Casimir Effect on Frequency Response of Superharmonic Resonance of NEMS Resonators

This paper investigates the frequency response of superharmonic resonance of the second order of electrostatically actuated nano-electro-mechanical system (NEMS) resonator sensor. The structure of the MEMS device is a resonator cantilever over a ground plate under Alternating Current (AC) voltage. Superharmonic resonance insinuates that the AC voltage is operating in a frequency near one-fourth the natural frequency of the resonator. The forces acting on the system are electrostatic, damping and Casimir force. For the electrostatic force, the AC voltage is in the category of hard excitation in order to induce a bifurcation phenomenon. For Casimir forces to affect the system, the gap distance between the cantilever resonator and base plate is in the range of 20 nm to 1 μm. The differential equation of motion is converted to dimensionless by choosing the gap as reference length for deflections, the length of the resonator for the axial coordinate, and reference time based on the characteristics of the structure. The Method of Multiple Scales (MMS) is used to model the characteristic of the system. MMS transforms the nonlinear partial differential equation of motion into two simpler problems, namely zero-order and first-order. The influences of parameters (i.e. Casimir, damping, second voltage and fringe) were also investigated.