Extension of rotating-analyzer ellipsometry to generalized ellipsometry

Determination of the dielectric function tensor from uniaxial TiO2

Mathias Schubert, Bernd Rheinländer, John A Woollam, Blaine Johs, Craig M. Herzinger

Research output: Contribution to journalArticle

147 Citations (Scopus)

Abstract

For what is the first time, to our knowledge, we report on the extension of spectroscopic rotating-analyzer ellipsometry to generalized ellipsometry to define and to determine three essentially normalized elements of the optical Jones matrix J [R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 1521 (1972)]. These elements are measured in reflection over the spectral range of 3.5–4.5 eV on different surface orientations of uniaxial TiO2cut from the same bulk crystal. With a wavelength-by-wavelength regression and a 4 × 4 generalized matrix algebra, both refractive and absorption indices for the ordinary and the extraordinary waves, no, ko, ne, and ke, are determined. The inclinations and the azimuths of the optic axes with respect to the sample normal and plane of incidence were determined as well. The latter are confirmed by x-ray diffraction and polarization microscopy. Hence the spectrally dependent dielectric function tensor in laboratory coordinates is obtained. Very good agreement between measured and calculated data for the normalized Jones elements for the respective sample orientations and positions are presented. This technique may become an important tool for investigating layered systems with nonscalar dielectric susceptibilities.

Original languageEnglish (US)
Pages (from-to)875-883
Number of pages9
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume13
Issue number4
DOIs
StatePublished - Jan 1 1996

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Ellipsometry
ellipsometry
Tensors
analyzers
tensors
Wavelength
azimuth
wavelengths
Crystal orientation
inclination
regression analysis
Optics
Microscopic examination
algebra
x ray diffraction
incidence
Diffraction
optics
Polarization
refractivity

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition

Cite this

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title = "Extension of rotating-analyzer ellipsometry to generalized ellipsometry: Determination of the dielectric function tensor from uniaxial TiO2",
abstract = "For what is the first time, to our knowledge, we report on the extension of spectroscopic rotating-analyzer ellipsometry to generalized ellipsometry to define and to determine three essentially normalized elements of the optical Jones matrix J [R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 1521 (1972)]. These elements are measured in reflection over the spectral range of 3.5–4.5 eV on different surface orientations of uniaxial TiO2cut from the same bulk crystal. With a wavelength-by-wavelength regression and a 4 × 4 generalized matrix algebra, both refractive and absorption indices for the ordinary and the extraordinary waves, no, ko, ne, and ke, are determined. The inclinations and the azimuths of the optic axes with respect to the sample normal and plane of incidence were determined as well. The latter are confirmed by x-ray diffraction and polarization microscopy. Hence the spectrally dependent dielectric function tensor in laboratory coordinates is obtained. Very good agreement between measured and calculated data for the normalized Jones elements for the respective sample orientations and positions are presented. This technique may become an important tool for investigating layered systems with nonscalar dielectric susceptibilities.",
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AU - Johs, Blaine

AU - Herzinger, Craig M.

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N2 - For what is the first time, to our knowledge, we report on the extension of spectroscopic rotating-analyzer ellipsometry to generalized ellipsometry to define and to determine three essentially normalized elements of the optical Jones matrix J [R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 1521 (1972)]. These elements are measured in reflection over the spectral range of 3.5–4.5 eV on different surface orientations of uniaxial TiO2cut from the same bulk crystal. With a wavelength-by-wavelength regression and a 4 × 4 generalized matrix algebra, both refractive and absorption indices for the ordinary and the extraordinary waves, no, ko, ne, and ke, are determined. The inclinations and the azimuths of the optic axes with respect to the sample normal and plane of incidence were determined as well. The latter are confirmed by x-ray diffraction and polarization microscopy. Hence the spectrally dependent dielectric function tensor in laboratory coordinates is obtained. Very good agreement between measured and calculated data for the normalized Jones elements for the respective sample orientations and positions are presented. This technique may become an important tool for investigating layered systems with nonscalar dielectric susceptibilities.

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