A fully automatized method for the unambiguous wavelength-by-wavelength determination of the thickness and optical property of a very thin film with a transparent range

Abstract

Spectroscopic ellipsometry is a powerful method with high surface sensitivity that can be used to monitor the growth of even sub-monolayer films. However, analysis of ultrathin films is complicated by the correlation between the dielectric constant and thickness. This problem is usually resolved by fixing one or the other value, limiting the information that can be extracted. Here, we propose a method to determine unambiguously the refractive index, extinction coefficient, and thickness of a film when a transparent range is available in the energy range investigated. We decompose the analysis in three steps. First, the thickness of the film is determined from the transparent range of the film. Then, knowing the thickness of the layer, an initial estimation of the refractive index and extinction coefficient is made based on a first-order Taylor expansion of the ellipsometric ratio. Finally, using this estimation, a numerical iteration is done to ensure convergence of the fit toward the solution. A theoretical example of the method is given for two different thicknesses of TiO2 films. Finally, the method is applied to the experimental data measured during the atomic layer deposition of a thin film of Hf0.5Zr0.5O2 grown on Si. The thickness, refractive index, and extinction coefficient are retrieved with high precision (respectively, 0.01 and 0.002) in the energy range of 3.5–6.5 eV. A detailed analysis is presented on the accuracy of the retrieved values and their dependency on random and systematic errors for different energy ranges.