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Author: Rathsfeld, Andreas × End date: 2014 × Start date: 2012 × DDC: 510 × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × WGL Institute: WIAS ×

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Now showing 1 - 4 of 4
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    Modeling of line roughness and its impact on the diffraction intensities and the reconstructed critical dimensions in scatterometry
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Gross, Hermann; Henn, Mark-Alexander; Heidenreich, Sebastian; Rathsfeld, Andreas; Bär, Markus
    We investigate the impact of line edge and line width roughness (LER, LWR) on the measured diffraction intensities in angular resolved extreme ultraviolet (EUV) scatterometry for a periodic line-space structure designed for EUV lithography. LER and LWR with typical amplitudes of a few nanometers were previously neglected in the course of the profile reconstruction. The 2D rigorous numerical simulations of the diffraction process for periodic structures are carried out with the finite element method (FEM) providing a numerical solution of the two-dimensional Helmholtz equation. To model roughness, multiple calculations are performed for domains with large periods, containing many pairs of line and space with stochastically chosen line and space widths. A systematic decrease of the mean efficiencies for higher diffraction orders along with increasing variances is observed and established for different degrees of roughness. ...
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    Finite element method to fluid-solid interaction problems with unbounded periodic interfaces
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Hu, Guanghui; Rathsfeld, Andreas; Yin, Tao
    Consider a time-harmonic acoustic plane wave incident onto a doubly periodic (biperiodic) surface from above. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid fluid of constant mass density, whereas the region below is occupied by an isotropic and linearly elastic solid body characterized by its Lamé constants. This paper is concerned with a variational approach to the fluid-solid interaction problems with unbounded biperiodic Lipschitz interfaces between the domains of the acoustic and elastic waves. The existence of quasi-periodic solutions in Sobolev spaces is established at arbitrary frequency of incidence, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. A finite element scheme coupled with Dirichlet-to-Neumann mappings is proposed. The Dirichlet-to-Neumann mappings are approximated by truncated Rayleigh series expansions, and, finally, numerical tests in 2D are performed.
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    Convergence analysis of the FEM coupled with Fourier-mode expansion for the electromagnetic scattering by biperiodic structures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Rathsfeld, Andreas
    Scattering of time-harmonic electromagnetic plane waves by a doubly periodic surface structure in R3 can be simulated by a boundary value problem of the time-harmonic curl-curl equation. For a truncated FEM domain, non-local boundary value conditions are required in order to satisfy the radiation conditions for the upper and lower half spaces. Alternatively to boundary integral formulations, to approximate radiation conditions and absorbing boundary methods, Huber et al. [11] have proposed a coupling method based on an idea of Nitsche. In the case of profile gratings with perfectly conducting substrate, the authors have shown previously that a slightly modified variational equation can be proven to be equivalent to the boundary value problem and to be uniquely solvable. Now it is shown that this result can be used to prove convergence for the FEM coupled by truncated wave mode expansion. This result covers transmission gratings and gratings bounded by additional multi-layer systems.
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    Reflection of plane waves by rough surfaces in the sense of Born approximation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Arnold, Thomas; Rathsfeld, Andreas
    The topic of the present paper is the reflection of electromagnetic plane waves by rough surfaces, i.e., by smooth and bounded perturbations of planar faces. Moreover, the contrast between the cover material and the substrate beneath the rough surface is supposed to be low. In this case, a modification of Stearns' formula based on Born approximation and Fourier techniques is derived for a special class of surfaces. This class contains the graphs of functions if the interface function is a radially modulated almost periodic function. For the Born formula to converge, a sufficient and almost necessary condition is given. A further technical condition is defined, which guarantees the existence of the corresponding far field of the Born approximation. This far field contains plane waves, far-field terms like those for bounded scatterers, and, additionally, a new type of terms. The derived formulas can be used for the fast numerical computations of far fields and for the statistics of random rough