Hp-finite element method for simulating light scattering from complex 3D structures

Abstract

Methods for solving Maxwell's equations are integral part of optical metrology and computational lithography setups. Applications require accurate geometrical resolution, high numerical accuracy and/or low computation times. We present a finite-element based electromagnetic field solver relying on unstructured 3D meshes and adaptive hp-refinement. We apply the method for simulating light scattering off arrays of high aspect-ratio nano-posts and FinFETs.

Time-harmonic optical chirality in inhomogeneous space

“…For this as well as for all simulations of this study, we use the FEM solver JCMsuite 34,35 wherein the chirality densities for isotropic media (15,16) as well as for anisotropic media (12,13) and the chirality flux density (14) are readily implemented and in which we use finely tuned numerical parameters to ensure well converged results. For the stated results, we use locally adapted polynomial degrees p of the finite elements, so-called hp-FEM, 36 to both model the spatial discretization of the helix fine enough and reduce computational resources. Using (a) setup (b) transmission for CPL (c) chiral vs. energy quantities for RPL Figure 6: Gold helix surrounded by air in hexagonal lattice with lattice constant √ 3a (a).…”

Method for fast computation of angular light scattering spectra from 2D periodic arrays

“…Please see a previous publication for details on the numerical settings for hp-refinement. 8 Agreement of results obtained with the Schur complement method and with standard FEM is expected, however, small deviations of the numerical results within the ranges of numerical discretization errors are due to differences in numerical treatment of transparent boundaries in the Schur complement and in the standard FEM case.…”

“…and the solutions are used in (8) to assemble the θ dependent Schur complement: Table 1. Right: Visualization of the mesh discretizing the geometry (only silicon parts shown).…”

“…We demonstrate results that are based on JCMsuite, a FEM solver for the linear Maxwell's equations in frequency domain. The implementation contains features like higher-order edge-elements, 6 domain-decomposition, 7 hp-adaptivity, 8 and model order reduction. 9 It is applied to tasks in computational lithography and metrology [10][11][12][13] as well as to further fields in technology and research, see, e.g., for an overview.…”

Modelling of standard and specialty fibre-based systems using finite element methods

“…6D. For the corresponding FEM computation, higherorder finite elements (p=3) are used 5 . In our computational setup, we first compute the modes of the involved fibres (Fibre 1, 2, 3), then we compute the overlap integrals (which is done in a postprocess, utilizing the higher-order FEM discretization of the field distributions).…”