An analytical model considering size effect for calculating the pull-in voltage of electrostatically actuated micro curled cantilever beams

An analytical model for calculating the pull-in voltage of micro cantilever beams subject to electrostatic force is developed based on a modified stress theory in this paper. The analytical model considers size effect, the fringing fields between the micro curled beam and the substrate as well as the initial curling induced by the residual stress gradient. The analytical solution of pull-in voltage is obtained by the energy method, and simply rearranged to the multiplication of the classical pull-in voltage model and a modification term. Further, the present model is validated by the experimental data obtained by Gupta, and the material length scale parameter for polysilicon micro cantilever beams is also estimated by the least square error method. Very good agreement is observed between the present work results and the experimental data. This study may be helpful to characterize the size-dependent mechanical properties of MEMS. Consequently, the proposed analytical solution can be used as an efficient tool for designing the high reliability cantilever-type MEMS products.