The nonlinearity cancellation phenomenon in micromechanical resonators

Abstract

In this paper, we present comprehensive analysis of the nonlinearities in a micromechanical clamped-clamped beam resonator. A nonlinear model which incorporates both mechanical and electrostatic nonlinear effects is established for the resonator and verified by experimental results. Both the nonlinear model and experimental results show that the first-order cancellation between the mechanical and electrostatic nonlinear spring constants occurs at about 45 V dc polarization voltage for a 193 kHz resonator in vacuum pressure of 37.5 µTorr. Our study also reveals that the nonlinearity cancellation is helpful in optimizing the overall resonator performance. On top of improving the frequency stability of the resonator by reducing its amplitude-frequency coefficient to almost zero, the nonlinearity cancellation also boosts the critical vibration amplitude of the resonator (0.57 µm for the beam resonator with 2 µm nominal gap spacing), leading to better power handling capabilities. The results from the clamped-clamped beam resonator studied in this work can be easily generalized and applied to other types of resonators.