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