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Photonic Crystal Waveguides: Simulation and Fabrication. Antonios Giannopoulos ECE 345 December 5, 2003. Overview. Objective Theoretical Background Band Simulation and Results FDTD Simulation and Results Fabrication Process: Ideality vs. Reality Fabrication Results Conclusion.

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## Photonic Crystal Waveguides: Simulation and Fabrication

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**Photonic Crystal Waveguides:Simulation and Fabrication**Antonios Giannopoulos ECE 345 December 5, 2003**Overview**• Objective • Theoretical Background • Band Simulation and Results • FDTD Simulation and Results • Fabrication Process: Ideality vs. Reality • Fabrication Results • Conclusion**Project Objective**• Obtain electromagnetic dispersion data using plane wave expansion method and FDTD simulation • Simulate functioning waveguide using FDTD simulation • Design Fabrication Process • Fabricate**What is a Photonic Crystal?**Electrons in atomic crystals Shrödinger equation Photons in photonic crystal Maxwell’s equations V(r)=V(r+R) (r)=(r+R) -Periodic boundary conditions result in Bloch states. -In atomic crystal this is realized by an electronic band structure -Similar thing happens in photonic crystals**What is a Photonic Crystal?**• Certain structure have photonic band-gaps! • Can use them to your advantage *Stephen G. Johnson, MIT**How Do You Solve for the Bands?**••••Plane Wave expansion method•••• Start with Fourier expansion and Substitute….. ….substitute more Get linear eigenvalue problem**How Do You Solve for the Bands?**FDTD Simulation FDTD = Finite Difference Time domain Basically discretize time and space and solve Maxwell’s Equations with ’s instead of derivatives**FDTD Band simulation**a r Measure the output Scanning the wavelength of injected light gives transmittance and thus location of photonic band Inject Light Red = air, White = GaAs (n ≈ 3.5)**FDTD Band simulation**In plane electric field band gap at 1.55m for a =.558 m z x Ex (m)**So What? How is This Useful?**• Band gap only applies for infinite crystal • Can introduce defects in crystal to • Defects can be engineered to sustain guided or resonant modes WAVEGUIDES!!**Waveguide simulation**Inject light and see what happens Simple check for guidance: Does light come out of the side? If yes then no guidance If light seems to be guided, check to make sure it is. Light**Waveguide simulation**Looks like guidance but is very lossy. There is a simple solution.**Waveguide simulation**dX*sqrt(3)*a Vary width of defect to maximize transmittance**Waveguide simulation**dX=.2 gives 96% transmittance over 8 m**Waveguide simulation**Also need to check for loss due to non-optimal slab thickness Let slab thickness = d*a. Then scan d. ….Know good design, time to make devices….**Fabrication Process**STARTING PIECE 400nm 1000nm ~3mm**Fabrication Process**DEFINE SLAB SiO2 deposition using PlasmaLab PECVD Ti deposition using Cooke evaporator SiO2 etch using PlasmaLab Freon RIE**Fabrication Process**PATTERING Use FEI Focused Ion Beam (FIB) Uses focused beam of Gallium ions to sputter atoms off the surface Process very sensitive to changes in beam conditions**Fabrication Process**HOLE DEFINITION Use PlasmaTherm Inductively Coupled Plasma (ICP) RIE to etch holes Etch time ~ 8.5 min**Fabrication Process**UNDERCUT Use 10:1 NH4F:HF buffered oxide etch to remove SiO2 and undercut AlAs. Etch time ~ 2 min DONE!!!**Problems With Fabrication Process**• FIB beam condition are inconsistent. This leads to problems in resolution and hole shape. Also, doesn’t make true cylinders. • FIB doesn’t turn off between holes the area between holes ends up getting etched in ICP • ICP will make slightly sloped sidewalls, especially if etch mask doesn’t have a uniform thickness For Example…….**Reality with the FIB**Sloped sidewalls**Reality with the ICP**ICP etches thin oxide left next to holes by FIB. This results in the GaAs underneath to be etched for part of the process.**Result of Reality**-Holes are no longer cylindrical. -Wider at the top than at the bottom.**Real Fabrication**Pattern for FIB 14.5 Periods Horizontally, 20 Periods Vertically**Real Fabrication**Designed for 420nm diameter holes FIB stigmation problem results in elliptical holes Beam doesn’t turn off**Fabrication Failure**Holes made too large cause the structure to fall apart after undercut. Puts upper limit on hole size and thus band gap size**Another Fabrication Failure**Tried to directly FIB the GaAs surface. But… sputtered atoms have to go somewhere, i.e. back into the holes**Another Fabrication Problem**Smaller holes give more sloped sidewall**More Real Fabrication**Tilted so that interior of holes is visible. Notice sloped sidewalls and non-uniform edge**More Real Fabrication**FIB stigmation adjusted. Holes ended up close to being circle. (Tilted view)**More Real Fabrication**Previous picture with normal view**Conclusion**• a=.558 m , r/a =.38, and d=.55a gives approximately 99.79% transmission over 8 m • Process works but needs development. Possible implementation of electron beam lithography as opposed to FIB**Acknowledgements**• Prof. Kent Choquette for his guidance, intellectual stimulation and support • Daniel Grasso and Robin Kim for their assistance in my earlier days of processing

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