Nonlinear dynamics of nanomechanical beam resonators: improving the performance ofNEMS-based sensors

Abstract

In order to compensate for the loss of performance when scaling resonant sensors down toNEMS, it proves extremely useful to study the behavior of resonators up to very highdisplacements and hence high nonlinearities. This work describes a comprehensivenonlinear multiphysics model based on the Euler–Bernoulli equation which includes bothmechanical and electrostatic nonlinearities valid up to displacements comparable to the gapin the case of an electrostatically actuated doubly clamped beam. Moreover, the modeltakes into account the fringing field effects, significant for thin resonators. The model hasbeen compared to both numerical integrations and electrical measurements of devicesfabricated on 200 mm SOI wafers; it shows very good agreement with both. Animportant contribution of this work is the provision for closed-form expressions ofthe critical amplitude and the pull-in domain initiation amplitude including allnonlinearities. This model allows designers to cancel out nonlinearities by tuning somedesign parameters and thus gives the possibility to drive the resonator beyondits critical amplitude. Consequently, the sensor performance can be enhancedto the maximum below the pull-in instability, while keeping a linear behavior.