Nonlinear limits for single-crystal silicon microresonators

Nonlinear effects in single-crystal silicon microresonators are analyzed with the focus on mechanical nonlinearities. The bulk acoustic wave (BAW) resonators are shown to have orders-of-magnitude higher energy storage capability than flexural beam resonators. The bifurcation point for the silicon BAW resonators is measured and the maximum vibration amplitude is shown to approach the intrinsic material limit. The importance of nonlinearities in setting the limit for vibration energy storage is demonstrated in oscillator applications. The phase noise calculated for silicon microresonator-based oscillators is compared to the conventional macroscopic quartz-based oscillators, and it is shown that the higher energy density attainable with the silicon resonators can partially compensate for the small microresonator size. Scaling law for microresonator phase noise is developed.