Optical properties of bulk c-ZrO 2, c-MgO and a-As 2S 3 determined by variable angle spectroscopic ellipsometry

Abstract

In this paper spectroscopic ellipsometry is used to determine the dielectric function (refractive index) of three bulk materials: cubic zirconia (c-ZrO 2), cubic magnesium oxide (c-MgO) and amorphous (vitreous) arsenic sulfide (a-As 2S 3) from 130 nm in the vacuum ultraviolet to 33 μ in the infrared. This work utilizes the very wide spectral coverage and sensitivity of modern spectroscopic ellipsometers to determine bulk optical properties of these materials over a wide spectral range. Ellipsometric psi and delta data at multiple angles of incidence were fit to extract the dielectric function of each material. Intensity transmission data were also acquired at normal incidence and fit simultaneously with the psi and delta data when possible. Including transmission data in the analysis greatly improves sensitivity to small absorption features. The ellipsometric delta data were very sensitive to surface quality. Therefore, it was very important to include surface roughness in all models to avoid non-physical absorption artifacts in the optical constants. The experimental data were fit in the transparent spectral range to determine the real part of the dielectric function and the surface roughness. Fixing the surface roughness then allows the optical constants to be determined by a direct fit for ε 1 and ε 2 at each measured psi-delta data point. Combinations of multiple Gaussian, Lorentz, and Tauc–Lorentz dispersion functions were then used to fit the experimental data. The different shapes of each function allow fitting a wide range of absorption features throughout the ultraviolet, visible and infrared spectral ranges. Combining multiple oscillator types provides a very flexible approach to fitting optical constants over a wide spectral range while simultaneously enforcing Kramers–Kronig consistency in the fitted optical constants.