Modeling and Simulation of Mechanically Coupled MEMS ...€¦ · Purpose 2 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® • Create a

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


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Model used for Simulations


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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


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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


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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)


-200

-150

-100

-50

0

50

100

150

200

30000 30500 31000 31500 32000 32500 33000 33500

Ph

as

e (

De

g)

Frequency (Hz)


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Resonance

Reference Side not at Resonance

Reference Side at 31.964kHz (Resonance)


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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


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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%


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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


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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



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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


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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


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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.


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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


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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.


Department

https://www.comsol.com/paper/download/101075/Guvench.pdf

https://www.comsol.com/paper/download/44730/Nelson.pdf

Thank You

Questions?


Department

Documents

Modeling and Simulation of Mechanically Coupled MEMS ...€¦ · Purpose 2 Modeling and Simulation of Mechanically Coupled MEMS Resonators Using COMSOL Multiphysics® • Create a