Download - Toward an Electrically-Pumped Silicon Laser Modeling and Optimization_Thesis_Presentation
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Toward an Electrically-Pumped Toward an Electrically-Pumped Silicon Laser: Optimization and Silicon Laser: Optimization and
ModelingModeling
Daniel B. RileyM.S. Defense
Department of Electrical and Computer EngineeringUniversity of Rochester
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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
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Outline Motivation MURI Silicon Laser Project Theoretical Background Simulation and Results Summary and Conclusions
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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
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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.
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Benefit of Photonic Systems
L. Pavesi and D.J. Lockwood. “Silicon Photonics” in Topics in Applied Physics”. 94. 1 – 90.
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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/
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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.
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Outline Motivation MURI Silicon Laser Project Theoretical Background Simulation and Results Summary and Conclusions
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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 ncEr 3+
SiO2:Er (low index)
nc-Si (high index)
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Electrical Injection – Dipole Energy Coupling
1 Walters, R., Bourianoff, G., Atwater, H., Nature 04. 143, Feb. 2005.
Energy TransferSi-nc
Er3+
Exciton Recombination
Resonant Absorption
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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
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Outline Motivation MURI Silicon Laser Project Theoretical Background Simulation and Results Conclusions and Future Outlook
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Theory – Important Concepts
t
BE
JDH
t
0 B
0 D
02
tEE
2
Maxwell’s Equations
Wave Equation
Vector Algebra1
v
000
n
HB
ED
Stokes’ TheoremDivergence Theorem
0)(ˆ0)(ˆ
0)(ˆ0)(ˆ
12
12
12
12
DDBBHHEE
ssss
Boundary conditions at a dielectric interface
Continuous components “D-B normal, E-H tangential”
D1 D2
B1 B2
E1 E2
H1 H2
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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
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Slot Confined Waveguide Recall boundary conditions at
a dielectric interface D1,normal = D2,normal
D1 = n12
E1
D2 = n22
E2
n2 > n1
E1 > E2 by factor of n22/ n1
2
n1n2
n1
n2
n1
Libson, M, et.al. “Guiding Light in Void nanostructure”. Optics Letters. 29. 1209, Jun 2004.
x
z
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Transverse E-field of fundamental TM mode
Libson, M. “Guiding Light in Void nanostructure”. Optics Express. 12. 2004.
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Outline Motivation – Photonics Overview MURI Silicon Laser Project Theoretical Background Simulation and Results Summary, Conclusions and Future Outlook
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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 ncEr 3+
SiO2 (low index)
nc-Si (high index)
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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
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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
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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
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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
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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
Con
finem
ent F
acto
r (%
)
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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
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Power Distribution of Mode in z Direction
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Power Distribution of Mode
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Power Distribution Cross Section (x=0)
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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)
EffectiveRatio
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
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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 2.40.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
Thickness ratio between SiO2 and Si layer
Con
finem
ent f
acto
r
TMM and FDTD result for multilayer thickness of 0.38 m
TE mode confinementTM mode confinementFDTD data points for TMFDTD 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 SiO2 layer
Con
finem
ent f
acto
r
TMM result for multilayer thickness of 0.52 m
TE mode confinementTM mode confinement
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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
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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
1.4Modal gain for TE and TM polarization by TMM
gain/loss coefficient ratio
mod
e lo
ss/g
ain
(1/c
m)
TE mode gainTM mode gain
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Outline Motivation - Photonics Overview MURI Silicon Laser Project Theoretical Background Simulation and Results Summary and Conclusions
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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
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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
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Thank you for ListeningThank you for Listening
Please ask questions if you have them.