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Spontaneousformationofgrapheneondiamond(111)drivenbyB-dopinginducedsurfacereconstructionChaoLua,b,HongxinYangc,JingXud,LifangXua,MairbekChshievc,ShengbaiZhange,ChangzhiGua,f,g,*aInstituteofPhysics,ChineseAcademyofSciences,Beijing100190,ChinabChinaAcademyofEngineeringPhysics,Mianyang621700,ChinacSPINTEC,UMRCEA/CNRS/UJF-Grenoble1/Grenoble-INP,INAC,GrenobleF-38054,FrancedDepartmentofPhysics,RenminUniversityofChina,Beijing100872,ChinaeDepartmentofPhysics,AppliedPhysicsandAstronomy,RensselaerPolytechnicInstitute,Troy,NY12180,USAfCollaborativeInnovationCenterofQuantumMatter,Beijing,ChinagSchoolofPhysicalSciences,CASKeyLaboratoryofVacuumPhysics,UniversityofChineseAcademyofSciences,Beijing100190,ChinaarticleinfoArticlehistory:Received20November2016Receivedinrevisedform4January2017Accepted10January2017Availableonline11January2017abstractSpontaneousconstructionofgrapheneonboron-dopeddiamond(111)surfacehasbeenfoundinrst-principlescalculations.
Boron-doping-inducedsurfacereconstructionisthemechanismresponsibleforthediamond-to-graphenephasetransition.
Furthermore,theeffectonthesurfaceisunexpectedlyobservedatanydopingdepthdowntothe7thlayer,andalowconcentrationofsubstituentboroneonlyeiseffectiveforgrapheneformation.
Amazingly,whenboronatomsareincorporatedintothefthlayer,thedirectoptimizationofthe11surfaceautomaticallygivesrisetoagraphenestructurefromtherstbilayerwithnoenergybarrier,indicatingthattheformationofgrapheneisspontaneous.
Thesendingsprovideanalternativestrategyforgraphenesynthesisonwide-gapinsulatorswithhighthermalconductivity.
2017ElsevierLtd.
Allrightsreserved.
1.
IntroductionSincesuccessfully"re-discovery"in2004[1,2],graphenehasbeenamaterialofgreatinterestowingtoitsverygoodthermalconductivity,mechanicalstiffnessandextraordinaryelectronictransportproperties[3e5],includinghighcarriermobilityandballistictransport,whicharegenerallypreserveduptoroomtemperature[6e8].
Thesepropertiesgivegraphenegreatpotentialasamaterialfortechnologicalapplicationsasasuccessorofsiliconinthepost-Moore'slawera[9e11],inspintronics[12e15]andinquantumcomputing[16].
Oneofthemainrequirementsforsuchapplicationsisabilitytogrowuniformgrapheneonaninsulatingsubstrate[17].
Unlikesuspendedgraphene,whichisasemi-metal[1,18],epitaxiallygrowngrapheneonaninsulatormayopenabandgapattheDiracpointduetothebreakingofsublatticesym-metryinducedbythegraphene-substrateinteraction[19,20].
Twoinsulatingmaterialsthathavebeenusedverysuccessfullyasasubstrateforgraphenegrowth/synthesisareSiCandhexagonalboronnitride(hBN)[21e23].
Recently,graphene-on-diamondstructuresanddevicesshowedgreatlyimprovedperformance,duetotheexcellentpropertiesofdiamondsubstrate[24e28].
However,fewinvestigationisreportedsofarregardingthepossi-bilityofsynthesizinggraphenedirectlyondiamond[29].
Moreover,averysmalllatticemismatchbetweengrapheneandthediamond(111)surfacemakesthelatteranidealcandidateasasubstrateforgraphene.
Investigatingthepossibilityofgraphenegrowthonadiamondsubstrateisthegoalofthepresentwork,whichmayprovideaviablealternativeforgraphenesynthesisonC-terminatedSiC(0001)andhBN[30,31],andofearlierreportsoflocalgraphi-tizationondiamond(111)surface[32,33].
Thismethodofgraphenesynthesisondiamondisanalternativeforovercomingtheover-heatingproblemingraphene-baseddevices,inviewofthehighthermalconductivityofdiamondcombinedwiththehugeelec-tricalconductivityofgraphene.
Inthisletter,wereportsystematicallyinvestigatingthepossi-bilityofgrapheneconstructiononborondopeddiamond(111)surfaceforvariousdopingconcentrationsanddepths,usingrst-*Correspondingauthor.
InstituteofPhysics,ChineseAcademyofSciences,Beijing100190,China.
E-mailaddress:czgu@iphy.
ac.
cn(C.
Gu).
ContentslistsavailableatScienceDirectCarbonjournalhomepage:www.
elsevier.
com/locate/carbonhttp://dx.
doi.
org/10.
1016/j.
carbon.
2017.
01.
0300008-6223/2017ElsevierLtd.
Allrightsreserved.
Carbon115(2017)388e393principlescalculations,ndingthatgraphenecanformspontane-ouslywithoutanypotentialbarrierwhenBisincorporatedinsurfacelayerswitharelativelylowconcentration.
Incontrasttowhatmightbeexpected,thedoping'seffectonthesurfaceisstrongerastheBatomsarelocateddeeper,untilthe7thlayer,wherethesituationislikesubstitutioninbulk.
Boron-dopinginducedsurfacereconstructionisconsideredtobethephysicalmechanismofthediamond-to-graphenephasetransition.
2.
MethodsOurrst-principlescalculationswerecarriedoutusingtheViennaabinitiosimulationpackage(VASP)[34].
Theelectron-coreinteractionsweredescribedbytheVanderbiltultrasoftpseudopo-tential[35]andtheexchangecorrelationenergyobtainedwithinthegeneralizedgradientapproximation(GGA)[36].
AplanewavebasissetwasusedtoexpandtheKohn-Shamorbitals,withakineticenergycutoffof350eV.
Thetheoreticallatticeconstantofdiamondwastakentobeequalto3.
574inallcalculations,andtheMonkhorst-Packscheme[37]wasusedfortheBrillouinzoneintegrationwitha221k-pointmesh.
Duringenergymini-mization,theatomsaresettobefullyrelaxedexceptthoseinthebottomtwolayers,whicharexedattheirrespectivepositions.
Toavoidinteractionbetweenthetopandbottomsurfaces,18layersofcarbonatomsinthesupercell,withthebottomlayerterminatedbyhydrogenandmorethan15ofvacuum,wasusedtosimulatediamond(111).
Thesideandtopviewsofdiamond(111)areshowninFig.
1(a)and(b),respectively.
Thedistancesfortherstseveralbilayers(BL)arealsoprovided,showingthattherstlayerofcar-bonatomsshiftsinwardandformsstrongerbondswiththesecondlayerofcarbonafterrelaxationinpurediamond(111)surface.
Atthesametime,therstbilayerisshiftedoutwardandformsweakbondswiththesecondbilayer.
However,suchsmallchangeisnotyetenoughtoseparatetherstbilayerofcarbonatomsintogra-phenefromthediamondphase.
3.
ResultsanddiscussionsInordertostimulatethediamond-to-graphenephasetransi-tion,weintroducedboronintodiamond(111)takingintoaccountthatitrepresentsthemostcommonimpurityinbothnaturalandchemicalvapordeposited(CVD)diamond.
Thestabledopingpo-sitionofboronindiamondissubstitutionalratherthaninterstitial[38].
Fig.
2(a)and(b)showtheoptimizedstructureswithboronatomsincorporatedintotherstandthethirdlayersofdiamond(111),respectively.
Onecanseethatwithboronatomsintherstlayer(Fig.
2(a)),theverticaldistancebetweenasurfaceBatomandaneighboringCatomisslightlysmaller(0.
23)thantheverticaldistancebetweenasurfaceCatomandaneighboringCatominpurediamond(0.
27)(Fig.
1(a)).
Whenboronatomsareincorpo-ratedintothethirdlayer(Fig.
2(b)),theverticaldistancebetweenthecarbonatomintherstlayerandthesecond-layerneighborthatsitsontopoftheboronatomisreducedfrom0.
27to0.
05,whilethedistancebetweentherstbilayerandthesecondbilayerisincreasedto2.
0.
Whenboronisdopedintothethirdlayer,itformscovalentbondswiththethreenearestcarbonatomsinthefourthlayersinceithasonlythreeelectronsintheoutershell.
Thus,itleadstoaweakerbondingwithatopcarbonatominthesecondlayer(denotedbyCtop),andthentheinteractionbetweentherstandsecondbilayerbecomesweaker.
Inthiscase,theCtopatomformssp2-likehybridizedbondswiththeneighboringcarbonatomsintherstlayer,whiletheremainingcarbonatomsinthesecondlayerstillformsp3-likebondswiththeircounterpartsintherstlayer.
Additionally,onecanseethat1/4boronconcentrationinthethirdlayerresultsin3/4ofthecarbonatomsintherstlayerformingsp2bondswithCtopatomsinthesecondlayer,eliminating3/4ofthedanglingbondsofthe(111)surface.
Amazingly,whenboronatomsareincorporatedintothefthlayer,thedirectoptimizationof11surfaceautomaticallygivesrisetoagraphenestructurefromtherstbilayerwithnoenergybarrier,indicatingthattheformationofgrapheneisspontaneous(Fig.
2(candd)).
Beingadjustedtothediamondlattice,thedistancebetweenneighborcarbonatomswithinthegraphenelayerisabout1.
45,whichisveryclosetothenearest-neighbordistanceof1.
42ingraphene.
Thedistancebetweengraphenelayeranddiamondsubstratestabilizesatabout3.
30,whichiscomparabletothedistanceof3.
35betweenthelayersingraphite.
Thus,astructuralphasetransitionfromdiamondtographeneondiamond(111)substratetrulyoccurredinthissimulation.
NotethatthestructurebelowthegraphenelayerinFig.
2(d)isverysimilartothethird-layer-dopingstructureinFig.
2(b).
Thesamephasetransitionhappensforthestructurewithboronatomsincorporatedintotheseventhlayer.
Inthiscasethersttwobilayersofdiamond(111)surfacearereconstructedintotwographenelayers.
Whenboronatomsaredopeddeeperbeyondtheseventhlayer,thesituationisinsteadbulkincorporationandhaslittleeffectonthesurface.
Therelativeenergiesoftheboron-dopedstructuresoptimizedabovearesummarizedinFig.
3,representedbybluestars.
Theenergiesdecreasewithdopingdepthinazigzagwaytilltothe7thlayer,andthenabruptlyjumpfromthe8thlayer.
Generally,themorethesp3-to-sp2transitionhappens,thelowertheenergyis.
Fig.
1.
(a)Sideviewofdiamond(111).
(b)Topviewof1bilayerofdiamond(111);biggreyballsrepresentcarbonatomsintherstlayer,whilesmallblueballsindicatecarbonatomsinthesecondlayer.
(Acolourversionofthisgurecanbeviewedonline.
)C.
Luetal.
/Carbon115(2017)388e393389Theenergyofthethird-layer-dopingislowerthantherst-layer-doping,becausethethird-layer-dopingcausesmoresp3-to-sp2transitionsandeliminatesmoresurfacedanglingbonds.
Thefth-layer-doping(seventh-layer-doping)hasevenlowerenergy,becauseithasonelayer(twolayers)ofgrapheneinsteadofonebilayer(twobi-layers)ofdiamondcomparedwiththethird-layer-doping.
Thesecond-,fourth-andsixth-layer-dopinghavehigherenergiesbecausethesestructuresreducethesurfacedanglingbondslessefciently.
OnecanseethatuponBdoping,allrelaxed11diamond(111)surfaceenergiesdecrease,duetotheeliminationofdanglingbonds.
However,those11surfacescanbereconstructedfurthertoPandey-chainstructures[39].
TherelativeenergiesforPandey-chainreconstructionsurfacesarecalculatedandrepresentedbyblackballsinFig.
3,showingthattheenergiessteadilyincreasewithdopingdepthstartingfromthelowestenergyintherstlayer,andnallyapproachingthevalueofthePandey-chainstructureofbulkdoping.
ThisindicatesthatthedopingeffectonthesurfaceisweakerasthedopingboronatomisdeeperinPandey-chainstructures,asexpected.
Nowwecomparetheenergiesbetweenoptimized11surfaceandPandey-chainsurface.
Inmostcases,Pandey-chainsurfacehaslowerenergywhichmeansthat11surfacecanbefurtherreconstructedtoPandey-chainstructure.
However,whenboronisinthefth(seventh)layer,adramaticchangeoccurs:thecrossoverbetweenthebluecurveandblackcurvetakesplace,whereuponthePandey-chainstructurehashigherenergy.
Thisclearlyshowsthatthespontaneouslyformedgrapheneondiamond(111),iftriggeredbyboronincorporationinthefth-layer,isthegroundstateratherthanthereconstructedPandey-chain.
Asthesp2hybridizedbondislowerinenergythanthesp3bonds,suchareconstructionprocessfavorssurfacestabilitymorestrongly[40].
Afterward,ifthesubstratebelowthegraphenelayerinFig.
2(d)isfurtherreconstructedintothePandey-chainstructure,thetotalenergywouldbemuchdecreased,asdenotedFig.
2.
(a)and(b)Optimizeddiamond(111)with1/4ofthecarbonatomsintherstandthirdlayerreplacedbyboronatoms,respectively.
(c)and(d)Initialandoptimizedstructures,respectively,bothwith1/4ofthecarbonatomsinthefthlayerreplacedbyboronatoms.
(e)and(f)Initialandoptimizedstructures,respectively,bothwith1/16borondopingconcentrationinthefthlayer.
Pinkballsrepresentincorporatedboronatoms,andgreyballsindicatecarbonatoms.
In(e)and(f),theblueballsrepresentcarbonatomsbeforeandafterforminghexagonalgraphitestructureintherstbilayer,whilethepurpleballsrepresentcarbonatomsbeforeandafterformingsp2bondswithCtopatom.
(Acolourversionofthisgurecanbeviewedonline.
)C.
Luetal.
/Carbon115(2017)388e393390bytheredsquareinFig.
3.
Whydoesthisstructurephasetransitionfromdiamondsp3tographenesp2happenondiamond(111)surfacewhenboronisdopedatthefthlayer,andwhyis1/4dopingdensityenoughtomakethetransitionTounderstanditsorigin,weinvestigatedatypicalmodelwithasingleBatomina33surfacecellincor-poratedintothefthlayerofdiamond(111)(1/16borondopingconcentration),asshowninFig.
2(e).
Afteroptimization,ahexag-onalgraphene-likestructurewithabondlengthof1.
44bulgesdramaticallyintherstbilayer,showninblueinFig.
2(f).
ThedistancebetweenthethreeCatomsinpurpleatthe3rdlayerandthethreeCatomsatthe2ndlayer,inblue,iselongatedto2.
42,indicatingmuchweakerbonding,ornomorebondingatall,be-tweenthem[41].
Now,wepresentindetailaphysicaldescriptionofhowaBatominducesformationofthegraphene-likering.
Onceaboronatomisincorporatedintothe5thlayer,theBatomformscovalentbondswithitsthreenearestCatomsatthe6thlayer,whileitcreatesadanglingbondonaCtopatomatthe4thlayerrightontopoftheBatom.
Infact,theroleofthedopedBatomatthe5thlayerissimplytointroduceadanglingbondunderneaththeCtopatom.
BoththeCtopatomandallCatomsatthesurfacewithdanglingbondshaveastrongtendencyofchangingfromthesp3statetothesp2stateinordertoreducethenumberofdanglingbonds.
Then,theCtopatomwillnegotiatewiththethreeneigh-boringcarbonatomsatthe3rdlayer,showninpurpleinFig.
2(e),tochangetogethertothesp2state,andsurfaceatomspersuadeCatomsatthe2ndlayertodothesame.
Then,thoseCatomsatthe2ndlayerand3rdlayerwillcommunicatetoaccepttheproposaltobeinthesp2state.
Finally,onecanseethattheCtopislifteduptoanelongateddistanceof1.
89andformssp2hybridizedbondswiththethreeneighboringcarbonatoms,showninpurpleinFig.
2(f),andthesixCatomsontopoftheBintherstbilayerformasp2hexagonalgraphene-likestructure.
Thereupon,thethreebondsbetweenpurplecarbonatomsinthe2ndbilayerandtheblueatomsinthe1stbilayervanish,sinceallofthemhaveonlysp2hybridizedbonds.
Itisworthemphasizingagainthatthethreesp3bondsarenotbroken,butratherdisappearduetothetransitionfromsp3tosp2state.
So,wehaveshownthatasingledopedboronatomatthefthlayerinducesformationofonegraphene-likeringonthesurface.
Byincreasingthedopingconcentrationto1/4,therstbilayeriscompletelygraphitizedasshowninFig.
2(d).
ThisdensityrequiresthateachdopedBatommustinducethetransformationoffourcarbonsp3bondsbetweenthe1stbilayerandthe2ndbilayerintothesp2state.
TwodifferentprocessesareresponsibleforthisphaseFig.
3.
Relativeenergyof1/4borondopeddiamond(111)with11reconstructedandPandey-chainreconstructedsurfacesasfunctionsofthedepthofboronincorporation.
Linesserveonlytoguidetheeye.
(Acolourversionofthisgurecanbeviewedonline.
)Fig.
4.
Chargedistribution(e/2)acrosstheplanedeterminedbyboron(white),thenearestcarbon(black)ontopofboronandoneofthenearestcarbonbelowboronforthe1/4boronincorporatedinfthlayerdiamondofFig.
2(d).
Akeytotheothercolorsisshownontherightsideethegradientfrombluetoredshowschargedensityfromlowertohigher.
(Acolourversionofthisgurecanbeviewedonline.
)C.
Luetal.
/Carbon115(2017)388e393391transition,indirectandindirectmanners,respectively.
Thedirectprocesswasalreadydescribedabove:asingleBatomatthe5thlayercreatesasix-foldgraphite-likering,wherethreesp3bondshavechangedtosp2,inducedbytheBatom.
Now,onemorebondislefttobeunderstood.
Weneedtolookagainatthesix-foldgraphite-likeringstructurecreatedbyasingleBatom.
Onceitisformed,allsixCatomsareinsp2states,inwhichthreeCatomsatthe2ndlayerchangetothesp2state,andthreeCatomsatthe1stlayertransformtothesp2state.
NotethatthethreeCatomsatthe1stlayerwillaffectneighboringCatomsatthe2ndlayer,outsideofthering.
Whenthosegraphite-likeringsformaperiodicstructureinour22surfacecellwith1/4Bdopingdensity,thelastsp3-bondedCatomatthe2ndlayerissurroundedbythreegraphite-likeringsanditconnectstothreerst-layerCatomsintheserings.
Together,thesethreesurroundingsp2-stateCatomsenablethelastsp3-to-sp2transitionofaCatomatthe2ndlayer.
Inordertocheckthispicture,werepeatedthecalculation,eliminatingseveralintermediatestepsduringtheoptimization,showingclearlythatthegrapheneringsappearveryquicklyafterjustafewoptimizationstepsinwhichthreesp3bondsatopeachBatomdisappear,andlater,theBatom'sonlyremainingsp3bondbecomesweakerandweaker,andnallydisappeartoo.
Thisisanindirectprocessandcouldberegardedasa2nd-ordereffectofdopedBatoms,sinceitresultsfromthecollectiveeffortsofthreesurroundedCatomsinthreeringsthatformedearlierintheprocess.
Eventually,boththedirectandindirectprocessestrans-formallCatomsatthe1stbilayerintothesp2statewhereuponthegraphenehasbeenautomaticallyconstructed.
Finally,weplottedthechargedistribution,showninFig.
4,for1/4concentrationofboronincorporatedintothefthlayerindia-mond(111)(asshowninFig.
2(d)).
Inordertoseethedifferencesbetweentheboron-to-CtopbondingandthebondingoftheboronatomtotheCatomsbelowit,wechosetoinvestigatemorecloselytheplaneformedbyaboronatom,itsCtopatomandoneCatombelowtheboron.
Onecanclearlyseethatboron'sbondingtotheCtopatomismuchweakerthanitsbondingtotheCatombelow,indicatingthattheCtopatomhasadanglingbond.
Asaresult,thecarbonatomsinthefourthlayershiftupwardabitandusetheirdanglingbondstoformstrongersp2bondswithcarboninthethirdlayer.
4.
ConclusionsInsummary,weinvestigatedtheformationofgrapheneonboron-dopeddiamond(111)surfacebyusingrst-principlescal-culations,demonstratingthatgraphenecanbespontaneouslyconstructedwith1/4substitutionaldopingofboronatomsinthefthlayerofdiamond(111).
SurfacereconstructioninducedbytheB-dopingisthephysicaloriginoftheobserveddiamond-to-graphenephasetransition.
The1stbi-layerofdiamond(111)be-comesgrapheneduetosurfacereconstruction,drivenbyastrongtendencyofsurfacecarbonatomstotransformtothesp2state,combinedwiththeinuenceofsub-surfacedopingwithBatoms.
Thisresultpavesthewaytoadirectapproachforgraphenesyn-thesisonwidebandgapmaterials,whichwillattractsignicantinterestinviewofthewidespreadquestforgraphene-basedelec-tronicswithhighthermalconductivity.
AcknowledgmentsThisworkissupportedbytheNationalNaturalScienceFoun-dationofChinaunderGrantNos.
51272278,61390503,91323304,and11574369;MOSTunderGrantNo.
2016YFA0200402,XDB07020200,NanosciencesFoundationinGrenobleandFrenchANRPNANOProject"Nanosim-Graphene",andtheU.
S.
DepartmentofEnergyunderGrantNo.
DE-SC0002623.
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