Abstract-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.[1246]

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Phase noise in capacitively coupled microresonator-based oscillators is investigated. A detailed analysis of noise mixing mechanisms in the resonator is presented, and the capacitive transduction is shown to be the dominant mechanism for low-frequency 1=f -noise mixing into the carrier sidebands. Thus, the capacitively coupled micromechanical resonators are expected to be more prone to the 1=f -noise aliasing than piezoelectrically coupled resonators. The analytical work is complemented with simulations, and a highly efficient and accurate simulation method for a quantitative noise analysis in closed-loop oscillator applications is presented. Measured phase noise for a microresonator-based oscillator is found to agree with the developed analytical and simulated noise models.

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A micromechanical 13.1 MHz bulk acoustic mode (BAW) silicon resonator is demonstrated. The vihration mode can be characterized as a 2-D plate expansion that preserves the original square shape. The prototype resonator is fabricated of single-crystal silicon by reactive ion etching a silicon-on-insulator (SOI) wafer. The measured high quality factor ( Q = 130000) and current output (&AX 160 PA) make the resonator suitable for reference oscillator applications. An electrical equivalent circuit based on physical device parameters is derived and experimentally verified.

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