Complete M odel

Petar Matavulj Complete SQWL Model

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


Cladding

laye

r

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


kIS1 kIS2

kI S2

IG2aN

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


kIS2IG2aN

kIS1

kI S1

SCH 1

GW+ leakage


3

SCH 1 layer (right)

kDd IS1dt

k(1- )(IS1+ IS2 )

C DV jG

SCL

bN IG2 cN IG

3

IGR G

D G1

D G2

GW states

d IGdtAQW

1 IGaN

GW

SCH 1,2

IGaN

GC

INaN

GE

GW

QW

bN IN2 cN IN

3

QW

INR N

D N1

D N2

d INdtAQW

1

photon emission

QW

gateway states

SCH layers


G (IN )SN

NG (IN )SN2

lasing

photon emission

+

-

C PR P SNbN IN2


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

kIS2IG2aN

kIS1

kI S1

SCH 1

GW+ leakage


3

SCH 1 layer (left)

kDd IS1dt


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

kIS1 kIS2

kI S2

IG2aN

SCH 2

GW+ leakage


3 Dd IS2

dtk

SCH 2 layer (right)


bN IG2 cN IG

3

IGR G

D G1

D G2

GW states

d IGdtAQW

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

IGaN

GW

SCH 1,2

IGaN

GC

INaN

GE

GW

QW


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

IGaN

GW

SCH 1,2

IGaN

GC

INaN

GE

GW

QW

bN IN2 cN IN

3

QW

INR N

D N1

D N2

d INdtAQW

1


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

bN IN2

photon emission

+

-

C PR P SN

G (IN )SN

NG (IN )SN2

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


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Complete M odel