contribution to the analysis of high-speed single quantum well laser response: effect of leakage...

Contribution to the Contribution to the AAnalnalysis of ysis of High-Speed Single Quantum High-Speed Single Quantum

Well Laser ResponseWell Laser Response:: Effect of Leakage CurrentEffect of Leakage Current

Petar MatavuljPhD Thesis

Petar Matavulj – PhD Thesis

Nobel Nobel Prize inPrize in PhysicsPhysics2000.2000.

Zhores I. Alferov For developing semiconductor heterostructures used

in high-speed- and opto-electronics Laser diodes

First Nobel Prize in Optoelectronics.


Main PurposeMain Purpose

Versatile analysis of laser diode response considered

in all operating conditions including wide group of relevant physical

processes

Forming concrete model Physical model Efficient numerical tool

exact and fast user-friendly for usual electrical engineers


Analyzed device optimization for special applications

application in optical communicationso Finding extreme value of bandwidth and threshold

current

Main PurposeMain Purpose


SQWL ConsideredSQWL Considered

LQW = 8nm

LSCH = 76,150,300nm

LR = 2.5m

LL = 300m

poliam idupper contact

p-contactp-cladding

n-cladding

n+-substrat

bottom contact

activelayer

x for InIn G a As

x 1 - x

0.00.2

0.0 0.6x for A l

A l G a Asx 1 - x

intrinsic

cladding

P = 1018cm-3

N = 5x1017cm-3

0 = 980nm


WhyWhy QWL? QWL?

Lower threshold current for one order of magnitude Lower threshold current dependence of

temperature

Differential gain higher double Up to 50% higher bandwidth

Superior for applications in optical communicatons.

Better energy efficiency.

Faster laser diode.


What Kind of Analysis?What Kind of Analysis?

In three operating conditions DC response

L-I curve (current-voltage characteristic), Ith – threshold current AC response

frequency response, f-3dB – bandwidth (cut-off frequency) Transient response

real diode response change, onD – time on delay, ER – extinction ratio

Complex group of physical processes Effect of leakage current

o analyzed first time


SQWL Response ModelingSQWL Response Modeling

Forming closed system of rate equations and its solving

Development of complete procedure for solving system of equations for used physical model Approximation of exact physics up to the limit for numerical

computing

Complex and unnecessary for determined

characteristic parameter optimization.

Simple, efficient and enough exact.

Used method.


Rate EquationsRate Equations

One-level rate equationso DHL

Two equations; for electrons NQW and photons S.


Rate EquationsRate Equations

Two-level rate equationso QWL

Three equations; for 3D electrons NS, for 2D electrons NQW and for photons S.


Rate EquationsRate Equations Three-level rate equations

o QWL

Four equations; for 3D electrons NS, for quazi-2D electrons NG, for 2D electrons NQW and for photons S.

Gateway states

important for

fast processes

gateway states


MModelodeling Insideing Inside

Application in optical communications

Fast responses , energy efficiency (QWL)

Three-level rate equations

Including

effect of leakage current

carrier leakage

right layer – SCH2 layer

Extended system of rate equations - five equations(for 3D electrons in left SCH1 layer, for 3D electrons in right SCH2 layer,

For quazi-2D electrons in gateway states, for 2D electrons in QW and for photons )



Encompassed

Physical model

enough exact



Numerical toolEfficient (fast) and user-friendly for usual electrical engineers.

SPICE (the best choice)

Integration optoelectronic with classical electronic components.

Construction of equivalent electric circuitfrom defined system of rate equations

Solving stability and convergence problems in

formed SPICE program



Built

Numerical tool

reliable and suitable for interactive work


Result OverviewResult Overview

Response analysis Two-level rate equations

o Nagarajan (1991.) – frequency response

o Nguyen (1995.) – TLLM, frequency response and transient response (leakage current not include)

Three-level rate equationso McDonald (1995.) – frequency response (first time analyzed

three-level system, improved Nagarajan’s model)

Response SPICE analysis ( three operating conditions)

One-level rate equations (DHL)o Tucker (1981.) – first SPICE model for semiconducter laser


Two-level rate equations o Gao (1990) – first equivalent electric circuit of QWL (two-port

model)

o Lu (1995.) – SPICE model of SQWL, improved Tucker’s model

o Bewtra (1995.) – SPICE modeling of QWL thermal characteristics

Three-level rate equationso Tsou (1997.) – the most complex SPICE model of SQWL up to

now incorporate parasitic subcircuit

o Rossi (1998.) – first SPICE model of multimode MQWL simulated laser with output emission 0=1.55m

main drawback is very simple form of equivalent circuit

Result OverviewResult Overview


Result OverviewResult Overview - - ConclusionConclusion

Effect of leakage currenthasn’t modeled

Complete model

which include carrier leakage,

is formed (2001).


CompleteComplete MModelodel

Extended system of three-level rate equations Five equations (four for electrons and one for photons)

Derived complete equivalent electric circuit of SQWL

Six main box-subcircuit and six binding box-subcircuit

Formed stabile and convergent SPICE program Give possibilities for simulation SQWL in all three

operating conditions


Cl

addi

ngla

yer

CladdinglayerSCH 1 SCH 2QW

ener

gy

coordinate

current injection ( I )

x

photon emission

G

D

G

D

C E

N QW

N G

N S1

N S2

L SCH

diffusionGW

diffusionleakage

capture emisson

L SCHL QW

GW region

ExtendedExtended SySystem stem of Thof Thrree-level Rate ee-level Rate EquationsEquations – – Included Physical ProcessesIncluded Physical Processes

N G


ExtendedExtended SySystem stem of Thof Thrree-level Rate ee-level Rate EquationsEquations – – Included Physical ProcessesIncluded Physical Processes

Carrier diffusion from both SCH layers in gateway states and vice versa (D, G)

Carrier leakage beyond QW () Carrier capture and emission from QW All recombination processes

monomolecular (AS,AQW), bimolecular (BS,BQW) and Auger recombinations (CS,CQW)

Nonlinearity of gain nonlinear gain () and nonlinear dependence of material gain

( g ~ ln() ) Parasitic effects of bindings in equivalent circuit –

parasitic subcircuit


ExtendedExtended SySystem stem of Thof Thrreee-level Rate e-level Rate EquationsEquations

D

S2S1S

S

QW

G

G

D

S1

S

S1 NNR

V

VNN

qV

I

dt

dN

2

D

S1S2S

S

QW

G

G

D

S2S2 NNR

V

VNN

dt

dN

2

G

GGQW

E

QW

C

G

QW

S

D

S2S1G NNR

NN

V

VNN

dt

dN

1

SSNgNRNN

dt

dNQWQWQW

E

QW

C

GQW

1

2QWQW

PQW NB

S-SSNg

dt

dS

1


ExtendedExtended SySystem stem of Thof Thrree-level Rate ee-level Rate EquationsEquations

3QWS,

2QWS,QWS,QWS, NCNBNANR

30QW

20QW0QW

3QW

2QWQW

0G NCNBNA

NCNBNAGNg ln


Complete Equivalent Electric Circuit Complete Equivalent Electric Circuit of SQWLof SQWL

carriers in adequate layers arm currents

QWG,QWQWNG, NAqVI S1,2D

QWS1,2 N

qVI

;

Extended system of

three-level rate equations

photon emission output voltage

CN S

SS

Equivalent system of

current equations



Equivalent system of

current equationsKirchhoff ‘s laws

Complete equivalent electric circuit of SQWL


kIS1kIS2

kI S2

IG

2aN

SCH 2

GW+ leakage

ka SIS2 kb SIS22 kc SIS2

3 Dd IS2

dtk

SCH 2 layer (right)


I R p

C s

R sub

R s

C p

L p


kIS2

IG

2aNkIS1

kI S1

SCH 1

GW+ leakage


3

SCH 1 layer (right)

kDd IS1

dt

k(1- )(IS1 + IS2 )

C DV jG

SCL

b N IG2 c N IG

3

IG

R G

D G1

D G2

GW states

d IG

dtAQW

1 IG

aN

GW

SCH 1,2

IG

aN

GC

IN

aN

GE

GW

QW

b N IN2 c N IN

3

QW

IN

R N

D N1

D N2

d IN

dtAQW

1

photon emission

QW

gateway states

SCH layers


G (IN )S N

N G (IN )S N2

lasing

photon emission

+

-

C PR P

S Nb N IN2


Complete Equivalent Electric Circuit Complete Equivalent Electric Circuit of SQWLof SQWL– – Subcircuit Subcircuit forfor LLeeftft SCH SCH11 LayerLayer

kIS2

IG

2aNkIS1

kI S1

SCH 1

GW+ leakage


3

SCH 1 layer (left)

kDd IS1

dt


Complete Equivalent Electric Circuit Complete Equivalent Electric Circuit of SQWL of SQWL – – SSubcircuit ubcircuit forfor RRight SCHight SCH22 Layer Layer

kIS1kIS2

kI S2

IG

2aN

SCH 2

GW+ leakage


3 Dd IS2

dtk

SCH 2 layer (right)


b N IG2 c N IG

3

IG

R G

D G1

D G2

GW states

d IG

dtAQW

1

Complete Equivalent Electric Circuit Complete Equivalent Electric Circuit of SQWL of SQWL – – Subcircuit Subcircuit forfor GGateway ateway SStatestates

k(1- )(IS1 + IS2 )

C DV jG

SCL

IG

aN

GW

SCH 1,2

IG

aN

GC

IN

aN

GE

GW

QW


Complete Equivalent Electric Circuit Complete Equivalent Electric Circuit of SQWL of SQWL – – Subcircuit Subcircuit forfor QWQW

IG

aN

GW

SCH 1,2

IG

aN

GC

IN

aN

GE

GW

QW

b N IN2 c N IN

3

QW

IN

R N

D N1

D N2

d IN

dtAQW

1


Complete Equivalent Electric Circuit Complete Equivalent Electric Circuit of SQWL of SQWL – – Subcircuit Subcircuit forfor OOutput utput PPhoton hoton EEmissionmission

b N IN2

photon emission

+

-

C PR P

S N

G (IN )S N

N G (IN )S N2

lasing


Complete Equivalent Electric Circuit Complete Equivalent Electric Circuit of SQWL of SQWL – – PParaarassititicic SSububcircuitcircuit

I R p

C s

R sub

R s

C p

L p



SPICE SPICE PProgramrogram

Complete equivalent electric circuit

Selection of SQWL parametersvariable parameters

SPICE program

Solving stability and

convergence

Incorporation in SPICE


Response Response AAnalysis – nalysis – DC DC RResponseesponseL-I L-I CCurveurve

76

150

30050mv

100mv

150mv

0mv0mA 1mA 2mA 3mA

=0

LSCH(nm)

Injection current - I

SN


Response Response AAnalysis – nalysis – DC DC RResponseesponseThreshold Threshold CCurrent urrent - I- Ithth

IIthth(mA)(mA)

1.29

1.13

1.02

0mV

4mV

8mV

0.9mA 1.1mA 1.3mA 1.5mA

=0

Injection current - I

SN


Response Response AAnalysis – nalysis – DC DC RResponseesponseThreshold Threshold CCurrent urrent - I- Ithth(())

>0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.81.01.21.41.61.83.6

3.7

I th(m

A)

LSCH(nm)

76150300


Response Response AAnalysis – nalysis – AC AC RResponseesponseFrequency Frequency RResponse esponse – – PParasitic arasitic SSubcircuitubcircuit

Frequency

SN

1GHz 3GHz 10GHz 15GHz0V

250V

500VLSCH=300nm;=0IB=2mA

IB=15mA

parasitic subcircuitwithout

with


Response Response AAnalysis – nalysis – AC AC RResponseesponseFrequency Frequency RResponse esponse -- C Comparisonomparison

LSCH=76nm

SN(V)

Frequency (GHz)

IB=15mA

0.6 0.8 1 2 6 8 10 40

25

50

75

100

125

150

175

200

225

250

4 20 400

LSCH=300nm

=0=0.9

=0


Response Response AAnalysis – nalysis – AC AC RResponse esponse

Bandwidth Bandwidth - f- f-3db-3db(())

LSCH(nm)

76150

300

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

f -3dB

(GH

z)

IB=2mA

0.785

> 0.9


Response Response AAnalysis – nalysis – AC AC RResponse esponse

Bandwidth Bandwidth - f- f-3db-3db(())

LSCH(nm)

76150300

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0

2

4

6

8

10

12

14

f -3dB

(GH

z)

IB=15mA

0.09

0.74> 0.9


2102.53.5

Time2.0ns 3.0ns 4.0ns 5.0ns 6.0ns 7.0ns1.5ns

0V

0.5V

1.0V

1.5V

2.0V

2.5V

3.0V

SN

LSCH=76nm;IB=0mA;=0

5

Response Response AAnalysis – nalysis – TranTran RResponseesponseLaser Laser Start Start - - AnimaAnimattiionon

IP= mA15


Time2.0ns 3.0ns 4.0ns 5.0ns 6.0ns 7.0ns1.5ns

0V

0.5V

1.0V

1.5V

2.0V

2.5V

3.0V

SN

LSCH=76nm;IB=0mA;=0

IP= 2,2.5, 3.5,5,10,15mA

input current impulse

Response Response AAnalysis – nalysis – TranTran RResponseesponseLaser Laser StartStart


Response Response AAnalysis – nalysis – TranTran RResponse esponse NormaliNormalizedzed R Responseesponse

Time

2.0ns 3.0ns 4.0ns 5.0ns 6.0ns 7.0ns1.5ns

SN

IP/Ith=5;=0

0V

0.5V

1.0V

1.5V

2.0V

IB/Ith=0

IB/Ith=15

LSCH(nm)

76300


Response Response AAnalysis – nalysis – TranTran RResponse esponse Influence of Influence of CCarrier arrier LLeakageeakage

IB=0mA

IB=15mA

0

0.5

IP=5mA;LSCH=300nm

Time

2.0ns 3.0ns 4.0ns 5.0ns 6.0ns 7.0ns1.5ns

SN

0V

0.5V

1.0V

1.5V

2.0V


Response Response AAnalysis – nalysis – TranTran RResponseesponse Laser Laser TTime on ime on DDelay elay - - onDonD(())

76150300

LSCH(nm)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

onD

(ns)

IB=0mA, IP=5mA

>0

0.60.81.01.21.41.61.82.02.22.4


Response Response AAnalysis – nalysis – TranTran RResponse esponse Extinction ratioExtinction ratio - ER- ER(())

76300

LSCH(nm)

IB=76300

2 15 mA

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

IP=5mA; >0

1.30

1.32

1.34

1.36

6789

10

ER


New model – Complete model of SQWL Complete equivalent electric circuit of SQWL

Analysis of leakage current effects – first time Influence of leakage current is important in all

operation condition of SQWL and

can’t be neglected.

ConclusionConclusion – – ThesisThesis ContributionContribution


ConclusionConclusion – – ThesisThesis ContributionContribution Influence of Leakage CurrentInfluence of Leakage Current

Increasing threshold current if carrier leakage increase for large thickness of SCH layers.

Carrier leakage always reduce SQWL bandwidth, especially for larger thickness of SCH layers and higher bias currents.

Critical leakage factor. Increasing laser time on delay if increase carrier

leakage, especially for larger thickness of SCH layers;

ER don’t depend of carrier leakage.

contribution to the analysis of high-speed single quantum well laser response: effect of leakage...

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system of equations

nm slide

time slide

d electrons n qw

d electrons n s

d electrons n g

level rate equations

laser response