Analytical estimates of the pull-in voltage in MEMS and NEMS

Giovanni Bianchi*, Enrico Radi
Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia,
Via Amendola 2, 42122, Reggio Emilia, Italy

* Corresponding author. Email giovanni.bianchi@unimore.it

Abstract
Micro- or Nano-Electro-Mechanical Systems, MEMS-NEMS, are currently employed in a wide variety of applications, ranging from mechanical or electronic engineering to chemistry or biology. The growing interest in this technology is due to notable need for accurate ultrasmall instruments and equipment characterized by very diminutive size, low power consumption, high precision, reliability and compatibility with the integrated circuits [1]. The micro- or nanocantilever beam electrode, suspended above a conductive substrate and actuated by a voltage difference, is the fundamental component of many MEMS and NEMS devices. Moreover, due to their smart mechanical and electronic properties and the recent progress in their fabrication, carbon nanotubes are significantly exploited in industrial applications, such as sensors, nanoactuators, memory devices and nanotweezers, becoming essential components in NEMS [2]. Recent research remarks the role of micropumps in drug delivery systems able to regulate very small and accurate volumes in various industrial, chemical and biomedical applications. Electrostatic micropumps typically are composed of two parallel, thin, circular micro- or nanoplates. The membrane of the electrostatic micropump can be actuated and displaced towards the fixed electrode by applying a voltage across the electrodes. When the actuation voltage is removed, the displaced membrane releases and returns to its original position. In general, under the action of the electrostatic force and intermolecular surface forces, particularly significant at the micro- or nanoscale, the movable electrode deflects toward to the substrate, thus reducing the separation distance between the electrodes. Correspondingly, the magnitude of the attractive forces increases until at a critical voltage, named the pull-in voltage, the flexible electrode collapses onto the substrate. In this work, an analytical method is proposed for estimating the pull-in voltage and the correspondent deflection accurately, thus providing a useful tool for the effective design of innovative MEMS and NEMS devices [3].

Bibliography
[1]	A. Koochi, M. Abadyan, Nonliner Differential Equations in Micro/nano Mechanics. Application in Micro/nano Structures and Electromechanical Systems, Elsevier, 2020. 
[2]	G. Bianchi, E. Radi, Analytical estimates of the pull-in voltage for carbon nanotubes considering tip-charge concentration and intermolecular forces, Meccanica, 55 (2020) 193–209. https://doi.org/10.1007/s11012-019-01119-8
[3]	E. Radi, G. Bianchi, L. di Ruvo, Upper and lower bounds for the pull-in parameters of a micro or nanocantilever on a flexible support, Int. J. Nonlin. Mech. 92 (2017) 176-186. https://doi.org/10.1016/j.ijnonlinmec.2017.03.011