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Complete M odel. Extended s y stem of three-level rate equations Five equations ( four for ele c tron s and one for ph oton s ) Derived complete equivalent electric circuit of SQWL Six main box-subcircuit and six binding box - subcircuit Form ed stabil e and c onvergent SPICE program - PowerPoint PPT Presentation
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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
Petar Matavulj Complete SQWL Model
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
Petar Matavulj Complete SQWL Model
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
Petar Matavulj Complete SQWL Model
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
Petar Matavulj Complete SQWL Model
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
Petar Matavulj Complete SQWL Model
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
Petar Matavulj Complete SQWL Model
Complete Equivalent Electric Circuit Complete Equivalent Electric Circuit of SQWLof SQWL
Equivalent system of
current equationsKirchhoff ‘s laws
Complete equivalent electric circuit of SQWL
Petar Matavulj Complete SQWL Model
kIS1 kIS2
kI S2
IG2aN
SCH 2
GW+ leakage
ka SIS2 kb SIS22 kc SIS2
3 Dd IS2
dtk
SCH 2 layer (right)
Complete Equivalent Electric Circuit Complete Equivalent Electric Circuit of SQWLof SQWL
I R p
C s
R sub
R s
C p
L p
parasitic subcircuit
kIS2IG2aN
kIS1
kI S1
SCH 1
GW+ leakage
ka SIS1 kb SIS12 kc SIS1
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
parasitic subcircuit
G (IN )SN
NG (IN )SN2
lasing
photon emission
+
-
C PR P SNbN IN2
Petar Matavulj Complete SQWL Model
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
ka SIS1 kb SIS12 kc SIS1
3
SCH 1 layer (left)
kDd IS1dt
Petar Matavulj Complete SQWL Model
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
ka SIS2 kb SIS22 kc SIS2
3 Dd IS2
dtk
SCH 2 layer (right)
Petar Matavulj Complete SQWL Model
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
Petar Matavulj Complete SQWL Model
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
Petar Matavulj Complete SQWL Model
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
Petar Matavulj Complete SQWL Model
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
parasitic subcircuit
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