Automatic Selection of Dispersion Models in Spectroscopic Ellipsometry Using a Hierarchical Genetic Algorithm

In spectroscopic ellipsometry, the selection of an appropriate dispersion model is essential for accurate optical parameter extraction. Traditional approaches rely on fixed dispersion laws chosen based on prior knowledge, which can lead to suboptimal or biased results. We propose a novel Hierarchical Genetic Algorithm (HGA) framework that autonomously selects the optimal dispersion model from a set of candidates, without requiring a priori assumptions. The method maintains a computational cost comparable to that of classical genetic algorithms (CGA), while offering the added advantage of exploring multiple models simultaneously through a hierarchical structure. Simulations on a silica layer deposited on a silicon substrate under known thickness conditions demonstrate excellent agreement with theoretical values (fitness between 10⁻³ and 10⁻⁶, refractive index errors below 0.1%). Experimental validation on silicon samples confirms the effectiveness of the HGA, yielding results consistent with conventional methods, but without the need for predefined model selection. This approach significantly enhances the flexibility and reliability of ellipsometric characterization. The computational analysis was performed using a code developed in-house with the Matlab environment, allowing accurate calculation and simulation of the index dispersion over a wide spectral range.