Enhancements to FDTD modeling for optical metrology applications

Abstract

This paper presents Finite Difference Time Domain (FDTD) method based on discretised Maxwell curl equations and widely used in microwave circuit design - as a promising tool for new optical metrology purposes. We focus on periodic FDTD formulations for scattering problems. The interest in efficient full-wave modelling of periodic structures has arisen due to their increasing applications as slow wave transmission lines, photonic crystals, and metamaterials. Recently, new efforts have been made to incorporate the FDTD algorithms into the scatterometry overlay technology (SCOL) toolkit. In SCOL, multilayered grating targets on silicon wafers are illuminated with polarised light at a particular angle of incidence; reflected signal of the 0 th diffraction order is processed to extract the information about misalignment between grating layers. Since the illumination spot size typically covers tens or even hundreds of grating periods, direct 3D FDTD modelling of such an electrically large problem needs long computing times. The periodic FDTD algorithm discussed herein, built upon Floquet theorem, allows reduction of the modelling problem to one or just a few periods. As a consequence, it substantially speeds up the simulation. The incident wave is modelled as a plane wave. The reflected wave is extracted via near-to-far (NTF) transformation as in antenna analysis. We cross-calibrate the FDTD algorithm against other numerical techniques better established in optical metrology, like Rigorous Coupled Wave Analysis (RCWA). For a benchmark of multilayered rectangular grating composition illuminated with light within the 500 to 700 nm spectrum, we show that the FDTD and RCWA results for the 0 th diffraction order reflection coefficient are in excellent agreement. The FDTD approach is more flexible as it further allows quantitative characterisation of non-rectangular periodic structures, higher-order diffraction rays, and periodicity violation. This work was done in the framework of the SOCOT Consortium [18], sponsored by the European Commission under the IST 6 th Framework Programme, Contract No. 016403.