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Comparison of pull‐in voltages in MEMS using 3D FEM and analytical approaches

Francisc Bölöni (L2EP‐USTL, Villeneuve d'Ascq, France)
Abdelkader Benabou (L2EP‐USTL, Villeneuve d'Ascq, France)
Abdelmounaïm Tounzi (L2EP‐USTL, Villeneuve d'Ascq, France)



Electrostatic microelectromechanical systems are characterized by the pull‐in instability, associated to a pull‐in voltage. A good design requires an accurate model of this pull‐in phenomenon. The purpose of this paper is to present two approaches to building finite element method (FEM) based models.


Closed form expressions for the computation of the pull‐in voltage, can provide fast results within reliable accuracy, except when treating cases of extreme fringing fields. FEM‐based models come handy when high accuracy is needed. In the first model presented in this paper, the FEM is used to solve the electrostatic problem, while the mechanical problem is solved using a simplified Euler‐Bernoulli beam equation. The second model is a pure FEM model coupling the electrostatic and mechanical problems iteratively through the electrical force. Results for both scalar and vector potential formulations for the FEM models are presented.


In this paper a comparative study of simple pull‐in structures is presented, between analytical and 3D FEM‐based models. A comparison with analytical models and experimental results is also realized.

Research limitations/implications

The coupling between the electrostatic and mechanical problem in the presented approaches, is iterative. Therefore, to improve the accuracy of the presented model, a strong coupling is needed.


In the presented FEM‐analytical model, the electrostatic problem is solved in both, scalar and vector electric potential formulations. This allows defining an upper and a lower limit for the electrostatic force and consequently for the pull‐in voltage.



Bölöni, F., Benabou, A. and Tounzi, A. (2010), "Comparison of pull‐in voltages in MEMS using 3D FEM and analytical approaches", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 29 No. 6, pp. 1653-1661.



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