Cheng-Kuanghuang, Ruizhu,Qiang Fu,Qingzhao ,And Dapengyu

Allrightsreserved

PrintedintheUnitedStatesofAmerica

AdvancedScienceLetters

Vol.4,3398–3402,2011

PlanarField EmissionCurrentfrom

IndividualCarbonNanotubes

Cheng-KuangHuang, RuiZhu,Qiang Fu,QingZhao∗,and DapengYu∗

StateKeyLaboratory forMesoscopicPhysicsandElectron MicroscopyLaboratory, DepartmentofPhysics,Peking University, Beijing100871,People’sRepublic ofChina

Carbonnanotube(CNT)planar ﬁeldemitterswere fabricatedonaSiO2/Sisubstrate.The anode,cathodeand CNTalllayon the samesubstrateforthe promising advantageofintergratibilitywithplanar technology.The emissioncurrent wasacquiredinascanningelectronmicroscope(SEM).Despitetheasymmetry(tip-electrode) ofourﬁeldemissionsample,asymmetricalI–VcurveconsistentwiththeFowler-Nordheimtheorywasacquired. Using Zener theory on quantumtunneling ininsulators,the observed phenomenonwasexplainedto be a possibleleakagecurrent through theinsulating SiO2 instead ofrealﬁeldemission.Moreover, thesimulatedlocal electric ﬁeldsatthe emitter apex excludethe possibilityofan accountableemissioncurrent. Ourresultsare of great importanceinstudying planar ﬁeldemissionsince itdrawsattentiontoavoid mistaking leakagecurrent fortheactual ﬁeldemissioncurrent inplanar ﬁeldemissiondevices.

Keywords: PlanarField Emission,CarbonNanotube,Leakage Current, Zener Tunneling, Finite Element

Method.

Received:11March2011.Accepted:14March2011.

1. INTRODUCTION

The ﬁeld induced emission of electrons from cold cathodes is a well understoodphenomenonand is, at present,still an activeresearchareaformanyone-dimensional nanowiresand nanotubes.1–8 Twoimportantparametersdeterminingtheperfor- manceofaﬁeldemitter:theradiusofcurvatureoftheemitter tip,andtheaspectratiooftheemitter:generally, thesharperthe emitter,thebettertheﬁeldemission properties. Carbonnano- tubes(CNTs)areobviouslythemostprospective candidatesas ﬁeldemitterswiththeverysmallradiuscurvature ofthetipon nanoscaleandverylargeaspectratio.Acknowledging this,CNT ﬁeldemitters havedrawnmuchattention lately,andhavebeen demonstratedtohaveoutstandingﬁeldemissionproperties.9–15

Theyareshowncapableofdelivering1 ApersingleCNTand highcurrentdensityinexcessof1A/cm2.

Mostofthepioneer worksontheCNTﬁeldelectron emitters weredesignedwithintheframework ofthetraditional vacuum tubes.Thethree-dimensional tip-to-electrodesetupwasadopted; theanodeandthecathodeareseparatedbyahighvacuumempty space(Fig.1(a)).Planarﬁeldemission ingeneral,istheﬁeld emission achieved onand/oracrossasubstrate; itischaracter- izedbythefactthatthecathode,theanode,andtheemitterslay onaninsulatingsubstrate.16 Sotheelectronemissionisreduced fromthree-dimensionaltotwo-dimensional.Figures1(b)and(c) illustratestheseplanardevices:(b)isthesocalledtip–tip(or

∗Authorstowhomcorrespondenceshouldbeaddressed.

bilateral)conﬁguration and(c)isthetip-electrode(orunilateral) conﬁguration. Thebeneﬁtsofsuchadesignincludeusageof thinnerCNTemitters,integratabilitywithplanartechnology, sta- bleconstruction, andetc.Theconceptisidealfortheincorpora- tionof emitterdevicesintointegratedcircuits.However,it is only untilrecently—withthedevelopmentofnanotechnology andthe adventofsophisticated instrumentsandfabricationtechniques— thatdevicesbasedontheideawererealized.17

Manyrecentreportsonplanarﬁeldemission havechosento assembletheemitterandelectrodesondopedSiwaferswith aSiO2 insulatinglayer(typicallyafewhundrednanometersin

thickness).1618–22 Employingsuchconstructions,agatevoltage

canbeapplied,whichcanincreasethefunctional optionsofthe ﬁeldemitterdevice.Theinherent problem withsuchaconstruc- tionisthatleakagecurrentthroughtheinsulator isveryeasily neglected. Inthisreport,asigniﬁcant leakagewasfoundinthe insulator layerinourplanarﬁeldemission devicebasedonindi- vidualCNT.Furthermore,theI–Vrelationcloselyresemblesthat of ﬁeldemissionwithsimilarFowler-Nordheim(FN)plots.Thus, onecaneasilymistaketheobtained currentforactualﬁeldemis- sionphenomenon. Possiblereasonswerecarefullyanalyzedfor theobservedresults.And suggestionswere giveninordertocon- ﬁrmtheexperimentaldatatoberealﬁeldemission.

2. EXPERIMENTALDETAILS

TheCNTsinthisinvestigation weregrownviaachemicalvapor deposition (CVD) method23 on a pre-marked, highly doped,

3398 Adv. Sci. Lett. Vol.4,No.11/12, 2011 1936-6612/2011/4/3398/005 doi:10.1166/asl.2011.2049

Fig.1. Anillustration ofa traditional vacuumﬁeldemissionsetupcharacterizedby twotopologically separated electrodes.(b) and (c) are twopossible conﬁgurationsofa planar ﬁeldemissiondevice: (b)withtwoopposingemitter isthe tip–tip(orbilateral) conﬁguration.And(c)withonlyone emitter is the tip-electrode(orunilateral) conﬁguration;theplanar devicesare characterizedbythefactthattheelectrodesshareacommonsubstrate.

Si substrate covered with a 500 nm SiO2 insulating layer. Thismethodproduces roughlystraightCNTslyingalongthe samedirection,convenient forproducingplanarﬁeldemitters. Figure2(a)istheSEMmicrograph oftheas-grownCNTonthe premarkedsubstrate.

Forthemeasurement ofﬁeldemissioncurrent,Ti(20nm)/Au (30nm)electrodes weredeposited ontheindividual as-grown CNTsusingstandardelectronbeamlithography (EBL)andlift- offprocess.Similartotheworkpreviouslyreported,16 sharply tippedglassneedleswereemployedincuttingtheCNTunder an optical microscope (Fig. 2(b)). Our procedures produced a tip-electrode planar CNT emitter like those illustrated in Figure1(c);thesurfacemorphologyofthepreparedCNT emitter

wascharacterized withanatomicforcemicroscope(SEIKO SPI3800N) undercontactmode(Fig.2(b)).TheCNTemitter apparently foldedbackuponitselfatthetip;thesurfaceanalysis ofanuncoupledpart(blue arrow)andtheapex(redarrow)ofthe emitterrevealsadiameter of∼3.6nm(bluebox)and∼3.9nm (redbox)respectively. Hence,consideringuncertainties andthe coupling, theapparentapexdiameterisestimated tobe∼9nm. Thelengthoftheemitterisapproximately2.6 m;therefore, givinganaspectratioofabout289.

I–Vmeasurements oftheplanarﬁeldemissioncurrentonthe individual CNTwereconducted inaSEMchamberunderavac- uumof2×10−6 Torr.AKeithley-6430Sub-FemtoampRemote SourceMetertogetherwithitspre-ampliﬁerwasusedtoapply

Fig.2. TheSEMmicrographoftheas-grownCNTs,layingalone thesamedirection ontheSiO2/Sisubstrate.(b)Anillustrated demonstrationshowing CNT emittersreadily fabricatedwiththe use ofglassneedletipsunder an optical microscope.(c)AFMmicrographofourpreparedCNTemitter: the colorboxes are surfaceanalysis,they correspondtothe site ofthe colorarrows onthe image. The CNTdiameteris∼3.6 nm(bluebox),however,due toafoldingback oftheCNTatthetip,theapparentdiameterisovertwicetheactual CNTdiameter(redbox).

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Fig.3. An illustration of the measurment setup in a SEM with a vac- uum environment of 10−6 Torr; a keithley-6430Sub-FemtoampRemote SourceMeterwasused to sourcethe voltage and measurethe current. (b) The SEM micrographofthe testedplanar CNTemitter before current acquisition.

thevoltageandmeasure theemission current;thevoltagewas ramped in steps of 1 V. The peripheral circuit resistance of oursetupwaslessthan5Ohm.Theelectronbeamwasini- tially used to determinethe tip-electrodedistance(∼14 m) thensubsequentlyturnedofffortheemission currentacquisition. Figure3(a)isaschematicillustrationofthecurrentmeasurement setup,andtheSEMmicrographofthetestedplanarCNTemitter isshowninFigure3(b).

3. RESULTS ANDDISCUSSION

Figure4(a)showsthemeasuredI–Vcurve:theforwardcurve istheobtained currentwhenanegative biasisappliedonthe emitter partandthereverse curvetheviceversa.Theonsetvolt- ageat1nAwasaround10V.Comparingtheresultstothe

115Vonsetvoltageofasimilarlythintraditional singleCNT emitter,withatip-electrodedistanceofamere1 m,reported byBonardetal.,11 theapparentimprovement ofﬁeldemission propertiesisquitesigniﬁcant. Theonsetvoltageofourplanar CNTemitters ismuchsmallerthanmostofthereported CNT emittersintraditionalsetups.1124–26 TheobtainedI–Vimpliesa bilateralemissioninnature;itbearsresemblance tothatprevi- ouslyobtainedfromatip–tipconﬁguration inplanarﬁeldemis- siondevicesbySong16 andWang.27 Moreover,complyingwith theFowler-Nordheimtheory,2829 theFNplot(insetofFig.4(a)) ofthecurvedoesrevealalineartrendatemission ﬁeldstrengths. Soifitisrealﬁeldemission,theimprovement issigniﬁcant. However,considering thefactthatanasymmetric tip-electrode conﬁgurationwas deliberatelyprepared(Fig. 1(c)), the result seemsabsurd,sinceitshouldgivecurrentonlywhennegative biaswasappliedontheCNT,andnoemission currentwhen positivevoltagewasapplied.Thesymmetricshapeofthecurve

Fig.4. I–Vcurve acquiredfromthe planar CNT. The forward curve isin the sensethat a negativebias isapplied on the emitter. The inset shows the correspondingFNplotofthe emissiondata; the linearitycomplies with theFNtheory. (b)isanillustrationofanelectronwithenergy−W tunneling through the ﬁeldtiltedbands;Eg isthe band gap (here, analogoustothe workfunction (c)isthe current (ej),calculatedfromZener’sexpression, tunneling intothe conductionband versusthe applied ﬁeld;the inset shows thecorrespondingFNplot.

Fisconventionally writtenas:F= V/d:Vistheappliedvolt- age, isthegeometricenhancementfactor,andd isthetip- electrodedistance.ThelawrelatingIandFisthuswrittenas29

makesusassumealeakagecurrentmightexistbetweentheelec-

15×10−6 V

2exp

104

×exp

644×109 15d

−

trodesthroughtheinsulatingSiO2 layer,forleakagecurrentis

independentofthedirectionofbiasvoltage.Nevertheless,this

I=A d

(1)

alonecannotaccountfortheconsistencyoftheI–Vwithﬁeld

emissiontheory.

TheFNﬁeldemissiontheoryisbasicallytherationalization ofthequantumtunnelingphenomenon.28 Thetheoryhasbeen provedusefulindescribingtherelationship betweentheﬁeld emissioncurrentI andthelocalﬁeldF attheemittersurface.

whereA hasthedimensionofanaream2 and isthework function ineVoftheemitting material. FromEq.(1)itcanbe observedthatiflnI/V2 isplottedagainstI/V,then,atemis- sionﬁeldrange,onewillarriveatalinearfunctionwithaslope

−644×102 15d/ ;thisisthesocalledFNplot.Byﬁttingthe

experimentaldatainaFNplot,either ortheﬁeldenhancement

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Adv. Sci. Lett. 4,3398–3402,2011

factor canbedetermined.Usuallyitistheenhancementfactor thatiscalculatedfor,sinceitisameasureofemitterperformance. TheFNplothasalsobeenusedoverthepastasasupporting evidenceforﬁeldemission.Despite this,thefollowingparagraph willproveittobeonlyanecessaryconditionforﬁeldemission. Returningtothequestionathand,withtheFNlawinmind, ourobservedcurrent should alsobeexpressibleinarelation sim- ilartoEq.(1)toshowsuchanalogousbehaviorasﬁeldemission. Infact,thephenomenonisknownasinternalﬁeldemissionof insulators;itwasﬁrsttreatedbyZenerin1935.30 Theideais basicallyshowninFigure4(b),anenergylevelversusposition illustrationforinsulatorsorsemiconductorswithabandgapEg betweenthevalenceandconductionband.Uponapplicationof anelectricﬁeld,thebandgapedgesbecometiltedinspace.An electronwithenergy−W withrespecttothevalancebandedge canmaketransitionstotheconductionbandnotonlyvertically (requiringanenergyEg+W),butalsohorizontally,owingto theappliedﬁeld.Namely,thevalenceelectronscantunnelintoa currentcarryingbandstate.Theexpressionderivedlimitingthe rateoftransitionis,asexpected,anexponential.Itiswrittenas

RESEARCH ARTICLE

Fig.5. Thesliceplotofcalculatedlocalﬁeldsforbothconﬁgurations.Asit isshown, forthetraditionalconﬁgurationthetipﬁeldisaround5times larger than theplanar setup.

asinglestandingCNT:1.45 minlength,a7.5nmradius,and anapproximately1 mtip-electrodedistance.Meanwhile,the modelbentCNTforplanarconﬁgurationinourcase,lyingon a500nmthickSiO2,is5nminradiusandroughly2 mlong

eFa

j exp

2 ma2

−h2 ∗eF∗

(2)

withatip-electrodedistanceofabout14 m.Ahemispherical

capwasdrawntomodelthetipheadforbothcases.Thevolt- ageappliedontheemitterischosenas115Vsoastomodel

whereaisthespatialperiodicityofelectronpotentialenergy,

mistheelectron mass,Eg istheenergybandgap,andFisthe appliedlocalﬁeld.Intuitively,theelectricﬁeldFherecanalso berelatedtotheappliedvoltagethroughananalogousenhance-

theonsetvoltage(thevoltagerequiredtoextractacurrentof

1nA)reportedbyBonardetal.11 Thecalculatedﬁeldattheapex ofthefreestandingmodelandplanarmodelwas∼5×109 and

mentfactor.Figure4(c)isaplotofcurrentI(electroniccharge

∼1×10

V/mrespectively(Fig.5).Theelectricﬁeldattheapex

e×Eq. (2))versuselectricﬁeldconsideringreasonablevaluesfor theparametersinourexperimentalsetup:a=50×10−9m(pre- sumingthinneramorphousSiO2atleakagesites)andEg=91eV forSiO2;thecalculationisaperiodicboundaryestimationusing thethicknessoftheamorphousSiO2 asalargeunitcell.The curvethusobtainedsharesimilarities withthatofvacuumﬁeld emission.Toshowthiscurvewillderiveasimilarlinearityina FNplot,Eq.(2)isrewrittenas

oftheCNTinplanarconﬁgurationisonlyﬁfthofthatinfree

standingconﬁguration.In other words,the onsetﬁeldfor vacuum ﬁeldemission inourcasewasnotachieved, sotheobtainedI–V curvecouldnotbevacuumﬁeldemission,inaccordancewith ourpreviousexplanation.

Although wehaveprovedthecurrenttobeofleakagethrough theinsulatinglayer,theoriginofsuchalargeleakageisdifﬁ- culttoidentify.RepeatedexperimentswithorwithoutCNTdo notalwaysrevealsigniﬁcantleakagecurrentwithinthevoltage

=ln

e2a

−

2ma 2

(3)

sourcerange(200V):therearecaseswherearelativeﬂatcurve

(nocurrent)isobtainedandsometimesthephenomenonistrig-

F2 Fh

h2 ∗eF∗

geredbyabreakdownﬁrst.Theevidencessuggestthatleakage

ContrarytoFNlaw,theleadingpartoftherighthandsideof Eq.(3)(lne2a/Fh )isherealsoafunctionoflocalﬁeld;one wouldexpecttoseeanon-linearrelation.Nonetheless,theplot ofEq.(3)(Fig.4(c)inset)doesstillrevealalinearrelation. Thereasonforthisisthatthevariationoflne2a/Fh issmall withintheﬁeldrangeofobservable Zenertunneling.Withinthis ﬁeldrange,lne2a/Fhvaried 1∼07whereas thesecondterm

2ma 2/h2∗eF∗ varied 2∼133;theformerisonlyabout

5.2%ofthelatter.Sowhenweplotlnej/F2 against−1/F

asshownininsetofFigure4(c),alinearrelationship similaras FNplotwasobtained. Thisisthemainreasonformistaking the obtained linear“FNplot”forrealvacuumﬁeldemission tun- neling.Infact,itistheleakagecurrentthroughSiO2 insulating layerexplainedintheframework ofZenerTheory.Thisresult supportsourinitialassumptionsandspeculations.

Tocompleteouranalysis,theelectricﬁeldattheCNTtip iscalculatedusingComsolMultiphysics, acommercialprogram basedonﬁniteelementmethod,isemployed.Foraquantita- tivecomparison,atraditionalconﬁgurationwasconsideredalong withtheconﬁguration inthisstudy.Thedimensioninthetradi- tionalcasecloselyfollowsthosereportedbyBonardetal.11 on

maybeduetodefectsintheinsulatinglayer,localsiteswhere theSiO2 isthinner.Thedefectsmaybeoriginally presentfrom fabrication processorintroduced bymaterialbreakdown from localstaticchargeaccumulation. Itisalsoreasonabletoassume breakdown fromtheappliedﬁeldthroughaﬁeldenhancement mechanismanalogoustothevacuumﬁeldemissionsituation.

Ourresultsandanalysissuggest,where theFNtheoryisappli- cable,the linearityof FN plot is onlya necessarycondition (atleastinplanaremission setups)forrealﬁeldemission; other testsmustbeperformed inordertoconﬁrmtheresults.Foruni- lateralassemblies,areproducible asymmetricI–Vcurve,from negativetopositivebiasshouldbesufﬁcient.Meanwhile, for symmetricbilateralassemblies,leakagebetweenelectrodeandSi wafermustbere-examined afterobservingasupposedvacuum ﬁeldemission.

4. CONCLUSIONS

Carefully designed CNTplanarsystemforﬁeldemission was fabricated. UtilizingSEMtoprovidethevacuumandprecise measurements,aplanarﬁeldemissioncurrentfromtheplanar

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RESEARCH ARTICLE Adv. Sci. Lett. 4,3398–3402,2011

CNTwasobserved.TheobtainedI–Vwassymmetric forfor- wardandreversebiasandtheFNplotcomplied withtheFN theory.Butourtiptoelectrodeexperimental setupshouldgive asymmetricI–Vcurveinsteadofasymmetricone.Finiteele- mentcalculations ofourplanardevicerevealedthefactthatthe onsetﬁeldstrengthforvacuumﬁeldemission wasnotachieved. Thusthecurrentcannotbeoriginated fromtheCNT.Meticulous analysis basedonZenertheoryrevealsthecurrenttobeorigi- natedfromleakagethroughtheinsulating SiO2 layerinsteadof realvacuumﬁeldemissionphenomenon. Thelargeleakagewas attributedtopossibledefectsintheSiO2 layer.

Oneoftheaimsinstudying planarﬁeldemission isits prospectsinintegratedcircuits.Ourworkisofgreatimportance instudyingﬁeldemissionfromplanarﬁeldemissiondevices sinceitiseasytomistakenly identifytheobtainedcurrenttobe originated fromvacuumﬁeldemissioninsteadofotherpossible casessuchasleakagefrominsulatinglayer.

Acknowledgments:This project is ﬁnancially supported by the National Natural Science Foundation of China (NSFC 50902004 and 11023003), and National 973 projects (No.2007CB936202, 2009CB623703, MOST)fromChina’s MinistryofScienceandTechnology andtheResearchFundfor theDoctoralProgramofHigherEducation.

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