Structural and electronic properties of cubic HfO2 surfaces - 图文

Available online at www.sciencedirect.comComputationalMaterialsScience44(2008)46–52

www.elsevier.com/locate/commatsci

StructuralandelectronicpropertiesofcubicHfO2surfaces

G.H.Chen,Z.F.Hou,X.G.Gong*SurfacePhysicsLaboratoryandDepartmentofPhysics,FudanUniversity,Shanghai200433,China

Availableonline6March2008

Abstract

Usingthe?rst-principlesmethodwithinthegeneralizedgradientapproximation,wehaveperformedasystematicstudyonthestruc-turalandelectronicpropertiesofcubicHfO2surfaces.We?ndthatthemostenergeticallyfavorablesurfacesare(110)and(111)ter-minatedwithsingleoxygenlayer,bothofwhicharestoichiometric.Theatomicrelaxationintoplayersofsurface(111)-Oand(110)exhibitsverysimilarbehavior,i.e.cationsrelaxinwardwhileanionsoutward.ThiscouldbewellunderstoodbytheionicfeatureoftheHf–Obond.Bothofthetwosurfacesstudiedareinsulatingwithoutanysurfacestateintheenergygap.ó2008ElsevierB.V.Allrightsreserved.

PACS:68.35.Md;68.47.Gh;73.20.At;81.10.AjKeywords:Highj;HfO2;Surfaces;First-principles

1.Introduction

Hafniumdioxide(HfO2)recentlyattractsmuchatten-tioninthegatestackofmetaloxidesemiconductor?eld-e?ecttransistors(MOSFETs)duetoitsrelativelyhighdielectricconstant,widebandgapandgoodstabilityuponSi,andsoon[1].In2006itwasreportedhafniumbasedoxideswassuccessfullyemployedasgatedielectricin45nmtransistortechnologybyIntel[2].Howevertheper-formanceofHfO2dielectricintegratedintosilicontechnol-ogyisessentiallydeterminedbytheupperinterfacebetweengateelectrodeandHfO2aswellasthebottominterfacebetweenHfO2andSichannel.Thestudyonsur-facepropertiesofHfO2ispreliminaryandnecessaryforunderstandingthebehaviorofthesetwointerfaces.Inpre-vioustheoreticalstudiesoninterfacesofmetalgate/HfO2[3,4],HfO2=Si[5–8],andHfO2=SiO2[9],theorientationofHfO2layersismostlychosenas(001)surfacesbasedontheconsiderationoflatticematching.Althoughthesemodelingstudieshavesuccessfullypredictedsomephysical

*Correspondingauthor.

E-mailaddress:xggong@fudan.edu.cn(X.G.Gong).

propertiesofinterfaces,?rst-principlescalculationsonsur-faceenergiesofmonoclinicHfO2haveshownthat[10]e??111Tand(111)surfacesarethermodynamicallyfavoredsurfaceswhilethe(001)faceiskineticallyfavored,whicharealsosupportedbytheX-raydi?raction(XRD)spectraofHfO2thin?lmsgrownorannealedatdi?erenttempera-tures[11–15].ForgatestackofMOSFETs,HfO2gatedielectricmustbethermodynamicallystableonSisub-strate.Therefore,inordertobuildmorerealisticmodelforinterfacesrelatedtoHfO2,acompleteunderstandingofsurfacepropertiesofHfO2?lmisrequired.Researchworkonthistopicisstilllimited,andonlymonoclinicHfO2surfaceshavebeenreported[10].Furthermore,thee?ectofterminationlayerofsurfacesonelectronicstruc-tureofHfO2?lmswasneglectedintheworkofMukho-padhyayetal.[10].However,ane?ectivemetallizationofHfO2surfacebyheatingtoT>600??Cwasdetectedbylowenergyionspectroscopyinrecentexperimentalstudy[16],suggestingthattheterminationofoutmostsurfacelayersigni?cantlya?ectsthesurfaceelectronicstructuresofHfO2?lms.Ithasbeenshownthatthecrystal?elde?ectsinHfO2polymorphsmainlyresultinthedi?erentwidthoflowerconductionbands[17],therefore,wealternativelychoosecubicphaseofHfO2todetailedly

0927-0256/$-seefrontmatteró2008ElsevierB.V.Allrightsreserved.doi:10.1016/j.commatsci.2008.01.051

G.H.Chenetal./ComputationalMaterialsScience44(2008)46–5247

understandthesurfacepropertiesofHfO2.Inthiswork,?rst-principlescalculationsareperformedtosystematicallystudytheatomicstructures,stabilities,andelectronicstruc-turesoflowMillerindexsurfaces(i.e.(100),(110)and(111))withvariousterminationlayersofcubicHfO2.Thispaperisorganizedasfollows.Thenextsectiondescribesthecomputationaldetailsofthisstudy.Inthethirdsectionwediscussthebulkproperties,surfaceener-gies,atomicrelaxationsofsurfaces,andsurfaceelectronicstructuresofcubicHfO2aswell.Inthelastsectionwedrawsomegeneralconclusions.2.Computationaldetails

AllsimulationsherearecarriedoutusingplanewavepseudopotentialmethodasimplementedintheViennaabinitiosimulationpackage(VASP)[18,19].Theexchange-correlationfunctionalistreatedwithinthegeneralizedgra-dientapproximationandparameterizedbyPerdew–Wangformula[20].Theinteractionbetweenionsandelectronsisdescribedbyultra-softVanderbiltpseudopotentials[21,22].Thewavefunctionsareexpandedinplanewaveuptoacuto?energyof495eV.Brillouin-zoneintegrationsareapproximatedbyusingthespecialk-pointsamplingofMonhkorst–Packscheme[23].Atomicrelaxationsareper-formedwithintheconjugatedgradientschemeandtheforceA

?oneachatomisconvergedtobelessthan0.01eV/.FortheelectronicminimizationthespecialDavisonblockiterationalgorithm[24]isadoptedandatoleranceof0.02meVforabsolutedi?erenceoftotalenergyisusedduringtheelectronicself-consistentloop.Inthecalcula-tionsofcubicHfO2bulk,ameshsizeof5?5?5isusedfork-pointsampling.

TomodelthesurfacesofcubicHfO2,weusedthewell-known‘‘slab”approach,inwhichperiodicboundarycon-ditionsareappliedtothesurfacesupercellincludingaslabofatomiclayersandavacuumregionasshowninFig.1.Inpresentwork,wefocusonthesurfaceenergiesandcor-respondinglocalrelaxationsratherthanthecomplexreconstructions,therefore,1?1unitcellsareusedforthelowMillerindex(i.e.(100),(110),and(111))surfacesofcubicHfO2inourcalculations.Toguaranteesurfacesonbothsidesoftheslabbeingequivalentandeliminatethenetdipolemoment,weemployaslabwithamirrorsymmetry.ForcubicHfO2,its(100)surfacemaybetermi-natedeitherbyoneatomicHforOlayer(labeledas–Hfand–O,respectively),andits(111)surfacecouldbetermi-natedbyoneatomicHflayer,oneatomicOlayer,ortwoatomicOlayers(labeledas–Hf,–O,andtively).Thevacuumlayerof10A

?–OO,respec-isenoughtoavoidtheinteractionsbetweenperiodicslabsofatomiclayers.11or12atomiclayersareusedintheslabforeachcase.ThestructuresofsupercellsforthesurfacesofcubicHfO2studiedhereareshowninFig.1.Thek-meshes11?11?1,8?12?1,and12?12?1areusedinthecalculationsof(100),(110)and(111)surfacesofcubicHfO2,respectively.

Fig.1.TheballandstickmodelforthesurfacestructuresofcubicHfO2.‘–Hf’,‘–O’,and‘–OO’meanthesurfacesareterminatedbyoneHfatomlayer,oneOatomlayer,andtwoOatomlayers,respectively.BigballsrepresentHfatoms,andsmallonesforOatoms.

3.Resultsanddiscussions3.1.Bulkproperties

Thelatticeconstantaof5.06A

?andthebulkmodulusB0of261GPaforcubicHfO2bulkareobtainedinpresentwork.Bothofthemareingoodagreementwithothercal-culationresults[17,25]andavailableexperimentalvalue

(aexpt?5:08A)

?[26].Thedensityofstates(DOS)ofbulkcubicHfO2isshowninFig.2.Thevalencebandsaresplitintotwodiscontinuousgroups.Thelowerpartbetweenà20eVandà15eVismostlycomposedofOsstatesandtheupperonemainlycomesfromOpstatesalongwithafractionofHfdstates.WhileHfdstatesmainlycontributetotheconductionbands.Itcanalsobeseenthatthevalencebandmaximum(VBM)andtheconductionbandminimum(CBM)ofbulkcubicHfO2mostlycomefromtheOpstatesandHfdstates,respectively.Thus,ourresultsindicatethatHf–ObondinginHfO2exhibitsstrongioniccharacteristicswithweakcovalency.TheseareingoodagreementwithpreviouslycalculatedresultsofcubicHfO2basedonavarietyofcomputationalmethods[27,28].

48G.H.Chenetal./ComputationalMaterialsScience44(2008)46–52

8aEVBM6)42O2fH/0set3bsapts( 2dsetatS1 fo y0ticsn1.5eD10.50-20-15-10-505Energy (eV)Fig.2.(a)Totaldensityofstates(DOS)ofcubicHfO2,(b)partialDOSofHfatom,and(c)partialDOSofOatom.EVBMdenotesthevalencebandmaximum.ThebondingcharacteristicsincubicstructureofHfO2is

essentiallysimilartothatinmonoclinicHfO2[29],althoughtheatomiccoordinationsareslightlydi?erent.Inmonoclinicstructure,theoxygenatomiseitherthreefoldorfourfoldcoordinated,whilealltheHfatomsareinasev-enfold-coordinatedcon?guration[25,29].Incubicphase,thecoordinationnumberofHfiseight,whiletheOatomisfourfoldcoordinated[25].PreviousstudyonelectronicstructuresofHfO2polymorphssuggeststhatthecrystal?elde?ectsduetoatomiccoordinationsmainlyresultindi?erentwidthoflowerconductionbands[17],thusweexpectsurfaceelectronicstructuresofcubicHfO2discussedbelowcouldbeextendedtothoseofotherphases.3.2.Surfaceenergies

Tocomparethestabilityofvarioussurfaces,thesurfaceenergies(Esurf)shouldbetakenintoaccount.ForHfO2,Esurfiscalculatedas:Esurf?

1fEslabHfO2

2A

totàNHfEtot

àeNOà2NHfTlOg;e1T

whereEslabEtotreferstothetotalenergyoftheslabsupercell,HfOtot2

istheenergyforbulkHfO2performulaunit(f.u.),andAisthesurfacearea.NHfandNOarenumbersofHfatomsandoxygenatomsintheslab,sotheeNOà2NHfTequalstoexcessiveoxygenbeyondstoichiometricHfO2unitsintheslab.lInordertostudytheOisthechemicalpotentialofoxygen.dependenceofsurfacestabilityontheenvironment,lOisassumedtovarybetweenthermody-namicallyallowedchemicalpotentiall0HfO2

,wherel0

ofoxygenOandlandtakenO

Oisthechemicalpotentialashalf

oftotalenergyofoneO2molecule,andlHfO2

isrelatedwithlHfOO2

Hfthrough

lHfO2t2lHfO2?EHfOHfOtot2:

e2T

BecausetheformationenergyeDEHfO2

TofbulkHfO2isde?nedas:

f

DEHfO2f?EHfOtot

2

àl00Hfà2lO;e3T

wherel0energyHfisthechemicalpotentialofHfandtakenasthetotalofbulkHfperf.u.,wecanobtainthevariationrangeoflO:

l0t1HfO2

2

DEf6lO6l0OO:e4T

ThecalculatedsurfaceenergiesforlowMillerindexsur-facesofcubicHfO2arelistedinTable1.Boththevaluesofsurfaceenergiesbeforeandafterstructuralrelaxationarelistedforcomparison,andthechangeofsurfaceenergiesduetorelaxationisgivenbyTsurf.Tsurfisde?nedas[30],

Tsurf??Esurfsurf??=Esurf

relaxedàEunrelaxedunrelaxed;

e5T

whereEsurfsurf

unrelaxedandErelaxedarethesurfaceenergiesbeforeandafterstructuralrelaxation,respectively.ItcanbeseenthatthesurfaceenergiesofalllowMillerindexsurfacesofcubicHfO2aredecreasedbystructuralrelaxation.Thevar-iationorderoftheabsolutevalueofsurfaceenergiesofcu-bicHfO2duetostructuralrelaxationis:e110T>e111T-OO>e100T-O>e100T-Hf>e111T-Hf>e111T-O.Obviouslythesurfaceenergyof(110)surfacechangesmostdrastically.Inordertocomparethestabilityofsur-facesofcubicHfO2,thesurfaceenergiesofrelaxed(100)-Hf,(100)-O,(110),(111)-Hf,(111)-OO,and(111)-OsurfacesversusthechemicalpotentialofoxygenareplottedinFig.3.Underoxygen-richconditionsthesta-bilityoflowMillerindexsurfacesofcubicHfO2followsinthesequenceas:e111T-O>e110T>e100T-O>e111T-OO>e100T-Hf>e111T-Hf,whileunderoxygen-de?cientconditionsitchangesto:e111T-O>e110T>e100T-Hf>e111T-Hf>e100T-O>e111T-OO.Itindicatesthat(111)-Oand(110)arethemoststablesurfaces.ThisisbasicallysimilartosurfacesofcubicZrO2withsamestructureofHfO2.Theunrelaxedsurfaceenergiesof(100),(110)and(111)surfacesofcubicZrO2havebeencalculatedbyChristensenandCarter[31],theyfoundthat(111)surface

Table1

CalculatedsurfaceenergiesEsurfemJ=m2Tforlow-indexsurfacesofcubicHfO2Face

EsurfelO?l0OT

EsurfelO?l0Ot1HfO22DEf

TRelaxedUnrelaxedTsurf

RelaxedUnrelaxedTsurf(100)2650

28085.63935395111.66-Hf

(100)-O1017510410

2.26347237076.34(110)1526223031.61526223031.6(111)267328114.9110416105541.31-Hf(111)12537129162.93479451727.31-OO(111)-O934

996

6.22

934

996

6.22

G.H.Chenetal./ComputationalMaterialsScience44(2008)46–52

49

{100} -Hf{100} -O{110}12{111} -Hf{111} -OO{111} -O)2m/J(9 ygrenE eca6fruS30-10-5Chemical Potential of O (eV)Fig.3.SurfaceenergiesforvarioussurfacesofcubicHfO2versuschemicalpotentialofoxygen.ofcubicZrO2isthemoststableone.Thesecouldbeunder-stoodbythat(111)surfacesofcubicHfO2andZrO2sat-isfythecompactnessandelectrostaticconditions[31].Inaddition,becausethe(111)-Oand(110)surfacesofcubicHfO2arestoichiometric,theirsurfaceenergiesareindepen-dentofthevariationofchemicalpotentialofoxygen.3.3.Surfacerelaxation

Inpresentwork,wefocusontheatomicrelaxationalongthesurfacenormalandneglectthereconstruction.Sincethe(111)-Oand(110)surfacesofcubicHfO2areenergeticallythemoststableonesasdiscussedinabovesec-tion,hereweparticularlypresentanddiscusstheatomicrelaxationsinthesetwosurfaces.

Toobtainthedetailedinformationofatomicrelaxationineachatomiclayer,wecalculatetheabsolutedisplace-mentDzofeachatomiclayerandthechangeoflayerdis-tanceDd.Duringourcalculations,thesurfacenormalwaschosenasthez-axis.Here,theDzisgivenbyDz?zrelaxedàzunrelaxed,wherezunrelaxedandzrelaxedarezcoor-dinatesofatombeforeandafterrelaxation,respectively.If

Table2

Atomicrelaxationin(110)surfaceofcubicHfO2nDznDdn;nt1zOnàzHf

n

HfOHfO1à0.2250.049à0.4080.0530.27420.183à0.0040.243à0.012à0.1873

à0.06

0.008

–

–

0.068

nislayernumber,Dzn(A

?)istheabsolutedisplacementofatomalongz-directionandDdn;nt1(A

?)denoteschangen+1duetorelaxation.zOn

àzHfn

(A?ofdistancebetweenlayernand)denotestherumplingofHfandOatomslayers.

Table3

Atomicrelaxationsin(111)-OsurfaceofcubicHfO2nAtomDznDdn;nt11O0.0320.0682Hfà0.035à0.0053Oà0.03à0.0484O0.0180.0075

Hf

0.011

–

nislayernumber,Dzn(A

?)isthedisplacementofatomalongz-direction(thepositiveindicatesinward)andDdn;nt1(A

?atomsmoveoutwardandthenegativemeans

)denoteschangeofdistancebetweenlayernandn+1duetorelaxation.

Dzisnegative,itindicatesthatatommovestowardtheinnerlayerbyrelaxation,otherwise,atommovestowardouterlayer.Weshouldpointoutthattwoorthreeatomiclayersincenterpartoftheslabare?xedduringthestruc-turalrelaxationsinourcalculations.Ddisde?nedasthedi?erencebetweendrelaxedanddunrelaxed(i.e.Dd?drelaxedà

Fig.4.Projectedbulkbandstructuresofvarioussurfaces:(a)Hf-terminated(100),(b)Hf-terminated(111),(c)O-terminated(100),(d)

doubleOatomlayerterminated(111)surface,(e)(110)and(f)oneOatomlayerterminated(111).ThepositionoftheFermilevelEFofsurfaceismarkedbythedottedline.