Polynomial inversion of the single transparent layer problem in ellipsometry in case of multiple measurements

Abstract

In a previous paper (J. P. Drolet et al., J. Opt. Soc. Am. A 11, 3284 (1994) [1]) it has been shown that for a single transparent layer the dielectric constant satisfies a fifth degree polynomial and the problem of extracting the layer refractive index and the thickness from a single ellipsometric measurement is then reduced to finding the roots of this polynomial. Here we extend this result in the case of multiple ellipsometric measurements, taken, e.g., at a different incidence angle, layer thickness, ambient and/or different wavelengths. It is shown that in these cases the minimization procedure for determining the layer thickness and the layer dielectric constant can also be reduced to a much simpler and stable procedure of finding the polynomial roots. This approach to the problem directly gives all possible solutions (global minima) without the need for initial guesses and parameter's ranges, thus avoiding inherent problems of the general minimization procedure. In addition, it is faster than the minimization procedure and is time deterministic, which makes it suitable for in‐situ and real time ellipsometric data reduction. Several methods based on this approach are considered and their performance and error propagation robustness evaluated and compared. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)