Mathematical modeling of electrostatic MEMS with tailored dielectric properties

The "pull-in" or "snap-down" instability in electrostatically actuated microelectromechanical systems (MEMS) presents a ubiquitous challenge in MEMS technology of great importance. In this instability, when applied voltages are increased beyond a critical value, there is no longer a steady-state configuration of the device where mechanical members remain separate. This severely restricts the range of stable operation of many devices. In an attempt to reduce the effects of this instability, researchers have suggested spatially tailoring the dielectric properties of MEMS devices. Here, a mathematical model of an idealized electrostatically actuated MEMS device is constructed and analyzed for the purpose of investigating this possibility. The pull-in instability is characterized in terms of the bifurcation diagram for the mathematical model. Variations in this bifurcation diagram for various dielectric profiles are studied, yielding insight into flow this technique may be used to increase the stable range of operation of electrostatically actuated MEMS devices.