Pseudodielectric functions of uniaxial materials in certain symmetry directions

Abstract

The pseudodielectric function is often used to represent ellipsometric data and corresponds to the actual dielectric functions of materials when there is no surface overlayer and the material is isotropic. If a uniaxial material is oriented such that the optic axis is in the plane of incidence or is perpendicular to the plane of incidence, then the cross-polarization terms are zero and appropriate pseudodielectric functions can be determined from the ellipsometry data. We calculate the pseudodielectric functions for uniaxial crystals in three primary symmetry directions: (1) the optic axis is perpendicular to the plane of incidence, (2) the optic axis is in the plane of the sample surface and parallel to the plane of incidence, and (3) the optic axis is in the plane of the sample surface and perpendicular to the plane of incidence. These results are expanded in terms of the difference in the ordinary and extraordinary dielectric functions and compared with the approximation of Aspnes [J. Opt. Soc. Am. 70, 1275 (1980)]. Comparisons are made with experimental results on oriented crystals of rutile (TiO2), and a simple procedure is presented to determine the complex dielectric function from standard ellipsometry techniques.

Optical spectroscopy of charge transfer transitions in multiferroic manganites, ferrites, and related insulators

“…We performed our study using a variable-angle spectroscopic ellipsometer as described elsewhere. [27][28][29][30][31] The technique of optical ellipsometry provides significant advantages over conventional reflection and transmittance methods in that it is self-normalizing and does not require reference measurements. The optical complex pseudodielectric function = Ј − iЉ is obtained directly without the Kramers-Krönig transformation.…”

“…27 For isotropic crystals this function gives the value of the dielectric function of the material = ps if a surface roughness is taken into account properly. In the case of uniaxial crystals 28,29 the pseudodielectric function extracted from the measurements performed for two different orientations of the sample are a good approximation for the true dielectric function of the crystal. Thus, ps measured with p-polarized light for a crystal with the optical axis z lying in the plane of incidence gives the value of zz and, subsequently, of the extraordinary refractive and absorption indices.…”

Above-band-gap dielectric functions of ZnGeAs2: Ellipsometric measurements and quasiparticle self-consistentGWcalculations

“…12 Our data concern the intrinsic ε of a ZnGeAs 2 thin film grown epitaxially on GaAs. Since ZnGeAs 2 grows with its c axis normal to the surface and SE measurements are dominated by the component(s) of the ε tensor perpendicular to the c axis (here parallel to the measurement surface), 13,14 our data are a close approximation to the component ε a of ε. This is the component relevant for normal-incidence illumination.…”

Ellipsometric study of single-crystal γ-InSe from 1.5 to 9.2 eV

“…͗ Ќ ͘ spectra obtained on an optically uniaxial crystal oriented with the optic axis perpendicular to the crystal surface are a close approximation to the ordinary component o of the dielectric tensor of the crystal, since the c-axis contribution is reduced approximately by 1 / ͗͘. 7,8 This approximation has been shown to be valid for single-crystal TiO 2 , which is highly anisotropic ͉͑⌬n͉Ϸ0.3͒ below the fundamental absorption edge. 8 Although a recent SE study 9 of wurtzite ZnO and GaN found a large discrepancy between ͗ Ќ ͘ and o in the transparent and excitonic-absorption regions, the discrepancy above the band gap is relatively small.…”