Multiple minima in the ellipsometric error function

A study of the multiple minima problem was performed for a simple case using simulations. The test case was static (usually ex-situ) spectroscopic ellipsometry of thick dielectric films on crystalline silicon substrates taken at high sensitivity conditions near the s-wave antireflection angle-of-incidence (AOI). Analysis of the data was performed using the Levenberg-Marquardt algorithm with the unbiased tan Psi and cos Delta estimator. A large number of minima were observed on both sides of the main minimum, albeit with larger values of the error function. Moreover, data simulated at additional AOIs and/or at additional wavelengths showed an even higher number of minima. Three ways to overcome this problem are suggested: using another estimator, reducing the sensitivity of the data or performing a grid search. (C) 1998 Elsevier Science S.A.