Reduced basis method for the electromagnetic scattering problem: a case study for FinFETs
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Optical 3D simulations in many-query and real-time contexts require new solution strategies. We study an adaptive, error controlled reduced basis method for solving parameterized time-harmonic optical scattering problems. Application fields are, among others, design and optimization problems of nano-optical devices as well as inverse problems for parameter reconstructions occurring e. g. in optical metrology. The reduced basis method presented here relies on a finite element modeling of the scattering problem with parameterization of materials, geometries and sources.
KeywordsFinite element method Reduced basis method Electromagnetic field Model reduction Optical critical dimension metrology
The results were obtained at the Berlin Joint Lab for Optical Simulations for Energy Research (BerOSE) of Helmholtz-Zentrum Berlin für Materialien und Energie, Zuse Institute Berlin and Freie Universität Berlin. This research was carried out in the framework of Matheon supported by Einstein Foundation Berlin through ECMath within subprojects SE6 and OT5.
- Barrault, M., Maday, Y., Nguyen, N.C., Patera, A.T.: An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. 339, 667–672 (2004)Google Scholar
- Bunday, B., Germer, T.A., Vartanian, V., Cordes, A., Cepler, A., Settens, C.: Gaps analysis for CD metrology beyond the 22nm node. In: Proceedings of SPIE, vol. 8681 (2013)Google Scholar
- Burger, S., Zschiedrich, L., Pomplun, J., Herrmann, S., Schmidt, F.: Hp-finite element method for simulating light scattering from complex 3D structures. In: Proceedings of SPIE, vol. 9424 (2015)Google Scholar
- Palik, E.D.: Handbook of Optical Constants of Solids. Bd. 3. Academic Press, Cambridge (1998)Google Scholar
- Pomplun, J.: Reduced Basis Method for Electromagnetic Scattering Problems. Ph.D. thesis, Free University Berlin (2010)Google Scholar
- Pomplun, J., Schmidt, F.: Accelerated a posteriori error estimation for the reduced basis method with application to 3D electromagnetic scattering problems. SIAM J. Sci. Comput. 32, 498–520 (2010)Google Scholar
- Pomplun, J., Burger, S., Zschiedrich, L., Schmidt, F.: Reduced basis method for real-time inverse scatterometry. In: Proceedings of SPIE, vol. 8083 (2011)Google Scholar
- Prudhomme, C., Rovas, D.V., Veroy, K., Machiels, L., Maday, Y., Patera, A.T., Turinici, G.: Reliable real-time solution of parametrized partial differential equations: reduced-basis output bound methods. J. Fluids Eng. 124, 70–80 (2002)Google Scholar
- Rozza, G., Huynh, D.B.P., Patera, A.T.: Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Methods Eng. 15, 229–275 (2008)Google Scholar
- Zschiedrich, L.: Transparent Boundary Conditions for Maxwells Equations: Numerical Concepts Beyond the PML Method. Ph.D. thesis, FU Berlin (2009)Google Scholar