Photonic Band-gap Masks to Enhance Resolution and Depth of Focus John Nistler, Koby Duckworth, Jiri Chaloupka, and Matt Brock Proc. SPIE Vol. 6517, 65171F (Mar. 19, 2007) By Marshal Miller 4/18/2007
Outline Background Simulation data Phase Shift Mask (PSM) Finite Difference Time Domain (FDTD) Photonic Crystals Simulation data Comparison of Photonic Bandgap Enhanced (PBE) masks to current PSM technology
Phase Shift Mask Alternating Aperture Phase Shift Mask (AAPSM) Uses etch into quartz of mask to produce 180o phase difference Destructive interference allows printing of sub wavelength features Features of 65nm can be printed with 193nm illumination Out of phase by 180 degrees
Finite Difference Time Domain Grid-based differential time-domain numerical method Maxwell’s differential equations converted to difference equations and discretized Simulation domain broken up into fixed size cells Equations solved in leapfrog manner
Photonic Crystals Block of transparent material with tiny holes or nanotubes arranged in a lattice pattern, abruptly changing permitivity and permeability Ex: Silicon with tiny air holes Creates confinement in one of the materials, allowing only certain energy states, separated by a forbidden region, the band-gap By adjusting the size of holes and contrast in refractive index can tune properties of photonic crystals
Negative Refraction only images close objects does not require [ Veselago, 1968 negative e, m ] opposite of ordinary lens: only images close objects does not require curved lens can exceed classical diffraction limit Slide from SPIE short course on photonic crystals
Basic Simulation Geometry Quartz/glass opening on left etched to make the phase difference between the two openings 180 degrees Undercut and non-undercut etch tested For 248nm phase trench: .2439um For 193nm phase trench: .1721um
Simulation Results: All TE AAPSM 248nm: 180nm line space pattern PBE 248nm: 80nm line space pattern PBE 248nm: 180nm line space pattern PBE 193nm 30nm line space pattern
Final Comparison Using 193nm TE illumination Photonic Band Gap enhanced reticles show capability of producing near field image with 25 nm features Existing Phase Shift Technology can only produce near field images down to 65nm Authors claim manufacturable approach for validating results is indicated, but not explained due to proprietary information about Photonic Bandgap materials Paper not specific about materials used or geometries simulated for PBE masks, only simulation results given
The End Questions?
Extra
Properties of Bulk Crystals by Bloch’s theorem band diagram (dispersion relation) (cartoon) backwards slope: negative refraction photonic band gap dw/dk 0: slow light (e.g. DFB lasers) conserved frequency w strong curvature: super-prisms, … (+ negative refraction) synthetic medium for propagation conserved wavevector k Slide from SPIE short course on photonic crystals http://ab-initio.mit.edu/photons/tutorial/