Russian Microelectronics

, Volume 47, Issue 6, pp 393–406 | Cite as

Operational Features of MEMS with an Even Number of Electrodes

  • V. P. DragunovEmail author
  • D. I. OstertakEmail author


The results of investigations on the influence of the nonparallelism of electrodes on electromechanical interactions in imbalanced Micro Electro Mechanical Systems (MEMS) with comb electrode structures in the modes with a controllable voltage and charge are presented. The formulas for the calculation of the potential energy, electrostatic force, critical voltage, critical charge, and the magnitude of critical displacement of a movable electrode under different inclinations of the electrodes, which are necessary for the MEMS design, taking into account their real design features, are derived. It was stated that increasing the mutual inclination and the number of electrodes reduces the modulation depth of the capacitance Cmax/Cmin of the imbalanced capacitors with nonparallel electrodes, which can significantly limit the achievable modulation depth of the capacitance of tunable MEMS, especially when there are a large number of electrodes. It is revealed that in imbalanced MEMS, in the case of controllable voltage, when increasing the relative inclination of the electrodes, the electrostatic attraction force between charged electrodes decreases and the magnitudes of the critical voltage and displacement increase. Increasing the number of electrodes of an imbalanced capacitor will lead to a decrease in the range of the controllable displacement of the movable electrodes and the magnitude of the critical voltage. It is stated that under an invariable charge and nonparallel electrodes in imbalanced MEMS with a comb electrode structure a pull-in effect appears. When increasing the relative inclination of the electrodes, the electrostatic attraction force between the charged electrodes increases and the quantities of the critical charge and displacement decrease. When increasing the number of electrodes in imbalanced MEMS with a comb electrode structure in the invariable charge mode, the value of the critical displacement decreases monotonically and the magnitude of the critical charge rises.



The study was conducted with the financial support of the Ministry of Education and Science of the Russian Federation as a basic part of a state task, project code 8.6847.2017/8.9 on “Development of theoretical backgrounds for the design of digital telecommunication equipment containing microwave attenuators, bandpass/bandstop filters and printed microstripline antennas.”

We thank I.G. Neizvestnyi for his attention to our work and his valuable comments.


  1. 1.
    Pokhlebkin, D., MEMS in the structure of electronic industry in Russia, in Proceedings of the Semicon Russia 2014 Conference, May 14–15, Russia. 28554959-Frost-sullivan-mems-v-strukture-elektronnoy-otrasli-rossii-dmitriy-pohlebkin-frost-sullivan.html. Accessed March 30, 2018.Google Scholar
  2. 2.
    Zhang, W.-M., Yan, H., Peng, Z.-K., and Meng, G., Electrostatic pull-in instability in MEMS/NEMS: a review, Sens. Actuators, A, 2014, vol. 214, pp. 187–218. Scholar
  3. 3.
    Dragunov, V.P. and Ostertak, D.I., The analysis of electromechanical operation of in-plane oberlap MEMS converter, Nauch. Vestn. NGTU, 2009, no. 2 (35), pp. 115–127.Google Scholar
  4. 4.
    Dragunov, V.P. and Ostertak, D.I., Interrelation of electromechanical parameters of MEMP of bridge type, Dokl. Akad. Nauk Vyssh. Shkoly RF, 2009, no. 1 (12), pp. 88–98.Google Scholar
  5. 5.
    Dragunov, V.P. and Ostertak, D.I., Limit characteristics of microelectromechanical energy converters, Nauch. Vestn. NGTU, 2009, no. 1 (34), pp. 129–142.Google Scholar
  6. 6.
    Dorzhiev, V., Dragunov, V., Karami, A., Galayko, D., and Basset, P., MEMS electrostatic vibration energy harvester without switches and inductive elements, J. Phys.: Conf. Ser., 2014, vol. 557, no. 1, p. 012126.Google Scholar
  7. 7.
    Ostertak, D.I., Analysis of electrostatic interactions in plane-parallel MEMS with allowance for edge effects in the 3D approximation, Dokl. Akad. Nauk Vyssh. Shkoly RF, 2017, no. 1 (34), pp. 116–132. doi 10.17212/1727-2769-2017-1-116-132Google Scholar
  8. 8.
    Blum, K.E. and Ostertak, D.I., Capacitance calculation of the comb variable capacitor for the electrostatic vibration energy harvester in consideration of fringing field effects, Nano- Mikrosist. Tekh., 2016, vol. 18, no. 7, pp. 424–431.Google Scholar
  9. 9.
    Dragunov, V.P. and Ostertak, D.I., Electrostatic interactions in MEMS with a counter-pin structure, Dokl. Akad. Nauk Vyssh. Shkoly RF, 2009, no. 1 (12), pp. 99–106.Google Scholar
  10. 10.
    Dragunov, V.P. and Ostertak, D.I., Electrostatic interactions in MEMS with plane-parallel electrodes. Part II. Estimation of electrostatic forces, Nano- Mikrosist. Tekh., 2010, no. 8, pp. 40–47.Google Scholar
  11. 11.
    Hillenbrand, J., Pondrom, P., and Sessler, G.M., Electret transducer for vibration-based energy harvesting, Appl. Phys. Lett., 2015, vol. 106, p. 183902.CrossRefGoogle Scholar
  12. 12.
    Pondrom, P., Sessler, G.M., Bös, J., and Melz, T., Compact electret energy harvester with high power output, Appl. Phys. Lett., 2016, vol. 109, p. 053906.CrossRefGoogle Scholar
  13. 13.
    Guilllemet, R., Basset, P., Galayko, D., Cottone, F., Marty, F., and Bourouina, T., Wideband MEMS electrostatic vibration energy harvesters based on gap-closing interdigited combs with a trapezoidal section, in Proceedings of the IEEE 26th International Conference on MEMS, Taipei, 2013, pp. 817–820. doi 10.1109/ MEMSYS.2013.6474368Google Scholar
  14. 14.
    Ardito, R., Baldasarre, L., and Corigliano, A., On the numerical evaluation of capacitance and electrostatic forces in MEMS, in Proceedings of the 10th International Conference on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2009, pp. 1–8. Scholar
  15. 15.
    Dragunov, V.P., Kiselev, D.E., and Sinitskii, R.E., Features of electromechanical interactions in MEMS with non-parallel electrodes, Nano- Mikrosist. Tekh., 2017, no. 6, pp. 360–369. doi 10.17587/nmst.19.360-369Google Scholar
  16. 16.
    Dragunov, V.P., Sinitskii, R.E., and Kiselev, D.E., Effect of non-parallel electrodes on MEMS characteristics in controlled charge mode, Dokl. Akad. Nauk Vyssh. Shkoly RF, 2017, no. 1 (34), pp. 58–71. doi 10.17212/1727-2769-2017-1-58-71Google Scholar
  17. 17.
    Dragunov, V.P. and Lyutaeva, M.N., Parameters estimation of the MEM transducer with electrodes produced from different materials, in Proceedings of the 2009 International School and Seminar on Modern Problems of Nanoelectronics, Micro- and Nanosystem Technologies, INTERNANO, 2009, pp. 93–96.Google Scholar
  18. 18.
    Kuehne, I., Frey, A., Marinkovic, D., Eckstein, G., and Seidel, H., Power MEMS—a capacitive vibration-to-electrical energy converter with built-in voltage, Sens. Actuators, A, 2008, vol. 142, pp. 263–269.CrossRefGoogle Scholar
  19. 19.
    Varpula, A., Laakso, S.J., Havia, T., Kyynäräinen, J., and Prunnila, M., Contacting mode operation of work function energy harvester, J. Phys.: Conf. Ser., 2014, vol. 557, p. 012010.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia

Personalised recommendations