Electronics Ch1

NTUEEElectronics L.H.Lu 11

CHAPTER1ELECTRONICSANDSEMICONDUCTORS

ChapterOutline1.1Signals1.2FrequencySpectrumofSignals1.3AnalogandDigitalSignals1.4Amplifiers1.5CircuitModelsforAmplifiers1.6FrequencyResponseofAmplifiers1.7IntrinsicSemiconductors1.8DopedSemiconductors1.9CurrentFlowinSemiconductors1.10Thepn JunctionwithOpenCircuitTerminals1.11Thepn JunctionwithAppliedVoltage1.12CapacitiveEffectsinthepn Junction

1.1Signals

SignalprocessingSignalscanbeofavarietyofformsinordertocarryinformationfromthephysicalworldItismostconvenienttoprocesssignalsbyelectronicsystem,therefore,thesignalsarefirst

convertedintoanelectricform(voltageorcurrent)bytransducers

SignalsourcesThevenin form:(voltagesourcevs +seriesresistanceRs) Presentingthesignalbyavoltageform IspreferredwhenRs islow(Rs canbeneglected)

Nortonform:(currentsourceis +shuntresistanceRs) Presentingthesignalbyacurrentform IspreferredwhenRs ishigh(Rs canbeneglected)

Inelectronicssystems,thesignalistakenfromoneofthetwoformsforanalysisTwoformsareinterchangeablewithvs(t)=is(t)Rs


Transducer SignalProcessor TransducerInputsignal(voice,speed,pressure,etc.)

Outputsignal(voice,speed,pressure,etc.)

ElectricalSignals ElectricalSignalsv(t)

t

v(t)

t

1.2FrequencySpectrumofSignals

SinusoidalsignalAsinusoidalsignalisgivenas:va(t)=|Va|sin(at+a )Characterizedbyitsamplitude(|Va|),frequency(a)andphase(a )

FrequencydomainrepresentationAnytimedomainsignalcanbeexpressedbyitsfrequencyspectrum Periodicsignal Fourierseries Nonperiodicsignal Fouriertransform

PeriodicsignalThefundamentalfrequencyofperiodicsignalsisdefinedas0 =2/T.Aperiodicsignalcanbeexpressedasthesumofsinusoidsatharmonicfrequencies(n0)Example:asquarewavewithperiodT


...)5sin5

13sin

3

1(sin

4)( 000 tttVtv

Timedomainrepresentation Frequencydomainrepresentation

va(t)

t

Va

Ta

NonperiodicsignalTheFouriertransformisappliedtoanonperiodicfunctionoftimeThespectrumofanonperiodicsignalcontainsallpossiblefrequencies


FrequencydomainrepresentationTimedomainrepresentation

...)5sin5

13sin

3

1(sin

4)( 000 tttVtv

1.3AnalogandDigitalSignals

SignalclassificationAnalogsignal:signalcantakeonanyvalueDigitalsignal:canonlytakeonfinitequantizationlevelsContinuoustimesignal:definedatanytimeinstantDiscretetimesignal:definedonlyatthesamplinginstantsSampling:theamplitudeismeasuredatequaltimeintervalsQuantization:representthesamplesbyfinitevaluesQuantizationerror: Differencebetweensampledvalueandquantizedvalue Canbereducedbyincreasingthequantizationlevels

DataconversionAnalogtodigitalconverter(ADC):

Digitaltoanalogconverter(DAC):


A/Dconverter

...

b0b1bN1

vA

Analoginput

Digitaloutput

D/Aconverter

.

.

.

b0b1

bN1

vD

Analogoutput

Digitalinput

vA =vD +quantizationerror

111

00 2....22

NND bbbv

3,3,3,2,3,3

Continuoustimeanalogsignal

Digitalsignal

Quantizationerror

v(t)

t

Discretetimeanalogsignal

t

Sampling

Quantization3

2

1

0t

t

1.4Amplifiers

GainofamplifiersVoltagegainAv vO/vICurrentgainAi iO/iIPowergainAp vO iO/vI iIAmplifiergainsaredimensionless(ratioofsimilarlydimensionedquantities)Voltageandcurrentgaincanbepositiveornegativedependingonthepolarityofthevoltageand

thecurrentThegainisfrequentlyexpressedindecibels: VoltagegainAv (dB) 20log|Av| CurrentgainAi (dB) 20log|Ai| PowergainAp (dB) 10log|Ap| Gain>0dB |A|>1(amplification) Gain

TransfercharacteristicsoflinearamplifierTheplotofoutputresponsevs.input transfercharacteristicsForlinearamplifier,thetransfercharacteristicisastraightline

passingtheoriginwithslope=AvItisdesirabletohavelinearamplifiercharacteristicsformostof

theapplicationsOutputwaveformisanenlargedcopyoftheinput:vO(t)=AvvI(t)NohigherpowertermsofvI attheoutput

AmplifiersaturationPractically,theamplifiertransfercharacteristicremainslinear

overonlyalimitedrangeofinputandoutputvoltagesTheamplifiercanbeusedasalinearamplifierforinputswing:

L/Av vI L+/Av vO =AvvIForinputlargerthantheswinglimitation,theoutputwaveform

willbetruncated,resultinginnonlineardistortionThenonlinearitypropertiescanbeexpressedas:

vO =a0+a1vI+a2vI2+a3vI3 ..


NonlineartransfercharacteristicsandbiasingInpracticalamplifiers,thetransfercharacteristicsmayexhibitnonlinearitiesofvariousmagnitudeThenonlinearitycharacteristicswillresultinsignaldistortionduringamplificationInordertousethecircuitasalinearamplifier: Usedcbiastooperatethecircuitnearthemiddleofthetransfercurve quiescentpoint Superimposethetimevarying(ac)signalonthedcbiasattheinput Besurethatthesignalswingissufficientlysmallforgoodlinearapproximation Thetimevarying(ac)componentsattheoutputisthedesiredoutputsignal


vO (t)

vI (t)

vO

vI

Q

Slope=Av

VI

VO

)()( tvVtv iII )()( tvVtv oOO

)()( tvAtv ivo Qat

I

Ov dv

dvA |

Symbolconvention:dcquantities:IC,VDIncremental(ac)quantities:ic(t),vd(t)Totalinstantaneous(ac+dc)quantities:iC(t),vD(t)

iC(t)=IC+ic(t)vD(t)=VD+vd(t)


1.5CircuitModelsforAmplifiers

ConceptofequivalentcircuitPracticalamplifiercircuitcouldberathercomplexUseasimplifiedmodeltorepresentthepropertiesandbehavioroftheamplifierTheanalysisresultsdonotchangebyreplacingtheoriginalcircuitwiththeequivalentcircuit

VoltageamplifiersAsimplifiedtwoportmodeliswidelyusedforunilateral voltageamplifiers

Themodeliscomposedofthreecomponents: Inputresistance(Ri):theresistancebylookingintotheinputport Outputresistance(Ro):theresistancebylookingintotheoutputport Opencircuitvoltagegain(Avo):thevoltagegain(vo/vi)withoutputopencircuit

Circuitanalysiswithsignalsourceandload: Voltagegain: Overallgain: Idealvoltageamplifier:Ri = andRo =0


oL

Lvo

i

ov RR

RAvvA

oL

Lvo

si

i

s

ov RR

RARR

RvvG

VoltageAmplifier

CircuitparametersintheamplifiermodelThemodelcanbeusedtoreplaceanyunilateralamplifierbypropercircuitparameters

Theparameterscanbeobtainedbycircuitanalysisormeasurement Analysis(measurement)oftheinputresistance:Theresistancebylookingintotheinputport

(findix foragivenvx orfindvx foragivenix) Analysis(measurement)oftheoutputresistance:Setvi =0byinputshortTheresistancebylookingintotheoutputport

(findix foragivenvx orfindvx foragivenix) Analysis(measurement)oftheopencircuitvoltagegain:Givenvx atinputFindopencircuitoutputvoltagevovo isdividedbyvx


vx

vx

vx

ix

ix

vo

Ri vx/ix

Ro vx/ix

Avo vo/vx

CascadeamplifierMultiplestagesofamplifiersmaybecascadedtomeettheapplicationrequirementTheanalysiscanbeperformedbyreplacingeachstagewiththevoltageamplifiermodel

BufferamplifierImpedancemismatchmayresultinareducedvoltageswingattheloadBufferamplifiercanbeusedtoalleviatetheproblem Thegainofthebufferamplifiercanbelow(~1) Thebufferamplifierhashighinputresistanceandlowoutputresistance


AmplifiertypesVoltageamplifier:gainofinterestisdefinedbyvo/vi (V/V)Currentamplifier:gainofinterestisdefinedbyio/ii (A/A)Transconductane amplifier:gainofinterest isdefinedbyio/vi(1)Transimpedance amplifier:gainofinterestisdefinedbyvo/ii ()

Amplifiermodels

UnilateralmodelsTheamplifiermodelsconsideredareunilateral;thatis,signalflowonlyfrominputtooutputThemodelissimpleandeasytousesuchthatanalysiscanbesimplifiedNotallamplifiersareunilateralandmorecomplicatedmodelsmaybeneededfortheanalysis


VoltageAmplifier

Transimpedance AmplifierTransconductance Amplifier

CurrentAmplifier

Circuitanalysisforamplifiers


vo =Avovi RL /(RL+Ro)vo /vs =Avo[Ri /(Ri+Rs)][RL /(RL+Ro)]Foridealcase(Ri ,Ro 0):vo /vs =Avo

io =Gmvi Ro /(RL+Ro)io /vs =Gm[Ri /(Ri+Rs)][Ro /(RL+Ro)]Foridealcase(Ri ,Ro ):io /vs =Gm

VoltageAmplifier Transconductance Amplifier

CurrentAmplifier Transimpdeance Amplifier

io =Aisii Ro /(RL+Ro)io /is =AisRsRo /[(RL+Ro)(Ri+Rs)]Foridealcase(Ri 0,Ro ):io /is =Ais

vo =Rmii RL /(RL+Ro)vo /is =RmRsRL /[(RL+Ro)(Ri+Rs)]Foridealcase(Ri 0,Ro 0):vo /is =Rm

Exercise1.12(Textbook)Exercise1.13(Textbook)Exercise1.14(Textbook)

Exercise1: ForavoltageamplifierwithRi =100k,Ro =10k andAvo =20,finditsequivalentmodelsascurrent,transconductance andtransimpedance amplifiers.

Exercise2: Considertwoamplifierstagesarecascaded.ThemodelofthefirststageisgivenbyRi =1M,Ro =10k andAvo =20,whilethemodelofthesecondstageisgivenbyRi =100k,Ro =10 andAvo =2.(1) Findthevoltageamplifiermodelforthecascadeamplifier.(2) ForRs =100k andRL =100 ,findAv andGv.


1.6FrequencyResponseofAmplifiers

ConceptoffrequencyresponseTheinputsignaltoanamplifiercanbeexpressedasthesumofsinusoidalsignalsFrequencyresponse:thecharacteristicsofanamplifierintermsofitsresponsetoinputsinusoidals

ofdifferentfrequencies

MeasuringtheamplifierfrequencyresponseApplyingasinusoidalsignaltoalinearamplifier,theoutputisasinusoidalatthesamefrequencyTheoutputsinusoidalwillingeneralhaveadifferentamplitudeandashiftedphaseTransferfunctionT()isdefinedasafunctionoffrequencytoevaluatethefrequencyresponse MagnitudeofT()isthevoltagegainoftheamplifier:|T()|=Vo/Vi PhaseofT() isthephaseshiftbetweeninputandoutputsignals:T()=

AmplifierbandwidthThebandwidthisdefinedwithin3dBfromtheflatgainForsignalcontainingcomponentsoutsidethebandwidth,theoutputwaveformwillbedistorted


vi(t)=Visin(t+ )

vo(t)=Vosin(t+ +)3dB

Flatgain

FrequencydependentcomponentsinamplifiersThefrequencyresponseofamplifiersismainlyduetofrequencydependentcomponentsThemostwidelyusedcomponentsarecapacitorsandinductors

CapacitorsCurrentvoltagerelation:Forsinusoidalsignals:Theratioofvoltageamplitudeandcurrentamplitudeisproportionalto1/C,andisconsidereda

frequencydependentimpedancePhasoranalysis:

InductorsCurrentvoltagerelation:Forsinusoidalsignals:TheratioofvoltageamplitudeandcurrentamplitudeisproportionaltoL,andisconsidereda

frequencydependentimpedancePhasoranalysis:

NTUEEElectronics L.H.Lu

)()( tvdtdCti CC

)sin()()cos()( 00 tCVtitVtv CC

CjIVZeCVItCVti

eVVtVtv

CCC

jCC

jCC

/1/

)sin()(

)cos()()2/(

00

00

)()( tidtdLtv LL

)sin()()cos()( 00 tCItvtIti LL

LjIVZeLIVtLItv

eIItIti

LLL

jLL

jLL

/

)sin()(

)cos()()2/(

00

00

117

DerivingthetransferfunctionofamplifiersComplexfrequency(s) TreataninductanceL asanimpedance sL TreatacapacitanceC asanimpedance1/sC DerivethetransferfunctionwithphysicalfrequencyT(s)=Vo/Vi

Physicalfrequency(replaces byj) TreataninductanceL asanimpedance jL TreatacapacitanceC asanimpedance1/jC DerivethetransferfunctionwithphysicalfrequencyT(j)=Vo/Vi

EvaluatingthefrequencyresponseofamplifiersThetransferfunctionforphysicalfrequencyisgenerallyacomplexvalueasafunctionofThemagnitude|T()|definesthevoltagegainofasinusoidalatThephaseT()definesthephaseshiftofasinusoidalat Themagnitudeandphasearegenerallyplottedversusfrequencytoevaluatethefrequencyresponse

FrequencydomainanalysisUseFourierseries/FouriertransformtorepresentatimedomaininputsignalUsethefreq.responsetodeterminetheamplitude/phaseofthesinusoidalcomponentsattheoutputThetimedomainoutputsignalcanbeobtainedbyaddingtheoutputsinusoidalcomponentsExample:vi(t)= Ansin(nt+n)=A1sin(1t+1)+A2sin(2t+2)+ ..

vo(t)=A1|T(1)|sin(1t+1+T(1))+A2|T(2)|sin(2t+2+T(2))+ ..NTUEEElectronics L.H.Lu 118

NTUEEElectronics L.H.Lu

RCjCjRCj

jVjVjT

i

o

1

1

/1

/1

)(

)()(

Singletimeconstant(STC)networksThenetworkisgenerallycomposedofonereactivecomponent(L orC)andoneresistanceMostSTCnetworkscanbeclassifiedintotwocategories:lowpass (LP)andhighpass (HP)

LowpassSTC

Straightlineapproximations: Lowfrequencymagnitude:|K|indB Cornerfrequency:0 Fastevaluationofgainandphase

Bodeplot

0/1)(form General j

KjT

20 )/(1

|)T(j| Magnitude K

)/(tan)( Phase 01 jT

)/(tan180or 01

119

Exercise3: Findthetransferfunctionandplotitsfrequencyresponse.IsitaSTCnetwork?

Exercise4:Findthetransferfunctionandplotitsfrequencyresponse.IsitaSTCnetwork?

Exercise5: AvoltageamplifierismodeledasRi =100k,Ro =10k andAvo =20V/V.ConsiderthecasewhereRs ofthesignalsourceis25k andtheamplifierisloadedwith10k||100nF.(1) Findthetransferfunction(Vo/Vs)andplotitsfrequencyresponse.(2) Giventhatvs(t)=10cos(102t)+5cos(104t)+3cos(106t)V,findvo(t).


1.7IntrinsicSemiconductors

CovalentbondEachvalenceelectronofasiliconatomissharedbyoneofitsfournearestneighborsElectronsservedascovalentbondsaretightlyboundtothenucleus

ElectronholepairAt0K,nofreecarriersareavailable SibehavesasaninsulatorAtroomtemperature,asmallamountofcovalentbondswillbebrokenbythethermalenergy electronholepairgenerationasfreecarriers

Bothelectronsandholesarefreetomove cancontributetocurrentconduction


CarrierconcentrationinintrinsicsemiconductorForintrinsicsemiconductorsatthermalequilibrium,electronholegenerationandrecommendation

ratesareequalTheelectronandholeconcentrationsremainunchangedatthermalequilibriumTheconductanceofintrinsicsemiconductorisproportionaltothecarrierconcentrationThecarrierconcentrationisgivenby n =p =ni (intrinsiccarrierconcentration) np =ni2 ni2(T)=BT3eEg /kT ni increasesastemperatureincreases ni decreasesastemperaturedecreases

IntrinsiccarrierconcentrationforSiatroomtemperature:ni =1.51010 /cm3Theconductivityisrelativelylowduetothecarrierconcentration


ExtrinsicsemiconductorExtrinsic(doped)semiconductor=intrinsicsemiconductor+impuritiesAccordingtothespeciesofimpurities,extrinsicsemiconductorcanbeeitherntypeorptype

ntypesemiconductorThedonorimpuritieshave5valenceelectrons

areaddedintosiliconP,As,SbarecommonlyusedasdonorTheSiatomisreplacedbyadonoratomDonorionsareboundedinthelatticestructureand

thusdonatefreeelectronswithoutcontributingholesByaddingdonoratomsintointrinsicsemiconductor,

thenumberofelectronsincreases(n>p) ntypesemiconductor

Majoritycarrier:electronMinoritycarrier:hole


ptypesemiconductorTheacceptorimpurityhas3valenceelectron(Boron)Th SiatomisreplacedbyanacceptoratomTheboronlacksonevalenceelectron.Itleaves

avacancyinthebondstructureThisvacancycanacceptelectronattheexpenseof

creatinganewvacancyAcceptorcreatesaholewithoutcontributing

freeelectronByaddingacceptorintointrinsicsemiconductor,

thenumberofholesincrease(p>n) ptypesemiconductor

Majoritycarrier:holeMinoritycarrier:electron


CarrierconcentrationChargeneutrality: Particleswithpositivecharge:p:holeconcentration(mobile);ND:donorconcentration(immobile) Particleswithnegativecharge:n:electronconcentration(mobile);NA:acceptorconcentration(immobile) Chargeneutrality (positivecharge=negativecharge): NAn =NDp

Massactionlaw np =ni2 forsemiconductorunderthermalequilibrium

Forntypesemiconductor

Forptypesemiconductor

Exercise1.27(Textbook)Exercise6:WhatmustND besuchthatn =10000p atroomtemperature(T =300K)


n =ND pnp =ni2

])2

(11[2

2

D

iD

NnNn

nnp i /2 ifND ni Di Nnp /2

DNn

p =NA nnp =ni2

])2

(11[2

2

A

iA

NnNp

pnn i /2 ifNA ni Ai Nnn /2

ANp

1.9CurrentFlowinSemiconductors

FreecarriersinsemiconductorsMobileparticleswithpositiveornegativecharges:electronsandholesThetransportationofcarriersresultsincurrentconductioninsemiconductors

CarrierdriftThermalmotionintheabsenceofelectricfield: Thedirectionofflightbeingchangedateachcollisionwiththeheavy,almoststationaryions Statistically,aelectronhasarandomthermalmotioninthecrystalstructure Netdisplacementoveralongperiodoftimeiszero nonetcurrentflow(I =0)

ThermalmotionunderelectricfieldE: Thecombinedmotionofelectronunderelectricfieldhasarandomandadriftcomponent Still,nonetdisplacementduetorandommotioncomponentoveralongperiodoftime Thedriftcomponentprovidestheelectronanetdisplacement

Driftisthecarriermovementduetotheexistenceofelectricfield


Speed(instantaneous)>0NonetdisplacementVelocity(average)=0

ElectricfieldE =0 ElectricfieldE 0

Speed(instantaneous)>0DriftcomponentduetoEVelocity(average) 0

MobilityF =qE a = F /m* (m* istheeffectivemassofelectron)

Assumethetimeintervalbetweencollisionistcoll andthedriftvelocityimmediatelyafterthecollisionis0

Thentheaveragevelocityoftheelectronduetotheelectricfieldis:

Mobility()indicateshowfastanelectron/holecanmoveundercertainelectricfieldintensity n isusedtospecifythemobilityofelectronSimilarly, p isusedtospecifythemobilityofholeInmostcases,electronmobilityislargerthanholemobilityinasemiconductor

CarrierdriftinsemiconductorSemiconductorparameters: Electronconcentration:n(1/cm3) Electronmobility:n (cm2/V) Holeconcentration:p(1/cm3) Holemobility:p (cm2/V)

Dimensions: Crosssectionarea:A (cm2) Length:L(cm)


EtmqEatdriftv collcolld *22)( )/Vseccm( 2

2*m

qtEv colld

A

L

DriftcurrentinsemiconductorElectroncurrent: TimeintervalforelectronsflowingacrossL:T =L/vd =L/nE (sec) Totalelectroncharge:Qn =qnAL (Coulomb) ElectrondriftcurrentIn,drift =Qn/T=qnAL/T=qnnEA (A) CurrentdensityJn,drift =In,drift/A =qnnE (A/cm2)

Holecurrent: TimeintervalforholesflowingacrossL:T =L/vd =L/pE (sec) Totalholecharge:Qp =qpAL (Coulomb) HoledriftcurrentIp,drift =Qp/T=qpAL/T=qppEA (A) CurrentdensityJp,drift =Ip,drift /A =qppE (A/cm2)

Theelectroncurrentandholecurrentareinthesamedirection Totaldriftcurrentdensity:Jdrift=Jn,drift +Jp,drift =(qnn +qpp)E=E

Conductivity =qnn +qpp (cm)1OhmsLow

I =JA =EA =VA/L =V/R (A)R =L/A =L/A ()


CarrierdiffusionDiffusionisamanifestationofthethermalrandommotionofparticles SectionI:total#=6(3movingtotheleftand3movingtotheright) SectionII:total#=4(2movingtotheleftand2movingtotheright) Netflux:1movingacrosstheinterfacefromsectionItosectionII

Statistically,anetcarrierflowfromhightolowconcentrationregioninainhomogeneousmaterial

EinsteinRelation:Dp/p =Dn/ n =kT/q =VT (thermalvoltage)TotaldiffusioncurrentdensityBothelectronandholediffusioncontributetocurrentconductionTotaldiffusioncurrentdensity:


I II

dxdpqD

dxdnqDJJJ pndiffpdiffndiff )()(

dxdpqDJ pdiffp )(

dxdnqDJ ndiffn )(

Dn:diffusionconstant(diffusivity)ofe

Dp:diffusionconstant(diffusivity)ofh+

GradedsemiconductorForanonuniformsemiconductor,thedopingconcentrationisrepresentedasND(x)ThemobilecarrierwilldiffuseduetothenonuniformdistributionTheuncompensatedspacechargebuildsupafield(potential)forthesystemtoreachequilibriumNonetcurrentflowsatanypointunderequilibriumThebuiltinpotentialcanbederivedunderthermalequilibriumbetweenpointswithdifferent

dopingconcentration


dxdV

dxdp

pVE T

dxdpDEp pp

pdpVdV T

0dxdpqDEqpJ ppp

TVVepp /21 212

11221 ln p

pVVVV TTVVenn /21 21

dxdV

dxdn

nVE T

dxdnDEn nn

ndnVdV T

0dxdnqDEqnJ nnn

1

21221 ln n

nVVVV T

Builtinpotentialfromholeconcentration

Builtinpotentialfromelectronconcentrationn(x)

ND(x)

x

Electrondiffusion

Electrondrift

E

Excesspositivespacecharge

Excessnegativemobilecharge

n(x)

ND(x)

x

Electrondiffusion

CurrentinsemiconductorsDriftcurrent:Jdrift =qnnE +qppEDiffusioncurrent:Jdiff =qDn(dn/dx) qDp(dp/dx)Totalcurrent:J =Jn +Jp =(qnnE +qDn(dn/dx))+(qppE qDp(dp/dx))

Exercise7:Asiliconbarhasacrosssectionalareaof4cm2 andalengthof10cm.(1) ForintrinsicSiwith n =1350cm2/Vsandn =480cm2/Vs,findtheresistanceofthe

baratT =300K.(2) ForextrinsicSiwithNA =1016 /cm3,n =1100cm2/Vsandn =400cm2/Vs,findthe

resistanceofthebaratT =300K.Exercise1.28(Textbook)Example1.9(Textbook)Exercise1.29(Textbook)


E

e

h

Jn

Jp

1.10Thepn JunctionwithOpenCircuitTerminals

Physicalstructureofapn junctionClosecontactofantypesemiconductorandaptypesemiconductorAtwoterminaldevicewithanodeandcathode

pnjunctionincontact

Majority carriersarecrossingtheinterfacebydiffusionandrecombinedintheothersideLeavinguncompensatedspacechargesND+ andNA depletionregionIndepletionregion,electricfield(potential)buildsupduetotheuncompensatedspacechargesThebuiltinpotentialbehavesasanenergybarrier,reducingthemajoritycarrierdiffusionThisfieldresultsinminority carrierdriftacrosstheinterfaceintheoppositedirectiontodiffusion


ptype:dopingconcentration:NA

ntype:dopingconcentrationND

ptype(NA)ntype (ND)

pnjunctionformation(thermalequilibrium)DepletionregionincreasesduetomajoritycarrierdiffusionacrossthejunctionThebuiltinpotentialfromuncompensatedspacechargeincreasesasabarrierforcarrierdiffusionMinoritycarriersaresweptacrossthejunctioninthepresenceofthebuiltinfield driftcurrentEquilibriumisreachedwhenJdiff andJdrift areequalinmagnitudeandoppositeindirectionNonetcurrentflowsacrossthejunction


holediffusionholedriftelectrondiffusionelectrondrift

Jp =0

Jn =0

20

0

0

00 lnlnln||

i

DAT

n

pT

p

nT n

NNVpp

VnnVV

NeutralRegion

NeutralRegion

DepletionRegion

ptype(NA)ntype (ND)E

V0ptype

ntype

ThedepletionregionStepgradedjunction(abruptjunction)isusedforanalysisCarriersarefullydepletedinthedepletionregionNeutralregioninntypeandptypeoutsidedepletionregionBuiltinpotential:V0 =VT ln (NAND /ni2)Poissonsequation:Derivationofpnjunctionatequilibrium:


SidxdE

dxVd

2

2

2max0

max

/ln2/)(

///

iDATpn

SipASinDSiv

pAnD

nNNVxxEVEdxV

xqNxqNEdxE

xqNxqN

AD

DASi

DAA

DSi

DAD

ASipn NN

NNqV

NNqNNV

NNqNNVxxW

000 2

)(

2

)(

2

D

Si

qNVW 02 ForNA>>ND:

A

Si

qNVW 02 ForND>>NA:

2/ln2/))(/( iDATpnSinDpAnD

nNNVxxxqN

xNxN

Chargedensity(v)

Electricfield(E)

Electrostaticpotential(V)

Potentialofelectron

xp xn

xp xn

xpxn

Emax

x

x

x

V0

qNA

qND

CarrierdistributionNeutralntyperegion: Majoritycarriernn =nn0 =ND Minoritycarrierpn =pn0 =ni2/ND

Neutralptyperegion: Majoritycarrierpp =pp0 =NA Minoritycarriernp =np0 =ni2/NA

Depletionregion: n =0 p =0

NonetcurrentflowsacrossthejunctionBuiltinpotentialacrossthepnjunction: Fromholedensity: Fromelectrondensity:

Example1.10(Textbook)Exercise1.32(Textbook)


1018

1014

1010

106

102

102

cm3

xp xn

pp0

np0

nn0

pn0

V0V0

)/ln()/ln(|| 2000 iDATnpT nNNVppVV )/ln()/ln(|| 2000 iDATpnT nNNVnnVV

1.11Thepn JunctionwithanAppliedVoltage

DepletionregionForwardbias:VF reducesthedepletionregionandtheenergybarrierReversebias:VR increasesthedepletionregionandtheenergybarrier


Chargedensity(v)

xnxp

qND

qNA

x

Electricfield(E)

xnxp Emax

x

x


xnxp

V0+VR

Chargedensity( v)

xnxp

qND

qNA

x

Electricfield(E)

xnxp Emax

x

x


xnxpV0VF

Forwardbias(V=VF) Reversebias(V=VR)

SipASinD xqNxqNE //max

AD

ADSi

NNNN

qVVW )(2 0

)(

)(2 0

DAD

ASi

DA

An NNqN

VVNWNN

Nx

)(

)(2 0

DAA

DSi

DA

Dp NNqN

VVNWNN

Nx

MinoritycarrierdistributionduetojunctionbiasMinoritycarrierdistributionisinfluencedbythejunctionbiasDiffusioncurrentsexistduetononuniformcarrierdistributionJunctionbiascondition: Zerobias(equilibrium):V =0 Forwardbias:V =VF Reversebias:V =VR

Minoritycarrierdistributionforallbiasconditions:

n (p):excessminoritycarrierlifetime Ln =Dnn (Lp =Dpp ):diffusionlength

Boundarycondition: pn(x=xn)=pp0exp[(V0V)/VT]=pn0exp(V/VT) pn(x =)=pn0 np(x=xp)=nn0exp[(V0V)/VT]=np0exp(V/VT) np(x=)=np0


0/)(/

0

0/)(/

0

)1()(

)1()(

pLxxVV

pp

nLxxVV

nn

neenxn

peepxpnpT

pnT

1018

1010

102

cm3pp0

np0

nn0

pn0

1018

1010

102

cm3pp0

np0

nn0

pn0

1018

1010

102

cm3

pp0

np0

nn0

pn0

np0eV/VT

pn0eV/VT

pn0eV/VT

ZeroBias(V =0)

ForwardBias(V =VF>0)

ReverseBias(V=VR

JunctioncurrentdensityAssumenocarriergenerationandrecombinationwithinthedepletionregion:

Jn(xp)=Jn(xn)andJp(xp)=Jp(xn)DiffusioncurrentsJp andJn attheedgeofthedepletionregioncanbeobtainedby:

Totaljunctioncurrent:J(x)=Jn(x)+Jp(x)=Jn(xp)+Jp(xp)=Jn(xp)+Jp(xn) AssumeJp andJn donotchangeacrossthedepletionregion:Jp(xp)= Jp(xn)andJn(xp)=Jn(xn) Thetotalcurrentcanbeexpressedas:J(x)=Jn(x)+Jp(x)=Jn(xp)+Jp(xp)=Jn(xp)+Jp(xn)

TheIVcharacteristicsofthepn junctionThejunctioncurrentdependsonthejunctionvoltageThejunctioncurrentisproportionaltothejunctionareaThejunctioncurrentisgivenby

Saturationcurrent:


)1()(

)1()(

/0

/0

Tp

T

n

VV

n

pnx

pnpn

VV

p

npx

npnp

eLnqD

dxdn

qDxJ

eLpqD

dxdpqDxJ

)1()1()()( //00

kTqVskTqV

p

np

n

pnnppn eJeL

pqDLnqD

xJxJJ

An

n

Dp

pi

n

pn

p

nps NL

DNLD

qAnLnD

LpD

qAI 200

)1( / kTqVs eII

ReversebreakdownBreakdownvoltage:areversejunctionbiasVR=VZAlargereversecurrentflowswhenreversebiasexceedsVZForbreakdownvoltage5V avalanchebreakdownBreakdownisnondestructiveifthepowerdissipationislimited

Zener breakdownStrongelectricfieldinthedepletionregionbreakscovalentbonds,generatingelectronholepairsGeneratedelectrons(holes)aresweptintontype(ptyperegion)forareversecurrentZener breakdownnormallytakesplaceforpn junctionwithhighdopingconcentration

AvalanchebreakdownTheminoritycarriersthatcrossthedepletionregiongainsufficientkineticenergyduetothefieldThecarrierswithhighkineticenergybreakcovalentbondsinatomsduringcollisionMorecarriersareacceleratedbythefieldforavalanchereactionAvalanchenormallytakesplacefirstforpn junctionwithlowdopingconcentration

Example1.11(Textbook)


Breakdownregion

Comparisonofbreakdownmechanism


Zener breakdownAvalanchebreakdown

Electricfield(E)

Chargedensity(v)

qNA

qND


Emax

Breakdownvoltage

Electricfield(E)

Emax

Chargedensity(v)

qND

qNA


Breakdownvoltage

1.12CapacitiveEffectsinthepn Junction

DepletionorjunctioncapacitanceThedepletionwidthiscontrolledbytheterminalvoltageThechangeofterminalvoltage(dV)willresultindQ atthe

edgeofthedepletionregion capacitanceThejunctioncapacitanceduetospacechargeisCj =dQ/dVR

Cj canalsobeestimatedbyaparallelplatecapacitor:

Underforwardbiasconditions,W reduces largerCjUnderreversebiasconditions,W increases smallerCjGeneralformulaofjunctioncapacitanceforarbitrarydopingprofile:


00

00

0

0

1

2

11

2

)(2

VNNNNqAC

VVC

VVNNNNqA

wAC

VVNNNN

qW

DA

DASij

Rj

RDA

DASi

dep

Sij

RAD

ADSi

AD

AD

R

Si

R

nD

Rj NN

NNVVVqA

dVwqANd

dVdQC )(2 0

0

mRjj V

VCC )1(0

00

Chargedensity

ntypeptype

positivespacecharge(donors)

negativespacecharge(acceptors)

DiffusioncapacitanceExcessminoritycarrierstoredinneutralregionschangewiththeterminalvoltage capacitanceByintegrationtheexcessminoritycarriersatbothsides:

Smallsignaldiffusioncapacitance:

Cd islargeunderforwardbiasconditionsCd isneglectedunderreversebiasconditions

CapacitanceofpnjunctionOperatedatforwardbias:C =Cj +CdOperatedatreversebias:C CjTotalcapacitanceincreasesasamorepositivejunctionvoltageisapplied

Exercise1.40(Textbook)


IIIIDLI

DL

QQQ Tnnppnn

np

p

pnp

22

IVdV

dQC

eIeIIQ

T

Td

VVsT

kTqVsTT

T

)(

//

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Electronics Ch1

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