The sensitivity of spectroscopic ellipsometry data to multilayer model parameters is shown to be a strong function of the angle of incidence. A quantitative study of sensitivity versus angle of incidence is performed for a GaAs-AlxGa1−xAs-GaAs substrate structure, showing that maximum sensitivity to layer thicknesses and AlGaAs composition occurs near the wavelength-dependent principal angle. These results are verified by experimental measurements on two molecular-beam epitaxy grown samples. New spectral features, not found in previous ellipsometry studies of similar structures, are also reported.
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.
General considerations are applied to optimize the sensitivity of ellipsometric measurements for thin films on a substrate. s- or p-wave suppression conditions are found to give maximum sensitivity. Approximate values of the optical parameters of the films and substrate are used to calculate discrete film thicknesses for the s- or p-wave suppression to occur. For null fixed-wavelength ellipsometry, these calculations are limited to experimentally available wavelengths, e.g., at strong emission lines from a Hg lamp. Films with thicknesses near the calculated ones are then deposited on the substrate. The ellipsometric parameters ψ and Δ are obtained at multiple angles of incidence and wavelengths, and a least-squares procedure is used for the analysis. The method has been applied to silicon nitride films on GaAs. The problem of correlation between the calculated optical parameters of the system is addressed. It is shown that the multiple-wavelength analysis decreases significantly the correlations as compared to single-wavelength analysis.
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