The nonlinear electrostatic behavior for shaped electrode actuators

The nonlinear electrostatic pull-in behavior of shaped actuators in micro-electro-mechanical systems (MEMS) is investigated in this article. The differential quadrature method (DQM) was used to solve the nonlinear interaction between the curved electrostatic field force and the deflection of shaped cantilever actuators. Various electro-statically actuated micro-structures, such as cantilever beam-type and fixed-fixed beam-type shaped actuators are studied. The proposed models include the fringing effects of the electrical field. Both the small beam deflection and the large beam deflection models are implemented in this work to elucidate the possible effect of the deflection model on the accuracy. The results calculated from the proposed model agree closely with the measured data. The numerical results reveal that the profile shapes of the actuators may not only influence the distribution of the electrostatic force but also considerably change the nonlinear pull-in voltage.