Nonlinear Modeling and Investigating the Nonlinear Effects on Frequency Response of Silicon Bulk-Mode Ring Resonator

This paper presents a nonlinear analytical model for silicon micromechanical ring resonators with bulk-mode vibrations. A distributed element model has been developed to describe the dynamic behavior of the micromechanical ring resonator. This model shows the nonlinear effects in a silicon ring resonator focusing on the effect of large amplitudes around the resonance frequency, material and electrical nonlinearities. Through the combination of geometrical and material nonlinearities, closed-form expressions for third- order nonlinearity in mechanical stiffness of bulk-mode ring resonators are obtained. Using the perturbation method and the method of harmonic balance, the expressions for describing the effect of nonlinearities on the resonance frequency and stability are derived. The results, which show the effect of varying the AC-drive voltage, initial gap spacing, DC-bias voltage and the quality factor on the frequency response and resonant frequencies, are discussed in detail. The nonlinear model introduces an appropriate method in the field of bulk-mode ring resonator design for achieving sufficient power handling and low motional resistance.