Mechanics of nanoscale beams in liquid electrolytes: beam deflections, pull-in instability, and stiction

Abstract

The pressure between two parallel planar surfaces at equal electric potentials is derived using the modified Poisson-Boltzmann (MPB) equation to account for finite ion size. The effects of finite ion size are presented for a z:z symmetric electrolyte and compared with the pressure derived by the classical Poisson-Boltzmann (PB) equation. The pressures predicted by the two models differ more as the bulk ion concentration, surface potential, and ion size increase. The ratio of the pressures predicted by the two models is presented by varying the ion concentration, surface potential, ion size and distance of separation. The ratio of pressures is relatively independent of the distance of separation between the two surfaces. An elastic beam suspended horizontally over a substrate in liquid electrolyte is subjected to electric, osmotic, and van der Waals forces. The continuous beam structure, not a discrete spring, which is governed by four nondimensional parameters, is solved using the finite element method. The effects of ion concentration and electric potentials to the pull-in instability are especially focused by parametric studies with a carbon nanotube cantilever beam. The pull-in voltage of a double-wall carbon nanotube suspended over a graphite substrate in liquid can be less than or greater than the pull-in voltage in air, depending on the bulk ion concentration. The critical separation between the double-walled carbon nanotube (DWCNT) and the substrate increases with the bulk ion concentration. However, for a given bulk ion concentration, the critical separation is independent of the electric potentials. Furthermore, the critical separation is approximately equal in liquid and air. Stiction, the most common failure mode of the cantilever-based devices, is studied in a liquid environment, including elastic energy, electrochemical work done, van der Waals work done and surface adhesion energy. We extend the classical energy method of the beam peeling for micro-electro-mechanical systems (MEMS) in the air to an energy method for nano-electro-mechanical systems (NEMS) in liquid electrolyte. We demonstrate a useful numerical processing method to find the parameters to free the stiction of the beams and to obtain the detachment length of the beams.