MEMS Dynamic Microphone Design and FabricationENMA 490 Capstone Final Report, 10 May 2010Abbigale Boyle, Steven Crist, Mike Grapes, Karam Hijji, Alex Kao, Stephen Kitt, Paul Lambert, Christine Lao, Ashley Lidie, Marshall Schroederz-component of magnetic fluxrectangular magnet 50 m x 50 m x 25 m, 0.5 T

OutlineGeneral TheoryMotivationDesign ComponentsCoilMagnetsCantileverFabrication and PrototypeFuture WorkBudgetEthicsLessons

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Overview of Device Motivation and Design*

Dynamic Microphone Modelhttp://www.burninggrooves.com/images/12.gifBulk Dynamic Microphone DesignMEMS Dynamic Microphone DesignFaradays law:our goal

New ideaProof of concept Powerless signal generationOffers alternative to piezoelectric and electret designsMotivationGlobal market for MEMS microphonesIn 2006: $140 million, less than 12 companiesIn 2011: $922 million, number of companies projected to doubleAnnual average growth rate of 45.7%1.1 billion units projected in 2013!

Applications of MEMS Microphones

Market Projections and Statistics from www.mindbranch.com

Power Consumption in Common Alternative Technologies*

Power Consumption in Common Alternative Technologies*

Piezoelectric and Electret microphones No power required for signal generationPower Consumption in Common Alternative Technologies*

Design ComponentsBasic design:*

Magnetic Material SelectionUltimate design goal was to limit fabrication cost for industrial productionElectroplatingLow CostHigh Deposition RateSelectively pattern w/ photoresist

Arnold et al.*

BHmax (kJ/m3)Remanence (T)CoNiP1.3-1.8.06-.1CoNiMnP0.6-140.2-0.3CoPtP 52-690.3-1.0

Permanent Magnet DesignObjective:Fill the allotted space with a magnet arrangement which will produce maximum voltageVoltage produced given by Faradays Law

is the flux through the coilMaximize the flux density i.e. field produced by the magnetApproached this by asking some reasonable questions*

Permanent Magnet DesignQuestion #1: In or out of plane?Flux is ; take component perpendicular to A

Answer: Only out of plane will give desired flux change*supplemental material on magnet simulations

Permanent Magnet DesignQuestion #2: Is there an optimal aspect ratio?BHmax = maximum energy available to do work (pushing electrons, for example) For open circuit application, ideal to design geometry to operate at (BH)max (Arnold 2009)No magnet provides its full remanence unless in closed-circuit; instead, operates in second quadrantWhy?Self-demagnetization*

Permanent Magnet DesignAnswer: Yes; optimal aspect ratio is 2.83 to operate at (BH)max (see supplemental slides for full calculation)Question #3: plate or array?Answer: only array is feasibleArray: magnets 10 um x 10 um x 28 (30 um max thickness)Plate: single magnet 1.35 mm x 1.35 mm x 3.82 mm thickFinal result:CoNiMnPArray of 10 um x 10 um x 28 um 10 um spacing (ease of fabrication)Magnetized out of plane*

Design ComponentsBasic design:*

Modeling the Cantilever AnalyticallyObjective: Develop an analytical model for the oscillatory behavior of the cantilever using the classic differential equation for a damped harmonic oscillator

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Modeling the Cantilever Analytically*

Modeling the Cantilever Analytically*

Modeling the Cantilever AnalyticallyTwo contributions:1. Mechanical Slide Film: Damping generated by lateral motion of oscillator with respect to substrate (negligible with respect to other forms of damping)

Squeeze Film: Trapped air between oscillator and substrate exerts an opposing forceKim et al. 1999*

Modeling the Cantilever AnalyticallyDamping ConstantTwo contributions:1. Mechanical2. Electromagneticm is dependent onThe magnetic field produced by the magnetThe current density,

this meansZero current = zero magnetic dampingUse device as a voltage source (~ infinite resistance) to minimize EM damping*see supplemental slides for full calculation

Modeling the Cantilever Analytically*

Quality Factor and Signal-to-NoiseThe quality factor describes the energy dissipated in an oscillatory systemQ > = underdampedQ < = overdampedFor a mechanical system:

Signal to noise: ratio of signal amplitude to noise amplitude*

Thermal NoiseRandom thermal motion of atoms results in small displacements of cantileverElectrical NoiseJohnsonFlat frequency spectrumIrreducible Dependant on resistanceShotRandom fluctuation in currentCharges act independently of each other*

Solving the Differential EquationCantilever motion modeled as a sinusoidal driven harmonic oscillator:

Steady-state solution:

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What is an optimal frequency response?Looking for an even output across the range of human hearing (20 20,000 Hz)In our case, we want a constant voltage amplitudeWhat part of the cantilever response affects the voltage output?

If the flux varies relatively slowly over z (and it does), the voltage depends primarily on the velocityOptimize for flat velocity responsesee supplemental slides for full derivation*

Optimizing Frequency ResponseRange of human hearing: 20-20,000Hz3 types 0 at low end0 at high end0 within rangeDamping allows for flat velocity2,500 Hz chosen because of high signal/noise ratio and flat response *supplementary slides with S/N, A, and V

Signal/noise ratio at 3 moderate resonances2,500Hz10,000Hz15,000HzAvg. S/N16.68.26.6

Optimizing Frequency ResponseFor 0 = 2500Hz t = 3.06mmFor best response, L = W = 3mmGap height dictates damping constantTo flatten response, used gap height = 30 mmResults in a damping of = 2.35x10-2 kg/s *

Final ParametersCantileverL = W = 3mmt = 3.06 umkeff = 0.468 N/mmeff = 7.5x10-8 kg = 2.35x10-2 kg/s Q = 7.93x10-3

Magnet array9800 magnets140 magnets x 70 magnets10 m x 10 m x 28 m*

Output Voltagez(t) = cantilever motionN = equivalent # of coils = 10,453Need to show:Flat responseSufficient signalGood translation of volume, frequencyVoltage output from cantilever is:*

Output Voltage (2)Volume ReplicationFrequency Replication*

Fabrication*

Fabrication Cont.Crystalbond two wafers together on their patterned sidesPattern oxide on bottom, and then etch through SiAttach Coil

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Prototype ProcessingObstaclesThick Photoresist:Under developedOver developedSkipped:Magnet array protection during SiO2/Si etchesGold removalSi etchingCrystalbond adhesion incompleteDoubled-sided etching/sliding wafersPost-etch cantilever behaviorEtching awayCurling upSolutionsPatterningSU-8Better alignerBetter masks (chrome on glass)Si etchingDRIE (deep reactive ion etching)*more picturesstress

Testing4 cantilevers testedElectrically connected to oscilloscopeUnsuccessfully looked for measurable signal produced by soundWhat could have gone wrongSolder: high resistance or incomplete circuitOutput too lowDeflection too small -> cantilevers too stiff -> Si layerMagnets removed during handlingGap height larger than planned *

Future TestingFrequency responseSupply sound of constant volume, varied frequency (20-20,000 Hz), look for flatness of responseAmplitude responseConstant frequency, varied volume (30-80 dB? Depending on application), look for response proportional to pressure wave amplitudeOff-axis responseMeasure signal produced for sound at angles to cantileverImpulse responseMeasures microphone response to brief sounds, necessary when observing brief or rapidly-occuring sounds*

Prototype: Budget and Time*

Item DesciptionSupplierCost65K DPI Mylar Masks (4 total)Photoplot/$295.00 Includes shipping and file formattingFineline ImagingInductors (40 total)CoilCraftFree30 x 1mH inductors of differing dimensions10 x 6.8mH inductorsWires, Solder + Soldering IronMikeFree3" Silicon Wafers (12 total)Dr. PhaneufFree500nm oxide grown(Thank you!)Fab Lab hourly useFab Lab$1,582.00 Estimated 28.25 hours$56 per hourEstimated Total$1,877.00

IndividualHoursPaul32Abbie23.5Ashley7Alex3Karam2TOTAL67.5

Ethical Issues in Scaling UpFabrication:Safety for WorkersWaste in wet processingActual fabricationDeveloping working processTransition to mass productionConsumer:Not enough magnetic material to be harmfulProtective packaging removes health riskDisposal Small waste concentrations*

What Have We Learned?Prepare for the worst! Nothing goes as exactly plannedProblem solving skills Teamwork is necessary for successPracticality of microprocessingSometimes the 3rd time is still not the charmHigher understanding of spring-mass systemUtilize unfamiliar software packages

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AcknowledgementsDr. PhaneufDr. BriberDr. WuttigDr. AnkemJohn AbrahamsTom LoughranDon DevoeCoilcraftFineline Imaging*

Questions?*

Supplemental Slides*

Intellectual Merit Demonstrate a functional MEMS magnetic sensor Model mechanical behavior of millimeter scale cantilever supporting a substantial mass Investigate magnetic induction at a small scale Optimize magnetic properties of small magnet arrays Apply electroplating to large aspect ratios

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Design Evolution1st Generation: Drumhead OscillatorBulk micromachiningSurface micromachiningPlanar

Abandoned due to insufficient deflection under acoustic loading.

2nd Generation: Air-bridge/Cantilever OscillatorSingle MagnetDual MagnetMicro-magnet Array*

Bulk MicromachiningPrimary Challenge: Electroplating the magnet beneath the diaphragm

Attributes for Prototype: Releasing the diaphragm is a simple processSi*

Surface MicromachiningPrimary Challenge: Fabricating the diaphragm and acoustic cavity above the magnet

Attributes for Prototype: Electroplating magnet can occur early in the process flowSiO2*

PlanarPrimary Challenge: Interfacial stresses between magnet, adhesion layer, and diaphragm may cause delamination under acoustic loading.

Attributes for Prototype: Arrays of smaller magnets may reduce interfacial stresses

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Single Magnet CantileverMagnetCoilSiSiO2Not drawn to scalePrimary Challenge: Positioning the magnet to maximize the flux change under acoustic loading.Attributes for Prototype: Electroplating the magnet on the cantilever simplifies the fabrication process*

Dual-Magnet with Coil Cantilever Primary Challenge: Flux change is not directed through coil (no EM induction)

Attributes for Prototype: Magnetic field behavior of multiple magnets*

PrototypeCurrent Design:-SiO2 cantilever-Different Magnet SpacingArrays of magnets with spacing of 0 m (monolithic plate), 10, 20, 30, and 40 m-Back etched acoustic cavity-Prefabricated surface inductor (6800 H Coilcraft)

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Diaphragm vs. CantileverDiaphragm

Cantilever

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Derivation of Load-Line SlopeThe constitutive relation for a permanent magnet is

In open-circuit conditions, a permanent magnet generates a self-demagnetizing field Hd which is proportional to the magnetization Bi

If we take H = Hd,

This B/H is the slope of the load line which designates the magnets operating point.(1)(2)(3)*

Optimal B/H for CoNiMnPWe have:Need an expression for N*

N for Rectangular Prism

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Plotting thisAfter all that, we get something thats essentially linear!

AR = 2.83*

Simulating Rectangular Permanent MagnetsExpressions constructed by considering molecular surface currents + Biot-Savart law

Reference: G.Xiao-fan, Y.Yong, and Z.Xiao-jing, Analytic expression of magnetic field distribution of rectangular permanent magnets, Applied Mathematics and Mechanics, vol.25, pp.297306, Mar. 2004.*

Simulating Arrays of Identical MagnetsSimple addition between magnetsWrite using basic functions w/ shifted coordinates

This is very inefficient to calculate for large arraysActual simulations used stamping method*

Calculating Effective MassD= linear densityL= length

dm=Ddx D*L= massmd mdmcMmag*

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Two ScenariosTypical Cantilever:

mc- concentrated mass (tip mass)md- distributed mass (cantilever mass)Sarid, Dror. Scanning Force Microscopy. Revised ed. New York: Oxford, 1994. 13-21. PrintOur System Total Effective Mass: Plate case

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Magnetic Damping Parameter (1)Force exerted on a loop of wire by a magnet:

I = element of current in the loopdL = infinitesimal arc length of the loopJ = current densitydV = infinitesimally small volume of the loopThe current density can be written as:

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Magnetic Damping Parameter (2)Combining the expression for current density into the force expression:

Assuming a cylindrical geometry for simplicity:

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Magnetic Damping Parameter (3)Setting up the integral to obtain the force:

The magnetic damping parameter is found by:

F is dependent on the magnetic field of the magnet*

Magnetic Damping Parameter (4)F is dependent upon the current density,

Zero Current = Zero Magnetic Damping

Treat device like a voltage source and minimize the current flowing through to eliminate magnetic damping*

Experimental Determination of Interfacial StressFabricate cantilevers with magnetic films of different thicknesses and areasDetermine cantilever length change using optical microscopyDeflection results in a normalized length change, lfNumerically solve for radius of curvatureCalculate corresponding stress

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Static StressTo determine if cantilever can support much thicker array of magnetsFor a rectangular beam loaded at one end:max = 3dEt/(2l2)D = max. deflection, E = Youngs mod, t = thickness, l = lengthmax = 52.5 kPa, well within tensile strength of SiO2*

Signal to noise vs frequency*

Amplitude + Velocity vs frequency*

Damping effectsLow damping: 30mm, Moderate damping: 150mm, High damping 300mm B=2.35x10-2 kg/sB=1.88x10-4 kg/sB=2.35x10-5 kg/s*

Structural SimulationsCOMSOL and analytical simulations agreeFor varying sound levelSomewhat for varying lengthIssues with element sizePossible solutionsFurther simulationsFrequency responseAcoustic analysisRealistic DampingCorrelation with magnetics*

Silicon Dioxide:L= 1mmt= .5umE=70 Gpav=.17

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Sound LevelPressure (Pa)Comsol Defelection(m)Analytical Deflecton (m)% Difference202.00E-042.71E-082.84E-084.75904059253.55E-044.70E-085.05E-087.414680851306.31E-047.65E-088.98E-0817.3545098351.12E-031.53E-071.60E-074.344444444402.00E-032.53E-072.84E-0712.21225296453.55E-034.75E-075.05E-076.284506.31E-031.00E-068.98E-07-10.2238551.12E-021.66E-061.60E-06-3.827108434602.00E-023.05E-062.84E-06-6.919016393653.55E-025.26E-065.05E-06-4.021102662706.31E-029.62E-068.98E-06-6.677546778751.12E-011.71E-051.60E-05-6.639181287802.00E-013.02E-052.84E-05-5.994370861

COMSOL Simulations - Deflection SimulationsSource of systematic error: width and spring constantUsed extrapolation to estimate deflection values for 3 mm geometry (50dB) 77mm agrees reasonably with analytical value of 87mm- better than the COMSOL value of 780mm*

COMSOL Simulations Frequency ResponseFrequency response calculates the steady-state response from harmonic loadsIn our case, it measures the max deflection at each frequencyThese deflections are arbitrary - only relative to each otherGeometry: 3mmx3mmx.5mm thick Array of 496 Magnets: 50mmx50mmx20mmInputsMass of each magnet: 4x10-10 kgMass of cantilever: 1x10-8 kgSound Pressure at 50dB: 6.3x10-3 Pa*

COMSOL Simulations - Frequency Response3mmx3mmx.5mm cantilever, 496 magnets at 50x50x20mm, real mass and 50dB sound level*

Near 0HzResonance near 300HzVery hard to visualize this on the full spectrum graph

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Appendix for Abbies slideUnderdevelopedOverdevelopedUnder/Overdeveloped*

Appendix for Abbies slideTMAHThe Good (1m) The Bad(0.5 m) The Ugly (1 m)*

Appendix for Abbies slide

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Neq: the number of coils of wire needed to produce the same inductance as a magnetic core inductorInductance of a cylindrical coil wrapped around a magnetic core:

Solving this equation for N and setting =1 yields NeqEquivalent Number of Coils (1)*

Equivalent Number of Coils (2)Have values for everything except A and lSolve for the ratio A/l

Then solve for Neq*

Calculating Induced VoltageFaradays Law of Induction

N is the equivalent number of coils: 10,453Flux:Average over A:Time dep.:Derivative:This is not quite the full story, because entire cantilever does not move at v(t)

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Calculating Induced VoltageCalculate an average velocity to account for this; velocity at distance x along the cantilever is

Average velocity is given by

Integrating

So we need an extra ; adding this in,*

Frequency Response of Commercial (Audio-Technica) MicrophonesCondenser (AT4049b)Range: 20-20,000Hz

Ribbon (AT4080)Range: 20-18,000Hzwww.audio-technica.com*

Applications: Hearing AidTypically use electret condenser microphonesLinear response from 50-6000Hz, new directional microphones from 6000-8000HzMicrophone size varies4mm x 3mm x 1 mm5.47mm x 5.47mm x 4.62Our microphone: 8mm x 5mm x 4.2mmBy changing coil, could achieve 5mm x 5mm x 3mm

www.bradingrao.com*

PackagingGlob Top on backside to protect coil (Dymax 9001-E-v3.7)Machine cone-shaped holes in thin polymer sheet to attach on top

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References "Body, Human." The New Book of Knowledge. New York: Grolier, 1967: 285. Borwick, John. Microphones: Technology and Technique. London: Focal, 1990. Print.

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SourcesPedersen et al.http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6THG-3VCTDGR-T&_user=961305&_coverDate=09%2F15%2F1998&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1276503526&_rerunOrigin=google&_acct=C000049425&_version=1&_urlVersion=0&_userid=961305&md5=0050f247f9f563e4056f98705a48bcf4Sheplak et al.http://microfluids.engin.brown.edu/Breuer_Papers/Conferences/AIAA99-0606_Microphone.pdfArnold et al.http://www.img.ufl.edu/publications/A%20Piezoresistive%20Microphone%20for%20Aeroacoustic%20Measurements_Conference_November2001.pdfLee et al.http://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1433&context=nanopub

MEMS Microphones: A Global Technology, Industry and Market Analysishttp://www.mindbranch.com/MEMS-MICROPHONES-Global-R3450-6/

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*Marshall*Mike*Mike*Mike*Mike*Mike*Mike*http://hypertextbook.com/facts/2003/ChrisDAmbrose.shtml- for human hearing rangeMicrophone textbook- types of microphones*For CoNiMnP, (B/H)max = ?N = expressionHow to solve?**Solution to B/H = 5.77 is aspect ratio of 2.83*Steve C

*Steve C*Steve K

*Steve K

*Steve K

*Steve K

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