Nonlinearities in a high-Q SOI Lamé-mode bulk resonator

In this paper, a detailed study of the nonlinearities in a high-Q SOI Lamé-mode bulk resonator is reported. The bulk resonator is designed to operate at 6.35 MHz with a quality factor of 1.7 million at air pressure below 100 Pa. As the vibration amplitude increases, the transmission curve of the resonator progressively bends to lower frequencies due to spring softening effects. The model parameters of the resonator are quantified based on some preliminary experimental results and verified by numerical calculation. Compared with a flexural-mode beam resonator, the Lamé-mode bulk resonator is much less susceptible to nonlinear effects and thus can store three orders of magnitude more vibration energy before frequency hysteresis occurs. Closed-loop measurement further demonstrates that the ultra-high quality factor and superior power handling capability enable the Lamé-mode based oscillator to achieve 42 dB lower phase noise than the flexural-mode one at 10 Hz offset from the carrier frequency