In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic nonlinearities valid up to displacements comparable to the gap in the case of an electrostatically actuated doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to both numerical integrations and electrical measurements of devices fabricated on 200 mm SOI wafers; it shows very good agreement with both. An important contribution of this work is the provision for closed-form expressions of the critical amplitude and the pull-in domain initiation amplitude including all nonlinearities. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility to drive the resonator beyond its critical amplitude. Consequently, the sensor performance can be enhanced to the maximum below the pull-in instability, while keeping a linear behavior.

We report the experimental observation of a four-bifurcation-point (or five possible amplitudes for a given frequency) behavior of electrostatically actuated micromechanical resonators, called the mixed (first hardening then softening) behavior. We also demonstrate both analytically and experimentally tuning the bifurcation topology of this behavior via an electrostatic mechanism. An analytical model allows for the qualitative as well as quantitative explanation of the experiments and serves as a simple tool for design of nonlinear micromechanical devices under high drive.