A New Mathematical Model for a Membrane MEMS Device

The membrane MEMSs represent a good design solution for the industry requirements about the construction of micro-dimensional devices, because easily constructible and extremely versatile. In this domain, the experience of the authors in the modeling of membrane MEMS devices has matured. In this chapter, they present a formalization of stationary $1D$-membrane MEMS in which the electric field magnitude, $|mathbf{E}|$, is proportional to the curvature of the membrane, $C$, obtaining a semilinear elliptic model. Next, techniques based on fixed point Theorems provide results of existence, while an approach based on the joint use of Poincar'e's inequality and Gronwall's Lemma establish conditions of uniqueness. Finally, some numerical tests complete the work.