MOLECULAR DYNAMICS SIMULATION OF LOW ENERGY CLUSTER DEPOSITION DURING DIFFUSION-LIMITED THIN FILM GROWTH

Nano%wtumdMaterials,Vol. 8, No, 3, pp. ‘253-268,1997

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MOLECULAR DYNAMICS SIMULATION OF LOW ENERGY CLUSTER DEPOSITION DURING DIFFUSION-LIMITED THIN FILM GROWTH C.L.Kelchner andA.E. DeFristo Departmentof Chemistry Iowa StateUniversity,Ames,Iowa (Accepted February 10, 1997) Abstract-Molecular dynamics simulations permit multiple-layer thin film growth to b~ studied in detail, using reliable interatomic potentials for fcc metals from corrected e~ective medium theory. Results arepresentedfor the homoepitaxial deposition of 20ML on Pd(OOl) and CU(OOI)near OK via low energy deposition of 5- and 10-atom clusters, along with preliminaq resultsfor deposition of 100-atom clusters. Thinfilms grown via low energy cluster deposition are found to be more three-dimensional thanfilms grown via single atom deposition. The increased surface roughness can be attributed to thefollowing factors: (i) most deposition events add atoms to two or more layers; and (ii) the growth of (111)facets on the surface produces manypartiaily exposed atoms. Neither of thesefeatures was observed during the deposition ofsingleatoms. Thin films grown by deposition of larger clusters tend to be rougher than those produced by smaller clusters at this low temperature. @1997Acta Metallurgic Inc.

INTRODUCTION Detailedstudyof the growthof thinfilmscan leadto furtherunderstandingand controlof the depositionprocessand finalstructureof thefilm. Thisis importantfor manyapplicationsof thin filmtechnologysincethemechanical,electrical,optical,andmagneticpropertiesof the film can dependstronglyon the fdm’sstructure. One method of growinga thin film is to depositsingleatoms under ultrahighvacuum conditionsto ensure a clean surface(e.g., molecularbeam epitaxy). Experimentaldeposition techniquesmay deposita rangeof smallclustersizesratherthan singleatomsas intended. The clustersizedistributiondependson theexperimentalconditions(e.g.,beamtemperature)and can range from mostly monomerswith a few dimers and timers to larger clusterswith very few monomers. The size of the depositedclustersmay affect the growth mechanismsand final structureof a thin film. Someexperimentaltechniquesintentionallydepositclusterswithina controlledsizerange, suchas ionizedclusterbeamdeposition(ICBD)(1)andenergeticclusterimpact(ECI)(2). These methodsseekto formcompact,stronglyadheringthinfilmsby depositingacceleratedclusterions whichlocallyheatthesurfaeeupondeposition.Moleculardynamicssimulations(3,4)ofECIhave shownthat this excessheatcan melttheclusterand localsurfacearea, allowinglateralmobility 253

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CL KELCHNER ANDAE DEPRISTO

of the cluster atoms as the clusterbreaks up and annealingany impact-createddefects. The depositedclustersw generallyhuge(1000atomsor more)and havean initialkineticenergyof 1-10eV per atom. Other experimentsuse low energyclusterbeam deposition(LECBD)where the kinetic energyper atomis muchlessthanan atom’sbindingenergywithinthecluster(5). Thistechnique can produce“nanocrystallinestructured”thinfdmsandleadto theformationof newphasesby a randomclusterstackingmechanismas theclustersare soft-landedon the surface. The resulting thin films are, therefore,stronglyaffectedby the size, structure,and propertiesof the original clusters. Theseclusterdetailsdo not affectthe finalfilmas stronglyin ICBDor ECI, where the most importantparameteris the kineticenergyper clusteratom. Moleculardynamics(MD) can be used to study the growth of thin fiims in detail by followingthe motionof individualatomsand clustersas theyare depositedand determiningthe variousprocessesinvolvedas theyadsorbon thesurface.Theprimaryconcernwhen simulating depositionprocesseswith MD is the computationaltime scale, which is at least ten orders of magnitudeshorterthan experimentaltime scales. This limitationcan be obviatedby choosing systems where only short time scale (picosecond)processesare importantso that the MD simulationand the experimentcan observethe sameevents. For example,thermallyactivated self-diffusionon the (001)surfaceof Pd and Cu is extremelyslowat 80 K, i.e., 1atomichop per 105years for an activationenergyof 0.4 eV The film growthis thus determinedsolelyby the depositiondynamicswhichpersistforonlypicosecondsaftera depositionevent. MDis therefore an appropriatemethodto studythesesystemsat verylow temperature. A numberof MD simulationshavebeenreportedfor depositionof a singleclusteronto a cleansurface(6),butonlyafew theoreticalstudieshaveconsideredmultiple-layerfilmgrowthvia clusterdeposition.Intwo-dimensionalMDsimulationsusingaLennardJonespotential,Miiller(7) foundthattheclusterenergyperatomplayedan importantrolein thequalityof thethinfilm. Low energy clusters remainednearly intact upon depositionand produced“polycrystalline”films, whereas higherenergyclusters(energyper atom close to the atomicbond strength)produced homoepitaxial growth and very high energy clusters greatly damaged the surface. A three-dimensional(3D)simulationusingtheembeddedatommethodforMo(3)resultedin similar conclusionsandagreedwithexperimentalresults.Eachofthesesimulationsusedonelargecluster size, 91 atoms(=700in 3D) in Ref. (7) and 1043atomsin Ref. (3). A thirdmultiple-layerMD simulation,thisoneof Si clusterdepositionon Si(lll) (8),studiedtheeffectof theclustersizeas wellas thesubstrateandclustertemperaturesandtheinitialclusterenergy.Combinationsof these growthconditionswere identifiedthatproducedthe highsurfacediffusionand spreadingof the clusterupondepositionconsiderednecessaryfor epitaxialgrowth. The presentwork studiesthe growthof thin filmsvia the low energydepositionof small clusters. Wecomparethedepositionof 10-atomclustersto previousresultsfor thedepositionof singleatoms(9)duringhomoepitaxialthinfilmgrowthofmetals,specificallyPd/Pd(OOl)andCu/ CU(OO1) nearOK. Wealsoexploretheeffectof differentclustersizeson thegrowthmechanisms and finalstructureof the thin films. SIMULATIONPROCEDURE The MD simulationsuse the simplestformof correctedeffectivemedium(CEM)theory, known as MD/MC-CEM,whichprovidesaccurateinteractionpotentialsfor metals (10,11,12).

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DEPOSITION USING MD

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CEM theory determinesthe interactionenergyof a systemin any geometryby calculatingthe energyof eachatomina referencesystempluscorrectiontermsforthedifferencein Coulomband kinetic-exchange-comelation energiesbetweenthe interactingsystemand the atom-in-reference system.Thismethodhasbeenextensivelydescribedelscwhere(lO,ll), includinga recentcritical review {12),and no furtherdetailsare givenhere. Periodicboundaryconditionsareusedin thesurfaceplane(inxand y). Thesquarefcc(OOl) surfacehasfouractivelayersandonefixedlayerat thestartof thesimulation,with 11x 11atoms in each layerformostof thesimulations.Thesurfaceis initializedfroma Boltzmanndistribution at 80 K. This low temperaturewas chosento eliminatethermalsurfacediffusionon the (001) surface. (Theeffectof thisparticulartemperatureisdiscussedfurtherin thenextsection.)Except for the initialfixedlayerwhichremainsfixedand the lowestactivelayer(i.e., theone closesttO thefixedlayer)whichis treatedbyLangevindynamicstomimica constanttemperatureheatbath, all atoms follow Newton’sequationsthroughoutthe simulation. The thicknessof this slab is sufficientfor bothaccuratetemperaturecontrol,sincetheenergyflowis controlledby the forces betweenthe surfaceand subsurfaceatoms(13),and the low-energyimpactson the surface. Thegeometryandatomicvelocitiesofthedepositingclusteraminitializcctseparately before thefirstdepositionevent.Theclusteriscutfromthefccbulkcrystalandquenchedtoreacha stable structure,thenrelaxedat the specifiedclustertemperature.Wechosea temperatureof 100K for convenience,sincetheclustertemperaturehasbeenobservedtohavelittleeffecton thedeposition processin MD simulations(8). Thisproceduredoesnotguaranteetheminimumenergystructure of theclusterbut doesfinda low-energy,compactstructure.Subsequentclustersin thedeposition process use this same geometry,randomlyrotated in space, and the same initial temperature distributionscaledto givethe chosenclustertemperature. One newclusteris placedoutof theinteractionrangeabovethesurface(+z direction)with randomxandycoordinatesandasmallinitialkineticenergyof0.25eVdirectedtowardthesurface. (Both the coordinatesand kineticenergyreferto the cluster’scenterof mass.) After a specified time, anotherclusteris placedabovethe surfaceand the depositionprocessis repeateduntilthe desirednumberof clustershavebeen deposited.The depositionrate is chosenso that the time betweendepositioneventsis longenoughfora singledepositedclusterto completelyrelax upon adsorption. This ensuresthat one depositionevent does not directlyaffect the next. Further increasingthetimebetweendepositions(decreasingthedepositionrate)wouldhaveno effecton the resultsbecauselongtime scaleprocessesdo notoccurat suchlow temperatureon either the computationalor experimentaltimescale. The minimumtime between depositioneventsmust increasewith cluster size. As the adsorptionenergyof a depositingclusterincreaseswithclustersize,sodoesthe timerequiredfor this energyto dissipatethroughoutthe system. Thusan MD simulationof a thinfilm grownby depositionof smallclustersrequiresroughlythe samecomputationaltime as that of a thin film grownby depositionof singleatoms. Forlargeclusters,thecomputationaltimecouldbe reduced sincethe adsorptionenergyincreasesmoreslowlywithclustersizedue to the highcoordination of the clusteratomsand therelativelyfew bondsto the surfaceuponadsorption. The morphologyof thegrowingfilmcansuggestpossiblemechanismsby whichdeposited atomsfindstableadsorptionsitesonthesurface.Onewayto measuretheroughnessof thesurface is to calculatethe interfacewidth,w. The interfacewidthis definedto be the standarddeviation of thedistributionof theexposedlayers’heightinunitsoftheideallayerspacing,andiscalculated from the followingequation(14):

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CL KELCHNER ANDAEDEPRISTO

W2= ~(j–j)2Nj

[1]

j=o

Nj is the net numberof exposedatomsin layerjwherej=O is the top substratelayer. The mean heightof the surfaceis ~. The totalcoveragein monolayer (ML)is denotedby t3tOt intherest of this article,and the interfacewidthis plottedaftereach depositionevent. DEPOSITIONOF 1O-ATOMCLUSTERS Su#ace Structure

In the vaporphase,thecompact10-atomclusterhasvibrationaland rotationalmotiondue to its internalenergy(temperate) as wellas a netvelocitydirectedtowardthe substratedue to its initialkineticenergy. Thevelocityof theclusterincreasesas it is attractedto the surface,and theclusterlandswithsomeimpactdueto thestrongadsorptionenergy(about3 eVperatom). For the smalltotalkineticenergyof 0.25eV (i.e.,0.025eV/atom),thisimpactis notenoughto create defectsor otherwisedisruptthe structureof the substrate. The depositingatomscan pushintothe top substratelayerduringimpact,particularlyif a few atomsreach the surfaceslightlybeforetherestof thecluster. Mostof theseatomsrecoilout of the substrateas the clusterfinds stableadsorptionsiteson the surface.However,we have observedexchangeof clusteratomswiththe substrateduringthe adsorptionprocess. The final cluster structure is unchangedin these homoepitaxialsystems,but this mechanism will be importantwhen studyingheteroepitaxy. Theclusteratomsmustrearrangetofitintothefour-foldhollowadsorptionsitesonthe(001) surface. For the 10-atomclusters,this rearrangementis completedwithin 2-3 ps of the first attractionto the substrate. The final structureof a 10-atomclusterdepositedon a clean (001) substrateis usuallythree-dimensionalwith 1-2atomsin the secondadsorbatelayer. All of the atomsin thesecondlayerareincompletefour-foldhollowsitescreatedby theotherclusteratoms. A 10-atomclustercan also flattenintoa singlelayeruponadsorption.The adsorbedclustersare fairlycompact;thelargestdimensioninanydirectionisonlyfouratomsforthe8-10atomsfound in the first layer. When clusters are depositedon a rough surface containingislands and other defect structures,theadsorptionprocessis notassimple.Adepositingclusteris stronglyattractedto the first atom within its interactionrange,and on a roughsurfacethis is often the top or side of an existingisland.Theclustercanadsorbontothesideofanisland,addingatomstoaboutthreelayers of the structure.As the surfacegrows,thenumberand sizeof islandsincreaseand thelikelihood thata depositingclusterwillreachthesubstratequicklydiminishes.Thelargersizeof thecluster increasesthe probabilitythat one or moreof its atoms,and thereforethe entire cluster,will be attracted to a nearby island during deposition,rather than continuingto move normal to the substrate. This resultsin large islandson the surfacewith deep channelsbetweenthem. The channelsare only 1-3atomswideat thebaseof theislandsand are generallynot filledin during furtherdeposition. Themoststrikingfeatureofthesesurfacesistheformationoffcc(lll) facetsdtingthinfilm growthvia low energyclusterdeposition.Eachfaceof a perfectpyramidon the (001)surfaceis

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Figure 1.Top view of Cu/Cu(OOl)surfaceat etot= 6 MLduring depositionof 10-atom clusters, A (111) facet and a (100)-type vertical wall can be seen. There are 10 adsorbate layers growing and the substrate (darkest atoms) is still exposed, (Atom shadinglightens with height from the substrate.)

257

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Figure 2. Sideviewof the surfacein Figure 1 (takenfromthe loweredge).

a (111)facet. For example,a 4-atomhighpyramidhas 16atomsin the fmt (bottom)layer,nine in the secondlayer,fourin the thirdlayer,and onein thefourth(top)layer. Thispyramidhas a 4-atomhigh (111)faceton each of its fourfaces. Figure 1 showsthe structureof a (111)faceton the surfaceof a thinfilm. Figure2 shows the same surface from the side, and a large (111)facet can be clearly seen on the right. For convenience,we havedefinedthe minimumsizeof a (111)facetto be 3 atomshighand 2 atoms wide. Thetallest(l 11)facetswehaveobservedduringdepositionof 10-atomclustersare 12atoms highand the widestare6 atomsacross. Mostof thefacetsare only4-5 atomshighand 3-4atoms wide. One or moreatomsfroma depositingclustermay stickon the (111)facetwhiletherest of theclustermovestonearbyadsorptionsites.Theseatomscanstayonthefacetfortenstohundreds of picosecond. An earlierstudyof singleatomdepositionon thesepyramids(15)indicatedthat Pd atomsme morelikelythanCu to stayon the(lll)facetforthe fiist5 psafterdeposition. This differencewas not observedto be significantin the currentMD simulations. Whilethediffusionrateonthe(001)surfaceis negligibleat80K,thisis nottrueforthe(111) surfacewherethe activationbarrierto diffusionis muchsmaller(16)and diffusioncan occuron thetime-scaleofmicrosecondsat80K. Hence,thesingleatomsadsorbedonthe(111)facetinthese simulationsmaynotbeintheirfinaladsorptionsites.However,thetime-scaleofan MDsimulation cannotincludesuchdiffusionevents,andthusasimulationat80KisequivalenttooneatOKwhere

258

CL KELGHNER ANDAE DEPRISTO

all thermallyactivateddiffusionis eliminated.The resultis that the MD simulations,although performedat 80 K, ideallyshouldbe comparedto experimentsperformedat (or close to) OK, Distinct(111)facetsformonlyon a relativelyflatsurface.The(111)facetsareobservedas soon as 3-atomhigh islandsare formedon the substrate(6[Ot= 1 ML for most simulationsof 10-atomclusterdeposition).Thesefacetsgrowas moreclustersare depositedon and near them by addingatomson the facet and by addingentireclustersto severallayerson the facet which extendsthefacetlaterally.As thesurfacebecomesrougher,the(111)facetsbegintodisappear.It maybethatthesurfacereachesamaximumnumberorsizeof(11l) facetsinagivenareaandcannot continueto grow by propagatingthe facets. Anotherpossibilityis that the randomdeposition processmay depositseveralclustersin sucha way thattheydestructivelyinterferewith the facet growth,e.g., distortinga (111)facetor simplycoveringit. Theeffectis thatthe (111)facetsare coveredby atomsadsorbedon thefacetand by atomsin overhangsitesnearthe top of the (111) facet. An overhangsitehasbeendefinedpreviously(9) as a four-foldhollowsitethatis missing one or more of its four supportingatoms. For the current MD simulations,we modify this definitiontoincludeonlythosefour-foldhollowsitesthataremissingexactlyonesupportingatom. Sitesthataremissingtwoormoresupportingatomscanoftenbemoreaccuratelydescribedassites on the (111)facet. (Thiswas not thecaseduringsingleatomdepositionsince(111)facetswere not clearly formed.) An exceptionis madefor overhangingrows, wheremostof the atomsare missingtwo supportingatoms. Overhangingatomsare a consequenceof thefact thatthedepositingclustersare attracted to theislandsonthesurfaceandthuscannotdepositin thenarrowgapsbetweentheislands.When a clusterlandson thetopor sideofan existingisland,manyof theatomsremainin overhangsites or adsorbon the(111)facetinordertomaintainthestrongbondingwithinthecluster,eventhough a nearbysitemayoffergreaterenergeticstabilityfora givenatom.Thecostofbreakingthebonds in theatom’spresentsiteis too greatforit to moveto anothersite,i.e.,theenergeticbarrierto site changeis too high. This is a functionof the extremelylow temperatureof the simulation,since at highertemperaturethethermalmotionwouldincreasethekineticsitehoppingrate. Whilewe havebeenunableto fiid anymicrostructuralexperimentalevidencefortheseparticularoverhang sites, other overhangsare well-known,for example,in the columnargrowthregime of sputter deposition. It isclearthatatomsdo notalwaysadsorbinthemostenergeticallyfavorablesites in such cases,and the sameargumentscan be appliedhereas well. The overhangingatoms lead to the next distinctstage of thin fdm growth, namely the disappeamnceof the (111)facetsand gradualsmoothingof thesurfacestructure.Thistransition doesnot appearto occurat a specificE),Oforinterface widthvalue, Thesidesof theislandsduring thisnextstageoffilmgrowthareoftenvertical(100)-typefacesata45° anglefromthe(111)facets. Theseverticalfacesarecreatedbyoverhangingatoms(notoverhangingrows)at thecomeroftwo (111)facetsandcanbe morethansixatomswide. Figure1showsanexampleof thisverticalwall (or step)fromthe top (leftsideof figure).Otherdistortedstructuresare alsoobservedin mostof the simulationsdue to edgedislocationsformedon islandsand otherdefects. A multi-atomrearrangementeventmayoccurduringthedepositionprocesswhichcovers someofthedeepchannelsbetweenislandsbyconnectingthetopfewlayersoftwoormoreislands. Theserearrangementsare typicallysmallerthanthoseseenduringsingleatomdeposition(9)and do not fillthedeepholes,leavinglargevoidsin thefilm. Muchof thesurfaceis thensmoothand (111)facetsagainbeginto grow,repeatingthecycle. Thesurfacemayalsobecomesmootheras

CLUSTER &msmoru USING MD

259

depositingclustersgraduallycoverholeson thesurfacewithoverhangingrowsand atoms,rather thanby a specificrearrangementevent. Notethatthesemechanismsforsmoothingare localized, so thatit is possibleto find(111)facetsgrowingon onesectionof thesurface,such as the top of a largeisland,even thoughanotherpartof the surfaceis stillveryrough. Thisis onereasonwhy it issodifficulttoquantifythetransitionbctwecn(111)facetgrowthandothergrowthmechanisms. The growthof a thinfilmcan be illustratedby plottingtheinterfacewidthas a functionof coverage,asseeninFigure3fortwoPd/Pd(OOl)simutationsofIo-atomclusterdeposition.Figure 3 showsmany of the same featuresthat wereobservedfor depositionof singleatoms (9). For instance,the suddendecreaseat 9fo,= 10ML indicatesa multi-atomrearrangementeventwhich smoothesout the film surface. Thesetypesof eventsoccurmuchearlierin the filmsgrown by cluster deposition than those grown by single atom deposition. We have seen multi-atom rearrangementeventsfor coveragesas low as 5 ML in the MD simulationsof 1(.-atomcluster deposition.Incontrast,theinterfacewidthduringsingleatomdepositionsteadilyincreasesfort3iOt e 20 ML with no large-scalemulti-atomcvcnta(9), The interfacewidthof a thin filmgrownby clusterdepositionis largerthan that of a film grownby singleatomdeposition,indicatinga roughersurface. In previousresults(9) for single atomdepositionof Cu/Cu(OOl)andPd/Pd(OOl),themaximuminterfacewidthwas 2.1 for 9r0,S 20 ML. For 10-atomclusterdeposition,themaximuminterfacewidthis 5.1 (inunitaof theideal Iayerspacing).Table1showstheinterfacewidthat severalcoveragesduringdepositionof single atoms and 5- and 10-atomclusters.

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260

CL KELGHNER ANDAE DEPMSTO

TABLE1 Rangeof InterfaceWidthat SeveralCoveragesforAll Simulationsof Deposition via SingleAtomsandNO DifferentClusterSizes. (ResultsfrombethCuandPd areincludedfor single atom and 5-atomclusters. Only Pd is included in the 10-atomcluster results for the two surfacesixes. Eachcolumnrepresents4-5 simulations.) etot

5 ML 10ML 15 ML

single atom 11x 11

5-atom 11x 11

10-atom 11x 11

10-atom 17x 17

0.7- 0.9

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The depositionof clustersincreasesthe surfaceroughnessmuch momquicklythan does singleatomdeposition.The maximumnumberof layersexposedon thesurface(i.e., the number <15 of growinglayers)rangesfrom 14-25forO~Ot _ MLduringthinfilmgrowthvia 10-atomcluster deposition. The correspondingmaximumduringsingleatom depositionis only 6-12 exposed layers. Furthermore,during10-atomclusterdepositionthesubstrateis typicallyexposeduntil(llOf = 2 ML =6 ML and can stillbe exposedat etO,= 15ML,whereasit is completelycoveredby El,Ol duringsingleatomdeposition.Thisincreasedsurfaceroughnessduringclusterdepositioncan be attributedto two factors:(i) mostdepositioneventsadd atomsto twoor morelayers;and (ii) the (111)facetshavemanyparthlly exposedatoms.Neitherofthesefeatureswasobservedduringthe depositionof singleatoms. The interfacewidthis a usefultoolto analyzea singlesimulationand to get an idea of the overallroughnessof thesystem.Note,however,thattherandomnatureof thedepositionprocess in a small surface area can produce a large variation in interface width between any two simulations,as seen in Figures3,4, and 6. Detailedcomparisonof the interfacewidth for two simulationsis simplynot meaningfulunlessthey used the same randomaimingpoints for the depositedclusters. Therandomdepositioneffectscan be diminishedby eitherdepositingovera very largesurfaceareaor averagingmanysmallsimulations.(Thiswouldalsoaverageout many of the interestingfeaturesof the interfacewidth.) For this initialstudy of low energy cluster deposition,neithersolutionwasdeemedpracticalfor theselengthyMD simulations. System Size Effects

The sizeof thesystemcanplayan importantroleif it is smallenoughforthesurfacedefects developedduring thin film growthto interactwith one anotherthroughthe periodicboundary conditions. It has been determined(9) thata surfaceof 11x 11atomsis sufficientto studythe growthof homoepitaxialthinfilmsviasingleatomdeposition.However,thedepositionof small clustersin thepresentstudyinducesrougherfilmgrowththanthatof singleatomsand thesystem size may influencethe results. The interfacewidthof two MD simulationswith a largersystemsize of 17 x 17 atoms is presentedin Figure4. This largersurfacearea allowseach islandto begin growingin a more isolatedenvironmentand producesmoreislandsoverall. Note that the interfacewidthdisplays

CLUSTER DEPOSITION USING MD

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Figure4. Sameas Figure3 for a 17x 17surfacesize. fewer sharpincreasesand decreasesin Figure4 thanfor the smaller11x 11systemin Figure 3, althoughthe magnitudeof w is similarfor both systemsizes. The lack of oscillationsin w over a largersurfaceareaisexpectedsincethegrowthpatternsduetotherandomdepositioneventsare averagedoutto someextent.Forexample,a smallnxirmngementeventonthe 17x 17surfacedoes not affectthe interfacewidthas muchas a similareventon the 11x 11surfacebecausetheeffect on wis dampedoutby thelargernumberofatoms. (Thisdiffenmcedueto thesystemsizewasnot seenin singleatomdepositionresultsbecausetheinterfacewidthwasalreadyfairlysteadyforthe smallersystem.) This comparisoncan be quantifiedby fittingthe interfacewidth to a power law of the coverage:w =AO~, where(1is thegrowthexponentinaccordancewiththedynamicscalingtheory (18). The fittingparametersand theRMSdeviationarelisted inTable2fordepositionof 20 ML by 10-atomclustersof Pd/Pd(OOl)andCu/Cu(OOl).Thefit is worsefor the 11x 11simulations, as indicatedbythekwgeRMSdeviations.Thisreflectstheregionsofsuddenchangeinthesurface structure(e.g.,inFigure3)thatcannotbeaccuratelymodeledbya simplepowerlawfunction.The 17x 17simulations,on theotherhand,exhibita smallRMSdeviationandrelativeuniformityof thegrowthforthelargersystem,i.e., fewerregionsofsuddenrougheningor smoothingof thefilm surfaceduringgrowth(Figure4). Therandomeventsonthesurfaceduringdepositionand growth are beginningto be averagedout even overthisrelativelysmallsurfacearea of 17x 17atoms. The diffenmcein thequalityof thefitfor thetwo systemsizessuggeststhata largesystem is necessarytoreliablydeterminethegrowthexponent,(ll,inthedynamicscalingtheory.However, it is notclearthatthesurfaceeventsareaffectedbythesystemsize.Theinterfacewidthyieldsless detailedinformationaboutthelocalsurfacestructureasthesystemsizeincreases,thuschangesin the interfacewidth behaviorwith systemsize do not necessarilyreflectchangesin the surface behavior. (In fact, w shouldbecomea featurelesscurvefor an infinitesystemor for the average

262

CL KELCHNER ANOAE DEPRISTO

TABLE2 The Interface Width is Fit to w = A@ for Deposition of 20 ML by 10-Atom Pd Clusters on Pd(OOl). Averagingw over the simulationsfor each surfacesize yields the fitting parametersgiven in the “averagedw“ row. The RMS deviationfrom the fit is also listed and indicatesthe poor qualityof the fit for the 11x 11surface size.

A

averagedw

11 x 11 surface RMs P

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17 x 17 surface P

RMs

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0.348 0.142 0.212

0.882 1.048 0.801

0.439 0.429 0.635

0.154

1.225

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of manyfinitesystems.)Fromvisualanalysisof thesurfacestructure and depositionevents,no significantdifferencein the growthprocesshasbeenobservedbetweenthe two differentsystem sizesin the MD simulations. Comparison of Cu and Pd

For mostof the smaller(11 x 11)Pd/Pd(OOl)simulationsreportedhere, an identicalMD simulationwas done for Cu/Cu(OOl),includingthe same set of randomaiming points for the depositingclusters.Thispermitsthedirectcomparisonof theresultsforthesetwometals. Figure 5 presentsthe interfacewidthfromonesimulationforbothCu andPd. The interfacewidthsfor Cu and Pd are indistinguishablefor (l,Ot<5-10 MLfora givensetof simulations,suggestingthat any significantdifferencein thegrowthmechanismsforthesetwometalsat lowtemperaturedoes not appearuntilthe thinfilmis wellwithinthemultiple-layergrowthregime. Whilesomeof the simulationsindicatethatCu growsmoreroughlythanPdby thetime15ML havebeendeposited, as inFigure5, othersimulationsindicatetheopposite.ThediffenmcesbetweenCu andPdare not significantin the scopeof the currentanalysis. CLUSTER SIZE EFFECTS 5-Atom Clusters

Thedepositionof5-atomclustersproducessomewhatdifferentresultsthanthosediscussed abovefor the 10-atomclusters.A compact5-atomclusterdepositedon a flat (001)surfacewith a smallkineticenergy(0.25eVtotal,orO.05eVperatom)typicallyflattensintoa singlelayersuch thatallof theatomsadsorbdirectlyon thesurface.Althoughtheclusterbindingenergydecreases as the clusterflattens,energyis gainedfrom the new bondsto the surface. The net adsorption energyper atomis generallylargerfora 5-atomclusterthanfora 10-atomclusterdueto thelower degreeof coordinationin thesmallerclusterandthehigherrelativenumberofbondsformedwith the surface.

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Figure5. Interfacewidthduringdepositionof 10-atomclustersof Cu/Cu(OOl)and Pd/Pd@Ol), 11x 11.All simulationparametersare identicalincludingthe set of randomaimingpoints.

Thislargeamountofenergyincreasesthemobilityoftheatomsastheyreachthesurfaceand resultsin a varietyof finalstructuresfor thedepositedcluster.Whena small,compactclusteris deposited,severalatomsmaycompeteforthesameadsorptionsiteonthesurface.Anatommight not remainin the firststablesiteit findssinceall of theatomsin thedepositingclustermustfmd astableadsorptionsite. (Thisisadecidedcontrasttothesingle-atomdepositionprocess(9).) The adsorptionenergyof a neighboringclusteratommaybepartiallytransferredto thatf~st-adsorbed atomand allowit to samplea largernumberof sites. Similarlytheimpactof neighboringcluster atomsmay transfermomentumto thefwstatom,in effectknockingtheadsorbedatomout of the way for the nextclusteratomto takeits place. This“mobility”oftheclusteratomslastsfor only 5-10 ps and is not seen at all for somedepositedclusters. Theresultof thisincreasedmobilityisevidentinthefinalstructureofthedepositedclusters, in that the clusterdoes not necessarilyremainintactonceall of the atomsare adsorbedon the surface. In fact, one or all of the adsorbedclusteratomsmay not be withina nearestneighbor distanceof anyotherclusteratom. Thisdoesnotoccurasoften fordepositionof10-atomclusters sincetheincreasedcoordinationofatomsinthelargerclustermakesitmoredifficultforindividual atomstobreakawayduringadsorption.Also,someoftheatomsintheIargerclusterremaininnew adsorptionsitescreatedinthesecondlayerratherthanadsorbingdirectlyonthesurface,decreasing both the totaladsorptionenergyand the sitecompetitionof the cluster. Feweroverhangingatomsareobservedonthesurfaceduringdepositionof5-atomclusters, indicatingthattheemptyfour-foldhollowsitesmaybe filledmoreeftlcientlythanforbothlarger clusterdepositionand single-atomdeposition.Thisis in agreementwith the increasedmobility of the smallclustersduringthe adsorptionprocess.

CL KELGHNER ANDAE DEPRISTO

4.0 3.5 3.0: ~ 2.5: .3 u f-l 2,0: 3 .-

1.5: 1.0: 0.5:7 ~ : / 0.0 ‘

i? ”4’&

’A’

lb

1> 1’4 1’6 1’8 2’0

etOt (Ml.)

Figure6. Interfacewidthduringdepositionof 5-atomPd clusterson Pd(OOl),11x 11,for two simulationswith differentsetsof randomaimingpointsfor the depositedclusters. Overall,the depositionof smallerclusterscan leadto a smoothersurfacethan seen for the larger, 10-atomclusters. Figure6 plots the interfacewidthfor two Pd/Pd(OOl)simulationsof 5-atomclusterdeposition,andoneis noticeablylowerthanthatfor 10-atomclusterdepositionin Figure3. The (111)facetsarestillobservedduringdepositionof 5-atomclustersbut theytendto besmallerthanforthe 10-atomclusterdeposition.Thesmallersizeofthe5-atomclustersincreases theprobabilitythattheymayreachthebaseofaholeorgapbetweenislandswithoutbeingattracted to the sidewalls as occursforthe 10-atomclusters.Thismaynotdecreasethesurfaceroughness, however,sincea clusteradsorbedhighon a sidewall can blocklowerexposedlayers from the surfaceas effectivelyas one landingfurtherdownin the holeitself. Notethatthesmallerclustersizedoesnotguaranteea smoothersurface,asillustratedby the uppercurvein Figure6, sincethe effectsof the randomaimingpointsare stillprominentdue to the smallsurfacearea. Nonetheless,on averagethe largerclustersproducea roughersurfaceas seen in Figure7. The size of the system(11 x 11atoms)doesnot appearto influencethe surfacestructure duringdepositionof 5-atomclusters. The islandsand othersurfacestructuresare smallerthan duringdepositionof 10-atomclustersanddo notsignificantlyinterferewithoneanotherthrough the periodicboundaryconditions. 100-Atom Clusters

The depositionof a 100-atomclusteris in somerespectssimplerthan that of the smaller 5-atom and 10-atomclusters. This large,sphericallycompactclusterhas a rough diameterof nearly six atoms and results in atomsbeing added to at least four layers on the surface. The adsorptionenergyplusthesmallinitialkineticenergy(0.0025eV/atom)of theclusteris notlarge

CLUSTER DEPOSITION USING MD

4.0+ —

0.0 ]

265

10-atomclusters

2’ ‘4’ ‘&’‘$’ 10 ‘ 12 ‘ 1’4 If) 1’8 20 etot (ML)

Figure7. Interfacewidthduringdepositionof Pd/Pd(OOl),11x 11. Resultsare averagedover 2-4 simulationsfor each clustersizeto showthe generaltrend. enough to allow the cluster to flatten into a two-dimensionalstructure,as has been seen for simulationsusinghigh temperatureor energeticclusterdeposition(3,7). Depositionof the first 100-atomclusteron a clean (001)surfaceresultsin a single,4- to 5-atomhigh pyramidwith (111)facetedsides. The close-packedclusteratomsrearrangeupon adsorptionto matchthefcc(OOl)structureof thesubstratewhileretainingtheirhighcoordination withintheclusterasmuchaspossible.Thisrearrangementis completewithin5-7ps of thecluster reachingthesurface.Fewerthanhalfof theclusteratomsadsorbdirectlyon thesurface.The final structureof a 100-atomclusterdepositedon a clean (001)surfacetypicallyconsistsof about35 atomsin the first adsorbatelayerand 30 atomsin the secondlayer. Subsequentclustersmayaddto thesidesof thispyramidor adsorbon anothercleanareaof the surface. On a roughsurface,atomsalongthe sidesof thedepositingclustermay also adsorb on one or moreadjacentislands.Aftera fewclustershavebeendeposited,however,anyexposed substratearearemainingintheseMDsimulationsisnotbigenoughforanotherclustertoreachthe surfacewithoutbeingattractedto a nearbyisland. OnedepositedNM-atomclustercoversmore thanone-fourthof the 11x 11substratesurfacearea. RealisticMDsimulationsofthinfilmgrowth via depositionof 100-atomclusterswouldrequirea muchlargersurfacearea (perhaps50 x 50 atoms)to avoideffectsfromtheperiodicboundaryconditions.Unfortunately,sucha simulation is not practicalat this time. Therefon%we restrictour commentsto the depositionprocessof a single 100-atomclusterand somegeneralobservationsaboutthefilmgrowthprocesswith these large clusters. As a depositing 100-atomcluster adsorbs on the top few layers of a pyramid face, overhangingrows are formedto minimizethedisruptionto theclusterstructure.Thiscan result in severalrows of overhangingatomsstackedon top of one another,formingan inverted(111) facet. Each atom in an overhangingrow hasonlytwo supportingatoms,exceptfor thoseon the

266

CL KELCHNFR ANDAE DEPRISTO

endsof the row whichcan havethree(oronlyone)supportingatoms. The overhangingrowsare stabilizedby nearest neighborsabove them in the clusterrather than by supportingatoms in standardfour-foldhollowsiteson the surface. Thisavoidsthebond-breakingwithinthe cluster whichwouldoccurif theclusteratomsweretoextendthe(111)facetby addingto morelayersof the pyramid. One 100-atomclustercan coverall or partof a holein the surfaceif it happensto land on topofone. Thestabilityofoverhangingrowsandthehighcoordinationofmostatomsinthecluster eliminatethe needfor a largestructuralrearrangementof theclusteruponadsorption.However, some rearrangementshave been observedfor 100-atomclusters. The mostcommonstructural changeiscausedby theclustershearingalongthe(111)planeto movepartof theclustertoa lower layer shortlyafter deposition.

CONCLUSIONS The growthbehaviorof a clusterdepositedthin fiim in the multilayerregime cannotbe simplyextrapolatedfromtheinitialstagesof deposition.Thisis in agreementwithearlierresults (9) forthedepositionof singleatoms. However,thinfilmgrowthviaclusterdepositiongenerally cannotbe extrapolatedfromsingleatomdepositionresults,sincedepositionof a clustercan be a mom complicatedeventas seen in this and previousMD studies(6). For example,the strong bondingwithina clustercanaffectthefinalstructureoftheclusteron thesurface,ascancollisions betweenindividualclusteratoms(8)as theclusteradsorbsonthesurface.Theexplicitsimulation of multiple-layerthinfilmgrowthviaclusterdeposition,usingreliableinteratomicpotentialsfor metals,is thereforenecessay to elucidatethe growthmechanisms. Wehavealsostudiedtheeffectofclustersize,animportantparameterwithoutadirectanalog in the depositionof singleatoms. Thin filmsgrownby depositionof largerclusterstend to be rougherthan thoseproducedby depositionof smallerclustersat very low temperature. This is partlydueto thefactthatlargerclustersaremorelikelyto be attractedto an existingislandon the surfacethanto landina holeornarrowgapbetweenislands.Also,theatomsinlargerclustershave a higher coordinationand thus are more likely to retain the originalcluster structure upon adsorption.The 5- and 10-atomclustersstudiedheretendto mergeon the growingsurfaceand losetheirclusteridentities.Depositionof thesesmallclustersdoesnotproduce“nanocrystalline structured”thin films. Instead,it appearsthat largerclustersare requiredin order to retain the cluster’sshapeand propertiesupondeposition.Indicationsof thisare foundin the depositionof 100-atomclusters,wheretheoriginalclusterbondingis preservedby allowinga largeportionof the clusterto remainin overhangingsitesandrows. From these results, it is clear that the presenceand size of clustersduring low energy depositioncan greatlyaffectthefinalstructureof a thinfilmas comparedto depositionof single atoms. If highqualitythin filmsare desiredvia lowenergydepositionat very low temperature, the depositionof singleatomsis prefemedoverthatof smallclusters. ACKNOWLEDGMENTS This workwas supportedby NationalScienceFoundationgrantCHE-9224884.

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