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 chi(2). Even in the simplest cases chi(2) is dependent on at least five parameters. The global minimization of chi(2) benefits from careful selection of the SE instrument state such that chi(2) 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 chi(2) increases. The purpose of the paper is to examine the distribution of local minimum and discontinuities in chi(2) 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. (C) 1998 Optical Society of America.