Dielectric Function Tensor Research Articles

Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial TiO_2

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 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 TiO2 cut 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.

Theoretical determination of angularly-integrated energy loss functions for anisotropic materials

Abstract The general expression for angularly integrated electron-energy-loss functions for anisotropic materials is derived for arbitrary specimen orientations with respect to the incident angle of a fast electron. For uniaxial (tetragonal, trigonal and hexagonal) and biaxial (orthorhombic) crystal systems, the angularly integrated electron-energy-loss functions in the core loss region are linear combinations of the components of the dielectric function for the electron beam travelling along any one of the principal crystallographic axes. This suggests a novel method of determining the anisotropic dielectric function tensor from angularly integrated energy-loss spectra, which can be implemented for a convergent probe. The spatial resolution of the anisotropy in the localized electronic structure is then only limited by the probe size and can be as small as a few nanometres in a dedicated scanning transmission electron microscope.