Comprehensive Reduced-Order Models of Electrostatically Actuated Curved MEMS Switches and Their Dynamics Including Impact and Bounce

As Micro and Nano Electro-Mechanical devices continue to find more applications, the electrostatically actuated micro-beam remains one of the most frequently used structures due to its usefulness and relative simplicity of fabrication. Accurate models of these devices which are valid under a wide range of circumstances are important both for design as well as metrology efforts. Often certain device parameters are implicitly extracted via a mathematical model when they are very difficult to measure directly. This work details the development and results of a reduced-order model for the behavior of an electrostatically actuated beam. The model accounts for arbitrary initial curvature, residual stress, flexible boundary conditions and contact, while including accurate sub-models for the electrostatic and damping forces. The equation of motion of the beam is discretized via the traditional Galerkin method. Static and dynamic solutions are found through specified displacement schemes and direct time integration, respectively. The rich behavior of these systems can easily be seen in the results. Arched doubly-clamped beams can show a variety of bi-stable configurations and tri-stable solutions can be seen in the post-contact behavior of cantilever beams. Dynamic solutions reveal phenomena such as dynamic pull-in, dynamic snap-through, and bouncing behavior. The widely valid model presented here generally converges quickly and is well suited for design, analysis and uncertainty quantification.