Analysis of a Model for Electrical Discharge in MEMS

TL;DR

This paper investigates the mathematical modeling of electrical discharge phenomena in MEMS devices, establishing local existence of solutions for the coupled nonlinear system describing electron, ion densities, and electric potential.

Contribution

It introduces a new analysis proving local well-posedness for a coupled nonlinear elliptic-parabolic system modeling MEMS discharges.

Findings

Proved local-in-time existence of weak solutions.

Applied compactness techniques from drift-diffusion equations.

Enhanced understanding of MEMS discharge dynamics.

Abstract

We study the local well-posedness of the solution to a coupled nonlinear elliptic-parabolic system which models electrical discharge in a Micro-Electro-Mechanical System (MEMS). A simple MEMS capacitor device contains two plates acting as the capacitor's electrodes, one of which is flexible, and which are separated by a narrow gas-filled gap. In the event of the flexible plate approaching the other, electrical discharge can occur. This is modelled here by two parabolic equations, for densities of electrons and positive ions, and an elliptic equation for electric potential. We show the local-in-time existence of a weak solution for the coupled system. Compactness techniques, used previously in the study of drift-diffusion equations, are employed in our proof.