Nanogap Electrodes

www.advmat.de

REVIEWNanogapElectrodesByTaoLi,WenpingHu,*andDaobenZhu*

switches[6,7]andtransistors,[8–10]havebeen

accordinglydesignedandreported.AlltheNanogapelectrodes(namely,apairofelectrodeswithananometergap)areaboveaspectsrendermoleculesasidealfundamentalbuildingblocksforthefabricationofnanometer-sizeddevicescandidatesforthenextgenerationofandcircuits.Theyarealsoimportanttoolsfortheexaminationofmaterialelectronics.propertiesatthenanometerscale,evenatthemolecularscale.Inthisreview,Despitealltheseadvantages,therethetechniquesforthefabricationofnanogapelectrodes,thepreparationofremainmanychallengesbeforemolecular

computerscometoreality.Themainassembleddevicesbasedonthenanogapelectrodes,andthepotentialobstacleliesinhowtointegratenanometer-applicationofthesenanodevicesforanalysisofmaterialpropertiesaresizedmoleculestomacroscopicelectronicintroduced.Thehistory,theresearchstatus,andtheprospectsofnanogapcircuits.Therearemainlytwoapproacheselectrodesarealsodiscussed.forwiringmoleculesbetweenelectrodes.

Onemethodistomaketop-contactjunc-

tions,whichincludesscanningprobe1.Introductionmicroscopy(scanningtunnelingmicroscopy(STM)andcon-

ductingatomicforcemicroscopy(AFM)),[11–22]crosswire

Motivatedbytherapiddevelopmentofsemiconductortechnol-junctions,[23–25]mercurydropelectrodes[26,27]andthermallyogies,andguidedbythefamousMoore’sLaw,[1]thepaceatwhichdepositedmetal?lms.[6]Alldevicesmanufacturedbythiskindofthenumberoftransistorspersquareinchonintegratedcircuitmethodcanbecategorizedas‘prototypedevices’,whichareveryboardswoulddoubleabouteveryoneandahalfyearshasbeenusefulforfundamentalinvestigationsandhavealreadyprovidedkeptformorethan40years.Nowadays,thefeaturesizeofthemanyimportantresults.[4–7,11–27]However,thesedevicesarefartransistorshasbeenreducedtobelow50nmandthescalinghasfrompracticalapplications,aswecannotimagineananometerledtoanunprecedentedlevelofintegrationwithapromisinglydevicecarryingahugescanningprobemicroscopy(SPM)systemhigherperformanceandlowerpowerconsumption.However,orothersystems.Theotherwayutilizesnanogapelectrodes[28–32]thislevelofscalingisgraduallyapproachingtheminiaturizationtoformmetal/molecule/http://wendang.chazidian.comparedwiththelimitsofsilicontechnology,whichisforeseentoface‘prototypedevices’,devicesbasedonnanogapelectrodeswithfundamentallimitationswithinadecade.conductivemetalnanowirecircuitsandfunctionalmoleculesAsinglemolecule,evenanatom,representstheultimatelimitinsertedinthedesiredpositionhavethepotentialabilitytorealize[2]thatwecanhandlesofar.Asearlyas1974,AviramandRatnersuperintegratedcircuits,soaremorelikelyusedinpracticalhadpredictedthatindividualmoleculessomedaywouldbeusedapplications.Moreover,becausethenanogapelectrodesareascircuitelementsindevicesandthedreamofutilizingfabricatedbeforethemolecularcomponentsaresubsequentlymoleculesasfunctionalunitsinelectroniccircuitshasmotivatedinserted,thejunctioncanbecharacterizedwithandwithoutresearchersforyears.Ifthiscomestrue,itwouldbepossibletomoleculesinplace,whichfacilitatesthedistinctionoftheintegratetransistorsinthebillions.Themolecular-baseddevicesintrinsicmoleculeproperties.Furthermore,asmostnanogap[3]possessuniqueadvantagesforelectronicapplications,suchaselectrodespresentaplanarcon?guration,itwouldbeeasierforlowercost,lowerpowerdissipation,higheref?ciency,abilityofhigherdensityintegrationandtotaketheunderlyingsubstrateasself-assemblyandrecognition,distinctopticalandelectronicagatecontacttotunetheelectricalpropertiesofthemolecularproperties,andsynthetictailoringabilitybyelaboratechoiceofcomponents.Becauseofthesuperiorcharacteristicsandgeometryandcomposition.Avarietyofspeci?celectronicpromisingfuture,nanogapelectrodeshaveattractedworldwide[4,5]functionsperformedbysinglemolecules,includingrecti?ers,attentionfornearly20years.Manystudieshavebeenreported

andsigni?cantprogresshasbeenmadefromfabricating

techniquestodeviceapplications.Inthisreview,wediscuss[*]T.Li,Prof.W.Hu,Prof.D.Zhuthemanufacturemethodsofnanogapelectrodes,theintegrationBeijingNationalLaboratoryforMolecularSciences

KeyLaboratoryofOrganicSolidsofmolecularcomponentsfornanodevices,andthepotentialInstituteofChemistryapplicationsofnanogapelectrodesformaterialanalysis.ChineseAcademyofSciences

Beijing100190(PRChina)

E-mail:huwp@http://wendang.chazidian.com;zhudb@http://wendang.chazidian.com

T.Li

GraduateSchoolofChineseAcademyofSciences

Beijing100039(PRChina)2.MethodsofFabricatingNanogapElectrodesTypicaldimensionsoftargetmoleculesarewellbelow5nm,so

fabricatingelectrodeswithseparationsthataresuitableforDOI:10.1002/adma.200900864

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speci?cmoleculesisaverychallengingmissionbecauseitgoesbeyondthecapabilityoftraditionalmicrofabricationtechnologies.Also,ifthegapistoosmall,itwouldbeverylikelytopositthemoleculeinatenseanddistortedstate,resultinginunexpectedperformances.So,theprecisecontrolofthespacingmakesitREVIEW

TaoLigrewupinShandongprovince,China.HereceivedhisB.Sc.degree(2005)intheSchoolofMaterialsandEngi-moredif?culttopreparesuchkindsofdevices.DespitetheneeringfromBeiHangUniver-obstacles,severaleffectiveandcreativemethodsoffabricatingsity.HethenjoinedtheInstitutenanogapelectrodeswithcontrolledspacinghavebeenreportedinofChemistry,ChineseAcademythelastfewyears,includingmechanicalbreakjunctions,[33]ofSciencesasaPh.D.candi-electron-beamlithography,[34]electrochemicalplating,[35]electro-date.Hisresearchfocusesonmigration,[36]focusedionbeamlithography,[32]shadowmaskelectrochemistryandmolecularevaporation,[9]scanningprobeandatomicforcemicroscopyelectronics.

lithography,[37]on-wirelithography,[38]molecularrulers[39]etc.Alltheabovemethodshaveprovidedpromisingresultsandhavetheirowncharacteristics.Differentmethodsarefrequentlycombinedtoobtainadesiredcon?guration.Forexample,WenpingHuisaProfessorofelectron-beamlithographyisoftenusedto?rstlyrealizenanogaptheInstituteofChemistry,electrodeswithspaceat10–20nm,andthenothertechniques,ChineseAcademyofSciences.suchasshadowmaskevaporation,areimplementedtofurtherHereceivedhisPh.D.fromthenarrowthegapwidthtoa1!5nmscale.Institutein1999.HethenjoinedOsakaUniversityasaresearchfellowofJapanSociety2.1.MechanicalControllableBreakJunctions

forthePromotionofSciencesandStuttgartUniversityasanAmechanicalcontrollablebreak(MCB)junctionwas?rstAlexandervonHumboldt.InintroducedbyMorelandandhisco-workersfromtheUS2003heworkedforNipponNationalBureauofStandardstoformanelectrontunnelingTelephoneandTelegraph,and

junction.[40]ThismethodwasthenadoptedcreativelybyReedthen

returnedto

the

institute.Hisresearchfocusesonetal.fromYaleUniversitytofabricatenanogapelectrodes,whichmolecularelectronicsandhehasmorethan120refereedyieldedelectrodeswithaseparationofseveralnanometers.[33,41]Apublications.

schematicdrawingofthesamplemountingoftheMCBtechniqueispresentedinFigure1.Anotchedmetallicwireis

DaobenZhuisaprofessoroftheInstituteofChemistry,ChineseAcademyofSciences.Hewasselectedasan

academicianoftheChineseAcademyofSciencesin1997.Hegraduatedin1968fromtheEastChinaUniversityofScienceandTechnology.AsavisitingscientistheperformedresearchwithProf.HeinzStaabintheMax–PlanckInstituteforMedi-calResearchinHeidelbergduring1977–1979and1985–1986.Heservedasvice-director(1988–1992)anddirector(1992–2000)oftheInstituteofChemistry,andasvice-presidentofNationalNaturalScienceFoundationofChina(2000–2008).He

isthevice-presidentoftheChinese

ChemicalSociety.Hisresearchinterestsincludemolecularmaterialsanddevices.

Figure1.Thesamplemountinginathreepointbendingcon?guration.gluedtoanelasticsubstrate,whichservesasthebendingbeam.Thebendingbeamconsistsof?exiblephosphorusbronzecoveredwithaninsulatinglayerofcapton.ThejunctionisformedbybreakingtheelectrodeThesubstrateisbentbypushingitscenterwithadrivingrodandmaterial.Thisisachievedbybendingthebeam.Theelongationofconsequentlythenotchedwireisfractured,afterwhichantheungluedsection,u,isconcentratedonthenotchandwillresultinaadjustabletunnelinggapcanbeestablished.Thesurfacescanbefractureofthematerial.Avoltageonthepiezoelementisusedfor?nebroughttogetheragain,andthedistancecanbecontrolledbyaadjustmentofthecouplingbetweenthetwoelectrodes.Reproducedwithpiezoelectricelement.Thebreakingprocessismostlyconductedpermissionfrom[41].Copyright1996IOPPublishingLimited.underlowtemperatureandhighvacuumconditions,andthis

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guaranteestwoatomicallycleansurfaces.Any

elasticsubstratecanbeusedinprinciple,

whilethatmadeofphosphorbronze[28,42,43]is

oftenchosenbecauseitismore?exible,

compatiblewith?neelectronbeamlithogra-

phy,andallowsamuchwiderrangeofmetals

tobestudied.Aninsulatinglayerisdeposited

onthesubstratebeforethemetallicnanos-

tructureistransferredusingstandardelectron

beamlithographytechniques.Thenotched

sectionisusuallymadewithascalpelby

rollingitoverthe?lament.Othermethods

mayalsobeinvolveddependingoncertain

propertiesofdifferentmetals.Forexample,a

sparkmethodwasusedwhendealingwith

thesemimetalSb.[44]Toensurethatthe

notchedsectionwasunglued,selectiveetching

(e.g.,isotropicreactiveionetching)[28]of

theinsulatinglayerwasoftenperformedto

produceametallicbridgesuspendedbetween

anchoringpads.TheMCBtechniqueisvery

stable(downto0.2pmhÀ1).[43]Moreover,the

contactsizecanbecontinuouslyadjusted

underthecontrolofanultra?nepiezoelectric

componentwithoutpollutingthejunction.In

addition,afterthetargetmoleculeisanchoredFigure2.a)Schematicofthemeasurementprocess.A)Thegoldwireofthebreakjunctionbeforebetweenthegap,themechanicalstressisbreakingandtipformation.B)Afteradditionofbenzene-1,4-dithiol,SAMsformonthegoldwire

surfaces.C)Mechanicalbreakageofthewireinsolutionproducestwoopposinggoldcontactsthatcontrolledaswell.

MCBjunctionsarewidelyusedforsingle-arecoveredbyaSAM.D)Afterthesolventisevaporated,thegoldcontactsareslowlymoved

togetheruntiltheonsetofconductanceisachieved.Steps(C)and(D)(withoutsolution)canbemolecule,evensingle-atomdevicesincludingrepeatednumeroustimestotestforreproducibility.b)Aschematicofabenzene-1,4-dithiolateone-atommetallicpointcontacts[42–50]andSAMbetweenproximalgoldelectrodesformedinaMCB.ThethiolateisnormallyH-terminatedmetal–molecule–metaljunctions.[28,33,41,51–57]afterdeposition;endgroupsdenotedasXcanbeeitherHorAu,withtheAupotentiallyarisingvanRuitenbeeketal.[42–49]workdistinguish-fromapreviouscontact/retractionevent.ThesemoleculesremainnearlyperpendiculartotheAu

ablyinthis?eld,especiallyonmakingatomicsurface,makingothermolecularorientationsunlikely.Reproducedwithpermissionfrom[33].sizecontactsandtunneljunctions.TheCopyright1997Science.

metallicpointcontactsweremadebybringing

twofreshlypreparedelectrodesbackinto

contactunderpreciseadjustmentofthepiezo

element.Asforsingle-moleculedevices,moleculesareoftenenhancedRamanscattering(SERS)methodtocharacterizeself-assembledtointegratebetweenmetalleads.Reedandmoleculesinananogapwithacontinuouslyadjustablegapwidth.[33]TheSERSintensitydependedcriticallyonthegapwidthandtheTouretal.successfullyself-assembledbenzene-1,4-dithiol

incidentlightpolarization,whichindicatedsuccessfuldetectionmoleculesonagoldwirebeforetheMCBprocess.Mechanical

ofthesamplemoleculesinsidethegap.breakageofthewireinsolutionproducedtwoopposinggold

AlthoughtheMCBmethodisveryusefulforfundamentalcontactsthatwereself-assembledmonolayer(SAM)-covered.The

investigation,suchaselectronictransportatamolecularscale,ittipswerethenslowlymovedtogetheruntiltheonsetof

isnotfaciletofabricatehighlyintegratedmoleculardevicesconductancewasachieved,whichindicatedthatasingle-[56]becauseoftheconstraintofthepiezoelectriccomponents,andmoleculejunctionwasmade(Fig.2).Rieletal.investigated

itisnoteasytobuilddeviceswiththreeorevenmoreelectrodes.theconductanceswitchingbehaviorofsinglebipyridyl-dinitro

Italsoappearstobedif?culttocontrollablyfabricaterelativelyoligophenylene-ethynylenedithoil(BPDN-DT)moleculescon-

largegaps.tactedbytwosymmetricleadsusingtheMCBtechnique.The

metal–singlemolecule–metalsystemcanbecontrolledand

reversiblyswitchedbetweentwodistinctstatesevenafter2.2.ElectrochemicalandChemicalDepositionforperformingmorethan500positiveandnegativesweeps

http://wendang.chazidian.comparingwiththeexperimentalresultsfrom

bipyridyloligophenylene-ethynylenedithiol(BP-DT)molecules,

theyconcludedthattheswitchingbehaviorwascausedbytheElectrochemicalandchemicaldepositionmethods,combinednitrogroupsofBPDN-DT,whicheliminatedtheaffectofwithstandardlithographytechniques,provideasimple,accurate,electrodepropertiesormolecule–metalinterfaces.Morerecently,andreproduciblewayforthefabricationofnanogapelectrodes.[57]Tianetal.distinguishablycombinedMCBwithasurface-Theinitialelectrodeswitharelativelylargegaparefabricated

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conventionallithographytechniquesonsub-

strates,e.g.,Si/SiO2.Thegapisthennarrowed

downtoananometerorevenatomicscaleby

depositingspeci?catomsontothelithogra-

phicallyde?nedelectrodes.Also,theprocessREVIEW

canbereversedinthedissolutionmodefor

controlledetchingofatomsfromthejunction

tosolution,thuswideningthegapbacktothe

sub-micrometerscale.

Thismethodrequiresnospecialtechnique

orsystem,[58]andcanconvenientlyprepare

gapsthatrangefromseveralangstromsto

10nm,whichisthebestscalefor?tting

desiredmoleculesornanocrystalsfornano-

devices.Thesimplicityandrobustnessofthe

techniqueprovidesapromisingmethodfor

thefabricationoflarge-scaleandhighly

integratednanodevices.Furthermore,the

gapdimensioncanbesimultaneouslymoni-

toredandpreciselycontrolledbyusingaFigure3.SEMimagesofthesamplespreparedat3kHzwithdifferentDtvalues:a)Dt¼9s,feedbacksystem.Thefeedbacksignal,takingd¼26nm;b)Dt¼25s,d¼16nm;c)Dt¼42s,d¼7nm;d)Dt¼62s,d%1nm.Reproducedanelectroplatingmethodasanexample,iswithpermissionfrom[31].Copyright2005Wiley-VCH.

frequentlythecurrent?owingthroughthegap

electrodes,whichismonitoredduringthe

depositionprocess.[35,59–66]Whentheelectrodesareveryclosebutdeposition,thefabricationprocesswasself-terminated.Anothernotyettouching,themonitorcurrentisextremelysensitivetoadvantageoftheelectrochemicaldepositionmethodistheabilityelectrodedistance,soitiseasytocontroltheseparationonantofabricateasymmetricnanogapelectrodes(e.g.,agoldandaatomicscalebystoppingtheelectrodepositionprocessatplatinum?nger)andnanogapelectrodeswiththreeormoreprede?nedconductancevalues.Unlikeacurrent-feedbackmode?ngers,[61]asdemonstratedbyKashimuraetal.,whichwereboththatusesbothfacingelectrodesasaworkingelectrode(WE),Tiandif?culttoachievewithconventionallithographictechniquesandetal.[58]inventedamethodforthecontrollableelectrochemicalsuperiortotheMCBorSPMtechniquesdiscussedabove.fabricationofelectrodeswithananometer/angstrom-sizedgapWhenperformedwithgold,thedrawbackofelectroplatingliesusingthepotentialdistributionintheelectricdoublelayerasinthedif?cultyofobtainingasimplegoldelectrolyteandspecialfeedback,whereintwofacingelectrodesservedastheworkingcareshouldbetakentoavoidgeneratinghighlytoxichydrocyanicelectrodeandreferenceelectrode(RE),respectively.Thepotentialacidgases.Accordingly,UmenoandHirakawa[69]introducedadifferencebetweentheWEandtheRE(Vgap)wasmonitoredsimpleandcost-effectivewaybyusingan‘iodinetincture’asancontinuouslyduringtheelectrodepositionprocess.Thevalueofelectrolyteforgoldelectroplating,whichwasfreeoftoxicVgapremainedconstantuntilthegapwasnarrowedtobelowacompoundsorstrongacids.Kervennicetal.[59]foundthatcertainvalue,andthenitdecreasedwithtimeand?nallycomparedwithgolddeposition,Ptpromisedahigherreprodu-approachedzerotoindicateaconductingstate.Thisresultcibilityandstabilityoftheelectrodes,andpairsofplatinumindicatesthatVgapcouldalsobeusedasafeedbacksignaltoelectrodeswithaseparationbetween20and3.5nmwerecontrolthegapwidth.Liuetal.[31,67]?nelytunedtheelectrodegapobtainednicely.

widthbyutilizinghigh-frequencyimpedanceinfeedback.TheyComparedwiththeelectroplatingmethod,surface-catalyzedstudiedthealternatingcurrent(ac)voltagefrequencydependencychemicaldepositionrepresentsasimplerwaytoobtainnarrowonthe?nalgapsizeandobtainedgapsof30nmbyusingagapelectrodespre-patternedbyconventionallithography,asithigh-frequencyfeedbacksignalwithhighaccuracyandreprodu-doesnotevenhavetocarryanexternalcircuit.Bylocalizingacibility.Thegapsizeisaffectedbythefrequencyandamplitudeofcatalystontheinitialelectrodes,themetalatomscanbeselectivelytheacsignalanditcanbe?nelytunedtoaround1nmbysimplydepositedontotheelectrodesurfaceassistedbyreductiveagents.controllingthesubsequentdepositiontime(Fig.3).Taoetal.[68]Onejustneedtoimmersethechipsintoastocksolutionachievedniceatom-sizegapsandcontactsbetweenelectrodescontainingmetalionsandamildreducingagent,andthegapfabricatedwithaself-terminatedelectrochemicalmethodbaseddistancedependsonthereactiontimeandreactantconcentration,onabuilt-inself-terminationmechanism.Anexternalresistorwhichendowsthismethodwithcontrollabilityandmass(Rext)wasconnectedtooneoftheelectrodesandthe?nalgapproducibility.Guandcoworkers[70]?rstlymodi?edthegoldwidthcouldbepredeterminedbyelaboratelychoosing1/Rextleadswith2-mercaptoethylamine,theaminogroupsofwhichcomparedwiththeconductancequantum(G0¼2e2/h).ThegapbindPdIIparticlestocatalyzethedepositionofmetalliccopper,resistance(Rgap)decreasedwithtime,andresistancesinserieswhichresultedinanelectrodenanogapof45nm.Yunetal.[71](RextandRgap)sharedthetotalappliedbiasvoltage(V0).FinallyreportedthecreativefabricationofintegratednanogapelectrodeswhenRgapwasmuchsmallerthanRext,Vgapapproached0,whichofafewnanometersinseparationwithayieldover90%(Fig.4).meantalmostnoappliedvoltagewasusedforetchingandTheyproposedthattheAudepositionrateofthegapedge

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Figure5.Obliqueangledepositionwithanelevatedmaskfortheprep-arationoftwometalelectrodesspacedtoafewnanometers.Reproducedwithpermissionfrom[9].Copyright2003NaturePublishing

Group.

Figure4.a)Opticalandb)?eldemissionscanningelectronmicroscopy(FESEM)imagesofanarrayofnanogapswithsub-5nmseparationsaftersurface-catalyzedchemicaldeposition.FESEMimagesoftwo-?ngerednanogapelectrodeswithmagni?cationsofc)Â40000andd)Â320000.Reproducedwithpermissionfrom[71].Copyright2006AmericanInstituteof

Physics.

smallerthanthatoftheotheredgesoftheelectrodesbecauseofthemass-transportlimitationinthenarrowgapandconsequentlytheplatingprocessslowsdownastheelectrodesapproachtunnelingdistances.Multi-?ngerednanogapelectrodescanalsobeconvenientlypreparedbyanelectrolessplatingmethod.[72]Ifthefabricationprocessofchemicaldepositioncanbemonitoredinrealtimeandthemaincontrollingfactors,suchasreactiontimeandreactantconcentration,aremoretheoreticalratherthanempirical,amuchbettercontrollabilityofthismethodcanbeexpected.

2.3.ObliqueAngleShadowEvaporationforNanogapElectrodes

TheobliqueangleshadowevaporationmethodwaspioneeredbyDolan[73]in1977.Thistechniquewasthenadoptedandre?nedforthefabricationofnanogapelectrodes.Shadowevaporationisoftencombinedwithopticalandelectron-beamlithographytode?nemetalleads.[9,74–76]Bysuspendingthemaskabovethesubstrateandcontrollingthedirectionofthedepositionangletobeobliqueagainstthesurfacenormal(Fig.5),featuresizesthataresmallerthanthoseofthemaskscanbeobtainedperfectlyasreportedbyBjørnholmandhiscolleagues.[9]Gaplengthsbetweentheelectrodesoflessthan10nmcanbereproduciblyfabricatedinthisway.Thegapsizecanbeadjustedbychangingstepwisethetiltangleuntiladesiredspaceisobtained,[76]andin-situsampleconductancemeasurementscanhelpto?ndtheproperangle,[77]whichendowsthismethodwithhighcontrollability.

Ifthesubstrateisuneven,itcanprovideasimilareffectasanelevatedmaskandcansimplifythefabricationprocess.Accordingly,double-angleevaporation[78,79]ofthinmetallic?lmswasintroduced.Bysimplychangingthe?lmthickness,theseparationoftheelectrodescanbeadjusted.Furthermore,evenwithoutemployingconventionallithographymethods,nanogap

electrodescanalsobeaccuratelyfabricated.Kawaietal.[80]developedamethodbasedonobliqueangleshadowevaporationtoconstructnanogapelectrodeswithoutawetprocesstomeasuretheelectricalcharacteristicsofmoleculesaftertheywerepositionedonthesubstrate(Fig.6).Thegaplengthbetweentheelectrodeswaseasilycontrolledunder100nmandatop-contactcon?gurationpreventedstructuraldeformationofthemolecules.Moreover,thismethodissuitabletoreliablyfabricatenanogaparraysformolecularelectronics.Forexample,Sunetal.[81]achievedthefabricationofgapelectrodearraysassmallas3nminlargequantities,andappliedthemtotheelectricalstudyofnanocrystalssuccessfully.Frequentlyobliqueangleshadowevaporationmethodisconductedatlowtempera-ture[9](e.g.,inliquidhelium),asundersuchconditionsthegrainsizesofthemetaldepositsarerelativelysmall,whichresultsinthegapwidthremainingclosertothedesignedvalue.Inthissense,otherimprovements,suchasusingmetalswithsmallergranules,decreasingthe?lmthickness,andadjustingtheevaporationrate,canbemadetoenableanarrowergap-widthdistribution.[78]

2.4.ElectromigrationandElectricalBreakdownMethodforNanogapElectrodes

2.4.1.ElectromigrationforNanogapElectrodes

Thephenomenonofelectromigrationhasbeenknownformorethan100years.[82]Inanappliedelectric?eld,themomentum

of

Figure6.Procedureoftheangle-controlledshadow-maskingmethod.Thewidthofthemetalmaskshownin(e)isactuallymuchwiderthanthatshownintheillustration.Reproducedwithpermissionfrom[80].Copyright2004IOPPublishingLimited.

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