Multistability of cantilever MEMS/NEMS switches induced by electrostatic and surface forces

MEMS/NEMS switches are used in a variety of portable electronics and RF telecommunications systems. MEMS/NEMS switches are ideally bi-stable, with one ON and one OFF state and a reliable switching between the two induced by electrical actuation. Presented herein is an exploration into non-ideal behavior, i.e. tri-stability, and parametric sensitivity of a generalization of cantilever MEMS/NEMS switches. The representative system model employs multiphysics features based on Euler–Bernoulli beam theory, parallel plate capacitance for electrostatics, and a Lennard-Jones form of surface interaction. The geometry, material properties, and surface features of the device are condensed into just a few dimensionless quantities, creating a parameter space of low enough dimensionality to provide accessible representations of all system equilibria within physically relevant ranges. Analysis of this system model offers insight regarding conditions necessary for bi- and tri-stability in such systems, which are crucial for informing studies on switching dynamics and various device performance metrics.