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NCN
Lecture20:Electrostaticsofpnjunctiondiodes
u amma s ra u [email protected]
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Outline
1) Introductionto
p
n
junctions
2 Drawin banddia rams
3) Accuratesolutioninequilibrium
Ref.Semiconductor
Device
Fundamentals,
Chapter
5
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WhatisaDiodegoodfor.
solarcells GaAslasers
OrganicLED
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. .
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pnJunctionDevices
Symbols
AN
D
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TopicMap
signal
SignalDiode
Schottky
BJT/HBT
MOS
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DrawingBandDiagraminEquilibrium
( )+ = + D AD q p n N N equilibrium
N N N r g
t q= +
J
= =
1 = +JP P P
pr g
N N N
Smallsignaldn/dt~jtxnTransient fullsolution
P P Pqp E qD p= J
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PandNdopedMaterialSidebySide
NdopedE Pdoped
ConductionBand
EcEF
ConductionBand
EF
ValenceBandV
ValenceBand
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kko e ec ron rans er un er
ordinary circumstances!
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FormingaJunction
N N
= ND
Junction
x
2
0=
Ain n N
Actual Carrier
Concentrations
n-side p-side
n p
ln(n),
np
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Bulk Region Bulk RegionDepleted
Region x
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FormationofaJunction
DN AN
+
ln(ND)
ln(n)ln(p)
Q= n+N NqND DepletedRegion
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-qNA
xn xp
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SketchofElectrostatics
positionPotential
Vbi
E ieldmax = =os s
npo
A Dx N
q
E K xK N
q
position
p-n+ND-NA qND
Depleted
Region
10
Bulk Region
-qNABulk Region
xpxn
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SketchofElectrostatics
Potential xnxp
position
BandDiagram
position
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Outline
1) Introductiontopnjunctions
2) Drawingbanddiagrams
3) Analyticalsolutioninequilibrium
4) Banddiagramwithappliedbias
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ShortcuttoBanddiagram
Neutral Neutral
Space
Charge
DN AN
2C
EF
1
V
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BuiltinPotential:boundaryconditions@infinity
qVbi
11
Eg,2
2
1 1 2 2 2+ + = + gb ,i EqV
2 1 12 2 = +
g ,biEqV
( )2
1
1
2 2 = + + +
B B
Ag ,
V , C ,
Dk T ln k N
NT ln
N
NE
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( )2
2 1
12= + g , BB E
D
T
C
A
/ k
V , ,
k T ln
N N e
NN
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InterfaceBoundaryConditions
D
E=(D/ko)
pos on
xn xp
positionxn xp
01 0 21 2(0 ) (0 ) = = =EKD E DK
2
1
(0 ) (0 ) +=K
E E
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Displacementiscontinuousacrosstheinterface,fieldneednotbe..
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BuiltinvoltageforHomojunctions
Neutral Neutral
Space
Charge
DN AN
Vacuumlevel1bi
C
EV
EF
16
( )2
2 1
2 1
= + g , Bbi B E / k T V , C
A D
,
qV k T ln
N N e
N N2
= =g B
A AB BE / k T
C
D D
iV
k T ln k T ln
n N N e
NN NN
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AnalyticalSolutionofPoissonEquation
Depleted Region
Q=
n+N N
q D
qNAposition
xn xp
2d V + =
0 2S D Adx
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AnalyticalSolutionforHomojunctions
(Charge)p-n+ND-NA
qND -qNA ( )0
0
= Ds
nqNEk
x
xn xp
position
( )0
0
+ = As
p
qN
k
xE
Efield =D An pN x N x
positionPotential
( ) ( )0 0 += +
n p
bi
E x E xqVVbi
position 22
0 02 2
= + AD pns s
qN xxqN
k k
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DepletionRegionsinHomojunctions
Neutral Neutral
Space
Charge
xn xp
D A
=xN N x 2 k N
22A pnD
qNq xN x
pn
( )=
+D A
n
D
bixN Nq N
0 02 2 =bi s sk k ( )0
= +s
D
A A
p
D
bix N N Vq N
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HW: Solve the same problem for a hetero-junction
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CompleteAnalyticalSolution
N P
x
0=0=
-xp 0 xn
EV
xn
-xp -xp xn0x x x-xp xn
-qNA
..........
................
0
0
=
A
os
D
qNp
K
qNn
x x
dx x
E
............. ,0
os
p nx x x x x( )
00
= p
x xA
xS
qNd dx
K
E0
( )0
=
nx D
x xS
qd
Ndx
K
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..........
0
( ) ( ) 0
= + ppS
AqxN
x x x x
K
E ..........
0
( ) ( ) 0
= D nn
S
q x x x
Nx x
K
E
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Outline
1 Introductionto n unctiontransistors
2) Drawingbanddiagrams
4) Banddiagramwithappliedbias
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TopicMap
signal
SignalDiode
Schottky
BJT/HBT
MOS
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ApplyingBiastopnJunction
ln I
2
. us on m e
2. Ambipolar transport
6,7
3. High injection
-A
5. Breakdown
4
5
6. Trap-assisted R-G
7. Esaki Tunneling
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ForwardandReverseBias
DN AN
Forward Bias
DN
AN
Reverse Bias
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BandDiagramwithAppliedBias
( )D AD q p n N N +
= + Banddiagram(now)
N N N r g
t q= +
J
=
1P P P
pr g
= +J
N N N
Nextclass
P P Pqp E qD p= J
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ApplyingaBias:PoissonEquation
qVbi
EF-EV
EC-EF
bi
( ) in EF
q(Vbi-V)( )
( ) = p i
i
F
i
Ep x n e
C
-n
Fp-EV
-qV ( )2 = pn FFin p n e
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DepletionWidths
GND-V DN AN
xn xp
02
( )s
A bin
k NV Vx
=
22AD n p
qNqN xx =
D A pn D A D
0 02 2s skk ( )0
( )s D
bi
A A D
p Vq N N N V= +
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Whataboutheterojunctions?
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FieldsandDepletionatForward/ReverseBiasesVA0
NP
VA0
ElectricField
Position
atforwardbiases
Position
A0Significantincreaseof
peakfieldatreverse
bias
Potential VA0
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Conclusion
importanttopicyoulearninthiscourse.Banddiagram
sagrap ca wayo qu c yso v ng o ssonequat on.
2) If youconsistentlyfollowtherulesofdrawingband
diagrams,youwillalwaysgetcorrectresults.Tryto
followtherules,notguessthefinalresult.
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