Abstract
This paper presents a finite element method (FEM) simulation study for the frequency response analysis of a capacitive comb-drive resonator based on micro-electro-mechanical systems technology. The post-manufactured design parameters of the resonator are firstly determined after the Modified Silicon on Glass fabrication process by using the parameter extraction method. Then, these results are used to form a 3D structure of the fabricated device. Elmer FEM, an open-source finite element software for multi-physics problems, is selected within the several options for the frequency response analysis of the formed 3D structure. During the FEM analysis, an optimized mesh structure is imported to Elmer FEM for the 3D model of the resonator. Next, the frequency response analyses of the resonator are implemented with a flowchart by using Elmer FEM for a fixed AC level and various DC voltages. The parameter extraction outcomes obtained from probe test data and theoretically calculated values are crosschecked with the output of analyses obtained from the Elmer FEM. The FEM simulation results are compared with the experimental data for the frequency response analyses, the motional parameters and the motional current values as well as the rest capacitance. Furthermore, the approximation error of the simulated results of FEM analysis is calculated. Thus, the capacitive microstructures can be designed more precisely by considering expected quality factor value and fabrication-related deviations.
Graphical abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Acar C, Shkel AM (2005) Structurally decoupled micromachined gyroscopes with post-release capacitance enhancement. J Micromech Microeng 15:109
Ahmadian M, Jafari K (2019) A graphene-based wide-band MEMS accelerometer sensor dependent on wavelength modulation. IEEE Sens J 19(15):6226–6232. https://doi.org/10.1109/JSEN.2019.2908881
Ahrens J, Geveci B, Law C (2005) ParaView: an end-user tool for large data visualization, visualization handbook, Chap. 36, 1st edn. Elsevier, Amsterdam, pp 717–31
Bao M, Yang H (2007) Squeeze film air damping in MEMS. Sens Actuators A 136(1):3–27
Bao M, Yang H, Yin H, Shen S (2000) Effects of electrostatic forces generated by the driving signal on capacitive sensing devices. Sens Actuators A Phys 84(3):213–219. https://doi.org/10.1016/S0924-4247(00)00312-5
Bedair SS, Fedder GK (2004) CMOS MEMS oscillator for gas chemical detection. Sensors. https://doi.org/10.1109/ICSENS.2004.1426330
Chen F, Wen Z, Xu D, Zhou W, Li X (2021) An anti-aliasing and self-clocking ΣΔM cobweb-like disk resonant MEMS gyroscope with extended input range. In: 2021 IEEE 34th international conference on micro electro mechanical systems (MEMS), pp 334–337. https://doi.org/10.1109/MEMS51782.2021.9375143
Chiou J-C, Lin Y-J, Kuo C-F (2008) Extending the traveling range with a cascade electrostatic comb-drive actuator. J Micromech Microeng. https://doi.org/10.1088/0960-1317/18/1/015018
COMSOL Multiphysics® - MEMS Module (2020) A 3D biased resonator: stationary, eigenfrequency, frequency domain, and pull-in analyses. https://www.comsol.com/model/a-3d-biased-resonator-stationary-eigenfrequency-frequency-domain-and-pull-in-ana-11748. Accessed 24 Feb 2023
Debin S, Jie X, Chunju W, Bin G (2009) Hybrid forging processes of micro-double gear using micro-forming technology. Int J Manuf Technol 44:238–243. https://doi.org/10.1007/s00170-008-1829-2
Do C, Erbes A, Yan J, Seshia AA (2016) Design and implementation of a low-power hybrid capacitive MEMS oscillator. Microelectron J 56:1–9. https://doi.org/10.1016/j.mejo.2016.07.007
Electricite de France, Code-Aster (2011) Analysis of structures and thermo-mechanics for studies & research, EDF – R&D, www.code-aster.org. Accessed 22 Aug 2021
Frangi A, Laghi G, Langfelder G, Minotti P, Zerbini S (2015) Optimization of sensing stators in capacitive MEMS operating at resonance. J Microelectromech Syst 24(4):1077–1084. https://doi.org/10.1109/JMEMS.2014.2381515
Grade JD, Yasumura KY, Jerman H (2003) A DRIE comb-drive actuator with large, stable deflection range for use as an optical shutter. TRANSDUCER '03. https://doi.org/10.1109/SENSOR.2003.1215380
Guo ZY, Lin LT, Zhao QC, Yang ZC, Xie H, Yan GZ (2010) A lateral-axis microelectromechanical tuning-fork gyroscope with decoupled comb drive operating at atmospheric pressure. J Microelectromech Syst 19(3):458–468. https://doi.org/10.1109/JMEMS.2010.2046477
Hauptmann P (1991) Resonant sensors and applications. Sens Actuators A 26(1–3):371–377. https://doi.org/10.1016/0924-4247(91)87018-X
Henrotte F, Hameyer K (2004) Computation of electromagnetic force densities: Maxwell stress tensor vs virtual work principle. J Comput Appl 168(1):235–243. https://doi.org/10.1016/j.cam.2003.06.012
Hu F, Xu N, Wang W, Wang Y, Zhang W, Han J, Zhang W (2016) A dynamically tunable terahertz metamaterial absorber based on an electrostatic MEMS actuator and electrical dipole resonator array. J Micromech Microeng 26:1
Iqbal F, Lee B (2018) A study on measurement variations in resonant characteristics of electrostatically actuated MEMS resonators. Micromachines 9(4):173. https://doi.org/10.3390/mi9040173
Kainz A, Steiner H, Schalko J, Jachimowicz A, Kohl F, Stifter M, Beigelbeck R, Keplinger F, Hortschitz W (2018) Distortion-free measurement of electric field strength with a MEMS sensor. Nat Electron 1:68–73. https://doi.org/10.1038/s41928-017-0009-5
Khan N, Ahamed MJ (2020) Design and development of a MEMS butterfly resonator using synchronizing beam and out of plane actuation. Microsyst Technol 26:1643–1652. https://doi.org/10.1007/s00542-019-04705-8
Knick CR, Sharar DJ, Wilson AA, Smith GL, Morris CJ, Bruck HA (2019) High frequency, low power, electrically actuated shape memory alloy MEMS bimorph thermal actuators. J Micromech Microeng 29(7):075005
Kumar R, Rab S, Pant BD, Maji S (2018) Design, development and characterization of MEMS silicon diaphragm force sensor. Vacuum 153:211–216. https://doi.org/10.1016/j.vacuum.2018.04.029
Lee JE-Y, Seshia AA (2011) Direct parameter extraction in feedthrough-embedded capacitive MEMS resonators. Sens Actuator A Phys 167:237–244. https://doi.org/10.1016/j.sna.2011.02.016
Lin L, Howe RT, Pisano AP (1998) Microelectromechanical filters for signal processing. J Microelectromech Syst 7(3):286–294. https://doi.org/10.1109/84.709645
Liu M, Gorman DG (1995) Formulation of Rayleigh damping and its extension. Comput Struct 57(2):277–285. https://doi.org/10.1016/0045-7949(94)00611-6
Naik S, Hikihara T (2011) Characterization of a MEMS resonator with extended hysteresis. IEICE Electron Express 8(5):291–298. https://doi.org/10.1587/elex.8.291
Naik S, Hikihara T (2014) Synchronization in coupled MEMS resonators. In: In V, Palacios A, Longhini P (eds) International conference on theory and application in nonlinear dynamics (ICAND 2012). Understanding complex systems. Springer, Cham. https://doi.org/10.1007/978-3-319-02925-2_31
Raback P, Malinen M, Ruokolainen J, Pursula A, Zwinger T (eds) (2019) Elmer models manual. CSC-IT Center for Science, Espoo
Rabenimanana T, Walter V, Kacem N, Moal PL, Bourbon G, Lardies J (2019) Mass sensor using mode localization in two weakly coupled MEMS cantilevers with different length: Design and experimental model validation. Sens Actuator A Phys 295:643–652. https://doi.org/10.1016/j.sna.2019.06.004
Riegel J, Mayer W, Havre Y (2021) FreeCAD (Version 0.18.4R) https://www.freecadweb.org. Accessed 22 Aug 2021
Sabry Y, Medhat M, Bourouina T, Khalil D (2012) Parameter extraction of MEMS comb-drive near-resonance equivalent circuit: physically-based technique for a unique solution. J Micro Nanolith MEMS MOEMS. https://doi.org/10.1117/1.JMM.11.2.021205
Sathya S, Pavithra M, Muruganand S (2016) Simulation of electrostatic actuation in integrated comb drive MEMS resonator for energy harvester applications. Mater Sci Eng. https://doi.org/10.1088/1757-899X/149/1/012050
Shoaib M, Hisham N, Basheer N et al (2016) Frequency and displacement analysis of electrostatic cantilever-based MEMS sensor. Analog Integr Circ Sig Process 88:1–11. https://doi.org/10.1007/s10470-016-0695-3
Soysal U, Marty F, Géhin E, Motzkus C, Algré E (2020) Fabrication, electrical characterization and sub-ng mass resolution of sub-μm air-gap bulk mode MEMS mass sensors for the detection of airborne particles. Microelectron Eng 221:111190. https://doi.org/10.1016/j.mee.2019.111190
Su SXP, Yang HS, Agogino AM (2005) A resonant accelerometer with two-stage microleverage mechanisms fabricated by SOI-MEMS technology. IEEE Sens J 5(6):1214–1223. https://doi.org/10.1109/JSEN.2005.857876
Tan Y, Zhou R, Zhang H, Lu G, Li Z (2006) Modeling and simulation of the lag effect in a deep reactive ion etching process. J Micromech Microeng 16:2570–2575. https://doi.org/10.1088/0960-1317/16/12/008
Tanner D et al (2003) Resonant frequency method for monitoring MEMS fabrication. SPIE’s Proc 4980:220–228
Tez S, Akin T (2012) Comparison of two alternative fabrication processes for a three-axis capacitive MEMS accelerometer. Procedia Eng 47:342–345. https://doi.org/10.1016/j.proeng.2012.09.153
Tez S, Kaya M (2021) Development of algorithms in open-source Elmer FEM for frequency response and biased modal analysis of MEMS cantilever. J Comput Electron 20:1020–1031. https://doi.org/10.1007/s10825-021-01672-0
Tez S, Ak M (2023) Integration of conducting polymers with MEMS lateral comb-drive resonator via electrodeposition for VOCs detection. J Mater Sci 58:3078–3093. https://doi.org/10.1007/s10853-023-08203-1
Tez S, Aykutlu U, Torunbalci MM, Akin T (2015) A bulk-micromachined three-axis capacitive MEMS accelerometer on a single die. J Microelectromech Syst 24(5):1264–1274. https://doi.org/10.1109/JMEMS.2015.2451079
Tian WC, Chen ZQ, Cao YR (2016) Analysis and test of a new MEMS micro-actuator. Microsyst Technol 22:943–952
Tilmans HAC (1996) Equivalent circuit representation of electromechanical transducers: I. Lumper-parameter systems. J Micromech Microeng 6:157–176. https://doi.org/10.1088/0960-1317/6/1/036
Tu C et al (2020) Dissipation analysis methods and Q-enhancement strategies in piezoelectric MEMS laterally vibrating resonators: a review. Sensors 20(17):4978. https://doi.org/10.3390/s20174978
Wang W, Jia J, Li J (2013) Slide film damping in microelectromechanical system devices. Proc Inst Mech Eng Part N J Nanoeng Nanosyst 227(4):162–170
Wang S et al (2018) A MEMS resonant accelerometer for low-frequency vibration detection. Sens Actuators A Phys 283:151–158. https://doi.org/10.1016/j.sna.2018.09.055
Yamane D, Matsushima T, Konishi T, Toshiyoshi H, Masu K, Machida K (2016) A dual-axis MEMS capacitive inertial sensor with high-density proof mass. Microsyst Technol 22(3):459–464. https://doi.org/10.1007/s00542-015-2539-y
Zhang J et al (2015) Microelectromechanical resonant accelerometer designed with a high sensitivity. Sensors (Basel, Switzerland) 15(12):30293–310. https://doi.org/10.3390/s151229803
Zotov SA, Simon BR, Trusov AA, Shkel AM (2015) High quality factor resonant MEMS accelerometer with continuous thermal compensation. IEEE Sens J 15(9):5045–5052. https://doi.org/10.1109/JSEN.2015.2432021
Acknowledgements
This study was supported by the Scientific and Technological Research Council of Türkiye (TÜBİTAK) under the grant number 116E231. The authors thank TÜBİTAK for financial support.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Tez, S., Kaya, M. A simulation study verified by experimental test results for frequency response analysis of MEMS comb-drive resonator. Microsyst Technol 29, 1281–1293 (2023). https://doi.org/10.1007/s00542-023-05487-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00542-023-05487-w