Influence of nonlinear intermolecular forces on the harmonic behavior of NEM resonators

This paper investigates the nonlinear effects introduced by the intermolecular forces on the static and harmonic behavior of electrostatically transduced nano-electromechanical (NEM) resonators using a lumped parameter model. We compute the pull-in parameters and study the full impact of the intermolecular forces on the spring softening effect, computing the non-linear terms using a Taylor expansion. We look at the impact on the resonance frequency and the maximum linear vibration amplitude of NEM resonators. From the set of case studies, we find that the non-linear intermolecular forces can have large effects on low stiffness structures. In particular, we report on a doubly clamped beam (DCB) resonator for which the intermolecular nonlinearity is expected to produce a 1% frequency shift and a 33% reduction in the maximum linear vibration amplitude.