Analysis of electromechanical boundary effects on the pull-in of micromachined fixed-fixed beams

Using a commercial finite-element simulation tool, this work considers some of the electromechanical effects commonly neglected during the analysis of electrostatically actuated fixed-fixed beams. These structures are used in many applications of micromechanical systems, from relay switches and RF resonators to thin film characterization tests, but much of the analytical modelling of the device behaviour disregards the effects of electrostatic field fringing, plane-strain conditions and anchor compliance. It is shown that the cumulative total of these errors can be substantial, and may lead to large discrepancies in the expected operational characteristics of the device. We quantify the influence of these effects on the electrostatic pull-in of fixed-fixed beams, and illustrate some of the limitations of ideal pull-in theory. In order to more accurately predict the pull-in voltage for a real structure, a model is developed that combines ideal case theory with anchor compliance correction factors extracted using finite-element analysis. Three common anchor types (ideal, step-up and cup-style) are characterized. The final model takes account of the compliance of the beam anchors, electrostatic field fringing and plane-strain effects, and agrees well with simulated results.