Nonlinearities in single-crystal silicon micromechanical resonators

The fundamental performance limit of single-crystal silicon resonators set by device nonlinearities in characterized. Using Leeson´s model for near carrier phase noise, the nonlinearity is shown to set the scaling limit in miniaturizing oscillators. A circuit model based on discretization of distributed mass and nonlinear elasticity is introduced to accurately simulate the large amplitude vibrations. Based on published data for the third-order silicon stiffness tensor, the fundamental material nonlinearity limit is estimated. This theoretical limit is compared to measured nonlinearities in bulk acoustic wave (BAW) micromechanical resonators. The material set and measured nonlinearities are of same order-of-magnitude showing that the maximum vibration amplitude of studied BAW microresonators is near the fundamental limit. The maximum strain for single-crystal silicon resonators set by hysteresis limit is estimated to be 2/spl middot/10/sup -3/ (fracture limit 10/sup -2/), which corresponds to the maximum energy density of E/sub m//V=3/spl middot/10/sup 5/ J/m/sup 3/. This value is at least two orders-of-magnitude higher than for shear-mode quartz resonators, which partially compensates for the small size of MEMS components.