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 χ<sup>2</sup>. Even in the simplest cases χ<sup>2</sup> is dependent on at least five parameters. The global minimization of χ<sup>2</sup> benefits from careful selection of the SE instrument state such that χ<sup>2</sup> 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 χ<sup>2</sup> increases. The purpose of the paper is to examine the distribution of local minimum and discontinuities in χ<sup>2</sup> 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.
© 1998 Optical Society of America
David U. Fluckiger, "Analytic methods in the determination of optical properties by spectral ellipsometry," J. Opt. Soc. Am. A 15, 2228-2232 (1998)