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www.nanohub.org
NCN
Lecture25:SchottkyDiode(I)
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Outline
1) Importanceof
metal
semiconductor
junctions
2) Equilibriumbanddiagrams
3) DCThermioniccurrent(simplederivation)
e . em con uc or ev ce un amen a s, ap er ,p.
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MetalsemiconductorDiode
Symbols
D
MetalWire
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N
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ApplicationsofMSDiode.
Detectors STMonsemiconductor
www.fzjuelich.de/ibn/index.php?index=674
OriginalBipolar CNTTransistors
4
Originally,Gelena(PbS),Si assemiconductorand
PhosporBronzeformetal(catswhisker)
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Outline
1) Importanceofmetalsemiconductorjunctions
2) Equilibriumbanddiagrams
3) DCThermioniccurrent(simplederivation)
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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
= =
1P P P
pr g
= +J
N N N
Smallsignaldn/dt~jtnTransient fullsol.
P P Pqp qD p= J E
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BandDiagram
DN
Vacuumlevel
E
M
EV
F
Negligible..
A p D nN x N x=
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BuiltinPotential:bc@Infinity
M
B
b Mi = M Bbi = D
N
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B
C
BN
=
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CompleteAnalyticalSolution
DepletionApproximation
N
E
Xnx
Actual Xn x
N x
QM =QDQD =NDXn
max
0 0
n
s sK K
= =
Bq
x
Xn
C
E
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max
max2
n = xXn
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AnalyticalSolution(SimpleApproach)
Charge( )
0
0 nD
s
qN
k
x
+ =E
xp
xn+
Position( ) 00 ?
M
s
p
k
==
E
Efield
D n pM
Position ( ) ( )0 02 2
bi
n pqV
xx +
= +E E
22
0 02 2
MD pn
s s
qNqN
k k
xx
= +
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DepletionRegions
xnxp
D
pD MnxN N x=0 0
2 2 1s sM bi bin
k kNV Vx
=
22pMD
bn
i
qNqNqV
xx= +
D M D D
02
s Dk N
0 0ss ( ) bi M M Dp q N NN= +
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Outline
1) Importanceofmetalsemiconductorjunctions2) Equilibriumbanddiagrams
3) DCThermioniccurrent(simplederivation)
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TopicMap
signal
SignalDiode
Schottky
BJT/HBT
MOS
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BandDiagramwithAppliedBias
( )D AD q p n N N + = + Banddiagram
N N N r g
t q= +
J
=
1P P P
pr g
= +J
N N N w w
Needtheoryofthermionicemission
P P Pqp qD p= J E
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BanddiagramwithBias
E -EqVbi-V
ForwardBias
VA
ECEF
qVbi
ReverseBias
AEC-EF
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DepletionRegionswithBias
xnxp
( )0 02 2 1
s M sn bi bi A
k N k x V V V =
D M D D
( )0 0s D p bi
M M D
x Vq N N N = +
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IVCharacteristics
ForwardBias MetalN-typeSemi.
VAIEc
EV
EFEFSEFM
1,2,3
I
ReverseBias
EFM
6,7
4
Ec
EFEFS
5
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EV
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LeftBoundaryCondition
ECq(Vbi-VA)
( )(( ) )
0
m s A s m AT AJ V
J
J VJ
J
V
V
=
=
(0)( (0)00) s mmT sA JJ V J = = = detailed balance( (0 )) 0s mm s JJ =
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T A s m s m A
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SemiconductortoMetalFlux
bi AV V
)
2( m
m s
T
thA
kJn
q eV
= ( )
2
s k
hs
T
A tm q eJ V = bi AqV qV
V
2
s th kT kT q e e
=
2
m th kT kT n
q e e
=
q(VbiVA)
VAEC-EF
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TotalFlux
m Aq qV
m th kT kT qn
2
T s m s m A
1
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SemiconductortoMetalFlux
bi AV V
)
2( m
m s
T
thA
kJn
q eV
= ( )
2
s k
hs
T
A tm q eJ V = bi AqV qV
V
2
s th kT kT q e e
=
2
m th kT kT n
q e e
=
q(VbiVA)
VAEC-EF
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TotalFlux
m Aq qV
m th kT kT qn
2
T s m s m A
1
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Diffusionvs.ThermionicEmission
n
Fpn
Checkthatbothgivesthesameresu ora o e
F
Fn
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Conclusion
Schottkybarrierdiodeisamajoritycarrierdeviceofgreat
historicalimportance.
Therearesimilaritiesanddifferenceswith n unctiondiode:
forelectrostatics,itbehaveslikeaonesideddiode,but
current,thedriftdiffusionapproachrequiresmodification.
Thetrapassistedcurrent,avalanchebreakdown,Zener
tunnelingallcouldbecalculatedinamannerverysimilarto
junctiondiode.
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