Domain-Decomposition-Method-for-Maxwell’s-Equations-Scattering-off-Periodic-Structures.pdfVIP

Domain Decomposition Method for Maxwell’s Equations: Scattering off Periodic Structures Achim Sch¨adle 1, Lin Zschiedrich, Sven Burger, Roland Klose 1, Frank Schmidt ZIB Berlin, Takustr. 7, D-14195 Berlin, Germany JCMwave GmbH, Haarer Str. 14a, D-85640 Putzbrunn, Germany Abstract We present a domain decomposition approach for the computation of the electro- magnetic field within periodic structures. We use a Schwarz method with transpar- ent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light prop- agation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simula- tion of next generation lithography masks on a standard personal computer. Key words: domain decomposition, conical diffraction, electro-magnetic scattering, Maxwell’s equations, Lithography, EUV, finite elements, perfectly matched layer method 1991 MSC: 65N55 1 Introduction The fabrication of semiconductor chips is essentially based on an optical pro- jection system. The pattern on a photolithography mask is transfered onto Email addresses: schaedle@zib.de, lin.zschiedrich@, sven.burger@, klose@zib.de, frank.schmidt@zib.de (Frank Schmidt). 1 Supported by the DFG Research Center Matheon ”Mathematics for key tech- nologies” in Berlin. Preprint submitted to J. Comput. Phys. 21 May 2006 k = (k , k , k ) Illuminating Plane Wave