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 50 μ m x 25 μ m, 0.5 T
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
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
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 to measure resistance change.
-Sheplak et al.
Excitation Voltage: 10V
Power Consumption: 0.7 mW
-Arnold et al.
Excitation Voltage: 3V
Power Consumption: 15mW +/- 2.5mW
http://www.acoustics.org/press/137th/pires1.jpg
6
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.
-SheplakBias
et al.
Voltage: 4V
Excitation Voltage: 10V
Capacitance: 10.1 pF
Power Consumption: 0.7 mW
Power Consumption: 1.96mW
-Arnold et al.
Excitation Voltage: 3V
Power Consumption: 15mW +/- 2.5mW
http://www.acoustics.org/press/137th/pires1.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 required for signal generation
Mode
of Power Consumption:
Required bias voltage
between
plates
Piezoelectric
Microphone
Electret
Microphone
-Pedersen et al.
Bias Voltage: 4V
Capacitance: 10.1 pF
Power Consumption: 1.96mW
http://www.acoustics.org/press/137th/pirel1.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?
•Permanent
A pre-fabricated
inductor
magnetsurface-mount
array considerations:
(Coilcraft
• Magnet DO1607B,
material? 6.8 mH)
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 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.
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
dF
V =N
dt
• 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…
12
Permanent Magnet Design
• Question #1: In or out of plane?
– Flux is F = B · A; take component perpendicular to A
supplemental material on magnet simulations
In-plane magnet
Out-of-plane magnet
• Answer: Only out of plane will give desired flux change
13
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
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
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
15
Design Components
Basic design:
Permanentoscillation
Cantilever
magnet array
determines
considerations:
frequency
•response
Magnet of
material?
microphone
• Magnetization
Material?
direction?
• Magnet
Dimensions?
dimensions?
Optimized using anlytical simulation
16
Objective: Develop an analytical model for
the oscillatory behavior of the cantilever
using the classic differential equation for a
damped harmonic oscillator
F = meff x + gx + keff x
Modeling the Cantilever Analytically
17
Modeling the Cantilever Analytically
F = meff x + gx + keff x
Forcing Term
In our application, the force is due to a pressure wave:
F = P ´ A = AP0 sin(wt + kx )
For sound:
P0 = 10
æ L p [ dB ] ö
ç
÷
ç 20 ÷
è
ø
´ Pref
Pref = 20 ìPa (threshold of human hearing)
w = 2pf
k=
w
343 m/s
18
Modeling the Cantilever Analytically
F = meff x + gx + keff x
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
F = meff x + gx + keff x
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
h eff l 4 Kim et al. 1999
g = 0.422 3
g
20
Modeling the Cantilever Analytically
F = meff x + gx + keff x
Damping Constant
Two contributions:
1. Mechanical
2. Electromagnetic
gm =
Fdamp
2mv
=
ps
m
ò
• γm is dependent on
• The magnetic field produced by the magnet
• The current density, σ
top
ò
R2
bottom R1
2
Brad
rdrdz
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
F = meff x + gx + keff x
Spring Constant
;
Magnets are ~10x as thick as the cantilever,
so k is ~1000x larger for magnets
Springs in Series:
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:
Q=
meff k
g
• Signal to noise: ratio of signal amplitude to
noise amplitude
S/N =
Asignal
Anoise
23
Thermal Noise
• Random thermal
motion of atoms results
in small displacements
of cantilever
Electrical Noise
• Johnson
• Shot
– Flat frequency spectrum
– Irreducible
– Dependant on resistance
Vnoise , RMS = (4kTRB )
1/ 2
– Random fluctuation in current
– Charges act independently of
each other
I noise , RMS = (2qI dc B)
1/ 2
24
Solving the Differential Equation
• Cantilever motion modeled as a sinusoidal
driven harmonic oscillator:
d x
dx
m 2 +g
+ kx = F0 sin(wt )
dt
dt
2
• Steady-state solution:
x(t ) =
F0
m (w - w ) + g w
2
2
0
2 2
2
2
cos(wt - j )
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?
V (t ) =
3 æd
ö
NAç Bavg ( f - z (t ))÷v(t )
4 è dt
ø
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:
20-20,000Hz
• 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
supplementary slides with S/N, A, and V
Signal/noise ratio at 3 moderate resonances
Avg. S/N
2,500Hz
10,000Hz
15,000Hz
16.6
8.2
6.6
27
Optimizing Frequency Response
• For ω0 = 2500Hz
 t = 3.06mm
• For best response,
L = W = 3mm
• Gap height dictates
damping constant
– To flatten response,
used gap height = 30 mm
• Results in a damping of
γ = 2.35x10-2 kg/s
28
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
29
Output Voltage
Voltage output from
cantilever is:
3 æd
ö
V (t ) = NAç Bavg ( f - z (t ))÷v(t )
4 è dt
ø
• 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
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
Pattern oxide on bottom, and then etch through Si
Attach Coil
33
Prototype Processing
Obstacles
• 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
Solutions
•Patterning
•SU-8
•Better aligner
•Better masks (chrome on glass)
•Si etching
•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 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 (2020,000 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
36
Prototype: Budget and Time
Item Desciption
65K DPI Mylar Masks (4 total)
Includes shipping and file formatting
Supplier
Photoplot/
Fineline Imaging
Cost
$295.00
Inductors (40 total)
30 x 1mH inductors of differing
dimensions
10 x 6.8mH inductors
Wires, Solder + Soldering Iron
CoilCraft
Free
Mike
Free
3" Silicon Wafers (12 total)
500nm oxide grown
Dr. Phaneuf
(Thank you!)
Free
Fab Lab hourly use
Estimated 28.25 hours
$56 per hour
Estimated Total
Fab Lab
$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 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 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
39
Acknowledgements
•
•
•
•
•
•
•
•
•
Dr. Phaneuf
Dr. Briber
Dr. Wuttig
Dr. Ankem
John Abrahams
Tom Loughran
Don Devoe
Coilcraft
Fineline Imaging
40
Questions?
41
Supplemental Slides
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
1st 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
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
SiO2
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 delamination under acoustic loading.
Attributes for Prototype: Arrays of smaller magnets may reduce interfacial stresses
47
Single Magnet Cantilever
Coil
Magnet
SiO2
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
48
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
49
Prototype
Current 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)
Diaphragm vs. Cantilever
• Diaphragm
d max
• Cantilever
Pa 4
=
64D
3s (1 - u ) æ L ö
d=
ç ÷
E
ètø
2
50
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 CoNiMnP
Characteristic B-H for CoNiMnP
10
8
6
BHmax = 11.5 kJ/m3
(B/H)max = -5.77
We have:
4
B (kG)
2
-2
0
-1.5
-1
-0.5
0
-2
-4
-6
-8
-10
H (kOe)
Need an expression for N
0.5
1
1.5
2
53
N for Rectangular Prism
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)
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 = 2.83
55
Simulating Rectangular Permanent Magnets
• Expressions constructed by considering
molecular surface currents + Biot-Savart law
Bx = -
K
[G(a - x, y, z )+ G(a - x, b - y, z )- G(x, y, z )- G(x, b - y, z )]0h
2
By = -
K
[G(b - y, x, z )+ G(b - y, a - x, z )- G(x, y, z )- G(y, a - x, z )]0h
2
B z = - K [f (y, a - x, z )+ f (b - y, a - x, z )
+ f (x, b - y, z )+ f (a - x, b - y, z )+ f (b - y, x, z )
+ f (y, x, z )+ f (a - x, y, z )+ f (x, y, z )]0h
æ g 2 + g 2 + (g - z )2 - g ö
1
2
3
0
2 ÷
G(g 1 , g 2 , g 3 ) = lnç
ç
÷
2
2
2
(
)
g
+
g
+
g
z
+
g
1
2
3
0
2
è
ø
ì
éj
ïïarctan ê 1
f (j1 , j 2 , j 3 ) = í
êj 2
ë
ï
ïî
j3 - z0
j12 + j 22 + (j 3 - z 0 )2
0
ù
ú if j 3 ¹ 0
ú
û
if j 3 = 0
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 basic functions w/ shifted coordinates
Barray ( x, y, z ) = åå B( x - dm, y - dn, z )
m
n
• 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
mc
Mmag
58
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:
Our System Total Effective Mass:
Plate case
Cantilever length,X (limits 0
Our Magnet Portion (limits L/2
L
L)
60
Magnetic Damping Parameter (1)
• Force exerted on a loop of wire by a magnet:
dFz = I (dL Ä B) z = J (dV Ä B) z
–
–
–
–
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:
J = s (v Ä B) = svBrad
61
Magnetic Damping Parameter (2)
• Combining the expression for current density into
the force expression:
dFz = svB dV
2
rad
• Assuming a cylindrical geometry for simplicity:
dFz = svB rdrdzd q
2
rad
= 2psvB rdrdz
2
rad
62
Magnetic Damping Parameter (3)
• Setting up the integral to obtain the force:
Fdamping = 2psv ò
top
ò
R2
bottom R1
B rdrdz
2
rad
• The magnetic damping parameter is found by:
bF =
Fdamp
2mv
=
ps
ò
m
top
ò
R2
bottom R1
B rdrdz
2
rad
• βF is dependent on the magnetic field of the magnet
63
Magnetic Damping Parameter (4)
bF =
Fdamp
2mv
=
ps
ò
m
top
ò
R2
bottom R1
B rdrdz
2
rad
• 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 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 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
66
Signal to noise vs frequency
67
Amplitude + Velocity vs frequency
Amplitude (m)
Amplitude and Velocity
1.20E-07
0.000003
1.00E-07
0.0000025
8.00E-08
0.000002
6.00E-08
0.0000015
Amplitude
Velocity
4.00E-08
0.000001
2.00E-08
0.0000005
0.00E+00
0
5000
10000
15000
20000
25000
Frequency (Hz)
30000
35000
0
40000
68
Damping effects
Low damping: 30mm, Moderate damping: 150mm, High damping 300mm
B=2.35x10-2 kg/s
B=1.88x10-4 kg/s
B=2.35x10-5 kg/s
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
3.50E-05
3.00E-05
Deflection (m)
2.50E-05
2.00E-05
Comsol Deflection
1.50E-05
Analytical Deflection
1.00E-05
5.00E-06
0.00E+00
0
10
20
30
40
50
Sound Level (dB)
Sound Level
Pressure (Pa)
20
25
30
35
40
45
50
55
60
65
70
75
80
2.00E-04
3.55E-04
6.31E-04
1.12E-03
2.00E-03
3.55E-03
6.31E-03
1.12E-02
2.00E-02
3.55E-02
6.31E-02
1.12E-01
2.00E-01
60
70
80
90
Silicon Dioxide:
L= 1mm
t= .5um
E=70 Gpa
v=.17
Comsol Defelection(m)
Analytical Deflecton (m)
% Difference
2.71E-08
2.84E-08
4.75904059
4.70E-08
5.05E-08
7.414680851
7.65E-08
8.98E-08
17.3545098
1.53E-07
1.60E-07
4.344444444
2.53E-07
2.84E-07
12.21225296
4.75E-07
5.05E-07
6.284
1.00E-06
8.98E-07
-10.2238
1.66E-06
1.60E-06
-3.827108434
3.05E-06
2.84E-06
-6.919016393
5.26E-06
5.05E-06
-4.021102662
9.62E-06
8.98E-06
-6.677546778
1.71E-05
1.60E-05
-6.639181287
3.02E-05
2.84E-05
-5.994370861
71
COMSOL Simulations - Deflection
Simulations
Deflection vs Sound Pressure from COMSOL
(numerical) and Calculations (analytical)
3.50E-05
3.00E-05
2.50E-05
Deflection (m)
• Source of systematic
error: width and spring
constant
• Used 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
2.00E-05
Numerical
1.50E-05
Analytical
1.00E-05
5.00E-06
0.00E+00
0
20
40
60
Sound Level (dB)
80
100
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: 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
73
COMSOL Simulations - Frequency Response
Deflection vs Frequency- 0 to 30 kHz
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
20
25
30
Frequency (kHz)
Normalized Deflection (m)
Deflection vs Frequency- 2 to 30 kHz
1.E-07
9.E-08
8.E-08
7.E-08
6.E-08
5.E-08
4.E-08
3.E-08
2.E-08
1.E-08
0.E+00
8,500Hz
12,000Hz
0
5
10
15
20
25
30
35
Frequency (kHz)
3mmx3mmx.5mm cantilever, 496 magnets at 50x50x20mm, real mass and 50dB sound level
74
Near 0Hz
1.E-05
300Hz
1.E-05
1.E-05
Normalized Deflection (m)
• Resonance near 300Hz
• Very hard to visualize
this on the full
spectrum graph
Deflection vs Frequency - 0 to 2000Hz
8.E-06
6.E-06
4.E-06
2.E-06
0.E+00
0
500
1,000
1,500
Frequency (Hz)
2,000
2,500
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 Ugly (1 μm)
77
Appendix for Abbie’s slide
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:
L=
m0 mKN A
2
l
• Solving this equation for N and setting μ=1 yields Neq
79
Equivalent Number of Coils (2)
• Have values for everything except A and l
• Solve for the ratio A/l
A
L
=
= 6.052 E - 5m
2
l m0 mKN
• Then solve for Neq
L 1
N eq =
= 10,452.8
m0 K A
l
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 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 (AT4049b)
– Range: 20-20,000Hz
• Ribbon (AT4080)
– Range: 20-18,000Hz
www.audio-technica.com
83
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
84
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
85
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=ArticleURL&_udi=B6THG-3VCTDGRT&_user=961305&_coverDate=09%2F15%2F1998&_rdoc=1&_fmt=high&_orig=se
arch&_sort=d&_docanchor=&view=c&_searchStrId=1276503526&_rerunOrigin=g
oogle&_acct=C000049425&_version=1&_urlVersion=0&_userid=961305&md5=00
50f247f9f563e4056f98705a48bcf4
Sheplak et al.
http://microfluids.engin.brown.edu/Breuer_Papers/Conferences/AIAA990606_Microphone.pdf
Arnold et al.
http://www.img.ufl.edu/publications/A%20Piezoresistive%20Microphone%20for%20A
eroacoustic%20Measurements_Conference_November2001.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-R3450-6/