Effect of coupled modes on pull-in voltage and frequency tuning of a NEMS device

A dynamic microelectromechanical system and a nanoelectromechanical system are designed to operate over a desired frequency range. There exist different types of frequency tuning mechanisms such as tuning due to the electrostatic softening effect and the hardening effect because of the axial tension. These two effects are discussed quite often in many studies. In this paper, we discuss about the case where both the effects can be accounted simultaneously to obtain frequency tuning. To model the effects, we take a fixed–fixed beam separated by a bottom and a side electrode. Subsequently, we solve the coupled elasticity and electrostatic equation using a Galerkin method to obtain the frequencies of two orthogonal modes, namely, the in-plane and out-of-plane modes. After validating the model with experimental results available in the literature, we study the coupled effects of these two modes on the pull-in effect and frequency tuning. It is found that the pull-in voltage can be increased by the intermodal coupling. The coupling region of the two modes can be controlled by selecting appropriate gaps between the beam and the side and bottom electrodes, respectively. (paper)