Applications of the 3D electromagnetic model to some challenging optical problems

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Applications of the 3D electromagnetic model to
somechallenging optical problems

• September 24, 2004
• Xiuhong wei, Paul Urbach, Arther Wachters

Supported by the Dutch Ministry of Economic
Affairs under project TS01044
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• Configurations
• 2D or 3D
• Non-periodic structure (Isolated pit in
  multilayer)
• Periodic in one direction (row of pits)
• Periodic in two directions (bi-gratings)
• Periodic in three directions (3D crystals)
• Source
• Unrestricted incident field (plane wave, focused
  spot)
• Imposed current density

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• Materials
• Linear.
• In general anisotropic, (absorbing)
  dielectrics and/or conductors
• Magnetic anisotropic materials (for
  completeness)
• Materials could be inhomogeneous

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• Mathematical Model
• Given field
  incident field
• 
  imposed current
• Total field
• Maxwell equations are equivalent to Vector
  Helmholtz Equation
• Scattered field
• The scattered field satisfies the Sommerfeld
  radiation condition.

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• Variational formulation
• EE0Es

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• Calculate E0 in Multilayer
• S-polarization, i
• P-polarization, j
• is the source term
• Tangential field h(z), e(z) in basis (i,l)

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• Up and down recursion
• Amplitude for planewave
• Where are the
  tangential source term.

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• Numerical calculation
• Construction of Matrix
• Matrix property
• Complex symmetric
• indefinite

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• Iterative solver
• RCM(reversing Cuthill-Mckee) reordering
• Precondition
• ILUTP(incomplete LU threshold pivoting)
• to solve a problem with 300,000 unknows, a
  fill-in is needed of more than 600, which takes
  about 25hours on a Hewlett Packard machine (CPU
  107 FLOPS/sec)..
• Compare with MRILU(Matries reordering ILU)
• More suitable for Finite Difference Method
• Complex problems give an extra complication
• Krylov subspace method BICGSTAB (bi-conjugate
  gradient stabilized algorithm )

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• Propagation outside of computational domain
• The field of Electric Dipole in free space
• However we need the field of electric
• dipole in Multilayer
• Calculated by Fourier transformation plane wave
  expansion
• Using recursion as for calculating E0

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• Stratton-Chu formula

Observation point
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• Results Near Field Optical Recording
• Background
• Geometry

In the SIL kx ? nSIL kx kx ? nSIL kx Hence,
Saptially frequences of the spot are increased ,
which means the spot became smaller ? /2 nSIL
Cross section
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• ? 405nm
• NAeffective 1.9
• Spotsize
• ?/2NAeff106nm
• Grooves(track)
• Track pitch226nm

Top view
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Top view
Energy density, wall angle 55, E // groove
Energy density , wall angle 55, E ? groove
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Top view
Energy density, wall angle 85, E //groove
Energy density , wall angle 85, E ? groove
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Cross section xz-plane
Energy density, wall angle 55, E//groove
Energy density , wall angle 55, E ? groove
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Cross section yz-plane
Energy density, wall angle 55, E // groove
Energy density , wall angle 55, E ? groove
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• Lithography
• Background
• Geometry

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• Material Crome
• ? 193nm
• High NA lithography
• nCr0.86 1.65 I
• Perpendicular incident
• planewave

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Top view
Serif mask, E?
Square mask, E?
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Top view
Square mask, E?
Square mask, E?
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Top view
Square mask, finite conduct, E?
Square mask, Perfect conduct, E?
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Cross section yz-plane
Square mask, finite conduct, E?
Square mask, Perfect conduct, E?
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Far field
Square mask, E?
Square mask, E?
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acknowledge

• Our cluster in Philips, Paul Urbach, Arthur
  wachters, Jan Veerman
• Delft mathematical department, Kees Vuik, Kees
  Oosterlee, Yogi Erlangga, Mari Berglund
• Shell staffs, Rene-Edouard Plessix, Wim Mulder