PROCEEDINGS OF THE RUSSIAN HIGHER SCHOOL
ACADEMY OF SCIENCES

Abstract
During the process of designing capacitive microelectromechanical systems (MEMS) it is necessary to calculate electric capacitance and electrostatic forces acting between different elements of the construction. These parameters are often evaluated using analytical expressions which do not take into account fringing field effects or by means of numerical computation which takes into account these effects but requires a lot of time and powerful computers that hamper further optimization. At initial stages of MEMS design it is essential to have fast, accurate and evident methods of electrostatic interaction calculation. Therefore analytical expressions allowing evaluating capacitances and electrostatic forces with an accuracy sufficient for practical application are of great interest. This work is devoted to experimental and theoretical study of electro­static interactions in parallel-plate MEMS within a 3D-approach. Dependences of capacitance and electrostatic forces on the interelectrode gap, electrode thickness, and the length-to-width ratio are calculated using the finite element method. On the basis of the calculation approximation formulas for capacitance and electrostatic forces evaluation taking into account fringing field effects have been obtained. A comparison between experimental and theoretical results demonstrates a good coincidence. Applicability limits of the formulas obtained with regard to fringing field effects within 3D, 2D, and 1D-approaches are estimated.

References

1. Palmer H.B. Capacitance of a parallel-plate capacitor by the Schwartz-Christoffel trans-formation. Electrical Engineering, 1937, vol. 56, iss. 3, pp. 363–368. doi: 10.1109/ EE.1937.6540485.
2. Elliot R.S. Electromagnetics: history, theory, and applications. New York, McGraw-Hill, 1966. 631 p.
3. Dragunov V.P., Ostertak D.I. Elektrostaticheskie vzaimodeistviya v MEMS s ploskoparallel'nymi elektrodami. Ch. 1. Raschet emkostei [Electrostatic Interactions in MEMS with Plane-Parallel Electrodes. Pt. 1. Estimation of the capacitance]. Nano- i mikrosistemnaya tekhnika – Journal of Nano and Microsystem Technique, 2010, no. 7, pp. 37–41.
4. Dragunov V.P., Ostertak D.I. Elektrostaticheskie vzaimodeistviya v MEMS s ploskoparallel'nymi elektrodami. Ch. 2. Raschet elektrostaticheskikh sil [Electrostatic interactions in MEMS with plane-parallel electrodes. Pt. 2. Estimation of electrostatic forces]. Nano- i mikrosistemnaya tekhnika – Journal of Nano and Microsystem Technique, 2010, no. 8, pp. 40–47.
5. Dragunov V.P., Ostertak D.I. Raschet normal'noi sostavlyayushchei elektrostaticheskoi sily v MEMS [Calculation of the normal component of the electrostatic force in MEMS]. Sbornik nauchnykh trudov Novosibirskogo gosudarstvennogo tekhnicheskogo universiteta – Transaction of scientific papers of the Novosibirsk state technical university, 2009, no. 1 (55), pp. 40–45.
6. Dragunov V.P., Kolchuzhin V.A., Ostertak D.I. Vliyanie kraevykh effektov na elektricheskuyu emkost' v MEMS [Fringing field effect on electric capacitance in MEMS]. Doklady Akademii nauk vysshei shkoly Rossiiskoi Federatsii – Proceedings of the Russian higher school Academy of sciences, 2009, no. 2 (13), pp. 97–105.
7. Leus V., Elata D. Fringing field effect in electrostatic actuators. Technical Report ETR, 2004, vol. 2, pp. 2–15.
8. Dragunov V.P., Dorzhiev V.Yu. Vliyanie kraevykh effektov na funktsionirovanie MEMS [Fringing field effects influence on MEMS functioning]. Doklady Akademii nauk vysshei shkoly Rossiiskoi Federatsii – Proceedings of the Russian higher school Academy of scien­ces, 2016, no. 1, pp. 48–61.
9. Dorzhiev V.Yu., Dragunov V.P., Ostertak D.I. Raschet emkosti MEMS v 2D-priblizhenii [Calculation of MEMS capacity in 2D-approximation]. Sbornik nauchnykh trudov Novosibirskogo gosudarstvennogo tekhnicheskogo universiteta – Transaction of scientific papers of the Novosibirsk state technical university, 2010, no. 4 (62), pp. 73–80.
10. Hosseini M., Zhu G., Peter Y.-A. A new formulation of fringing capacitance and its application to the control of parallel-plate electrostatic micro actuators. Analog Integrated Circuits and Signal Processing, 2007, vol. 53, iss. 2, pp. 119–128. doi: 10.1007/s10470-007-9067-3.
11. Iossel' Yu.Ya., Kochanov E.S., Strunskii M.G. Raschet elektricheskoi emkosti [Electric capacitance calculation]. Leningrad, Energoizdat Publ., 1981. 288 p.

Просмотров аннотации: 2037
Скачиваний полного текста: 928
Просмотров интерактивной версии: 0