Heterogeneous dielectric properties in MEMS models

TL;DR

This paper models the complex electrostatic and mechanical interactions in MEMS devices with heterogeneous dielectric materials, deriving equations that account for dielectric jumps and reduced models under specific assumptions.

Contribution

It introduces a new framework for modeling MEMS with heterogeneous dielectrics, including derivation of governing equations and reduced models for thin or small aspect ratio devices.

Findings

Derivation of coupled electrostatic and mechanical equations from energy principles

Formulation of a free boundary transmission problem due to dielectric heterogeneity

Development of simplified models for thin or small aspect ratio MEMS devices

Abstract

An idealized electrostatically actuated microelectromechanical system (MEMS) involving an elastic plate with a heterogeneous dielectric material is considered. Starting from the electrostatic and mechanical energies, the governing evolution equations for the electrostatic potential and the plate deflection are derived from the corresponding energy balance. This leads to a free boundary transmission problem due to a jump of the dielectric permittivity across the interface separating elastic plate and free space. Reduced models retaining the influence of the heterogeneity of the elastic plate under suitable assumptions are obtained when either the elastic's plate thickness or the aspect ratio of the device vanishes.