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 flux rectangular magnet 50 μ m x 50 μ m x 25 μ m, 0.5 T
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. z-component of magnetic flux rectangular magnet 50 μ m x 50 μ m x 25 μ m, 0.5 T. - PowerPoint PPT Presentation
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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
•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
6
Condenser Microphone Mode of Power Consumption: Required bias voltage between plates
-Pedersen et al.Bias Voltage: 4VCapacitance: 10.1 pFPower Consumption: 1.96mW
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?
• 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…
11
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
12
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
13
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
14
Design ComponentsBasic design:
Cantilever oscillation determines frequency response of microphone• Material?• Dimensions?Optimized using anlytical simulation
Objective: Develop an analytical model for the oscillatory behavior of the cantilever using the classic differential equation for a damped harmonic oscillator
16
Modeling the Cantilever Analytically
Forcing TermIn our application, the force is due to a pressure wave:
For sound:
17
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
18
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
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
37
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
38
Acknowledgements
• Dr. Phaneuf• Dr. Briber• Dr. Wuttig• Dr. Ankem• John Abrahams• Tom Loughran• Don Devoe• Coilcraft• Fineline Imaging
39
Questions?
40
Supplemental Slides
41
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
Abandoned due to insufficient deflection under acoustic loading.
2nd Generation: Air-bridge/Cantilever Oscillator• Single Magnet• Dual Magnet• Micro-magnet Array
43
Bulk Micromachining
Primary Challenge: Electroplating the magnet beneath the diaphragm
Attributes for Prototype: Releasing the diaphragm is a simple process
Si
44
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
45
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
46
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
47
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
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)
49
Diaphragm vs. Cantilever
• Diaphragm
• Cantilever
50
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)
53
Plotting this…
After all that, we get something that’s essentially linear!
AR = 2.83
54
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.
55
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
56
Calculating Effective Mass
D= linear densityL= length
dm=Ddx D*L= mass
md
md
mc
Mmag
57
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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:
59
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:
60
Magnetic Damping Parameter (2)
• Combining the expression for current density into the force expression:
• Assuming a cylindrical geometry for simplicity:
61
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
62
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
63
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
64
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
65
Signal to noise vs frequency
66
Amplitude + Velocity vs frequency
67
Damping effects
Low damping: 30m, Moderate damping: 150m, High damping 300m