MEMS Dynamic Microphone Design and Fabrication

ENMA 490 Capstone Final Report, 10 May 2010

Abbigale Boyle, Steven Crist, Mike Grapes, Karam Hijji, Alex Kao, Stephen Kitt, Paul Lambert, Christine Lao, Ashley Lidie, Marshall Schroeder

z-component of magnetic fluxrectangular magnet 50 μ m x 50 μ m x 25 μ m, 0.5 T

Outline• General Theory• Motivation• Design Components– Coil– Magnets– Cantilever

• Fabrication and Prototype• Future Work• Budget• Ethics• Lessons

2

Overview of Device Motivation and Design

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Dynamic Microphone Model

http://www.burninggrooves.com/images/12.gif

Bulk Dynamic Microphone Design MEMS Dynamic Microphone Design

Wires carrying AC signal

Magnet(s) Cantilever

Prefabricated Inductor Coil

Faraday’s law:our goal

•New idea•Proof of concept• Powerless signal generation•Offers alternative to piezoelectric and

electret designs

Motivation

Graph from www.isupply.com

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

Market Projections and Statistics from www.mindbranch.com

Power Consumption in Common Alternative Technologies

Piezoresisitive MicrophoneMode of Power Consumption: Excitation voltage to measure resistance change.

-Sheplak et al.Excitation Voltage: 10VPower Consumption: 0.7 mW

-Arnold et al.Excitation Voltage: 3VPower Consumption: 15mW +/- 2.5mW

http://www.acoustics.org/press/137th/pires1.jpg

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Condenser Microphone Mode of Power Consumption: Required bias voltage between plates

-Pedersen et al.Bias Voltage: 4VCapacitance: 10.1 pFPower Consumption: 1.96mW

http://www.totalvenue.com.au/articles/microphones/mic-condenser.gif

Power Consumption in Common Alternative Technologies

Piezoresisitive MicrophoneMode of Power Consumption: Excitation voltage to measure resistance change.

-Sheplak et al.Excitation Voltage: 10VPower Consumption: 0.7 mW

-Arnold et al.Excitation Voltage: 3VPower Consumption: 15mW +/- 2.5mW

http://www.acoustics.org/press/137th/pires1.jpg

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Piezoelectric and Electret microphones No power required for signal generation

http://www.acoustics.org/press/137th/pirel1.jpg

Piezoelectric Microphone Electret Microphone

http://hyperphysics.phy-astr.gsu.edu/hbase/audio/imgaud/etret.gif

Power Consumption in Common Alternative Technologies

Condenser Microphone Mode of Power Consumption: Required bias voltage between plates

-Pedersen et al.Bias Voltage: 4VCapacitance: 10.1 pFPower Consumption: 1.96mW

http://www.totalvenue.com.au/articles/microphones/mic-condenser.gif

8

Design Components

Basic design:

What?• A pre-fabricated surface-mount inductor (Coilcraft DO1607B, 6.8 mH)Why?• Compensate for small flux with large coil• Why make it yourself (hard) when other people already do it?

Permanent magnet array considerations:• Magnet material?• Magnetization direction?• Magnet dimensions?

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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 (kJ/m3) Remanence (T)

CoNiP 1.3-1.8 .06-.1

CoNiMnP 0.6-14 0.2-0.3

CoPtP 52-69 0.3-1.0 Arnold et al.

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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…

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Permanent Magnet Design• Question #1: In or out of plane?– Flux is ; take component perpendicular to A

• Answer: Only out of plane will give desired flux change

Out-of-plane magnetIn-plane magnet

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supplemental material on magnet simulations

Permanent Magnet Design• Question #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 quadrant

• Why?– Self-demagnetization

slope = B/H = f(N)? partial demagnetization (0 < N < 1), some remanence available

slope = 0: complete demagnetization (N = 1), no remanence available

slope = ∞: no demagnetization (N = 0), full remanence available

slope = (B/H)max

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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 10 um x 28 (30 um max thickness)– Plate: single magnet 1.35 mm x 1.35 mm x 3.82 mm thick

• Final result:– CoNiMnP– Array of 10 um x 10 um x 28 um • 10 um spacing (ease of fabrication)

– Magnetized out of plane

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Design ComponentsBasic design:

Cantilever oscillation determines frequency response of microphone• Material?• Dimensions?Optimized using anlytical simulation

Permanent magnet array considerations:• Magnet material?• Magnetization direction?• Magnet dimensions?

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Modeling the Cantilever Analytically

Objective: 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

Forcing TermIn our application, the force is due to a pressure wave:

For sound:

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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

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Modeling the Cantilever Analytically

Damping ConstantTwo 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

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Modeling the Cantilever Analytically

Damping ConstantTwo contributions:1. Mechanical2. Electromagnetic

• γm is dependent on• The magnetic field produced by the magnet• The current density, σ

this means…• Zero current = zero magnetic damping• Use device as a voltage source (~ infinite resistance) to minimize EM

damping

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see supplemental slides for full calculation

Modeling the Cantilever Analytically

Spring Constant;

Magnets are ~10x as thick as the cantilever, so k is ~1000x larger for magnets

Springs in Series:

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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

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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

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Solving the Differential Equation

• Cantilever motion modeled as a sinusoidal driven harmonic oscillator:

• Steady-state solution:

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source: www.audio-technica.com

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?

• If the flux varies relatively slowly over z (and it does), the voltage depends primarily on the velocity

• Optimize for flat velocity response

see supplemental slides for full derivation

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Optimizing Frequency Response• Range of human hearing:

20-20,000Hz• 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

Signal/noise ratio at 3 moderate resonances

2,500Hz 10,000Hz 15,000Hz

Avg. S/N 16.6 8.2 6.6

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supplementary slides with S/N, A, and V

Optimizing Frequency Response

• For ω0 = 2500Hz t = 3.06m

• For best response, L = W = 3mm

• Gap height dictates damping constant– To flatten response,

used gap height = 30 m• Results in a damping of

γ = 2.35x10-2 kg/s

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Final Parameters

• Cantilever– L = W = 3mm– t = 3.06 um– keff

= 0.468 N/m

– meff = 7.5x10-8 kg

– γ = 2.35x10-2 kg/s

– Q = 7.93x10-3

• Magnet array– 9800 magnets– 140 magnets x 70 magnets– 10 μm x 10 μm x 28 μm

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Output Voltage

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

frequency

Voltage output from cantilever is:

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Output Voltage (2)

• Volume Replication • Frequency Replication

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Fabrication1. Grow 3 µm thick oxide and use E-beam deposition to deposit Cr and

Au2. Use mask to pattern photoresist, then etch the Cr, Au, and oxide to

create cantilever shape

3. Pattern array for magnets in photoresist4. Electroplate magnets and magnetize5. Pattern photoresist to protect magnets and remove excess metal

layers

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Fabrication Cont.

6. Crystalbond™ two wafers together on their patterned sides7. Pattern oxide on bottom, and then etch through Si8. Attach Coil

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Prototype ProcessingObstacles

• Thick Photoresist:– Under developed– Over developed

• Skipped:– Magnet array protection during

SiO2/Si etches– Gold removal

• Si etching– Crystalbond™ adhesion

incomplete– Doubled-sided etching/sliding

wafers• Post-etch cantilever behavior

– Etching away– Curling up

Solutions•Patterning

•SU-8•Better aligner•Better masks (chrome on glass)

•Si etching•DRIE (deep reactive ion etching)

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more picturesstress

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

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Future Testing• Frequency response– Supply sound of constant volume, varied frequency (20-

20,000 Hz), look for flatness of response• Amplitude response– Constant frequency, varied volume (30-80 dB? 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

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Prototype: Budget and TimeItem Desciption Supplier Cost

65K DPI Mylar Masks (4 total) Photoplot/ $295.00 Includes shipping and file formatting Fineline Imaging

Inductors (40 total) CoilCraft Free

30 x 1mH inductors of differing dimensions

10 x 6.8mH inductors Wires, Solder + Soldering Iron Mike Free

3" Silicon Wafers (12 total) Dr. Phaneuf Free500nm oxide grown (Thank you!)

Fab Lab hourly use Fab Lab $1,582.00

Estimated 28.25 hours $56 per hour

Estimated Total $1,877.00

Individual HoursPaul 32

Abbie 23.5Ashley 7

Alex 3Karam 2TOTAL 67.5

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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

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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 3rd time is still not the charm• Higher understanding of spring-mass system• Utilize unfamiliar software packages

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Acknowledgements

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

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Questions?

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Supplemental Slides

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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 Oscillator• Bulk micromachining• Surface micromachining• Planar

Abandoned due to insufficient deflection under acoustic loading.

2nd Generation: Air-bridge/Cantilever Oscillator• Single Magnet• Dual Magnet• Micro-magnet Array

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Bulk Micromachining

Primary Challenge: Electroplating the magnet beneath the diaphragm

Attributes for Prototype: Releasing the diaphragm is a simple process

Si

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Surface Micromachining

Primary Challenge: Fabricating the diaphragm and acoustic cavity above the magnet

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

SiO2

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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

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Single Magnet Cantilever

MagnetCoil

Si

SiO2

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

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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

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PrototypeCurrent Design:-SiO2 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)

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Diaphragm vs. Cantilever

• Diaphragm

• 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 magnet’s operating point.

(1)

(2)

(3)

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Optimal B/H for CoNiMnP

We have:

Need an expression for N

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N for Rectangular Prism

Finally, if we assume a square cross-section, we can reduce to a single variable:

This has three variables, but we can reduce it to two by rewriting in terms of aspect ratios:

For a rectangular prism with dimensions 2a x 2b x 2c and magnetization in the c direction, the demagnetization factor can be written (Aharoni 1998)

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Plotting this…

After all that, we get something that’s essentially linear!

AR = 2.83

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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.

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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

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Calculating Effective Mass

D= linear densityL= length

dm=Ddx D*L= mass

md

md

mc

Mmag

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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 System Total Effective Mass: Plate case

Cantilever length,X (limits 0 L

Our Magnet Portion (limits L/2 L)

• Our Cantilever:

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Magnetic Damping Parameter (1)

• Force exerted on a loop of wire by a magnet:

– I = element of current in the loop– dL = infinitesimal arc length of the loop– J = current density– dV = infinitesimally small volume of the loop

• The 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:

• βF is dependent on the magnetic field of the magnet

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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

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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

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Static Stress

• To determine if cantilever can support much thicker array of magnets

• For a rectangular beam loaded at one end:– σmax = 3dEt/(2l2)

– D = max. deflection, E = Young’s mod, t = thickness, l = length

– σmax = 52.5 kPa, well within tensile strength of SiO2

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Signal to noise vs frequency

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Amplitude + Velocity vs frequency

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Damping effects

Low damping: 30m, Moderate damping: 150m, High damping 300m

B=2.35x10-2 kg/s B=1.88x10-4 kg/s B=2.35x10-5 kg/s

68

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

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Sound Level Pressure (Pa) Comsol Defelection(m) Analytical Deflecton (m) % Difference20 2.00E-04 2.71E-08 2.84E-08 4.7590405925 3.55E-04 4.70E-08 5.05E-08 7.41468085130 6.31E-04 7.65E-08 8.98E-08 17.354509835 1.12E-03 1.53E-07 1.60E-07 4.34444444440 2.00E-03 2.53E-07 2.84E-07 12.2122529645 3.55E-03 4.75E-07 5.05E-07 6.28450 6.31E-03 1.00E-06 8.98E-07 -10.223855 1.12E-02 1.66E-06 1.60E-06 -3.82710843460 2.00E-02 3.05E-06 2.84E-06 -6.91901639365 3.55E-02 5.26E-06 5.05E-06 -4.02110266270 6.31E-02 9.62E-06 8.98E-06 -6.67754677875 1.12E-01 1.71E-05 1.60E-05 -6.63918128780 2.00E-01 3.02E-05 2.84E-05 -5.994370861

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

70

COMSOL Simulations - Deflection Simulations

• Source of systematic error: width and spring constant

• Used extrapolation to estimate deflection values for 3 mm geometry (50dB) – 77m agrees reasonably

with analytical value of 87m- better than the COMSOL value of 780m

71

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: 3mmx3mmx.5mm thick – Array of 496 Magnets: 50mmx50mmx20mm

• Inputs– Mass of each magnet: 4x10-10 kg– Mass of cantilever: 1x10-8 kg– Sound Pressure at 50dB: 6.3x10-3 Pa

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COMSOL Simulations - Frequency Response

3mmx3mmx.5m cantilever, 496 magnets at 50x50x20m, real mass and 50dB sound level

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Near 0Hz

• Resonance near 300Hz• Very hard to visualize

this on the full spectrum graph

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Appendix for Abbie’s slide

Underdeveloped Overdeveloped

Under/Overdeveloped

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Appendix for Abbie’s slideTMAH

The Good (1μm) The Bad(0.5 μm) The Ugly (1 μm)

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Appendix for Abbie’s slide77

• 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

Equivalent Number of Coils (1)

78

Equivalent Number of Coils (2)

• Have values for everything except A and l• Solve for the ratio A/l

• Then solve for Neq

79

Calculating Induced VoltageFaraday’s 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)

80

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 ¾; adding this in,

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Frequency Response of Commercial (Audio-Technica) Microphones

• Condenser (AT4049b)– Range: 20-20,000Hz

• Ribbon (AT4080)– Range: 20-18,000Hz

www.audio-technica.com

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Applications: Hearing Aid

• Typically use electret condenser microphones• Linear response from 50-6000Hz, new directional

microphones from 6000-8000Hz• Microphone size varies

– 4mm x 3mm x 1 mm– 5.47mm x 5.47mm x 4.62

• Our microphone: – 8mm x 5mm x 4.2mm– By changing coil, could achieve 5mm x 5mm x 3mm

www.bradingrao.com

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Packaging

• Glob 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=0050f247f9f563e4056f98705a48bcf4

Sheplak 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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