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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

Photonic Crystal Waveguides:Simulation and Fabrication

Antonios Giannopoulos

ECE 345

December 5, 2003

overview
Overview
  • Objective
  • Theoretical Background
  • Band Simulation and Results
  • FDTD Simulation and Results
  • Fabrication Process: Ideality vs. Reality
  • Fabrication Results
  • Conclusion
project objective
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
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 crystal1
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
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 bands1
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
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 simulation1
FDTD Band simulation

In plane electric field band gap at 1.55m for a =.558 m

z

x

Ex

(m)

so what how is this useful
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
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 simulation1
Waveguide simulation

Looks like guidance but is very lossy.

There is a simple solution.

waveguide simulation2
Waveguide simulation

dX*sqrt(3)*a

Vary width of defect to maximize transmittance

waveguide simulation3
Waveguide simulation

dX=.2 gives 96% transmittance over 8 m

waveguide simulation6
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
Fabrication Process

STARTING PIECE

400nm

1000nm

~3mm

fabrication process1
Fabrication Process

DEFINE SLAB

SiO2 deposition using PlasmaLab PECVD

Ti deposition using Cooke evaporator

SiO2 etch using PlasmaLab Freon RIE

fabrication process2
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 process3
Fabrication Process

HOLE DEFINITION

Use PlasmaTherm Inductively Coupled Plasma (ICP) RIE to etch holes

Etch time ~ 8.5 min

fabrication process4
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
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
Reality with the FIB

Sloped sidewalls

reality with the icp
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
Result of Reality

-Holes are no longer cylindrical.

-Wider at the top than at the bottom.

real fabrication
Real Fabrication

Pattern for FIB

14.5 Periods Horizontally, 20 Periods Vertically

real fabrication3
Real Fabrication

Designed for 420nm diameter holes

FIB stigmation problem results in elliptical holes

Beam doesn’t turn off

fabrication failure
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
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
Another Fabrication Problem

Smaller holes give more sloped sidewall

more real fabrication
More Real Fabrication

Tilted so that interior of holes is visible.

Notice sloped sidewalls and non-uniform edge

more real fabrication1
More Real Fabrication

FIB stigmation adjusted. Holes ended up close to being circle.

(Tilted view)

more real fabrication2
More Real Fabrication

Previous picture with normal view

conclusion
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
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