Externally-resonatedlinearmicrovibromotorformicroassemblyKazuhiroSaito - PDF document

Externally-resonatedlinearmicrovibromotorformicroassemblyKazuhiroSaitouandSoungjinJ.WouDepartmentofMechanicalEngineeringandAppliedMechanicsUniversityofMichigan,AnnArbor,MI48109{2125,USAABSTRACTAnewdesignofalinearmicrovibromotorforon-substratenepositioningofmicro-scalecomponentsispresentedwhereamicrolinearsliderisactuatedbyvibratoryimpactsexertedbymicrocantileverimpacters.Thesemicrocantileverimpactersareselectivelyresonatedbyshakingtheentiresubstratewithapiezoelectricvibrator,requiringnoneedforbuilt-indrivingmechanismssuchaselectrostaticcombactuatorsasreportedpreviously.1,2Thisselectiveresonanceofthemicrocantileverimpactersviaanexternalvibrationenergyeldprovideswithaverysimplemeansofcontrollingforwardandbackwardmotionofthemicrolinearslider,facilitatingassemblyanddisassemblyofamicrocomponentonasubstrate.Thedouble-Vbeamsuspensiondesignisemployedinthemicrocantileverimpactersforlargerdisplacementinthelateraldirectionwhileachievinghigherstinessinthetransversaldirection.Ananalyticalmodelofthedeviceisderivedinordertoobtain,throughtheSimulatedAnnealingalgorithm,anoptimaldesignwhichmaximizestranslationspeedofthelinearslideratdesiredexternalinputfrequencies.Prototypesoftheexternally-resonatedlinearmicrovibromotorarefabricatedusingthethree-layerpolysiliconsurfacemicromachiningprocessprovidedbytheMCNCMUMPSservice.Keywords:microassembly,on-substratenepositioning,microelectro-mechanicalsystems(MEMS),microlinearvibromotor,micromechanicalresonator.1.INTRODUCTIONAssemblyhasnotbeenanissueofresearchinmicroelectromechanicalsystems(MEMS).Thisisbecauseoneofthelargestadvantagesofsurfacemicrofabricationtechnologies,whichMEMSisbasedon,isnoneedforassembly;anentiresystem(,achip)withmultiplecomponentscanbefabricatedinprocessesinvolvingnoassembly.Asthecomplexityofthesystemincreases,however,theneedforassembly,aswellasdisassembly,becomesmoreevidentsincecomplexintegratedsystemsoftensuerfromlowreliabilityduetothelackofmodularityamongsubsystems.ThisisespeciallytrueforMEMS,whichoftenrequirecomplexelectromechanicalintegrationandpackaging.Despitethesedemands,nopracticalassembly/disassemblymethodsofmicro-scalecomponentssuitableforautomationhasbeendevelopedsofar.AssemblyinMEMS,ifneeded,istypicallydonebymanualoperationofmicroprobesormicrotweezers(Suchminiaturizationoftheconventionalpick-and-placeroboticassembly,however,experiencesextremedicultyinhandlingandpositioningcomponentswithsizeslessthanamillimeter,duetothesurfaceadhesionforceswhichcausestickingamongcomponentsandhandlingdevices.Figure1illustratespick-and-placeassemblyofamicro-scalecomponentusingamicrogripper.Surfaceadhesionforcessuchaselectrostatic,vanderWaals,andsurfacetensionforcescausethecomponenttosticktothegripperduringtheapproach(Figure1(b))andtherelease(Figure1(d))phases.Mechanicalshockcanbeappliedtothegrippertodropthestuckcomponent(Figure1(e)),withthepriceofinaccuratepositioningofthereleasedcomponent(Figure1(f)).Onewaytoovercomethisproblemistodesignadeviceonthesubstratethatfacilitatescomponentpositioningsothatgrosspositioningisdoneintheconventionalpick-and-placefashion,whereasnepositioningisdonebytheon-substratepositioningdevice.ThisconceptisillustratedinFigure2,whereaon-substratelinearactuatorpushesainaccuratelypositionedmicrocomponent(,asaresultofthe\shockrelease"showninFigure1(e)and(f))againstaxtureanchoredtothesubstrate(Figure2(a)),achievingprecisepositioningofthecomponent(Figure2(b)).Thelinearactuatoralsoshouldbeabletore-opentoreleasethepositionedcomponenttofacilitatethepotentialneedsfordisassembly(Figure2(c)). Correspondingauthor;Phone:(734)763{0036,Fax:(734)647{3170,E-mail:kazu@umich.eduorwithotherprocesseswhicharemoreeectiveforgrosspositioning{seeSection5foranexample. Stick to gripper b) c) Stick f) Inaccurate positioning Figure1.Typicalpick-and-placeassemblyinmicroscale(modiedfrom).(a)Agripperapproachestoacom-ponent;(b)Thecomponentstickstothegripper;(c)thegrippergraspsthecomponent;(d)Thecomponentistransportedtoadesiredlocation;(e)Thecomponentisreleasedwithshock;(f)Thecomponentisplacedatinaccu-rateposition. a) Anchored fixture Inaccurately positioned component b) Figure2.Precisecomponentpositioningandreleasewithaon-substratelinearactuatorandaxture.(a)inaccu-ratelypositionedcomponent;(b)accuratelypositionedcomponent;(c)releaseofthecomponentfordisassembly.Thispaperdescribesadesignofsuchamicrolinearactuatorfornepositioningofamicro-tomeso-scalecomponentonasubstrate.ThedesignisbasedonalinearmicrovibromotorreportedbyDanemanetal.amicrolinearsliderisactuatedbyvibratoryimpactsexertedbymicrocantileverimpacters.Dissimilartotheirdesign,however,thesemicrocantileverimpactersareselectivelyresonatedbyshakingtheentiresubstratewithapiezoelectricvibrator,requiringnoneedforbuilt-indrivingmechanismssuchaselectrostaticcombactuators.Thisselectiveresonanceofthemicrocantileverimpactersviaanexternalvibrationenergyeldprovideswithaverysimplemeansofcontrollingforwardandbackwardmotionofthemicrolinearslider,facilitatingassemblyanddisassemblyofamicrocomponentonasubstrate.Thedouble-Vbeamsuspensiondesignisemployedinthemicrocantileverimpactersforlargerdisplacementinthelateraldirectionwhileachievinghigherstinessinthetransversaldirection.Ananalyticalmodelofthedeviceisderivedinordertoobtain,throughtheSimulatedAnnealingalgorithm,anoptimaldesignwhichmaximizestranslationspeedofthelinearslideratdesiredexternalinputfrequencies.Prototypesoftheexternally-resonatedlinearmicrovibromotorarefabricatedusingthethree-layerpolysiliconsurfacemicromachiningprocessprovidedbytheMCNCMUMPSservice.2.RELATEDWORKIntheeortsofthedevelopmentofabulkassemblymethodformicro-tomeso-scalecomponents,severalapproacheshavebeenproposedtoincorporateself-positioningtomicroassembly.YehandSmithintegratedtrapezoidalGaAsmicroblocksonaSisubstratewithtrapezoidalholesbydispensingtheseinacarrier uid(ethanol)ontotheSisubstrate.Cohn,KimandPisanoexperimentedwiththeself-assemblyofsmallhexagonalparts(1indiameter)byplacingaquantityofthemonaslightlyconcavediaphragmthatwasagitatedwithaloudspeaker.Hosokawa,ShimoyamaandMiuraexperimentedwiththeself-assemblyofmicropartswhicharebroughttogetheronawatersurfacebysurfacetensionofthewater.Bohringer,Goldberg,Cohn,HoweandPisanoproposedamethodtopositionsub-millimeterpartsusingultrasonicvibrationtoeliminatefrictionandadhesion,andelectrostaticforcestopositionandalignpartsinparallel.Whilenoexternalpositioning/handlingofcomponentsisnecessaryinthese componentAnchored fixtureCavity for gross positioning Linear sliderFlange Impacter massFolded cantilever Backward impactersForward impacters Figure3.Aschematictopviewoftheexternally-resonatedlinearmicrovibromotorforon-substrateprecisepositioning.methods,thecomponentsareonlygrosslypositioned,requiringauxiliarymeanstoachieveprecisepositioningneededforpracticalmicroelectromechanicalapplications.Otherworkhasbeendoneontheuseofmechanicalforcetobothself-positionandfastencomponentssothatassemblyrequirespositioning/handlingofcomponents.Judy,Cho,HoweandPisanofabricatedalaterally-de ectingcantileveronthesidewallofapolysiliconmesawhichadjuststhepositionofotherstructuresattachingtothecantilever,andprovidesthebearingforcesbetweenstructures.Burgett,PisterandFearingusedspringloadedlatchestoself-positiontheplateswithinmicrofabricatedhinges.Prasad,BohringerandMacDonaldfabricatedamicrosnapfastenerwith1{2widelaterally-de ectingchamferedlatches.Thesemethodsdonotconsiderthepotentialneedfordisassembly,hencenon-destructiveremovalofthefastenedcomponentsisextremelydicultorevenimpossible.3.DESIGN3.1.OperationalprincipleOurdesignoftheexternally-resonatedlinearmicrovibromotorformicroassemblyisbasedonalinearmicrovibro-motorreportedbyDanemanetal.whereamicrolinearsliderisactuatedbyvibratoryimpactsexertedbymicrocantileverimpacters.Dissimilartotheirdesign,however,thesemicrocantileverimpactersareselectivelyresonatedexternalpiezoelectricvibration,requiringnoneedforbuilt-indrivingmechanismssuchaselectrostaticcombactuators.AsillustratesinFigure3,itconsistsofalinearsliderlocatedbetweentwopairsoffoldedcantileverimpactersanchoredonthesubstratewhichcanexertforwardandbackwardvibratoryimpactstothesidesoftheslider,dependingonwhichpairofimpactersisresonatedbyexternalvibration.Figure4illustratesthethree-stepoperationofthelinearmicrovibromotor.First,thesubstrateisshakenwithapiezoelectricvibratoratthefrequencyThisexternalvibrationresonatesonlytheforwardimpacters,causingthelinearslidertomoveright(Figure4(a)).Thismotioncausestheslidertopushamicrocomponentagainstananchoredxture,achievingprecisepositioning(Figure4(b)).Next,thesubstrateisshakenatthefrequency.Thisexternalvibrationresonatesonlythebackwardimpactersandmovestheslidertotheleft(Figure4(c)),releasingthepositionedcomponent.Thisselectiveresonanceofthemicrocantileverimpactersviaanexternalvibrationenergyeldprovideswithverysimplemeansofcontrollingforwardandbackwardmotionofthemicrolinearslider,withoutexplicitroutingtodirectenergytoeachoftheimpacters.Thispropertyoftheselectiveresonancewouldbeparticularlyusefulinthesituationwhereanumberoflinearmicrovibromotorsareimplementedinatwo-dimensionalarrayinordertopositionmultiplemicrocomponentssimultaneously.Bydesigningtheforwardandbackwardimpacterstohave f1f2 b)C) Figure4.Three-stepoperationoftheexternally-resonatedlinearmicrovibromotor.(a)theresonanceofforwardimpacters,(b)theresultingforwardslidingmotionandtheresonanceofthebackwardimpacters,(c)theresultingbackwardslidingmotion. qgzxy Figure5.Aclosed-upviewofaimpactermassandtheslidersidewall.dierentresonancefrequencies,eachlinearmicrovibromotorinthearraycanbeoperatedindependentlybytheexternalpiezoelectricvibrationsdrivenbythesumofthesignalswithappropriateresonancefrequencies.InFigure4,notethatthedirectionoftheexternalvibrationisnotparalleltothedirectionofimpacters'oscillation,thedirectionofimpact).Therefore,itisthecomponentoftheexternalvibrationparalleltothedirectionofimpactthatcausestheresonanceinthemicroimpacters.Anothercomponentofexternalvibrationcausestheimpacterstodeformperpendiculartothedirectionofimpact,whichisundesirableforecientoperationofthelinearmicrovibromotor.Themicrocantileverimpacters,therefore,shouldhavehighstinessinthedirectionperpendiculartothedirectionofimpact,whilekeepingtherelativelylowstinessinthedirectionofimpact.Toachievethisgoal,thedouble-Vbeamsuspensiondesignisemployedinthemicrocantileverimpacters,whichrealizeshighertransversalstinessthantheconventionalfoldedparallelbeamdesignwithoutaectingthelateralstiness.3.2.ModelingEquationsofmotionsofalumpedparametermodeloftheimpacter-slidersystemillustratedinFigure3isderivedinordertoobtainanoptimaldesignwhichmaximizestranslationspeedofthelinearslideratdesiredexternalinputfrequencies.Figure5showstheclosed-upviewofaimpactermassandtheslidersidewall,where(x;y)denotethecoordinatesystemfortheimpacterposition,and(; )denotethecoordinatesystemforthesliderposition.Theaxesarerotatedfromaxesbytheimpactangle.Thefollowingassumptionsaremadeinderivationofthelumpedparametermodel:Theimpactersandthesliderdonotmoveinthedirectionperpendiculartothesubstrate.Theimpactersarecompletelyrigidindirection.Theslideriscompletelyrigid,andthereisnoclearanceindirectionbetweenthe angeandtheslider. Thereisnofrictionbetweenthesubstrateandtheimpactermass.Animpactbetweentheimpactermassandtheslidersidewalloccursinstantaneously.Impactsbythetwoimpactersinapairoccursimultaneously.Giventheseassumptions,animpactercanbemodeledasasimplemass-spring-dampersystemwithanexternalforceinputextext)(1),andarethemass,viscousdampingcoecient,andspringconstantofaimpacter,respectively.AssumingCoutetteair owbetweenthesubstrateandtheimpactermass,andsmalllateraldisplacementofthefoldedbeams,theseparametersareexpressedas14,4hwl(2) (3) l3 (4)isthemassdensityoftheimpactermaterial(polysilicon);andaretheplanerarea(includingtheareaofthejoiningmemberoftwofoldedbeams)andthicknessoftheimpactermass,respectively;,andaretheheight,width,andtotallengthofthetwosegmentsofaV-beam,respectively;istheviscosityoftheair;istheverticalgapbetweenthesubstrateandtheimpactermass;isYoung'smodulusofthebeammaterial(polysilicon);andisthehalfoftheanglebetweenthetwosegmentsofaV-beam.Assumingthesubstrateisshakenwiththeexternalvibration)indirection,theinertialforceext)exertedtoaimpacteris:extcos()(5)Similarly,theequationofmotionofthelinearsliderisgivenas:)(6)isthemassofthesliderandisanetforceexertedtotheslider:0if=0andextext)otherwise(7)istheviscousdampingcoecientoftheslider;extcos()istheinertialforceexertedtotheslider;andarestaticanddynamicfrictionalforces,respectively.TheparametersandaregivensimilarlytoEquations2and3.Anobliqueimpactoftheimpactertipstotheslidersidewallismodeledasanimpactwithrestitutionindirection,andanimpactwithinstantaneousmomentumtransferindirection.bethedistancebetweentheimpactertipandtheslidersidewallmeasuredindirectionasshowninFigure5.Ifxc,thereisnoimpact.At,theimpactertipcontactstheslidersidewall.Inindirection,thefollowingboundaryconditionmodelstheenergydissipationoftheimpacteratanimpact:(8)andareimpactervelocitiesindirectionrightbeforeandrightaftertheimpact,andisthecoecientofrestitution.Indirection,linearmomentumistransferredfromtheimpacterstotheslider.Consideringtherearetwoimpacterstodrivetheslider:(9)andareslidervelocitiesindirectionrightbeforeandrightaftertheimpact.RearrangingEquations8and9givestheboundaryconditiontomodeltheenergytransfertotheslideratanimpact: (1+(10) Table1.Thephysicalconstantvaluesusedinthesimulation Parameter Value[unit] Note  33[g=cm LPCVDpolysilicon 1:5[s] airat20 E 169[GPa Polysilicon s 20[ betweenLPCVDpolysiliconlayers Fd betweenLPCVDpolysiliconlayers e 0:5 betweenLPCVDpolysiliconsidewalls TheequationsofmotiondenedasEquations1through10arenumericallyintegratedwiththeforth-orderRungeKuttamethodtopredictandoptimizeadesignoftheexternally-resonatedlinearmicrovibromotor.Thevaluesofandusedinthenumericalsimulationare15and45,respectively.Thevaluesof,andareconstrainedbytheMUMPsprocessprovidedbyMCNCusedfordevicefabricationdiscussedinSection4.Theyaresettobe,and3,respectively.ThephysicalconstantvaluesusedinthesimulationareshowninTable1.Thevaluesofandaccountfornotonlythefrictionbetweenthesubstrateandthesliderbutalsotheslopbetweentheslideranditsguide,andareestimatedbasedonsincetheslidersizeanditsfabricationprocessarevirtuallyidentical.Inordertofacilitatefaircomparisonofdeviceperformanceswithdierentinputfrequencies,thepowerinputfromtheexternalvibrationiskeptconstant.Sincethepowerinputfromtheexternalvibrationisproportionalto,thisquantityiskeptataconstantvalueof50Figure6showsresultsofnumericalintegrationoftheaboveequationsofmotion1through10inthetimeperiodfromrommsec]toomsec]withtwoexternalinputfrequencies:(a))kHz]and(b))kHz].Foreachinputfrequency,thetopgureshowsthetimeplotofthesliderposition,andthebottomgureshowsthetimeplotoftheimpacterposition.Theparametervaluescommontobothguresarearem2],w=4:0[m],l=600[[m],andthesliderareais88m].ThesevaluesgivetheimpacternaturalfrequencycykHz],where k=m.Theinitialcondition(is(00)inbothcases.Notethattheslidermovesapproximatelythreetimesfasterwhendrivenwith6kHz(Figure6(b))thanwhendrivenwith5kHz,anaturalfrequencyoftheimpacter(Figure6(a)).Thisincreaseinthesystemresonancefrequencyisduetothenonlinear\hardeningspring"behaviorobservedinmanydynamicsystemsinvolvingimpactsoftenapproximatedbyadampedDungoscillator)(11);;�0areconstantsand)isaperiodicfunctionoftimeAsothernonlinearoscillatorysystems,theDung-likenonlinearsystemsexhibitinstabilitieswhereasmallperturbationoftheinitialcondition())completelychangesthefrequencyresponseofthesystem.Suchinstabilitiescanoccurintheimpacter-slidersystemasdenedinEquations1through10,sinceitislikelythattheinitialpositionoftheimpactermassvariesateveryoperationofthedeviceduetothestickingbetweentheimpactermassandthesubstrate,andbetweentheimpactertipsandtheslidersidewall.Figure7showsthefrequencyresponsesoftheimpacter-slidersystemwiththesameparameterasinFigure6withtheinitialimpacterpositions)=00m].Thesystemfrequencyresponseinthiscaseistheaveragesliderspeedduringthegiventimeperiod.Basedontheobservationthatthechangeinthesliderpositionatanimpactisamonotonouslyincreasingfunctionofthelinearmomentumoftheimpactersrightbeforetheimpact,thesystemresponseisdenedasfollows: (12)))istheinitialcondition,isavectorofthesystemparameters,istheinputfrequency,isthenumberofimpactsoccurredduringthetimeperiodfrom,and;:::;nisthetimewhen Forinstance,thisvaluegivestheexternalvibrationamplitudeatthefrequencykHz,whichisreasonableforactuationwithapiezoelectricstackvibrator. a)b) 0 0.5 1 1.5 2 2.5 3 0 0.05 0.1 0.15 0.2 0.25 0.3 time [msec]slider position [um] 0.5 1 1.5 2 2.5 3 -4 -2 0 2 4 time [msec]impactor position [um] impact point 0.5 1 1.5 2 2.5 3 0 0.05 0.1 0.15 0.2 0.25 0.3 time [msec]slider position [um] 0.5 1 1.5 2 2.5 3 -4 -2 0 2 4 time [msec]impactor position [um] impact point Figure6.Thesimulatedvibromotorperformances.(a)a)kHz];and(b)b)kHzThetopgureshowsthetimeplotofthesliderposition,andthebottomgureshowsthetimeplotoftheimpacterposition. 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 100 200 300 400 500 600 700 800 900 normalized input frequency (omega/omegan)response [um/msec2]x(t0) = 0.0 [um] x(t0) = 1.0 [um] x(t0) = 2.0 [um] x(t0) = 3.0 [um] Figure7.Thefrequencyresponsesoftheimpacter-slidersystemfortheinitialimpacterpositionsnsm].thesecondimpact,thethirdimpact,etc.occurred.Notethat)isnotincludedintheabovesumtoavoidaccountingfortherstimpactduetotheinitialimpacterposition.AsshowninFigure7,theinputfrequenciesatwhichthesuddentransitionsinthesystemresponseoccur(bifurcationpoints)variesfordierentinitialimpacterpositions.Althoughtheabovedynamicmodelsharessomesimilaritiestotheonepresentedinet.altherearetwoessentialdierencestobenoted.First,themodelinwassolvedbypiercingtogethertheindependently-solvedanalyticalsolutionsforimpactandnon-impactcases,whereastheabovesolutionisobtainedthroughnumericalintegrationofthesystemmodel.In,piercingtogethertwoanalyticalsolutionswasfeasiblesincetheimpacterneutralpositioncouldbeadjustedwiththeDCbiastothecombactuatorssuchthattheimpacttotheslidersidewalloccursjustatthefreeoscillationamplitudeoftheimpacters,minimizingthenonlineareectsduetothe impact.Ontheotherhand,thesystemmodelneedstobenumericallysolvedintheabovesinceourinterestisthefulldynamicbehaviorofthesystemin\early"impactcases,wheretheimpactsoccurfarbeforetheimpactersreachtheirfreeoscillationamplitudes.Insuchcases,piercingtogethertwoanalyticalsolutionscannotpredictthedynamicbehaviorofthesystem,mostnotablythenonlineareectsillustratedinFigure7.Second,in,theslidersidewallwasmodeledasaverystispringandadamper,whereasintheaboveitismodeledasarigidwallwithrestitution.Modelingthesidewallasastispringandadamperprovidesastraightforwardanalyticalsolutionduringimpact,16,17,1althoughnumericalintegrationofsuchamodelrequiressmalltimestepduringimpact,resultinginincreasedcomputationaltime.Ontheotherhand,therestitutionmodel,employedinnumerousworkonimpactdynamicsmodeling(18,19,2)requiresmuchlesscomputationaltimefornumericalintegrationduetotheassumptionoftheinstantaneousimpact.Thesimplerestitutionmodelisemployedintheabovesinceinourworknumericallysolvingthesystemmodelisessential,andalsothenumericalsimulationisrepeatedlyusedduringdesignoptimizationdiscussesinthenextsection.3.3.DesignoptimizationThesystemfrequencyresponseasdenedinEquation12providesanobjectivefunctionforanoptimalvibromotordesignthatmaximizestranslationspeedofthelinearslideratadesiredexternalinputfrequency.Forreliableoperationofthedevice,thedesignshouldbeoptimizedformaximumsliderspeedinthepresenceofsmallperturbationoftheinitialconditions.TheinstabilityofthesystemresponseillustratedinFigure7requirestheoptimizationtomaximizethesystemresponseattheworstcasescenario,,tomaximizetheminimumresponseamongpossibleperturbationoftheinitialcondition.Inaddition,theforwardimpactersshouldnotrespondtotheinputfrequencyforthebackwardimpacters,andviseversa.Theseconsiderationssuggestthefollowingmax-minformulationofanoptimaldesignproblemoftheforwardimpacters:max)(13)s.t.max)=0(14)(15)(16)isthesystemfrequencyresponseasdenedinEquation12,andandaretheinputfrequenciesfortheforwardandbackwardimpacters,respectively.Equation14constraintsthatafeasibledesignshouldnotrespondtothebackwardinputfrequencyregardlessoftheinitialcondition.SwitchinginEquation13andEquation14givesaformulationforthebackwardimpacters.Notethattheevaluationof)requiresonlytheimpacterdynamicsasdenedinEquations1,4,5,and8.Thedesignparameters,therefore,onlyconsistsoftheonesfortheimpacters:theplanerareaoftheimpactermass;thewidthandthetotallengthofthetwosegmentsofaV-beam;andthedistancebetweentheimpactertipandtheslidersidewallmeasuredindirection.ThelowerboundsoftheseparametersaregivenbytheimpactergeometryillustratedinFigure5andtheminimumfeaturelength2,asspeciedbytheMUMPSprocess.Sincetheseparametersarenotupperbounded,thesetisdenedasfollows:A;w;l;c(17)Itisassumedthattheperturbationintheinitialconditionisonlyintheinitialimpacterpositionduetothestickingbetweentheimpactermassandthesubstrateandbetweentheimpactermassandtheslidersidewall,andisboundedand.Inotherwords,c;v)=0(18)Using)asanobjectivefunctionratherthanmoredirectmeasuresofthesliderspeed,),hastwopracticaladvantagesfordesignoptimization.First,theevaluationofisfarlesscomputationallyexpensivethantheevaluationofthequantitiesinvolvingthesliderdynamicssuchas).Second,thepredictionofthedeviceperformancebasedonisnotnecessarilylessaccuratethanthepredictionbasedonthesliderdynamics,sinceitdoesnotinvolvephenomenologicalconstantssuchasand,whoseaccurateestimatesareextremelydiculttoobtain. Table2.ResultfromanoptimizationforrkHz]anddkHz Parameter[unit] Forwardimpacter Backwardimpacter A[ 45446 [ 5.6774 4.0354 [ 795.74 795.27 [ 5.2046 2.6676 kHz 5.8199 2.0385 (t0 -2.6000 -2.6676 1 2 3 4 5 6 7 8 0 50 100 150 200 250 300 350 400 450 500 input frequency [kHz]response [um/msec2] forward inputfrequency forward naturalfrequency backward inputfrequency backward naturalfrequency Figure8.Frequencyresponsesoftheforward(right)andbackward(left)impactersoptimizedforrkHzanddkHzSincethegradient-basednonlinearprogrammingalgorithmsfailduetothediscontinuouschangeinthesystemresponseillustratedinFigure7,theaboveoptimizationproblemissolvedusingtheSimulatedAnnealingalgorithm.Table2showstheresultfromanoptimizationoftheforwardandbackwardimpactersfortheforwardinputfrequencyequencykHz]andthebackwardinputfrequencyequencykHz].Notethattheinitialimpacterposition)oftheforwardimpacterthatgivesminimumresponseisapproximately,nottheminimumpossiblevalueforthebackwardimpacter.ThiscontradictsthetrendillustratedinFigure7,wherethesystemresponsebecomessmalleras)decreases.Furtheranalysesrevealthatfor,therstimpactduetothelargeinitialde ectiontriggersbifurcationintheresponsewhichresultsintheresponselargerthanforFigure8showsthefrequencyresponsesoftheforward(right)andbackward(left)impactersinTable2.Alsoplottedonthegurearetheforwardandbackwardinputfrequencies,andthenaturalfrequenciesoftheoptimalimpacters.Itcanbeeasilyseenfromthegurethattheshapesandtherelativelocationofthetworesponsecurvesareoptimizedsuchthattheforwardimpacterhasamaximumresponseattheforwardinputfrequencywhileachievingzeroresponseatthebackwardinputfrequency,andviseversa4.FABRICATIONANDTESTINGPrototypesofexternally-resonatedlinearmicrovibromotorsarefabricatedusingthethree-layerpolysiliconsurfacemicromachiningprocessprovidedbytheMCNCMUMPSservice,wherethebottompolysiliconlayerservesasagroundplane,andthemiddleandthetoppolysiliconlayersareusedformicromechanicalstructures.Figure9 f) Figure9.Abasic owoftheMUMPSprocess.(a)Depositandpatternthebottompolysiliconlayer;(b)DepositandpatterntherstPSGsacriciallayer;(c)Depositandpatternthemiddlepolysiliconlayer;(d)DepositandpatternthesecondPSGsacriciallayer;(e)depositandpatternthetoppolysiliconlayer;(f)DissolvethesacriciallayersinHFsolution. a)b)Figure10.Fabricatedprototypesoftheexternally-resonatedtolinearmicrovibromotorwithapproximately600inthesliderlength.PreliminarytestingsuggestedtheseveralmodicationstoproducethedesigncongurationshowninFigures3.illustratesabasic owoftheMUMPSprocess.Aseriesofguresshowstransversalcrosssectionsofthemicrolinearsliderbeingfabricated.First,thebottompolysiliconlayer(referredtoasPoly0)isdepositedandpatternedonasiliconsubstrateusinglowpressurechemicalvapordeposition(LPCVD),asshowninFigure9(a).Thisisfollowedbythedepositionandpatterningofa0thicksacriciallayerofLPCVDphosphosilicateglass(PSG).DimplesarewetetchedonthisPSGlayertoreducefrictionbetweenthebottomandmiddlepolysiliconlayersatthecompletionofthefabricationprocess(Figure9(b)).OntopofthePSGlayer,a2thickLPCVDpolysiliconlayer(referredtoasPoly1)isdepositedandpatterned.Figure9(c)showsthecrosssectionalpatternoftheslidermadeofPoly1.AfterthedepositionandpatterningofanotherPSGsacriciallayer(showninFigure9(d)),andapolysiliconlayer(referredtoasPoly2:showninFigure9(e))),thePSGlayersaredissolvedinanetchingsolution(HF),releasingthemechanicalstructuremadeofPoly1andPoly2(Figure9(f)).Priortothefabricationoftheoptimaldevicedesigns,twotypesofprototypesarefabricatedforpreliminarytesting,whosephotosareshowninFigure10.Theseprototypesaretestedfortheforwardandbackwardmotionviaexternalvibrationappliedbyanpiezoelectricstackvibratorgluedtothedicewithdryepoxy.ThispreliminarytestingsuggestedtheseveralmodicationstoproducethedesigncongurationshowninFigure3.Figure11showamasklayoutofanarrayofthesedevices,eachoptimizedforadierentinputfrequency,with\dummy"microcomponents.Thesizeofthedummysquarecomponentsis500,madewithPoly1layerintheMUMPSprocess.Thesedummymicrocomponentsareanchoredtothesubstratewithaverythinpolysiliconstructurewhichcanbeeasilybrokenwithaprobetipatthetesting.Thefabricationofthesedevicesarecurrentlyinprogress.Uponthecompletionoffabrication,testingistobedoneonthepositioningandreleaseofthedummymicrocomponentsagainsttheanchoredxtureelements,aswellasonthecrosstalkamongtheimpactersofdierentvibromotorsonasubstrate. http://mems.mcnc.org/mumps.htmlfordetails. Figure11.Anarrayoftheexternally-resonatedmicrovibromotorswith\dummy"microcomponents,eachofwhichisoptimizedforadierentinputfrequency.Thesizeofthesquaremicrocomponentsis5005.DISCUSSIONANDFUTUREWORKThisworkpresenteddesign,analysis,andoptimizationofalinearmicrovibromotorforon-substratenepositioningofmicro-scalecomponents,whereamicrolinearsliderisactuatedbyvibratoryimpactsexertedbymicrocantileverimpacters.Thesemicrocantileverimpactersareselectivelyresonatedbyshakingtheentiresubstratewithapiezo-electricvibrator,requiringnoneedforbuilt-indrivingmechanismssuchaselectrostaticcombactuatorsasreported1,2Thisselectiveresonanceofthemicrocantileverimpactersviaanexternalvibrationenergyeldprovideswithaverysimplemeansofcontrollingforwardandbackwardmotionofthemicrolinearslider,facilitatingassemblyanddisassemblyofamicrocomponentonasubstrate.Ananalyticalmodelofthedeviceisderivedinordertoobtain,throughtheSimulatedAnnealingalgorithm,anoptimaldesignwhichmaximizestranslationspeedofthelinearslideratdesiredexternalinputfrequencies.Prototypesoftheexternally-resonatedlinearmicrovibromotorarefabricatedusingthethree-layerpolysiliconsurfacemicromachiningprocessprovidedbytheMCNCMUMPSAsdiscussedinSection1,grosspositioningofamicrocomponentneedstobedonepriortoon-substratenepositioningusinganexternally-resonatedlinearmicrovibromotor.Althoughthegrosspositioningcouldbedonesequentiallyinpick-and-placefashion,vibratorypalletization,apartorientingmethodcommontocentimeter-scalemechanicalparts,couldprovideecientmeansofparallelgrosspositioningofmicrocomponents.Duringthepalletization,surfaceadhesionforcescanbevirtuallyeliminatedbyapplyingverticalvibrationinultrasonicrangeasrecentlyreportedin.Suchverticalvibrationcanalsofacilitatetheoperationofthelinearmicrovibromotorbyreducingthefrictionbetweenamicrocomponentandthesubstrate.Thecurrentnepositioningscheme,however,lacksapositivefasteningmeanstosecuretheattachmentofthecomponenttothesubstrate.Therefore,thedesignmodicationofthelinearslider,theetchedcavity,and/oranchoredxtureshouldbeinvestigatedinordertoachieveselectivefasteningandreleaseofacomponent.Forthis,theapplicationofremovablemicromechanicallatchingfasteners,ormicro\mousetraps,"willbeconsideredasapossiblefasteningmeans.Oneofthemostpromisingapplicationsofthemicroassembly/disassemblyasdescribedinthispaperisbare-chipinterconnectioninmulti-chipmodule(MCM),whichrequiresaprecisionassembly/disassemblyofmeso-scalecomponentswithhighdensityelectricalinterconnection.AlthoughthechipscurrentlyusedinMCMsaretypicallyin5{10mmscale,theadventoftheassembly/disassemblymethodbyusingtheexternally-resonatedlinearmicrovibromotorpresentedinthispaperwouldstimulatefurtherdisintegrationofsubsystemcomponentstoimprovetheoverallsystemmodularity,whichinturnwouldreducethesizesofthecomponentstobeassembled. 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