Deformable MEMS with Fringing Field: Models, Uniqueness Conditions and Membrane Profile Recovering

Fringing Field

A particular 1D II-order differential semi-linear elliptic model for electrostatic membrane MEMS devices, which is well-known in the literature, considers the amplitude of the electric field locally proportional to the membrane’s geometric curvature, which contains a term involving the fringing field according to Pelesko and Driscoll’s theory. Thus, in this paper, we will begin from this elliptical model, of which the uniqueness condition for the solution does not depend on the electromechanical properties of the membrane’s constituent material. In particular, after analyzing the model’s advantages and disadvantages, we present a new uniqueness condition for the solution depending on the properties listed above, which appears to be more important than the existence condition of the solution that is well-known in literature. Therefore, once the fringing field’s mode of action on the electrostatic force acting on the membrane is evaluated, suitable numerical techniques are used and compared to recover the membrane profile without ghost solutions and to propose an innovative criterion for selecting the membrane material, which depends on the electrical operative parameters and vice-versa. Finally, the possible industrial uses of the studied device are evaluated.