CHAPTER1 Electrical Properties of Metallic Nanowires for Nanoelectronic Applications
Carmen M. Lilley and Qiaojian Huang
ManyresearchershavefocusedonmetallicnanowireNWmaterials,suchasCu,Ag,andAunanowires,asbasicmaterialbuildingblocksfornanoelectronics.Thischapterwaswrittenwiththeintentionofprovidinganoverviewofelectricalpropertiesofmetallicnanowirematerialsusefultoresearchersandengineers.Researchersmay.ndtheinformationusefulindesigningnanoscaleelectricalsystemsbe-foretheyfabricatedevices.Thechapterisdividedsothatwebeginwithanoverviewofbasicelectricalproperties,suchaselectricalre-sistivityandthermalcoef.cientsofresistivity.Inaddition,wediscussparametersthatin.uencetheelectricalpropertiesatthenanoscale,suchassizeandsurfaceeffects.Finally,thischapterconcludeswithadiscussiononthefailurepropertiesofmetallicnanowires,suchasfailurefromJouleheatingandelectromigration,sothatthereliabil-ityofmaterialsystemcomponentscanbeconsideredinthedesignofnanoscaleelectricalsystems.
1.1 Introduction
Nanowireshaveawiderangeofapplicationsinelectronicsystems,forexampleasinterconnectwiresin.eld-effecttransistors,1 resonators,2.5nanomagnets,6.8and spintronic systems.9,10Nanowiresarealsocriticalcomponentsusedinthedesignofnanoelectrome-chanicalsystemsNEMSs,wheretheyhaveapplicationsasintercon-nectsincircuitsandsensorstodetectchemicalorbiologicalagents.
Aconsiderablechallengeisthesuccessfulintegrationofthesetypesofnanotechnologyintolargerscalesystemswithmultipleplatformsofintegration,sothatthenanosystemscaninteractwiththemacroscaleworld.Microscaleelectricalsystemsarealogicalchoiceasthe.rstplatformforintegrationofnanosystems,becausetheyaretheclosesttothenanosystemlengthscaleamongcurrentmanufacturedelec-tronicproducts.Thismakesmicrosystemsthebestcandidateasaplatformforintegrationandalinkforcontrolledinteractionwiththemacroscaleworld.Thesuccessfulintegrationofnanosystemsintomi-croscaleelectronicsdependsonstablematerialpropertiesthatarereli-ableforatleasta10-yearlifecyclewithgreaterthanatrillioncyclesofoperation.11 However,mostnanoscalesystemsfabricatedtodatearepronetomaterialinstabilitiesforexample,oxidationofsurfacesoragglomerationofquantumdotsorcarbonnano.bersthatnegativelyaffecttheirusefulness.
Therehasbeenmuchresearchintheareaofmodelingandchar-acterizationofsurfacepropertiesandcrystallinestructureofmetallicnanowiresandhowthesepropertiesin.uencetheirelectricalproper-ties.Withinthenanoscaledomain,forinstance,therehasbeencon-siderableresearchonthesizedependenceofelectricalresistivity.Forexample,asananowire’scriticaldimensiondecreasesfromhundredstotensofnanometers,theirelectricalresistivitywillincreasebecauseofsizeandsurfaceeffects.Asthecriticaldimensionsdecreasefurther,todimensionssmallerthan1nm,theirelectrontransportpropertieswillexhibitauniqueshifttoquantizedbehaviorthatcanonlybemodeledbyquantummechanics.Todate,however,thereislimitedresearchonthelong-termstabilityoftheseproperties.Itshouldbenotedthatthesurfaceandstructuralpropertiesofnanomaterialsmayleadtounexpectedmaterialfailures,whichareasigni.cantobstacletothereliabilityofthesematerialsystems.
Someofthemostcommonmetallicnanowirematerialsusedbyresearchersareface-centeredcubicFCCmetalssuchascopperCu,silverAg,andgoldAusynthesizedbybottom-upandtop-downapproaches.Foramonolithicnanowire,theelectricalandfailurepropertiesofthenanowirewillvarywithsizeandsurfaceproper-ties.Therefore,thischaptergivesanoverviewofelectricalproper-tiesofCu,Ag,andAunanowirematerialswithcriticaldimensionsofa10-to100-nmsizescale.Thein.uenceofsizeandsurfaceonthematerialpropertiesisalsodiscussed.Theaimofthischapteristoprovidethereaderwithpracticalinformationonmaterialprop-ertyconsiderationsofmetallicnanowireswhenplanningtodesignananoelectronicsystem.Inaddition,byprovidinginformationonfailureproperties,scientistsandengineerswillbeabletoincorpo-ratereliabilityofmaterialcomponentsintotheirdesignprocesses.Itisexpectedthatscientistsandengineerswill.ndthisinformationuseful for the practical design and fabrication of nanoelectronic systems.
1.1.1 Size and Surface Effects on Electrical Properties of Nanowires
Figure1.1illustratesthepercentageofsurfaceatomswithrespecttobulkatomsforanFCCclose-packednanoparticleofCuwithdi-ametersrangingfrom0.25to50.9nm.12 Ascanbeseen,theratioofsurfaceatomstobulkatomsbecomesincreasinglylargeastheparti-clesbecomesmaller.Therehasbeenmuchfocusonhowsurfacein-.uencesthematerialpropertiesofnanoscalestructures,wheresomeofthesesurfaceeffectsmayleadtochangesintheelectrical13,14or mechanical15.18propertiesofNWs.Forexample,apparentvariationsinmeasuredelasticmodulusforNWshavebeenattributedtoacom-binationofeffectsfromsurfacestressandsurfaceelasticity;seeforexampleRefs.15,16,and18.Inaddition,sizehasbeenfoundtoin-.uencetheelectricalresistivityofnanowires.Forexample,itisnowwellknownthatnanowireswithdimensionsbelow10nmcanex-hibitquantizedresistivitybehavior;andthisbehaviorhasbeenstud-iedextensivelyusingmoleculardynamicsimulationmethods.Fornanowiresizeslargerthan10nm,electronsurfacescatteringandelec-trongrainboundaryscatteringhavebeenshowntocauseanonlinearchangeintheelectricalresistivity.Fortheselargernanowirediame-ters,thewell-establishedkinetictheorycommonlyreferredtoastheFuchs-Sondheimertheoryhasbeenusedtomodeltheeffectsfromelectronsurfacescattering,andMayadas-Schatzkestheoryhasbeenusedtomodeltheeffectsfromelectrongrainboundaryscattering.
% of Surface Atoms
110 100 90 80 70 60 50 40 30 20 10 0
0 1020304050 Diameter nm of FCC Cu Nanoparticle
FIGURE1.1GraphofthepercentageofsurfaceatomswithrespecttobulkatomsforFCCclose-packedCunanoparticles.
InSection1.2,wepresentareviewofthesetheoreticalmodelsforsizeandsurfaceeffectsontheelectricalresistivityofananowire.
1.1.2 Stability of Nanomaterial Properties—Surface Matters
Adsorptionofsurfacecontaminantsisanothertypeofsurfaceeffectthatmaycausechangesinmaterialpropertiesatthenanoscale.Forexample,variationsintensilestrengthofAuNWswereattributedtothepresenceofcarbonC,oxygenO,andnitrogenN.17 Sim-ilarly,exposuretoairorothersourcesofcontaminantsmayaffectthemeasuredresistanceandlong-termreliabilityofmetalNWs.14,19Forexample,researchershavefoundthattheagingmechanismsforpermalloys,suchasthoseofnickelNiandironFe,werearesultofoxidationanddiffusionofthisoxygenintothebulkNWmaterial.Thisoxidationandthesubsequentdiffusionofoxygencausetheelectricalresistivityofthenanowiretoincrease.Consequently,itwasfoundthatcappingthenanowiresurface,suchaswithathinsurface.lmofgold15nm,preventedsurfaceoxidationandthusalsotheincreaseinelectricalresistance.19 However, Au has very high mobility and can readily contaminate silicon-on-insulator SOI devices at the wafer level.20 Therefore,itisunlikelythatAuwouldbeusedtofabricatenanoscaleelectronicsthatwouldbeintegratedintomicroelectronicsinacommercialfabricationsetting.Aspreviouslymentioned,thereislimitedpublishedresearchonthestabilityofnanoscalematerialproperties.However,researchersshouldtakenote:surfacecontami-nantsmayaffecttheirdesignofnanoscaleelectronicsystems,andtheymay.nditusefultoidentifythesurfacecompositionofthenanoma-terialsasawaytoidentifywhethersurfacecontaminantshaveanysigni.cantimpactontheirdesigns.
Asdiscussedpreviously,therelativeratioofsurfaceatomstobulkorvolumeatomsinnanoscalesystemsincreasesdramaticallyasthenanostructuresdecreaseinsize.Thismayalsoin.uencemate-rialdiffusionatthesurface,becausetherearemoreatomspositionedatthesurface,andthesesurfaceatomsmaybedetachedmoreeas-ilyfromtheirequilibriumpositions.Thiswouldresultinmaterialshavingsurfacediffusionatlowertemperaturesascomparedtobulktemperatures.21 Thislowerdiffusiontemperatureorenhanceddif-fusivityhasanimportantimpactonthestabilityofananowire.Forexample,Karabacaketal.recentlypublishedapremeltingtempera-tureof673to773Kforcoppernanorodarrayswithadiameterofapproximately100nm.21 Thispremeltingtemperaturerangeislowerthanthebulkmeltingtemperatureandisbelievedtobearesultofthenanowiresize.Otherresearchershavealsofoundthatalthoughthecurrent-to-failuredensityincreasesaswiresbecomesmaller,themeantemperaturetofailuremayactuallydecreaseascomparedtothebulkmelting temperatures.21,22Adecreaseinthetemperatureformaterialdiffusivitythereforemayaffectthemateriallifetimewheretheymayfailfromsucheffectsaselectromigration.
1.2 Electrical Resistivity of Metallic Nanowires
1.2.1 Electron Surface Scattering
Aspreviouslymentioned,sizeeffectsonelectricalresistivityformetal-licnanowireshavebeenmodeledbyvariousresearchersusingtwowell-establishedtheories,Fuchs-Sondheimerforelectronsurfacescat-tering,andMayadas-Schatzkesforgrainboundaryscattering.Thissectionprovidesabriefoverviewofthesetheories,andtheirappli-cationtoexperimentalresultsisdiscussedinthefollowingsection.Fuchs-Sondheimertheoryisalsocalledkinetictheoryandisawell-establishedtheorytomodelnonlinearchangesinelectricalresistivityforthin.lms.23,24Chambersappliedthistheorytomodeltheelec-tricalresistanceofwires.25 Herein,wewillpresenttheanalysisforatrapezoidalnanowiresystemusingChambers’sapproach,becausethismoregeneralgeometrycanbeappliedtomodelsquare,rectangu-lar,trapezoidal,andtriangularnanowiresallofwhichcanresultfromvariousnanofabricationmethods.Thevariablepisusedtocharac-terizetheprobabilityofelasticelectronre.ectionatthesurfacewherep=1foratotalelasticre.ectionandp=0forapurelydiffusescatter-ingandiscalledtheelectronsurfacescatteringcoef.cient.Forpurelyspecularscatteringp=0,thetheoreticalresistivitycanbeexpressedas
2ππ
ρo 32 .LOP
p=0,λ=dsdφdθsinθcosθ1.exp
ρFS4πsλ
s 00
1.1
whereρoisthebulkresistivityofthematerial,λistheelectronmeanfreepathofthematerial,sisthecross-sectionalsurfaceareaofthewire,pointOisonthesurfaceofacross-sectionalareaofthewire,andPisapointlocatedonthewiresurface.ThevectorOPconnectspointOtopointPandhasthelengthLOP.ThevectorOP. is the projection of the vector OP onto surface s. The angle φ is the radial angle for OP., and θ is the azimuthal angle of vector OP. Equation
1.1isintegratedoverallpointsonthesurfaces.Inessence,themeanfreepathforelectronsisreducedduetoelectronsurfacescatteringonthewiresurfacewhichcausesanincreaseinresistivityforthewireascomparedtothebulkmaterial.
B
TheequationfortheelectricalresistivityofatrapezoidalwireisgiveninEq.1.2.ToderivethisequationfromEq.1.1,we.rstconsiderapointOinthecrosssectionandelectronspassingthroughitinthedirectionofOP,wherePisonthetopwiresurface,asshowninFig.1.2.TheintegrationofEq.1.1isoveralllocationsthroughoutthewirecrosssections,withLOPbeingthedistancefromthelocationofpointOinthecrosssectiontothepointPonthewiresurfaceinthedirectionoftheazimuthalangleθandtheradialangleφ.Fromthiscalculation,theresultantelectronmeanfreepathinthewireisreducedtoλ[1.exp.Lλ OP ] because of electron scattering on the wire surface.25 InFig.1.2,thedimensions2a,2b,andharethetopwidth,bottomwidth,andheightforthetrapezoidalwire,respectively.Thebottomangleofthetrapezoidwireisgivenby
h
α = arctan 1.2
b . a
Thecross-sectionareaofthetrapezoidwireiswrittenas
2a+2bh
s==a+bh1.3
2
Byexaminingthein-planecrosssectionoftrapezoidABCDthesur-facesandtheprojectionofOPOP.fromtheelectrontravelingpath,
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