Graphical Abstract Figure

Synchronization Enhancement in Nonlinear MEMS Oscillator Vis Electrothermal Adjustment

Graphical Abstract Figure

Synchronization Enhancement in Nonlinear MEMS Oscillator Vis Electrothermal Adjustment

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Abstract

Synchronization in microelectromechanical systems (MEMS) typically encounters the impact of electrothermal phenomena, often in conjunction with piezoresistive detection or frequency tuning. However, the electrothermal effects on synchronization have not been previously explored. This paper investigates the electrothermal effects on synchronization bandwidth and frequency stability in a nonlinear MEMS arch oscillator. Experimental results demonstrate a non-monotonic pattern in synchronization bandwidth as electrothermal current increases, corroborated by theoretical models based on quality factors and equivalent nonlinearity. Drawing from theoretical analysis, which suggests that synchronization can be enhanced by adjusting feedback and perturbation strength, we achieved a 5.72-fold enhancement in synchronization bandwidth in our experiments. Furthermore, we observed that increased electrothermal significantly improves frequency stability. We developed a model based on the Allan deviation that incorporates electrothermal temperature to evaluate frequency stability, and this model successfully verified our experimental results. These experimental and theoretical findings highlight the potential of electrothermal effects to enhance synchronization and frequency stability in MEMS devices, paving the way for more robust sensor technology applications.

References

1.
Zhu
,
J.
,
Liu
,
X.
,
Shi
,
Q.
,
He
,
T.
,
Sun
,
Z.
,
Guo
,
X.
,
Liu
,
W.
,
Sulaiman
,
O. B.
,
Dong
,
B.
, and
Lee
,
C.
,
2019
, “
Development Trends and Perspectives of Future Sensors and MEMS/NEMS
,”
Micromachines
,
11
(
1
), p.
031104
.
2.
Toprak
,
A.
, and
Tigli
,
O.
,
2014
, “
Piezoelectric Energy Harvesting: State-of-the-Art and Challenges
,”
Appl. Phys. Rev.
,
1
(
3
), p.
31104
.
3.
Yao
,
W.
,
Wang
,
C.
,
Sun
,
Y.
, and
Zhou
,
C.
,
2022
, “
Robust Multimode Function Synchronization of Memristive Neural Networks With Parameter Perturbations and Time-Varying Delays
,”
IEEE Trans. Syst. Man Cybern. Syst.
,
52
(
1
), pp.
260
274
.
4.
Ma
,
J.
,
Wu
,
F.
,
Alsaedi
,
A.
, and
Tang
,
J.
,
2018
, “
Crack Synchronization of Chaotic Circuits Under Field Coupling
,”
Nonlinear Dyn.
,
93
(
4
), pp.
2057
2069
.
5.
Buonomo
,
A.
,
Kennedy
,
M. P.
, and
Lo Schiavo
,
A.
,
2011
, “
On the Synchronization Condition for Superharmonic Coupled QVCOs
,”
IEEE Trans. Circuits Syst.
,
58
(
7
), pp.
1637
1646
.
6.
Oberreiter
,
L.
,
Seifert
,
U.
, and
Barato
,
A. C.
,
2021
, “
Stochastic Discrete Time Crystals: Entropy Production and Subharmonic Synchronization
,”
Phys. Rev. Lett.
,
126
(
2
), p.
020603
.
7.
Pu
,
D.
,
Huan
,
R.
, and
Wei
,
X.
,
2017
, “
Frequency Stability Improvement for Piezoresistive Micromechanical Oscillators Via Synchronization
,”
AIP Adv.
,
7
(
3
), p.
035204
.
8.
Wei
,
X.
,
Xu
,
M.
,
Yang
,
Q.
,
Xu
,
L.
,
Qi
,
Y.
,
Ren
,
Z.
,
Ren
,
J.
,
Huan
,
R.
, and
Jiang
,
Z.
,
2024
, “
MEMS Huygens Clock Based on Synchronized Micromechanical Resonators
,”
Engineering
,
36
(
1
), pp.
124
131
.
9.
Huan
,
R.
,
Pu
,
D.
,
Wang
,
X.
, and
Wei
,
X.
,
2019
, “
Effects of Phase Delay on Synchronization in a Nonlinear Micromechanical Oscillator
,”
Appl. Phys. Lett.
,
114
(
23
), p.
233501
.
10.
Shi
,
Z.
,
Pu
,
D.
,
Wang
,
X.
,
Huan
,
R.
,
Jiang
,
Z.
, and
Wei
,
X.
,
2021
, “
Phase-Delay Induced Variation of Synchronization Bandwidth and Frequency Stability in a Micromechanical Oscillator
,”
Nonlinear Dyn.
,
105
(
4
), pp.
2981
2994
.
11.
Shi
,
Z.
,
Pu
,
D.
,
Lv
,
Q.
,
Huan
,
R.
,
Wang
,
X.
,
Xiao
,
Z.
,
Jiang
,
Z.
, and
Wei
,
X.
,
2023
, “
Enhancement of Synchronization Bandwidth in an Arch Beam
,”
J. Sound Vib.
,
545
, p.
117415
.
12.
Martineau
,
S.
,
Saffold
,
T.
,
Chang
,
T. T.
, and
Ronellenfitsch
,
H.
,
2022
, “
Enhancing Synchronization by Optimal Correlated Noise
,”
Phys. Rev. Lett.
,
128
(
9
), p.
098301
.
13.
Xu
,
L.
,
Ren
,
J.
,
Jiang
,
Z.
,
Jia
,
Y.
, and
Wei
,
X.
,
2022
, “
Effect of Joule Heating on the Performance of Micromechanical Piezoresistive Oscillator
,”
Sens. Actuat. A
,
333
, p.
113234
.
14.
Alcheikh
,
N.
,
Tella
,
S. A.
, and
Younis
,
M. I.
,
2018
, “
Adjustable Static and Dynamic Actuation of Clamped-Guided Beams Using Electrothermal Axial Loads
,”
Sens. Actuat. A
,
273
, pp.
19
29
.
15.
Miller
,
J. M. L.
,
Zhu
,
H.
,
Heinz
,
D. B.
,
Chen
,
Y.
,
Flader
,
I. B.
,
Shin
,
D. D.
,
Lee
,
J. E. Y.
, and
Kenny
,
T. W.
,
2018
, “
Thermal-Piezoresistive Tuning of the Effective Quality Factor of a Micromechanical Resonator
,”
Phys. Rev. Appl.
,
10
(
4
), p.
044055
.
16.
Hajjaj
,
A. Z.
,
Jaber
,
N.
,
Hafiz
,
M. A. A.
,
Ilyas
,
S.
, and
Younis
,
M. I.
,
2018
, “
Multiple Internal Resonances in MEMS Arch Resonators
,”
Phys. Lett. A
,
382
(
47
), pp.
3393
3398
.
17.
Hall
,
A. R.
,
Herrera-May
,
A. L.
,
Tapia
,
J. A.
,
Domínguez-Nicolás
,
S. M.
,
Juarez-Aguirre
,
R.
,
Gutierrez-D
,
E. A.
,
Flores
,
A.
,
Figueras
,
E.
, and
Manjarrez
,
E.
,
2014
, “
Improved Detection of Magnetic Signals by a MEMS Sensor Using Stochastic Resonance
,”
PLoS One
,
9
(
10
), p.
e109534
.
18.
Zhang
,
W.
,
Zhu
,
H.
, and
Lee
,
J. E. Y.
,
2015
, “
Piezoresistive Transduction in a Double-Ended Tuning Fork SOI MEMS Resonator for Enhanced Linear Electrical Performance
,”
IEEE Trans. Electron Devices
,
62
(
5
), pp.
1596
1602
.
19.
Hajjaj
,
A. Z.
,
Alfosail
,
F. K.
, and
Younis
,
M. I.
,
2018
, “
Two-to-One Internal Resonance of MEMS Arch Resonators
,”
Int. J. Non Linear Mech.
,
107
, pp.
64
72
.
20.
Hajjaj
,
A. Z.
,
Alcheikh
,
N.
, and
Younis
,
M. I.
,
2017
, “
The Static and Dynamic Behavior of MEMS Arch Resonators Near Veering and the Impact of Initial Shapes
,”
Int. J. Non Linear Mech.
,
95
, pp.
277
286
.
21.
Hajjaj
,
A. Z.
,
Ramini
,
A.
,
Alcheikh
,
N.
, and
Younis
,
M. I.
,
2017
, “
Electrothermally Tunable Arch Resonator
,”
J. Microelectromech. Syst.
,
26
(
4
), pp.
837
845
.
22.
Xiao
,
Z.
,
Shi
,
Z.
,
Wang
,
X.
,
Wei
,
X.
, and
Huan
,
R.
,
2024
, “
Dual-Jump Amplification in an Electric-Thermal Adjusted Arch Beam Micro-Resonator
,”
Sens. Actuat. A
,
365,
p.
114925
.
23.
Xu
,
W.
,
Xie
,
L.
, and
Ying
,
Y.
,
2017
, “
Mechanisms and Applications of Terahertz Metamaterial Sensing: A Review
,”
Nanoscale
,
9
(
37
), pp.
13864
13878
.
24.
Tao
,
Y.
,
Boss
,
J. M.
,
Moores
,
B. A.
, and
Degen
,
C. L.
,
2014
, “
Single-Crystal Diamond Nanomechanical Resonators With Quality Factors Exceeding One Million
,”
Nat. Commun.
,
5
(
1
), p.
3638
.
25.
Kim
,
B.
,
Hopcroft
,
M. A.
,
Candler
,
R. N.
,
Jha
,
C. M.
,
Agarwal
,
M.
,
Melamud
,
R.
,
Chandorkar
,
S. A.
,
Yama
,
G.
, and
Kenny
,
T. W.
,
2008
, “
Temperature Dependence of Quality Factor in MEMS Resonators
,”
J. Microelectromech. Syst.
,
17
(
3
), pp.
755
766
.
26.
Qu
,
T.
, and
Jackson
,
I.
,
2022
, “
Dynamic Modulus, Internal Friction, and Transient Creep at High Temperature in Austenitic Stainless Steel
,”
Mater. Today Commun.
,
30
, p.
103073
.
27.
Tsubono
,
K.
,
Owa
,
S.
,
Mio
,
N.
,
Akasaka
,
N.
, and
Hirakawa
,
H.
,
1987
, “
Internal Frictions of Austenitic Stainless Steels at Low Temperature
,”
Cryogenics (Guildford)
,
27
(
4
), pp.
217
218
.
28.
Yoo
,
K.
,
Chung
,
K.
,
Yoo
,
J.
, and
Song
,
H.
,
2007
, “
The Low Temperature Sintering Properties of Modifird PbTiO3 Ceramics
,”
Integr. Ferroelectr.
,
90
(
1
), pp.
20
29
.
29.
Zippo
,
A.
,
Barbieri
,
M.
, and
Pellicano
,
F.
,
2019
, “
Temperature Gradient Effect on Dynamic Properties of a Polymeric Circular Cylindrical Shell
,”
Compos. Struct.
,
216
, pp.
301
314
.
30.
Ramini
,
A. H.
,
Hennawi
,
Q. M.
, and
Younis
,
M. I.
,
2016
, “
Theoretical and Experimental Investigation of the Nonlinear Behavior of an Electrostatically Actuated In-Plane MEMS Arch
,”
J. Microelectromech. Syst.
,
25
(
3
), pp.
570
578
.
31.
Ouakad
,
H. M.
, and
Younis
,
M. I.
,
2014
, “
Dynamic Response of MEMS Sensor Near Fundamental and Higher-Order Frequencies
,”
IEEE
, pp.
1956
1959
.
32.
Kacem
,
N.
, and
Hentz
,
S.
,
2009
, “
Bifurcation Topology Tuning of a Mixed Behavior in Nonlinear Micromechanical Resonators
,”
Appl. Phys. Lett.
,
95
(
18
), p.
183104
.
33.
Kroupa
,
V. F.
,
1983
, “
Frequency Synthesis by Phase Lock
,”
Proc. IEEE
,
71
(
6
), pp.
783
784
.
34.
Shoshani
,
O.
,
Heywood
,
D.
,
Yang
,
Y.
,
Kenny
,
T. W.
, and
Shaw
,
S. W.
,
2016
, “
Phase Noise Reduction in an MEMS Oscillator Using a Nonlinearly Enhanced Synchronization Domain
,”
J. Microelectromech. Syst.
,
25
(
5
), pp.
870
876
.
35.
Demir
,
A.
, and
Hanay
,
M. S.
,
2020
, “
Fundamental Sensitivity Limitations of Nanomechanical Resonant Sensors Due to Thermomechanical Noise
,”
IEEE Sens. J.
,
20
(
4
), pp.
1947
1961
.
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