In this study, an accurate analytic semi-linear elliptic differential model for a circular membrane MEMS device, which considers the effect of the fringing field on the membrane curvature recovering, is presented. A novel algebraic condition, related to the membrane electromechanical properties, able to govern the uniqueness of the solution, is also demonstrated. Numerical results for the membrane profile, obtained by using the Shooting techniques, the Keller-Box scheme, and the III/IV Stage Lobatto IIIa formulas, have been carried out, and their performances have been compared. The convergence conditions, and the possible presence of ghost solutions, have been evaluated and discussed. Finally, a practical criterion for choosing the membrane material as a function of the MEMS specific application is presented.
Keywords: fringing field; membrane MEMS devices; numerical methods for BVPs; semi-linear elliptic problems.