MEMS Dynamic Microphone Project · University of Maryland ENMA 490 2010 MEMS Dynamic Microphone...

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University of Maryland ENMA 490 2010 MEMS Dynamic Microphone Project Final Report Abbigale Boyle, Steve Crist, Mike Grapes, Karam Hijji, Alex Kao, Stephen Kitt, Paul Lambert, Christine Lau, Ashlie Lidie, Marshall Shroeder

Transcript of MEMS Dynamic Microphone Project · University of Maryland ENMA 490 2010 MEMS Dynamic Microphone...

UniversityofMaryland

ENMA4902010

MEMSDynamicMicrophoneProjectFinalReportAbbigaleBoyle,SteveCrist,MikeGrapes,KaramHijji,AlexKao,StephenKitt,PaulLambert,ChristineLau,AshlieLidie,MarshallShroeder

TableofContentsMotivation .........................................................................................................................................................4PowerConsumptiononAlternativeTechnologies........................................................................4SpringConstant,EffectiveMass,Deflection.....................................................................................4EffectiveMass .............................................................................................................................................6Deflection......................................................................................................................................................7MechanicalDamping...............................................................................................................................8DerivingtheMagneticDampingParameter ................................................................................8

Noise..................................................................................................................................................................10ThermalNoise .........................................................................................................................................10ElectricalNoise .......................................................................................................................................11

Stress.................................................................................................................................................................11StaticStress...............................................................................................................................................11DeterminationofInterfacialStress...............................................................................................12

ModelingCantileverMotion ..................................................................................................................12NumericalSimulationsandOptimizationofDesign..................................................................13NumericalSimulations........................................................................................................................13OptimizingtheDesign .........................................................................................................................13

Magnetism......................................................................................................................................................14Objective.....................................................................................................................................................14EffectofMagnetizationDirection ..................................................................................................14TheMagnetOperatingPoint ............................................................................................................15TheMaximumEnergyDensity(BH)max .......................................................................................15TheLoadLineSlope..............................................................................................................................16CalculatingtheDemagnetizationFactor.....................................................................................16SelectionofArraysoverPlates........................................................................................................17AnalyticalModelforRectangularMagnets ...............................................................................17MagneticFieldProducedbyanArrayofIdenticalMagnets .............................................18AlternativeMethodsforArrayComputation ...........................................................................18

CalculatingtheInducedVoltage..........................................................................................................19

FindingtheEquivalentNumberofCoils.....................................................................................19TimeDependenceoftheFlux...........................................................................................................20AverageVelocityofHalfCantilever...............................................................................................20ComputingOutputVoltages..............................................................................................................21

ProcessandMaterialSelection ............................................................................................................22MagneticMaterialSelection..............................................................................................................22Fabrication................................................................................................................................................22PrototypingProcess .............................................................................................................................23Etching ........................................................................................................................................................24

Ethics ................................................................................................................................................................27Application.....................................................................................................................................................28Packaging...................................................................................................................................................28HearingAids.............................................................................................................................................28

Appendix.........................................................................................................................................................29Supplemental................................................................................................................................................41Citations...........................................................................................................................................................47Acknowledgments......................................................................................................................................49

MotivationTherelentlessminiaturizationofelectronicdeviceshaspromotedthedevelopment

andincorporationofmicroelectromechanicalsystems(MEMS)intoeverydayitemssuchashearingaids,laptops,mobilephones,videocameras,andcars.Eachoftheseitemsrequiresaudio processing and includes some form of microphone. Current research focused onMEMS microphones has revolved around condenser, piezoresistive, piezoelectric, andelectret models. Condenser and piezoresistive microphones require a power source forsignal generation while piezoelectric and electret models do not. Another microphonemodel that does not require a power source for signal generation is the dynamicmicrophone.Usingelectromagneticinductiontotranslatesoundtoanelectricalsignal,thisdesignhasbeenapplied tomacro‐scaledevices,buthas notbeen translated to themicro‐scale.Thisprojectismotivatedbythenoveltranslationofthedynamicmicrophonedesigntothemicro‐scaleforpowerlesssignalgenerationinelectronicdevices.

Thedesignprocesswillencompassmanycriticalelementsofmaterialsengineeringincluding microprocessing, mechanics, thermodynamics, kinetics, and solid state physics,withhighlightsfromotherformsofengineeringincludingelectricalandmechanical.

`The market demand for MEMS microphones has continuously increased for thepast7years. Figure1shows the previous andprojectedvalues for the numberofMEMSmicrophones shipped each year. If the MEMS dynamic microphone design can competewith currently usedmodelswith respect to frequency response and dynamic range, thentheincreasingdemand trendisreassuringthat thesemicrophoneswillhaveanincreasingimpactonfutureelectronicapplications.

PowerConsumptiononAlternativeTechnologies PreviousMEMSmicrophonestructuresemployvarious(techniques)suchas

piezoresistiveandcapacitivedesigns.Piezoresistivemicrophonesfunctionthroughanexcitationvoltage,whilethecapacitive(i.e.condenser)functionthroughanappliedbiasvoltagebetweentwoplates.Forthepiezoresistivemicrophonesthepowerconsumptionrangedfrom0.7mW[1]toalargerpowerconsumptionof15mW[2].Inthesecasestheinputvoltagewas10Vand3Vrespectively.Inaddition,wefoundthatCondensermicrophones,whichwerealsopowerconsuming,used1.96mWunderabiasvoltageof4V[3].

SpringConstant,EffectiveMass,Deflection

AsprogresscontinuesinthedesignandfabricationofaMEMSdynamicmicrophoneitbecomesincreasinglyimportanttounderstandhoweachcomponentofthedesignwillbehave.Intermsofthecantileverdesign,oneofthemostimportantcharacteristicstodetermineistheresonantfrequency.Resonanceisthetendencyofasystemtooscillateatlargeamplitudesatspecificfrequencies,evenwhenthedrivingforceissmall.Itisnecessarytounderstandatwhichfrequenciesthistypeofbehaviorwillbeobservedsothatinvalid

dataisnotcollectedand/ordamagecanbepreventedtothedevice.Resonantfrequencyofacantilever,ω0,calculatedbytheharmonicoscillatorformulaisdescribedbyEq.1,wherekisthespringconstantandmeffistheeffectivemassofthesystem.

(Eq.1)

Thefirststepincalculatingthereasonantfrequencyistofindthespringconstantofourcantilever.ThespringconstantofacantileverwithYoung’smodulus,E;length,l;andmomentofintertia,I,isrepresentedbyEq.2.

(Eq.2)

Equation3describesthemomentofinertiaofacantileverwithathickness,d,andwidth,w[4].Substitutingequation3intoequation2depictsthespringconstantrelationshipwithrespecttothecantileverdimensionsandmaterialparameters(Eq4).

(EQ3)

(EQ4)

WhencalculatingthespringconstantwemusttakeintoaccountthedimensionsoftheSiO2cantileveraswellastheCoNiMnPmagnetsthataretobedepositedontop.Figure2illustratesageneralschematicofhowthemagnetswillbedepositedinanarraylikefashionontopofthecantilever.Table1dictatesthedimensionsofourmagnetarraydesignusing10umx10umx28umCoNiMnPmicromagnets.

UponobservationofFigure2wenoticethatcantileverisdividedupintoalternatingsectionswherethereisonlytheSiO2cantileverandsectionswithdepositedmagnets.Thus,equation4mustbemodifiedsothatwetakeintoaccountthevaryingareasofmaterial,thickness,andlength.Thesealternatingareasofthecantileveractinseriesofoneanotherintermsoftherelativespringconstant,thereforewecanuseequation5tocalculatethespringconstantofmultiplespringsinseries[5].

(Eq.5)

Asmentionedearlierthethicknessofeachmagnetisapproximately10xaslargeasthethicknessoftheSiO2cantilever.Whenfindingthespringconstantsofmagnetportionsusingequation4,thethicknessisraisedtothethirdpowerandkofthemagnetendsupbeingaboutthreeordersofmagnitudelargerthanthekoftheSIO2portions.Whentakingtheinverseofalargeconstantwefindthatthetermswillapproachzeroandtendnottoeffecttheoverallspringconstant,thusallowingthespringconstantcalculationtobemadeonlyusingtheportionsofSiO2actinginseries.Substitutingequation4intoequation5undertheseconditionswillyieldthesolutiontofindingthespringconstantforourSiO2cantileverwithCoNiMnPmagnetsdepositedontop(Eq6).

(Eq.6)

WherenspacerepresentsthenumberofbareSiO2sectionslocatedbetweenmagnetrowsacrosstheentirecantilever.Fromequation6,weareabletocalculatetheexpectedspringconstantofthedesignshowninTable1usingaYoung’sModulusof70GPa,awidthof3mm,andathicknessof3um.FromTable1wecanseethatthespringconstantcalculatedis.442N/m.

EffectiveMass The next step in calculating the resonant frequency is to determine the effectivemass of our oscillating cantilever system. When performing this type of analysis, it isimportant to take into account both themass of the cantilever aswell as themass of themagnetsdepositedacrossthetop.However,sincetheentirecantileverisnotgoingtomoveatthesamevelocityasthedepositedmagnets,themassofthebeamcannotsimplybeaddedtothemassofthemagnets.Theeffectivemassofthesystemisthemassatwhichmustbeaddedtothedepositedmassinordertoaccuratelypredictthebehaviorofthesystem.Figure3aisacasedescribedbyD.Saridinhisbook,ScanningForceMicroscopy.InthebookSaridpointsoutthatmdisthedistributedmassofthebeamandmcistheconcentratedmassat thetip.Withaconcentratedmassatthe tip theeffectivemassiscalculatedthroughEQ7[4].

(Eq.7)

However,ourcantilever(depictedbyFigure3b)willhaveadistributedarrayofmagnetsrangingapproximatelyacrossthesecondhalfofthecantilever.Therefore,itisassumedthatboththemassofthecantileverandmassofthemagnetsareconsidereddistributedmassesoverspecificlengthsofentirebeam.Sinceeffectivemassmeasuresthedifferenceinvelocityofourbeamandmagnetswecantaketheintegralofthedeflectioninproportiontothelocationofthemagnetsincomparisonwiththedeflectionattheendofthecantilever(Eq.8).

(Eq.8) Wecanusethedensity,D,andequationforcantileverdeflection,(Eq.9),totransformthemassintegraltoanintegralwithrespecttoposition,(Eq.10).In(Eq.9),thevariablePrepresentssoundpressure;andinEq.10thevariableLrepresentsthecantileverlength.

(Eq.9)

(Eq.10)

To find the distributed mass, md, of the cantilever the integral was taken on thelimitsof[0,L/2].Tofindthedistributedmassofthemagnets,mmag,theintegralwastakenonthelimitsof[L/2,L].Whenaddingthetwovaluesobtainedtogetherweareleftwith(Eq.11) showing that aboutonequarter ofeachmass isadded together in order toobtainaneffectivemass.

(Eq.11)

As the behavior of aMEMS cantilever is relatively unknownwe hope that furtherresearch and analysis of our experimental data will help determine which calculation ofeffectivemassismoreapplicabletoourcase.

DeflectionThroughout the design process, a reoccurring problem the group faced was

obtainingadeflectionlargeenoughtoinduceasignificantamountofmagneticflux.Thegoalinthisareaofdesignwastogenerateadeflection,attheleast,ontheorderofmicrons.Itisbelievedthatthisistheminimumamountofdeflectionneededtoinduceareadablecurrent.Once that plateau is reached,wewould be able to change parameter designs to generatelarger deflection. The group had approached the problem in several different waysthroughout the first half of the design project. Initially, it was believed that a diaphragmcouldbeplacedalongthesiliconwaferfollowedbyanetchtoproduceawell.Thefirststepindeterminingthefeasibilityofthisdesignwastodeterminethemagnitudeofpressureourdiaphragm would be subject to. Sound level and pressure are related through (Eq. 12)whereLpisthesoundlevelindB,prefisareferencepressureof20μPa,andprmsisthesoundpressurebeingmeasured.Table1depictssoundlevelsalongthehumanhearingrangeandtheirrespectivepressures.

(Eq.12) Thedeflectionequationforacircularplatediaphragmisshownby(Eq.13)wherePisthesoundpressureinPa,aistheradiusinmeters,andDistheflexuralrigidityinPa‐m4.However,afterinitialinspection,thedeflectionscreatedwouldbeentirelytoosmalltomeasureasthesoundpressurealongthehumanearhearingrangeisrelativelylow.Thus,theideawasquicklydepartedfrom.

(Eq.13) Atthispoint in thedesignitwassuggestedthatweutilizeacantilevertypedesignbecauseitisoftenusedtogeneratelargedeflectionswhenthepressureislimited.InMEMScantileverdevices,deflectionvsappliedstress,σ,isoftenrepresentedbyStoney’sEquationlisted as (Eq. 14). In the equation, L is cantilever length and t is the thickness inmeters.Poission’s ration, ν, and Young’s Modulus, E, are also represented in Stoney’s Equation.UsingasilicondioxidecantileverwithL=1mmandt=.5μm,Table2wasgeneratedrelatingdeflectionalongvarioussoundlevels(E=70GPa,v=.17).

(Eq.14)

Normal speakingvolume isaround50db,whichweused tobeouraverage soundlevel. Figure 4 represents the steady‐state deflection of a normal SiO2 cantilever with alengthandwidthof3mmandathicknessof3um.Theplotshowsthataswesurpassabout62dB the steady‐state deflection of our cantileverwill reach 1um. Although deflection issmall we are more focused on the velocity our cantilever will be moving in order togenerateamagneticflux.

MechanicalDamping Oneimportantcontribution to themechanicaldampingofourcantileversystemisviscousdamping.AsthecantileveroscillatesinresponsetoacousticvibrationsasshowninFigure5, themotionof thecantilever is dampeddue to theresponse forces developed indisplacingthesurroundingair.Viscousdampingcanbedividedintosqueezefilmandslidefilmcontributions.Squeezefilmdamping describes the forces generated by displacing the thin layer of air between thecantileverandthesubstrate.Theseforcesincreasinglydominatewithincreasingcantileversize and decreasing air‐gap. The damping coefficient used to account for this velocity –dependentdampingforceisgivenbythefollowingexpression:

(Eq.15)

wherelisthesidelengthofthesquarecantilever,gistheairgap,and istheeffectiveviscosityofair.Withaneffectiveviscosityof18.6μPas,asquarecantileversidelengthof3millimeters, and an estimated gap height of 30 microns, the damping coefficient isapproximately 2.35E‐2 kg s‐1. Slide film damping describes the lateral motion of thecantileverwithrespecttothefixedsubstrate.Duetothelargedimensionsofthecantileverinthisdevice,thesecontributionstothedampingarenegligible. CorrespondencewithDr.Wuttigrevealedthatinternalfrictionconsiderationsforacantileverwiththesedimensionsisnegligibleatatmosphericpressure.

DerivingtheMagneticDampingParameterWhenanincidentsoundwavecausesthecantilever,andthustheattachedmagnets,

to oscillate, the magnets’ magnetic field changes over time in the reference frame of thestationaryinductioncoils. Thiscorresponds toachangingmagneticfluxthrough theareaenclosed by the coil loops that generates an induced current according to Faraday’s law.However,theinducedcurrentinthecoilsalsocreatesanopposingmagneticfieldasaresultofLenz’slaw.Theforcecreatedbythisinducedmagneticfieldactstodampenthemotionofthecantileverandmayadverselyaffectthesignalofourdevice.Therefore,itisimportantto obtain a magnetic damping parameter that allows us to account for this force in theoverallmotionofourcantileverdevice.Intheirpaper,“Eddycurrentdampingofamagnetmoving throughapipe,”Hahnetal.describeda theoreticalprocedurefordeterminingthemagneticdampingparameter[7]. Applyingtheirthoughtprocess tooursituationallowsustosimilarlyderiveanexpressionforthemagneticdampingparameterofourdevice.

First of all, the z‐component of the force exerted on a small element of current‐carryingloopofwirebyamagnetcanbeexpressedby:

zzzBVdJBLdIdF )()( !=!=

rr(Eq.16)

Fz=z‐componentoftheforceI=elementofcurrentintheloopdL=infinitesimalarclengthoftheloopJ=currentdensitydV=infinitesimallysmallvolumeoftheloop

Because of thecrossproduct in theequation,only theradially directed componentof themagneticfieldneedstobeconsidered,asitistheonlycomponentthatcausesaforceinthez‐direction. It is important to note that even though equation (16) represents the forceexertedonthecurrentloopfromthemagnet,thisisequaltotheforceexertedonthemagnetfromtheinducedcurrentinthecoilbecauseofNewton’sthirdlaw[7].

Inordertoapplyequation(16)toourspecificproblem,weneedanexpressionforJ.FollowingtheexampleofHahnetal.,Jcanbewrittenas:

radvBBvJ !! ="= )(

rr(Eq.17)

J=currentdensityσ=conductivityofthecoilwiresv=speedofthemagnetBrad=radialcomponentofthemagnet’smagneticfield

Using this expression for J and substituting it into equation (16) gives the followingequationfortheforce:

VdvBdFradz

r2!= (Eq.18)

Now, in order to determine dV, the volume of the conducting material, we assume acylindricalgeometryforthecoil.Withthisassumption(andusingcylindricalcoordinates),equation(18)becomes:

rdrdzvB

rdrdzdvBdF

rad

radz

2

2

2!"

#"

=

=(Eq.19)

Toobtainthetotaldampingforce,weintegrateequation(19)overtheentirevolumeofthecoil, i.e. from thebottomof thecoil to the top,and from the inner radiusR1 to the outerradiusR2:

! !=top

bottom

R

Rraddamping rdrdzBvF

2

1

22"# (Eq.20)

Having obtained an expression for the total damping force exerted on themagnet/cantileverbytheinducedmagneticfield,wecannowdefinethemagneticdampingparameter.Foradriven,dampedharmonicoscillator[7]:

mv

F

m

b damping

22==! (Eq.21)

b=constantm=massoftheoscillatingmass

Bysubstitutingequation(20)intoequation(21),weobtainthefollowingexpressionforthemagneticdampingparameterofoursystem:

! !==top

bottom

R

Rrad

damp

F rdrdzBmmv

F 2

1

2

2

"#$ (Eq.22)

Equation(22)showsthatthemagneticdampingisdependentonthemagneticfieldexperiencedbythecoils.However,thismagneticfieldchangesovertime.Thus,inordertofullymodelthemagneticdamping,thetime‐dependentbehaviorofthemagneticfieldneedstobedetermined,eitherthroughanalyticalornumericalmeans.

Beforesuchcalculationsaremade,though,itisimportanttonotethatsinceboththedampingforceandthemagneticdampingparameterdependuponthecurrentdensity,themagneticdampinginthesystemwillbezerowhennocurrentflowsthroughthecoils.Thus,bytreatingourdevice likeavoltagesourceandminimizingtheamountofcurrentflowingthrough,wecaneliminatethemagneticdampinginourdevice.

NoiseNoisecancomeinavarietyofformsthatcaneitherbereducedorareirreducible.Forexample,thebackgroundnoisethatcanbefoundfromanunshieldedwireorfromsomethingsuchastheairconditioncanbereduced.Howeverthenoisesuchasthermalorelectricalnoisethatareinherentinthecircuitorthematerialareformsofnoisethatcannotbereduced.

ThermalNoiseTheJohnsonnoise,orthermalnoise,mustbetakenintoaccountinordertodeterminewhetheritwillnoticeablyaffectoursoundfrequencyinput.Thermalnoiseisrandomthermalfluctuationwhichresultsinpositionalfluctuationsofthecantilever[8].Weuse(Eq.23)todeterminetheeffectthattheJohnsonnoisewillhaveonourcantilever.ThevalueobtainedgivesadeflectionvaluefromtheJohnsonnoise,andthiswillshowwhetherthethermalnoisedoeshaveaclearimpactonourmicrophone.Theequationforthermalnoisedeflectionisshownbelow[4].

](Eq.23)

Inthisequation,Qactsasthequalityfactor,ω0istheresonantfrequency,ωisthefrequencyatwhichthecantilevervibrates,kisthespringconstant,Bisthebandwidth,KistheBoltzmannconstant,andTisthetemperature.

Qualityfactorisameasureofhowunderdampedanoscillatoris,andthehighertheQvalue,thelowertherateofenergylossrelativetotheenergystoredintheoscillator,andthustheoscillatordiesoutmoreslowly.InordertosolvefortheJohnsonnoise,wemustsolveforthequalityfactor,theequationforwhichisshownbelow.

(Eq.24)

Inthisequation,Misthemass,kisthespringconstant,andDisthedampingfactorwhichisdeterminedfromthemechanicaldampingsystem.AftersolvingfortheJohnsonnoiseusingthevaryingvalues,wefoundthattheinduceddeflectionwasminimal(ontheordernanometers).

ElectricalNoiseTherearetwoformsofelectricalnoisethatwemusttakeintoaccountaswelltoseewhatsortofcurrentsandvoltagesareproduced.TheothertypeofJohnsonnoiseorresistorJohnsonNoiseresultsfromagitationoftheelectronsintheloadresistorregardlessofappliedvoltage.Ithasaflatfrequencyresponsebecausethereisthesamenoisepowerineachhertzoffrequency.FortheJohnsonnoise,weusetheequationshownbelow[9].

(Eq.25)

Shotnoiseisanotherkindofelectricalnoisethatoccurswhenthefinitenumberofdiscreteparticles,electronsinthiscase,issmallenoughtocausestatisticalfluctuationsinthemeasurements.Theequationusedtofindthefluctuatingcurrentisgivenin(Eq.26)[9].

(Eq.26)

Stress

StaticStressOneofourquestionswhendesigningourdevicewaswhetherathin0.5μmSiO2

cantileverwouldbeabletosupportmuchthickermagnetarrayswithoutbreaking.Themagnetarrayscauseatensilestressonthetopofthecantileverandacompressivestressonthebottomofthecantilever;theSiO2willfailduetothetensilestress,sinceitstensilestrengthismuchlowerthanitscompressivestrength.ThetensilestrengthofSiO2is55MPa,sothemicrophonewillfailifthestressonthecantileverexceedsthisvalue.Whilethetotalstressonthecantilevervarieswiththesoundpressureincidentonit,thestaticstressinthecantileverisdeterminedbythedeflectionofthecantilever,itsthicknessanditslength.Thespecificequationforthestaticstressinthecantileveris: σmax=3dEt/(2l2) (Eq.27)wheredisthecantileverdeflection,EistheYoung’smodulusofSiO2,tisthecantileverthickness,andlisthecantileverlength.Silicondioxide’selasticmodulusis70GPa,andourcantileveris3mmlongand0.5μmlong,andthestaticdeflectionofthecantilever(whichisafunctionofthecantilever’slength,thickness,andelasticmodulus)wascalculatedtobe4.5μm,sothemaximumstaticstressinthecantileverisfoundtobeapproximately52.5kPa,whichiswellwithinthetensilestrengthofSiO2.WhilethepresenceofcracksintheSiO2couldleadtoreductionofthecantileverstrength,thesecrackswouldhavetobequitelargetolowerthecantilever’stensilestrengthby3ordersofmagnitude,sowecanbequiteconfidentthatthedevicewillnotfailduetothestaticpressureonthecantilever.

DeterminationofInterfacialStress Duringanythinfilmprocessing,delaminationandtheinterfacesbetweenlayersareextremely important. During theprototypingprocessof thisproject someof themagnetsdelaminated from the cantilever surface, indicating that the thickness of the depositedmagnets introduces a stress that is greater than themaximum interfacial stress thatwillallowasecurebondbetweenthetwolayers.Unfortunatelytheresourcesfordeterminingtheinterfacialstressbetweenthemagnetandthecantileverwerenotavailableduring theperiods of this project, but methodology was developed for determining the interfacialstress. Given the appropriate amount of time and resources the first step would be tofabricatemultiplewafersofcantileversanddepositvaryingthicknessofthemagnetrangingfrom 5 um to 35 um. The deposition of the magnet should result in a bending of thecantilever,andwiththisbendingtherewouldbeanapparentchangeintheoveralllengthofthecantilever.Thebendingisdescribedby

Whereδis thedeflection,r is theradiusofcurvature,andl isthe lengthof thecantilever.This lengthchangewouldbemeasuredusingopticalmicroscopy,andcanbecompared tothedeflectionofthecantileverbythefollowingequations,wherelfisthelengthchange.

Thetwodeflectionscanbesetequalandsolvednumericallyfortheradiusofcurvature.Assumingthatthesecantileversbehaveasthinfilms,theinterfacialstressinthecantileverscanbedescribedbyStoney’sequation,whereEsisthemodulusofthesubstrate,dsisthethicknessofthesubstrate,dfisthethicknessofthedepositedfilm,andvsisthePossion’sratioofthesubstrate.

Afternumericallycalculatingtheinterfacialstressofeachcantilever,aplotcouldbeconstructedofinterfacialstressversusmagnetthickness,whichwouldprovidearangeatwhichtheinterfacialstresswouldbetoohighanddelaminationwouldoccur.Inturn,thiswouldalsoprovidethemaximummagnetthicknessthatcouldbeusedinthedesign.

ModelingCantileverMotion

The motion of our cantilever can be modeled as a sinusoidal driven harmonicoscillator,whichisdescribedbythefollowingdifferentialequation:

)sin(02

2

tFkxdt

dx

dt

xdm !" =++ (Eq.28)

m=massofthecantileverx=positionofthecantilevert=time

γ=dampingcoefficientk=springconstantF0=maximumamplitudeofthedrivingforceω=angularfrequencyofthedrivingforce

Both the transientand steady‐state solutions to thisdifferential equation arewellknown.Because thetransientpartofthesolutionquicklyapproacheszeroasthetimeapproachesinfinity, it isnot necessary forus toconsider it. Whatweare interested in is the steady‐statesolution,sinceitpersistsaslongastheappliedforceexists.Thesolutiontoequation(27)is:

)cos()(

)(22222

0

2

0 !""#""

$+$

= t

m

Ftx (Eq.29)

ω0=angularresonantfrequencyφ=phasedifference

Whenyou take thederivativeof x(t)withrespect to time to obtain anexpression for thevelocityofthecantilever,theangularfrequencytermcomesoutofthetrigonometricterm.Thus,thevelocityisdirectlydependentonthefrequency. Toobtainaflatresponseinourdevice,thisdependenceneedstobetakenintoaccount.

NumericalSimulationsandOptimizationofDesign

NumericalSimulations Sinceourproposeddevicehadsuchasimpledesign,numericalsimulationsdidnotplayalargeroleinthedesignprocess.Rather,themaingoalofthenumericalsimulationswastomakesureouranalyticalexpressionswerevalidforthisdevice.Usingateststructure(1mmx1mmx1µm)inCOMSOL,wemanagedtomakesureouranalyticalexpressionforstaticdeflectionagreedwiththevalueproducedbyCOMSOL.Figure6showsaplotofdeflectionversussoundpressureforboththeanalyticalexpressionandCOMSOL.Thereisaslightdeviationtowardstheendofthecurve,andwebelievethisisbecauseCOMSOLhasmoreinformationaboutthematerialthantheanalyticalexpressionrequires‐mostimportantly,thewidthofthecantilever.Thisfactorplaysaslightroleinthespringconstantequation,soCOMSOLmightusethespringconstantinitscalculations,andthereforegetslightlydifferentnumbers. Weattemptedtodofurthersimulationsinvolvingtheactualstructure,frequencyresponse,andpossiblestresses,buttheCOMSOLprogramwasunabletodomostofthesecalculationseffectivelyduetothehighaspectratiosinourdesign.Themaximumelementsizemustbenolargerthantheminimumdimensionofthemodel,andbecausewewereworkingwithacantilevermillimeterslongwiththicknessesrangingfromahalfmicrontoafewmicrons,theprogramranoutofmemorywhenitattemptedtodomostcalculations.Wewereabletogetroughnumbersbymanuallyincreasingtheelementsize,butthesenumbersmightbeunreasonableandunrealistic.Thereforewedecidedtodotherestofthedesignusingouranalyticalexpressions.Sincethegeometryissosimple,theseexpressionsshouldgiveagoodideaofhowthedevicefunctions.

OptimizingtheDesign Afterwefoundgoodanalyticalequationsdescribingthespringconstant,effectivemass,resonantfrequency,cantilevermotion,anddamping,weproceededtoalterthese

valuesinordertooptimizeourdesign.Therewereseveralfactorsweneededtoweighinordertooptimizeourdesign.Weneededtomakesurethatthefrequencyresponsewasflat,thesignaltonoiseratiowasreasonable‐above10,andweneededtomakesurethatthedesignwasfeasibletofabricate.Forresonantfrequency,wehadseveraloptions.Firstoptionwastoputtheresonanceatthelowendofthefrequencyrange(20‐20,00Hz,therangeofhumanhearing)[10],thereforegettingaresponsethatslopesdownwards.Secondpossibilitywastoputtheresonanceatthehighendoftherangewithlowdamping,ideallygettingaflatcurvewithapeakattheend.Finally,wecouldputtheresonanceinthemiddleoftherangeandflattenouttheresponsewithsufficientdamping[11].RepresentationsofthesethreeoptionsinourdesignareshowninFigures7,8,and9.Theslopeofthe20Hzcaseistoohigh,asistheslopeofthe50,000Hzcase;thereforewechosethe2,500Hzcase.Wepicked2,500Hzspecificallybecauseastheresonantfrequencygothigher,thesignaltonoiseratiowoulddecrease,andasitgotlower,theresponsebecamelessflat.2,500Hz,however,providesaveryflatresponse,aswellasanaveragesignaltonoiseratioof16.Thisnumberisalsoattractivebecausechangingthecantileverthicknesstoabout3µmwhilekeepingtherestofthedimensionsthesameisallthatisneededtoachieve2,500Hzforresonance. Ourotherdimensionswereinitiallywellthoughtoutsowedidnotchangethem.Thelengthandthicknesswereboth3mmforourprototype,anduponexaminingthisanalytically,3mmgivesanoptimalresponse.Loweringthelengthorwidthresultsinapeakformingattheresonance,andwithsuchhighdampingitisnotpossibletodampfurther.Increasingthelengthorwidthresultsinaflatterresponse,howeverthesignaltonoiseratiodropsoff,eventuallygoingunder10.Therefore,asquarecantileverwithlengthandwidthof3mmprovidesagoodresponse.Theotherdimensionwewerechangingwasthegapheight,whichisinverselyproportionaltodamping.Togetenoughdampingforaflatresponse,thisneedstobedecreasedfromourprototypevalueof150µmto30µm.Itisdifficulttoraisethedampinganyfurther,asdecreasingthegapheightfurtherisproblematicduringfabrication.

Magnetism

Objective Giventhecantileverdesign,theoverarchinggoalofmagnetdesignwastofindawaytocoverthe1.5mmx3mmsecondhalfofthecantileverwithmagnets,whichwouldproducethelargestfluxchangeperunittimeinthecoilmountedbelow.Theproblemwasapproachedbyidentifyingalloftherestrictionsonthemagnets,andthenpickingadesignwhichsatisfiedallofthem.Thefirsthastodowiththedirectionofmagnetization.

EffectofMagnetizationDirection Theequationformagneticfluxthroughasurfaceis,

.The dot product means that only the component of the magnetic field which isperpendiculartothesurface contributestotheflux.Thisplacessomeinitialrestrictionsonmagnetdesign,sinceourcoilismounteddirectlybelowthemagnetsandparalleltothe

cantilever. Looking at the vertical component of the magnetic field , we see that itcancels out above andbelow amagnetmagnetized in‐plane. This is illustrated in figure10(a)below.Suchfieldtopographyisuselessintheintendedapplicationbecausethefluxacrossanyhorizontallineaddstozero,yieldingnonetflux.Incontrast,aplatepoledout‐of‐planehas a clear net component in the vertical direction (figure10(b)). This tells usthat the first restriction on magnet design is that it must allow for out‐of‐planemagnetization.Thedimensionsrequiredtodothisarediscussednext.

TheMagnetOperatingPoint MagnetsaretypicallycharacterizedbytheirB–Hloop.AmagnetizingfieldHisexertedonthemagnet,typicallyusinganelectromagneticyoke,andtheresultingmagneticmomentisrecorded to yield a graph such as that in figure 10. The intersection with the y‐axis isreported as the remanence, Br, and the intersection with the x‐axis is reported as thecoercivity,Hc(thesearehighlightedinfigure10).Onemightthinkthatwhenthemagnetiswithdrawnfromthistestingapparatus, itwould thenprovidethefullremanence,Br,sincethereisnolongeramagnetizingfield.However,eveninnormaloperation,thereisalmostalwaysanegativeHappliedtothemagnet.Itcomesfromdemagnetization.According toParker,demagnetizationresultswhen“free polesare established anda fieldpotential­Hd[thedemagnetizingfield]existsbetweenthepoles.Inthiscase,thepotentialresultsfromsomeoftheintrinsicmagnetizationreturninginternallyacrossthemagnet”[11].Inessence, thedemagnetizing fieldprovidesanegativeHwhichpushes themagnet awayfromBrandintothesecondquadrant.ThemagnitudeofHdisdeterminedbygeometry.Thedetails of this are discussedbelow, but this fact’s impact is in bringing geometry into thediscussiononmagnetdesign.Dependingontheintendedapplication,themagnetgeometryshouldbedesignedtoforcethemagnettooperateatacertainpointontheB–Hloop.Forourapplication,thispointis(BH)max.

TheMaximumEnergyDensity(BH)max The area contained by a B – H hysteresis loop corresponds to the energy that is being stored by the magnet each cycle. The concept of (BH)max is to find the point in the second quadrant of the B – H curve which creates the largest enclosed rectangle under the graph. This is illustrated schematically in figure 11. According to Arnold, “This value represents an operating point where the magnet can supply the most magnetic energy to an air gap”[12]. Since this is indeed our goal (as well as the goal of most magnetic MEMS design), we designed our magnets to operate at (BH)max. A typical B – H curve for CoNiMnP is shown in figure 12. For this sample, (BH)max occurs at B = 0.29 T and H = -39.8 kA m-1. The value of (BH)max is thus 11.5 kJ m-3. In order to harness this maximum energy, we want to design the magnet geometry so that the demagnetizing field Hd = -39.8 kA m-1.

TheLoadLineSlope The permanent magnet operating point is designated as the intersection between the B – H loop and a line originating at the origin and passing through the B – H loop. This line is termed the magnet “load line” and is characterized by a slope which depends on the magnitude of the demagnetizing field. The constitutive relation for a permanent magnet is (Eq. 30) where is the total induction, is the magnetizing field, and is the magnetization of the permanent magnet. Since the demagnetizing field arises due to the magnetization of the sample, it is typically written as a portion of the magnetization, i.e.

Where is a demagnetization factor between 0 and 1 and depending on the magnet geometry. Rewriting, we have

(Eq. 31) The magnet induction under the influence of demagnetization, , can be written, in analogy with (Eq. 30), (Eq. 32) Plugging (Eq. 31) into (Eq. 32), we have

and rearranging, we obtain the “very useful”[12] load line slope

(Eq. 33)

This value of designates the slope of the load line. Recalling the B and H values for (BH)max for CoNiMnP, we seek a load line slope

(Eq. 34) This corresponds to a demagnetization factor

(Eq. 35) The question remains, what magnet geometry will satisfy (Eq. 35)? This is discussed next.

CalculatingtheDemagnetizationFactor The demagnetization coefficient is just a number, but it can only be calculated, in general, by working through very complex physics. Fortunately, this work has been done for many common geometries. In our case, we chose square prisms because they are easy to pattern and fabricate. Aharoni reports a general expression for the demagnetization coefficient of a rectangular prism[1Error!Referencesourcenotfound.], where the dimensions of the prism are and magnetization is assumed in the direction, and is the demagnetization factor. This expression was more general than we

needed, so we reduced it to a single variable by assuming a square cross section. If we let

, we obtain

This can be plotted directly (Figure 3) or used to plot the load line slope (Figure 4). Most importantly, it can be solved to determine the aspect ratio (thickness/width) required to operate at (BH)max. The result is:

SelectionofArraysoverPlates Given the aspect ratio of 2.83, a single plate covering the allotted surface would have been thicker than 4 mm. According to the literature[1Error!Referencesourcenotfound.], 30 µm is a more reasonable upper limit on the thickness to which CoNiMnP can be plated. Because of this, we opted for an array of small magnets with the optimal aspect ratio, rather than a single plate which would have had very little external field. Since for a given aspect ratio, the largest field is obtained from the magnet with the largest volume, we took the 30 µm thickness as our design constraint and selected an optimal magnet geometry of 10 µm x 10 µm x 28 µm. Allowing for some space along the edges, the 1.5 mm x 3 mm area will hold 9800 of these magnets in a square array 70 magnets x 140 magnets.

AnalyticalModelforRectangularMagnetsThe magnetic field of permanent magnet rectangular prisms can be calculated analytically[15] by considering the molecular currents at the surfaces of the magnet and using the Biot-Savart law, which describes the magnetic field produced by moving charge. The results of this calculation are[Error! Reference source not found.5]:

(Eq. 36)

(Eq. 37)

(Eq. 38) where

(Eq. 39)

(Eq. 40)

(Eq. 41) Using these expressions, all three components of the field produced by the magnet can be calculated for any point , provided only that the component of the field is known at one point. The expressions assume a magnet with one corner at the origin, extending in the positive

and directions.

MagneticFieldProducedbyanArrayofIdenticalMagnetsGiven an expression for a single magnet, it is straightforward in theory to calculate the field produced by an array of identical magnets. This field is the simple sum of the field contribution from each individual magnet. If we have an array of magnets spaced apart (center-to-center), then the contribution from a magnet away in and away in can be written in terms of the original equations as

(Eq. 42) The total field at that point is the sum of all such contributions,

(Eq. 43) By calculating this for a range of points, a three-dimensional picture of the flux distribution around a magnet array can be formed.

AlternativeMethodsforArrayComputationEven with analytical expressions in hand, a computer remains the fastest, most efficient way to evaluate complex expressions over a range of values. Typically, calculations which would take hours for a human being can be performed in seconds. However, even computers do calculations at finite speeds, and we ran into this wall when trying to compute the magnetic field for the large arrays used in our design. Equation (43) above is a simple, theoretically exact, and easily understood expression for the field produced by an array, but it is horribly inefficient to compute. The problem is this: (Eq. 43) takes into account too much. For a small array, say 3 x 3, evaluating the field at each point involves evaluating the field contribution from 9 different magnets and adding them. This is manageable, and indeed necessary. We are likely to incur substantial error if we don’t include the contribution from every magnet in the total. Consider, however, the effect of scaling, say to our final array of 140 x 70 magnets spanning a space of 1.5 mm x 3 mm. Now, to calculate the field at each point we must include the field contribution from 9800 different magnets. Extrapolating from the time taken to model smaller arrays, this would take many thousands of years. Clearly, an approximation is in order. The approximation that must be made involves reducing the number of magnets we consider to be acting on any given point. This is a reasonable approximation to make because the

magnetic field falls off as . A small 10 micron by 10 micron magnet on one side of the array is not going to contribute any significant field to a point 1000 microns away, or even 500. In practice, we used the same terminology as found in other materials science subjects and defined the number of “nearest neighbors” in the calculation. Considering two nearest neighbors meant allowing the magnetic field from all the magnets 2 away or closer to impact the field around a magnet, etc. Testing with small arrays, we found that considering 5 nearest neighbors was sufficient to reduce the error between the approximate and exact solutions below 1%. This setting was used for the final simulation of our array. The final simulation strategy was based on this and the fact that all the magnets in the array are identical. This allowed us to do a single magnetic field calculation rather than iterative calculations. The magnetic field is calculated around a single magnet over a large enough area to cover the requested number of nearest neighbors. Then, this single magnet field is “stamped” across the entire array by offsetting its coordinates. Like physical stamps that overlap, the portions of the stamped field that overlap with previous stamps are added, so that the net result is

an array with interactions considered out to the desired number of nearest neighbors. The MATLAB script used for this calculation is included in the supplemental section.

CalculatingtheInducedVoltageFaraday’slawofinductionis

(Eq.44)Theinducedvoltageisproportionaltothetimerate‐of‐changeofthemagneticflux,weightedbythenumberofturnsofconductorthefluxispassingthrough.Inourcase,theconductorisnotasimpleloopbutratheraninductorwithsomecoilswrappedaroundahighlypermeablecore.Onewaytothinkaboutthevalueof inthiscaseisthatit’stheequivalentnumberofturnsinanair‐coredsolenoid.

FindingtheEquivalentNumberofCoilsForuseinothercalculations,weneededtofindawaytorepresenttheinductorswehadasan equivalent number of coils, Neq. In essence, Neq represents the theoretical number ofcoilsaninductorwouldneedinorder toproduce thesameinductanceif itdidnothaveamagnetic core. FromCoilcraft (themanufacturerof the inductorsweobtained),weknewthatforthe6.8mHinductor:

N=603.5μ=300

whereN is thenumberof loopsofwire in the inductorandμ is therelativepermeability.Nowforacylindricalcoilinductor,theinductanceisgivenbythefollowingexpression:

l

AKNL

2

0µµ

=

(Eq.46)

μ0=permeabilityoffreespace=1.257E‐6(m*kg)/(s2*A2)K=Nagaokacoefficient=0.8181N=numberofloopsA=crosssectionalareaofthewireinm2l=lengthofthecoilinm

SolvingthisequationforNwhilesettingμequalto1wouldyieldNeq.However,wedidnotknowthevalueofA/l.Thus,thefirststepwastosolveforA/l:

2

0KN

L

l

A

µµ= (Eq.47)

Plugginginalltheappropriatevalues,wefoundthatA/lwasequalto6.052E‐5m.Wethensolved(Eq.46)forN:

lAK

LN

1

0µµ

= (Eq.48)

Finally,tofindNeq,weusedthevalueswehadforL,μ0,K,andA/linequation(Eq.47)andsetμequalto1.Afterdoingthis,wefoundthatNeqwasequalto10,452.8turns.

TimeDependenceoftheFluxWiththisinhand,itremainstocomputethetimederivativeoftheflux.Assumingwehave

,theequationofmotionofthecantilever,wecanincorporateitstimedependenceintothemagneticfieldequationsas

(Eq.49)Thefluxisdefinedas

(Eq.50)For inthe plane,only willcontributetotheflux,andwecansubstitutetheaverage overeachplanefortheintegral,anaturalthingtodosincethiswillultimatelybecomputednumerically:

(Eq.51)Nowwehavethefluxasafunctionof .Togetthetime‐dependenceoftheflux,wegobacktothetimedependentfieldequationtoget

(Eq.52)Ifthecoilisadistance awayfromthemagnets,wegetsomethingthatonlydependson :

Thetime‐derivativeofthisis

(Eq.53)

where isthevelocityofthecantilever.Fromthisexpressioncomesthebasicoptimizationcriteria:assumingthefluxvariesrelativelyslowlyover ,thevelocitytermwilldominateandtheresponsewillessentiallyfollowthevelocity.Leavingitasisfornowandpluggingbackinto(Eq.44),theinducedvoltagewillbe

(Eq.54)Thisisalmostthecompletestory,butnotquite.Theequationofmotion onlydescribesthemotionattheverytipofthecantilever.Obviously,thevelocityatthetipisnotthesameasthevelocityinthemiddleofthecantilever,butthemagnetarrayspansthisdistance.Tomaketheexpressionmoreaccurate,weshouldconsiderthefactthatnotallofthecantilevermovesatthesamevelocity.Wecandothisusinganaveragevelocity.

AverageVelocityofHalfCantilever

Thevelocityofthecantileveratsomedistance alongitslengthis

(Eq.55)

where isthelengthofthecantileverand isitsvelocityatthetip.Intermsofintegrals,anaverageiswrittenas

(Eq.56)

Applyingthistoourcase,wherewe’reinterestedintheaveragevelocityoverthesecondhalfofthecantilever,weget

Inthiscase, ,sowehave

(Eq.57)

Apparently,themissingfactorin(Eq.54)wasthis .Addingitin,weobtainafinalanswerof

(Eq.58)

ComputingOutputVoltagesUsing (47), and given the solutions to the equation of motion discussed previously, it’spossibletocomputetheoutputvoltageforawiderangeofcases.Ofprimaryconcernare:(1) flatness of response across the microphone’s working range, (2) large enough signalacrosstheworkingrange,(3)faithfulreproductionofthevolumeofincomingsoundwaves,and(4)faithfulreproductionofthewavelengthofincomingsoundwaves.Requirements(1)and(2)aresatisfiedbyfigure15intheappendix,whichshowsalmostflat response across the range 20 – 20000 Hz with a voltage amplitude of about 71microvolts throughout. The sound level here is about 50 dB, which is normal speakingvolume.Forrequirement(3), figure16 in theappendixshowsa logarithmicvoltagebehaviorwithvolume level. The decibel is defined logarithmically because human hearing isapproximatelylogarithmic(forsomethingtosoundtwiceasloud,theactualsoundpressuremustbeabout10timesas large). Acorrespondinglogarithmicvoltageoutputmeans thatupon re‐amplification, different sounds should have the same “volume relationships” asbefore. Again,this isoptimal. Notethattheflatnessofresponsepersistsacrossall soundlevels.Finally,forrequirement(4),figure17showsaninputsoundwave(top)withvolume50dBandfrequency10kHz,anditscorrespondingoutputvoltage(bottom),againwithfrequency10kHzandoutputvoltage 72microvolts (aswe shouldexpect fromfigure 15). Wenotethattheoutputvoltageisphase‐shiftedby90degreessincetheoutputisproportionaltothederivativeof the input. Other than that, theoutputappears tobe a symmetric sinewavewhich closely replicates the original. This is the behaviorwewould expect if therewereonly a time derivative term in the output. As said above, this is because the spatialderivativeofthefluxoverthesmalloscillationrange(about150nm)ismuchsmallerthanthevelocity.

ProcessandMaterialSelection

MagneticMaterialSelection The first step in determining the best magnetic material to utilize was firstly selecting the process that would allow for microfabrication of a magnetic array with small dimensions. Electroplating offers a low cost, high deposition rate for multimicron magnetic films. In addition, electroplating has the ability to selectively deposit the material using photoresist masks. Other vapor deposition techniques such as evaporation, sputtering, and pulse laser deposition are slow, more costly processes requiring post deposition polishing and etching steps. The group decided to move forward with electroplating as it offered maximum productivity with less fabrication cost. Referencing “Permanent Magnets for MEMS” by Arnold, it was noticed that most studied microfabricated magnets that can be electrodeposited were of cobalt nature. Some of the electrodeposited iron alloys had to be annealed at a temperature greater than 400OC, which was deemed unfavorable to prevent further defect formation in our system. The two main materials with the best-determined characteristics were found to be CoNiMnP and Co-PtP. Co-PtP has demonstrated a BHmax on the upwards of 69 kJ/m3 and a maximum remanance of 1.0 T. In previous studies, CoNiMnP has only demonstrated a BHmax on the upwards of 14 kJ/m3 with a remanance of 0.3 T. The larger maximum energy product (BHmax) of Co-PtP shows that a greater magnetic flux can be achieved with a smaller volume of magnetic material. The alloy also generates a large magnetic field of 1 T. However, Co-PtP is very costly as it contains platinum. In an effort to control ultimate fabrication cost, the group decided to move forward with CoNiMnP. The alloy also has the ability to form films on the magnitude of tens of microns, which allows us to produce a sufficient energy product by producing a thicker film. Thus, our limited resources lead us to CoNiMnP as our magnetic material. For future work, the group would look into using Co-PtP as its larger maximum energy product would allow for a smaller magnetic film. In addition, other more costly techniques such as sputtering or pulse laser deposition could be used in accordance with magnetic materials displaying much greater energy products, including rare earth metals which have demonstrated bulk magnetic properties [17].

Fabrication Inordertoappropriatesufficient time tofabricateourprototype,wedecidedonaprocessflowmid‐March.ToensurethatourprocesseswouldbeabletobecompletedintheFabLab at the University of Maryland, members of our groupmetwith FabLab staff andthoroughlydiscussedthemeritsofourprocess. Ourprocedureinvolvedaround30steps,including metal deposition, 4 different photolithography steps, etching, electroplating,device construction, and ultimately device characterization. For the sake of time, wedecidedona0.5μmthickSiO2cantileverthatwas3mmby3mmwithanarrayof50μmby

50μmmagnetsat itsend. CoNiMnPwaschosenasthemagneticmaterial,andavarietyofarray patterns were chosen for the wafer in hopes of testing for the ideal spacing ofmagnets.Thereweretobetencantileversperwafer,twowith140x70magnetarrayandthe other eight with rectangular arrays of 50μm by 50μm magnets that differed in thespacingbetweenthemagnets.

We procured (100) silicon wafers with 500nm and 1000nm of silicon dioxidealreadydepositedonbothsidesfromDr.PhaneufandtheFabLab,respectively.Thewafersweretohavechromium(200Å)andgold(2000Å)deposited,thenusephotolithographytooutlinethecantilevers,etchingawaytheCr/AuandSiO2wheretheopenareasurroundingthecantileverwillbe.Averythick(~25μm)photoresistlayerwastobeusednexttoactasa mold for electroplating the magnet arrays. Once the magnets had been deposited andmagnetized, photolithography was to be used to “protect” the magnets and remove thesurrounding Cr/Au. The wafers were then to be bonded together, magnet‐side‐in, andphotolithography was to be used to define the areas to be opened surrounding thecantilever.ThebacksideSiO2wouldberemovedandthentheSiwouldbeetchedthroughtothe front of thewafer,where therewould be a released SiO2 cantilever. The photoresistwould be carefully removed and then the inductorswithwire leads already soldered onwould be expoxied to the back of thewafers, underneath the pits. After that, thewaferswere tobecleaved into individual devices, connected to an amplifierandoscilloscope forreadingsand a frequency generatorwas tobe used to producevaryingdecibel levelsandfrequencies.

PrototypingProcessAtotalofthreewaferswereusedforthefabricationofdevices: twowaferswith1micronoxidelayersoneachsurface,andonewaferwith500nanometersofoxideoneachsurface.The first step in our processwas to apply the chrome‐gold adhesion layer to thewafers.This was done using an Airco Temescal 4‐pocket electron beam evaporator system.Approximately 200 angstroms of chrome were evaporated onto the wafer, followed byapproximately 2000 angstroms of gold. This was followed by a 10‐minute bake of thewafersona120ºChotplateintendedtopreventunwantedgoldetching.Next,Shipley1813photoresistwasspunonto thewaferfor40secondsat4000rpm,and thewaferwassoft‐baked for 60 secondsat90ºC. Next, the firstmask (defining the cantilevers)wasused topatternthephotoresist,whichwasexposedfor11secondsanddevelopedin3:1AZ‐400Kdeveloperfor45seconds.Oncethephotoresisthadbeensuccessfullydeveloped,thewaferswerehardbakedat120ºCfor5minutes.Afterthephotolithography,thegoldsurroundingthe soon‐to‐be cantilevers was etched away using AU‐5 etchant, the chrome was etchedusingCR‐7etchant,andtheoxidewasetchedusing6:1bufferedoxideetchant.TheShipleyphotoresistwasthenstrippedoffusingastandardresiststripper.

Thenext step in the process involveddepositing themagnet arrays onto the goldadhesionlayeronthecantilevers. Inordertoelectroplatewell‐definedarraysofmagnets25micronsthickandwiththedesiredshape,itwasnecessarytoapplyalayerofphotoresistatleast25micronsthickandpatternittocontainpitswithverticalsidewalls.ThethickestphotoresistavailabletouswasAZP4620,whichistypicallyspuntoathicknessofaround12microns.ThismeantthattwoconsecutiveapplicationsofAZP4620hadtobedoneinorderto achieve our desired results. This was done by spinning one layer of photoresist ataround1000rpm for30 seconds, thenapplyingEdgeBeadRemover to thewaferedge toremove the thickphotoresistbead that accumulateshere, then soft‐baking thewaferon a

90ºC hot plate for 5 minutes, and then repeating this process a second time. After thephotoresistwas applied, thewaferswereallowed to sit for 60minutesbeforecontinuingwith photolithography. After the 60 minutes had passed, the second photolithographymask(definingthemagnets)wasalignedoverthecantileveroutlines,andthephotoresistwasexposedfor95seconds,thendevelopedin3:1AZ‐400Kdeveloperfor2minutes.Thisrecipeforexposureanddevelopmentwasdecideduponafternumerousotherrecipesweretried, and is still not totally desirable in that the bottoms of the pits we were trying topattern tended to be somewhat underexposed, whereas the tops of the pits tended tobecomeoverexposed. Thisresultedinbothnon‐idealadhesionbetweenthemagnetsandgold as well as less‐than‐desirable magnet geometry. However, time and budgetaryrestraintspreventedusfromdevelopingabetterprocess.Forfuturefabrication,wewouldprocureathickerphotoresist,suchasSU8,whichwouldlikelygiveusbetterfeaturequalityat large thicknesses. Use of a glass photolithographymask, as opposed to a plastic one,wouldlikelyhelpinimprovingfeaturequalityaswell.Afterpatterningthemagnetpits,themagnets were electroplated into the pits. Immediately after electroplating the magnets,somemagnetswerevisiblycrackedandflaking,andoncewemagnetizedthemagnets ina0.5Tfield,significantdelaminationwasobserved.After electroplating, the resist on the wafer was stripped. Next, the front sides of twowaferswereadhered togetherusingCrystalbondwax. This stepwasintendedtoserveasprotection for the front sides of thewafers during the back‐side etch,which is to follow,since time restraints prohibited us fromprotecting themagnetswith a photoresist layer.However,itwasobservedthatthewetback‐sideetchdegradedtheCrystalbond,causingthewaferstoseparate,meaningthewaxdidnotserveitsintendedpurpose.This,ontopofthefactthatmovementofthewafersagainstoneanotherduringCrystalbondapplicationmayhave caused magnet and cantilever damage, means that in future fabrications this stepwouldbeomitted.AftertheCrystalbondwasapplied,Shipley1813photoresistwasappliedto the backsides of each wafer using the spinning procedure described above. Sincephotoresist was applied on both sides of the two‐wafer structure, baking was donesuspended in an oven for 15 minutes at 90ºC to avoid damage to the photoresist. Thephotoresistwasthenpatternedwiththefinalphotolithographymask(defining theholetobeetchedthrough thebackofthewafer),beingexposedfor11secondsanddevelopedin3:1 AZ‐400K for 45 seconds. Next, the wafers were hard‐baked in a 120ºC oven for 30minutes, and the exposed oxide on the back surfaces of thewaferswas etchedusing 6:1bufferedoxideetchant.Then,aholewasetchedthroughthesiliconfromthewaferbacksideclearthroughtothesilicondioxideofthecantilever.ThiswasdoneusingTMAHheatedto102ºC. TheTMAH simultaneously removed the photoresist remainingon thewafer. Theetching process took several hours, and had several undesirable results such as theshrinkage of cantilevers and the incomplete removal of silicon. We were hesitant tocontinue etching until all silicon was removed for fear that the extremely delicate oxidecantileverswouldbreakorbeexcessivelyetchedbytheTMAHaswell.

Etching The wafers were removed from the TMAH after 5.5 hours of etching, ahead ofschedule, as it was noticed that the wafers had etched completely through. They wereobservedtobeslidingfromeachother,meaningthatthecrystalbondhadnotmadeatightseal between thewafers. TheTMAHwas able to get between thewafers and etch the Si

from the front, leading to a shortened time to etch through the entirewafer. Thewaferswerenotseparatedandwererinsedina1Lbeakerofdeionizedwaterstillbondedtoeachother. In order to remove the crystalbond to inspect thewafers, theywere left in 1L ofacetone for19hours post‐deionizedwater rinse. After the acetone soak thewaferswerecarefullyseparatedandinspected.Therewasnodamagetothefrontofthewafersandthecantilevers had almost completely retained their original form. However, it was obviousthat the cantilevers were not released and that there was still much Si to etch awayunderneaththecantilever.AnattemptwasmadetomeasurethethicknessoftheSietching,butallprofilometersavailabletouswereunabletomeasureadistancegreaterthan150μmandthusunabletogiveusameasurement. Visual inspectionledustobelieve that therewasstillabouthalfoftheoriginalthicknessoftheSitoetchawayunderneaththecantilever.

Inspection under the microscope showed varying levels of damage to the magnetarrays.Asmentionedbefore,atthispointallmagneticplateshaddelaminated,soonlytheeightcantileverswithactualmagneticarrayswereinspected.Oneofthetwo1μmthicknesswafers, which were Crystalbonded together during etching in TMAH, had their magneticarraysmostly intact. Outofeightarrays, threewere fully intact and threewerepartiallyintact. The arrays that were partially [or less] intact seemed resultant of the golddelaminatingcompletelyaslargestretchesofgoldweremissingonthecantilever,seefigure18. The other wafer’s magnetic arrays appeared to have been ripped off, as the goldbetweenthemagnetsremainedandarectangulargridofmissinggoldsquareswerepresentwherethemagnetsoncestood,seefigure19.Itwashypothesizedthatthecauseofthissortofmagnetdelaminationwas from thewafers rubbing togetherwhenCrystalbonded. Thestresseswere greater than the adhesionof theAu/SiO2 interface, assumedbecauseof thelack ofgoldwhere themagnetswere, so themagnetscameoff. Ifwewere able to find adelaminatedmagnet,wecouldhaveinspectedthebottomsofthemtoconfirmifitwastheAu/SiO2interfacethatfailed. Themagnetarraysonthe0.5μmwaferweredissatisfactory,butthemagneticpresencewasmuchgreaterthan thatofthesecond1μmwafer. Manyofthecantileversonthe0.5μmwafershowedsignsofthegolddelaminating,butsomeshowedsigns ofgeneralpoormagneticgrowth,meaning thephotolithography/electroplating stepwas to blame, not the etching process. Cantilevers on all three wafers, showed signs ofstressesastheywerecurlingdownwardsattheirends,eventhoughnotallofthesiliconhadbeenremovedfromthecantilevers.

Afteragroupdiscussionandaddressingconcerns aboutcurlingcantilevers, itwasdecided that further Si etching should be attempted. Due to the crystalbonding beingineffective and seemingly little TMAH damage done to the frontside of the wafers, thewaferswere submerged individually into the TMAH. Only the 0.5μmwafer and the 1μmwaferwith intactarrayswere involved in this step,as thesecond1μmwaferwasuselessafter thefirstetch. The twowafersremainedin theTMAHfor1.5hoursandwereslowlyremovedandsubmergedin1Lofdeionizedwaterforrinsing.Oncerinsedandair‐dried,thewafers were inspected. The Si had yet to be etched completely from underneath thecantilevers,butthecantileversthemselveshadshownenoughdegradationthatcontinuingetchingwould destroy them. Thecantilevers on the0.5μmwaferhadall degraded to thepointthatnoinspectionunderthemicroscopewasrequiredtoruleitoutasunusable.Fourcantilevers on the remaining 1μmwafer, however, had still retainedmore than~60%oftheir magnetic array. They showed even more curling than before the 1.5 hour etch,continuing tocurldownwards. Ifetchingweretocontinue, itwasassumedthat sowouldthecurlingofthecantilevers,whichwouldrenderthemunusablefortesting.Itwasdecidedthat7hourstotalofetchingwas themostthat thewaferscouldhandlewithoutrenderingallthreeuselessandweproceededtopreparethesingleremainingwaferfortesting.WetetchingoftheSiO2wasselectedintheprocessfloworiginallybecauseitwas thought that

theFabLabdidnotprovideanyalternatives. Incompletecommunicationwith the FabLabstaffperpetuatedthischoicebyleavingthemunawareofourintentions.Inretrospect,deepreactiveionetchingwouldhavebeenabetterprocesstouseforetchingthroughthewafer.Itwouldhavebeensingle‐sided,fasterbyabout5hours,andwouldnothavedegradedtheSiO2 cantilevers themselves. Using deep reactive ion etching would have also meant theavoidance of Crystalbond andmost likelywould have prevented the delamination of thegoldandmagnetarrays. Also,thedesignofthedeviceshouldbechangedinordertotakeinto consideration the stresses on the cantilevers as the curling of the cantilevers wasalready nearly too great to allow testing, even with a thick Si backside reinforcement.Testingforstresseshasalreadybeendiscussed.

Onceitwasdecidedtohaltetchingandcontinueonwiththefabrication,wemovedon to cleave the wafer into individual devices. We used one of our dummy wafers topractice cleaving the wafer, but it cleaved in undesired directions. Having individualdeviceswasnotessentialtoourtestingprocess,itwasmerelyaconvenience,sowedecidedtoforgo that step. ThesetbackduetononcompliantwafercleavingwasnotbeingabletoperformVSMtesting. Wehadsetasideawaferthathadthemagnetarraysdeposited,butnocantileversdefined.ItwasintendedtobecleavedintoindividualarraysandeacharraywasplannedtobemountedintoaVSMtotestfortheirdifferingmagneticbehavior,iftherewas any. Their MH curves would have been analyzed for the coercivity, magneticsaturation, and remanentmagnetizaion of the arrays. Sincewedid not cleave individualdevices,wewereunabletohaveseparatedarraysforVSMtesting.Thedecisiontoskipthewafer cleaving was heavily motivated by time constraints and a severe lack of room formistakes,but if enough timeandcarewas taken,awaferhosting thecantileverscouldbecleavedintoindividualdevices. Duetothedevicesbeingsodelicate,thewireleadsweresolderedontheinductorsbeforebeingattachedtothecantileverdevices.Theinductorsusedandtheircontactswerebothsmallso30AWG,~0.25mmdiameter,wireswereusedasleads.Theyweresolderedonusingabasicsolderingironandsolder.Aftersoldering,athinlayerofLoctiteepoxywasappliedtotheouteredgesoftheopenareassurroundingthecantileversonthebacksideofthefourdeviceswhichweredeemedmostlikelytoyieldpositiveresults.Immediatelyafterapplication,theinductorsweregentlypressedagainsttheepoxiedareasandleft to sit for40 minutes completely undisturbed and then were only subjected to minimal wafertranslocationfora12hourperiod. Thewafersat forabout2daysbeforebeingmoved totesting. Wewereabletoacquireasoundpressurelevelmeterthroughapersonalcontactanddevicessuchasanoscilloscope,frequencygenerator,andampfromtheDemonstrationLaboratory in the Physics department at the University of Maryland. The actual testingperformedconsistedoftryingtoseeanyobservablesignalproducedintheinductorinthepresence of sound compared with the absence of sound. This test was not successful,renderingothertestsonthisprototypeunnecessary.Thepotentialcausesoffailureforthisprototypearenumerous.Thesiliconremainingonthecantileversmayhavebeensothickas to make the deflection of the cantilevers imperceptibly small. The total cantileverthickness is not known because no method could be devised to measure them using theequipment at our disposal, asmentioned above. Another cause of failure could be that alargepercentageofmagnetswereremovedduringhandling of thewafer for testing. Theamount ofmagnets remaining on the devices is not currently known, as thewaferswereonly characterized in an optical microscope before the handlingwhich may have causedcatastrophicmagnet removal. A thirdcauseof failurecouldbe poorelectrical connectionbetween the inductors, leads, and oscilloscope. The resistances of the inductors weremeasured during testing, and most of the coils either had unusually high resistances,indicatinghighcontactresistance,ordidnotformaconductingcircuitatall.Thissuggests

thatdifferentelectricalconnectionmethodsmayneedtobeusedinordertoimplementthedevices. Had the microphone displayed a measurable signal in the presence of sound,additionaltestscouldhavebeenperformed.Onetestwouldbetoprovidethemicrophonewith a sound of constant volume and a frequency varied over the device’s useful range(approximately30‐30,000Hz)inordertoobservetheamplitudeofthesignalproduced.Aflat frequency response is desired, as thiswill more accurately record the volume of thesound produced. Another test is to provide the microphone with a sound of constantfrequency (typically1000Hz)andvaryingamplitudes inorder tosee theresponseof themicrophone to different volumes. A signal which is proportional to the volume of theincident sound is desired. A third test is to measure the microphone’s response to aconstant sound incident on thedeviceatvarying angles to thecantilever’s normalvector.Desirableoff‐axisresponsesdifferbasedonthemicrophone’sapplication;omnidirectionalregistry of sound is desired in some cases but not in others. A final test is to supply anextremelybriefpulseofsoundtothemicrophoneandobservethesignalthatitproduces.Amicrophone will not stop producing signal instantly after the incident sound has ceased,and the signal produced after theend of the incident sound isdependenton the physicalmakeupof themicrophone. Knowledgeof thesignal profileproducedby themicrophoneforaverybriefsoundinacontrolledenvironmentisimportantwhentryingtoobserveandcharacterizebriefor rapidlyoccurringnoises,as theresponseof themicrophonemustbeaccountedforinordertointerprettheproducedsignalcorrectly.

Ethics When considering the ethics of our project, the majority of the concern is drawntowardsthefabricationprocessitself. Post‐production,themicrophonecouldbeusedforrecordingdiscussionswithoutconsent,butthelabelof“unethical” forthatpurposevariesonthepersonasked,anditisagrayarea.Thematerialsofthemicrophoneitselfareprettyharmless,butthemagneticmaterial,CoNiMnP,couldpossiblybeahealthriskwitha largeenough dose. However, the amount of magnetic material included with each device, theprotectivehousingaroundit,andunlikelihoodofdelaminationmeansthat therewouldbeno significant ingestion, inhalation,or skincontact risks. Also, these devices are so smallthatthescaleofimproperdisposalwouldhavetobemassiveinordertoposeasignificantenvironmentalrisk. Thetrueconcernwiththisdeviceistheenvironmentimplicationsofitsfabrication.Ourcurrentfabricationdesigninvolvesfourphotolithographicsteps,meaningfourdifferentlayersof photoresist toberemoved, aswell as developerandphotoresist strip. The goldthatwasdepositedwillbealmostcompletelyremovedinourprocessflow,alsoproducingwaste.Whendevelopingaworkingfabricationprocess,itshouldbekeptinmindthatextrasteps increase waste, so they should be avoided. It is also advantageous as extra stepsusuallyincreasethelikelihoodoferror.Also,theetchantsinvolvedprovideahumanhealthhazard, so it would be best if these steps were minimized or completed without directhumanparticipation.

Unfortunately for our device, the process of perfecting a fabrication procedure isgoingtoproducealotofwaste.Forourprototype,weused5‐6waferstoonlyendupwithonesomewhatusablewaferandusednearly¼ofajarofphotoresistwhentryingtoperfectourthickphotoresistexposuremethods.Ourprototypealonecausedthedisposalof1Lofphotoresist strip. Even if trying to use different processes, waste will still be produced.

Deep reactive ion etching uses SF6, which has been labeled the most potent greenhousegas[18].Sincetheorydoesn’talwayscarryovertoreality,manywaferswillbeusedupwhentryingtosuccessfullybuildthedevice.Inordertotestfordifferentproperties,likeresidualstressesormagneticbehavior,waferswillhavetobesacrificedaftergoingthroughall thewaste‐producing fabricationsteps. While it is good to try to reduce theamountofwasteproduced,ithastobeacceptedthatforthisdevicetobeproducedforuseintherealworld,some sacrifices have to be made. What has to be considered is theworth of this devicebalancedagainstthewasteitwillproducetoperfectitandreproduceit.

Application

Packaging Itwillbenecessaryfortheimplementationofthedevicetohavepackaging.Intheeffortofsavingtime,wehavecameupwithonepotentialpackagingscheme,butmoreoptionswouldneedtoberesearchedtodeterminewhatpackagingschemewouldactuallybebest.Itwillbeimportanttoconsiderthedeviceapplicationswhendeterminingthedimensionsofthepackage,sothesearesubjecttochange. Thefirstmethodwecouldutilizeistheglobtopmethodtoprotectthebackside.Thiswouldalsodoubleasanextralevelofsecurityforthecoiltopreventitfromfallingout.AgreatresinforthissimpleapplicationwouldbeathixotropicviscousresinlikeDymax9001‐E‐v3.7[19].Itisimportanttohavethixotropyandviscositytoachievetheappropriatethicknesswhilepreventingbleedandalsotoeliminatevoids[20]. Thetopsiderequiresabitmorethoughtwithregardtoitsprotection.ItisspeculatedthatonecouldeasilymachinethinpolymersheetsofamateriallikeNylontomakeholesinthemtosurroundthecantileverandmagnets.Theactualshapeoftheholeisimportantsoitdoesnotinterferewithorscatterthesoundwavesthecantileveristryingtopickup.Infact,perhapsthiscanevenassistinthecollectionofthesoundwaves.Ahornshapeisspeculatedtobethebestshapeduetopreviousworkinsoundcollection[21].Specificsaboutthisshapewouldneedtoberesearchedmoretooptimizetheamountofsoundwavesthatreachthecantilever.Animageofthispotentialpackagingoptionisshowninfigure20intheappendix.

HearingAids Hearingaidsaredevicesusedtoamplifysoundsothewearercanhearsoundswithwhat remains of their hearing. The main functional portions of the hearing aid are themicrophone, amplifier, receiver, and the power supply. The microphone is a transducerthatconvertsthesoundsignalintoelectricalenergy.Theamplifierincreasestheamplitudeandthereceiverconvertsthatbacktosoundsoitcanbeheardintheindividual'sear[22].Intypical hearing aids, electret condenser microphones are used[23,24]. These types ofmicrophonesarediscussedinfurtherdetailintheBackgroundportionofthisreport. Thesedevicesarecurrently linearinresponsefrom50Hzto8000Hz[22]. Asshownabove, our device's range has exceeded this range, so we can adequately sustain the

operation of a hearing aid with our device. Another aspect of our design integration isensureourdevicecanfitintothecurrentdesignofhearingaids.Thereareseveraldifferenttypesofhearingaidfits,butthetwomostpopulararebehindtheear(BTE)andintheear(ITE).Ofthesetwo,theBTEhearingaidhasbecomemoreprevalentduetotechnologythatallowsforbettersoundquality,anditsplacementmakesforbetteracquisitionofdirectionalsoundwaves. Apotential concernwith the implementationof thedevice is its ability todirectlyreplace the electret condenser microphone. The size of our device with packaging isapproximately 8mm by 5mm by 4.2mm. However, by choosing a separate coil we canreduce the overall parameters to about 5mm by 5mm by 3mm. Electret condensermicrophonesareontheorderof4mmx3mmx1mmor5.47mmx5.47mmx4.62mmbasedon two separate sources[23,25]. The actual size of the microphone likely varies on theparticularmanufacturer,sodiscreteparametersareimpossibletodetermine.Becauseourmicrophone is just slightly larger than the above mentioned parameters, butwe feel ourmicrophone could be implementedwith just a slight change in the hearing aid design toallowroomforthemicrophone. Lessaugmentationofthehearingaidwillbenecessaryifwe can choose a separate coil. This is evidence that our microphone can make for asuccessful hearing aid microphone. The hope is to reduce the power needed to run thedevice while maintaining approximately the same frequency response and physical size.Perhaps by using our dynamic microphone, less battery power is needed and batteriescouldbereplacedlessfrequently.

Appendix

Figure1­NumberofMEMSmicrophonesshippedperyearwithprojectswww.isupply.com

Figure2­SchematicrepresentationofanSiO2cantileverwithanarrayofmagnetsdepositedontop. Lmain(mm) Lspace(um) nspace Ledge(um) #of

MagnetsSpringConstant(N/m)

MagnetArray

1.475 21.3 69 66 9800 .442

Table1­AcollectionofdimensionsdescribingthemagnetarrayelectroplatedontheSiO2cantilever.Thespringconstantofthedesignisincludedaswell.

Figure3­a)SchematicDiagramofcantileverwithconcentratedmassattip.b)Schematicdiagramofourcantileverwithanarrayofmagnetsdepositedoveralength. k(N/m)PlateDesign 0.490Design1 0.420Design2 0.442Design3 0.408Design4 0.442Table2­CalculatedspringconstantsofeachcantileverdesignusingEQ6anddimensionslistedinTable1

.

md

md

mc

Mmag

a)

b)

Figure 4-A steady state deflection plot of an SiO2 cantilever with a length and width of 3mm and thickness of 3um against sound level.

Figure5‐Oscillating cantilever. In the device the rigid stationary substrate will be the prefabricated inductor.

Figure6­Plotof deflection vs sound level for COMSOL and the analytical expression

Figure7-Frequency response with resonant frequency at 20Hz and very low damping- sound pressure at 50dB

Figure8­Frequency response with resonant frequency at 50,000Hz with very low damping- sound pressure at 50dB.

Figure9­Frequency response with resonant frequency at 2,500Hz and high damping- sound pressure at 50dB.

-0.1

-0.05

0

0.05

0.1

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Figure10 – Plots of the vertical component of magnetic field for a) in-plane, and b) out-of-plane magnets. Note that the magnitudes for in-plane magnetization are larger than for out-of-plane, but the flux direction is such that it completely cancels below the magnet. Out-of-plane magnetization, on the other hand, yields a flux topography that can be harnessed.

Figure11 – Typical plots of magnetization (M) and magnetic induction (B) vs. magnetizing field (H) for a permanent magnet. Indicated are the remanence (Br), the coercivity (Hc), and the maximum energy product (BH)max, as well as the intrinsic coercivity (Hci), which is the intersection of the M – H curve with the x-axis (adapted from [1])

Figure12 – Typical B – H loop for CoNiMnP (as measured by myself) with the value of (BH)max labeled

0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

aspect ratio (thickness/length)

demagnetization factor

Figure13 – Plot of demagnetization factor, , vs. aspect ratio, . As the aspect ratio increases to infinity, the demagnetization factor decreases to zero, indicating there is almost no demagnetizing effect. In the opposite limit of low aspect ratio (a thin plate), the demagnetization factor increases to 1, indicating almost complete demagnetization (not a useful condition).

0 2 4 6 8 100

5

10

15

20

25

aspect ratio (thickness/length)

load line slope (B/H)

Figure14 – Plot of load line slope, B/H, vs. aspect ratio revealing a linear trend. For the target load line slope of 5.77, we require an aspect ratio of 2.83.

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

frequency (kHz)

voltage (microvolts)

Figure15­Voltageresponseat50dB

0 5 10 15 20 25 3010

-8

10-7

10-6

10-5

10-4

10-3

10-2

frequency (kHz)

output voltage (V)

Figure16­Outputvoltageatvaryingsoundvalues.

0 0.1 0.2 0.3 0.4 0.5-10 mPa

-5 mPa

atmosphere

+5 mPa

+10 mPa

time (ms)

pressure

Input Sound (50 dB, 10kHz)

0 0.1 0.2 0.3 0.4 0.5-100

-50

0

50

100

time (ms)

output voltage (microvolts)

Output Voltage

Figure17­Inputsoundpressureandoutputvoltagevs.time.

Figure18­Goldstripsmissingoncantileverarray.

Figure19­Missingmagneticpiecesoncantilevers.

SupplementalThe following MATLAB script takes user input for magnet and array dimensions, the

number of nearest neighbors to consider, the resolution of the mesh in the x-y plane and z

direction, and the dimensions of a rectangular integration surface and outputs the

appropriate field expressions, the magnetic field calculated for a single magnet, the

magnetic field for the array produced by stamping the single field, and the flux through

the integration surface at each point in the z mesh.

Figure20­Schematic design of potential package for the microphone

% Given asked-for parameters, creates structures eq.*, single.*, and % array.*, where * = Bx, By, or Bz. eq.* contains the equations used to % calculate single.*, which is the field produced by a single magnet. % array.* contains the flux data for the entire array, which is obtained by % "stamping" the single magnet data across an array. flux.* is also % produced; flux.val contains the surface integral computed at each value % of flux.z % User input - magnets a = input('\nmagnet x dimension? '); b = input('magnet y dimension? '); c = input('magnet z (magnetization) dimension? '); sfield = input('Bz (strength at x-y surface?) '); % User input - array nx = input('\nnumber of array elements in x direction? '); ny = input('number of array elements in y direction? '); d = input('array spacing? '); % User input - evaluation criteria surfx = input('\nsubsurface x dimension? '); surfy = input('subsurface y dimension? '); zl = input('lower end of z range? '); zu = input('upper end of z range? '); nn = input('number of nearest neighbors to consider (0 = single mag)? '); mr = input('x-y mesh resolution (be sure it''s an even factor of all

dimensions)? '); mrz = input('z mesh resolution? '); % Put pertinent data into the properties structure to help remember % what the model is of clear properties properties.dimensions = sprintf('%d x %d x %d thick',a,b,c); properties.strength = sprintf('%.3f T',sfield); properties.array = sprintf('%d x %d, spacing %d',nx,ny,d); properties.intsurface = sprintf('%d x %d',surfx,surfy); properties.zrange = sprintf('%d to %d',zl,zu); properties.mesh = sprintf('nearest neighbors: %d x-y resolution: %d z

resolution: %d',nn,mr,mrz); % Turn off warnings (there will be a lot of them) warning off all % Start timer tic % Create constituent functions G = @(a,b,c,z0) log((sqrt(a.^2+b.^2+(c-z0).^2)-b)./(sqrt(a.^2+b.^2+(c-

z0).^2)+b)); sx = @(x,y,z,h) G(a-x,y,z,h)+G(a-x,b-y,z,h)-G(x,y,z,h)-G(x,b-y,z,h); sy = @(x,y,z,h) G(b-y,x,z,h)+G(b-y,a-x,z,h)-G(y,x,z,h)-G(y,a-x,z,h); sz = @(x,y,z,h) phi(y,a-x,z,h)+phi(b-y,a-x,z,h)+phi(x,b-y,z,h)+phi(a-x,b-

y,z,h)+phi(b-y,x,z,h)+phi(y,x,z,h)+phi(a-x,y,z,h)+phi(x,y,z,h); % Calculate field constant K J = -(sfield*pi)/((4*pi*10^-7)*[(phi(b/2,a/2,c,c)+phi(a/2,b/2,c,c))-

(phi(b/2,a/2,c,0)+phi(a/2,b/2,c,0))]); K = (4*pi*10^-7)*J/(4*pi); % Create field functions

clear eq eq.Bx = @(x,y,z) -K/2*(sx(x,y,z,c)-sx(x,y,z,0)); eq.By = @(x,y,z) -K/2*(sy(x,y,z,c)-sy(x,y,z,0)); eq.Bz = @(x,y,z) -K*(sz(x,y,z,c)-sz(x,y,z,0)); % Calculate array extents l = nx*a+(nx-1)*d; w = ny*b+(ny-1)*d; dx = d + a; dy = d + b; % Initialize single magnet evaluation mesh and array matrices xsize = (2*nn*dx+l)/mr+1; ysize = (2*nn*dy+w)/mr+1; zsize = (zu-zl)/mrz+1; clear single array [single.x,single.y,single.z] = meshgrid(-nn*dx:mr:(a+nn*dx),-

nn*dy:mr:(b+nn*dy),zl:mrz:zu); [array.x,array.y,array.z] = meshgrid(-nn*dx:mr:(l+nn*dx),-

nn*dy:mr:(w+nn*dy),zl:mrz:zu); array.Bx = zeros(xsize,ysize,zsize); array.By = zeros(xsize,ysize,zsize); array.Bz = zeros(xsize,ysize,zsize); % Calculate single magnet field home; status = sprintf('Calculating field for a single magnet...') single.Bx = eq.Bx(single.x,single.y,single.z); single.By = eq.By(single.x,single.y,single.z); single.Bz = eq.Bz(single.x,single.y,single.z); home; status = sprintf('Calculating field for a single magnet... Done') % Construct field for entire array by "stamping" single field home; status = sprintf('Calculating field for a single magnet...

Done\n\nStamping...') for xa = 1:nx for ya = 1:ny for za = 1:zsize bxoffset = padarray(single.Bx(:,:,za),[(xa-1)*dx/mr (ya-

1)*dy/mr],0,'pre'); byoffset = padarray(single.By(:,:,za),[(xa-1)*dx/mr (ya-

1)*dy/mr],0,'pre'); bzoffset = padarray(single.Bz(:,:,za),[(xa-1)*dx/mr (ya-

1)*dy/mr],0,'pre'); bxoffset = padarray(bxoffset,[(nx-xa)*dx/mr (ny-

ya)*dy/mr],0,'post'); byoffset = padarray(byoffset,[(nx-xa)*dx/mr (ny-

ya)*dy/mr],0,'post'); bzoffset = padarray(bzoffset,[(nx-xa)*dx/mr (ny-

ya)*dy/mr],0,'post'); array.Bx(:,:,za) = array.Bx(:,:,za)+bxoffset; array.By(:,:,za) = array.By(:,:,za)+byoffset; array.Bz(:,:,za) = array.Bz(:,:,za)+bzoffset; end end end home; status = sprintf('Calculating field for a single magnet... Done\n\nStamping...

Done')

% Create subset of data to restrict to integration surface home; status = sprintf('Calculating field for a single magnet... Done\n\nStamping...

Done\n\nIntegrating... ') clear flux for za = 1:zsize flux.val(za) = mean(mean(array.Bz((xsize-surfx/mr)/2:(xsize-

surfx/mr)/2+surfx/mr,(ysize-surfy/mr)/2:(ysize-surfy/mr)/2+surfy/mr,za)))*surfx*surfy;

flux.z(za) = array.z(1,1,za); end home; status = sprintf('Calculating field for a single magnet... Done\n\nStamping...

Done\n\nIntegrating... Done') % Delete temporary functions/variables (remove this line to retain in % workspace) clear a b c sfield G phi sx sy sz J K l w dx dy nx ny d zd mr xa ya status

counter bxoffset byoffset bzoffset za nn surfx surfy xsize ysize zsize zu zl mrz

% Stop timer, print elapsed toc

ProposedProcessingProcedure

Step DescriptionNecessaryEquipment/Materials Notes

1Grow500nmthermaloxideon2waferstomake1µmtotalthickness FurnacewithFlowingO2

2remainedat500nmasreceived

2 SputterCrto200Å ElectronBeamDeposition 3 SputterAuto2000Å ElectronBeamDeposition 4 SpinprotectivePRonbackside Shipley1813PRandspinner 5 Spinphotoresistonfrontside Shipley1813PRandspinner 6 Alignmask1,exposeanddevelop MaskalignerwithUVlight

Mask1*,developingsolution, Chem.Bench

7 EtchAuwithAu‐5 Solution,Chem.Bench 660nm/min8 EtchCrwithCr‐7 Solution,Chem.Bench 170nm/min9 EtchOxidewith6:1BOE Solution,Chem.Bench 100nm/min10 PhotoresistStrip Solution,Chem.Bench

11 SpinPRLayer1 AZP4620ThickPRandspinnerthickformagnets

12 SpinPRLayer2 AZP4620ThickPRandspinnerthickformagnets

13 Alignmask2,exposeanddevelop MaskalignerwithUVlight Mask2*,developingsolution,

Chem.Bench 14 O2plasmacleaning ARL 15 Electroplating ARL,CoNiMnPprecursors 16 Magnetize VSMinChem/Nuc 17 PhotoresistStrip Solution,Chem.Bench

18 SpinPR AZP4620ThickPRandspinnerthickforprotect

19 AlignMask3,exposeanddevelop MaskalignerwithUVlight Mask3*,developingsolution, Chem.Bench 20 EtchAuwithAu‐5 Solution,Chem.Bench 660nm/min21 EtchCrwithCr‐7 Solution,Chem.Bench 170nm/min22 PhotoresistStrip Solution,Chem.Bench

23CrystalbondWaxtwowaferstogether Crystalbond

Waxontopsides

24Spinphotoresistonbacksidesofwafers Shipley1813PRandspinner

25 Alignmask4,exposeanddevelop MaskalignerwithUVlight (onbacksidesofbothwafers) Mask4*,developingsolution, Chem.Bench

26EtchOxideonbacksidewith6:1BOE Solution,Chem.Bench 100nm/min

27EtchSifrombacksidethrough,TMAH TMAH,Chem.Bench ~1000nm/min

28 Cleavewaferintoindividualdevices Scribe

29 SolderwiresontocoillowTsolder,smallsolderingiron

30 Epoxycoilsinplace Epoxy 31 FrequencyandAmplituderesponse MEMILLab

MaskImages

Procurement/Payments

Mask1:PatternCantileversontopside.RemoveAuandCr,andetchoxideintocantilevershape.Cantileverdimensions3mmx3mm.Topsidepit4mmx6mm.

Mask2:Patternspacesformagnetsoncantilever.ElectroplatingputsmagnetsintoPRvacancies.Magnetdimensions50x50x25microns.Spacingbetweenmagnetsvaryperdevicefrom10micronsto40microns.

Mask3:Patternprotectivelayerformagnetstoremovetherestofthemetallizationlayer.PRisthenremovedandwaxplacedontoptoprotectthetopsideduringbacksideprocessing.

Mask4:Patternonbackside.EtchtheoxideandthenetchtheSiallthewaythroughtothecantilever.Backsidepit5mmx7mm.

ItemDesciption Supplier Cost65KDPIMylarMasks(4total) Photoplot/FinelineImaging $295.00

Includesshippingandfileformatting

Inductors(40total) CoilCraft Free30x1mHinductorsofdiffering

dimensions 10x6.8mHinductors

Wires,Solder+SolderingIron Mike Free

3"SiliconWafers(12total) Dr.Phaneuf Free500nmoxidegrown (Thankyou!)

FabLabhourlyuse FabLab $1,582.00

Estimated28.25hours $56perhour

EstimatedTotal $1,877.00

ManHoursworkingonPrototypeIndividual Hours

Paul 32Abbie 23.5Ashley 7Alex 3Karam 2TOTAL 67.5

Citations[1]Sheplak,M.,Seiner,J.,Breuer,K.,Schmidt,M.,“AMEMSMicrophoneforAeroacousticsMeasurements.”Dept.ofAerospaceEngineering,Mechanics,andEngineering,UniversityofFlorida.<http://microfluids.engin.brown.edu/Breuer_Papers/Conferences/AIAA99‐0606_Microphone.pdf>.[2]D.P.Arnold,T.Nishida,andM.Sheplak,“Piezoresistivemicrophoneforaeroacousticmeasurement,”Proceedingsof2001ASMEInternationalMechanicalEngineeringCongressandExposition,NewYorkMEMS‐23841(ASME,NewYork,NewYork,2001).http://iopscience.iop.org/0960‐1317/14/10/009/pdf/jmm4_10_009.pdf?ejredirect=migration.

[3]Li,Gang,YitshakZohar,andManWong."Piezoresistivemicrophonewithintegratedamplifierrealizedusingmetal‐inducedlaterallycrystallizedpolycrystallinesilicon."JournalofMicromechanicsandMicroengineering14(2004):1352‐1358.Web.5Apr.2010.<http://iopscience.iop.org/0960‐1317/14/10/009/pdf/jmm4_10_009.pdf?ejredirect=migration>.

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AcknowledgmentsWewouldfirstlyliketothankDrPhaneufforallhisadvisingandassistancethroughouttheproject. We would also like to thank the FabLab Staff for assisting us on our prototypefabricationandmakingsure thatwewereontherightpath. Inaddition,weappreciateallthe help from the other professors and companieswho gave us advice and assistedus infabricatingtheprototype.