Coupled electro-mechanics simulation methodology of the dynamic pull-in in micro-systems

The aim of this paper is to deal with multi-physics simulation of micro-electro-mechanical systems (MEMS) based on an advanced numerical methodology. MEMS are very small devices in which electric as well as mechanical and fluid phenomena appear and interact. Because of their microscopic scale, strong coupling effects arise between the different physical fields, and some forces, which were negligible at macroscopic scale, have to be taken into account. In order to accurately design such micro-electro-mechanical systems, it is of primary importance to be able to handle the strong coupling between the electric and the mechanical fields. In this paper, the finite element method (FEM) is used to model the electro-mechanical interactions and to perform static and transient analyses. The application example considered here is a micro-bridge consisting in a clamped-clamped beam suspended over a substrate (the lower electrode). When a voltage is applied between the beam and the substrate, electrostatic forces appear which force the beam to bend. When the applied voltage increases, the electrostatic force becomes dominant and the plates stick together. The corresponding critical voltage is called the pull-in voltage. When the dynamic behavior of the system is taken into account, it is shown that two new parameters have to be defined: the dynamic pull-in displacement and the dynamic pull-in time.