Size-dependent pull-in instability of electrostatically actuated microbeam-based MEMS

We present a size-dependent model for electrostatically actuated microbeam-based MEMS using strain gradient elasticity theory. The normalized pull-in voltage is shown to increase nonlinearly with the decrease of the beam height, and the size effect becomes prominent if the beam thickness is on the order of microns or smaller (i.e. when the beam dimension is comparable to the material length scale parameter). Very good agreement is found between the present model and available experimental data. The study may be helpful to characterize the mechanical properties of small size MEMS, or guide the design of microbeam-based devices for a wide range of potential applications.