Analytical model of the quasistatic mechanical behavior of galvanic piezoelectric microelectromechanical system switches

An analytical model of the quasistatic behavior of galvanic piezoelectric microelectromechanical system (MEMS) switches is described. The model is based on the Euler-Bernoulli beam equation. Two geometries often used in galvanic switches are investigated: the single clamped cantilever (SCC) and the double clamped beam (DCB). The effects from residual stress and thermal expansion are also taken into account. They are both described by an effective initial gap and an effective bending stiffness in the case of the SCC and the DCB, respectively. Using the analytical model, the beam is optimized with respect to contact force and restoring force. Finally, the scaling behavior of piezoelectric MEMS switches is investigated. The analytical model is benchmarked against the results from finite-element-method simulations, showing good agreement.