**RPI VCSEL Model Released in SmartSpice**

RPI VCSEL model was developed by Professor Michael Shur and his team from the Rensselaer Polytechnic Institute (RPI) [1]. A release of this model has been implemented within SmartSpice, and can be accessed by setting LEVEL=4 in the diode modelcard.

**Mixed Photonic/Electronic Simulation**

The optical devices are divided in three parts: emitters (laser
diode, LEDs), detectors and interconnects. To provide a Mixed Photonic/Electronic
simulation, the photonic signals are described in terms of electrical signals
and can therefore be integrated in ** SmartSpice** simulation.

RPI Vertical Cavity Surface Emitting Laser (VCSEL) model is an emitter diode whose optical output power is mapped into an electrical signal. It can therefore be connected to an optical interconnect such as a transmission line. The device is composed of electrical and optical sub-circuits. The electrical sub-circuit is a diode and the equivalent circuit of the device is a current controlled voltage source, as shown in Figure 1.

Figure 1. Optical emitter, interconnect and
detector.

Model Description

The electric sub-circuit is based on a diode LEVEL=1 Berkeley model. The optical sub-circuit is based on the first order rate equations of semiconductor lasers, as described in [2]:

These equations, involving the carrier density N and the photon density S, describe respectively the electrical properties of a semiconductor laser, and the optical behavior when some photons are produced.

The equivalent circuit of the model is shown in Figure 2.

Figure 2. RPI VCSEL equivalent circuit

Idiode, Ileak are diode and leakage currents, Rs is the diode resistance and
Cj the junction capacitance. Il, Isp, Ig, Rp, Cp are deduced from first order
rate equations (see [1]).

This model allows to simulate optical output power versus input current curves. Due to the strong thermal effects (see Figure 3.), a self-heating sub-circuit has also been added to take into account the thermal leakage current. It leads to an output-power rollover as the input current increases. It has been implemented as an internal node with thermal resistance Rth, thermal capacitance Cth, and thermal excitation Ith.

Figure 3. RPI VCSEL P - I characteristics.

Figure 4. Optical Output of a RPI VCSEL

device coupled with a Laser Driver Circuit.

**RPI VCSEL Model and SmartSpice**

RPI VCSEL model has been implemented as a diode device. The third node is accessible through device declaration:

Dxxx n+ n- o mname ...

n+, n- are respectively anode and cathode of the diode, voltage bias at “o” node is the optical power output in mW. The device can be connected to optical interconnects, such as transmission lines to provide a Mixed Electronic/Photonic simulation.

The model card for RPI VCSEL includes the following parameters:

**Optical Equations Parameters**

Parameter |
Description |
Units |
Default |

DA | Active region depth | m | 1.0E-8 |

TN | Electron lifetime | s | 1.0E-9 |

NTR | Trap density | m-3 | 0.0 |

BETA | Spontaneous emission factor | - | 1.0 |

TPH | Photon lifetime | s | 1.0 |

GAMMA | Optical confinement factor | - | 1.0 |

EPS | Gain compression parameter | m3 | 1.0 |

G0 | Gain slope | m2 | 1.0 |

VG | Group velocity | m/s | 3.0E8 |

LAMBDA | Wavelength of optical output | m | 8.0E-6 |

REF | Mirror reflectivity | - | 0.99 |

TOSS | Characteristic temperature of carrier lifetime | K | 30 |

C0 | Leakage saturation current | A/m2 | 1.0E-12 |

FRAC | Fraction of aluminum | - | 0.0 |

T1 | Fitting parameter | s | 0.0 |

IMAX | Maximum saturation current | A | 1.0 |

CM | Saturation knee parameter | - | 1.0 |

**Diode Parameters**

Parameter |
Description |
Units |
Default |

IS | Saturation current | A/m2 | 1.0E-14 |

TNOM | Parameter measurement temperature | K | TNOM (default) |

RS | Ohmic resistance | Ohm.m^{2} |
0.0 |

N | Emission coefficient | - | 1.0 |

TT | Transit time | s | 0.0 |

CJ0 | Junction capacitance | F/m^{2} |
0.0 |

VJ | Junction potential | V | 1.0 |

M | Grading coefficient | - | 0.5 |

EG | Activation energy | eV | 1.43 |

XTI | Saturation current temperature exponent | - | 3.0 |

FC | Forward bias junction fit parameter | - | 0.5 |

BV | Reverse breakdown voltage | V | -5.0 |

IBV | Current at reverse breakdown voltage | A | 1.0E-3 |

IKF | Forward knee current | A | 0.0 |

ISR | Recombination current | A/m^{2} |
0.0 |

NR | Recombination current slope | - | 2.0 |

KF | Flicker noise coefficient | - | 0.0 |

AF | Flicker noise exponent | - | 1.0 |

Thermal Sub-Circuit

Parameter |
Description |
Units |
Default |

CTH | Thermal capacitance | J.m^{2}/degC |
0.0 |

RTH | Thermal resistance (RTH = 0.0 : no self-heating) | degC.m^{2} /W |
0.0 |

The model supports DC, AC, TRAN and PZ analysis. Bypass calculation and VZERO
options have been implemented for a faster simulation when running large circuits.
RPI VCSEL model has also been optimized to take advantage of multi-processor
machines. Additional outputs have been added in ** SmartSpice**
implementation : SN and NN outputs are photon and carrier densities in the photonic
device.

References

- J. Deng, M. S. Shur, T. A. Fjeldly, S. Baier, “CAD Tools and Optical
Device Models for Mixed Electronic/Photonic VLSI”, International Journal
of High Speed Electronics and Systems, International Journal of High Speed
Electronics and Systems, Invited, Volume 10, No 1, pp. 299-308, March 2000.

- R. S. Tucker, “ Large-Signal Circuit Model for Simulation of Injection-Laser
Modulation Dynamics”, IEE Proceedings 128 (1981) 180-184.