This document summarizes Daniel B. Riley's M.S. defense on modeling and optimization of an electrically-pumped silicon laser. It motivates the need for integrated silicon photonics to overcome bandwidth bottlenecks in microelectronics. It describes a Multi-University Research Initiative project to develop a silicon laser using alternating layers of erbium-doped oxide and silicon nanocrystals. Electromagnetic simulations and theoretical modeling are presented to optimize the layer structure for high optical confinement factors. Gain-loss analysis using finite-difference time-domain and transfer matrix methods aims to determine threshold conditions for net optical gain. Future work is proposed to better understand polarization behavior and energy transfer processes.

1. Toward an Electrically-PumpedToward an Electrically-Pumped
Silicon Laser: Optimization andSilicon Laser: Optimization and
ModelingModeling
Daniel B. Riley
M.S. Defense
Department of Electrical and Computer Engineering
University of Rochester

2. 2
Acknowledgements
 Dr. Philippe Fauchet
 Fauchet Research Group
 Yijing Fu & Jidong Zhang
 Vicki Heberling
 MURI Silicon Laser
 Participating Institutions
 Funding Sources
 M.S. Thesis Examination Committee
 Dr. Thomas Hsiang – Electrical and Computer Engineering
 Dr. Miguel Alonso – Institute of Optics

3. 3
Outline
 Motivation
 MURI Silicon Laser Project
 Theoretical Background
 Simulation and Results
 Summary and Conclusions

4. 4
Limit of Microelectronics
 Dimensional shrink of microprocessors  Moore’s Law
 Barriers  materials, power dissipation, parasitic capacitance,
bandwidth bottleneck, lag of front side bus
 Performance limited as 10Mb/s/km threshold is approached
Available: http://www.intel.com/technology/mooreslaw

5. 5
Communication Links
 Transition from electrical links to optical links within the next
10 years – more solutions at all levels
 Chip to chip and intra chip stand to benefit most as strain on
processors increases – also most challenging
L. Pavesi and D.J. Lockwood. “Silicon Photonics” in Topics in Applied Physics”. 94. 1 – 90.

6. 6
Benefit of Photonic Systems
L. Pavesi and D.J. Lockwood. “Silicon Photonics” in Topics in Applied Physics”. 94. 1 – 90.

7. 7
Required Functionality
 Light generation, guiding, detection  no, yes, yes
 High speed (>1GHz) modulation  yes
 Low cost – high volume capability  yes
 CMOS compatibility  yes
Available: http://www.intel.com/research/platform/sp/

8. 8
Silicon: Good and Bad
 Silicon is cheap
 Easily integrated with existing
CMOS processes
 Poor light emitter
 Free carrier absorption at infrared
wavelengths (1.55μm)
L. Pavesi and D.J. Lockwood. “Silicon Photonics” in Topics in Applied Physics”. 94. 1 – 90.

9. 9
Outline
 Motivation
 MURI Silicon Laser Project
 Theoretical Background
 Simulation and Results
 Summary and Conclusions

10. 10
Project Task
 Extrinsic gain laser
 Horizontal slot waveguide structure w/ alternating nanolayers of Er-
doped oxide and nc-Si for optical cavity of Si laser system
Si nc
Er 3+
SiO2:Er (low index)
nc-Si (high index)

11. 11
Electrical Injection – Dipole Energy Coupling
1 Walters, R., Bourianoff, G., Atwater, H., Nature 04. 143, Feb. 2005.
Energy Transfer
Si-nc
Er3+
Exciton
Recombination
Resonant
Absorption

12. 12
MURI
 Optical gain engineering – minimize losses, maximize gain
in cavity by increasing optical mode confinement factor (CF)
Confinement factor
Net gain
Threshold current density for injection
Power consumption and dissipation
Device efficiency

13. 13
Outline
 Motivation
 MURI Silicon Laser Project
 Theoretical Background
 Simulation and Results
 Conclusions and Future Outlook

14. 14
Theory – Important Concepts
t∂
∂−
=×∇
B
E
J
D
H +
∂
∂
=×∇
t
0=⋅∇ B
0=⋅∇ D
02
=
∂
∂
−∇
t
E
E
2
µε
Maxwell’s Equations
Wave Equation
Vector Algebra
µε
1
=v
000 ε
ε
εµ
µε
==n
HB µ=
ED ε=
Stokes’ Theorem
Divergence Theorem
0)(ˆ
0)(ˆ
0)(ˆ
0)(ˆ
12
12
12
12
=−⋅
=−⋅
=−×
=−×
DD
BB
HH
EE
s
s
s
s
Boundary conditions
at a dielectric interface
Continuous components 
“D-B normal, E-H tangential”
D1 D2
B1 B2
E1
E2
H1 H2

15. 15
Planar Waveguide
 Maxwell’s Equations
 Wave Equation
 Boundary conditions for EM
fields
 Snell’s Law  TIR
 Waveguides
– n2 > n1 and n2 > n3
– Evanescent decay
n1
n2
n3

16. 16
Slot Confined Waveguide
 Recall boundary conditions at
a dielectric interface
 D1,normal = D2,normal
 D1 = n1
2
E1
 D2 = n2
2
E2
 n2 > n1
 E1 > E2 by factor of n2
2
/ n1
2
n1
n2
n1
n2
n1
Libson, M, et.al. “Guiding Light in Void nanostructure”. Optics Letters. 29. 1209, Jun 2004.
x
z

17. 17
Transverse E-field of fundamental TM mode
Libson, M. “Guiding Light in Void nanostructure”. Optics Express. 12. 2004.

18. 18
Outline
 Motivation – Photonics Overview
 MURI Silicon Laser Project
 Theoretical Background
 Simulation and Results
 Summary, Conclusions and Future Outlook

19. 19
Device Structure
 Single layer gain medium
 Si nc and Er grouped
together in one layer
 Alternating layers of nc-Si and Er
 Higher mode confinement
 Easier electrical injection into Si nc
 Controls dipole interaction length
between Si nc and Er during energy
transfer
n type device layer
p type device layer
SiO2 BOX
~3nm
~2nm
Si nc
Er 3+
SiO2 (low index)
nc-Si (high index)

20. 20
Device Geometry
Cap Layer (SiO2)
Substrate
(SiO2)
T_SiO2
T_Si
T_C
Multilayer Region
50nm
1μm
y
x
z
nc-Si
SiO2:Er
SiO2:Er
nc-Si
Slab Height
~370 – 400nm

21. 21
Tools and Methods
 3D device analysis is difficult
 RSoft Photonics CAD – numerical simulation
 FullWave – based on FDTD
 Matlab – data analysis
 Clarification of RSoft axis conventions - see previous page
 Transverse field oriented along x axis
 TM modes are of primary interest
 Transfer Matrix Method (TMM)
 Algorithm by Yijing Fu
 Comparison to FDTD

22. 22
Effective Index Method
 Think of multilayer region as single layer with effective index neff
 Effective index depends on both the thickness and index of each layer
 Effective index  like a weighted average
 Effective index method determines index of refraction “seen” by
propagating mode
neff

23. 23
CF vs. Ratio for 2D Slot Waveguide
 Based on equations for 2D slot structure
 Ratio of thickness between SiO2:Er layers and nc-Si layers is critical
 Saturation behavior of CF
Confinement Factor vs Ratio of Slot Width to
Waveguide Width
55
56
57
58
59
60
61
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Ratio of Slot Width to Waveguide Width
ConfinementFactor(%)

24. 24
Setup & Limitations
 Computing power
 Virtual memory limitation – much longer times, crashes
 Resolutions (x,y,z) >5nm per grid point
 Limitation on values of thickness, height, width, length
 Whole number values only
 Evenly divisible by resolution value for that dimension
 Restriction on possible devices for simulation
 Only a few structures chosen
 Scripting not possible
 Structures chosen based on above limitations, cutoff values
for single mode operation, and 2D model for optimum
thickness ratios

25. 25
Power Distribution of Mode in z Direction

26. 26
Power Distribution of Mode

27. 27
Power Distribution Cross Section (x=0)

28. 28
Table of Structures & Results
 Effective ratio accounts for extra layer of Si
 Range of optimum ratios covered
 Total height < 400nm for single mode operation
N Ratio
(SiO2:Si)
Effective
Ratio
T_Si
(nm)
T_SiO2
(nm)
Total Height
(nm)
CF (%)
6 2.00 1.71 20 40 380 42.57
7 1.50 1.31 20 30 370 48.56
7 1.75 1.53 20 35 405 52.03
8 0.80 0.71 25 20 385 61.56
8 1.25 1.11 20 25 380 58.46
9 1.00 0.90 20 20 380 60.41

29. 29
FDTD and TMM Results
 Graphs of CF versus effective thickness ratio betw. SiO2:Er and nc-Si
 Left: FDTD and TMM simulation results for both TM and TE modes
 Right: TMM results for both TM and TE modes
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
Thickness ratio between SiO
2
and Si layer
Confinementfactor
TMM and FDTD result for multilayer thickness of 0.38 µm
TE mode confinement
TM mode confinement
FDTD data points for TM
FDTD data points for TE
0.5 1 1.5 2 2.5
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Thickness ratio between Si and SiO
2
layer
Confinementfactor
TMM result for multilayer thickness of 0.52 µm
TE mode confinement
TM mode confinement

30. 30
Gain/Loss Analysis to Model Actual Device
 TM modes  lower loss than TE
 More of mode w/in gain layers
 Less in lossy Si
 Gain/loss coefficient ratio
 Lower limit such that net gain is achieved
 Choose 3 optimum structures from previous graphs
 Redo simulations with loss and gain mechanisms
 Vary gain/loss coefficient ratio
 Loss coefficient set – gain coefficient increased until net gain = 0
 Value of gain/loss coefficient when net gain = 0 is sought
 Determine value for net gain from maximum power at time
monitor with no loss or gain

31. 31
S&R – Gain/Loss Analysis: FDTD vs TMM
 Net gain vs. gain/loss coefficient ratio for both TM and TE modes
 Left: modal gain using TMM
 Right: propagation gain using FDTD
 Note agreement between the two methods
 TM net gain intercept ~ 0.25 for both as expected
 TE net gain intercept ~ 2.50 for both – not expected (should be ~1.00)
0 0.5 1 1.5 2 2.5 3
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Modal gain for TE and TM polarization by TMM
gain/loss coefficient ratio
modeloss/gain(1/cm)
TE mode gain
TM mode gain
0 0.5 1 1.5 2 2.5 3
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Gain/Loss coefficient ratio
ModalGaincoefficientA.U.
Propagation Gain from FDTD simulation
TM propagation gain
Reference
TE propagation gain
Reference

32. 32
Outline
 Motivation - Photonics Overview
 MURI Silicon Laser Project
 Theoretical Background
 Simulation and Results
 Summary and Conclusions

33. 33
Summary & Conclusions
 Silicon photonics
 2D slot waveguide as a model
 3D waveguide for cavity of Si based laser
 Gain/loss analysis
 Lower threshold current densities realized for less power
consumption and more efficient devices

34. 34
Future Considerations
 Further simulation in more powerful computational
environment for improved accuracy
 Propagation lengths > 10 μm – closer to actual device lengths
 Higher resolution values
 More diverse structures with varying geometrical dimensions
 Better understanding of TE mode behavior
 Explanation beside coupling effects?
 With respect to device – better understanding of Si nc  Er3+
energy transfer process

35. 35
Thank you for ListeningThank you for Listening
Please ask questions if you have them.