Electromechanical behavior of the curled cantilever beam

We propose an approximate analytical solution to the pull-in voltage of a microcurled cantilever beam. The analytical model considers the realistic situations, which include stress gradient, nonideal boundary conditions, and fringing field capacitance. The proposed analytical model can be used at wafer level for extracting the Young's modulus of the thin film of which the cantilever beam is made. The approximate analytical solution is obtained based on the Euler's beam model and the minimum energy method. The accuracy of the proposed model is verified to be more accurate than the other published models. The model presented in this work can be used for wafer-level evaluation of the material properties through simple electrical testing and is also expected to find use in the design of microelectromechanical devices.