Approach for extracting complex dielectric function spectra in weakly-absorbing regions

Ellipsometric spectra have been analyzed using a procedure whereby the complex dielectric function (ε = ε1 + iε2) is parameterized using different, physically realistic models in isolated regions of a single spectrum while layer thicknesses are kept common. The isolated spectral ranges correspond to regions where the material of interest is either non-absorbing or heavily absorbing and physically realistic models describing ε are available. Common structural parameters (thicknesses) obtained by this divided spectral range approach are used to extract ε by numerical inversion over the full spectral range. The divided spectral range analysis has been applied to study amorphous hydrogenated silicon, nanocrystalline zinc oxide, and epitaxial bismuth stannate thin films, as well as single crystal bismuth germanate. Layer thicknesses obtained from the divided range analysis are compared to those using continuous, but not necessarily physically supported, parameterizations of ε over the full spectral range. The divided spectral range analysis yields inverted spectra in ε which are free of discontinuities beyond noise present in experimental data and whose determination does not require any assumption to be made about the line shape of ε in weakly absorbing regions.