Preconditioning Dense Complex Linear Systems from a VIM Discretization: Discretizing Maxwell's equations using the volume integral method (VIM) - Couverture souple

Belachew, Melisew Tefera

 
9783846510124: Preconditioning Dense Complex Linear Systems from a VIM Discretization: Discretizing Maxwell's equations using the volume integral method (VIM)
Couverture souple
ISBN 10 : 3846510122 ISBN 13 : 9783846510124
Editeur : LAP LAMBERT Academic Publishing, 2011

Synopsis

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 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 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 for the electric field for a 2D-periodic grating (3D Maxwell's equations). The coefficient matrix A is almost full but matrix-vector multiplications can be performed. Therefore; systems should be solved with an iterative solution method.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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 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 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 for the electric field for a 2D-periodic grating (3D Maxwell's equations). The coefficient matrix A is almost full but matrix-vector multiplications can be performed. Therefore; systems should be solved with an iterative solution method.

Biographie de l'auteur

He is a lecturer at Haramaya University. He received his B.Sc. degree in Mathematics with distinction from Dilla University. He studied his 1st M.Sc. degree in Mathematics at Norwegian University of Science and Technology (Norway) and his 2nd M.Sc. degree in Industrial and Applied Mathematics at Eindhoven University of Technology (The Netherlands).

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2011
Langue
anglais
ISBN 10 
3846510122
ISBN 13 
9783846510124
Reliure
Broché
Nombre de pages
104
Coordonnées du fabricant
non disponible
Personne responsable
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