VCSEL simulation model Parameters extraction and …grouper.ieee.org/groups/802/3/OMEGA/public/nov_2019/...VCSEL simulation model Parameters extraction and veriﬁcation IEEE 802.3

IEEE 802.3 OMEGA Study Group - November 2019 Plenary

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Knowledge Development

Rubén Pé[email protected]

VCSEL simulation modelParameters extraction and verification

mailto:[email protected]


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VCSEL simple modeling

2

978-1-5090-0493-5/16/$31.00 c�2016 IEEE

A Compact Electro-optical VCSEL Model forHigh-Speed IC Design

Guido Belfiore, Mahdi Khafaji, Ronny Henker, Frank Ellinger , Senior Member, IEEEChair for Circuit Design and Network Theory

Technische Universitat DresdenHelmholtzstrasse 18, 01069 Dresden, Germany

E-mail: [email protected]

Abstract—This paper presents an accurate yet compact modelfor vertical cavity surface emitting lasers (VCSEL), which canbe extracted from simple DC and small-signal electro-opticalmeasurements. Since VCSELs are the bottleneck of high-speedelectro-optical transceivers, the model is essential in the designof high-speed laser drivers. VCSEL rate equations are used todescribe the electrical to optical conversion in the laser, whilenon-linear parasitcs are modelling the VCSEL interface. Themodel is applied to a commercially available VCSEL and thereis an excellent agreement between the simulated and measuredeye diagrams at different data rates and bias currents.

I. INTRODUCTION

An in-depth knowledge of the interface between the opticaland electrical components and an accurate prediction of aVCSEL behaviour is necessary to advance the state-of-the-artshort-range optical communications [1]. While the VCSEL’sphysics is thoroughly studied [2], it is difficult to find a modelwhich fits the small- and large-signal behaviour of the laserand at the same time, can simply be included in a circuitsimulator. Earlier efforts are either based on a linear electricalinterface [3], or require extensive optical measurements andextraction of laser’s rate equation parameters for each operat-ing point [4]. The aim of this paper is to provide a non-linearmodel requiring very limited amount of optical measurementswhich can be completely described by Verilog-A code. Animportant benefit of this compact model compared to otherworks is its accuracy in predicting the VCSEL responseat both high and low currents for different data rates. Thepresented model shows an excellent agreement with the small-and the large-signal VCSEL measurements. Utilizing such amodel would enable designing an equalization circuit or amulti-level driver to be tailored for a specific laser. As anexample, optimizing the bandwidth extension of the driverwith a VCSEL model can result in an optical data rate that isthree times higher than the VCSEL bandwidth [5].

II. VCSEL EQUIVALENT CIRCUIT

Fig. 1 shows the block diagram of the proposed VCSELmodel. The model is composed of two sections: the electronicinterface and the intrinsic laser behaviour. On one hand themodel represents the electronic parasitics given by the laserdiode. On the other hand the large-signal single mode rateequations describe the electro-optical conversion of the current

through the VCSEL active area to light. To validate the modeland compare it against a real device, a commercially available20 GHz, 850 nm VCSEL is utilized [6]. The VCSEL chipis contacted using a wafer prober and a cleaved multimodeoptical fibre. All the measurements are carried out in a fixedambient temperature and therefore the validation is done atone temprature. However, adding the temprature effect on thelaser model would not be cumbersome [4].

Cp

Ca(I)

Rm

Ra(I)

Electronic interface

Vj

D

A

C

out

S(t) = photon densityN(t) = carrier density

VCSEL rate equation:

I(t)

Lp

Fig. 1. VCSEL equivalent circuit. The current I(t) is the current through Ra

that is going to be converted in light. The rate equation are described in [7].N0=carrier density at transparency, �=optical confinement factor, g0=gainslope, ✏=gain saturation parameter, ⌧p=photon lifetime, ⌧n=carrier lifetime,e=electron charge, V a=volume of active region.

III. EXTRACTION OF ELECTRICAL PARASITICS

An accurate model of the electronic parasitics is necessaryfor the design of the laser driver output stage circuit. Theschematic of the electrical components describing the VCSELelectronic parasitcs is reported in Fig. 1, where Lp is theparasitic inductance of the connection between probes andVCSEL diode D, Cp is the capacitor of the VCSEL pad, Rm

is the resistance of the mirrors, Vj is the intrinsic voltage ofthe diode, and finally Ra and Ca are the active region resistorand capacitor, respectively. The resistors and capacitors valuesare extracted by fitting the circuit of Fig. 1 to the VCSELscattering parameter S11 measured at different bias currents fora range of frequencies from 0.1 to 40 GHz using a non-linearleast-squares solver. Since the values of Ra and Ca depend on

4 Submitted in Journal of Selected Topics in Quantum Electronics, Optoelectronic Device Simulation, 2003

be added to the other noise sources at the receiver level as wewill describe in V. Also, as quoted by several authors [11], thevalue of the relaxation frequency fR is proportional to thesquare root of the total photon number in the active layerirrespective of the number of excited transverse modes andthus of Spatial Hole Burning (SHB).

In order to get the optical output power response to an inputcurrent pulse we solve the semiconductor laser single-moderate equations [3],[8], as function of total photon and carriernumbers S and N given in (1) and (2). Rate equationparameters are defined on Table III.

nsp

pntN

NSS)S)(NN(GdtdS

τβ

τε +−−−= 1 (1)

nntN

NS)S)(NN(GeI

dtdN

τε −−−−= 1 (2)

Rate equations are expressed in function of the number ofcarriers N and photons S , and not of concentrations, as wasintroduced by G.P.Agrawal, [3], [8], this leads to symmetricalgain expressions needing less parameters such as theconfinement factor, the cavity volume and group index.

Our original approach here is to use exclusively systemparameters and some internal default parameters. Theseparameters are obtained essentially from the LI curve givingthe slope ηLI and the threshold current Ith and from the AMmodulation response giving the resonance frequency fR andbandpass f3dB and the oscillation damping factor ξ. The rateequations are used as behavioral semiconductor laserequations the aim is not to extract internal laser parameters butto fit as best as possible to laser data sheet and standardmeasurements.

The bi-linear dependence on carriers N minus transparencycarrier number Nt and photons S is used for the gain termGN(N − Nt)S, this corresponds to a first order expansion of theusual logarithmic carrier dependence in quantum wells. Thisapproximation is valid when considering operation abovethreshold where carrier variations are small [8], because ofcarrier clamping. The gain term is also proportional to the totalphoton number S because at our approximation SHB effectsare integrated as discussed above.

The resolution of these equations give the temporal behaviorof the optical power P(t). Thus a digital current input willresult in the corresponding digital optical power output. This isshown on Fig. 3.

0 1 2 3 4 5 6 7 8 9 10456789

10111213

0

0.20.40.60.81.01.2

Time t (10-8 s)

Inje

ctio

n C

urre

nt I

(mA

)O

ptic

al P

ower

P (

mW

)

Time t (10-8 s)0 1 2 3 4 5 6 7 8 9 10

Fig. 3. Simulation results of the optical power using COMSIS Software byresolution of the rate equations for a VCSEL with digital input injectioncurrent.

For wavelength dynamic variations, chirp, a third equationon phase is necessary. The relevant parameter is the opticalphase-amplitude Henry’s factor αH, which is rarely availablefrom manufacturers. αH can be derived from chirpmeasurements δν/δI function of modulation frequency fm.Chirp is not very relevant in datacom short distanceapplications and we will not consider it in our furtherdiscussion even though it could be very easily implemented inthe models.

B. VCSEL equivalent circuitA combination of the linear laser rate equations and the

Kirchoff's equations give an equivalent small-signal circuit ofthe VCSEL active zone shown on Fig. 4 which will be usefulfor the description of the input interface from drive electronicsto VCSEL. This circuit model gives a conversion betweenelectrical parameters and its physical counterparts, thecorresponding relations are given in (3). Electrical variablesare the injection current I and the junction voltage Vj.

p

Nr

jr

jN

n

nN

jjBj

SGC

L

CGrSG

CRTkNeC

τω

ω

ετ

==

=+==

220

02

1

11 (3)

VjCj Rj

L0

r0

p = η.i

I i

Fig. 4. VCSEL active zone equivalent electrical circuit, inputs are laserinjection current I and junction voltage Vj.

I(t)

2 VCSEL theory

Figure 2.2: Small signal electrical model of VCSEL with driving source [2]

Hpar(f) =1

1 + j f

fp

. (2.9)

This additional term is multiplied by the intrinsic transfer function of VCSEL (Hi(f)), pro-ducing the total electrical transfer function (H(f) = Hi(f) ·Hpar(f)) as [2]:

H(f) = C ·f2r

f2r � f2 + j f

2⇡�·

1

1 + j f

fp

. (2.10)

In the formula for the intrinsic modulation response in Eq. 2.8, we used an approximateexpression for fr,

fr ⇡1

2⇡

s�gg0Sb

⌧p(1 + "Sb), (2.11)

obtained by considering that ⌧p ⌧ ⌧�N and g0 ⇠ �"G [1].Using Eq. 2.11, the damping factor formula can be simplified to

� ⇡ K · f2r + �0 with K = 4⇡2

⌧p +

"

�gg0

�, (2.12)

where �0 = 1/⌧�N is the damping factor offset and K is the so-called K -factor.The bandwidth of the laser has three different limitations, each of which is defined by one of

the parameters in the denominator of Eq. 2.10 [5]. In order to reach the highest bandwidth,care must be taken in the design for both intrinsic and extrinsic limiting factors.

Eqs. 2.11 and 2.12 illustrate the intrinsic damping limitations of the laser. The resonancefrequency increases as a function of the photon density as fr /

pSb (by increasing the injection

current). On the other hand, the damping of the system increases at a faster pace since � /f2r / Sb, and will eventually limit the modulation bandwidth. If the extrinsic bandwidth limiting

factors are neglected, the highest achievable intrinsic 3dB bandwidth in a semiconductor laser(f3dB,max) is set by the K -factor and �0. By this assumption, the damping limited maximumbandwidth would be [2]:

f3dB,max = f3dB,damping ⇡ 2p2⇡

K� �0

2p2⇡

(2.13)

However, extrinsic effects from self-heating and electrical parasitics tend to reduce the maxi-mum bandwidth significantly and the damping limit is therefore seldom reached.

6

2 VCSEL theory

Figure 2.2: Small signal electrical model of VCSEL with driving source [2]

Hpar(f) =1

1 + j f

fp

. (2.9)

This additional term is multiplied by the intrinsic transfer function of VCSEL (Hi(f)), pro-ducing the total electrical transfer function (H(f) = Hi(f) ·Hpar(f)) as [2]:

H(f) = C ·f2r

f2r � f2 + j f

2⇡�·

1

1 + j f

fp

. (2.10)

In the formula for the intrinsic modulation response in Eq. 2.8, we used an approximateexpression for fr,

fr ⇡1

2⇡

s�gg0Sb

⌧p(1 + "Sb), (2.11)

obtained by considering that ⌧p ⌧ ⌧�N and g0 ⇠ �"G [1].Using Eq. 2.11, the damping factor formula can be simplified to

� ⇡ K · f2r + �0 with K = 4⇡2

⌧p +

"

�gg0

�, (2.12)

where �0 = 1/⌧�N is the damping factor offset and K is the so-called K -factor.The bandwidth of the laser has three different limitations, each of which is defined by one of

the parameters in the denominator of Eq. 2.10 [5]. In order to reach the highest bandwidth,care must be taken in the design for both intrinsic and extrinsic limiting factors.

Eqs. 2.11 and 2.12 illustrate the intrinsic damping limitations of the laser. The resonancefrequency increases as a function of the photon density as fr /

pSb (by increasing the injection

current). On the other hand, the damping of the system increases at a faster pace since � /f2r / Sb, and will eventually limit the modulation bandwidth. If the extrinsic bandwidth limiting

factors are neglected, the highest achievable intrinsic 3dB bandwidth in a semiconductor laser(f3dB,max) is set by the K -factor and �0. By this assumption, the damping limited maximumbandwidth would be [2]:

f3dB,max = f3dB,damping ⇡ 2p2⇡

K� �0

2p2⇡

(2.13)

However, extrinsic effects from self-heating and electrical parasitics tend to reduce the maxi-mum bandwidth significantly and the damping limit is therefore seldom reached.

6

Negligible in characterization setup

Extrinsic response

Intrinsic response

Small signal AC response

Carriers

Photons

Anode

Cathode

n-DBR

p-DBROxide apertures Quantum well

Substrate

PO =ηLIeSτ p


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0 0.5 1 1.5 2 2.5

(Ibias - Ith)1/2 (mA1/2)

0

2

4

6

8

10

12

14

16

Res

onan

ce fr

eq. F

r (G

Hz)

D-factor data per temperature (7.5 um)

-40 oC0 oC25 oC85 oC105 oC125 oC

VCSEL model parameters extraction

3

0 1 2 3 4 5 6 7 8 9 10Ibias (mA)

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

Vak

(V)

Vak characteristic per temperature (7.5 um)

-40 oC0 oC25 oC85 oC105 oC125 oC

0 1 2 3 4 5 6 7 8 9 10Ibias (mA)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

AOP

(mW

)

AOP characteristic per temperature (7.5 um)

-40 oC0 oC25 oC85 oC105 oC125 oC

0 50 100 150 200 250

Fr2 (GHz2)

10

20

30

40

50

60

70

80

90

Dam

ping

rate

(gam

ma)

(GH

z)

K-factor data per temperature (6.5 um)

-40 oC0 oC25 oC85 oC105 oC125 oC

0 1 2 3 4 5 6(Ibias - Ith) (mA)

4

6

8

10

12

14

16

18

Extri

nsic

pol

e Fc

(Ghz

)

Extrinsic data per temperature (7.5 um)

-40 oC0 oC25 oC85 oC105 oC125 oC

I-V

L-I

frγ

fp

τ pεnNt

GNτ nβsp

photon lifetime

normalized gain compression factor

transparency carrier number

differential gain

carrier lifetime

spontaneous emission fraction


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VCSEL simulation model

4

I (mA) Vak (V)

Vak(Ibias)

I (mA) Fp (Hz)

Fp(Ibias)

I in (mA)

taup (s)

epsn

nt

gn (s^-1)

taun (s)

betasp

dI out (mA)

Intrinsic Rate Equations

I in (mA)

Fp (Hz)I out (mA)

Extrinsic Response

I (mA)

taup (s)

epsn

nt

gn (s^-1)

taun (s)

betasp

Intrinsic Parameters

ith

dI (mA)

Ibias (mA)Po (mW)

Po(Ibias)

1I (mA)

2Ibias (mA)

1Po (mW)

2Vak (V)

3Ith (mA)

vcsel_mdl_drvrefS

Ith (mA)

I (mA)

Ibias (mA)

Driver Ref 1

<= 0

Eye Diagram NL

WS_SYMBOLRATE 26.88

Symbol Rate (GBd)

1e-9

vcsel_mdl_nl

I (mA)

Ibias (mA)

Po (mW)

Vak (V)

Ith (mA)

Model NL

vcsel_mdl_nl

vcsel_tb_eye


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GaAs 14G VCSEL, 10.625 GBd, -40ºC

5

IBIAS = 3 mA

6.5

um, s

ampl

e ID

#12

8.7

um, s

ampl

e ID

#4

IBIAS = 5 mA Transient simulation w/o noise

Transient simulation w/o noise


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GaAs 14G VCSEL, 10.625 GBd, 125ºC

6

8.7

um, s

ampl

e ID

#4

IBIAS = 4 mA

IBIAS = 3 mA

6.5

um, s

ampl

e ID

#12




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InGaAs 25G VCSEL, 26.88 GBd, -40ºC

7

IBIAS = 6 mA

7.5 um, sample ID #235116

Noiseless transient simulation

IBIAS = 5 mA




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InGaAs 25G VCSEL, 26.88 GBd, 125ºC

8

IBIAS = 5 mA



IBIAS = 4 mA




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Conclusions• VCSEL simulation model with parameters extracted from real L-I-V and AC

measurements has been presented

• VCSEL simulation model has been verified against real transient large signal measurements

• The VCSEL simulation model is trustworthy to carry out time-domain communications system simulations, to obtain receiver sensitivity and make link budget assessment

9


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Thank you

Documents

VCSEL simulation model Parameters extraction and …grouper.ieee.org/groups/802/3/OMEGA/public/nov_2019/...VCSEL simulation model Parameters extraction and veriﬁcation IEEE 802.3