Analytic methods in the determination of optical properties by spectral ellipsometry

Optical properties of bulk materials and thin films have long been determined by spectral ellipsometers (SE’s). Optical properties are determined by finding the global minimum of a merit function χ2. Even in the simplest cases χ2 is dependent on at least five parameters. The global minimization of χ2 benefits from careful selection of the SE instrument state such that χ2 is optimally smooth in some sense. Minimization methods that assume analyticity, such as the popular Levenberg–Marquardt algorithm, encounter problems as the number of nondifferentiable points in χ2 increases. The purpose of the paper is to examine the distribution of local minimum and discontinuities in χ2 as a function of incident angle and wavelength-range selection. With proper attention to the selection of the incident angle and wavelength range the robustness of the Levenberg–Marquardt algorithm may be extended in fixed-angle SE’s.