Parameter correlation and precision in multiple-angle ellipsometry.

A general procedure for the characterization of the optical parameters of a given surface using fixed wavelength multiple-angle-of-incidence ellipsometry is developed. Quantitative evaluation of estimated parameter precision is studied considering the sum of errors squared of a least squares fit, the parameter cross-correlation at this minimum, and the confidence limits of the parameters from variance-covariance relations. Most significantly, it is shown numerically that precision is improved when the solutions exhibit a lower correlation to the remaining parameters when a correct system model is used. Using the silicon dioxide-silicon substrate system we were able to determine the complex index of silicon and the extinction coefficient of the oxide with high precision. Once this was done it was possible to estimate with reasonable confidence the refractive index and particularly the thickness of the oxide despite an observed large cross-correlation coefficient between them. A wide range of starting values for the film refractive index n(f) and thickness t(f) always converged to a small sum of errors squared, and nearly identical values for n(f) and t(f) after accurate estimates were obtained for the other parameters of the system.