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

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_{DepartmentofMechanicalEngineering,ChungYuanChristianUniversity,200,ChungPeiRd.,ChungLiCity,TaoyuanCounty32023,Taiwan} b_{DepartmentofMechanicalEngineering,NationalKaohsiungUniversityofAppliedSciences,Kaohsiung807,Taiwan}

c_{DepartmentofMechanicalEngineering,NationalChengKungUniversity,Tainan701,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.

©2014ElsevierB.V.Allrightsreserved.

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

http://dx.doi.org/10.1016/j.apsusc.2014.08.015

C.-D.Wuetal./AppliedSurfaceScience316(2014)292–300 293

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

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

(a)

(b)

(c)

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.

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

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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