Academic Open Internet Journal ISSN 1311-4360 |
Volume 17, 2006 |
Simple behavioral PSPICE model of the vertical
cavity GaAs/GaAlAs laser
A.Wolczko PhD
Institute of Electronics
University of Science & Technology
Al.Mickiewicza 30
30-059 Krakow Poland
awolczko@uci.agh.edu.pl
Abstract: A nonlinear model of the VCSEL laser for PSPICE simulator of the electronic
circuits has a form of subcircuit .SUBCKT
VCSEL into input circuit file *.cir and is intended for electronic circuit design. All electrical signals and signal of optical
power (represented by an equivalent voltage) are analyzed. The behavioral
description of many electronic components is a commonly used method in SPICE
and this way of modeling has been chosen. The complete subcircuit file for
0.85mm Lasermate VCSEL, some examples of simulations, verification measurements
and final comments are contained in the paper.
Keywords : VCSEL, SPICE,
behavioral modeling
1. Introduction
The model of VCSEL would be easy to application for
electronic circuit designers who as a final users of lasers and other electronic components may not be familiar with
intrications of laser physics. Simulation in the circuit design process would
allow to analyze the mutual influences of the characteristics of the laser on
the values and shapes of circuit signals and the properties of the electrical
circuit on the output optical signal.
It is assumed that:
·
the model would be compatible with popular versions of SPICE installed
in PC computers
·
the model will be defined as library file in SPICE as a subcircuit and
in the main input file *.cir describing electronic circuit structure and types
of analyses this library will be invoked
·
commercially available VCSEL TFC-M85A4X5 from Lasermate Group [1] as a
basic model component is taken
·
the model would be applicable for other types of GaAs/GaAlAs VCSELs by
changing some easy to measure
parameters without change of the file structure.
The commonly used method of modeling of the different components
in SPICE is behavioral description of the object by determining voltage,
current, time and temperature relations at the external electrical nodes of the
modeled component. This method of modeling VCSEL is proposed.
2. Equivalent schematic
diagram.
Presented in figure 1 equivalent schematic diagram contains three
modules. First passive single port (AN,KA) represents laser diode as a load for
electronic driver. The second module driven by current I_{RS} with
nodes OOU,GNO models output optical signal. The third one driven by I_{RS}
and U_{D1} allows (during transient analysis) estimation of average
dissipated power in laser [2].
Fig.1. Equivalent schematic
diagram of the model
From electrical point of view laser diode D1 is a singe-port component (AN,KA) with parasitic RS, L1, CL of the case. This nonlinear single-port is a one part of the bigger electrical circuit (driver) and all voltages and current in that circuit are determined by: voltage/current characteristic of the laser diode and the rest components of the circuit. In SPICE a semiconductor diode is modeled by nonlinear equation. Measurements of characteristics (static and dynamic) makes possible to find most of needed parameters. On the base of references [3] and own measurements the set of parameters for V/I characteristic of modeled diode has been matched – part of figure 2 shows the result.
Fig.2 . Simulation 1-optical power 2-AN-KA voltage
The signal of the optical power is represented in the model by a
current source G_OPT at the nodes OOU-GNO (fig.1). Static characteristic P_{l}(I) is above threshold approximated by the 3-th order
polynomial which allows well match polynomial curve to typical S shape
nonlinearity of the laser ( the
rising part ,most important in practical applications, of the emission
characteristic 0¸P_{l}_{max} is modeled ) – see figure 2. The thermal changes of polynomial
coefficients were found experimentally. The threshold current I_{pr}(T)
is determined by equation [4]:
_{}
_{} |
(1) |
I_{Th} – minimal
threshold current vs. temperature
The current source G_OPT is
approximated by formula :
_{} |
(2) |
K – scaling factor
In the typical applications VCSEL lasers are pulse driven so that
pulse tests were done using ECL driver of VCSEL presented in paper [5].
Two dynamic effects influencing on dynamics of optical power are
simulated in the model [6].
Self resonance may be approximated by low pass second order
filter with two complex conjugate poles. Suitable Laplace formula has been
placed in circuit file.
In the case subtreshold driving (I_{min}<I_{pr})
some delay of leading edge of optical signal vs. current edge occurs. The delay
lasts until the threshold concentration of carriers in the laser cavity is
achieved. It is difficult to simulate such delay in electrical circuit. Two
switched capacitors CE,CE1 in the model only briefly approximate the mentioned
effect.
Power dissipated in the laser
junction causes the rise of temperature above ambient of the diode structure
because the thermal resistance junction/case is high. Parameter dT (7°C default for M85A4X5) is introduced to the model for calculations of
temperature dependent values. Parameter dT may be estimated by calculation of
average dissipated power multiplied by thermal resistance. Sometimes
complicated shapes of voltage and current pulses can make difficult that
estimation of power. The simple procedure in SPICE is helpful to obtain dT
during TRANSIENT analysis. The final voltage at node TOU represents average dT
and actualization of analysis is possible.
3. Subcircuit file.
The presented subcircuit
model shown below.
.SUBCKT VCSEL AN KA OOU GNO TOU
*
AN - VCSEL's anode
*
KA - VCSEL's kathode
*GNO - gnd for sources OOU,TOU
*
OOU - voltage source - represents optical power
*TOU - voltage source - represents temperature growth dT of selfheating
R_G KA 0 1E6
RS
21 20 1
D1
20 KA LVCSEL
CL
21 KA .5P
L1
AN 21 1N
.MODEL LVCSEL D Is=10E-13
EG=1.46 N=2.8 XTI=27 RS=26
TRS1=-1.25E-3
***** IMPORTANT PARAMETERS ENTERED TO THE MODEL BY USER
****
.PARAM T0=25 ITH=4.63E-3 K=390U
* K - scaling factor of
the optical power
*ITH - minimal threshold current of the laser [mA]
*
at temperature TO [oC]
* dT - default 7 [oC]
- see below
***** OPTICAL TURN-ON
DELAY OF THE LASER ****
.PARAM Z=1
*for Z=0 the calculation
of optical turn-on delay is INACTIVE
!!!
G_M GNO 41 21 20 1
RS1
41 40 26 TC1=-1.25E-3
RS2 40 46
1 TC1=-1.25E-3
D11 46 GNO LVCSEL1
.MODEL LVCSEL1 D Is=4E-12 EG=1.46 N=2.8
XTI=27 RS=0
CE GNO 45 5P
S1 45 40 30 GNO SWI
E_KL1 30 GNO VALUE={Z}
.MODEL SWI VSWITCH ROFF=1E4 RON=1
VOFF=0 VON=1
CE1 GNO 47 5P
S2 40 47 31 GNO SWI
E_KL2 31 GNO
VALUE={IF(V(21,20)<(IPR-.5E-3),Z,0)}
* EFFECT OF THE LASER SELF-RESONANCE
.PARAM F=30G D=.2
ELAP LA GNO LAPLACE
{V(40,46)}={1/(1+2*D*S/F+S**2/F**2)}
RLAP LA GNO 1E6
*
EMISSION FUNCTION Popt/I
.PARAM IPR={ITH*(1+1.1E-4*(TEMP-T0+dT)**2)}
.PARAM
A1={98.572-5.14E-2*(TEMP-27+dT)}
+A2={6.8351E3-85.92*(TEMP-27+dT)}
+A3={-6.5015E5+5214.3*(TEMP-27+dT)}
G_OPT GNO OOU VALUE={IF(V(LA,GNO)<IPR,
+0,K*(A1*(V(LA,GNO)-IPR)+A2*((V(LA,GNO)-IPR)**2)+A3*((V(LA,GNO)-IPR)**3)))}
R_OPT OOU 0 1K
* TEMPEREATURE GROWTH OF SELFHEATING dT
G_T GNO TOU VALUE={ABS(V(21,20)*V(20,KA))*RT}
R_T TOU GNO 1E6
C_T TOU GNO 50N
.PARAM dT=7 RT=900
* RT - thermal resistance
junction/case [oC/W]
*
C_T - averaging capacitor C_T[nF]=1*t[ns]
*
t - final time value for transient analysis
*
.IC V(TOU,GNO)=0 - initial condition for proper calculation of
dT using transient analysis
.ENDS
4. Illustrative simulations
and measurement verification.
In the next figures some examples of dynamic pulse simulations
and oscillograms are presented. The signal of the driver (upper curves) has
been approximated in simulations by frequently applied in SPICE PWL (piece wise
linear) manner and additionally sharp folds of the PWL were smoothed in
simulations by 3-th order Thomson filter . The optical responses are shown in
lower curves.
Fig.3. Oscillogram – near threshold driving
Fig.4. Simulation – near threshold driving
Fig.5. Oscillogram-square wave
Fig.6. Simulation-square wave
5. Conclusions.
Semiconductor lasers similarly as the other semiconductor components
have wide spread of their important parameters from piece to piece. The exact
modeling of such components needs of measuring of the substantial components
and entering actual parameters to circuit file. From measurements and
simulations was found that in the case of VCSEL there are two most important
parameters:
· threshold current I_{Th}
· average slope of static characteristic
(above threshold) K=dP/dI.
In all measurements presented in the article laser
receptacle was optically coupled to photodiode via graded index fiber 62.5/125 mm and for such connection K was
determined. Moreover determination of the temperature of minimal threshold
current, however troublesome, has important influence on the precision of modeling
and is recommended. Reader would notice that important equation (1) is valid
only for certain class of VCSELs but the structure of the model allows to
change the thermal dependence of the treshold current via modifications of one
line:
.PARAM IPR={ITH*(1+1.1E-4*(TEMP-T0+dT)**2)} for other lasers.
All important parameters are placed in the separated text lines .PARAM of the subcircuit file so that any modifications are easy to make.
References
[1] Specifications of TFC-M85A4X5
Lasermate, www.lasermate.com
[2] M.S.Shur
PPI VCSEL Model Released in Smart Spice
Journal for Circ.Simul. and SPICE Modeling Engineers Vol.13 No.4 Apr. 2003
[3] J.Guenter, J.Tatum,K.Johnson
Honeywell Optoelectronic Application, www.advancedopticalcomponents.com
Modulation Advanced Optical Components-Oxide VCSELs
[4] VCSEL SPICE model
Honeywell Optoelectronic Application, www.advancedopticalcomponents.com
[5] A.Wolczko
Circuit makes universal VCSEL
driver EDN July 10/2003 p.78¸80
[6] J.Tatum, D.Smith, J.Guenter, R.Johnson
High Speed Characteristics of VCSELs
Honeywell Optoelectronic Application, www.advancedopticalcomponents.com
Technical College - Bourgas,
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© March, 2000