ElectroOptical Modelling of VCSELBased Links

1
Electro-Optical Modelling of VCSEL-Based Links

• Thomas Christen
• Stefan Odermatt

Assistents Marc Jungo Gion Sialm
Semester Thesis from April 2th 2002 until July
5th 2002 at the Laboratory for Microwave
Electronics
2
Overview

• Introduction
• Circuit Diagrams vs HDLs
• Rate-Equations (0D)
• Modified Rate-Equations (2D)
• VCSEL-Based Links
• Conclusion

3
The Subject is...
4
The Goal is
...the implementation of an efficent time domain
model for the circuit simulator of Cadence.
5
VCSEL
(Vertical Cavity Surface Emitting Laser)

• Low threshold current
• Single mode beam
• Good coupling into fibers
• On-wafer probe testing
• lower cost and higher performance

6
Rate-Equations
spontaneous and non-radiative recombination
injected carriers
stimulated recombination






losses
spontaneous emission
stimulated emission
7
Circuit Diagrams vs HDLs
module vcsel_1D(INp,INn, OUT_N) inout INp, INn,
OUT_Pn, OUT_Popt electrical INp, INn voltage
OUT_Pn, OUT_N,OUT_Popt Analog begin V(INp,
INn) lt I(INp) R end

• No syntax rules
• Low abstraction level
• Structural behaviour
• Mathematically rigid
• Widely-used

• Knowledge of language
• High abstraction level
• Functional behaviour
• Mathematically flexible
• New technology

8
0D Transient Simulation
Carrier Density
Optical Power

• Verilog-A vs HSpice
• identically results
• Verilog-A easier

9
2D Model
Transverse Modes
Coupling into Fiber
10
2D Rate-Equations
Partial Differential Equation
Ordinary Differential Equation
d
?
d
d
?
d
11
Implementation in Verilog-A

• Bessel Function
• polynomial
• Mode Solver
• secant method
• Integration
• trapezoid rule

12
Results Transient Simulation
Optical Power
Time
13
2D Profile SHB
Photon
Carrier
Spatial Hole Burning (SHB)
14
2D Profile Different Losses
Near-Field profile
Carrier density profile

• Equal Losses
• radial symmetry
• Different Losses
• no symmetry

15
2D Profile Diffusion
Photon
Carrier

• Carrier Diffusion
• Carrier Density is smoothed

16
2D Profile Transient Simuation
17
Parasitics
18
VCSEL-Based Links
19
Pattern-Dependent Jitter
Below Threshold Bias
Above Threshold Bias
20
Signal Optimisation
Before Optimisation (initial values)
After Optimisation
21
Conclusion

• 0D VCSEL model
• 2D VCSEL model
• System Simulation