Finite Element Mode-ling of Damping of a Squeeze Gas Film in High-Frequency Microelectromechanical Switches with Capacitive Contact

Abstract

The damping effects of a squeeze gas film are one of the main components of damping and naturally arise in the designs of dynamic micromechanical devices, in particular, in high-frequency micromechanical switches with an electrostatic activation mechanism, in which the electrostatic drive consists of a fixed electrode in the form of a plate and a movable electrode in the form of a movable plate suspended on elastic suspensions for the case of capacitive contact. In the static mode of the device, a thin film of gas consisting of air molecules or other inert gas surrounding the device is located and held between the electrodes of the electrostatic drive. This article presents a mathematical model based on the obtained linear inhomogeneous Reynolds differential equation and performs finite element modeling of the pressure distribution in the plate of a suspended movable electrode during compression of a gas film during electrostatic activation of micromechanical switches with a capacitive contact and parallel arrangement of the electrodes of an electrostatic drive depending on the magnitude of the coefficient of this component of damping in a three-dimensional coordinate system, the dependences between the damping force and the elastic force of the compressible gas film on the value of the damping coefficient are also presented. The presented results are applicable to assess the effect of isothermal damping of a squeeze gas film on the dynamics of micromechanical devices, in particular, on the dynamic characteristics of high-frequency micromechanical switches with an electrostatic activation mechanism and a capacitive contact.