Extracting film thickness and optical constants from spectrophotometric data by evolutionary optimization

Abstract

In this paper, we propose a simple and elegant method to extract the thickness and the optical constants of various films from the reflectance and transmittance spectra in the wavelength range of 350 − 1000 nm. The underlying inverse problem is posed here as an optimization problem. To find unique solutions to this problem, we adopt an evolutionary optimization approach that drives a population of candidate solutions towards the global optimum. An ensemble of Tauc-Lorentz Oscillators (TLOs) and an ensemble of Gaussian Oscillators (GOs), are leveraged to compute the reflectance and transmittance spectra for different candidate thickness values and refractive index profiles. This model-based optimization is solved using two efficient evolutionary algorithms (EAs), namely genetic algorithm (GA) and covariance matrix adaptation evolution strategy (CMAES), such that the resulting spectra simultaneously fit all the given data points in the admissible wavelength range. Numerical results validate the effectiveness of the proposed approach in estimating the optical parameters of interest.