Effects of mold geometry and taper angles on the filling mechanism ofa nanoimprinted polymer using molecular dynamics

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AppliedSurfaceScience316(2014)292–300

ContentslistsavailableatScienceDirect

Applied

Surface

Science

j o u r n a l ho me p ag e :w w w . e l s e v i e r . c o m / l o c a t e / a p s u s c

Effects

of

mold

geometry

and

taper

angles

on

the

ﬁlling

mechanism

of

a

nanoimprinted

polymer

using

molecular

dynamics

Cheng-Da

Wu

a

_,

_Te-Hua

_Fang

b,∗

_,

_Jen-Fin

_Lin

c

a_Department_of_Mechanical_Engineering,_Chung_Yuan_Christian_University,_200,_Chung_Pei_Rd.,_Chung_Li_City,_Taoyuan_County_32023,_Taiwan b_Department_of_Mechanical_Engineering,_National_Kaohsiung_University_of_Applied_Sciences,_Kaohsiung_807,_Taiwan

c_Department_of_Mechanical_Engineering,_National_Cheng_Kung_University,_Tainan_701,_Taiwan

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received17June2014

Receivedinrevisedform2August2014 Accepted3August2014

Availableonline9August2014 Keywords: Nanoimprint Moleculardynamics Nanotribology Formationmechanism

a

b

s

t

r

a

c

t

Moleculardynamicssimulationsareusedtoinvestigatehowthenanoimprintlithographymechanism influencesthefillinginteractionandmechanicaldeformationonpolymethylmethacrylate(PMMA) sur-faces.Theeffectsoftwomoldgeometriesandvarioustaperangleswereinvestigatedusingstress,slip vector,moleculartrajectories,andappliedforceanalysis.ForthePMMAformationmechanismona concave-likemoldimprint,themoleculeswereextrudedupwardintothemoldspaceafterthemolecules ontwosidesweredownwardcompressedbythemold.Theformationmechanismisoppositetothatfor thetip-likemoldimprintbecausethemoleculesarefirstlycompresseddownwardbythetip.Theresults showthattheslowestfilledareasofthepatternwereatthetwocornersofthetipwherestressvalue waslow.Thefillingspeedinboththetip-likemoldandtheconcave-likemoldimprintincreasedwiththe taperangleincreasedduetofillingspaceandsmallercapillaryflow.Duetotheeffectofcapillaryflow, theconcave-likemoldneedsmuchmoreloadingforcetotransferthepatternthanthetip-likemold. Theloadingforceandcurveoscillationincreasedwiththetaperangleinthetip-likemoldimprint,but theysignificantlyincreasedwithdecreasingtaperangleintheconcave-likemold.Thehighstresswas mainlyconcentratedonthemoleculesnearthetipandunderneaththemoldforthetip-likemoldandthe concave-likemoldimprint,respectively.Therelationshipofthemagnitudeoftaperangletotheloading forceissimilartostressandslipvector.

1. Introduction

Nanoimprintlithography(NIL)isasimpletechniqueto fabri-catenanopatternsonlargesubstrates.NILhasbeenconsideredasa popularmethodwithhighresolution(sub-10nmfeaturesize),cost effectiveness,andhighthroughput[1,2].Althoughsomeprocessing methods,suchaselectronbeamlithographyandfocusedionbeam writing,canbeusedtoproducepatternswithfeaturesdownto sub-10nm,theyarenotpracticalenoughduetolowthroughput andhighcost.NILfabricatesnanopatternsbypressingahardmold withnanopatternsintoathin ﬁlm(polymerormetal)and then deformingtheﬁlmmechanically.

MoststudiesonNIL have focusedonexperiments. Chou[3]

employedNILtofabricateuniformpatternsovera15mmby18mm areaonpolymethylmethacrylate(PMMA)ﬁlms.Austin etal.[4]

demonstrated 5nm linewidth and 14nm linepitch in resist at

∗ Correspondingauthor.Tel.:+886738145265336.

E-mailaddresses:[email protected](C.-D.Wu),[email protected], [email protected](T.-H.Fang),jﬂ[email protected](J.-F.Lin).

roomtemperature.Hsuetal.[5]createdaPMMAfilmwith pho-toniccrystalstructuresintheorganiclight-emittingdiode(OLED) componentstoincreaselighteningefficiencyoftheOLED compo-nents.FewstudiesonNILhaveusednumericalmethods.Molecular dynamics(MD)simulationisapowerfulscientifictoolfor study-ingmaterialbehavioratthenanometerscale.Manynanosystems havebeenanalyzedusingMD,includingthedeformation[6]and hydrogenstoragecapacityofgraphenes[7,8],nanoforming[9,10], metalnanowiresundertorsion[11,12],anddip-pen nanolithog-raphy[13,14].ThepatternformationandmechanicsofNILwere investigatedbyvaryingtheimprinttemperature[15,16]and veloc-ity[15]andtaperangleofmold[17,18].Kangetal.[19]studied pattern transfer on an amorphous PMMA film by using molds withthevariousaspectratiopatterns.Theyfoundthatamountof springbackofresidualfilmincreaseswithincreasingaspectratioof pattern.Thefrictionforcebetweenamoldandafilmbecomeslarger thantheadhesionforcewhenthepatternaspectratioincreases.

Inthepresentstudy,ashort-rangeorderofPMMA molecule layerinthehorizontal directionisconsideredas theimprinted ﬁlm.Theeffectsofthemoldgeometries(tip-likeandconcave-like) andthetaperangleontheNILprocessareinvestigatedusingMD

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Fig.1.Schematicmodelsofthenanoimprintsimulation.Themoldgeometriesin(a)and(b)aretip-likeandconcave-like,respectively.In(c),thePMMAchainsarearranged inthehorizontaldirection,andchainstructuresarecapturedfromthePMMAsystems.Eachchainiscoloredafterthethermalequilibriumatatemperatureof300K.

simulations.Theobjectivesofthisstudyaretodeterminethe phys-icalbehaviorofdeformation,ﬁllingcharacteristics,imprintforce, stress,andslipvectordistributionduringtheimprintprocess.

2. Methodology

Fig.1(a)and(b)showsschematicmodelswithgeometriesof tip-likeandconcave-likeNILmolds,respectively.Theangleonthe moldischangedtostudytheeffectofthetaperangleon nanoim-printfilling.Themodelconsistsofanickel(Ni)moldandPMMAfilm withahorizontalarrangement,asshowninFig.1(c).TheNimold consistsofaperfectfaced-centeredcubic(FCC)singlecrystalwith alatticeconstantof0.352nm.Tosimplifytheimprintproblem,the moldwasassumedtobearigidbodywithaunitdisplacementof 0.003nmtoimprintpertimestep(imprintvelocityis30m/s).The timestepunitof10−15swasemployedforthewholesimulation. Thecharacteristicheightofthemoldwasfixedat5nm.Thewidth andheightofthePMMAfilm,whichwascomposedof100PMMA molecules,were15and20nm,respectively.Themolecularweight ofeachmoleculewas10,016(degreeofpolymerization=100).A two-dimensionalsystemwassimulatedwiththesurfacenormal paralleltotheZ-axis.X-,Y-,andZ-axeswereinthe (110),

¯100

, and (101) directions,respectively.Aperiodicboundarycondition wasappliedtotheX-andY-axes.FourﬁxedlayersofNiatomswere imposedbeneaththePMMAﬁlmtoconstrainthewholesystemin theverticaldirection.ThePMMAmoleculesobeyNewton’ssecond lawandtheirvelocitiesareadjustedtomaintainthemoleculesin anisothermalstateof300K.

ThepotentialenergymodelproposedbyOkadaet al.[20]is adoptedtodescribeinteractionsforthePMMAmolecules,asshown in Eq. (1).In this model, the united atom(UA) model is used, inwhichhydrogenatomsareincludedintheconnectingcarbon atoms;thusamethylorethylgroupistreatedandshowedasone interactingcarbonatom,asshowninFig.2.Theﬁgureshowsthe molecularstructureofPMMA,UAmodel,andtheschematicperiod forachain. U=

bonds kr(r−r0)2+

angles k

−0

2 +

torsions n

i=1 (Vncosn) +

improper torsions

K1(ϑ−ϑ0)+K2(ϑ−ϑ0)2

+

1,5nonbonds A r12− C r6 (1)

wheretheﬁrstandsecondtermsrepresentthebondstretching potential(r=bondlengthandr0=bondlengthinequilibrium)and

theangularbendingpotential(=bendingangleand0=bending

angleinequilibrium),respectively.Thethirdandfourthterms rep-resentthetorsionpotential(=torsionangle)andtheimproper torsionpotential(ϑ=sumofthreeneighboringbendingangles,ϑ0

=sumofthreeneighboringbendinganglesinequilibrium), respec-tively.TheﬁfthtermistheLennard–Jones(LJ)potentialbetween two atoms/molecules in the distance of four bond distances

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294 C.-D.Wuetal./AppliedSurfaceScience316(2014)292–300 CH3 C C CH2 O O CH3

(a)

(b)

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C1 C4S1 CDS C2 O2S OD C1S2 C1 C4S1 CDS C2 O2S OD C1S2 C1 C4S1 CDS C2 O2S OD C1S2

Fig.2.(a)MolecularstructureofPMMA,(b)unitatommodel,and(c)schematicperiodforachain.

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Fig.4. SnapshotsofMDsimulationofNILfortheconcave-likemoldwithataperangleof15◦_,₃₀◦_,_and₄₅◦_for_different_imprint_depths_(D).

(at1–5positions).TheLJpotentialisalsoadoptedtodescribethe interactionbetweentheNisubstrateandPMMAﬁlmwithacut-off radiusof 1nm;itsparametersarederived fromthelattice con-stantand adhesive energyof Ni[21].Lorentz–Berthelotmixing ruleisusedtoestimatethepotentialparametersfortwodifferent atoms/molecules[22].ThemethodsforpreparingtheinitialPMMA structureandrelaxationprocessweredescribedbyKangetal.[19]. Wheninitialchainswerearrangedinthehorizontaldirection,the obtainedPMMAconformationaftertherelaxationprocess approx-imatedtotheconformationwiththehorizontalarrangement.The thicknessofthePMMAﬁlmis20nm.

3. Resultsanddiscussion

3.1. Effectsofmoldgeometryandtaperangleanalyzedusing molecularconformation

Fig.3showssnapshotsofthenanoimprintﬁllingprocess sim-ulationforthetip-likemoldattaperanglesof30◦,40◦,and50◦, respectively.Thedegreeofsharpnessforthemold’stipdecreased

andthevolumeofthetipincreasedwithincreasing value.At the initialimprintdepth of 2.3nm shown in Fig.3,the chains at the surfaces were slightly folded around the mold tip, and thenthemoleculesontwosidesslightlyextrudedupward. Fold-ing was graduallydeveloped downward by the vander Waals forceinteraction ofthe mold–chainmolecules and chain–chain molecules.Whenthemoldwasimprintedatadeeperdepth,the moleculesexhibitedseverefoldingand accumulatedhighstrain energyaroundthetip.APMMAchainseparatedfromtheoriginal entangledchainsontherightsideofthetip.Themoleculesclosest totheheadofthetipwerethemostpulledanddragged.Duringthe patternformationprocess,theflowcharacteristicsatthesurface showed slight non-continuous behavior. The “non-continuous behavior”occursatpolymersurfacesduetothecomplexforces betweentheintra-andtheinter-molecules,leadingtoa discon-tinuousdeformation.Thenon-continuousfillingcharacteristicfor PMMA hasbeen foundin micro- and nano-indentation experi-ments[23].Flowmaybeimprovedbyincreasingthemolecular kineticenergy/temperature.Forthewholefillingprocess,itwas foundthattheslowestfilledareasofthepatternwereatthetwo

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296 C.-D.Wuetal./AppliedSurfaceScience316(2014)292–300

cornersofthetip.Accordingtothesimulationresults,thereisa clearrelationshipbetweenthefillingspeed,thepatterndensity, andthemagnitudeofthetaperangle.Whenamoldwithalarge taperanglewasimprintedintoPMMA,themolecularfillingspeed andpatterndensityincreasedduetoasmallerfillingspaceanda strongcapillaryeffect.Inthesecases,thecriticalimprintdepths atthecompletedfillingstagewere5.3,6.8,and8.9nmfortaper anglesof50◦,40◦,and30◦,respectively.Thecriticalimprintdepth isdefinedastheminimumdepthatwhichthemoldspaceisfilled completely.The pattern densitybecame highwhen the critical depthincreased.Once thecritical depthwasreached, only the chainsatthesurfacelayersweredeformedbythetipandthese chainssurroundedthetipinsequence. Thisis duetothechain moleculesbeingconstrainedbythestrongintra-moleculeforceand thevanderWaalsforceinteraction.MostPMMAmoleculesaway fromthetipremainedintheoriginalconformationwithaslightly higherdensity.

Fig.4showsnapshotsofthenanoimprintfillingprocess sim-ulationfortheconcave-likemoldattaperanglesof15◦,30◦,and 45◦,respectively.Unlikethefillingprocessforthetip-likemold cases,themoleculesunderneaththeconcavemoldwereupward extrudedintothemoldspaceafterthemoleculesontwosideswere downwardcompressedbythemold.Thespaceinside themold increasedwithincreasingtheconcaveanglefortheconcave-like mold.Attheinitialimprintstageatthedepthsof2.3and3.8nm, asmallfoldingoccurredatthesurfacechainswhichflowedinto theconcavemold.Themoleculesontwosideswerethenslightly downwardcompressed.OncethePMMAmoleculeswereextruded intothemold,thefoldingextentwasinverselyproportionaltothe angleoftheconcave,andthefillingabilitywasproportionaltothe taperangle.Similartothecaseofthetip-likemoldimprint,most moleculesbelowthemoldbottomkepttheoriginalhorizontal con-formation.Intheconcave-likemoldimprint,theslowestfillingarea wasonthetopoftheconcave.Comparingthetwomoldgeometries, themoldspacearemoredifficulttobefilledontheconcave-like moldthanonthetip-likeonebecauseofthecriticalcapillaryeffect, especiallyforsmalltaperangles.Seeingimprintatthetaperangle of15◦at13nmcriticalimprintdepth,untilthegreatimprintdepth reached,thePMMAmoleculesunderneaththemolddidnoteasily toflowintothespaceoftheconcavemoldbecauseallmolecules werealreadypacked.

3.2. Effectofmoldformandtaperangleanalyzedusingimprint force

Fig.5 shows the variation of the molddisplacement versus the loading force for the tip-like mold at taper angles of 30◦, 40◦,and50◦.Duringthewholeimprintprocess,allloadingforces increasedas themolddisplacement increasedbecausea larger forceisrequiredtoextrudemorePMMAmolecules.Attheinitial imprintstageatadepthof0–3nm,threeloadingforceincreased withasameslopeduetoslightcontact.Withincreasingimprint depth,theforcecurvesstarttoincreaseinoscillation.The magni-tudeofoscillationindicatestheextentoftheslip-stickinteraction forPMMAmoleculesimprintedbythemold.Theresultsshowthata moldwithalargetaperanglerequiresahighloadingforceunderthe sameimprintdepthbecausethecontactareabecomesbiggerand morePMMAmoleculesareaffectedbythetip.Untilcompletefilling (themolddisplacementsare5.3,6.8,and8.9nmfortaperanglesof 50◦,40◦,and30◦,respectively),thesimulatedforcesdidnotexhibit obviousforce-dropbehavior[17]becausePMMAisnotagood crys-tallinefilm.Forrectangulartipswithvariousaspectratiostothe mold[19],theextentofoscillationintheforcecurvewasverylow. Interestingly,allcurvesstartedtooscillateafterreachingthe com-pletefillingimprintdepth.Themagnitudeofoscillationincreased withthemolddisplacementandtaperangle.ThesnapshotsinFig.5

Fig.5. Variationofmolddisplacementversusloadingforceforthetip-likemold withtaperanglesof30◦,40◦,and50◦.Thesnapshotsshowtheﬁllingsimulationat theimprintdepthof9nmforthethreetaperangles.

showtheﬁllingsimulationattheimprintdepthof9nmforthree taperangles.Whenthemoldimprintswithalargetaperangle,the densityofthepatternandthemolecularpackingarehigher. There-fore,thestrongreactionforcedirectlyshowedonthemagnitudeof requiredloadingforce.Alargetaperanglehasahighshearaction, whichfurtherexplainsthelargeoscillationinthecurvesoflarge taperangle.

Fig.6showsthevariationofmolddisplacementversus load-ingforcefortheconcave-likemoldatanglesof15◦,30◦,and45◦. Attheinitialimprintstageatadepthof0–2nm,allloadingforces increasedequally.Comparedtothetip-likemold’sforcecurvein

Fig.5,theconcave-likemold’sforcecurvehasmuchmore oscil-lation anda higher imprintforce afteraninitialimprint depth of2.2nm.WhenthePMMAfilm wasimprintedbythemold,a higherforceindicatedthatthePMMAmoleculesdidnoteasilyflow intotheconcave-likemold.Themolecularfillingabilityincreases withincreasingtaperangle.Thecompletefillingsoftheimprint depthwere6.3,8.3,and13nmfortaperanglesof45◦,30◦,and15◦,

Fig.6.Variationofmolddisplacementversusloadingforcefortheconcave-like moldwithtaperanglesof15◦_,₃₀◦_,_and₄₅◦_.

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Fig.7. Stressdistributionsforthetip-likemoldatthecompletedﬁllingstagewiththethreetaperangles.(a)and(b)Showthenormalstressesof␴xxand␴zz,respectively.

(c)Showstheshearstress␴xz.

respectively.Theforcecurveforataperangleof15◦attheimprint depthof 13nm shows that a much higher forcevalue (around 10␮N)wasrequiredandkeepingextrudefewmoleculesintothe extremenarrowspace.Mostoftheimprintforcewascontinually absorbedbythePMMAmoleculesunderneaththemolduntilnew moleculeswereextrudedintothemold.

3.3. Stressﬁelddistributionanalysis

ThestressdistributionsofPMMAﬁlmfortheimprintprocessat thecompletedﬁllingstageforvariousmoldsandtaperanglesare showninFigs.7and8,inwhichtheyareinstantaneousstresses.

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Fig.8.Stressdistributionsfortheconcave-likemoldatthecompletedﬁllingstagewiththreetaperangles.(a)and(b)Showthenormalstressesof␴xxand␴zz,respectively.

(c)Showstheshearstress␴xz.

representedbytwonormalstresses,XXandZZ,andashearstress,

XZ.In theﬁgures,a criticalstressareaoccurredonthenormal

stressZZbecauseitwasstronglyconcentratedbythemold’stip.

Herethemoleculesnearthetiphadthemostseriouspacking.At thetwosidesofthetip,therearelowerstressareasofcompressed material;theyalsoappearinthelarge-scaleimprintanalyzedusing thecontinuumbodytheory[24,25].Fromthesimulationresults, thelowerstressareaisattheareas wherebethelatestﬁlling. Theparticleactivityinsomeareaswasmuch freerthanthat in

others.Theresultsshowthatthemoldwithasmalltaperangle imprintalwayshadhigherstressandanobviousstress concen-trationareanearthetipforeachstresscomponentduetoslower ﬁllingatsmalltaperangles.Thestressvaluedecreasedgradually withdeeperlayersanddistanceawayfromthetip.Inaddition,the normalstress(XX,horizontaldirection)washighunderthebulge

ofthePMMAﬁlmandunderthemoldpattern.ExtrudedPMMA moleculeswerecompressedintheX-direction,formingabulgein thePMMAﬁlm.ThislargeXX neartheextrusionexitblocksthe

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Fig.9.(a)–(c)Slipvectordistributionsforthetip-likemoldatthecompletedﬁllingstagewiththreetaperangles,respectively.(e)and(f)Slipvectordistributionforthe concave-likemoldatthreetaperangles.

PMMAfromsqueezingoutandmakesitdifﬁculttoobtainathin residuallayer.FortheshearstressXZ,alargershearstresswas

gen-eratednearthemold’stip,whichledtoserioussheardeformation andaruptureofthecontinuousmolecularlayer.

Thedistributionofhighstressareaisdifferentforthe concave-likemold, as shown in Fig.8. In both normal stress ﬁelds XX

andZZ,themainstressisconcentratedontheregionswherethe

moleculesﬂowintothemoldandunderneaththemold.The lat-terregionexhibitsbiggerstressvaluesthantheformer,because themoleculeswereextrudedintothemoldafterthemolecules underneaththemoldweredirectlycompressed.Eachstressﬁeld componentincreasedwithdecreasedtaperangledecreased.The resultsshowthattheshearstress(XZ)actionwassmallerthan

thatoftheothertwo normalstressesfor boththeconcave-like moldandthetip-likemold.Seeingthestressdistributionatthe mold with taper angle of 15◦, a surprising high stress under-neaththemoldindicated thatthePMMA moleculesunderwent alargeloadingbeforethematerialreachedthecompletedﬁlling state.

3.4. Slipvectordistributionanalysis

Theslipvectorshowsanotherkindofstraindistribution.Slip vectorwasevaluatedusingthemolecularpositiondifference.Itwas calculatedfromtheinitialpositionstothepositionsofmaximum imprintdepth;themoleculeswerecoloredbyavectortorepresent theextentofdisplacement.Themagnitudeofthevectoronthei-th moleculecanbecalculatedas:

s=

riini−rispe

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Themoleculeshadahighermagnitudeofslipvector, indicat-ingthattheamountofdisplacementwassigniﬁcant.Fig.9(a)–(c) showstheslipvectoranalysisforthecompletedﬁllingstateforthe tip-likemoldimprintatthreetaperangles.Duetotheconstrained forcefromtheintra-moleculesinthepolymer,theslipvector dis-tributionsatbothsidesarealmostsymmetrical.Itwasfoundthat themagnitudeoftheslipvectorincreasedasthetaperangleof themolddecreased.Atthesameimprintdepth,however,alarger taperangleimprintleadstoahigherslipvectorbecauseofthelarger

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contactareaanddeformationamount.Theeffectisclearlyshown inFig.9(b)and(c).Seeingthetaperangleof30◦inFig.9(a),there arethreemajorareasofhighslipvectordistribution;inorderof magnitudearetheareaclosesttothetip,theareanearthetip, andtheareaunderneaththemold,respectively.Themagnitudeof theﬁrsttwoslipareasisproportionaltothetaperangleandthe imprintdepth,butthemagnitudeoftheareaunderneaththemold isinverselyproportionaltothetaperangle.Fortheconcave-like moldimprintshowninFig.9(d)and(e),theareawiththehighest slipvectorisunderneaththemold,thesecondareaaremoleculesat theconcavemold.Intheconcave-likemoldimprint,theslipvector decreaseswithincreasingtaperangleatthesameimprintdepth becausemoreextrudedmoleculesaregenerated.Forataperangle of15◦,asshowninFig.9(e),theslipvectorwasextremelyhighand thedistributionwasuniformfromsurfacetodeeperlayers.Even moleculespackedinsidethemoldhadaveryhighvaluebecause allmoleculeswerecompressedstronglybythemold.

4. Conclusion

ThestressandslipbehaviorofimprintedPMMAsurfaceswere investigated using molecular dynamics. For the PMMA forma-tionmechanismontheconcave-likemoldimprint,themolecules wereextrudedupwardintothemoldspaceafterthemoleculeson twosidesweredownwardcompressedbythemold.The forma-tionmechanismisoppositetothatforthetip-likemoldimprint becausethemoleculeswerefirstlycompresseddownwardbythe tip,andthenthemoleculesontwosideswereextrudedupward. Alargertaperangleincreasesthefillingspeedinthetip-likemold andtheconcave-likemoldimprints,duetoincreasefillingspace andasmallercapillaryeffectbetweenthemoldwallsandPMMA molecules.Theconcave-likemoldneedsmuchmoreloadingforce thandoesthetip-likemoldtotransferthepattern.Theloading forceandcurveoscillationincreasedwithincreasingtaperanglein thetip-likemoldimprint,buttheyincreasedwithdecreasingtaper angleintheconcave-likemold.Thehighstresswasmainly concen-tratedonthemoleculesnearthetipandunderneaththemoldfor thetip-likemoldandtheconcave-likemoldimprints,respectively.

Therelationshipofthemagnitudeoftaperangletotheloadingforce issimilartothestressandtheslipvector.Theslipvectoranalysis showsthecharacteristicsoftheﬂowﬁeldforthetwomoldtypes andatthevarioustaperangles.

Acknowledgement

ThisworkwassupportedinpartbytheNationalScienceCouncil TaiwanunderGrantsNSC100-2628-E-151-003-MY3andNSC 100-2221-E-151-018-MY3.

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