principles of semiconductor devices-l25

8/8/2019 Principles of Semiconductor Devices-L25

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www.nanohub.org

NCN

Lecture25:SchottkyDiode(I)

[email protected]

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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


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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


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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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principles of semiconductor devices-l25

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