Size effect on the static behavior of electrostatically actuated microbeams

We present a new analytical model for electrostatically actuatedmicrobeams to explore the size effect by using the modified couple stress theory and the minimum total potential energy principle. A material length scale parameter is introduced to represent the size-dependent characteristics of microbeams. This model also accounts for the nonlinearities associated with the mid-plane stretching force and the electrostatical force. Numerical analysis for microbeams with clamped-clamped and cantilevered conditions has been performed. It is found that the intensity of size effect is closely associated with the thickness of the microbeam, and smaller beam thickness displays stronger size effect and hence yields smaller deflection and larger pull-in voltage. When the beam thickness is comparable to the material length scale parameter, the size effect is significant and the present theoretical model including the material length scale parameter is adequate for predicting the static behavior of microbeam-based MEMS.