. M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313-314, 323–332 (1998).
    [Crossref]
  27. M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
    [Crossref]
  28. This set comprises six real-valued quantities out of the eight possible values contained within the Jones matrix—lacking the light beam’s absolute intensity and absolute phase information. For a definition of the Jones matrix elements, see Refs. 15, 17, 18, 24-27, and references therein.
  29. G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313-314, 33–39 (1998).
    [Crossref]
  30. C. M. Herzinger, P. G. Snyder, B. Johs, J. A. Woollam, “InP optical constants between 0.75 and 5.0 eV determined by variable-angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 1715–1724 (1995).
    [Crossref]
  31. M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265–4274 (1996).
    [Crossref]
  32. T. E. Tiwald, M. Schubert, “Measurement of rutile TiO2 from 0.148 to 33 µm using generalized ellipsometry,” in Optical Diagnostic Methods For Inorganic Materials II, L. M. Hanssen, ed., Proc. SPIE4103, 19–29 (2000).
    [Crossref]
  33. R. Henn, C. Bernhard, A. Wittlin, M. Cardona, S. Uchida, “Far infrared ellipsometry using synchrotron radiation: the out-of-plane response of La2-xSrxCuO4,” Thin Solid Films 313-314, 643–648 (1998).
    [Crossref]
  34. J. Kircher, R. Henn, M. Cardona, P. L. Richards, G. P. Williams, “Far-infrared ellipsometry using synchrotron radiation,” J. Opt. Soc. Am. B 14, 705–712 (1997).
    [Crossref]
  35. J. Humlı́ček, R. Henn, M. Cardona, “Infrared vibrations in LaSrGaO4 and LaSrAlO4,” Phys. Rev. B 61, 14554–14563 (2000).
    [Crossref]
  36. T. E. Tiwald, J. A. Woollam, St. Zollner, J. Christiansen, R. B. Gregory, T. Wetteroth, S. R. Wilson, “Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry,” Phys. Rev. B 60, 11464–11474 (1999).
    [Crossref]
  37. M. Schubert, T. E. Tiwald, C. M. Herzinger, “Infrared dielectric anisotropy and phonon modes of sapphire,” Phys. Rev. B 61, 8187–8201 (2000).
    [Crossref]
  38. A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62, 7365–7377 (2000).
    [Crossref]
  39. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1985).
  40. In view of the generalized ellipsometry applications at oblique incidence, MO setups will be addressed as follows: the polar MO (PMO) setup with B parallel to the sample normal, the longitudinal MO (LMO) setup with B parallel to the sample surface and parallel to the plane of incidence, and the transverse MO (TMO) setup with B perpendicular to the sample normal and perpendicular to the plane of incidence. In the MO literature, different terms are in use: Near-normal-incidence reflection-type Kerr-effect measurements are referred to as transverse, longitudinal, and polar configurations, in conceptual agreement with the above notation. Faraday- and Voigt-effect measurements address transmission-type linear polarization rotation measurements in the above PMO and mixed LMO–TMO configurations, respectively. See Ref. 3 or Ref. 41. These configurations mostly result from the simplicity of the corresponding equations, which describe the polarized light reflection and transmission situations for the anisotropic materials. These requirements are now dispensed with because of the availability of explicit solutions for light propagation in arbitrarily nonsymmetric (MO) dielectric materials.21
  41. M. Mansuripur, The Physical Principles of Magneto-Optical Recording (Cambridge U. Press, Cambridge, UK, 1995).
  42. E. D. Palik, “Gallium arsenide (GaAs),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1998), Vol. I; pp. 429–444.
  43. E. Burstein, F. De Martini, eds., Polaritons (Pergamon, New York, 1974).
  44. D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev. 130, 2193–2198 (1963).
    [Crossref]
  45. St. Zollner, J. P. Carrejo, T. E. Tiwald, J. A. Woollam, “The origin of the Berreman effect in SiC homostructures,” Phys. Status Solidi B 208, R3–R4 (1998).
    [Crossref]
  46. J. Humlı́ček, “Infrared spectroscopy of LiF on Ag and Si,” Phys. Status Solidi B 215, 155–159 (1999).
    [Crossref]
  47. M. Schubert, B. Rheinländer, C. Cramer, H. Schmiedel, J. A. Woollam, B. Johs, C. M. Herzinger, “Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals,” J. Opt. Soc. Am. A 13, 1930–1940 (1996).
    [Crossref]
  48. A. Raymond, J. L. Robert, C. Bernard, “The electron effective mass in heavily doped GaAs,” J. Phys. C 12, 2289–2293 (1979).
    [Crossref]

2002 (1)

2001 (1)

M. Schubert, C. M. Herzinger, “Ellipsometry on anisotropic materials: Bragg conditions and phonons in dielectric helical thin films,” Phys. Status Solidi A 188, 1563–1575 (2001).
[Crossref]

2000 (3)

J. Humlı́ček, R. Henn, M. Cardona, “Infrared vibrations in LaSrGaO4 and LaSrAlO4,” Phys. Rev. B 61, 14554–14563 (2000).
[Crossref]

M. Schubert, T. E. Tiwald, C. M. Herzinger, “Infrared dielectric anisotropy and phonon modes of sapphire,” Phys. Rev. B 61, 8187–8201 (2000).
[Crossref]

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62, 7365–7377 (2000).
[Crossref]

1999 (3)

J. Humlı́ček, “Infrared spectroscopy of LiF on Ag and Si,” Phys. Status Solidi B 215, 155–159 (1999).
[Crossref]

T. E. Tiwald, J. A. Woollam, St. Zollner, J. Christiansen, R. B. Gregory, T. Wetteroth, S. R. Wilson, “Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry,” Phys. Rev. B 60, 11464–11474 (1999).
[Crossref]

M. Schubert, T. E. Tiwald, J. A. Woollam, “Explicit solutions for the optical properties of arbitrary magneto-optic materials in generalized ellipsometry,” Appl. Opt. 38, 177–187 (1999).
[Crossref]

1998 (6)

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313-314, 323–332 (1998).
[Crossref]

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313-314, 33–39 (1998).
[Crossref]

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

D. W. Thompson, M. J. De Vries, 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).
[Crossref]

R. Henn, C. Bernhard, A. Wittlin, M. Cardona, S. Uchida, “Far infrared ellipsometry using synchrotron radiation: the out-of-plane response of La2-xSrxCuO4,” Thin Solid Films 313-314, 643–648 (1998).
[Crossref]

St. Zollner, J. P. Carrejo, T. E. Tiwald, J. A. Woollam, “The origin of the Berreman effect in SiC homostructures,” Phys. Status Solidi B 208, R3–R4 (1998).
[Crossref]

1997 (1)

1996 (3)

1995 (1)

C. M. Herzinger, P. G. Snyder, B. Johs, J. A. Woollam, “InP optical constants between 0.75 and 5.0 eV determined by variable-angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 1715–1724 (1995).
[Crossref]

1979 (1)

A. Raymond, J. L. Robert, C. Bernard, “The electron effective mass in heavily doped GaAs,” J. Phys. C 12, 2289–2293 (1979).
[Crossref]

1974 (1)

R. F. Wallis, J. J. Brion, E. Burstein, A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9, 3424–3437 (1974).
[Crossref]

1973 (2)

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Interaction of surface magnetoplasmons and surface optical phonons in polar semiconductors,” Surf. Sci. 34, 73–80 (1973).
[Crossref]

A. Hartstein, E. Burstein, J. J. Brion, R. F. Wallis, “Surface polaritons on semi-infinite anisotropic media,” Surf. Sci. 34, 81–89 (1973).
[Crossref]

1972 (2)

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Theory of magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455–1458 (1972).
[Crossref]

R. M. A. Azzam, N. M. Bashara, “Generalized ellipsometry for surfaces with directional preference: application to diffraction gratings,” J. Opt. Soc. Am. 62, 1521–1523 (1972).
[Crossref]

1963 (1)

D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev. 130, 2193–2198 (1963).
[Crossref]

1961 (2)

G. B. Wright, B. Lax, “Magnetoreflection experiments in intermetallics,” J. Appl. Phys. 32, 2113–2117 (1961).
[Crossref]

M. Cardona, “Electron effective masses of InAs and GaAs as a function of temperature and doping,” Phys. Rev. 121, 752–758 (1961).
[Crossref]

Arnold, M. D.

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Aspnes, D. E.

D. E. Aspnes, “The accurate determination of optical properties by ellipsometry,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1998), Vol. I, pp. 89–112.

Azzam, R. M. A.

Bashara, N. M.

Bernard, C.

A. Raymond, J. L. Robert, C. Bernard, “The electron effective mass in heavily doped GaAs,” J. Phys. C 12, 2289–2293 (1979).
[Crossref]

Bernhard, C.

R. Henn, C. Bernhard, A. Wittlin, M. Cardona, S. Uchida, “Far infrared ellipsometry using synchrotron radiation: the out-of-plane response of La2-xSrxCuO4,” Thin Solid Films 313-314, 643–648 (1998).
[Crossref]

Berreman, D. W.

D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev. 130, 2193–2198 (1963).
[Crossref]

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]

Brion, J. J.

R. F. Wallis, J. J. Brion, E. Burstein, A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9, 3424–3437 (1974).
[Crossref]

A. Hartstein, E. Burstein, J. J. Brion, R. F. Wallis, “Surface polaritons on semi-infinite anisotropic media,” Surf. Sci. 34, 81–89 (1973).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Interaction of surface magnetoplasmons and surface optical phonons in polar semiconductors,” Surf. Sci. 34, 73–80 (1973).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Theory of magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455–1458 (1972).
[Crossref]

Burstein, E.

R. F. Wallis, J. J. Brion, E. Burstein, A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9, 3424–3437 (1974).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Interaction of surface magnetoplasmons and surface optical phonons in polar semiconductors,” Surf. Sci. 34, 73–80 (1973).
[Crossref]

A. Hartstein, E. Burstein, J. J. Brion, R. F. Wallis, “Surface polaritons on semi-infinite anisotropic media,” Surf. Sci. 34, 81–89 (1973).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Theory of magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455–1458 (1972).
[Crossref]

Cardona, M.

J. Humlı́ček, R. Henn, M. Cardona, “Infrared vibrations in LaSrGaO4 and LaSrAlO4,” Phys. Rev. B 61, 14554–14563 (2000).
[Crossref]

R. Henn, C. Bernhard, A. Wittlin, M. Cardona, S. Uchida, “Far infrared ellipsometry using synchrotron radiation: the out-of-plane response of La2-xSrxCuO4,” Thin Solid Films 313-314, 643–648 (1998).
[Crossref]

J. Kircher, R. Henn, M. Cardona, P. L. Richards, G. P. Williams, “Far-infrared ellipsometry using synchrotron radiation,” J. Opt. Soc. Am. B 14, 705–712 (1997).
[Crossref]

M. Cardona, “Electron effective masses of InAs and GaAs as a function of temperature and doping,” Phys. Rev. 121, 752–758 (1961).
[Crossref]

Carrejo, J. P.

St. Zollner, J. P. Carrejo, T. E. Tiwald, J. A. Woollam, “The origin of the Berreman effect in SiC homostructures,” Phys. Status Solidi B 208, R3–R4 (1998).
[Crossref]

Christiansen, J.

T. E. Tiwald, J. A. Woollam, St. Zollner, J. Christiansen, R. B. Gregory, T. Wetteroth, S. R. Wilson, “Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry,” Phys. Rev. B 60, 11464–11474 (1999).
[Crossref]

Cramer, C.

De Vries, M. J.

D. W. Thompson, M. J. De Vries, 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).
[Crossref]

Dollase, W.

Dollase, W. A.

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Drude, P.

P. Drude, The Theory of Optics, translated from German by C. R. Mann, R. A. Millikan (Longmans, Green, New York, 1902).

Einfeldt, S.

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62, 7365–7377 (2000).
[Crossref]

Gottschalch, V.

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Gregory, R. B.

T. E. Tiwald, J. A. Woollam, St. Zollner, J. Christiansen, R. B. Gregory, T. Wetteroth, S. R. Wilson, “Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry,” Phys. Rev. B 60, 11464–11474 (1999).
[Crossref]

Hartstein, A.

R. F. Wallis, J. J. Brion, E. Burstein, A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9, 3424–3437 (1974).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Interaction of surface magnetoplasmons and surface optical phonons in polar semiconductors,” Surf. Sci. 34, 73–80 (1973).
[Crossref]

A. Hartstein, E. Burstein, J. J. Brion, R. F. Wallis, “Surface polaritons on semi-infinite anisotropic media,” Surf. Sci. 34, 81–89 (1973).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Theory of magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455–1458 (1972).
[Crossref]

Henn, R.

J. Humlı́ček, R. Henn, M. Cardona, “Infrared vibrations in LaSrGaO4 and LaSrAlO4,” Phys. Rev. B 61, 14554–14563 (2000).
[Crossref]

R. Henn, C. Bernhard, A. Wittlin, M. Cardona, S. Uchida, “Far infrared ellipsometry using synchrotron radiation: the out-of-plane response of La2-xSrxCuO4,” Thin Solid Films 313-314, 643–648 (1998).
[Crossref]

J. Kircher, R. Henn, M. Cardona, P. L. Richards, G. P. Williams, “Far-infrared ellipsometry using synchrotron radiation,” J. Opt. Soc. Am. B 14, 705–712 (1997).
[Crossref]

Herzinger, C. M.

M. Schubert, C. M. Herzinger, “Ellipsometry on anisotropic materials: Bragg conditions and phonons in dielectric helical thin films,” Phys. Status Solidi A 188, 1563–1575 (2001).
[Crossref]

M. Schubert, T. E. Tiwald, C. M. Herzinger, “Infrared dielectric anisotropy and phonon modes of sapphire,” Phys. Rev. B 61, 8187–8201 (2000).
[Crossref]

M. Schubert, B. Rheinländer, C. Cramer, H. Schmiedel, J. A. Woollam, B. Johs, C. M. Herzinger, “Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals,” J. Opt. Soc. Am. A 13, 1930–1940 (1996).
[Crossref]

M. Schubert, B. Rheinländer, B. Johs, C. M. Herzinger, J. A. Woollam, “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]

C. M. Herzinger, P. G. Snyder, B. Johs, J. A. Woollam, “InP optical constants between 0.75 and 5.0 eV determined by variable-angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 1715–1724 (1995).
[Crossref]

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Hodgkinson, I. J.

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Hofmann, T.

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Holonyak, N.

C. M. Wolfe, N. Holonyak, G. E. Stillmann, Physical Properties of Semiconductors (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Hommel, D.

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62, 7365–7377 (2000).
[Crossref]

Humli´cek, J.

J. Humlı́ček, R. Henn, M. Cardona, “Infrared vibrations in LaSrGaO4 and LaSrAlO4,” Phys. Rev. B 61, 14554–14563 (2000).
[Crossref]

J. Humlı́ček, “Infrared spectroscopy of LiF on Ag and Si,” Phys. Status Solidi B 215, 155–159 (1999).
[Crossref]

Jellison, G. E.

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313-314, 33–39 (1998).
[Crossref]

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

Johs, B.

M. Schubert, B. Rheinländer, B. Johs, C. M. Herzinger, J. A. Woollam, “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]

M. Schubert, B. Rheinländer, C. Cramer, H. Schmiedel, J. A. Woollam, B. Johs, C. M. Herzinger, “Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals,” J. Opt. Soc. Am. A 13, 1930–1940 (1996).
[Crossref]

C. M. Herzinger, P. G. Snyder, B. Johs, J. A. Woollam, “InP optical constants between 0.75 and 5.0 eV determined by variable-angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 1715–1724 (1995).
[Crossref]

M. Schubert, B. Rheinländer, B. Johs, J. A. Woollam, “Application of generalized ellipsometry to complex optical systems,” in Polarimetry and Ellipsometry, M. Pluta, T. R. Wolinsky, eds., Proc. SPIE3094, 255–265 (1997).
[Crossref]

Kasic, A.

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62, 7365–7377 (2000).
[Crossref]

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Kircher, J.

Kittel, C.

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1985).

Lax, B.

G. B. Wright, B. Lax, “Magnetoreflection experiments in intermetallics,” J. Appl. Phys. 32, 2113–2117 (1961).
[Crossref]

Mansuripur, M.

M. Mansuripur, The Physical Principles of Magneto-Optical Recording (Cambridge U. Press, Cambridge, UK, 1995).

Neumann, H.

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Off, J.

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Palik, E. D.

E. D. Palik, “Gallium arsenide (GaAs),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1998), Vol. I; pp. 429–444.

Pidgeon, C. R.

C. R. Pidgeon, “Free carrier optical properties of semiconductors,” in Handbook of Semiconductors, M. Balkanski, ed. (North-Holland, Amsterdam, 1980), Vol. 2, pp. 223–228.

Raether, H.

H. Raether, Surface Polaritons (Springer, Berlin, 1988).

Raymond, A.

A. Raymond, J. L. Robert, C. Bernard, “The electron effective mass in heavily doped GaAs,” J. Phys. C 12, 2289–2293 (1979).
[Crossref]

Rheinländer, B.

Richards, P. L.

Robert, J. L.

A. Raymond, J. L. Robert, C. Bernard, “The electron effective mass in heavily doped GaAs,” J. Phys. C 12, 2289–2293 (1979).
[Crossref]

Röseler, A.

A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie, Berlin, 1992).

Schmiedel, H.

Scholz, F.

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Schubert, E.

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

Schubert, M.

M. Schubert, W. Dollase, “Generalized ellipsometry for biaxial absorbing minerals: determination of crystal orientation and optical constants from Sb2S3,” Opt. Lett. 27, 2073–2075 (2002).
[Crossref]

M. Schubert, C. M. Herzinger, “Ellipsometry on anisotropic materials: Bragg conditions and phonons in dielectric helical thin films,” Phys. Status Solidi A 188, 1563–1575 (2001).
[Crossref]

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62, 7365–7377 (2000).
[Crossref]

M. Schubert, T. E. Tiwald, C. M. Herzinger, “Infrared dielectric anisotropy and phonon modes of sapphire,” Phys. Rev. B 61, 8187–8201 (2000).
[Crossref]

M. Schubert, T. E. Tiwald, J. A. Woollam, “Explicit solutions for the optical properties of arbitrary magneto-optic materials in generalized ellipsometry,” Appl. Opt. 38, 177–187 (1999).
[Crossref]

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313-314, 323–332 (1998).
[Crossref]

M. Schubert, B. Rheinländer, B. Johs, C. M. Herzinger, J. A. Woollam, “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]

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265–4274 (1996).
[Crossref]

M. Schubert, B. Rheinländer, C. Cramer, H. Schmiedel, J. A. Woollam, B. Johs, C. M. Herzinger, “Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals,” J. Opt. Soc. Am. A 13, 1930–1940 (1996).
[Crossref]

T. E. Tiwald, M. Schubert, “Measurement of rutile TiO2 from 0.148 to 33 µm using generalized ellipsometry,” in Optical Diagnostic Methods For Inorganic Materials II, L. M. Hanssen, ed., Proc. SPIE4103, 19–29 (2000).
[Crossref]

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

M. Schubert, “Theory and application of generalized ellipsometry,” in Handbook of Ellipsometry, G. E. Irene, H. W. Tompkins, eds. (to be published).

M. Schubert, B. Rheinländer, B. Johs, J. A. Woollam, “Application of generalized ellipsometry to complex optical systems,” in Polarimetry and Ellipsometry, M. Pluta, T. R. Wolinsky, eds., Proc. SPIE3094, 255–265 (1997).
[Crossref]

Snyder, P. G.

C. M. Herzinger, P. G. Snyder, B. Johs, J. A. Woollam, “InP optical constants between 0.75 and 5.0 eV determined by variable-angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 1715–1724 (1995).
[Crossref]

Stillmann, G. E.

C. M. Wolfe, N. Holonyak, G. E. Stillmann, Physical Properties of Semiconductors (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Thompson, D. W.

D. W. Thompson, M. J. De Vries, 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).
[Crossref]

Tiwald, T. E.

M. Schubert, T. E. Tiwald, C. M. Herzinger, “Infrared dielectric anisotropy and phonon modes of sapphire,” Phys. Rev. B 61, 8187–8201 (2000).
[Crossref]

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62, 7365–7377 (2000).
[Crossref]

T. E. Tiwald, J. A. Woollam, St. Zollner, J. Christiansen, R. B. Gregory, T. Wetteroth, S. R. Wilson, “Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry,” Phys. Rev. B 60, 11464–11474 (1999).
[Crossref]

M. Schubert, T. E. Tiwald, J. A. Woollam, “Explicit solutions for the optical properties of arbitrary magneto-optic materials in generalized ellipsometry,” Appl. Opt. 38, 177–187 (1999).
[Crossref]

D. W. Thompson, M. J. De Vries, 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).
[Crossref]

St. Zollner, J. P. Carrejo, T. E. Tiwald, J. A. Woollam, “The origin of the Berreman effect in SiC homostructures,” Phys. Status Solidi B 208, R3–R4 (1998).
[Crossref]

T. E. Tiwald, M. Schubert, “Measurement of rutile TiO2 from 0.148 to 33 µm using generalized ellipsometry,” in Optical Diagnostic Methods For Inorganic Materials II, L. M. Hanssen, ed., Proc. SPIE4103, 19–29 (2000).
[Crossref]

Uchida, S.

R. Henn, C. Bernhard, A. Wittlin, M. Cardona, S. Uchida, “Far infrared ellipsometry using synchrotron radiation: the out-of-plane response of La2-xSrxCuO4,” Thin Solid Films 313-314, 643–648 (1998).
[Crossref]

Wallis, R. F.

R. F. Wallis, J. J. Brion, E. Burstein, A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9, 3424–3437 (1974).
[Crossref]

A. Hartstein, E. Burstein, J. J. Brion, R. F. Wallis, “Surface polaritons on semi-infinite anisotropic media,” Surf. Sci. 34, 81–89 (1973).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Interaction of surface magnetoplasmons and surface optical phonons in polar semiconductors,” Surf. Sci. 34, 73–80 (1973).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Theory of magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455–1458 (1972).
[Crossref]

Wetteroth, T.

T. E. Tiwald, J. A. Woollam, St. Zollner, J. Christiansen, R. B. Gregory, T. Wetteroth, S. R. Wilson, “Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry,” Phys. Rev. B 60, 11464–11474 (1999).
[Crossref]

Williams, G. P.

Wilson, S. R.

T. E. Tiwald, J. A. Woollam, St. Zollner, J. Christiansen, R. B. Gregory, T. Wetteroth, S. R. Wilson, “Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry,” Phys. Rev. B 60, 11464–11474 (1999).
[Crossref]

Wittlin, A.

R. Henn, C. Bernhard, A. Wittlin, M. Cardona, S. Uchida, “Far infrared ellipsometry using synchrotron radiation: the out-of-plane response of La2-xSrxCuO4,” Thin Solid Films 313-314, 643–648 (1998).
[Crossref]

Wolfe, C. M.

C. M. Wolfe, N. Holonyak, G. E. Stillmann, Physical Properties of Semiconductors (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Woollam, J. A.

M. Schubert, T. E. Tiwald, J. A. Woollam, “Explicit solutions for the optical properties of arbitrary magneto-optic materials in generalized ellipsometry,” Appl. Opt. 38, 177–187 (1999).
[Crossref]

T. E. Tiwald, J. A. Woollam, St. Zollner, J. Christiansen, R. B. Gregory, T. Wetteroth, S. R. Wilson, “Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry,” Phys. Rev. B 60, 11464–11474 (1999).
[Crossref]

St. Zollner, J. P. Carrejo, T. E. Tiwald, J. A. Woollam, “The origin of the Berreman effect in SiC homostructures,” Phys. Status Solidi B 208, R3–R4 (1998).
[Crossref]

D. W. Thompson, M. J. De Vries, 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).
[Crossref]

M. Schubert, B. Rheinländer, B. Johs, C. M. Herzinger, J. A. Woollam, “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]

M. Schubert, B. Rheinländer, C. Cramer, H. Schmiedel, J. A. Woollam, B. Johs, C. M. Herzinger, “Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals,” J. Opt. Soc. Am. A 13, 1930–1940 (1996).
[Crossref]

C. M. Herzinger, P. G. Snyder, B. Johs, J. A. Woollam, “InP optical constants between 0.75 and 5.0 eV determined by variable-angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 1715–1724 (1995).
[Crossref]

M. Schubert, B. Rheinländer, B. Johs, J. A. Woollam, “Application of generalized ellipsometry to complex optical systems,” in Polarimetry and Ellipsometry, M. Pluta, T. R. Wolinsky, eds., Proc. SPIE3094, 255–265 (1997).
[Crossref]

Wright, G. B.

G. B. Wright, B. Lax, “Magnetoreflection experiments in intermetallics,” J. Appl. Phys. 32, 2113–2117 (1961).
[Crossref]

Zollner, St.

T. E. Tiwald, J. A. Woollam, St. Zollner, J. Christiansen, R. B. Gregory, T. Wetteroth, S. R. Wilson, “Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry,” Phys. Rev. B 60, 11464–11474 (1999).
[Crossref]

St. Zollner, J. P. Carrejo, T. E. Tiwald, J. A. Woollam, “The origin of the Berreman effect in SiC homostructures,” Phys. Status Solidi B 208, R3–R4 (1998).
[Crossref]

Appl. Opt. (1)

J. Appl. Phys. (2)

C. M. Herzinger, P. G. Snyder, B. Johs, J. A. Woollam, “InP optical constants between 0.75 and 5.0 eV determined by variable-angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 1715–1724 (1995).
[Crossref]

G. B. Wright, B. Lax, “Magnetoreflection experiments in intermetallics,” J. Appl. Phys. 32, 2113–2117 (1961).
[Crossref]

J. Opt. Soc. Am. (1)

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

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

J. Phys. C (1)

A. Raymond, J. L. Robert, C. Bernard, “The electron effective mass in heavily doped GaAs,” J. Phys. C 12, 2289–2293 (1979).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (2)

M. Cardona, “Electron effective masses of InAs and GaAs as a function of temperature and doping,” Phys. Rev. 121, 752–758 (1961).
[Crossref]

D. W. Berreman, “Infrared absorption at longitudinal optic frequency in cubic crystal films,” Phys. Rev. 130, 2193–2198 (1963).
[Crossref]

Phys. Rev. B (7)

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

R. F. Wallis, J. J. Brion, E. Burstein, A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9, 3424–3437 (1974).
[Crossref]

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265–4274 (1996).
[Crossref]

J. Humlı́ček, R. Henn, M. Cardona, “Infrared vibrations in LaSrGaO4 and LaSrAlO4,” Phys. Rev. B 61, 14554–14563 (2000).
[Crossref]

T. E. Tiwald, J. A. Woollam, St. Zollner, J. Christiansen, R. B. Gregory, T. Wetteroth, S. R. Wilson, “Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry,” Phys. Rev. B 60, 11464–11474 (1999).
[Crossref]

M. Schubert, T. E. Tiwald, C. M. Herzinger, “Infrared dielectric anisotropy and phonon modes of sapphire,” Phys. Rev. B 61, 8187–8201 (2000).
[Crossref]

A. Kasic, M. Schubert, S. Einfeldt, D. Hommel, T. E. Tiwald, “Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry,” Phys. Rev. B 62, 7365–7377 (2000).
[Crossref]

Phys. Rev. Lett. (1)

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Theory of magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455–1458 (1972).
[Crossref]

Phys. Status Solidi A (1)

M. Schubert, C. M. Herzinger, “Ellipsometry on anisotropic materials: Bragg conditions and phonons in dielectric helical thin films,” Phys. Status Solidi A 188, 1563–1575 (2001).
[Crossref]

Phys. Status Solidi B (2)

St. Zollner, J. P. Carrejo, T. E. Tiwald, J. A. Woollam, “The origin of the Berreman effect in SiC homostructures,” Phys. Status Solidi B 208, R3–R4 (1998).
[Crossref]

J. Humlı́ček, “Infrared spectroscopy of LiF on Ag and Si,” Phys. Status Solidi B 215, 155–159 (1999).
[Crossref]

Surf. Sci. (2)

J. J. Brion, R. F. Wallis, A. Hartstein, E. Burstein, “Interaction of surface magnetoplasmons and surface optical phonons in polar semiconductors,” Surf. Sci. 34, 73–80 (1973).
[Crossref]

A. Hartstein, E. Burstein, J. J. Brion, R. F. Wallis, “Surface polaritons on semi-infinite anisotropic media,” Surf. Sci. 34, 81–89 (1973).
[Crossref]

Thin Solid Films (4)

D. W. Thompson, M. J. De Vries, 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).
[Crossref]

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313-314, 323–332 (1998).
[Crossref]

G. E. Jellison, “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313-314, 33–39 (1998).
[Crossref]

R. Henn, C. Bernhard, A. Wittlin, M. Cardona, S. Uchida, “Far infrared ellipsometry using synchrotron radiation: the out-of-plane response of La2-xSrxCuO4,” Thin Solid Films 313-314, 643–648 (1998).
[Crossref]

Other (20)

M. Schubert, A. Kasic, T. Hofmann, V. Gottschalch, J. Off, F. Scholz, E. Schubert, H. Neumann, I. J. Hodgkinson, M. D. Arnold, W. A. Dollase, C. M. Herzinger, “Generalized ellipsometry of complex mediums in layered systems,” in Complex Mediums III: Beyond Linear Isotropic Dielectrics, A. Lakhtakia, G. Dewar, M. W. McCall, eds., Proc. SPIE4806, 264–276 (2002).
[Crossref]

This set comprises six real-valued quantities out of the eight possible values contained within the Jones matrix—lacking the light beam’s absolute intensity and absolute phase information. For a definition of the Jones matrix elements, see Refs. 15, 17, 18, 24-27, and references therein.

T. E. Tiwald, M. Schubert, “Measurement of rutile TiO2 from 0.148 to 33 µm using generalized ellipsometry,” in Optical Diagnostic Methods For Inorganic Materials II, L. M. Hanssen, ed., Proc. SPIE4103, 19–29 (2000).
[Crossref]

M. Schubert, “Theory and application of generalized ellipsometry,” in Handbook of Ellipsometry, G. E. Irene, H. W. Tompkins, eds. (to be published).

M. Schubert, B. Rheinländer, B. Johs, J. A. Woollam, “Application of generalized ellipsometry to complex optical systems,” in Polarimetry and Ellipsometry, M. Pluta, T. R. Wolinsky, eds., Proc. SPIE3094, 255–265 (1997).
[Crossref]

C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1985).

In view of the generalized ellipsometry applications at oblique incidence, MO setups will be addressed as follows: the polar MO (PMO) setup with B parallel to the sample normal, the longitudinal MO (LMO) setup with B parallel to the sample surface and parallel to the plane of incidence, and the transverse MO (TMO) setup with B perpendicular to the sample normal and perpendicular to the plane of incidence. In the MO literature, different terms are in use: Near-normal-incidence reflection-type Kerr-effect measurements are referred to as transverse, longitudinal, and polar configurations, in conceptual agreement with the above notation. Faraday- and Voigt-effect measurements address transmission-type linear polarization rotation measurements in the above PMO and mixed LMO–TMO configurations, respectively. See Ref. 3 or Ref. 41. These configurations mostly result from the simplicity of the corresponding equations, which describe the polarized light reflection and transmission situations for the anisotropic materials. These requirements are now dispensed with because of the availability of explicit solutions for light propagation in arbitrarily nonsymmetric (MO) dielectric materials.21

M. Mansuripur, The Physical Principles of Magneto-Optical Recording (Cambridge U. Press, Cambridge, UK, 1995).

E. D. Palik, “Gallium arsenide (GaAs),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1998), Vol. I; pp. 429–444.

E. Burstein, F. De Martini, eds., Polaritons (Pergamon, New York, 1974).

Restrictions apply to highly conductive layers that are optically thick, such as highly doped semiconductor substrates, or metal films several hundreds of nanometers thick. As long as the layer with high free-carrier concentration is passing electromagnetic radiation on to the next constituent, the ellipsometric parameters will contain information about the buried layers.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1984).

D. E. Aspnes, “The accurate determination of optical properties by ellipsometry,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1998), Vol. I, pp. 89–112.

M. Schubert, “Infrared ellipsometry on III-V semiconductor layer structures,” Habilitationsschrift (Universität Leipzig, Leipzig, Germany), available at http://www.uni-leipzig.de/∼hlp/ellipsometrie .

The effective-mass concept addressed here descends from the similarity with the Newton force equation (acceleration of a body with mass m) and the acceleration experienced by a Bloch electron due to an external force. The inverse tensor obtained thereby depends on the curvature of the plots of electron energetic states versus electron momentum, which is diagonal by a suitable choice of axes. Different experiments require different concepts, resulting in definition of the effective conductivity mass, the density-of-states effective mass, the Hall effective mass, or the cyclotron effective mass, all of which are not discussed here. For the material investigated here (GaAs), the response of the zinc-blended, Γ-point conduction band (single-species, i.e., single-valley) Bloch electrons studied at infrared wavelengths is on a time scale much smaller than the average time between scattering events of the free electrons. One may also refer to the effective mass here as an (infrared) optical effective mass. See also Refs. 2 and 3.

C. M. Wolfe, N. Holonyak, G. E. Stillmann, Physical Properties of Semiconductors (Prentice-Hall, Englewood Cliffs, N.J., 1989).

C. R. Pidgeon, “Free carrier optical properties of semiconductors,” in Handbook of Semiconductors, M. Balkanski, ed. (North-Holland, Amsterdam, 1980), Vol. 2, pp. 223–228.

P. Drude, The Theory of Optics, translated from German by C. R. Mann, R. A. Millikan (Longmans, Green, New York, 1902).

H. Raether, Surface Polaritons (Springer, Berlin, 1988).

A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie, Berlin, 1992).

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Figures (6)

Fig. 1
Fig. 1

Schematic drawing (not to scale) of the light path through the magnet (solid line): M1, entrance mirror; M2, exit mirror; S, sample; P, magnet poles; B, magnetic field direction.

Fig. 2
Fig. 2

Experimental (dotted curves) and best-fit (solid curves) far-infrared Mueller matrix spectra obtained by generalized (Mueller matrix) ellipsometry for an i-GaAs(d)/n-GaAs homostructure at Φa=80°, affected by two mirror reflections (before and after the sample, as indicated in Fig. 1). Dotted vertical lines indicate frequencies of the interface modes FSP, SGW+, and SGW-, discussed in the text. The dashed vertical line denotes the wave number of the GaAs TO frequency.

Fig. 3
Fig. 3

Same as Fig. 2 but with the magnetic field perpendicular to the sample surface turned on and the spectra subtracted by the spectra shown in Fig. 2 (all spectra are differences between those at μ0H=2.3 T and H=0). Note the scale change to the left.

Fig. 4
Fig. 4

Wavelength-by-wavelength-inverted (dashed curves) and Drude-MDF best-fit (solid curves) far-infrared MO tensor element spectra xx and xy for the n-GaAs substrate obtained through model analysis of the experimental data shown in Fig. 5. The wavelength-by-wavelength-inverted spectra follow closely those predicted by Eqs. (15)–(17). (a) Im(xy), (b) Re(xy), (c) Im(xx), (d) Re(xx). The zz spectra are virtually identical to the xx spectra and are therefore omitted here.

Fig. 5
Fig. 5

Experimental (dotted curves) and best-fit (solid curves) far-infrared MO generalized ellipsometry (normalized Jones matrix element) spectra for the i-GaAs(d)/n-GaAs homostructure at Φa=80°. Upper set of curves: Ψpp at H=0. The dotted vertical lines indicate frequencies of the interface modes FSP, SGW+, and SGW-, discussed in the text. The dashed vertical line denotes the wave number of the GaAs TO frequency. Middle set of curves: Ψps, Ψsp at μ0H=2.3 T. Lower set of curves: difference spectra Ψpp(μ0H=2.3 T)-Ψpp(0).

Fig. 6
Fig. 6

Same as Fig. 5 but for delta spectra. Upper set of curves: Δpp at H=0, middle set of curves: Δps at μ0H=2.3 T, lower set of curves: Δsp at μ0H=2.3 T.

Tables (1)

Tables Icon

Table 1 Lattice [Eq. (18)], Free-Carrier [Eq. (13)], and MO MDF [Eqs. (15)–(17)] Best-Fit Parameters for the i-GaAs(d)-n-GaAs Layer Structurea

Equations (18)

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r=rpprsprpsrss.
rpprssRpp=tan Ψpp exp(iΔpp),
rpsrppRps=tan Ψps exp(iΔps),
rsprssRsp=tan Ψsp exp(iΔsp).
S0S1S2S3output=M11M12M13M14M21M22M23M24M31M32M33M34M41M42M43M44S0S1S2S3input.
rpprsprpsrss12(|rpp|2+|rss|2+|rsp|2+|rps|2)12(|rpp|2-|rss|2-|rsp|2+|rps|2)Re(rppr¯sp+r¯ssrps)Im(rppr¯sp+r¯ssrps)12(|rpp|2-|rss|2+|rsp|2-|rps|2)12(|rpp|2+|rss|2-|rsp|2-|rps|2)Re(rppr¯sp-r¯ssrps)Im(rppr¯sp-r¯ssrps)Re(rppr¯ps+r¯ssrsp)Re(rppr¯ps-r¯ssrsp)Re(rppr¯ss+r¯psrsp)Im(rppr¯ss-r¯psrsp)-Im(rppr¯ps+r¯ssrsp)-Im(rppr¯ps-r¯ssrsp)-Im(rppr¯ss+r¯psrsp)Re(rppr¯ss-r¯psrsp),
(FC-MO)(ω)=-i˜0ωσ,
mm0q(γ+t)v=[E+μ0H(v×h)].
(FC-MO)(ω)=-ωp*2(ω2I+iωγ)-iωωc×0-h3h2h30-h1-h2h10-1,
ωp*2Ne2˜0m0m-1,
ωcqμ0Hm0m-1
γp=emμ.
(FC)(ω)=-ωp*2ω(ω+iγp).
(FC-MO)(ω)=xxixy0-ixyxx000zz,
xx(ω)=-ωp*2ω+iγpω[(ω+iγp)2-ωc2],
zz(ω)=-ωp*21ω(ω+iγp),
xy(ω)=-ωp*2ωcω[(ω+iγp)2-ωc2].
L=ωLO2-ω2-iωγωTO2-ω2-iωγ,

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