FDTD Modeling of the Mueller Matrix Ellipsometric Response of Complex Structures: Challenges and Limitations for Plasmonic Metamaterials

The metrology section of the International Roadmap for Devices and Systems (IRDS) makes it clear that techniques for optical critical dimension (OCD), including scattering and ellipsometric variations, will continue to be of critical use for the foreseeable future [1]. To date, the Rigorous Coupled-Wave Analysis (RCWA)continues to be the method of choice in the modeling of optical data of structured 1D gratings. As the characterization performance demands continue to increase with smaller features size, larger material library, and ever increasing structure complexity, it becomes important to find complementary numerical tools toaccomplish this task. This is most relevant when metals are included in the structures of interest given the slow convergence rate of RCWA in plasmonic resonant conditions [2].

The Finite Difference Time Domain (FDTD) method provides attractive advantages including generality to address complex morphologies including non-periodic structures. In this presentation we demonstrate the use of the split-field method in FDTD to model the Mueller Matrix Ellipsometry (MME) data of real structures over abroad spectral range. The split-field method enables the FDTD computation of a broad spectral response at a fixed angle-of-incidence from a single simulation. This provides a computational advantage proportional to the number of wavelengths to be computed as compared to our previous results [3]. Taking advantage of this increased computational speed, a particle swarm algorithm is used to search the best-fit parameters with spectral density comparable to the experimental data. As a proof of principle, we use this approach to study plasmonic structure based on 1D PMMA gratings prepared on Au substrates using a single simulation to model the spectral range from 400 to1300 nm collected with a rotating compensator ellipsometer that can deliver the top three rows of the MME normalized to M11. We will present our perspectives for additional challenging materials characterization opportunities for which the FDTD method can provide significant advantages and benefits.