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MEMS Dynamic Microphone Design and Fabrication Abbigale Boyle, Steven Crist, Mike Grapes, Karam Hijji, MEMS Dynamic Microphone Design and Fabrication Abbigale Boyle, Steven Crist, Mike Grapes, Karam Hijji, Alex Kao, Stephen Kitt, Paul Lambert, Christine Lao, Ashley Lidie, Marshall Schroeder ENMA 490 Capstone Final Report, 10 May 2010 z-component of magnetic flux rectangular magnet 50 μ m x 25 μ m, 0. 5 T

2 Outline • General Theory • Motivation • Design Components – Coil – Magnets 2 Outline • General Theory • Motivation • Design Components – Coil – Magnets – Cantilever • • • Fabrication and Prototype Future Work Budget Ethics Lessons

3 Overview of Device Motivation and Design 3 Overview of Device Motivation and Design

Dynamic Microphone Model Faraday’s law: Bulk Dynamic Microphone Design our goal MEMS Dynamic Microphone Dynamic Microphone Model Faraday’s law: Bulk Dynamic Microphone Design our goal MEMS Dynamic Microphone Design Magnet(s) http: //www. burninggrooves. com/images/12. gif Prefabricated Inductor Coil Cantilever Wires carrying AC signal

Motivation Global market for MEMS microphones • In 2006: $140 million, less than 12 Motivation Global market for MEMS microphones • In 2006: $140 million, less than 12 companies • In 2011: $922 million, number of companies projected to double • Annual average growth rate of 45. 7% • 1. 1 billion units projected in 2013! Applications of MEMS Microphones Graph from www. isupply. com • New idea • Proof of concept • Powerless signal generation • Offers alternative to piezoelectric and electret designs Market Projections and Statistics from www. mindbranch. com

Power Consumption in Common Alternative Technologies Piezoresisitive Microphone Mode of Power Consumption: Excitation voltage Power Consumption in Common Alternative Technologies Piezoresisitive Microphone Mode of Power Consumption: Excitation voltage to measure resistance change. -Sheplak et al. Excitation Voltage: 10 V Power Consumption: 0. 7 m. W -Arnold et al. Excitation Voltage: 3 V Power Consumption: 15 m. W +/- 2. 5 m. W http: //www. acoustics. org/press/137 th/pires 1. jpg 6

Power Consumption in Common Alternative Technologies Condenser Microphone Mode of Power Consumption: Required bias Power Consumption in Common Alternative Technologies Condenser Microphone Mode of Power Consumption: Required bias voltage between plates Piezoresisitive Microphone Mode of Power Consumption: Excitation voltage to measure resistance change. -Pedersen et al. -Sheplak et al. Bias Voltage: 4 V Excitation Voltage: 10 V Capacitance: 10. 1 p. F Power Consumption: 0. 7 m. W Power Consumption: 1. 96 m. W -Arnold et al. Excitation Voltage: 3 V Power Consumption: 15 m. W +/- 2. 5 m. W http: //www. acoustics. org/press/137 th/pires 1. jpg http: //www. totalvenue. com. au/articles/microphones/mic-condenser. gif 7

Power Consumption in Common Alternative Technologies Piezoelectric and Electret microphones Condenser Microphone No power Power Consumption in Common Alternative Technologies Piezoelectric and Electret microphones Condenser Microphone No power required for signal generation Mode of Power Consumption: Required bias voltage between plates Piezoelectric Microphone Electret Microphone -Pedersen et al. Bias Voltage: 4 V Capacitance: 10. 1 p. F Power Consumption: 1. 96 m. W http: //www. acoustics. org/press/137 th/pirel 1. jpg http: //hyperphysics. phy-astr. gsu. edu/hbase/audio/imgaud/etret. gif http: //www. totalvenue. com. au/articles/microphones/mic-condenser. gif 8

9 Basic design: Design Components What? • A pre-fabricated surface-mount inductor Permanent magnet array 9 Basic design: Design Components What? • A pre-fabricated surface-mount inductor Permanent magnet array considerations: (Coilcraft DO 1607 B, 6. 8 m. H) • Magnet material? Why? • Magnetization direction? • Compensate for small flux with large coil Magnet dimensions? • Why make it yourself (hard) when other people already do it?

10 Magnetic Material Selection • Ultimate design goal was to limit fabrication cost for 10 Magnetic Material Selection • Ultimate design goal was to limit fabrication cost for industrial production • Electroplating – Low Cost – High Deposition Rate – Selectively pattern w/ photoresist BHmax (k. J/m 3) Remanence (T) Co. Ni. P 1. 3 -1. 8 . 06 -. 1 Co. Ni. Mn. P 0. 6 -14 0. 2 -0. 3 Co. Pt. P 52 -69 0. 3 -1. 0 Arnold et al.

11 Permanent Magnet Design • Objective: – Fill the allotted space with a magnet 11 Permanent Magnet Design • Objective: – Fill the allotted space with a magnet arrangement which will produce maximum voltage • Voltage produced given by Faraday’s Law • Φ is the flux through the coil – Maximize the “flux density” i. e. field produced by the magnet • Approached this by asking some reasonable questions…

Permanent Magnet Design • Question #1: In or out of plane? supplemental material on Permanent Magnet Design • Question #1: In or out of plane? supplemental material on magnet simulations – Flux is ; take component perpendicular to A In-plane magnet Out-of-plane magnet • Answer: Only out of plane will give desired flux change 12

Permanent Magnet Design • Question #2: Is there an optimal aspect ratio? • No Permanent Magnet Design • Question #2: Is there an optimal aspect ratio? • No magnet provides its full remanence unless in closed-circuit; instead, operates in second slope = (B/H) quadrant slope = B/H = f(N)? partial demagnetization (0 < N < 1), slope = ∞: no • Why? some remanence available 13 max demagnetization (N = 0), full remanence available – Self-demagnetization • For open circuit application, ideal to design geometry to operate at (BH)max (Arnold 2009) slope = 0: complete demagnetization (N = 1), no remanence available BHmax = maximum energy available to do work (pushing electrons, for example)

14 Permanent Magnet Design • Answer: Yes; optimal aspect ratio is 2. 83 to 14 Permanent Magnet Design • Answer: 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 feasible – Array: magnets 10 um x 28 (30 um max thickness) – Plate: single magnet 1. 35 mm x 3. 82 mm thick • Final result: – Co. Ni. Mn. P – Array of 10 um x 28 um • 10 um spacing (ease of fabrication) – Magnetized out of plane

15 Design Components Basic design: Cantilever oscillation determines frequency Permanent magnet array considerations: response 15 Design Components Basic design: Cantilever oscillation determines frequency Permanent magnet array considerations: response of microphone • Magnet material? • Material? Magnetization direction? • Dimensions? Magnet dimensions? Optimized using anlytical simulation

16 Objective: Develop an analytical model for the oscillatory behavior of the cantilever using 16 Objective: Develop an analytical model for the oscillatory behavior of the cantilever using the classic differential equation for a damped harmonic oscillator Modeling the Cantilever Analytically

17 Modeling the Cantilever Analytically Forcing Term In our application, the force is due 17 Modeling the Cantilever Analytically Forcing Term In our application, the force is due to a pressure wave: For sound:

18 Modeling the Cantilever Analytically Effective Mass • The whole cantilever does not move 18 Modeling the Cantilever Analytically Effective Mass • The whole cantilever does not move at the same velocity • Effective mass = mass weighted by velocity relative to max • Integrals give: Our System Total Effective Mass: Plate case

19 Modeling the Cantilever Analytically Damping Constant Two contributions: 1. Mechanical • Slide Film: 19 Modeling the Cantilever Analytically Damping Constant Two 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 force Kim et al. 1999

20 Modeling the Cantilever Analytically Damping Constant Two contributions: 1. Mechanical 2. Electromagnetic • 20 Modeling the Cantilever Analytically Damping Constant Two contributions: 1. Mechanical 2. Electromagnetic • γm is dependent on • The magnetic field produced by the magnet • The current density, σ see supplemental slides for full calculation this means… • Zero current = zero magnetic damping • Use device as a voltage source (~ infinite resistance) to minimize EM damping

21 Modeling the Cantilever Analytically Spring Constant ; Magnets are ~10 x as thick 21 Modeling the Cantilever Analytically Spring Constant ; Magnets are ~10 x as thick as the cantilever, so k is ~1000 x larger for magnets Springs in Series:

22 Quality Factor and Signal-to-Noise • The quality factor describes the energy dissipated in 22 Quality Factor and Signal-to-Noise • The quality factor describes the energy dissipated in an oscillatory system – Q > ½ = underdamped – Q < ½ = overdamped • For a mechanical system: • Signal to noise: ratio of signal amplitude to noise amplitude

23 Thermal Noise • Random thermal motion of atoms results in small displacements of 23 Thermal Noise • Random thermal motion of atoms results in small displacements of cantilever Electrical Noise • Johnson – Flat frequency spectrum – Irreducible – Dependant on resistance • Shot – Random fluctuation in current – Charges act independently of each other

24 Solving the Differential Equation • Cantilever motion modeled as a sinusoidal driven harmonic 24 Solving the Differential Equation • Cantilever motion modeled as a sinusoidal driven harmonic oscillator: • Steady-state solution:

25 What is an optimal frequency response? • Looking for an even output across 25 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 amplitude • What part of the cantilever response affects the voltage output? see supplemental slides for full derivation • If the flux varies relatively slowly over z (and it does), the voltage depends primarily on the velocity • Optimize for flat velocity response source: www. audio-technica. com

26 Optimizing Frequency Response • Range of human hearing: 20 -20, 000 Hz • 26 Optimizing Frequency Response • Range of human hearing: 20 -20, 000 Hz • 3 types – ω0 at low end – ω0 at high end – ω0 within range • Damping allows for flat velocity • 2, 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 resonances 2, 500 Hz Avg. S/N 10, 000 Hz 15, 000 Hz 16. 6 8. 2 6. 6

27 Optimizing Frequency Response • For ω0 = 2500 Hz t = 3. 06 27 Optimizing Frequency Response • For ω0 = 2500 Hz t = 3. 06 mm • For best response, L = W = 3 mm • Gap height dictates damping constant – To flatten response, used gap height = 30 mm • Results in a damping of γ = 2. 35 x 10 -2 kg/s

28 Final Parameters • Cantilever – – – L = W = 3 mm 28 Final Parameters • Cantilever – – – L = W = 3 mm t = 3. 06 um keff = 0. 468 N/m meff = 7. 5 x 10 -8 kg γ = 2. 35 x 10 -2 kg/s Q = 7. 93 x 10 -3 • Magnet array – 9800 magnets – 140 magnets x 70 magnets – 10 μm x 28 μm

29 Output Voltage output from cantilever is: • z(t) = cantilever motion • N 29 Output Voltage output from cantilever is: • z(t) = cantilever motion • N = equivalent # of coils = 10, 453 • Need to show: – Flat response – Sufficient signal – Good translation of volume, frequency

30 Output Voltage (2) • Volume Replication • Frequency Replication 30 Output Voltage (2) • Volume Replication • Frequency Replication

31 Fabrication 1. 2. 3. 4. 5. Grow 3 µm thick oxide and use 31 Fabrication 1. 2. 3. 4. 5. Grow 3 µm thick oxide and use E-beam deposition to deposit Cr and Au Use mask to pattern photoresist, then etch the Cr, Au, and oxide to create cantilever shape Pattern array for magnets in photoresist Electroplate magnets and magnetize Pattern photoresist to protect magnets and remove excess metal layers

32 Fabrication Cont. 6. 7. 8. Crystalbond™ two wafers together on their patterned sides 32 Fabrication Cont. 6. 7. 8. Crystalbond™ two wafers together on their patterned sides Pattern oxide on bottom, and then etch through Si Attach Coil

33 Prototype Processing Obstacles • Thick Photoresist: – Under developed – Over developed • 33 Prototype Processing Obstacles • Thick Photoresist: – Under developed – Over developed • Skipped: – Magnet array protection during Si. O 2/Si etches – Gold removal • Patterning – Crystalbond™ adhesion incomplete – Doubled-sided etching/sliding wafers Solutions • Si etching • SU-8 • Better aligner • Better masks (chrome on glass) • DRIE (deep reactive ion etching) • Post-etch cantilever behavior – Etching away – Curling up more pictures stress

34 Testing • 4 cantilevers tested • Electrically connected to oscilloscope • Unsuccessfully looked 34 Testing • 4 cantilevers tested • Electrically connected to oscilloscope • Unsuccessfully looked for measurable signal produced by sound • What could have gone wrong – Solder: high resistance or incomplete circuit – Output too low • Deflection too small -> cantilevers too stiff -> Si layer • Magnets removed during handling – Gap height larger than planned

35 Future Testing • Frequency response – Supply sound of constant volume, varied frequency 35 Future Testing • Frequency response – Supply sound of constant volume, varied frequency (2020, 000 Hz), look for flatness of response • Amplitude response – Constant frequency, varied volume (30 -80 d. B? Depending on application), look for response proportional to pressure wave amplitude • Off-axis response – Measure signal produced for sound at angles to cantilever • Impulse response – Measures microphone response to brief sounds, necessary when observing brief or rapidly-occuring sounds

36 Prototype: Budget and Time Item Desciption 65 K DPI Mylar Masks (4 total) 36 Prototype: Budget and Time Item Desciption 65 K DPI Mylar Masks (4 total) Includes shipping and file formatting Inductors (40 total) 30 x 1 m. H inductors of differing dimensions 10 x 6. 8 m. H inductors Wires, Solder + Soldering Iron 3" Silicon Wafers (12 total) 500 nm oxide grown Fab Lab hourly use Estimated 28. 25 hours $56 per hour Estimated Total Supplier Photoplot/ Fineline Imaging Coil. Craft Cost $295. 00 Free Mike Dr. Phaneuf (Thank you!) Fab Lab Free $1, 582. 00 $1, 877. 00 Individual Paul Abbie Ashley Alex Karam TOTAL Hours 32 23. 5 7 3 2 67. 5

37 Ethical Issues in Scaling Up • Fabrication: – Safety for Workers – Waste 37 Ethical Issues in Scaling Up • Fabrication: – Safety for Workers – Waste in wet processing • Actual fabrication • Developing working process • Transition to mass production • Consumer: – Not enough magnetic material to be harmful – Protective packaging removes health risk • Disposal – Small waste concentrations

38 What Have We Learned? • Prepare for the worst! Nothing goes as exactly 38 What Have We Learned? • Prepare for the worst! Nothing goes as exactly planned • Problem solving skills • Teamwork is necessary for success • Practicality of microprocessing • Sometimes the 3 rd time is still not the charm • Higher understanding of spring-mass system • Utilize unfamiliar software packages

Acknowledgements • • • Dr. Phaneuf Dr. Briber Dr. Wuttig Dr. Ankem John Abrahams Acknowledgements • • • Dr. Phaneuf Dr. Briber Dr. Wuttig Dr. Ankem John Abrahams Tom Loughran Don Devoe Coilcraft Fineline Imaging 39

40 Questions? 40 Questions?

41 Supplemental Slides 41 Supplemental Slides

42 Intellectual Merit • Demonstrate a functional MEMS magnetic sensor • Model mechanical behavior 42 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

43 Design Evolution 1 st Generation: Drumhead Oscillator • Bulk micromachining • Surface micromachining 43 Design Evolution 1 st Generation: Drumhead Oscillator • Bulk micromachining • Surface micromachining • Planar Abandoned due to insufficient deflection under acoustic loading. 2 nd Generation: Air-bridge/Cantilever Oscillator • Single Magnet • Dual Magnet • Micro-magnet Array

44 Bulk Micromachining Si Primary Challenge: Electroplating the magnet beneath the diaphragm Attributes for 44 Bulk Micromachining Si Primary Challenge: Electroplating the magnet beneath the diaphragm Attributes for Prototype: Releasing the diaphragm is a simple process

45 Surface Micromachining Si. O 2 Primary Challenge: Fabricating the diaphragm and acoustic cavity 45 Surface Micromachining Si. O 2 Primary Challenge: Fabricating the diaphragm and acoustic cavity above the magnet Attributes for Prototype: Electroplating magnet can occur early in the process flow

46 Planar Primary Challenge: Interfacial stresses between magnet, adhesion layer, and diaphragm may cause 46 Planar Primary 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

47 Single Magnet Cantilever Coil Magnet Si. O 2 Si Not drawn to scale 47 Single Magnet Cantilever Coil Magnet Si. O 2 Si Not drawn to scale Primary 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 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 48

49 Prototype Current Design: -Si. O 2 cantilever -Different Magnet Spacing Arrays of magnets 49 Prototype Current Design: -Si. O 2 cantilever -Different Magnet Spacing Arrays of magnets with spacing of 0 μm (monolithic plate), 10, 20, 30, and 40 μm -Back etched acoustic cavity -Prefabricated surface inductor (6800 μH Coilcraft)

Diaphragm vs. Cantilever • Diaphragm • Cantilever 50 Diaphragm vs. Cantilever • Diaphragm • Cantilever 50

51 Derivation of Load-Line Slope The constitutive relation for a permanent magnet is (1) 51 Derivation of Load-Line Slope The constitutive relation for a permanent magnet is (1) In open-circuit conditions, a permanent magnet generates a selfdemagnetizing field Hd which is proportional to the magnetization Bi (2) If we take H = Hd, (3) This B/H is the slope of the load line which designates the magnet’s operating point.

52 Optimal B/H for Co. Ni. Mn. P We have: Need an expression for 52 Optimal B/H for Co. Ni. Mn. P We have: Need an expression for N

53 N for Rectangular Prism For a rectangular prism with dimensions 2 a x 53 N for Rectangular Prism For a rectangular prism with dimensions 2 a x 2 b x 2 c and magnetization in the c direction, the demagnetization factor can be written (Aharoni 1998) This has three variables, but we can reduce it to two by rewriting in terms of aspect ratios: Finally, if we assume a square crosssection, we can reduce to a single variable:

54 Plotting this… After all that, we get something that’s essentially linear! AR = 54 Plotting this… After all that, we get something that’s essentially linear! AR = 2. 83

55 Simulating Rectangular Permanent Magnets • Expressions constructed by considering molecular surface currents + 55 Simulating Rectangular Permanent Magnets • Expressions 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. 297– 306, Mar. 2004.

56 Simulating Arrays of Identical Magnets • Simple addition between magnets – Write using 56 Simulating Arrays of Identical Magnets • Simple addition between magnets – Write using basic functions w/ shifted coordinates • This is very inefficient to calculate for large arrays • Actual simulations used “stamping” method

57 Calculating Effective Mass md md D= linear density L= length dm=Ddx D*L= mass 57 Calculating Effective Mass md md D= linear density L= length dm=Ddx D*L= mass mc Mmag

58 58

59 Two Scenarios • Typical Cantilever: mc- concentrated mass (tip mass) md- distributed mass 59 Two Scenarios • Typical Cantilever: mc- concentrated mass (tip mass) md- distributed mass (cantilever mass) Sarid, Dror. Scanning Force Microscopy. Revised ed. New York: Oxford, 1994. 13 -21. Print • Our Cantilever: Cantilever length, X (limits 0 L Our Magnet Portion (limits L/2 L) Our System Total Effective Mass: Plate case

60 Magnetic Damping Parameter (1) • Force exerted on a loop of wire by 60 Magnetic Damping Parameter (1) • Force exerted on a loop of wire by a magnet: – – I = element of current in the loop d. L = infinitesimal arc length of the loop J = current density d. V = infinitesimally small volume of the loop • The current density can be written as:

61 Magnetic Damping Parameter (2) • Combining the expression for current density into the 61 Magnetic Damping Parameter (2) • Combining the expression for current density into the force expression: • Assuming a cylindrical geometry for simplicity:

62 Magnetic Damping Parameter (3) • Setting up the integral to obtain the force: 62 Magnetic Damping Parameter (3) • Setting up the integral to obtain the force: • The magnetic damping parameter is found by: • βF is dependent on the magnetic field of the magnet

63 Magnetic Damping Parameter (4) • βF is dependent upon the current density, σ 63 Magnetic Damping Parameter (4) • βF is dependent upon the current density, σ • Zero Current = Zero Magnetic Damping • Treat device like a voltage source and minimize the current flowing through to eliminate magnetic damping

64 Experimental Determination of Interfacial Stress • Fabricate cantilevers with magnetic films of different 64 Experimental Determination of Interfacial Stress • Fabricate cantilevers with magnetic films of different thicknesses and areas • Determine cantilever length change using optical microscopy – Deflection results in a normalized length change, lf • Numerically solve for radius of curvature • Calculate corresponding stress

65 Static Stress • To determine if cantilever can support much thicker array of 65 Static Stress • To determine if cantilever can support much thicker array of magnets • For a rectangular beam loaded at one end: – σmax = 3 d. Et/(2 l 2) – D = max. deflection, E = Young’s mod, t = thickness, l = length – σmax = 52. 5 k. Pa, well within tensile strength of Si. O 2

66 Signal to noise vs frequency 66 Signal to noise vs frequency

67 Amplitude + Velocity vs frequency Amplitude and Velocity 3 E-06 1. 00 E-07 67 Amplitude + Velocity vs frequency Amplitude and Velocity 3 E-06 1. 00 E-07 2. 5 E-06 8. 00 E-08 Amplitude (m) 1. 20 E-07 2 E-06 6. 00 E-08 1. 5 E-06 Amplitude Velocity 4. 00 E-08 1 E-06 2. 00 E-08 5 E-07 0. 00 E+00 0 5000 10000 15000 20000 25000 Frequency (Hz) 30000 35000 0 40000

68 Damping effects Low damping: 30 mm, Moderate damping: 150 mm, High damping 300 68 Damping effects Low damping: 30 mm, Moderate damping: 150 mm, High damping 300 mm B=2. 35 x 10 -2 kg/s B=1. 88 x 10 -4 kg/s B=2. 35 x 10 -5 kg/s

69 Structural Simulations • COMSOL and analytical simulations agree – For varying sound level 69 Structural Simulations • COMSOL and analytical simulations agree – For varying sound level – Somewhat for varying length • Issues with element size • Possible solutions • Further simulations – – Frequency response Acoustic analysis Realistic Damping Correlation with magnetics

70 Deflection vs Sound Level 3. 50 E-05 3. 00 E-05 Deflection (m) 2. 70 Deflection vs Sound Level 3. 50 E-05 3. 00 E-05 Deflection (m) 2. 50 E-05 2. 00 E-05 Comsol Deflection 1. 50 E-05 Analytical Deflection 1. 00 E-05 5. 00 E-06 0. 00 E+00 0 20 Sound Level 40 60 Sound Level (d. B) Pressure (Pa) 20 25 30 35 40 45 50 55 60 65 70 75 80 2. 00 E-04 3. 55 E-04 6. 31 E-04 1. 12 E-03 2. 00 E-03 3. 55 E-03 6. 31 E-03 1. 12 E-02 2. 00 E-02 3. 55 E-02 6. 31 E-02 1. 12 E-01 2. 00 E-01 80 100 Silicon Dioxide: L= 1 mm t=. 5 um E=70 Gpa v=. 17 Comsol Defelection(m) Analytical Deflecton (m) % Difference 2. 71 E-08 2. 84 E-08 4. 75904059 4. 70 E-08 5. 05 E-08 7. 414680851 7. 65 E-08 8. 98 E-08 17. 3545098 1. 53 E-07 1. 60 E-07 4. 34444 2. 53 E-07 2. 84 E-07 12. 21225296 4. 75 E-07 5. 05 E-07 6. 284 1. 00 E-06 8. 98 E-07 -10. 2238 1. 66 E-06 1. 60 E-06 -3. 827108434 3. 05 E-06 2. 84 E-06 -6. 919016393 5. 26 E-06 5. 05 E-06 -4. 021102662 9. 62 E-06 8. 98 E-06 -6. 677546778 1. 71 E-05 1. 60 E-05 -6. 639181287 3. 02 E-05 2. 84 E-05 -5. 994370861

71 COMSOL Simulations - Deflection Simulations Deflection vs Sound Pressure from COMSOL (numerical) and 71 COMSOL Simulations - Deflection Simulations Deflection vs Sound Pressure from COMSOL (numerical) and Calculations (analytical) 3. 50 E-05 3. 00 E-05 2. 50 E-05 Deflection (m) • Source of systematic error: width and spring constant • Used extrapolation to estimate deflection values for 3 mm geometry (50 d. B) – 77 mm agrees reasonably with analytical value of 87 mm- better than the COMSOL value of 780 mm 2. 00 E-05 Numerical 1. 50 E-05 Analytical 1. 00 E-05 5. 00 E-06 0. 00 E+00 0 20 40 60 Sound Level (d. B) 80 100

72 COMSOL Simulations – Frequency Response • Frequency response calculates the steady-state response from 72 COMSOL Simulations – Frequency Response • Frequency response calculates the steady-state response from harmonic loads • In our case, it measures the max deflection at each frequency – These deflections are arbitrary - only relative to each other • Geometry: 3 mmx. 5 mm thick – Array of 496 Magnets: 50 mmx 20 mm • Inputs – Mass of each magnet: 4 x 10 -10 kg – Mass of cantilever: 1 x 10 -8 kg – Sound Pressure at 50 d. B: 6. 3 x 10 -3 Pa

73 COMSOL Simulations - Frequency Response Deflection vs Frequency- 0 to 30 k. Hz 73 COMSOL Simulations - Frequency Response Deflection vs Frequency- 0 to 30 k. Hz 7 E-05 Normalized Deflection (m) 6 E-05 5 E-05 4 E-05 3 E-05 2 E-05 1 E-05 0 E+00 0 5 10 15 Frequency (k. Hz) 20 25 30 3 mmx. 5 mm cantilever, 496 magnets at 50 x 20 mm, real mass and 50 d. B sound level

74 Near 0 Hz • Resonance near 300 Hz • Very hard to visualize 74 Near 0 Hz • Resonance near 300 Hz • Very hard to visualize this on the full spectrum graph

75 Appendix for Abbie’s slide Underdeveloped Overdeveloped Under/Overdeveloped 75 Appendix for Abbie’s slide Underdeveloped Overdeveloped Under/Overdeveloped

76 Appendix for Abbie’s slide TMAH The Good (1μm) The Bad(0. 5 μm) The 76 Appendix for Abbie’s slide TMAH The Good (1μm) The Bad(0. 5 μm) The Ugly (1 μm)

77 Appendix for Abbie’s slide 77 Appendix for Abbie’s slide

78 Equivalent Number of Coils (1) • Neq: the number of coils of wire 78 Equivalent Number of Coils (1) • Neq: the number of coils of wire needed to produce the same inductance as a magnetic core inductor • Inductance of a cylindrical coil wrapped around a magnetic core: • Solving this equation for N and setting μ=1 yields Neq

79 Equivalent Number of Coils (2) • Have values for everything except A and 79 Equivalent Number of Coils (2) • Have values for everything except A and l • Solve for the ratio A/l • Then solve for Neq

80 Calculating Induced Voltage Faraday’s Law of Induction N is the equivalent number of 80 Calculating Induced Voltage Faraday’s Law of Induction N is the equivalent number of coils: 10, 453 Flux: Average over A: Time dep. : Derivative: This is not quite the full story, because entire cantilever does not move at v(t)

81 Calculating Induced Voltage Calculate an average velocity to account for this; velocity at 81 Calculating Induced Voltage Calculate 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 ¾; adding this in,

82 Frequency Response of Commercial (Audio -Technica) Microphones • Condenser (AT 4049 b) – 82 Frequency Response of Commercial (Audio -Technica) Microphones • Condenser (AT 4049 b) – Range: 20 -20, 000 Hz • Ribbon (AT 4080) – Range: 20 -18, 000 Hz www. audio-technica. com

83 Applications: Hearing Aid • Typically use electret condenser microphones • Linear response from 83 Applications: Hearing Aid • Typically use electret condenser microphones • Linear response from 50 -6000 Hz, new directional microphones from 6000 -8000 Hz • Microphone size varies – 4 mm x 3 mm x 1 mm – 5. 47 mm x 4. 62 • Our microphone: – 8 mm x 5 mm x 4. 2 mm – By changing coil, could achieve 5 mm x 3 mm www. bradingrao. com

84 Packaging • Glob Top on backside to protect coil (Dymax 9001 -E-v 3. 84 Packaging • Glob Top on backside to protect coil (Dymax 9001 -E-v 3. 7) • Machine cone-shaped holes in thin polymer sheet to attach on top

85 85

86 References • 86 References • "Body, Human. " The New Book of Knowledge. New York: Grolier, 1967: 285. • Borwick, John. Microphones: Technology and Technique. London: Focal, 1990. Print.

87 Sources Pedersen et al. http: //www. sciencedirect. com/science? _ob=Article. URL&_udi=B 6 THG-3 VCTDGRT&_user=961305&_cover. 87 Sources Pedersen et al. http: //www. sciencedirect. com/science? _ob=Article. URL&_udi=B 6 THG-3 VCTDGRT&_user=961305&_cover. Date=09%2 F 15%2 F 1998&_rdoc=1&_fmt=high&_orig=se arch&_sort=d&_docanchor=&view=c&_search. Str. Id=1276503526&_rerun. Origin=g oogle&_acct=C 000049425&_version=1&_url. Version=0&_userid=961305&md 5=00 50 f 247 f 9 f 563 e 4056 f 98705 a 48 bcf 4 Sheplak et al. http: //microfluids. engin. brown. edu/Breuer_Papers/Conferences/AIAA 990606_Microphone. pdf Arnold et al. http: //www. img. ufl. edu/publications/A%20 Piezoresistive%20 Microphone%20 for%20 Aeroacoustic%20 Measurements_Conference_November 2001. pdf Lee et al. http: //docs. lib. purdue. edu/cgi/viewcontent. cgi? article=1433&context=nanopub MEMS Microphones: A Global Technology, Industry and Market Analysis http: //www. mindbranch. com/MEMS-MICROPHONES-Global-R 3450 -6/