Poster2

Laterally Confined Diblock Copolymer Thin Films August W. Bosse, Tanya L. Chantawansri, Glenn H. Fredrickson, and Carlos García-Cervera Departments of Chemical Engineering and Mathematics, UCSB FENA Theme 3: Modeling, Simulations and Computations

Objective Objective The Theproblem problemofofcontrolling controllingand andunderstanding understandingmicrodomain microdomainordering orderingininblock block copolymer copolymerthin thinfilms filmshas hasattracted attractedmuch muchattention attentionfrom frompolymer polymertechnologists. technologists.In In the thecontext contextofofblock blockcopolymer copolymerlithography, lithography,aachallenge challengeisistotoimprove improvelong-range long-range in-plane in-planeorder orderof ofmicrodomains. microdomains.Here Herewe wepresent presentaacomputational computationalstudy studyof ofmicronmicronscale, scale,lateral lateralconfinement confinementas asaameans meansofofachieving achievingdefect-free defect-freeconfigurations configurationsinin thin thinblock blockcopolymer copolymerfilms. films.Specifically, Specifically,we wewill willfocus focuson onthin thinfilms filmsof ofcylindercylinderforming formingAB ABdiblock diblockcopolymers copolymersconfined confinedlaterally laterallyby byaahexagonal hexagonalwell. well.Since Sincethe the size sizeofofthe thehexagonal hexagonalwell wellcan canbe bemade madecommensurate commensuratewith withthe theoptimal optimalhexagonal hexagonal lattice latticeformed formedby byblock blockcopolymer copolymercylinders cylindersininthe thebulk bulkand andplanar planarsteps stepsare areknown known totoimprove improveorder orderininadjacent adjacentmicrodomains, microdomains,ititisisreasonable reasonabletotohope hopethat that confinement confinementtotohexagonal hexagonalwells wellscan canreproducibly reproduciblyyield yielddefect-free defect-freeconfigurations. configurations. InInorder ordertotonumerically numericallysimulate simulatesuch suchaasystem, system,we weapply applyaaself-consistent self-consistentfield field theory theory(SCFT) (SCFT)model modelfor foran anAB ABdiblock diblockcopolymer copolymermelt meltcombined combinedwith withaamasking masking technique techniquetotodefine definethe thewell wellgeometry[1-3]. geometry[1-3].We Wehave havechosen chosenthe thesize sizeof ofthe the hexagonal hexagonalconfining confiningwell wellsuch suchthat thatnine ninecylinder cylinderrows rowsfit fitacross acrossthe thehexagon, hexagon, which whichcorresponds correspondstotoproposed proposedexperimental experimentalconfinement confinementsizes sizes(Kramer (Kramergroup group–– UCSB). UCSB).

‘‘A’ A’ Wetting Wetting

‘‘B’ B’ Wetting Wetting

Majority Majority Component Component

Minority Minority Component Component

The The Model Model

AB AB diblock diblock copolymer copolymer

Numerical Numerical SCFT SCFT

ss==contour contourvariable variableininunits unitsof ofNN(index (indexof ofpolymerization) polymerization) ff==fraction fractionof ofAAmonomers monomersin inan anAB ABdiblock diblockcopolymer copolymer

Hexagonal Hexagonal well well Modified ModifiedDiffusion DiffusionEquation: Equation:

Single SingleChain ChainPartition PartitionFunction: Function:

Density DensityEquations: Equations:

Introduction Introduction Block Blockcopolymer copolymerthin thinfilms filmsrepresent representaapromising promisingsub-optical sub-opticallithographic lithographictool. tool. In Inparticular, particular,there thereisisconsiderable considerabletechnological technologicalinterest interestininusing usingself-assembled self-assembled block blockcopolymer copolymermicrodomains microdomainstotodefine define10 10nm nmscale scalefeatures. features.Thin Thinfilms films consisting consistingof ofaalarge largearray arrayof ofmicrophase-separated microphase-separatedblock blockcopolymer copolymerspheres, spheres, cylinders, cylinders,or orlamellae lamellaecan canbe beused usedtotopattern patternaasubstrate substratewith withaacorresponding correspondingarray array of of10 10nn nnscale scaledots dotsor orlines. lines.Such Sucharrays arraysare arepotentially potentiallyuseful usefulininnext nextgeneration generation high-density high-densitymagnetic magneticmedia mediaand andsemiconductor semiconductordevices. devices.However, However,ififsuch suchdevices devices are aretotobe berealized, realized,the thefeature featurearrays arraysmust mustexhibit exhibithigh highuniformity uniformityand andorder. order. Although Althoughititisisconsiderably considerablydifficult difficulttotogenerate generatelarge, large,2D 2Darrays arraysof ofuniform, uniform, well-ordered well-orderedmicrodomains, microdomains,there therehas hasbeen beensubstantial substantialwork workon onenhancing enhancingorder orderinin block blockcopolymer copolymerthin thinfilms. films.Possible Possibletechniques techniquesofofinducing inducingorder orderinclude includeapplying applying external externalfields, fields,shearing shearingthe thefilm, film,and andgraphoepitaxy graphoepitaxy(lateral (lateralconfinement), confinement),among among others. others.Segalman Segalmanetetal.[4] al.[4]have haveexamined examinedthe theeffects effectsof ofaaplanar planarwall wallon onthe the ordering orderingof ofmicrodomains, microdomains,where wherethey theyobserved observedincreased increasedlateral lateralmicrodomain microdomain order orderwithin withinaaregion regionextending extendingapproximately approximately4.75 4.75μm μmfrom fromthe thewall. wall.Here Herewe we study studythe therole roleof ofconfinement confinementgeometry geometryby byinvestigating investigatingmicrodomain microdomainordering orderingofof block blockcopolymer copolymerthin thinfilms filmslaterally laterallyconfined confinedininaahexagonally-shaped hexagonally-shapedwell. well.

χχ==strength strengthof ofthe theAAand andBBsegment segmentrepulsive repulsiveinteractions interactions Figure Figure1:1:Representative Representativedensity densitycomposition compositionprofiles, profiles,ΦΦAA ininyellow yellowand andcorresponding correspondingVoronoi Voronoidiagrams diagrams(hexagon (hexagon

Figure Figure2:2:Representative Representativedensity densitycomposition compositionprofiles, profiles,ΦΦAA ininyellow yellowand andcorresponding correspondingVoronoi Voronoidiagrams diagrams(hexagon (hexagon

ininwhite, white,pentagon pentagoniningray, gray,and andheptagon heptagonininblack) black)for foran an A-attractive A-attractivewall. wall.(a) (a)and and(b) (b)are aredensity densityprofiles profilesand and

ininwhite, white,pentagon pentagoniningray, gray,and andheptagon heptagonininblack) black)for foraa B-attractive B-attractivewall. wall.(a) (a)and and(b) (b)are aredensity densityprofiles profilesand and

Voronoi Voronoidiagrams, diagrams, respectively, respectively,for forl l==15.00 15.00RRg,g,(c) (c)and and (d) (d)are arefor forl l==16.25 16.25RRg, ,and and(e) (e)and and(f) (f)are arefor forl l==17.75 17.75

Voronoi Voronoidiagrams, diagrams, respectively, respectively,for forl l==18.00 18.00RRg,g,(c) (c)and and (d) (d)are arefor forl l==19.00 19.00RRg, ,and and(e) (e)and and(f) (f)are arefor forl l==20.00 20.00

RRg. . g

RRg. . g

g

g

ll==hexagonal hexagonalside sidelength length

Saddle SaddlePoint PointEquations: Equations:

We Weuse useaahexagonal hexagonalwall wallfield, field,φφWW(r), (r),to tolaterally laterallyconfine confine the thepolymer polymermelt. melt.This Thisfield fieldisisspecified specifiedas asaasix-fold six-fold modulated modulatedtanh tanhfunction. function. Local Localincompressibility incompressibilityisisenforced enforcedby bythe thefollowing following constraint: constraint:φφA(r) (r)+φ +φB(r) (r)++φφW(r) (r)=1. =1. A

B

W

Discussion Discussion and and Future Future Plans Plans Quenched Quenched Simulations Simulations

Annealed Annealed Simuations Simuations

References References [1] [1]Fredrickson, Fredrickson,GH. GH.The TheEquilibrium EquilibriumTheory TheoryofofInhomogeneous InhomogeneousPolymers. Polymers.Clarendon Clarendon Press, Press,Oxford, Oxford,2006. 2006.

InIn order order toto examine examine how how hexagonal, hexagonal, lateral lateral confinement confinement influences influenceslong-range long-rangeorder orderininblock blockcopolymer copolymerthin thinfilms, films,we weconducted conducted 2D SCFT simulations. For all simulations we set f = 0.7, 2D SCFT simulations. For all simulations we set f = 0.7, thus thus the the majority majority block block component component isis A. A. For For the the quenched quenched simulations, simulations, χN χN isis held held fixed fixed atat χN χN == 17. 17. These These values values ofof f f and and χN χN yield yield SCFT SCFT solutions solutions corresponding correspondingtotohexagonally hexagonallyordered orderedcylindrical cylindricalmicrodomains. microdomains.For Forthe the annealing annealingsimulations simulationsχN χNisisramped rampedfrom fromχN χN==12 12totothe thefinal finalvalue valueofof χN χN==17. 17.The Thevalue valueofofχχwwNNwas wasselected selectedtotobe beχχwwNN==17 17ororχχwwNN==-17 -17for for an anAA–attractive –attractiveororB-attractive B-attractivewall wallrespectively. respectively. To To identify identify the the width width of of the the “commensurability “commensurability window” window” inin hexagon hexagon size size l l that that yields yields aa perfect perfect array array ofof microdomains, microdomains, we we report report both both the the average average total total number number ofof microdomains microdomains inside inside the the confining confining hexagon hexagon and andthe thestandard standarddeviation deviation(SD) (SD)ofofnearest nearestneighbors neighbors(NN) (NN) microdomain separations inside the confining hexagon <σ>. microdomain separations inside the confining hexagon <σ>.

[2] [2]Matsen, Matsen,MW. MW.Thin Thinfilms filmsblock blockcopolymer. copolymer.Journal JournalofofChemical ChemicalPhysics Physics106 106(1997), (1997), 7781. 7781. [3]Wu, [3]Wu,Y, Y,Cheng, Cheng,G, G,Katsov, Katsov,K, K,Sides SidesSW, SW,Wang WangJ,J,Tang, Tang,J,J,Fredrickson FredricksonGH, GH, Moskovits, Moskovits,M, M,and andStucky, Stucky,GD. GD.Chiral Chiralmesostructures mesostructuresby bynano-confinement. nano-confinement.Nature Nature Materials Materials33(2004), (2004),816. 816. [4] [4]Segalman, Segalman,RA, RA,Hexemer, Hexemer,A, A,and andKramer KramerEJ, EJ,Edge Edgeeffects effectson onthe theorder orderand andfreezing freezing ofofaa2D 2Darray arrayofofblock blockcopolymer copolymerspheres. spheres.Physical PhysicalReview ReviewLetters Letters91 91(2003), (2003),196101 196101

For For the the quenched quenched simulations, simulations, we we observe observe aa commensurability commensurability window windowofofl l==15.75 15.75totol l==17.00 17.00for forthe thecase caseofofan anA-attractive A-attractivewall. wall.For For the B-attractive wall, the ordered window extends from l = 18.75 to l the B-attractive wall, the ordered window extends from l = 18.75 to l== 19.25. 19.25.

Acknowledgements Acknowledgements We are grateful to Gila Stein, Edward Kramer, and Kirill Katsov for useful discussions.

For Forthe theannealed annealedsimulations, simulations,the theordered orderedwindow windowextends extendsfrom froml l ==15.75 15.75totol l==17.75 17.75for forthe theA-attractive A-attractivewall. wall.For Forthe theB-attractive B-attractivewall, wall, we wesee seean anordered orderedwindow windowthat thatextends extendsfrom froml l==17.75 17.75totol l==19.75. 19.75.Thus Thus the theχN χNannealing annealinghas haseffectively effectivelyequalized equalizedthe theordering orderingeffects effectsof ofthe theAAand and B-attractive B-attractive walls. walls. This This can can be be explained explained by by the the formation formation ofof aa wetting wettinglayer layerof ofmicrodomains microdomainsbelow below(χN) (χN)ODT . .

We are grateful to Gila Stein, Edward Kramer, and Kirill Katsov for useful discussions. Funding Fundingfor forthis thisproject projectwas wasprovided providedby bythe theMARCO MARCOCenter Centeron onFunctional FunctionalEngineered Engineered Nano NanoArchitectonics Architectonics(FENA). (FENA). This Thiswork workmade madeuse useof ofMRL MRLCentral CentralFacilities Facilitiessupported supportedby bythe theMRSEC MRSECProgram Programof ofthe the National Science Foundation under award No. DMR05-20415. National Science Foundation under award No. DMR05-20415.

Figure Figure3:3:Graphs Graphsofof(a) (a) vs. vs.l land and(c) (c) <σ> <σ>vs. vs.l lafter afteraaquench quenchfrom fromrandom randominitial initialconditions conditions totoχN = 17 for an A attractive wall (χ N = 17). There is a region form l = 15.75 to l = 17.00 χN = 17 for an A attractive wall (χwwN = 17). There is a region form l = 15.75 to l = 17.00over over which there is a perfect array of 61 hexagonally ordered microdomains. which there is a perfect array of 61 hexagonally ordered microdomains. Graphs Graphsofof(b) (b) vs. vs.l land and(d) (d) <σ> <σ>vs. vs.l lafter afteraaquench quenchfrom fromrandom randominitial initialconditions conditionstotoχN χN ==17 for a B attractive wall (χ N = -17). There is a region from l = 18.75 to l = 19.25 over which 17 for a B attractive wall (χwwN = -17). There is a region from l = 18.75 to l = 19.25 over which there thereisisaaperfect perfectarray arrayofof61 61hexagonally hexagonallyordered orderedmicrodomains. microdomains.

Figure Figure4:4:Graphs Graphsofof(a) (a) vs. vs.l land and(c) (c) <σ> <σ>vs. vs.l lafter afteraaχN χNanneal annealfrom fromrandom randominitial initialconditions conditionsatat χN χN==12 12totoχN χN==17 17for foran anAAattractive attractivewall wall(χ(χwwNN==17). 17).There Thereisisaaregion regionfrom froml l==15.75 15.75totol l==17.75 17.75over over which whichthere thereisisaaperfect perfectarray arrayofof61 61hexagonally hexagonallyordered orderedmicrodomains. microdomains. Graphs Graphsofof(b) (b) vs. vs.l land and(d) (d) <σ> <σ>vs. vs.l lafter afteraaχN χNanneal annealfrom fromrandom randominitial initialconditions conditionsatatχN χN ==12 12totoχN χN==17 17for foraaBBattractive attractivewall wall(χ(χwwNN==-17). -17).There Thereisisaaregion regionfrom froml l==17.75 17.75totol l== 19.75 19.75over overwhich whichthere thereisisaaperfect perfectarray arrayofof61 61hexagonally hexagonallyordered orderedmicrodomains. microdomains.

ODT

Future Future work work includes includes studying studying defect defect formation formation inin smaller smaller and and larger larger hexagonally hexagonally confined confined systems systems and and studying studying other other copolymer copolymer architectures architecturesand andthe therole roleof ofadditives. additives.In Inaddition, addition,we wewill willexplore exploreother other confinement confinementgeometries geometriessuch suchasastriangular triangularwells. wells.