Analysis of One-Dimensional and Two-Dimensional Thin Film “Pull-in” Phenomena Under the Influence of an Electrostatic Potential

Abstract

A thin one-dimensional rectangular or two-dimensional axisymmetric film is clamped at the perimeter. An electrostatic potential (V0*) applied to a pad directly underneath the film leads to a “pull-in” phenomenon. The electromagnetic energy stored in the capacitive film-pad dielectric gap is decoupled from the mechanical deformation of the film using the Dugdale-Barenblatt-Maugis cohesive zone approximation. The ratio of film-pad gap (g) to film thickness (h), or, γ=g∕h, is found to play a crucial role in the electromechanical behavior of the film. Solution spanning a wide range of γ is found such that V0*∝γ3∕2 for γ<0.5 and V0*∝γ5∕2 for γ>5. The new model leads to new design criteria for MEMS-RF-switches.