arXiv subjects

F. Schmidt

Publications and source records attributed to F. Schmidt.

53 records · Page 3Linked to original sources

arXiv2008

Finite Element Simulation of Light Propagation in Non-Periodic Mask Patterns

Rigorous electromagnetic field simulations are an essential part for scatterometry and mask pattern design. Today mainly periodic structures are considered in simulations. Non-periodic structures are typically modeled by large, artificially periodified computational domains. For systems with a large radius of influence this leads to very large computational domains to keep the error sufficiently small. In this paper we review recent advances in the rigorous simulation of isolated structures embedded into a surrounding media. We especially address the situation of a layered surrounding media (mask or wafer) with additional infinite inhomogeneities such as resist lines. Further we detail how to extract the far field information needed for the aerial image computation in the non-periodic setting.

physics.optics↗

arXiv2008

A Rigorous Finite-Element Domain Decomposition Method for Electromagnetic Near Field Simulations

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an accurate modeling of complicated geometrical features. However, from a numerical point of view solving the arising system of linear equations is very demanding even for medium sized 3D domains. In numerics, a domain decomposition method is a commonly used strategy to overcome this problem. Within this approach the overall computational domain is split up into smaller domains and interface conditions are used to assure continuity of the electromagnetic field. Unfortunately, standard implementations of the domain decomposition method as developed for electrostatic problems are not appropriate for wave propagation problems. In an earlier paper we therefore proposed a domain decomposition method adapted to electromagnetic field wave propagation problems. In this paper we apply this method to 3D mask simulation.

physics.optics↗

arXiv2007

Electromagnetic Field Simulations of Isolated and Periodic 3D Photomask Patterns

We present rigorous 3D EMF simulations of isolated features on photomasks using a newly developed finite-element method. We report on the current status of the finite-element solver JCMsuite, incorporating higher-order edge elements, adaptive refinement methods, and fast solution algorithms. We demonstrate that rigorous and accurate results on light scattering off isolated features can be achived at relatively low computational cost, compared to the standard approach of simulations on large-pitch, periodic computational domains.

physics.optics↗

arXiv2007

3D Simulations of Electromagnetic Fields in Nanostructures using the Time-Harmonic Finite-Element Method

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and optics design of nanostructured components. As has been shown in previous benchmarks some of the presently used methods suffer from low convergence rates and/or low accuracy of the results and exhibit very long computation times which makes application to extended 2D layout patterns impractical. We address 3D simulation tasks by using a finite-element solver which has been shown to be superior to competing methods by several orders of magnitude in accuracy and computational time for typical microlithography simulations. We report on the current status of the solver, incorporating higher order edge elements, adaptive refinement methods, and fast solution algorithms. Further, we investigate the performance of the solver in the 3D simulation project of light diffraction off an alternating phase-shift contact-hole mask.

physics.optics↗

arXiv2007

FEM investigation of leaky modes in hollow core photonic crystal fibers

Hollow-core holey fibers are promising candidates for low-loss guidance of light in various applications, e.g., for the use in laser guide star adaptive optics systems in optical astronomy. We present an accurate and fast method for the computation of light modes in arbitrarily shaped waveguides. Maxwell's equations are discretized using vectorial finite elements (FEM). We discuss how we utilize concepts like adaptive grid refinement, higher-order finite elements, and transparent boundary conditions for the computation of leaky modes in photonic crystal fibers. Further, we investigate the convergence behavior of our methods. We employ our FEM solver to design hollow-core photonic crystal fibers (HCPCF) whose cores are formed from 19 omitted cladding unit cells. We optimize the fiber geometry for minimal attenuation using multidimensional optimization taking into account radiation loss (leaky modes).

physics.optics↗

arXiv2007

Goal Oriented Adaptive Finite Element Method for the Precise Simulation of Optical Components

Adaptive finite elements are the method of choice for accurate simulations of optical components. However as shown recently by Bienstman et al. many finite element mode solvers fail to compute the propagation constant's imaginary part of a leaky waveguide with sufficient accuracy. In this paper we show that with a special goal oriented error estimator for capturing radiation losses this problem is overcome.

physics.optics↗

arXiv2006

Rigorous FEM-Simulation of EUV-Masks: Influence of Shape and Material Parameters

We present rigorous simulations of EUV masks with technological imperfections like side-wall angles and corner roundings. We perform an optimization of two different geometrical parameters in order to fit the numerical results to results obtained from experimental scatterometry measurements. For the numerical simulations we use an adaptive finite element approach on irregular meshes. This gives us the opportunity to model geometrical structures accurately. Moreover we comment on the use of domain decomposition techniques for EUV mask simulations. Geometric mask parameters have a great influence on the diffraction pattern. We show that using accurate simulation tools it is possible to deduce the relevant geometrical parameters of EUV masks from scatterometry measurements. This work results from a collaboration between Advanced Mask Technology Center (AMTC, mask fabrication), Physikalisch-Technische Bundesanstalt (PTB, scatterometry), Zuse Institute Berlin (ZIB), and JCMwave (numerical simulation).

physics.optics↗

arXiv2006

Rigorous Simulation of 3D Masks

We perform 3D lithography simulations by using a finite-element solver. To proof applicability to real 3D problems we investigate DUV light propagation through a structure of size 9 microns times 4 microns times 65 nm. On this relatively large computational domain we perform rigorous computations (No Hopkins) taking into account a grid of 11 times 21 source points with two polarization directions each. We obtain well converged results with an accuracy of the diffraction orders of about one percent. The results compare well to experimental aerial imaging results. We further investigate the convergence of 3D solutions towards quasi-exact results obtained with different methods.

physics.optics↗

arXiv2006

Benchmark of FEM, Waveguide and FDTD Algorithms for Rigorous Mask Simulation

An extremely fast time-harmonic finite element solver developed for the transmission analysis of photonic crystals was applied to mask simulation problems. The applicability was proven by examining a set of typical problems and by a benchmarking against two established methods (FDTD and a differential method) and an analytical example. The new finite element approach was up to 100 times faster than the competing approaches for moderate target accuracies, and it was the only method which allowed to reach high target accuracies.

physics.optics↗

arXiv2006

Advanced Finite Element Method for Nano-Resonators

Miniaturized optical resonators with spatial dimensions of the order of the wavelength of the trapped light offer prospects for a variety of new applications like quantum processing or construction of meta-materials. Light propagation in these structures is modelled by Maxwell's equations. For a deeper numerical analysis one may compute the scattered field when the structure is illuminated or one may compute the resonances of the structure. We therefore address in this paper the electromagnetic scattering problem as well as the computation of resonances in an open system. For the simulation efficient and reliable numerical methods are required which cope with the infinite domain. We use transparent boundary conditions based on the Perfectly Matched Layer Method (PML) combined with a novel adaptive strategy to determine optimal discretization parameters like the thickness of the sponge layer or the mesh width. Further a novel iterative solver for time-harmonic Maxwell's equations is presented.

physics.comp-ph↗

arXiv2005

Magnetic metamaterials at telecommunication and visible frequencies

Arrays of gold split-rings with 50-nm minimum feature size and with an LC resonance at 200-THz frequency (1500-nm wavelength) are fabricated. For normal incidence conditions, they exhibit a pronounced fundamental magnetic mode, arising from a coupling via the electric component of the incident light. For oblique incidence, a coupling via the magnetic component is demonstrated as well. Moreover, we identify a novel higher-order magnetic resonance at around 370 THz (800-nm wavelength) that evolves out of the Mie resonance for oblique incidence. Comparison with theory delivers good agreement and also shows that the structures allow for a negative magnetic permeability.

cond-mat.mtrl-sci↗

arXiv2005

Numerical Investigation of Light Scattering off Split-Ring Resonators

Recently, split ring-resonators (SRR's) have been realized experimentally in the near infrared (NIR) and optical regime. In this contribution we numerically investigate light propagation through an array of metallic SRR's in the NIR and optical regime and compare our results to experimental results. We find numerical solutions to the time-harmonic Maxwell's equations by using advanced finite-element-methods (FEM). The geometry of the problem is discretized with unstructured tetrahedral meshes. Higher order, vectorial elements (edge elements) are used as ansatz functions. Transparent boundary conditions and periodic boundary conditions are implemented, which allow to treat light scattering problems off periodic structures. This simulation tool enables us to obtain transmission and reflection spectra of plane waves which are incident onto the SRR array under arbitrary angles of incidence, with arbitrary polarization, and with arbitrary wavelength-dependencies of the permittivity tensor. We compare the computed spectra to experimental results and investigate resonances of the system.

cond-mat.mtrl-sci↗

arXiv2005

Search for Pulsed VHE gamma-ray Emission from Young Pulsars with H.E.S.S

Pulsars are commonly regarded as highly magnetized neutron stars, rotating up to several hundred times per second. Over 1,500 radio pulsars have been found so far, about 70 of which are X-ray pulsars, but only a handful have been observed in gamma rays. This high-energy emission is believed to be produced by the electrons accelerated to TeV energies in the pulsar magnetosphere, resulting in cascades of secondary particles. The H.E.S.S. experiment is a system of four imaging atmospheric Cherenkov telescopes in Namibia, which is sensitive to gamma rays above 100 GeV. Three young pulsars, Crab, Vela, and PSR B1706-44 have been observed with H.E.S.S. The results of the search for pulsed emission for these targets, and the constraints on the theories of pulsed very high energy gamma-ray emission, are summarized here.

astro-ph↗

arXiv2005

JCMmode: An Adaptive Finite Element Solver for the Computation of Leaky Modes

We present our simulation tool JCMmode for calculating propagating modes of an optical waveguide. As ansatz functions we use higher order, vectorial elements (Nedelec elements, edge elements). Further we construct transparent boundary conditions to deal with leaky modes even for problems with inhomogeneous exterior domains as for integrated hollow core Arrow waveguides. We have implemented an error estimator which steers the adaptive mesh refinement. This allows the precise computation of singularities near the metal's corner of a Plasmon-Polariton waveguide even for irregular shaped metal films on a standard personal computer.

physics.optics↗

arXiv2005

FEM Modelling of 3D Photonic Crystals and Photonic Crystal Waveguides

We present a finite-element simulation tool for calculating light fields in 3D nano-optical devices. This allows to solve challenging problems on a standard personal computer. We present solutions to eigenvalue problems, like Bloch-type eigenvalues in photonic crystals and photonic crystal waveguides, and to scattering problems, like the transmission through finite photonic crystals. The discretization is based on unstructured tetrahedral grids with an adaptive grid refinement controlled and steered by an error-estimator. As ansatz functions we use higher order, vectorial elements (Nedelec, edge elements). For a fast convergence of the solution we make use of advanced multi-grid algorithms adapted for the vectorial Maxwell's equations.

physics.optics↗

arXiv2000

Evidence for a three-nucleon-force effect in proton-deuteron elastic scattering

Developments in spin-polarized internal targets for storage rings have permitted measurements of 197 MeV polarized protons scattering from vector polarized deuterons. This work presents measurements of the polarization observables A_y, iT_11, and C_y,y in proton-deuteron elastic scattering. When compared to calculations with and without three-nucleon forces, the measurements indicate that three-nucleon forces make a significant contribution to the observables. This work indicates that three-body forces derived from static nuclear properties appear to be crucial to the description of dynamical properties.

nucl-ex↗

arXiv1995

Construction of Nonlinear Symplectic Six-Dimensional Thin-Lens Maps by Exponentiation

The aim of this paper is to construct six-dimensional symplectic thin-lens transport maps for the tracking program SIXTRACK, continuing an earlier report by using another method which consistes in applying Lie series and exponentiation as described by W. Groebner and for canonical systems by A.J. Dragt. We firstly use an approximate Hamiltonian obtained by a series expansion of the square root. Furthermore, nonlinear crossing terms due to the curvature in bending magnets are neglected. An improved Hamiltonian, excluding solenoids, is introduced in Appendix A by using the unexpanded square root mentioned above, but neglecting again nonlinear crossing terms...

acc-phys↗