**Phase Noise Reduction via Nonlinear Oscillation**

High quality factors are usually desired in MEMS oscillator as it will improve the oscillator's close-to-carrier noise. However, a possible alternative to improve phase noise is to oscillate the device at the critical vibration point. Previous research has shown that even though the frequency amplitude curve starts to show multi-value solutions as devices are driven into the nonlinear regime, frequency is a single-value function of the phase. Therefore, unlike open loop sweeps where instability occurs, stable operation can be achieved by controlling the close loop oscillation phase. At the critical bifurcation vibration point where the freq vs. phase curve is vertical, frequency is insensitive to phase, thus providing opportunities for phase noise reduction.

**Understanding the Effect of Doping on Material Nonlinearities**

**Understanding the Effect of Doping on Material Nonlinearities**

In recent years, there has been an increase interest of using heavily doped p- or n-type silicon for passive frequency-temperature compensation. Adding dopants to the silicon lattice will not only introduce free charge carriers, but will also cause a strain in the lattice due to a size dissimilarity between the silicon and the dopant atoms. These effects shift the semiconductor energy bands and result in a change in the material elastic constants, since any change in the total electronic energy content of the crystal will also contributes to the total elastic energy. Our experimental results clearly show a strong dependence of the nonlinearity character on the orientation, doping level, and vibrational mode shape. These results indicate that the doping can have a significant impact on the character and strength of the elastic nonlinearities in MEMS devices.

**Investigation of Nonlinear Coupling in Bulk Acoustic Mode Resonators **

**Investigation of Nonlinear Coupling in Bulk Acoustic Mode Resonators**

In this section, we demonstrate the effect of nonlinear coupling of between different bulk modes of silicon MEMS resonators (e.g. Lame mode resonator and Length extensional resonator). We observed experimentally that the coupling behavior has a strong dependence on the resonant mode order, the mode shape of the coupled modes, as well as the doping type, concentration, and crystal orientation, leading to a variety of complex phenomena which may need to be taken notice of when devices are used under dual-mode operations.