Abstract
In this study, the optimization of a circular dual back-plate condenser microphone has been done in order to increase the pull-in voltage, sensitivity and resonance frequency simultaneously. Microphone’s diaphragm is assumed as a circular micro-plate subjected to symmetric two-sided electrostatic force. An accurate eighth order polynomial function is determined as the first mode shape of the circular micro-plate and Galerkin decomposition method is employed to find the analytical formulations for the microphone metrics performance. The analytical relations are validated by comparing them with finite element results. Next, the applied voltage, gap size, diaphragm radius and thickness are assumed as the design variables and modified non-dominated sorting genetic algorithm is utilized for multi-objective optimization procedure. Considering low standard deviations and high mean values, a new design point is chosen among the suggested optimal points so that there is an increment in each of three objective functions. Compare to a fabricated sample of a dual back-plate microphone, for the new design point, pull-in voltage has increased more than 3.6 times, sensitivity has improved 4% and resonance frequency has extended 24%.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Azizollah Ganji B, Babaei Sedaghat S, Roncaglia A, Belsito L (2018) Design and fabrication of high performance condenser microphone using C-slotted diaphragm. Microsyst Technol 24:3133–3140
Bao M, Yang H (2007) Squeeze film air damping in MEMS. Sens Actuators A 136:3–27
Coello CAC, Lamont GB, Van Veldhuizen DA (2007) Evolutionary algorithms for solving multi-objective problems, vol 5. Springer, New York
Deb K (2001) Multi-objective optimization using evolutionary algorithms, vol 16. Wiley, New York
Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: International conference on parallel problem solving from nature. Springer, Berlin, pp 849–858
Faris W, Abdel-Rahman E, Nayfeh A (2002) Mechanical behavior of an electrostatically actuated micropump. In: 43rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, p 1303
Ganji BA, Majlis BY (2009) Design and fabrication of a new MEMS capacitive microphone using a perforated aluminum diaphragm. Sens Actuators A 149:29–37
Gembicki F, Haimes Y (1975) Approach to performance and sensitivity multiobjective optimization: the goal attainment method. IEEE Trans Autom Control 20:769–771
Jallouli A, Kacem N, Bourbon G, Le Moal P, Walter V, Lardies J (2016) Pull-in instability tuning in imperfect nonlinear circular microplates under electrostatic actuation. Phys Lett A 380:3886–3890
Karimipour I, Beni YT, Zeighampour H (2018) Nonlinear size-dependent pull-in instability and stress analysis of thin plate actuator based on enhanced continuum theories including nonlinear effects and surface energy. Microsyst Technol 24:1811–1839
Kwon SR, Huang W, Zhang S, Yuan FG, Jiang X (2016) Study on a flexoelectric microphone using barium strontium titanate. J Micromech Microeng 26:045001
Li C, Cordovilla F, Jagdheesh R, Ocaña JL (2017) Design and optimization of a novel structural MEMS piezoresistive pressure sensor. Microsyst Technol 23:4531–4541
Liu J, Martin DT, Kadirvel K, Nishida T, Cattafesta L, Sheplak M, Mann BP (2008a) Nonlinear model and system identification of a capacitive dual-backplate MEMS microphone. J Sound Vib 309:276–292
Liu J, Martin DT, Nishida T, Cattafesta LN, Sheplak M, Mann BP (2008b) Harmonic balance nonlinear identification of a capacitive dual-backplate MEMS microphone. J Microelectromech Syst 17:698–708
López-Arredondo J, Tlelo-Cuautle E, de la Fraga LG (2018) High-Q and wide-bandwidth capacitor multiplier optimized by NSGA-II. IETE J Res. https://doi.org/10.1080/03772063.2018.1436987
Martin DT, Liu J, Kadirvel K, Fox RM, Sheplak M, Nishida T (2007) A micromachined dual-backplate capacitive microphone for aeroacoustic measurements. J Microelectromech Syst 16:1289–1302
Medina L, Gilat R, Krylov S (2017) Modeling strategies of electrostatically actuated initially curved bistable micro plates. Int J Solids Struct 118:1–13
Mohammad I (2011) MEMS linear and nonlinear statics and dynamics. Springer, New York)
Nathanson HC, Newell WE, Wickstrom RA, Davis JR (1967) The resonant gate transistor. IEEE Trans Electron Devices 14:117–133
Papila M, Haftka RT, Nishida T, Sheplak M (2006) Piezoresistive microphone design pareto optimization: tradeoff between sensitivity and noise floor. J Microelectromech Syst 15:1632–1643
Pelesko J, Chen X (2003) Electrostatic deflections of circular elastic membranes. J Electrostat 57:1–12
Rashvand K, Rezazadeh G, Mobki H, Ghayesh MH (2013) On the size-dependent behavior of a capacitive circular micro-plate considering the variable length-scale parameter. Int J Mech Sci 77:333–342
Rayburn RA (2012) Eargle's the microphone book: from mono to stereo to surround—a guide to microphone design and application, 3rd edn. Focal Press, Oxford, pp 1–8
Rombach P, Müllenborn M, Klein U, Rasmussen K (2002) The first low voltage, low noise differential silicon microphone, technology development and measurement results. Sens Actuators A Phys 95:196–201
Saadatmand M, Shooshtari A (2018) Nonlinear vibration analysis of circular micro-plate in two-sided NEMS/MEMS capacitive system by using harmonic balance method. Acta Mech Sin. https://doi.org/10.1007/s10409-018-0794-8
Saeedivahdat A, Abdolkarimzadeh F, Feyzi A, Rezazadeh G, Tarverdilo S (2010) Effect of thermal stresses on stability and frequency response of a capacitive microphone. Microelectron J 41:865–873
Saghir S, Younis MI (2016) An investigation of the static and dynamic behavior of electrically actuated rectangular microplates. Int J Non-Linear Mech 85:81–93
Sajadi B, Goosen H, van Keulen F (2018) Electrostatic instability of micro-plates subjected to differential pressure: a semi-analytical approach. Int J Mech Sci 138:210–218
Taati E, Sina N (2018) Multi-objective optimization of functionally graded materials, thickness and aspect ratio in micro-beams embedded in an elastic medium. Struct Multidiscip Optim 58:262–285
Talebian S, Rezazadeh G, Fathalilou M, Toosi B (2010) Effect of temperature on pull-in voltage and natural frequency of an electrostatically actuated microplate. Mechatronics 20:666–673
Timoshenko SP, Woinowsky-Krieger S (1959) Theory of plates and shells. McGraw-hill, New York
Vo-Duy T, Duong-Gia D, Ho-Huu V, Vu-Do H, Nguyen-Thoi T (2017) Multi-objective optimization of laminated composite beam structures using NSGA-II algorithm. Compos Struct 168:498–509
Vogl GW, Nayfeh AH (2005) A reduced-order model for electrically actuated clamped circular plates. J Micromech Microeng 15:684
Wygant IO, Kupnik M, Khuri-Yakub BT (2018) An analytical model for capacitive pressure transducers with circular geometry. J Microelectromech Syst 27:448–456
Zargarpour N, Zarifi MH (2015) A piezoelectric micro-electromechanical microphone for implantable hearing aid applications. Microsyst Technol 21:893–902
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
About this article
Cite this article
Saadatmand, M., Kook, J. Multi-objective optimization of a circular dual back-plate MEMS microphone: tradeoff between pull-in voltage, sensitivity and resonance frequency. Microsyst Technol 25, 2937–2947 (2019). https://doi.org/10.1007/s00542-018-4240-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00542-018-4240-4