Microsystem Technologies

, Volume 24, Issue 5, pp 2137–2145 | Cite as

A novel expression obtained by using artificial bee colony algorithm to calculate pull-in voltage of fixed-fixed micro-actuators

  • Cevher Ak
  • Ali Yildiz
  • Ali Akdagli
Technical Paper


In this paper, a novel, computationally efficient and simple closed-form expression has been derived to accurately calculate the pull-in voltage value of fixed-fixed micro-actuator. At first, microelectromechanical systems actuators with various physical parameters have been simulated by a software that employs the finite element method, the pull-in voltage expression has been derived by using the artificial bee colony optimization algorithm together with the simulation data. Since the formula is derived from the simulation data, it implicitly contains the fringing field, mid-plane stretching and size effects. In order to verify the accuracy and robustness, the predictions of closed-form formula proposed in this work have been compared with those of the theoretical ones through the simulation and experimental studies previously presented in the literature. The key advantage of the presented method is delivering a satisfying estimation of the pull-in voltage with a simple and easy way.


  1. Ak C, Yildiz A (2014) an inversely designed model for calculating pull-in limit and position of electrostatic fixed-fixed beam actuator. Math Prob Eng. Google Scholar
  2. Ak C, Yildiz A (2016) A new analytical model to estimate the voltage value and position of the pull-in limit of a MEMS cantilever. Micromachines 7(4):53. CrossRefGoogle Scholar
  3. Akdagli A, Toktas A (2010) A novel expression in calculating resonant frequency of H-shaped compact microstrip antennas obtained by using artificial bee colony algorithm. J Electromagnet Wave 24:2049–4061. Google Scholar
  4. Akdagli A, Bicer MB, Ermis S (2011) A novel expression for resonant length obtained by using artificial bee colony algorithm in calculating resonant frequency of C-shaped compact microstrip antennas. Turk J Electr Eng Comput Sci 19:597–606. Google Scholar
  5. Alsaleem FM, Younis MI, Ruzziconi L (2010) An experimental and theoretical investigation of dynamic pull-in in MEMS resonators actuated electrostatically. J Microelectromech Syst 19:794–806. CrossRefGoogle Scholar
  6. Au AK, Lai H, Utela BR, Folch A (2011) Microvalves and micropumps for BioMEMS. Micromachines 2:179–220. CrossRefGoogle Scholar
  7. Batra RC, Porfiri M, Spinello D (2007) Review of modeling electrostatically actuated microelectromechanical systems. Smart Mater 16:R23–R31. CrossRefGoogle Scholar
  8. Bochobza-Degani O, Nemirovsky Y (2004) Experimental verification of a design methodology for torsion actuators based on a rapid pull-in solver. J Microelectromech Syst 13:121–130. CrossRefGoogle Scholar
  9. Chowdhury S, Ahmadi M, Miller WC (2006) Pull-in voltage study of electrostatically actuated fixed-fixed beams using a VLSI on-chip interconnect capacitance model. J Microelectromech Syst 15:639–651. CrossRefGoogle Scholar
  10. Chuang WC, Lee HL, Chang PZ, Hu YC (2010) Review on the modeling of electrostatic MEMS. Sensors 10:6149–6171. CrossRefGoogle Scholar
  11. Dean RN Jr, Luque A (2009) Applications of microelectromechanical systems in industrial processes and services. IEEE Trans Ind Electron 56:913–925. CrossRefGoogle Scholar
  12. Elata D, Bochobza-Degani O, Nemirovsky Y (2003) Analytical approach and numerical alpha-line method for pull-in hyper-surface extraction of electrostatic actuators with multiple uncoupled voltage sources. J Microelectromech Syst 12(5):681–691. CrossRefGoogle Scholar
  13. Eom K, Park HS, Yoon DS, Kwon T (2011) Nanomechanical resonators and their applications in biological/chemical detection. Nanomechanics Princ Phys Reports 503:115–163. Google Scholar
  14. Haluzan DT, Klymyshyn DM, Achenbach S, Börner M (2010) Reducing pull-in voltage by adjusting gap shape in electrostatically actuated cantilever and fixed-fixed beams. Micromachines 1:68–81. CrossRefGoogle Scholar
  15. Hannot SDA, Rixen DJ (2013) A palette of methods for computing pull-in curves for numerical models of microsystems. Finite Elem Anal Des 67:76–90. MathSciNetCrossRefzbMATHGoogle Scholar
  16. Hu YC, Lin DTW, Lee GD (2006) A closed form solution for the pull-in voltage of the micro bridge with initial stress subjected to electrostatic loads. In: IEEE international conference on nano/micro engineered and molecular systems, Zhuhai, pp 757–761. doi: 10.1109/NEMS.2006.334889
  17. Joglekar M, Pawaskar D (2011) Closed-form empirical relations to predict the dynamic pull-in parameters of electrostatically actuated tapered microcantilevers. J Micromech Microeng 21:105014. CrossRefGoogle Scholar
  18. Karaboga D, Akay B (2009) A survey: algorithms simulating bee swarm intelligence. Artif Intell Rev 31(1):68–85. Google Scholar
  19. Kuang JH, Chen CJ (2004) Dynamic characteristics of shaped micro-actuators solved using the differential quadrature method. J Micromech Microeng 14:647–655. CrossRefGoogle Scholar
  20. Lee KB (2007) Closed-form expressions for pull-in parameters of two-degree-of-freedom torsional microactuators. J Micromech Microeng 17:1853–1862. CrossRefGoogle Scholar
  21. Lee KB, Lin L, Cho YH (2008) A closed-form approach for frequency tunable comb resonators with curved finger contour. Sens Actuators A Phys 141:523–529. CrossRefGoogle Scholar
  22. Liu D, Friend KC, Yeo JL (2010) A brief review of actuation at the micro-scale using electrostatics, electromagnetics and piezoelectric ultrasonics. Sci Technol 31:115–123. Google Scholar
  23. Loh OY, Espinosa HD (2012) Nanoelectromechanical contact switches. Nat Nanotechnol 7:283–295. CrossRefGoogle Scholar
  24. Mojahedi M, Zand MM, Ahmadian MT (2010) Static pull-in analysis of electrostatically actuated microbems using homotopy perturbation method. Appl Math Model 34:1032–1041. MathSciNetCrossRefzbMATHGoogle Scholar
  25. Nathanson HC, Newell WE, Wickstrom RA, Davis JR Jr (1967) The resonant gate transistor. IEEE Trans Electron Devices 14:117–133. CrossRefGoogle Scholar
  26. Nisar A, Afzulpurkar N, Mahaisavariya B, Tuantranont A (2008) MEMS-based micropumps in drug delivery and biomedical applications. Sensors Actuators B 130:917–942. CrossRefGoogle Scholar
  27. O’Mahony C, Hill M, Mathewson A (2003) Analysis of electromechanical boundary effects on the pull-in of micromachined fixed-fixed beams. J Micromech Microeng 13:75–80. CrossRefGoogle Scholar
  28. Osterberg PM, Senturia SD (1997) M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures. J Microelectromech Syst 6:107–118. CrossRefGoogle Scholar
  29. Pamidighantam S, Puers R, Baert K, Tilmans HAC (2002) Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions. J Micromech Microeng 12:458–464. CrossRefGoogle Scholar
  30. Poelma RH, Sadeghian H, Noijen SPM, Zaal JJM, Zhang GQ (2011) A numerical experimental approach for characterizing the elastic properties of thin films: application of nanocantilevers. J Micromech Microeng 21(6):065003. CrossRefGoogle Scholar
  31. Pryputniewicz RJ (2007) Progress in microelectromechanical systems. Strain 43:13–25. CrossRefGoogle Scholar
  32. Rocha LA, Cretu E, Wolffenbuttel RF (2004) Analysis and analytical modeling of static pull-in with application to mems-based voltage reference and process monitoring. J Microelectromech Syst 13:342–354. CrossRefGoogle Scholar
  33. Rokni H, Seethaler RJ, Milani AS, Hosseini-Hashemi S, Li X-F (2013) Analytical closed-form solutions for size-dependent static pull-in behavior in electrostatic micro-actuators via Fredholm integral equation. Sens Actuators A 190:32–43. CrossRefGoogle Scholar
  34. Rong H, Huang QA, Nie M, Li W (2004) An analytical model for pull-in voltage of clamped-clamped multilayer beams. Sensors Actuators A 116:15–21. CrossRefGoogle Scholar
  35. Rottenberg X, Wolf ID, Nauwelaers BKJC, Raedt WD, Tilmans HAC (2007) Analytical model of the DC actuation of electrostatic MEMS devices with distributed dielectric charging and nonplanar electrodes. J Microelectromech Syst 16:1243–1253. CrossRefGoogle Scholar
  36. Roy AL, Bhattacharya A, Chaudhuri RR, Bhattacharyya TK (2012) Analysis of the pull-in phenomenon in microelectromechanical varactors. In: 25th Conference on VLSI Design (Hyderabad), pp 185–190. doi: 10.1109/VLSID.2012.68
  37. Sadeghian H, Rezazadeh G, Osterberg PM (2007) Application of the generalized differential quadrature method to the study of pull-in phenomena of MEMs switches. J Microelectromech Syst 16:1334–1340. CrossRefGoogle Scholar
  38. Siddique JI, Deaton R, Sabo E, Pelesko JA (2011) An experimental investigation of the theory of electrostatic deflections. J Electrostatics 69:1–6. CrossRefzbMATHGoogle Scholar
  39. Tang WC, Nguyen TCH, Howe RT (1989) Laterally driven polysilicon resonant microstructures. Sensors Actuators 20:25–32. CrossRefGoogle Scholar
  40. Tilmans HAC, Legtenberg R (2007) Electrostatically driven vacuum encapsulated polysilicon resonators: part II. Theory and performance. Sensors Actuators A 45:67–84. CrossRefGoogle Scholar
  41. Van Spengen WM, Puers R, Mertens R, Wolf ID (2002) Experimental characterization of stiction due to charging in RF MEMS. In: Proc IEEE Int Electron Devices Meeting Dig (San Francisco, CA), pp 901–904. doi: 10.1109/IEDM.2002.1175982
  42. Zhang WM, Meng G (2007) Nonlinear dynamic analysis of electrostatically actuated resonant MEMS sensors under parametric excitation. IEEE Sens J 7:370–380. CrossRefGoogle Scholar
  43. Zhang Y, Zhao YP (2006) Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading. Sensors Actuators A 127:366–380. CrossRefGoogle Scholar
  44. Zhang W, Baskaran R, Turner KL (2002) Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor. Sensors Actuators A 102:139–150. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.The Department of Electrical and Electronics EngineeringToros UniversityMersinTurkey
  2. 2.The Department of Electrical and Electronics EngineeringMersin UniversityMersinTurkey

Personalised recommendations