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APPLICATION OF ELLIPSOMETRY TO UNIAXIAL CRYSTALS.
Abstract
The complex ordinary (No) and extraordinary (Ne) refractive indices of an absorbing uniaxial crystal can be explicitly derived from the normalized diagonal (a) and off- diagonal (B) elements of one oblique-incidence (at angle ) reflection matrix measured by generalized ellipsometry on a crystal face that contains the optic axis at an oblique orientation (wfo or π/2) with respect to the plane of incidence At most four solution sets (No, Ne) are mathematically and physically consistent with one measurement set (a, β, φ, ω). In many cases, identification of the correct solution is feasible without additional measurements. If necessary, repeated measurements at a different value of or w will resolve the ambiguity; only one solution set remains invariant upon a change of or w, the correct set. A single measurement of reflectance (e.g., for p-polarized light) may be adequate. The analytic inversion method is used in an error analysis to determine optimum choices of angle of incidence ($ 50-70°) and crystal orientation (w 45°) that lead to minimum percentage errors of No and Ne for several uniaxial crystals.In conventional ellipsometry applied to uniaxial crystals, two measurements are taken with the optic axis parallel and perpendicular to crystal's surface. Two values of the normalized diagonal element a (β0) are measured, and the equations obtained are solved without resort to iterative methods. Sixteen solution sets (No, Ne) are obtained and the correct solution can be easily identified as before. An error analysis shows that the same range of angle of incidence (50°-70°), as before, leads to minimum percentage error of No and Ne for several uniaxial crystals.Measurements of the ordinary, No, and extraordinary, Ne, refractive indices of a cadmium sulphide crystal at selected wavelengths by generalized ellipsometry yield values that agree with published data.
Subject Area
Electrical engineering
Recommended Citation
ZAGHLOUL, MERVAT ANWAR EL-SHAZLY, "APPLICATION OF ELLIPSOMETRY TO UNIAXIAL CRYSTALS." (1976). ETD collection for University of Nebraska-Lincoln. AAI7625899.
https://digitalcommons.unl.edu/dissertations/AAI7625899