1. Applications of the 3D electromagnetic model to some challenging optical problems September 24, 2004 Xiuhong wei, Paul Urbach, Arther Wachters Supported by the Dutch Ministry of Economic Affairs under project TS01044

2. 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

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

4. 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.

5. Variational formulation –E=E 0 +E s

6. Calculate E 0 in Multilayer –S-polarization, i –P-polarization, j – is the source term –Tangential field h(z), e(z) in basis (i,l) k iziz i j l

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

9. Numerical calculation –Construction of Matrix –Matrix property Complex symmetric indefinite

10. 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 = 10 7 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 )

11. 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 E 0 –

12. Stratton-Chu formula Observation point

13. Results: Near Field Optical Recording Background Geometry Cross section In the SIL: k x  n SIL k x Hence, Saptially frequences of the spot are increased, which means the spot became smaller /2 n SIL

14. = 405nm NA effective = 1.9 Spotsize /2NA eff =106nm Grooves(track) Track pitch=226nm Top view

15. Energy density, wall angle 55, E // groove Energy density, wall angle 55, E  groove

16. Top view Energy density, wall angle 85, E //groove Energy density, wall angle 85, E  groove

17. Cross section xz-plane Energy density, wall angle 55, E//groove Energy density, wall angle 55, E  groove

18. Cross section yz-plane Energy density, wall angle 55, E // groove Energy density, wall angle 55, E  groove

19. –Lithography Background Geometry Incoherent Light source Condenser Mask Aperture stop Photoresist wafer Projection lens

20. Material: Crome = 193nm High NA lithography n Cr =0.86 + 1.65 I Perpendicular incident planewave 100nm 720nm 260nm 340nm

21. Top view Serif mask, E  Square mask, E 

22. Square mask, E  Top view

23. Square mask, finite conduct, E  Square mask, Perfect conduct, E  Top view

24. Cross section yz-plane Square mask, finite conduct, E  Square mask, Perfect conduct, E 

25. Far field Square mask, E  Square mask, E 

26. acknowledge Our cluster in Philips, Paul Urbach, Arthur wachters, Jan Veerman Delft mathematical department, Kees Vuik, Kees Oosterlee, Yogi Erlangga, Mari Berglund Shell staffs, Ren´e-Edouard Plessix, Wim Mulder