Band gap modulation of bilayer graphene by single and dual molecular doping: A van der Waals density-functional study

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Band gap modulation of bilayer graphene by single and

dual molecular doping: A van der Waals

density-functional study

Tao Hu, I.C. Gerber

To cite this version:

Tao Hu, I.C. Gerber. Band gap modulation of bilayer graphene by single and dual molecular doping:

A van der Waals density-functional study. Chemical Physics Letters, Elsevier, 2014, 616-617, pp.75-80.

�10.1016/j.cplett.2014.10.034�. �hal-01969523�

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ContentslistsavailableatScienceDirect

Chemical

Physics

Letters

j o ur na l h o me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / c p l e t t

Editor’s

choice

Band

gap

modulation

of

bilayer

graphene

by

single

and

dual

molecular

doping:

A

van

der

Waals

density-functional

study

Tao

Hu

a,b

_,

_Iann

_C.

_Gerber

a,∗

a_Université_de_Toulouse;_INSA,_UPS,_CNRS;_LPCNO₁₃₅_avenue_de_Rangueil,_F-31077_Toulouse,_France b_Department_of_Physics,_Pukyong_National_University,_Busan_608-737,_South_Korea

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received5August2014 Inﬁnalform15October2014 Availableonline22October2014

a

b

s

t

r

a

c

t

Densityfunctionalcalculationsincludinglong-rangedispersioneffectsdemonstratethatnon-covalent dopingwithanelectrondonoracceptorcoupleofmoleculescanopenanenergygapinabilayergraphene. Thebandgapmodulationcanbecontrollednotonlybythechoiceofadsorbedmolecules(n-dopant versusp-dopant)butalsobytheirconcentration.Adeepanalysisofthechargetransferrevealsthat chargeredistributioninbilayergrapheneisthekeyissueforgapopening,duetotheinducedinversion symmetrybreaking.Thedualmolecularnon-covalentdopingmodecanachievetheopeningofagapup to138meV.

1. Introduction

Graphenehasuniqueelectronictransport[1,2],mechanical[3],

andoptical[4]propertiesthatexhibitextraordinarypotentialfor

nanoelectronicapplications[5–8].However,pristinegraphene,in

themonolayer(MLG)orbilayer(BLG)states,isagaplesssemimetal,

thus limitingits applicationsin electronicnano-devices.

There-fore, considerable efforts have been made to open band gaps

inMLGor BLG.Boththeoreticaland experimentalstudieshave

demonstratedthatabandgapcanappearintheBernal-stacking

(AB-stacking) BLG, by breaking inversion symmetry [9–15], by

applyinganexternalelectricﬁeldforinstance[16–18],by

break-ingin-planesymmetry[19],byapplyingdifferenthomogeneous

strainstothetwolayers[20]orbyvaryingtheinterlayerspacing

[21].Moleculardopingisalsoanalternativebyprovoking

asym-metricchargedistributioningraphenelayers.Inanon-covalent

dopingprocessof graphene,thecarrierconcentration,which is

akeyfeatureforelectronics,canbecontrolledbythe

concentra-tionof theadsorbedmolecules, withoutintroducing signiﬁcant

latticedeformation[22–25].Currently,graphenegrowthprocess

onlyallowsmoleculardopantstobeabsorbedonthetopsideof

thegraphenelayers,althoughintercalationcannotbecompletely

excluded.Thebottomlayeris usuallydopedbytraditional

sub-strates[26]orbyspeciﬁcallymodiﬁedones[27],seeRefs.[28–30]

forBLGcases.

∗ Correspondingauthor.

E-mailaddress:igerber@insa-toulouse.fr(I.C.Gerber).

Theoreticallyspeaking,toyieldaccuratedescriptionof

inter-layerdistances,tocorrectlydescribethenon-covalentinteraction

betweengraphenelayersandchargetransfercomplexesinthe

den-sityfunctionaltheory(DFT)frameworkitismandatorytoinclude

nonlocaleffects[31].InprevioustheoreticalreportsonBLGdoping,

vanderWaalsforcesarenotexplicitlytakenintoaccount[12,32],

sincetraditionalexchange-correlationfunctionalsmissedthem.In

thisworkwehaveusedthesocalledvanderWaalsdensity

func-tional(vdW-DF)[33–35],whichhasbeensuccessfullyappliedon

layered[36,37]aswellasonsomemolecularsystems[38].

Inthisstudy,wereportthedopingofaBernal-stackingBLGby

severalorganicelectrondonoracceptormoleculesasfunctionof

theiradsorptionmodes.Ifonetypeofmolecule(acceptorordonor)

isadsorbedonasinglesideoftheBLG,itcorrespondstoasingle

moleculedopingmode.Whenatthesametime,topandbottom

layersarein interactionwitha n-dopantandp-dopant,

respec-tively,thishypotheticalsituationiscalleddualmoleculesdoping

modethroughoutthearticle.Despiteanyexperimentalresultson

thisspeciﬁcsettinghavenotbeenyetreportedintheliterature,

onecouldimagineathree-stepsproceduretorealizeit.By

choos-ing ﬁrstan appropriate moleculeor atoms (donoror acceptor)

thatcaneasilyintercalatebetweengraphenelayersorbetweena

graphenelayerandthesubstrate[39],andthenbysoftwashing,

somedopantsshouldstillremainboundonthedownsideofthe

BLG,duetolargerbindingenergies.Finally,adopant’ssolutionwith

oppositecharactershouldbedeposited,totransferchargefrom/to

theuppergraphenelayer.Thissettingalsomimicsinasensethe

effectofanappliedperpendicularelectricﬁeldontheBLGby

creat-ingadipolemomentonanatomiclength-scale.Thisdirectlyrelates

toexperimentalworksofRefs.[26,27].

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76 T.Hu,I.C.Gerber/ChemicalPhysicsLetters616–617(2014)75–80

ByusingDFTcalculations,wereportthatdualmoleculardoping

caninducetheopeningofasigniﬁcantbandgap.Itcanbecontrolled

aswellasthecarrierconcentration,inawiderrangebydualmode

doping.Asaconsequence,aﬁne-tuningthroughthethreshold

volt-ageoftheelectronicconductionproperties,thatisacrucialissue

forelectronicsapplication,ispotentiallyachieved.

2. Method

WehavestudiedadopedBLGsystem,inAB-stackingonly,using

periodicboundaryconditionwithinthesupercellapproach,witha

vacuumregionlargerthan1.5nmtoavoidinteractionbetweenthe

periodicimages.Thecalculationshavebeenperformedusingthe

VASPcode[40]withtheProjectedAugmentedWave(PAW)[41]

pseudopotentials.ThevdW-DF[42]functionalisusedfor

corre-lationandPBEforexchange[43].Anenergycutoffof400eVand

careaboutk-point samplinghave beentakento ensureenergy

convergencebelowfewmeV. Thek-pointgridsare3×3×1 for

largecellsand7×7×1forthesmallercells.Theconvergence

cri-terionfor calculationsisthat theforceoneachatomissmaller

than0.02eV ˚A−1.TheBaderChargeAnalysismethodisusedto

esti-matethechargetransfer, usingtheprogramof G.Henkelman’s

group[44].BLGismodeledeitherbyacellcontainingtwo(7×7)

monolayers(98carbonatomseachlayer)ortwo(4×4)monolayers

(32carbonatomseachlayer).Itallowstodiscussconcentration’s

effects,withthreepossibleconcentrations:onemoleculeper196

carbonatoms(0.51%)seeFig.1,onemoleculeper64carbonatoms

(1.56%)andonedonorandoneacceptormoleculeper196carbon

atoms(1%).Theseconcentrationscorrespondtostandard

experi-mentalsettingsofgraphenemoleculardoping[45],andallowto

avoidinteractionbetweenadsorbates withinperiodicboundary

conditions.Threeorganicmolecules,tetracyanoethylene(TCNE),

tetrathiafulvalene(TTF),tetrakis(dimethylamino)ethylene(TDAE),

areemployedasdopant.AsinRef.[24],wehaveinvestigatedall

thepossibleadsorptionsitesontheBLGmodels,intermsof

ener-geticandgeometricaspects.Theyareverysimilartothemonolayer

case,withverysmallenergydifferencesbetweenadsorptionsites.

Moreoverthechargetransfersfromthedifferentconﬁgurationsare

almostequal,asreportedinapreviousstudy[15].Thusonly

struc-tures,whichminimizethetotalenergy,aretakenintoconsideration

inthefollowing.

Fig.1. SchematicviewofthreemoleculesadsorbedonaBernalBLG.Foraneasier visualization,thecarbonatomsofthetwolayersofBLGareinbrown(upperlayer) andcyan(bottomlayer)respectively,whilemolecularcarbonatomsareinblack. Hydrogenatomsareingreen,nitrogeninblue.(Forinterpretationofthereferences tocolorinthisﬁgurelegend,thereaderisreferredtothewebversionofthisarticle.)

Fig.2. SchematicbandstructuremodelofdopedBLGclosetotheKpointshowing the“Mexicanhat”dispersion(redlines).Thedashedcurvesrepresentthequadratic dispersionofpristineBLG.TheblackdashedlinecorrespondstotheFermilevel.(For interpretationofthereferencestocolorinthisﬁgurelegend,thereaderisreferred tothewebversionofthisarticle.)

3. Resultsanddiscussion

3.1. ElectronicbandstructureofBLG

AccuratedescriptionofthebandstructureofpristineBLGisa

prerequisiteforadiscussionofdopedBLGelectronicstructures.In

theBernalstacking,pristineBLGbandstructurenearthespecial

KpointofthereducedBrillouinzone,showsaquadratic

disper-sion,seeFig.2.The␲,␲*statesandtwolowerenergybandsare

splitineachvalleybyinterlayercoupling[9,13],asinFig.3awhich

showstheDFTresults.Twobandsstandforthehighestoccupied

␲orbitalsandthelowestunoccupied␲orbitals(dashedblue).The

correspondingelectronandholeeffectivemassesarecalculatedto

be0.045m0and0.056m0.Thesevaluesagreeverywellwith

pre-viousDFTestimates[15],butoverestimateslightlyexperimental

ones[46]:0.041and0.036m0,respectively.Thebandsingreen

cor-respondtothetwonextlevels.WhentheBLGisdoped,agapatthe

DiracpointKcanappear(deﬁnedasEK)whereastheminimum

separationbetweenthebandsisEg.EDcanbedeﬁnedastheenergy

differencebetweenthemiddleofthebandgapatKpointandthe

Fermilevelofthesystem.Thus,ED,EgandEKareequalto0for

pristineBLG.Meanwhile,adopedBLGwillpossessthe“Mexican

hat”dispersion,thebandgap(Eg)isnolongernull.Moreoverthe

energyleveloftheDiracpointcanbeshiftedduetochargetransfer.

3.2. Singlemoleculardoping

3.2.1. Electrondonormoleculedoping

BandstructuresinFig.3cindicatethatTTF’sadsorptiondoesn’t

affectelectronicstructureofBLGexceptanupshiftofFermilevel

withan ED value of251meV. Thisis in contradictionwiththe

reportedbandgapof80meV[15].Onecouldﬁrstattributethis

dis-crepancytoaconcentrationeffect,sincewehave1TTFmolecule

per98C atoms,when 72C atoms wereused inSamuels’ work.

Howeverwhentheconcentrationisincreased,weonlyobservea

largershiftoftheFermilevel,withoutgapopening.Sowemay

attributethis difference,tothedifferentcomputationalsettings

usedandpossiblytotheexchange-correlationfunctionalchoice.

TheHOMO-derivedstateoftheTTFmoleculehybridizeswithone

oflow-energybandsoftheformerDiraccrossingpoint.Thecharge

transferbetweentheTTFmoleculeandtheBLGissmall0.1and

0.02edependingontheconcentration,asshowninTable1.

Onecouldexpectthatastrongerelectrondonorshouldbeable

toopena gapin aBLG. SinceTDAEmoleculehasa low

ioniza-tionenergythatapproachesthoseofalkaliatoms[47,48]itshould

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2 1 0 -1 -2 2 1 0 -1 -2 L L L L L L L L 2 1 0 -1 -2 2 1 0 -1 M K M K M K M K -2 Ε [ eV ] Ε [ eV ] Ε [ eV ] Ε [ eV ]

Fig.3. BandstructuresofapristineBLGandofdopedBLGswithmoleculesadsorbedononesideonly,calculatedusingvdW-DFfunctional,(a)PristineBLG(7×7),(b)TCNE dopedBLG(7×7),(c)TTFdopedBLG(7×7),(d)TDAEdopedBLG(7×7).(e)Fourzoom-inﬁgures(AroundKpoint)correspondingto(a)–(d).Thedashedlinecorrespondto theFermilevel.

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Table1

Chargetransfer(e)ofmoleculesandeachlayerofBLG:apositivevaluemeansanincreaseoftheelectronicdensitywhenanegativeonecorrespondstoalossoftheconsidered subsystem.Bandgapsvalues(meV)andtheDiracpointenergylevelshifts(meV)foreachdopedBLGsystemsarealsoincluded.

0.51% 1.56%

TCNE TTF TDAE TCNE TTF TDAE

CTBottomlayer −0.18 0.03 0.13 −0.05 0.006 0.05

CTToplayer −0.28 0.07 0.24 −0.23 0.011 0.12

CTMolecule 0.46 −0.1 −0.37 0.28 −0.017 −0.17

Bandgap(Eg) 103 0 85 113 0 110

Diracpointenergylevel(ED) 151 −251 −315 284 −413 −592

Table2

Interlayerspacing(Å)ofdopedBLGandpristineBLG.

TTF/BLG TDAE/BLG TCNE/BLG BLG Exp.[50]

PBE vdW PBE vdW PBE vdW PBE vdW

Distance 4.16 3.43 4.15 3.43 4.11 3.60 3.98 3.41 3.35

does.Indeed,theTDAEmoleculedonates0.37etotheBLG.Clearly,

theaccumulationsofchargesineachlayerarenotidentical(see

Table1).TDAEtransfers0.24etothetoplayer,and0.13etothe

bot-tomlayer,thusinducingcarrierconcentrationof9.3×1012_cm−2

and5.1×1012_cm−2_on_top_and_bottom_layer_{respectively.}_These

resultsshowthatthen-typedopingbyTDAEmoleculesismore

efﬁ-cientthanbyTTFones.Theelectronicbandstructuresarepresented

inFig.3d.Agap(85meV)isopenedinBLGwhenTDAEmolecules

areinvolved.ThegapattheDiracpointK(EK)is92meVandthe

Diracpointenergylevel(ED)isaround315meVbelowtheFermi

level.AdsorptionofTDAEmoleculeprovokeschargeredistribution

ingraphenelayer,whichproducesanelectrostaticﬁeld

perpen-diculartographenesurfacethatbreaksthesymmetryofBernal

BLG.Thisleadstoformationofagapbetween␲and␲*states.By

increasingTDAE’sconcentration,chargetransferpercarbonatom,

deﬁnedasthetotalchargeobtainedbyBLGdividedbythetotal

numberofCatoms)isincreasedfrom0.0019to0.0027e.

Conse-quently,thebandgapisenlargedby25meV,EDbecomes−592meV

andEKisaround124meV.Thedopingeffectisenhancedbya

highercoverageofmolecules.

3.2.2. Electronacceptormoleculedoping

Theadsorptionofa TCNEmoleculedoesn’taffecttheatomic

structure of the BLG. Moreover the total charge of the TCNE

moleculeisalmostidenticalaswithonemoleculeadsorbedona

MLG[24].Asforthedonormoleculecase,chargecontributionsof

thetwolayersareasymmetric;theupperlayeralittlemorecharge

(0.28e)than thesecondone(0.18e).Thischarge redistribution

inducedbyTCNE’sadsorptionalsocausesabandgapopeningas

showninFig.3b.TheDiracpointenergylevel(ED)lies151meV

abovetheFermilevel,whichsuggeststhatthemolecularhas

efﬁ-cientlyp-typedopedtheBLG.Abandgapopening(Eg)of103meVis

alsofound,whenEKis117meV.Ourresultsarecomparablewith

previouswork[15],inwhichitisreportedthatF2-HCNQobtains

0.51efromBLGandopensabandgapof118meV.Inthehigher

con-centrationcase,TCNEreceiveslesscharges,whileaveragecharge

contributionfromBLGincreases.ThelargervaluesofEg,ED,and

EK,113, 284and130meVrespectively, areaclear

manifesta-tionofastrongdopingeffect.Theworkfunctionincreasesfrom

4.9eV(lowconcentration)to5.1eV(highconcentration),whenthe

pristinevalueis4.25eV.

3.2.3. EffectsofvdWdispersioncorrections

GloballythechargetransferestimateswhenusingstandardPBE

asexchange-correlationfunctionalareveryclosetovdW-DFvalues

buttheBLG’selectronicstructureisverysensitivetotheinterlayer

spacing[49].SincePBEandvdW-DFprovidedifferentequilibrium

distancesbetweenthetwolayers,seeTable2,thebandstructures

ofBLGcalculatedwithPBEandvdW-DFfunctionalaredifferent.As

expectedtheinterlayerdistanceisoverestimatedwithPBE

func-tional,incomparisonwithexperimentalresults,whiletheinclusion

ofnonlocaleffectsinthefunctionalprovidesanacceptable

sepa-rationdespiteofalittleoverestimation.FortheTTF/BLGsystem,

noneofthetwobandstructurecalculationshaveagapopening.

ButtheFermilevelismoredownshifted(by50meV)inPBE.When

theTCNE moleculedopesthe BLG, The dopingis more

signiﬁ-cantforvdW-DFthanforpurePBEcalculations.TheDiracenergy

level(ED)isaround151meVabovetheFermilevelinboth

func-tionals.ThecorrespondingEgis59meVforPBEcalculation,while

thegapislargerwhendispersioneffectsaretakenintoaccount.

EKare87and117meV,forPBEandvdW-DFestimates

respec-tively.Asalreadymentioned,differenttypeoffunctionalsprovide

Fig.4. (a)SideviewofTTF/BLG/TCNEsystemandthecorrespondingcharge trans-fers,(b)SideviewofTDAE/BLG/TCNEsystemandthecorrespondingchargetransfers. Thevaluesontheleftarechargetransferfromonesubsystemtoanother,andvalues ontherightarethechargepossessedbycorrespondinglayer.

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L L _M _K L _M _K L Ε [ eV ] Ε [ eV ]

Fig.5.BandstructuresforTTF/BLG/TCNEsystem(a)andTDAE/BLG/TCNEsystem(b).(c)and(d)arezoom-inﬁguresaroundKpointneartheFermilevelfor(a)and(b), respectively.

distinctequilibriumgeometrieswhichdirectlyinﬂuencethe

elec-tronicstructureofthedopedBLG.

3.3. Dualmoleculardoping

If one side molecular doping succeeds to open a band gap

ina BLGit alsoshifts theFermi levelbeloworabovetheDirac

point depending onthe type of molecules absorbed. Moreover

theincreaseoftheadsorbate’sconcentrationenhancesthedoping,

withlargershiftsoftheFermilevel,andlargerbandgapsvalues.

Thusonecouldimaginetoadjustbandgapvalueswithmolecule’s

concentration.However,theincreaseofthebandgapislimiteddue

toachargetransfersaturationphenomenonalreadypresentatlow

concentration.Thesecondmajorproblemforpotentialapplications

isthattheFermilevelisnotlyinginthebandgap.Inthisrespect,

thedualmoleculesdopingshouldhelptocounterbalancetheFermi

levelshift.

Twotypesofconﬁgurationshavebeenaddressed:oneiswitha

TTFandaTCNEmoleculeadsorbedonthetopandthebottomof

theBLG.ThesecondoneusesTDAEandTCNEmoleculesasdopant.

Thecorrespondingsideviewsoftheoptimizedstructuresaswell

astheyieldedchargetransfersarepresentedinFig.4.Inthisdual

dopingmode,theTTFmoleculeprovidesasmallamountofcharge,

whiletheTCNEmoleculegets0.47efromtheBLG,Thiselectronic

densitymainlycomesfromtheclosestgraphenelayerbutalsofrom

theTTFmolecule.Indeedtheupperlayerisalmostneutral,when

theotheroneispositivelycharged.SincetheTDAEmoleculeisa

betterdonorthantheTTFspecies,0.43eisthustransferredtoBLG

isthesecondcase.AtthesametimetheTCNEmoleculereceives

0.51e. Theupperlayer,theoneclosertotheTDAEmolecule, is

nowpositivelycharged,whereasthesecondlayerisnownegatively

charged.Attheend,theBLGremainsalmostneutral,asofthecharge

hasbeenentirelytransferredfromtheTDAEtoTCNEmolecule,but

polarizingtheBLG.

Fig.5 presentshowdual dopingmodeaffects theelectronic

bandstructuresoftheBLG.IntheTTF/BLG/TCNEsystem,BLGis

p-typedoped(ED=72meV)duetoTCNE’sstrongerdopingability,

withabandgapof138meV.Thisvalueisalreadylargerthanthe

oneobtainedinthesingledopingmodeatthelargest

concentra-tion.Moreimportantly,theenergyleveloftheDiracpointisnow

shiftedbackinthevicinityoftheFermilevel.Ifastrongdonorlike

TDAEisusedthentheFermilevelisnowlocatedatthemaximum

ofthehighestvalenceband,theBLGbecomesasemi-conductor

withabandgapof100meV.Theelectronandholeeffectivemasses

aredrasticallychangedduetothegapopening,withvaluesbeing

0.22m0fortheelectronand1.23m0forthehole.Thisresultproves

thatideallyonecouldimagethataﬂexiblebandgaptuningcanbe

realizedbyadjustingtopandbottommolecule’sconcentration.

4. Conclusion

Insummary,moleculardopingprovokesanasymmetrycharge

distribution in graphene layers, which in turn, causes a band

gapopeninginAB-stackingBLG.Byincreasingtheconcentration,

dopingismoreefﬁcient:largershiftsoftheFermilevelandlarger

bandgapvaluesareobtained.Controllingmolecule’s

concentra-tionaswellastheadsorptionmodescanmodulatetheBLGband

gaps.Wehaveshownthatdualdopingmodemodulatetheband

gapvalueinaﬂexiblewayandtunetheDiracpointenergy

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usingstandard xc-functionalsare certainly underestimated and

moreaccuratevaluesshouldbeobtainedeitherbyusinghybrid

functionalsorGW calculations,butthisstudyliketheone

pub-lishedinRef.[15]provideﬁrstproofsoftheconceptofdualdoping

mode.

Acknowledgements

ThisworkwassupportedbyGENCI-CINES,GENCI-IDRISthrough

theprojectx2012096357andprojectx2013096649.Theauthors

wouldliketothanktheCALculenMIdi-Pyrénées(CALMIP,grant

2012/2013-P0812) for generous allocations of computer time.

Finally,T.HuwouldliketothankCSC-INSAprogramforﬁnancial

supportofhisPh.D.study

References

[1]K.S.Novoselov,Science306(2004)666.

[2]A.H.CastroNeto,F.Guinea,N.M.R.Peres,K.S.Novoselov,A.K.Geim,Rev.Mod. Phys.81(2009)109.

[3]C.Lee,X.Wei,J.W.Kysar,J.Hone,Science321(2008)385.

[4]F.Wang,Y.Zhang,C.Tian,C.Girit,A.Zettl,M.Crommie,Y.R.Shen,Science320 (2008)206.

[5]Y.-M.Lin,A.Valdes-Garcia,etal.,Science332(2011)1294. [6]M.Liu,etal.,Nature474(2011)64.

[7]Y.Zhang,etal.,Nature459(2009)820.

[8]F.Xia,T.Mueller,Y.Lin,A.Valdes-Garcia,P.Avouris,Nat.Nanotechnol.4(2009) 839.

[9]E.McCann,Phys.Rev.B:Condens.Matter74(2006)161403. [10]E.McCann,V.I.Fal’ko,Phys.Rev.Lett.96(2006)086805. [11]W.Zhang,etal.,ACSNano5(2011)7517.

[12]X.Tian,J.Xu,X.Wang,J.Phys.Chem.B114(2010)11377.

[13]T.Ohta,A.Bostwick,T.Seyller,K.Horn,E.Rotenberg,Science313(2006)951. [14]W.J.Yu,L.Liao,S.H.Chae,Y.H.Lee,X.Duan,NanoLett.11(2011)4759. [15]A.J.Samuels,J.D.Carey,ACSNano7(2013)2790,130227104203005. [16]E.V.Castro,etal.,Phys.Rev.Lett.99(2007)216802.

[17]Z.Q.Li,etal.,Phys.Rev.Lett.102(2009)037403.

[18]S.B.Kumar,J.Guo,Appl.Phys.Lett.98(2011)222101.

[19]X.Blase,A.Rubio,S.G.Louie,M.L.Cohen,Phys.Rev.B:Condens.Matter51 (1995)6868.

[20]S.-M.Choi,S.-H.Jhi,Y.-W.Son,NanoLett.10(2010)3486. [21]Y.Guo,W.Guo,C.Chen,Appl.Phys.Lett.92(2008)243101.

[22]Y.-H.Zhang,K.-G.Zhou,K.-F.Xie,J.Zeng,H.-L.Zhang,Y.Peng,Nanotechnology 21(2010)065201.

[23]Y.H.Lu,W.Chen,Y.P.Feng,P.M.He,J.Phys.Chem.B113(2009)2. [24]T.Hu,I.C.Gerber,J.Phys.Chem.C117(2013)2411.

[25]L.Chen,L.Wang,Z.Shuai,D.Beljonne,J.Phys.Chem.Lett.4(2013)2158. [26]C.Coletti,etal.,Phys.Rev.B:Condens.Matter81(2010)235401. [27]J.Park,etal.,Adv.Mater.24(2012)407.

[28]J.W.Yang,G.Lee,J.S.Kim,K.S.Kim,J.Phys.Chem.Lett.2(2011)2577. [29]T.H.Wang,Y.F.Zhu,Q.Jiang,J.Phys.Chem.C117(2013)12873. [30]T.H.Wang,Y.F.Zhu,Q.Jiang,Carbon77(2014)431.

[31]J.Klimeˇs,D.R.Bowler,A.Michaelides,Phys.Rev.B:Condens.Matter83(2011) 195131.

[32]L.Liu,Z.Shen,Appl.Phys.Lett.95(2009)252104.

[33]M.Dion,H.Rydberg,E.Schröder,D.C.Langreth,B.I.Lundqvist,Phys.Rev.Lett. 92(2004)246401.

[34]K.Berland,etal.,J.Chem.Phys.140(2014)18A539.

[35]P.Hyldgaard,K.Berland,E.Schröder,Phys.Rev.B:Condens.Matter90(2014) 075148.

[36]T.Björkman,A.Gulans,A.V.Krasheninnikov,R.M.Nieminen,J.Phys.Condens. Matter24(2012)424218.

[37]T.Björkman,J.Chem.Phys.141(2014)074708.

[38]A.Puzder,M.Dion,D.C.Langreth,J.Chem.Phys.124(2006)164105. [39]U.Starke,S.Forti,K.v.Emtsev,C.Coletti,MRSBull.37(2012)1177. [40]G.Kresse,J.Hafner,Phys.Rev.B:Condens.Matter47(1993)558. [41]G.Kresse,D.Joubert,Phys.Rev.B:Condens.Matter59(1999)1758. [42]A.Gulans,M.J.Puska,R.M.Nieminen,Phys.Rev.B:Condens.Matter79(2009)

201105.

[43]J.P.Perdew,K.Burke,M.Ernzerhof,Phys.Rev.Lett.77(1996)3865. [44]W.Tang,E.Sanville,G.Henkelman,J.Phys.Condens.Matter21(2009)084204. [45]H.Kim,etal.,Appl.Phys.Lett.105(2014)011605.

[46]K.Zou,X.Hong,J.Zhu,Phys.Rev.B:Condens.Matter84(2011)085408. [47]M.R.Pederson,N.Laouini,J.Clust.Sci.10(1999)557.

[48]H.Bock,H.Borrmann,Z.Havlas,H.Oberhammer,K.Ruppert,A.Simon,Angew. Chem.Int.Ed.Engl.30(1991)1678.

[49]T.Ohta,A.Bostwick,J.L.McChesney,T.Seyller,K.Horn,E.Rotenberg,Phys.Rev. Lett.98(2007)206802.