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<ul><li><p>Onthesimilaritiesbetweenmicro/nanolithographyandtopologyoptimizationprojectionmethodsMicheJansen1,BoyanS.Lazarov2,MattiasSchevenels3andOleSigmund2,*</p><p>1. DepartmentofCivilEngineering,KULeuven,Belgium,2. DepartmentofMechanicalEngineering,SolidMechanics,TechnicalUniversityofDenmark,Denmark3. DepartmentofArchitecture,UrbanismandPlanning,KULeuven,Belgium* Correspondingauthorandpresenter:email:sigmund@mek.dtu.dk</p><p>Theaimofthepaperistoincorporateamodelformicro/nanolithographyproductionprocessesintopologyoptimization.Theproductionprocessturnsouttobephysicallyanalogoustousingdensityprojectionfiltersintopologyoptimization.Usually,blueprintssuppliedbydesignerscannotdirectlybeusedasinputstolithographicprocessesduetotheproximityeffectwhichcausesroundingofsharpcornersandgeometricinteractionofcloselyspaceddesignelements.However,duetoaboveanalogy,projectionbasedtopologyoptimizationcandirectlyhandletheproximityeffectcorrection.Furthermore,itisdemonstratedthattherobustprojectionfiltercanbeusedtoaccountforuncertaintiesduetolithographicproductionprocesseswhichresultsinmanufacturableblueprintdesignsandeliminatestheneedforsubsequentcorrections.Densityprojectionschemes[1,2,3]havereceivedincreasedpopularityandareusedtoensurediscretenessofdesignsresultingfromdensitybasedtopologyoptimizationschemes.Combinedwiththerobustdesignapproach[4],projectionschemesmayalsoensuremeshconvergenceandminimumfeaturesizecontrolofbothsolidandvoidphases.Hitherto,onlytheprojectedfieldsintheseapproacheshavebeenassociatedwithphysicalfieldsandthedesignvariablefieldhasonlybeenconsideredasamathematicalentity.However,inthisworkweshowthatthedesignvariablefieldcanbeinterpreteddirectlyasthedosepatterninelectronbeambasedmicroandnanofabricationprocesses.Thefiltereddensityfieldcorrespondstothelocalexposurewhichisblurredcomparedtothedosepatternduetoscatteringeffectsoftheincomingelectronbeam.Thisobservationleadstophysicalandmathematicalinsightandwefurthersuggestmodifiedoptimizationproblemsthatensuresimplicityofthedosefieldandminimizemanufacturingtime[5].Inpracticalmicroandnanoprocessingproximityeffectsplayanimportantrole.Proximityeffectsentailthatcloselyneighboringholeswilletchdifferentlycomparedtomoredistantholeswiththesamenominalsize.ProximityeffectsaremodeledbyadoubleGaussianweightingfunctionforthedensityfilter.Parametersforthisfunctiondependonmanufacturingparameters,materialsandlayerthicknesses.Wediscussanddemonstratetheinfluenceofusingdifferentmaterialsforthedesignrealizations.[1]GuestJ,PrevostJ,BelytschkoT(2004).Achievingminimumlengthscaleintopologyoptimizationusingnodaldesignvariablesandprojectionfunctions.InternationalJournalforNumericalMethodsinEngineering61(2):238254.</p><p>[2]SigmundO(2007).Morphologybasedblackandwhitefiltersfortopologyoptimization.StructuralandMultidisciplinaryOptimization33(45):401424.</p><p>[3]XuS,CaiY,ChengG(2010).VolumepreservingnonlineardensityfilterbasedonHeavisidefunctions.StructuralandMultidisciplinaryOptimization41:495505.</p><p>[4]WangF,LazarovB,SigmundO(2011).Onprojectionmethods,convergenceandrobustformulationsintopologyoptimization.StructuralandMultidisciplinaryOptimization43:767784.</p><p>[5]Jansen,M.;Lazarov,B.S.;Schevenels,M.&amp;Sigmund,O(2013).Onthesimilaritiesbetweenmicro/nanolithographyandtopologyoptimizationprojectionmethods,submitted.</p></li></ul>

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