The pull-in behavior of electrostatically actuated bistable microstructures

The results of theoretical and experimental investigation of an initially curved clamped-clamped microbeam actuated by a distributed electrostatic force are presented. Reduced-order Galerkin and consistently constructed lumped models of the shallow Euler-Bernoulli arch were built and verified by numerical analysis, and the influence of various parameters on the stability was investigated. Due to the unique combination of generic mechanical and electrostatic nonlinearities, the voltage-deflection characteristic of the device may have two maxima implying the existence of sequential snap-through buckling and pull-in instability and of bistability of the beam. The first critical voltage can be higher or lower than the second one, while the stable deflections are significantly larger than in a straight beam. The minimal initial elevation required for the appearance of the snap-through in the electrostatically actuated beam is smaller than in the case of uniform deflection-independent loading; a closed-form approximation of this elevation was evaluated. The devices were fabricated from silicon on insulator (SOI) wafer using deep reactive ion etching and in-plane responses were characterized by means of optical and scanning electron microscopy. Model results obtained for the actual dimensions of the device were in good agreement with the experimental data.