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A distributed static model of capacitive MEMS microwave power detection chip

Ruifeng Li and Debo Wang

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 Corresponding author: Debo Wang, wdb@njupt.edu.cn

DOI: 10.1088/1674-4926/25100007CSTR: 32376.14.1674-4926.25100007

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Abstract: To improve the theoretical prediction accuracy of static mechanical quantities in MEMS cantilever beams for microwave power detection chips, a distributed static model is proposed based on the deflection equation. An analytical framework is established through the precise characterization of cantilever beam bending. The framework can accurately extract key electromechanical parameters, and the correlation between these parameters and geometric changes is systematically studied. Results show that the pull-in voltage increases with the gap but decreases with the length. The predicted pull-in voltage indicates a relative error of only 6.5% between the distributed static model and the simulation, which is significantly lower than that of the other two models. The overload power and sensitivity are also analyzed to facilitate performance trade-offs in chip design. The measured return loss varies between −66.46 dB and −10.56 dB over the 8−12 GHz frequency band, exhibiting a characteristic V-shaped trend. Moreover, the measured sensitivity of 66.5 fF/W closely matches the theoretical value of 69.3 fF/W, showing a relative error of 5.6%. These findings confirm that the distributed model outperforms the other two in terms of both accuracy and physical realism, thereby providing important reference for the design of microwave power detection chips.

Key words: MEMSpower detectioncantilever beamstatic modelsensitivity.



[1]
Liu Y C, Su Y Q, Weng Z C, et al. A MEMS fast steering mirror with 10 mm aperture for free-space optical communication. 2024 IEEE 37th International Conference on Micro Electro Mechanical Systems (MEMS). Austin, 2024: 1011
[2]
D R, K R D, Sravya M L, et al. Developing an Internet of Things (IoT) driven alert system for detecting and mitigating rash driving incidents. 2025 5th International Conference on Soft Computing for Security Applications (ICSCSA), 2025: 747
[3]
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[4]
Rotake D R, Darji A D. Stiffness and sensitivity analysis of microcantilever based piezoresistive sensor for bio-MEMS application. 2018 IEEE SENSORS, 2018: 1
[5]
Fernández L J, Wiegerink R J, Flokstra J, et al. A capacitive RF power sensor based on MEMS technology. J Micromech Microeng, 2006, 16(7): 1099 doi: 10.1088/0960-1317/16/7/001
[6]
Lin X Z, Ying J, Lin X Z. Analytical model of electrostatic fixed-fixed microbeam for pull-in voltage. 2008 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2008: 803
[7]
Shoaib M, Hamid N H B, Ali N B B Z, et al. Study of nonlinear pull-in voltage effects in electrostatic cantilever-based MEMS sensors. 2014 5th International Conference on Intelligent and Advanced Systems (ICIAS), 2014: 1
[8]
Zhang H Q, Li L F, Bai X J, et al. Mechanical model of MEMS cantilever beam of capacitive microwave power sensor. Microelectronics, 2019, 49(3): 373
[9]
Xie J C, Zuo W, Zhang C C, et al. Study on static mechanical model of MEMS cantilever beam. Microelectronics, 2020, 50(4): 543
[10]
Zhang C C, He Y, Xie J C, et al. Optimization of overload power of capacitive MEMS microwave power sensor. Microelectronics, 2021, 51(3): 434
[11]
Wang D B, Gu X F, Zhao J, et al. An in-line microwave power detection system based on double MEMS cantilever beams. IEEE Sens J, 2020, 20(18): 10476 doi: 10.1109/JSEN.2020.2994149
[12]
Xu Q R, Ding Z Y, Wang D B. Research on microwave power detection chips based on MEMS cantilever beams. Microelectronics, 2025, 55(2): 303
[13]
Xiong S L, Xu Q R, You A X, et al. Study on the second-order vibration model of dual-channel microwave power detection chip. IEEE Trans Electron Devices, 2025, 72(7): 3820 doi: 10.1109/TED.2025.3566358
[14]
Xu Q R, Chen X, Wang D B. A novel dual-channel MEMS microwave power detection chip with fixed beam. IEEE Trans Electron Devices, 2025, 72(8): 4385 doi: 10.1109/TED.2025.3584003
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Xu L, Fang Y M, Qie J J. Analysis of dynamic pull-in phenomena for parallel-plate electrostatic micro-actuator. Semicond Technol, 2012, 37(3): 176
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Fu W W, Fang Y M, Liu T. Analysis of statical pull-in phenomena for perforated-plate electrostatic micro-actuator. Chin J Electron Devices, 2014, 37(3): 395
[17]
Zuo W, Guo Q T, Ji X C, et al. Structural optimization of capacitive MEMS microwave power sensor. IEEE Sens J, 2020, 20(19): 11380 doi: 10.1109/JSEN.2020.2998075
[18]
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Wei L C, Mohammad A B, Kassim N M. Analytical modeling for determination of pull-in voltage for an electrostatic actuated MEMS cantilever beam. ICONIP '02. Proceedings of the 9th International Conference on Neural Information Processing. Computational Intelligence for the E-Age, 2002: 233
[21]
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[23]
Xin Z H, Sun H Y, Wang D B. A high-performance dual-channel MEMS microwave power sensor with cantilever beam. IEEE Sens J, 2023, 23(11): 11540 doi: 10.1109/JSEN.2023.3269035
[24]
Benfriha E, Adnane A, Cheriet M E, et al. Pyramidal Sun sensor calibration via dichotomy method. 2024 1st International Conference on Electrical, Computer, Telecommunication and Energy Technologies (ECTE-Tech), 2024: 1
[25]
Yi Z X, Liao X P. A capacitive power sensor based on the MEMS cantilever beam fabricated by GaAs MMIC technology. J Micromech Microeng, 2013, 23(3): 035001 doi: 10.1088/0960-1317/23/3/035001
[26]
Xu Q R, Ding Z Y, Wang D B. MEMS microwave power detection chip based on fixed beams and its model. J Semicond, 2025, 46(6): 062301 doi: 10.1088/1674-4926/24100018
[27]
Li C, Xiong J J, Wang D B. A novel capacitive microwave power sensor based on double MEMS cantilever beams. IEEE Sens J, 2022, 22(12): 11803 doi: 10.1109/JSEN.2022.3174556
[28]
Zhang Z Q, Liao X P. Suspended thermopile for microwave power sensors based on bulk MEMS and GaAs MMIC technology. IEEE Sens J, 2015, 15(4): 2019 doi: 10.1109/JSEN.2014.2382719
[29]
Kasambe P V, Barwaniwala A, Sonawane B, et al. Mathematical Modeling and Numerical Simulation of Novel Cantilever Beam Designs for Ohmic RF MEMS Switch Application2019 International Conference on Advances in Computing. Communication and Control (ICAC3), 2019: 1
Fig. 1.  (Color online) Structure of the microwave detection chip based on a cantilever beam.

Fig. 2.  (Color online) Structure of distributed static model.

Fig. 3.  (Color online) The variation of the proportionality coefficient C with a3.

Fig. 4.  (Color online) Deflection profile of the 300 μm cantilever beam across the 0−218 μm range.

Fig. 5.  (Color online) Deflection profile of the 300 μm beam across the 218−300 μm range.

Fig. 6.  (Color online) The lumped model.

Fig. 7.  (Color online) The pivoted model.

Fig. 8.  (Color online) Predicted pull-in voltage of 300 μm beam versus initial gap in different models.

Fig. 9.  (Color online) Sensitivity versus cantilever beam length and measuring electrode width.

Fig. 10.  (Color online) Schematic cross-section of the process flow.

Fig. 11.  (Color online) SEM images of the chip. (a) SEM image of the power detection chip with a 400 μm beam length. (b) The cantilever beam. (c) Hole of cantilever beam perforation. (d) Air bridge. (e) Enlarged air bridge structure.

Fig. 12.  (Color online) Power Detection Chip Test Platform.

Fig. 13.  (Color online) Measured results of return loss.

Fig. 14.  (Color online) Measured results of capacitance variation.

Table 1.   Structural parameters of the capacitive detection channel.

Symbol Description Chip1 Chip2 Chip3
E Young's modulus of the cantilever beam (gold) 79 GPa
ε0 Permittivity of air 8.85×10-12 F/m
Z0 Impedance of matched load 50 Ω
L Length of cantilever beam 200 μm 300 μm 400 μm
g0 The initial gap between the cantilever beam and the CPW 1.6 μm
t Thickness of the cantilever beam 2 μm
b Width of cantilever beam 150 μm 225 μm 300 μm
bs Width of measuring electrode 100 μm 200 μm 280 μm
x1 Horizontal distance between the left end of the measuring electrode and the anchor of the cantilever beam 8 μm 8 μm 28 μm
x2 Horizontal distance between the right end of the measuring electrode and the anchor of the cantilever beam 208 μm 208 μm 308 μm
x3 Horizontal distance between the left end of the CPW signal line and the anchor of the cantilever beam 118 μm 218 μm 318 μm
DownLoad: CSV

Table 2.   Pull-in voltage (V) in different models.

L/μmLumped
Model
Pivoted
Model
Distributed
Static
Simulation
2006.017.307.937.69
3002.673.243.833.57
4001.501.822.332.02
5000.961.171.601.53
6000.670.811.181.02
7000.490.500.920.79
DownLoad: CSV
[1]
Liu Y C, Su Y Q, Weng Z C, et al. A MEMS fast steering mirror with 10 mm aperture for free-space optical communication. 2024 IEEE 37th International Conference on Micro Electro Mechanical Systems (MEMS). Austin, 2024: 1011
[2]
D R, K R D, Sravya M L, et al. Developing an Internet of Things (IoT) driven alert system for detecting and mitigating rash driving incidents. 2025 5th International Conference on Soft Computing for Security Applications (ICSCSA), 2025: 747
[3]
Yi Z X, Liao X P. Measurements on intermodulation distortion of capacitive power sensor based on MEMS cantilever beam. IEEE Sens J, 2014, 14(3): 621 doi: 10.1109/JSEN.2013.2293147
[4]
Rotake D R, Darji A D. Stiffness and sensitivity analysis of microcantilever based piezoresistive sensor for bio-MEMS application. 2018 IEEE SENSORS, 2018: 1
[5]
Fernández L J, Wiegerink R J, Flokstra J, et al. A capacitive RF power sensor based on MEMS technology. J Micromech Microeng, 2006, 16(7): 1099 doi: 10.1088/0960-1317/16/7/001
[6]
Lin X Z, Ying J, Lin X Z. Analytical model of electrostatic fixed-fixed microbeam for pull-in voltage. 2008 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, 2008: 803
[7]
Shoaib M, Hamid N H B, Ali N B B Z, et al. Study of nonlinear pull-in voltage effects in electrostatic cantilever-based MEMS sensors. 2014 5th International Conference on Intelligent and Advanced Systems (ICIAS), 2014: 1
[8]
Zhang H Q, Li L F, Bai X J, et al. Mechanical model of MEMS cantilever beam of capacitive microwave power sensor. Microelectronics, 2019, 49(3): 373
[9]
Xie J C, Zuo W, Zhang C C, et al. Study on static mechanical model of MEMS cantilever beam. Microelectronics, 2020, 50(4): 543
[10]
Zhang C C, He Y, Xie J C, et al. Optimization of overload power of capacitive MEMS microwave power sensor. Microelectronics, 2021, 51(3): 434
[11]
Wang D B, Gu X F, Zhao J, et al. An in-line microwave power detection system based on double MEMS cantilever beams. IEEE Sens J, 2020, 20(18): 10476 doi: 10.1109/JSEN.2020.2994149
[12]
Xu Q R, Ding Z Y, Wang D B. Research on microwave power detection chips based on MEMS cantilever beams. Microelectronics, 2025, 55(2): 303
[13]
Xiong S L, Xu Q R, You A X, et al. Study on the second-order vibration model of dual-channel microwave power detection chip. IEEE Trans Electron Devices, 2025, 72(7): 3820 doi: 10.1109/TED.2025.3566358
[14]
Xu Q R, Chen X, Wang D B. A novel dual-channel MEMS microwave power detection chip with fixed beam. IEEE Trans Electron Devices, 2025, 72(8): 4385 doi: 10.1109/TED.2025.3584003
[15]
Xu L, Fang Y M, Qie J J. Analysis of dynamic pull-in phenomena for parallel-plate electrostatic micro-actuator. Semicond Technol, 2012, 37(3): 176
[16]
Fu W W, Fang Y M, Liu T. Analysis of statical pull-in phenomena for perforated-plate electrostatic micro-actuator. Chin J Electron Devices, 2014, 37(3): 395
[17]
Zuo W, Guo Q T, Ji X C, et al. Structural optimization of capacitive MEMS microwave power sensor. IEEE Sens J, 2020, 20(19): 11380 doi: 10.1109/JSEN.2020.2998075
[18]
Gere J M, Goodno B J. Mechanics of Materials. Stamford: Cengage Learning, 2013
[19]
Liu C. Foundations of MEMS. Beijing: China Machine Press, 2007 (in Chinese)
[20]
Wei L C, Mohammad A B, Kassim N M. Analytical modeling for determination of pull-in voltage for an electrostatic actuated MEMS cantilever beam. ICONIP '02. Proceedings of the 9th International Conference on Neural Information Processing. Computational Intelligence for the E-Age, 2002: 233
[21]
Bansal D, Bajpai A, Kumar P, et al. Effect of stress on pull-in voltage of RF MEMS SPDT switch. IEEE Trans Electron Devices, 2020, 67(5): 2147 doi: 10.1109/TED.2020.2982667
[22]
Pamidighantam S, Puers R, Baert K, et al. Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions. J Micromech Microeng, 2002, 12(4): 458 doi: 10.1088/0960-1317/12/4/319
[23]
Xin Z H, Sun H Y, Wang D B. A high-performance dual-channel MEMS microwave power sensor with cantilever beam. IEEE Sens J, 2023, 23(11): 11540 doi: 10.1109/JSEN.2023.3269035
[24]
Benfriha E, Adnane A, Cheriet M E, et al. Pyramidal Sun sensor calibration via dichotomy method. 2024 1st International Conference on Electrical, Computer, Telecommunication and Energy Technologies (ECTE-Tech), 2024: 1
[25]
Yi Z X, Liao X P. A capacitive power sensor based on the MEMS cantilever beam fabricated by GaAs MMIC technology. J Micromech Microeng, 2013, 23(3): 035001 doi: 10.1088/0960-1317/23/3/035001
[26]
Xu Q R, Ding Z Y, Wang D B. MEMS microwave power detection chip based on fixed beams and its model. J Semicond, 2025, 46(6): 062301 doi: 10.1088/1674-4926/24100018
[27]
Li C, Xiong J J, Wang D B. A novel capacitive microwave power sensor based on double MEMS cantilever beams. IEEE Sens J, 2022, 22(12): 11803 doi: 10.1109/JSEN.2022.3174556
[28]
Zhang Z Q, Liao X P. Suspended thermopile for microwave power sensors based on bulk MEMS and GaAs MMIC technology. IEEE Sens J, 2015, 15(4): 2019 doi: 10.1109/JSEN.2014.2382719
[29]
Kasambe P V, Barwaniwala A, Sonawane B, et al. Mathematical Modeling and Numerical Simulation of Novel Cantilever Beam Designs for Ohmic RF MEMS Switch Application2019 International Conference on Advances in Computing. Communication and Control (ICAC3), 2019: 1
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    Received: 11 October 2025 Revised: 05 December 2025 Online: Accepted Manuscript: 24 December 2025

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      Ruifeng Li, Debo Wang. A distributed static model of capacitive MEMS microwave power detection chip[J]. Journal of Semiconductors, 2025, In Press. doi: 10.1088/1674-4926/25100007 ****R F Li and D B Wang, A distributed static model of capacitive MEMS microwave power detection chip[J]. J. Semicond., 2025, accepted doi: 10.1088/1674-4926/25100007
      Citation:
      Ruifeng Li, Debo Wang. A distributed static model of capacitive MEMS microwave power detection chip[J]. Journal of Semiconductors, 2025, In Press. doi: 10.1088/1674-4926/25100007 ****
      R F Li and D B Wang, A distributed static model of capacitive MEMS microwave power detection chip[J]. J. Semicond., 2025, accepted doi: 10.1088/1674-4926/25100007

      A distributed static model of capacitive MEMS microwave power detection chip

      DOI: 10.1088/1674-4926/25100007
      CSTR: 32376.14.1674-4926.25100007
      More Information
      • Ruifeng Li was born in China in 2005. She studies at Nanjing University of Posts and Telecommunications for her undergraduate degree. Her interest is MEMS microwave power detection chip
      • Debo Wang was born in China in 1983. He received the B.S. degree in electronic science and technology from the Hebei University of Science and technology, Shijiazhuang, China, in 2007, the M.S. degree and the PhD degree in Key Laboratory of MEMS of the Ministry of Education from the southeast university, Nanjing, China, in 2010 and 2012. He is now a post-doctor in Nanjing University and an associate professor of the Nanjing University of Posts and Telecommunication. The discipline of his research focuses on the RF MEMS devices, particularly on microwave power sensor and its package
      • Corresponding author: wdb@njupt.edu.cn
      • Received Date: 2025-10-11
      • Revised Date: 2025-12-05
      • Available Online: 2025-12-24

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