Analysis of resonance frequency and pull-in voltages of curled micro-bimorph cantilevers

A systematic study is presented on the modelling, fabrication and measurements of curled micro-bimorph cantilevers, which are composed of a dielectric beam with a metal electrode layer coated on top. The device, having stress-induced upward curvature in the electrical off-state, functions as a vertical electrostatic actuator for nanometre displacements. A detailed analysis is carried out of the resonance frequency of the cantilever as a function of its length, deflection and thickness of the upper electrode layer, including the effect of undercut. A Galerkin-based static model is used to predict the pull-in voltages which are validated by measurements. A dynamic model is used to investigate the shift in resonance frequency by the electrostatic spring softening effect, which is evaluated against experimental data. The measured shift in resonance frequency is further extrapolated to non-destructively predict the pull-in voltages.