Drain breakdown in submicron MOSFETs-a review

www.elsevier.com/locate/microrel

Introductoryinvitedpaper

DrainbreakdowninsubmicronMOSFETs:areview

HeiWong

DepartmentofElectronicEngineering,CityUniversity,TatCheeAvenue,Kowloon,HongKong

Received6July1999

Abstract

Thispaperreviewsthephysicsandmodelsofdrainbreakdowninshort-channelMOSFET.Fourmechanisms,namely,(1)avalanchebreakdown(MImode),(2)®nitemultiplicationwithpositivefeedbackofthesubstratecurrent,and(3)parasitictransistorinducedbreakdownand(4)punchthrough,arediscussed.Sincethebreakdownmechanismshavedi󰂀erentdependenciesonitsdeviceparametersoperationconditions,thedeviceparametersshouldbeoptimizedtohavebetterreliabilitymarginsinthedown-scaledstructures.#2000ElsevierScienceLtd.Allrightsreserved.

1.Introduction

TheadvancesinVLSItechnologyhaveresultedinseveralhundredmillionsofdeepsubmicrontransistorsbeingintegratedinasinglesiliconchip.Thelatest0.17mmCMOStechnologyfor1GbitDRAMgenerationwillsoonbescaleddowntoabout0.07mmforthe64GbitDRAMlevelinyear2010[1±3].Itisnodoubtthatthereliabilityproblemshavebecomeextremelystringentinthesedevices[3±7].Recently,asurveywasconductedbytheQualityCouncil,ReliabilityTechnologyAdvisoryBoardtoprojectthereliabilityrelatedtechnologyconstraintsformicroelectronicsindustryintheyear2000[7].Accordingtothissurvey,thetop®veconcernsfromthemanufacturersaregatedielectricreliability,electromigration,electrostaticdis-charge(ESD),multilevel/dielectricintegrity,andhotcarriers.Amongstthese®veissues,fourofthemareactuallyrelatedtothehighelectric®eldreliabilityofmaterialsanddevices.Althoughtremendouse󰂀ortshavedevotedtotheinvestigationofgatedielectricre-liability[8±12],ESD[13±16]andhot-electrone󰂀ects

E-mailaddress:eehwong@cityu.edu.hk(H.Wong).

[17±29].DuringtheMOStechnologyevolutioninrecentfewdecades,thesupplyvoltagewassometimesnotscalingaccordinglyforeverytechnologygenerationbecauseofspeedrequirementsandstandardization[1].Wehaveexperiencedasmallerdownscalefactorinsupplyvoltagethanthegateoxidethicknesswhenmi-gratingfromthe1Mbittothe64MbitDRAMgener-ation.Meanwhile,thesimpleconstant-®eldrule[30,31]maynotbevalidfordeepsubmicronstructures.Asthe®elddependenciesofdeviceparametersmaybenolongerthesameasthoseofthecurrentstructuredevice.Hence,thehigh-®eldreliabilityenduranceoftheshort-channelMOSdeviceswillbestillacriticalconstrainevenaconstant-®eldscalingruleisadopted.Nevertheless,atentativescenarioforscalingofthesupplyvoltageandchannellength(seeFig.1)hasbeenproposedandmostlikelywillbeadoptedinthenext-generationintegratedcircuits[1].

Thebasicideaofthescalingrulesistoensurethebasicdevicephysicsofsmall-sizedtransistorsdoesnotchangesigni®cantly.Themostoftenandwidelyacceptedruleistheconstantelectric®eldscalingrule[30,31].Thisgoalcanbeachievedbyreducingitsgeo-metrybythesamefactorsasthesupplyvoltages.Althoughthescalingrulehasforeseenmanyproblems

0026-2714/00/$-seefrontmatter#2000ElsevierScienceLtd.Allrightsreserved.PII:S0026-2714(99)00086-4

4H.Wong/MicroelectronicsReliability40(2000)3±15

Fig.1.Proposeddrain±voltagescalingscenarioforthegiga-scaleMOStechnology[1].

inthedeviceminimization,someproblemscannotbepredictedwiththescalingruleasthedeviceshavebeenshrunktoveryclosetheirphysicalconstraints.Particularly,thereliabilitymarginsofintegratedcir-cuitshavebeencutdownsigni®cantly[1].Althoughtremendouse󰂀ortshavebeendevotedintoinvesti-gatingthescalinge󰂀ects,itisstillnotenough.Especiallyfordrainbreakdown,itisoftenmistakenthatthebreakdownvoltagewillbescalingwiththesamefactorasconstant®eldscalingruleisadopted.Recentstudiesrevealthatthedrainbreakdownvoltageisnotalinearlyscalableparameterandneedtobeoptimizedduringthedevicedesign[32,33].Table1showstwoschemesofscalingwithparametersrelatedtodrainbreakdown.Themajordi󰂀erencesbetweenthetwoschemesaretheelectric®eldandvoltagescal-ingfactors.Intheconstant-®eldscheme[30],theelec-tric®eldisconstantwhichrequiresthesupplyvoltagetobecutdownto1alandthedopantconcentration

Table1

ListofscalingrulesforparametersgoverningthedrainbreakdownQuantity

Symbol

increasesbyltimesifthetransistorfeaturesizeisscaledto1alXBothrequirementsproducedi󰂁cultiesinrealization.Fornoisemarginsandstandardizationrequirements,thesupplyvoltagemaynotbeabletoscalebytherequiredfactor.Whiletheincreaseofchanneldopantconcentrationbeyond1016cmÀ3willresultinsigni®cantmobilitydegradation.Tomeetthestandardizationconstraint,Baccaranietal.[34]pro-posedanon-constant®eldscalingscheme(seeTable1).Thisscheme,havingscaledtheelectric®eldupbylak(>1),willmakethedevicereliabilityevenworstandrequiresevenhigherconcentrationchanneldoping.Thispaperreviewsthephysicsandmodelsofdrainbreakdownandtheimpactofdevicescalingonthesemechanisms.Thephysicsunderlyingofthedrain-to-sourcebreakdownorsimplythedrainbreakdownofMOSFET'sisnowquiteclearafteralotofe󰂀ortshav-ingputinduringthelastdecade[32,33,35±45].Thedrainbreakdowncanresultfromimpactionization[32,35±40],aparasiticbipolartransistor[33,41,42],orthepunchthroughe󰂀ect[43±45].Abriefreviewontherecentachievementsonmodelingoftheimpactioniz-ationinMOSdeviceswillbegiveninSection2.Fundamentalphysicscanbefoundinthereviewpre-sentedbyMaesetal.[35].InSection3,characteristicsandtheoriesfordrainavalanchebreakdownwillbediscussed.TheactionsofparasitictransistorandpunchthroughindrainbreakdownwillbediscussedinSections4and5,respectively.

2.Impactionization

AsthefeaturesizeofintegratedMOSdevicesdecreasesfurther,thehighelectric®eldnearthedrainregionbecomesmorecrucialandhasposedalimitonthedeviceoperations,notablybyalargegatecurrent,substratecurrentandsubstantialthresholdvoltageshift.Hotelectrongenerationanddrainbreakdowncausedbytheimpactionizationinthehigh®eldregionnearthedrainandthekeyparametersfordescribing

ScalingfactorNon-constant®eld

Constant®eld1al1al1l1al

LineardimensionPotentialElectric®eld

ImpurityconcentrationCurrentL,W,toxVG,VD,fE

Na,Nd,NBIDS1al1aklakl2aklak2

H.Wong/MicroelectronicsReliability40(2000)3±155

thesethelengthmechanismsofvelocityaresaturationtheimpactregion.ionizationrateand2.1.Impactionizationrate

di󰂁cult.Exactcalculationoftheionizationrateis®eldhighapproximationThesolutionisgenerallyobtainedbyextremelythelocallowerelectric®eldsin(Wol󰂀'stwoseparatemodelcases,[46])oneforvery[47]).valuesoftheelectric®eld(Shockley'sandonemodelforregionHowever,validateinMOSthetransistorchanneliselectric®eldnearthedrainShockley'sWol󰂀'smodelnorlowneitherenoughhightoenoughvalidatetoposedelectricamodel,model.whichOkutoisaccurateandCrowell[48]thenpro-ation®eldregions.Unfortunately,inbothsincehightheandevalu-lowdownofionizationgenerallysubstrateinvolvescurrentorthedrainintegrationavalanchebreak-51],proximationthemathematicalrateoverthevelocitysaturationregionof[49±thelytical[48]istooformcomplicatedofOkutotoandbeCrowellap-widelycalculation.HencetheShockley'smodelusedinisana-stillandimpactusedionizationinmodelinginMOSFET'sthehotelectronsogenerationizationAccordingeventstricpercoe󰂁cient,toShockley'sunitlength,a,whichmodel[47],thefar.

impaction-isdeterminedisthenumberbyofionizationThe®eld,E,withthecharacteristics®eldthestrength,localelec-[47]

impactionizationratecanbeapproximatedbyB.a󰂈Aexp󰂅ÀBaE󰂆

󰂅1󰂆

whereof(1)inverseAisadistance.proportionalityAsmentionedconstantbefore,withadimensiondoesisanapproximationforthelowelectricexpressioncase,itcarriers.notBHence,consideritrequirestheenergythedistribution®ttingfunctionofbiasingtobemodi®edfordi󰂀erentprocessesparameteranddi󰂀erentAandandcm,respectivelyBareconditions.equal[52].toFor2.45electronsÂ105cmonÀ1andsilicon1.92surface,Â106V/A2.2.Impactionizationlength

(VSR)Ontheotherhand,thevelocity-saturation-regionwhereportantimpactlengthionizationorthewidthoccurs,ofistheonehigh-®eldofthemostregionim-Itparametersinshort-channelMOStransistors.strategovernsthesecurrentthedrainandhot-electronbreakdownvoltagegeneration.[32,33,53],sub-high-®eldphenomena,availableregionisprecisemodelingoftheTowidthstudyofbasedwereoneon[49,53].someAsindispensable.thosemodelsSeveralweremodelsdevelopedaredimensionalcrudeassumptionsapproximation,andtheirallofvalidity

themFig.ionization2.Power-lawmultiplicationapproximationfactor.

ofbias-dependentimpactfadesEmpiricaloutforMOSresultsthehaverecentdown-scaledMOSstructure.gateandoxidetransistorthickness,isgovernedshownthattheVSRlengthinbiasandbythechanneljunctiondepthandbasedSharma[53]developedanempiricallength.relationshipAroranotametersmodeledontheMINIMOSwell,[36]simulationresults,itwasciesintroducedhowever.toaccountSomeforofthemodelpar-izationAvarythebiasdependen-morefromdevicetodevice.

region,accuratelmodelforthewidthofimpaction-d,wasdevelopedrecently[51]whichis

󰀒

p󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁ldIld0ln

a󰂇u󰂇

u2󰂇2au󰂇1󰀓a󰂇1󰂅2󰂆

whereasaturation󰂈lld0󰂈p󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁eSitoxxjaeox󰂁

,u󰂈󰂅VDÀVDsat󰂆ald0Esandd0a󰂅LÀsourcevelocity;2ld0󰂆XESistheminimumelectric®eldforMOSFET,voltageVDSandVDsatarethedrain-to-oxide;respectively.andthedraintsaturationvoltageoftheoxchannelxisthethicknessofgatejoflength;isthedrainejunctiondepth;Listhee󰂀ectiveoxthatgatetionofloxideandsilicon,andeSirespectively.arethedielectricEq.(2)constantsindicatesdincreaseschannellength.

withthedrainvoltageandisafunc-asFig.[31]a2showsthewidthofimpactionizationregion®gure,isfunctionalsoofchannellengthandbias.Ko'smodelmationlshownforcomparison.Asshowninthedcalculatednelthelength(Ko'sandapproximation)usingtheoftenover-estimatesisconventionalindependentthelofapproxi-chan-dvalues.FornelmodellengthgivenanditinagreesEq.(2),veryldincreaseswellwithwiththenumerical

thechan-6H.Wong/MicroelectronicsReliability40(2000)3±15

Fig.saturation3.Apreciseregion.

modelforbias-dependentlengthofvelocity

resultsVforobservedthechannelrangelengthof1todownto0.5mmandVDÀDsatinVindevicewithL󰂈03X5V.mmAatlargersmallvalueerrorofisinsigni®cantDÀVDsatXAlthoughthedeviationmaybelarge,itationcarriersasatlowincalculatingdrainvoltagetheonlysubstratesmallcurrentgener-isonlylyticalbeareusedgenerated.forcomputerHowever,simulationexpressionamountofhotonly.(2)canbiasReaderdependentcalculation,modelsshouldareapproximations.bearslitistoocomplicatedtoconsiderForana-thed.Weinhavemindtothattreatmostldofastheaconstant.available2.3.Multiplicationfactor

latedTheas

avalanchemultiplicationfactorcanbecalcu-2󰂅3À1M󰂈1À

ld

0

ady

󰂅3󰂆

Furtherassumingthechannelelectric®eldisE󰂅y󰂆󰂈EScosh󰂅yald󰂆

󰂅4󰂆

andusingEqs.(1)and(2),wehave[49,50]

1󰀒

󰀓M󰂈1ÀAB󰂅VDSÀVDsat󰂆expÀldBVDSÀVDsat

󰂅5󰂆

NotethatEq.(5)isvalidfor󰂅VDSÀVDsat󰂆aldbESXingTothemakebreakdownthemathematicalvoltage,westepsapproximatetractableinEq.estimat-(5)as

Fig.down4.inSchematicMOSFET.

diagramshowingthedrainavalanchebreak-follow[32],

1󰀒VDS󰀓

M󰂈1Àa0ÀVDsatr

ldE0

󰂅6󰂆

whereE0isabout4Â105V/cmanda0isgivenby

󰀒󰀓

a0󰂈ABBldE0expÀE0󰂅7󰂆

As󰂅showninFig.3,Eq.(6)agreesover-estimatesVVForsmallvaluewellwithofVEq.(5)forDSÀDsat󰂆aldbE0XDS,Eq.(6)aareconstantstheforresultagivenofvalue(5).Theoflpowerindexand0d.

3.Drainavalanchebreakdown

causedDrain-to-sourcebreakdowninaMOSFETcancationbyin®nitemultiplication(MI)or®nitemultipli-beInimpactthewithMImodesubstrateofbreakdown,currentfeedbacktheelectrice󰂀ect®eld(MF)in[32].theriseneltoaionizationregionissu󰂁cientlylargeandgivesstratecurrentverybreakdowncurrentshouldlargemultiplicationfactorandthechan-feedbackbelargeenoughsuchthatthesub-takingplaceplace.doesOnnottheotheroccurisinsigni®canthand,beforeandtheMFbreakdowntheMIbreakdown®niteevenwhentheimpactmultiplicationmayfactortakeisbackgatebecausemodebiasthesubstratecurrentcanincreasetherenttoisofsmallbreakdownandenhancesthechannelcurrent.Thisandtheoccurswhenthesaturationcur-summariesthesubstratethephysicscurrentchanneloftheseispronounced.currentenhancementduetwobreakdownThismodes.sectiontheForcantlyelectricaMOStransistoroperatedinsaturationmode,electrons,and®eldcausesnearthedrainregionincreasessigni®-example,aretakingsweptanimpactinton-channelionization.thedrainMOSFETThegeneratedandenhancedasthe

anH.Wong/MicroelectronicsReliability40(2000)3±157

Fig.showing5.Drainnitetwomodescurrent±voltageofbreakdown.characteristicsSolidlinedepictedforatransistorofbreakdown.

modebreakdownanddashedcurveshowsthe®nitethemodein®-drainthecurrentsigni®cantlythesubstrate(seeFig.4).Ifwhereasthechanneltheholescurrent¯owentersintoassumingimpactholeareequal,thationizationwethehaveionizationregionratesisIDsatfor,electronandfurtherandID󰂈MIDsat

󰂅8󰂆Isub󰂈󰂅MÀ1󰂆IDsat

󰂅9󰂆

Sincestratetheconductivityofthesubstrateisacrosscurrente󰂀ectthesubstrate.maycauseThisalow,thesub-voltagepronouncedresultsvoltagedropincreaseswhichanceisRthechannelmodi®escurrent.thetransistorinthebodydropwillIfbethesubstratebiasingresist-andB,thevoltageVB󰂈IsubRB󰂈󰂅MÀ1󰂆IDsatRB

󰂅10󰂆

Theandsubstrate[32]

e󰂀ectsareductionvoltage,inVBthe,actsthresholdasthevoltage;back-gatenamelybiasV󰂈V󰀐p󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁Vp󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰀑

TT0ÀgB󰂇2fBÀ2fB󰂅11󰂆wherebiasVT0con.andfisthethresholdvoltagewithoutsubstrateBisthesurface-inversionpotentialofsili-theThegisthechannelreductionthebodye󰂀ectcoe󰂁cient.

changeofcurrent.inthresholdvoltageinturnenhanceschannelAlthoughcurrentdueaprecisetoVcalculationofBispossibleby

Fig.tage.

6.Plotofbreakdownvoltageasafunctionofgatevol-puttingequation,Eq.(10)intothecurrent-voltage(I±V)simulator,andyetmaybeimplementedinacircuitpresentedahere.theanalyticalForthesakeformofissimplicitytoocomplicatedandtotobee󰂀ectclearerby[32]

onthephysicalsaturationinsight,currentweassumecanbethatapproximatedthebodyhaveIDsat󰂈IDsat0󰂅1󰂇bgVB󰂆

󰂅12󰂆

wherebodyproximationbiasIDsat0andisthebissaturationanempiricalchannelcurrentwithoutofshouldbeaccurateenoughparameter.forsmallThisvalueap-becomesUsingVB.

Eq.(10)forVBandEq.(12),expression(8)ID󰂈

MIDsat0

1Àbg󰂅MÀ1󰂆RBIDsat0

󰂅13󰂆

BreakdownorvoltageaVtakesplacewhenMapproachestoin®nite0󰂅DSis

ÀVDsataldE0󰂆r󰂈1XItoccurswhenthedrainVBDI󰂈VDsat󰂇ldE0aÀ0

1ar

󰂅14󰂆

Fora®niteimpact(13),0󰂅VDSweÀhaveVDsataldE0󰂆r

󰂈1,multiplicationsubstitutingEq.(6)factorintoEq.or

ID󰂈

IDsat0

󰀒󰀓1Àar0󰂅1󰂇bgRBIDsat0󰂆

VDSÀVDsat

ldE0

Then,breakdownisalsopossiblewhenthedrainvol-

8H.Wong/MicroelectronicsReliability40(2000)3±15

tageisgivenby

VBDF󰂈VDsat󰂇ldE0Âa0󰂅1󰂇bgRBIDsat0󰂆

ÃÀ1ar

󰂅16󰂆

At(circles)Fig.thisvalue5thedenominatorofEq.(16)goestozero.forI±plotsVcharacteristicsthemeasuredin(curves)thebreakdownandcalculatedregionlengthann-channelMFdeterminedmodeof1.44ofbreakdown,mmMOSandtransistorchanneltheproductwidthwithe󰂀ectiveofchannelbg20Rmm.ForBcanbevoltageFig.andusingthecalculatedEq.(16)VforameasuredbreakdownDsatandIimental5,thecalculatedresultsagreewellDsat0withXAstheshownexper-involtagedoesindata.theSlightlyrangebetweenlargeerrors8andare9foundfordrain®eldnotagreeverywellwithEq.(5)VbecauseinlowEq.electric(6)theslowlyMOSFETregion.Also®rstnotedecreasesthattherapidlybreakdownandthenvoltageincreasesofFig.but6).(forSimilarVGb3V)asthegatevoltageincreases(seeobservedwithouttageturnaroundanyexperimentalinterpretation,resultswerealsoreported,behaviorbyMitros[54].ThegivencanmentinEqs.beexplainedofthebreakdownvol-(14)withthebreakdownvoltagecan®nitebeincausedthedrainandbyeithercurrent(16).in®niteaboutThesigni®cantmultiplicationitssaturationenhance-(MI)valueore󰂀ecttric(MF).multiplicationInthewithsubstratecurrentfeedbacklarge®eldintheimpactMIionizationmodeofbreakdown,regionissu󰂁cientlytheelec-Inenoughaddition,andresultstheinchannelaverylargecurrentmultiplicationshouldbefactor.largeinsigni®cantsuchthisandthatthetheMFsubstratebreakdowncurrentcannotfeedbackoccur.InisbeVapproximatedmodeofbreakdown,bythethedrainbreakdownsaturationvoltagecan1voltage,

TheDsat,plusaconstanto󰂀set,ldE0aÀar

(seeconstantso󰂀setdataandvalueprocessisgoverned0

Eq.(14)).parameters.fairlybytheionizationtothisrepresentedmodeofindashcurvesinFig.The5areexperimentalattributedmultiplicationBreakdownoccursfactormaybreakdown.

takeis®nite.placeThisevenmodewhenoftheimpactchannelwhenrentcurrenttheenhancementsaturationcurrentduetotheissmallbreakdownandthearethangovernedispronounced;bythenamely,channelbreakdownsaturationcharacteristicssubstratecur-currentrathercurrentthesoliddown.curvesisgateafunctionbiasaloneinFig.5ofaretheevenduegatethoughthesaturationtobias.thisDatamodeplottedofbreak-inshouldAccordingurationincreasewithtoEq.thegate(16),voltagethebreakdownasthevoltageHowever,voltagedecreasesbecauseisalmostthedirectlysecondproportionaldraintosat-VG.becomesfasterthantheincreasetermofVinEq.(16)DsatasVGdecreasewithlarger,thethegatebreakdownvoltageforvoltagetheMFturnsmodeoutof

aFig.nellength.

7.Plotofdrainbreakdownvoltageasafunctionofchan-breakdown.voltageAsdescribedinEq.Idecreasesparameters.andasisgovernedthedrain(16),bysaturationthebreakdownacurrent,Dsat0,increasestomodeincreaseReducingthebreakdownofthevoltagebulkresistivitynumberofdeviceduetowillthehelpimentofbreakdown.ItwasfoundinMitros'exper-MFvoltage[54]almostincreasesthatforp-channeldevices,thebreakdownstantwaso󰂀setequalslightlywiththegatevoltageandisandtodrainsaturationvoltageplusacon-follows.observed.channelForn-typeThesenosubstratesiliconobservationscurrentfeedbacke󰂀ectsubstratecanthatbeexplainedaslowdition,anddevices,thevoltagethedropbulkVresistivityisgenerallyusedinveryp-Bwillthanduethattheofionizationtheelectrons.rateAsofholesbeveryismuchsmall.smallerInad-drainFig.tothe7plotssubstratethecurrentaresult,nobreakdownchannel-lengthfeedbackdependencewasobserved.oferalthetrendbreakdownthatthevoltagebreakdownforVV.Thereisagen-theG󰂈1longchannelbychannellengthdevices.andSimilarreachesvoltageresultsasaturatedincreaseswithwerealsovalueforbreakdownMitros[54].IntheworkpresentedinRef.reportedgivendown,byEqs.voltage±channel(14)and(16).lengthForMIrelationships[32],themodeofbreak-areincreasesthetheasbreakdownthedrainvoltageofshort-channeldevicesofbreakdownbreakdown,channelbecomesthechannel-lengthshorter.saturationWhereasvoltageincreasesasdependenceforMFofmodetheRvoltageisgovernedbybothVDsatandsistanceBIDsatXNotethatthesaturationcurrentisapproximatelyproductisproportionalindependenttoofLchannelandÀ2providedwidthbulkre-that

andH.Wong/MicroelectronicsReliability40(2000)3±159

Fig.8.SchematicdiagramofPBT-inducedbreakdown.

theAndchannel-lengthsmalleratlowmodulatione󰂀ectisinsigni®cant.breakdownthangatethebias,seconde.g.termVG󰂈1V,VDsatismuchterm.assumptions.ThetheoreticalvoltageisplotgovernedinFig.mainlyinEq.6isbasedby(17)theandonsecondthethesemFordevicewithchannellengthof0.44Lm,2e󰂀ect.lawthebreakdownbecauseofvoltagethechannel-lengthdivergesslightlymodulationfromtheionizationInaddition,theelectroninjectedintothewillregionbytheparasitictransistor[33,41,42]impactnelalsoreducethebreakdownvoltageofshort-chan-lationFordevices.

short-channeldevices,thechannel-lengthmodu-channele󰂀ectbecomessigni®cantandwillenhancetheisdencereduced.current;Thus,consequently,thethebreakdownvoltagefound[38]asthatisthenolongerpoweraccurate.lawchannel-lengthRecentstudydepen-[32]whichafunctionofbreakdownthedrainvoltagesaturationcouldcurrent,beexpressedIDsat0,wellcharacteristicsasisthegovernedthresholdbythevoltage.gatevoltage,Henceaspecttheratio,asproperlyofashort-channeltransistorbreakdowncanbethatHowever,thedescribeddrainusingtheproposedmodelsprovidedsiticpunchthroughtransistorforverysaturationcurrentismodeledprecisely.[8]short-channeldeviceswherepara-ordi󰂀erentMFmode[43±45]inducedofbreakdownmayoccurbreakdownbefore[33,41±44]theMImodeordownI±Vtheoriescharacteristics.areneededtakingformodelingplace,completelythebreak-4.Parasitictransistor

downParasiticcouldbipolaronlytransistorbefound(PBT)inainducedshort-channel

break-MOSFETtutednarrowbysource,wheresubstratethebaseandwidthdrain,oftheseePBTFig.(consti-nounced.thatrentWhenthethecollectorPBTiscurrentofPBT8)isispro-soimpactwilltheionizationenhancetheturnon,thecollectorcur-regionchargecarriers¯owingintothe[41].drain-to-sourcebyThePBT-inducedbreakdownnearthedrainandreducesbreakdownvoltagehasbeensigni®cantlymodeledcurrentHsuetdropisal.calculated[41].However,basedonintheirthemodel,thedraingivenacrossmodelforhascalculatingthesubstrateovercomethisthedrawbackbreakdownandnoexplicitmeasuredvoltage[33].

voltage.formulaArecentistheForaMOStransistoroperatedinsaturationmode,dropsubstratesubstrate)acrosscurrentmaycauseapronouncedvoltagerentjunctionthesubstratesuchthattheemitter(source-proximated(Iisforwardlybiased.Thetotalcur-D)enterstheimpactionizationregioncanthebyIbeap-Dsat󰂇IC(whereICisthecollectorofernedparasitictransistor).Thecollectorcurrentaregov-reversebythecommon-baseampli®cationfactoraBandoftheparasiticsaturationtransistorcurrentandofthecanemitterbeapproximatedjunction(IasES)󰀒IC󰂈aBIESexp

qIsubRB

󰀓kT󰂅17󰂆

Assumingproductcanunitybeapproximatedemitterinjectionbye󰂁ciency,theaB±IESaBIES

󰂈qAjDnn2LinNAB

cschh

LLn󰂅18󰂆

Fig.istics.

9.PlotofsimulatedPBT-inducedbreakdowncharacter-10H.Wong/MicroelectronicsReliability40(2000)3±15

whereAj,ni,NAB,Larethee󰂀ectiveareaofemitter±basejunction,intrinsiccarrierconcentration,substratedopingconcentration,andthee󰂀ectivechannellengthoftheMOSFET,respectively.Dn,Lnarethedi󰂀usioncoe󰂁cientanddi󰂀usionlengthofelectroninthesub-strate,respectively.ThedraincurrentatbreakdownisID󰂈M󰂅IDsat󰂇IC󰂆

󰂅19󰂆

IDsatZ󰂇lnZ󰂇1󰂇ln󰂅aBIES󰂆󰂈0󰂅20󰂆

whereZ󰂈M󰂅MÀ1󰂆qRBakT

UsingEq.(6),thebreakdownvoltagecanbeap-proximatedby[33]

h󰀐p󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰂁󰀑iÀ1ar

VBDBIVDsat󰂇ldE0a01󰂇qRBakTZ

󰂅21󰂆

PuttingEq.(17)intoEq.(19)andconsideringdIDadM4Iatbreakdown,wehave[33]

Fig.9showsthebreakdowncharacteristicsforann-channelMOStransistorwithchannellengthof0.85mmandsubstrateresistanceof100OsimulatedusingMINIMOS.Twomodesofbreakdowncanbe

Fig.10.ChannelcarriersdistributionduringMFandPBTmodesofbreakdown.(a)electrondistributionwhenparasitictransistoriscuto󰂀;(b)electrondistributionwhenparasitictransistoristurnedon;(c)holedistributionwhenparasitictransistoriscuto󰂀;(d)holedistributionwhenparasitictransistoristurnedon.

H.Wong/MicroelectronicsReliability40(2000)3±1511

Fig.10(continued)

observedinthis®gure.ForVG󰂈0X5V,onlyonebreakdownhappensandthebreakdownvoltageisabout8.5V.ThisbreakdownisduetoMFbreakdownmechanism.Asthegatevoltageincreases,thebreak-downoccurstwotimesforsamegatebias.Fordraincurrentlessthan0.6A,the®rstbreakdownoccursandthebreakdownvoltagedecreasesasthedraincurrentorgatevoltagerises.ThisphenomenoncanbeexplainedwiththeMFbreakdownmechanismaspro-posedearlier[32].Fordraincurrentgreaterthan0.6A,thesecondbreakdown(PBT-inducedbreakdown)occurs.Unlikethe®rstbreakdown,thebreakdownvol-tageincreaseswithVG.AsatlargeVG,IDsatincreasesandZinEq.(21)decreases.Consequently,thebreak-downvoltageincreases.

Fig.10showsthee󰂀ectofparasitictransistoronthedistributionoflateralelectroncurrentdensity.InFig.10(a),thebiasconditionsareVG󰂈1VandVD󰂈7VwhichcorrespondstotheMFmodeofbreakdownshowninFig.9.Thelateralelectroncurrentdensityismainlycontributedbythechannelcurrent.InFig.10(b),thetransistorisoperatedatVG󰂈1VandVD󰂈8X4V.Underthesebiasingconditions,theparasitictransistor(PBT)isturnedon.ThecollectorcurrentofPBT(current¯owbeneaththeactivechannelregion)contributesthemajorcomponenttothelateralelectron

12H.Wong/MicroelectronicsReliability40(2000)3±15

VG󰂈1X0V.Thesolidlineshowninthe®gureiscalcu-latedusingEqs.(20)and(21)withe󰂀ectivecross-sec-tionalareaofparasitictransistor(i.e.parameterAjinEq.(18))asa®ttingparameter.Furthere󰂀ortsareneededforpreciseandsystematicestimationofthisparameterandthechangeofelectric®elddistributionsandtheimpactionizationlengthsmustbetakenintoaccountfordi󰂀erentdevices.Nevertheless,ourtheor-eticalcalculationpredictstherighttrendofthechanneldependenceofthePBTbreakdownvoltage.ThedecreaseofPBTbreakdownwithshrinkingthechannellengthisduetoseveralmechanismstakeplaceintran-sistor.Asthechannellengthisreduced,boththeemit-tercurrentofthePBTandthedrainsaturationcurrentwillincrease.Consequently,moreelectron±holepairsaregeneratedandthebreakdownvoltageisreduced.5.Punchthrough

Fig.11.Plotofbreakdownvoltage(PBTmode)asafunctionofchannellength.

current.ThelateralelectroncurrentdensityisatleastoneordergreaterthanthatatthebiasgiveninFig.10(a).Amorecompletedpicturecanbeseenbyview-ingthetransversalholecurrentdensitydistribution.AsshowninFig.10(c),whentheparasitictransistorisincuto󰂀mode,holecurrent¯owingfromdrainregiontothesubstrateregioncanbeobservedbecausetheMOStransistorisalreadyoperatedinthebreakdownregionwhereholesaregeneratedintheimpactionizationregionnearthedrain.WhenthePBTisturnedon(seeFig.10(d)),holecurrent¯owingfromdraintosub-strateisenhancedremarkably.InadditiontheholeconcentrationnearthesourceoftheMOStransistorisreducedsigni®cantlybecausethesourcenowactsastheemitteroftheparasiticnpntransistor.

Fig.11plotsthePBTbreakdownvoltageasafunc-tionofchannellengthforRB󰂈100Oat300Kand

Punchthrough(PT)hasbeenoneofthemajorcon-straintsforfurtherMOStransistorsminiaturization[43±45].EitanandFrohman-Bentchkowsky[45]furtherfoundthatthepunchthroughwilloccuratlowdrainbiasesduetothesurfaceminoritydi󰂀usioncur-rentwhenthedrain/sourcedepletionregionscontacted.Theminoritycarrierinjectioncanbefurtherenhancedwiththeband-bendingduetogate-inducedsurfacespacecharges.Punchthroughe󰂀ectisparticularlysig-ni®cantinshortchanneldeviceswithalowchanneldopingconcentration.Theoretically,thepunchthroughconditioncanbeestimatedbyequatingthedrainde-pletionregionwidthandthee󰂀ectivechannellength.However,punchthroughcouldoccuratadrainvoltagefarbelowthatrequiredformakingthedepletionregionsconnectedbecauseofdraininducedbarrierlowering(DIBL)[45,55].Phenomenologically,punch-throughwasde®nedasthevalueofdrainvoltageatwhichthedraincurrentreachesavalueof1mA[56].Thisiscertainlynotagoodde®nition.Itcannotbeusedtodi󰂀erentiatepunchthroughwithothermechan-

Table2

Comparisonofthedevice-parameterandoperation-conditiondependenciesofvariousbreakdownmechanismsParameters

BreakdownmodeIn®nitemultiplicationbreakdownvoltage

ChannellengthqSubstrateresistanceqGatevoltageQTemperatureQ

q±W±

FinitemultiplicationbreakdownvoltageqqQqw

PBT-induced

breakdownvoltagewWqQ

Punchthrough

characteristicvoltageqQqw

H.Wong/MicroelectronicsReliability40(2000)3±1513

isme󰂀ectandwithfornumericalatall.evenThedoesnotconsiderthechannelwidthsimulationpunchthrough[43,44],e󰂀ectsanareanalyticaloftenstudiedhowever.predictingimentalTablethe2summarizespunchthroughthevoltagenumericalisstillandlacking,modelexper-studiesresultstheliteratures[43,45].Althoughthesepunchthroughcannotparametervoltage,providethemethodqualitativeforestimatingresultsonthepunchthroughdependenciese󰂀ectinthearedevicestillusefuldesign.tominimizethethe6.Concludingremarks

MOSFETVariousbreakdownincreaseshavephenomenainshort-channelvaluesofdraincurrentbeenbeyondreviewed.thenormalThesigni®cantoperationmode),couldof(2)®nitebeduemultiplicationto(1)avalanchebreakdown(MItorthesubstratecurrent(MF),andwith(3)positiveparasiticfeedbacktransis-(PT).(PBT)dependenciesThoseinducedbreakdownbreakdownmechanismsand(4)havepunchthroughdi󰂀erentconditions.

onthedeviceparametersandoperationfourTable2summarizesthevariousmodesdiscussedtheandpunchthroughmechanisms.willVoltagedependenciesreducedofallaccordinglybreakdownoftheasbreakdownchannellengthbecomesshorter.However,thebreakdownvoltagedecreasesdecreasesofthefaster®niteandmultiplicationPBTmodeofofreducingMF,PBT,slower.andThePTbreakdownmodesvoltagedegradationbreakdownchannelthesubstrateresistancecanorbeincreasingsuppressedthebyincreasedoping.thechannelAsmentioneddopingtoearlier,higherthanitis10unwise16cmtoÀ3foraddition,signi®cantmobilitydegradationcannotwefoundthattheMImodewillofencounter.breakdownInandmaintainconstant-®eldbeimprovedscalingbyvaryingruleshouldthechanneldopingdenceMIofitsbreakdowncharacteristics.beappliedtocharacteristics,Fortemperaturedepen-turemodeofbreakdownisaweakfunctionitisshownthatpunchthroughonly.Therises.voltagebreakdownvoltageofMFofmodetempera-andperatureThisobservationisdecreasemainlygovernedasthetemperaturebytherent.temperatureThedependencebreakdownofIandthesubthresholdtem-Dsatcur-breakdownincreases.WhereasvoltagefallsforPBTquicklymode,asthethedueisticstothevoltagestrongincreasestemperatureasthedependenttemperaturerisesingitsofofbipolartransistor.Itwasreportedthatcharacter-operat-temperatureperformanceMOSdevicesigni®cantly.incryogenicHowever,regionwouldtheimprovedistinctcharacteristicsdependenciesFinally,itshouldcallforbeacarefulonthesenotedthatreviewdrainbreakdownmostonofthistheissue.device

modelingbevalidityvalid®eldofforbasedextendingdeeponsubmicronsomeapproximationsandmaynotShockleydevices.modeltoRegardlesshighelectrictherate[57].inregion,ballisticallyTheSiitwasfoundthattheimpactionizationfractionhasgreatofhigh-anisotropyenergyinlowenergyregionmoretravelalongthechannelcarriersareexpectedwhichquasi-tobeconstantsigni®cantmodel®eldscalingindeeprulessubmicrontransistorseventheextremelyforimpactionizationareisexpectedused[58±60].whichAnewimpactgoingionizationdi󰂁cult.constantsAlternatively,anewsetofShockleywillbedevicestousetheShockley'sismodelindispensableinifwearedeep-submicronwithanacceptablecateddeviceaccuracy.Itdeep-submicronseemsthatthemustbetoobtainedbemodeledfromaccurately.characteristicssimulations.

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