Dynamic behavior of an electrostatic MEMS resonator with repulsive actuation

Static and dynamic analyses of an electrostatic microbeam under repulsive force actuation are presented. The repulsive force, created through a specific electrode configuration, generates a net electrostatic force on the beam pushing it away from the substrate. This allows large out-of-plane actuation and eliminates the pull-in instability. For example, a dynamic amplitude of 15 \(\upmu \)m was recorded for a 500-\(\upmu \)m-long cantilever at a DC voltage of 195 V and an AC voltage of 1 V, while the initial gap was only 2 \(\upmu \)m. This study includes mathematical modeling and simulations for a cantilever and a clamped–clamped beam, as well as experimental validation. The beam is modeled using Euler–Bernoulli beam theory and electromechanical coupling effects. Cantilever tip displacement, clamped–clamped midpoint deflection, and natural frequency shifts are reported. Governing equations are solved numerically using the shooting method, which provides a complete picture of the beam dynamics. The numerical results are verified with experimental data from fabricated beams using PolyMUMPs standard fabrication. Frequency response results reveal a mixed softening and hardening behavior and secondary resonances originating from quadratic and cubic nonlinearities in the governing equations. The analysis provides insight for applications in optical and gas sensors where a large signal-to-noise ratio and, sometimes, a wide frequency bandwidth are desired.