Evaluation of different dispersion models for correlation of spectroscopic ellipsometry and X-ray reflectometry.

The importance of proper modeling of the materials' optical properties for interpretation of spectroscopic ellipsometry (SE) data is pretty much impossible to underestimate. In this study, the thickness-dependent titanium nitride (TiN) optical properties were represented by the multiple-oscillator Drude-Lorentz, Forouhi-Bloomer, and Lorentz optical dispersions with different numbers of parameters. The dielectric function of thin TiN films with intermediate behavior can be appropriately expressed in terms of 9-13 model parameters. Using X-ray reflectometry (XRR) as a reference technique and taking into account surface roughness of TiN films, it has been shown that three-term Lorentz dispersion model provides not only the best fit quality for the nominal thicknesses ranging from 125 Å to 350 Å but also an extremely good SE-XRR linear correlation with slope 1.05 ± 0.01, intercept -9.88 ± 2.06 Å, and R = 0.9998. Use of other dispersion models results in a somewhat worse correlation with XRR measurements. Thus, an appropriate modeling of the film optical properties is one of the factors needed to be considered to establish well-grounded and credible SE and XRR correlation in case of using XRR as a reference technique, i.e., calibrating SE using x-ray reflectivity.