Modeling the size dependent instability of NEMS sensor/actuator made of nano-wire with circular cross-section

It is well established that electromechanical response of a nano-electromechanical system (NEMS) might be size-dependent. Herein, the size dependent electrostatic instability of NEMS sensor/actuator fabricated from nano-wires with circular cross-section is theoretically investigated considering the effects of the Coulomb electrostatic and van der Waals molecular attractions. For this purpose, modified couple stress theory is applied to model the size effect on the instability of the system. The van der Waals and Coulomb attractions are computed from the simplified Lennard–Jones potential and the electrical capacitance model, respectively. In order to solve the nonlinear constitutive equation of the system, four different approaches including modified variational iteration method, monotonic iteration method, lumped parameter model and numerical solution are employed. It is found that when the diameter of the nano-wire is comparable with the intrinsic material length scale, size effect can substantially influence the pull-in voltage of the system. Interestingly, a coupling between van der Waals force and size dependency can affect the instability deflection of the sensor/actuator.