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Melisew Tefera Belachew(TU/e)
| Speaker: |
Melisew Fefera Belachew
(TU/e)
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| Date: |
Friday August 7, 2009
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| Title: |
Preconditioning Dense
Complex Linear Systems from a VIM Discretization (Master's Thesis
presentation)
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Abstract
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Angular-resolved
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 (metrology) 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 “simple” RCWA discretization method is too slow for 3D
applications whence one takes resort to either a finite element
discretization method (FEM), or recently, a volume-integral method
(VIM). At this moment in time, for several problems of interest, VIM
systems of equations can be solved faster then FEM systems of
equations. Therefore this presentation focuses on the solution of
(multiple) linear systems emanating from VIM. Each different linear
system depends in a non-linear manner on several geometry, material and
incoming light-wave parameters.
For a typical 2D-periodic application on resist VIM is a factor of 20
faster than RCWA. The VIM discretization leads to a dense complex
linear system Ax=b for the electric field for a 2D-periodic
grating (3D Maxwell equations). The NxN matrix A is almost full but
matrix-vector multiplications can be performed in Nlog(N) time.
Therefore systems should be solved with an iterative solution method.
In this presentation I will sketch the search for a suitable iterative
method and the construction of a preconditioner for speeding-up the
iterative solution process. I examine properties of A (such as positive
definite), A’s spectral properties, A’s sensitivity to the parameters,
the construction of a preconditioner and the parameter reconstruction
algorithm.
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