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

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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

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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.