On the development of Finite-Difference Time-Domain for modeling the spectroscopic ellipsometry response of 1D periodic structures

Abstract The use of the Finite-Difference Time-Domain method (FDTD method) for spectroscopic ellipsometry (SE) data analysis is desirable as it could provide a general method for advanced quantitative optical characterization of complex, non-layered, samples with applications to nanoscience and nanotechnology. In this contribution we demonstrate that the fully vectorial, time-domain, FDTD method approach to solve Maxwell's equations in the near-field can be used to accurately calculate the far-field SE response of periodic 1D structures. Using blazed gratings as models of periodic 1D structures, we calculate the SE response of two blazed gratings with 1200 and 2400 ln/mm using a five parameter morphological model and dielectric functions for Al and MgF 2 obtained from an independent SE analysis of commercial broad-band Al mirrors. Using an unbiased mean squared error (MSE ( ψ ,Δ) ) as figure of merit, two strategies are demonstrated to approach the best fit to SE measurements namely, parameter sweep and particle swarm parameter optimization. It is demonstrated that particle swarm enables the estimation of the best fit parameters from SE measurements at 45° angle of incidence (AoI). Good quantitative results were obtained for both samples with final MSE ( ψ ,Δ) values ~ 15.8 and ~ 2.6, respectively, for the 1200 and 2400 ln/mm gratings which were further confirmed by direct comparison to SE measurements at AoI = 55° yielding MSE ( ψ ,Δ) of ~ 22.8 and ~ 5.1. These results pave the way for a powerful and complimentary FDTD–SE approach due to the distinctive advantages of the FDTD method: (i) sources of error are well understood, leading to the ability to simulate a large variety of electromagnetic problems; (ii) potential to simulate arbitrary general subwavelength to nano-sized structures and in particular single nanostructures; (iii) calculation of broad spectral band results from a single simulation; (iv) natural capacity as a time-domain technique to study complex optical phenomena such as plasmonic and non-linear effects; and (v) ability to visualize field dynamics.