Non-linear statics and dynamics of nanoelectromechanical systems based on nanoplates and nanowires

Abstract

An analysis of the three-dimensional nanoelectromechanical systems (NEMS) is presented. Nanotubes could be a key one-dimensional element in future NEMS device; but they would be inadequate when two- or three-dimensional structures are required. A general free-energy-based formulation to treat statics and dynamics of three-dimensional NEMS, according to classical or quantum mechanics, is derved and presenteed; the method is then applied to nanoplates and nanowires. The equilibrium and stability of an elastic (e.g., graphene sheet) nanoplate-based NEMS under an electrical field and van der Waals forces (pauli's repulsion and large displacements are also discussed) are evaluated by minimizing the free energy and by the sign of the determinant of its Hessian matrix. The structural instability, arising at ythre so-called pull-in voltage, would correspond to the switch of the device. The amplitude and frequency of the thermal vibrations of the nanoplate are evaluated as a function of the applied voltage. The effect of the van der Waals forces on the NEMS dynamics is also presented. The amplitude and frequency of the oscillations at O K, from the uncertainty principle, are estimated.