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Preconditioning Dense Complex Linear Systems from a VIM Discretization: Discretizing Maxwell's equations using the volume integr,Used
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Angularresolved optical scatterometry is a new promising technology for metrology in lithography for the construction of VLSI chips such as DRAMs and CPUs. In order to measure the geometry dimensions and material properties of markers and interconnect lines, one needs to solve Maxwell's equations for an electromagnetic scattering problem. The well known RCWA discretization method is too slow for 3D applications whence one takes resort to either a finite element discretization method or a volume integral method (VIM). VIM systems of equations can be solved faster than FEM systems of equations. This book focuses on an iterative solution of linear systems emanating from VIM. Each different linear system depends in a nonlinear manner on several geometry, material and incoming lightwave parameters. For a typical 2Dperiodic application on resist, VIM is a factor of 20 faster than RCWA. The VIM discretization leads to a dense complex linear system for the electric field for a 2Dperiodic grating (3D Maxwell's equations). The coefficient matrix A is almost full but matrixvector multiplications can be performed. Therefore; systems should be solved with an iterative solution method.
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