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

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.