Modeling and Simulation of Mechanically Coupled MEMS Resonators Using
COMSOL Multiphysics®
J o s h u a W i s w e l l
D r . M u s t a f a G u v e n c h
U n i v e r s i t y o f S o u t h e r n M a i n e
O c t o b e r 5 t h 2 0 1 7
Purpose
2 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics®
• Create a COMSOL Multiphysics® model that represents the previously designed and
fabricated coupled MEMS resonators
• Investigate the effect of altering mass loadings
• Compare Eigenfrequency analysis results with frequency sweep results for
possible reduced simulation time
University of Southern Maine Engineering
Department
What are MEMS Resonators and What are Some Possible
Applications?
Microelectromechanical System Resonators
Resonate at specific frequencies based on mass and spring constant
Used in gas sensors for their sensitivity to mass
Two resonators - one with thin film to capture specific gas molecules-other as a
reference
A change in resonance will indicate the presence and amount of the gas absorbed
Response can be measured electrically through induced current from the
mechanical motion
𝑓 =1
2𝜋
𝑘
𝑚
3 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
Department
Fabricated Device
𝐶 =𝐴𝜀
𝑑𝐼 𝑡 =
𝑑(C ∙ 𝑉)
𝑑𝑡
4 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Model used for Simulations
5 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Magnitude and Phase of Single (Non Coupled) Resonator
0
5
10
15
20
25
30
35
40
45
50
33500 33510 33520 33530 33540 33550 33560 33570 33580 33590 33600
so
lid.d
isp
(R
ed
, u
m)
so
lid.u
Am
pY
(B
lue
, u
m)
Frequncy (Hz)
Displacement (um) vs Frequency of a Single Resonator
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
33500 33510 33520 33530 33540 33550 33560 33570 33580 33590 33600
Ph
ase
(d
eg
ree
s)
Frequency
Phase vs Frequency
6 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Simulated Coupled Resonator Frequency Response
0
10
20
30
40
50
60
29500 30000 30500 31000 31500 32000 32500 33000 33500 34000 34500
Dis
pla
ce
men
t (u
m),
Lo
ad
ed
/Go
ld s
ide
(R
ed
), R
efe
ren
ce
sid
e (
Blu
e)
Frequency (Hz)
Displacement (um) vs Frequency
Reference Side is Blue and Loaded (Gold) side is Red
7 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Coupled Resonators Frequency Response
0
1
2
3
4
5
6
30000 30500 31000 31500 32000 32500 33000 33500
Dis
pla
ce
me
nt
(um
)
Frequency (Hz)
Reference Side is Blue and Loaded (Gold) side is Red
-200
-150
-100
-50
0
50
100
150
200
30000 30500 31000 31500 32000 32500 33000 33500
Ph
as
e (
De
g)
Frequency (Hz)
8 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Resonance
Reference Side not at Resonance
Reference Side at 31.964kHz (Resonance)
9 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Real vs. SimulatedActual Simulated
Loaded Side Resonant Frequency 29,650 Hz 30,680 Hz
Reference Side Resonant Frequency 31,964 Hz 33,000Hz
Displacement At Resonant Frequency (Loaded) ≈1 μm 15.16 μm
Displacement At Resonant Frequency (Reference) ≈4 μm 54.30 μm
10 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Real vs. Simulated
Both resonant frequencies are shifted to the right by about 1kHz
Frequency difference between two resonant frequencies is less than 1% and is likely
lower due to observational error.
Frequency shift could be caused by slight differences between this model and the original
model, and manufacturing imperfections in the fabricated device
Resonant Frequency Difference (Simulated - Actual) % Difference
Loaded Side (30,680-29,650) 1,030 Hz 3.41%
Reference Side (33,000-31,964) 1,036 Hz 3.19%
Difference between the peaks 6 Hz 0.58%
11 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Varying Mass Simulation Setup
Start with single model shown
Define variable to sweep, increasing or decreasing density
Multiply variable by default density
Setup parameter sweep in frequency sweep study
12 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Magnitude vs. Frequency for Coupled Resonator as
Mass Increases
0
1
2
3
4
5
6
7
29400 29900 30400 30900 31400 31900 32400 32900 33400
Dis
pla
cem
ent
(um
), L
oaded/G
old
sid
e (
Red),
Refe
rence s
ide (
Blu
e)
Frequency (Hz)
Displacement VS Frequency of Coupled Resonators with Varying Loading Mass
140%
Go
ld
Density
220%
Gold
Density
40%
Go
ld
Density
Reference Side is Blue and Loaded (Gold) side is Red
13 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Coupled Resonators Resonant Frequency Plot
y = -808.64x + 31445R² = 0.9972
y = -305.77x + 33337R² = 0.9314
29000
29500
30000
30500
31000
31500
32000
32500
33000
33500
34000
0.00% 50.00% 100.00% 150.00% 200.00% 250.00%
Fre
qu
en
cy (
Hz),
Loaded/G
old
sid
e (
Red),
Refe
rence s
ide (
Blu
e)
Percent Density of Gold (%)
Frequency vs. Changing Load Density of Coupled Resonators from Frequency Sweep analysis
14 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Coupled Resonators Resonant Frequency Plot from Eigen
Frequencies
y = -173.13x + 33227R² = 0.8676
y = -824.68x + 31469R² = 0.9995
27000
28000
29000
30000
31000
32000
33000
34000
0.00% 50.00% 100.00% 150.00% 200.00% 250.00% 300.00% 350.00% 400.00% 450.00%
Fre
qu
en
cy (
Hz),
Loaded/G
old
sid
e (
Red),
Refe
rence s
ide (
Blu
e)
Percent Density of Gold (%)
Frequency VS Changing Load Density of Coupled Resonators from Eigen Frequency analysis
15 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Conclusion
• Simulation produced by COMSOL Multiphysics® was shown to be an
accurate representation of the characteristics of the real device.
• The simulation shows a mostly linear trend in the resonant frequency on the
mass-loaded side of the coupled resonator as indicated by the R-squared
value.
• Although mostly consistent in determining resonant frequencies, the
eigenfrequencies for the coupled resonators showed a misleading result
when the masses of the two similar, but not identical, resonators are equal.
16 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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Acknowledgements
• University of Southern Maine UROP (Undergraduate
Research Opportunities Program) fellowship
• Maine Space Grant Consortium, NASA and USM for
the funds to have the MEMS devices fabricated
17 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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References
1. COMSOL Multiphysics (Version 4.3) [Computer software]. (2012). Massachusetts: COMSOL, Inc.
2. Cowen, A., Hames, G., Monk, D., Wilcenski, S., & Hardy, B. , “SOIMUMPs Design Handbook”, MEMSCAP Inc. Retrieved March 10, 2015, from
http://www.memscap.com/__data/assets/pdf_file/0019/1774/SOIMUMPs.dr.v8.0.pdf
3. Crosby, J.V. and Guvench, M.G., “Experimentally Matched Finite Element Modeling of Thermally Actuated SOI MEMS Micro-Grippers Using COMSOL Multiphysics,"
Annual COMSOL Conference, Boston, MA, 2009. Available on line:
https://www.comsol.com/paper/download/101075/Guvench.pdf
4. Nelson, S., & Guvench, M. G., “COMSOL Multiphysics Modeling of Rotational Resonant MEMS Sensors with Electrothermal Drive”, Annual COMSOL Conference,
Boston, MA, 2009. https://www.comsol.com/paper/download/44730/Nelson.pdf
5. Solidworks 2014-2015: 64-bit (Version 2014-2015) [Computer software]. (2014). Concord, MA: SolidWorks Corporation.
6. Tao, G., & Choubey, B., “A Simple Technique to Readout and Characterize Coupled MEMS Resonators”, Journal of Microelectromechanical Systems”, 25(4), 617-
625, (2016) doi:10.1109/jmems.2016.2581118
7. Zhao, C., Wood, G. S., Xie, J., Chang, H., Pu, S. H., & Kraft, M., “A Comparative Study of Output Metrics for an MEMS Resonant Sensor Consisting of Three Weakly
Coupled Resonators,” Journal of Microelectromechanical Systems, 25(4), 626-636, (2016).
doi:10.1109/jmems.2016.2580529.
18 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
Department
Thank You
Questions?
19 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® University of Southern Maine Engineering
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