Extracting mechanical quality factor and eliminating feedthrough using harmonics of thermal-piezoresistive micromechanical resonators.

Thermal-actuation and piezoresistive-detection effects have been employed to pump the effective quality factor of MEMS resonators, targeting simple self-oscillation and better sensing performance in the air. However, the ratio of the pumped effective quality factor to the inherent mechanical quality factor, crucial for characterizing the amplification, is hard to obtain. The main difficulty stems from hidden Lorentz peaks caused by feedthrough effects and the pump effect once the current is applied. In this paper, we demonstrated the presence of high-order harmonic components in the output of thermal-piezoresistive resonators when the oscillation amplitude is sufficiently large. By utilizing second-order harmonics, we achieved the improvement in signal-to-bias ratio of, 20.85 dB compared to that without feedthrough cancellation and 9.67 dB compared to that using a de-embedded method when the bias current is 6.20 mA. Furthermore, the inherent mechanical quality factor is extracted at a low current of 1.8 mA with a value of 5800 using the second-order harmonics, and a nearly two orders of magnitude enhancement in Q factor can be obtained before entering the self-oscillation regime. An amplitude bias instability as good as 55 ppm and a frequency bias instability as good as 10 ppb are realized in the nonlinear operation regime with a pumped effective quality factor of 576k. The paper contributes to the fundamental understanding of the Q pump effect together with harmonic analysis of the thermal-piezoresistive resonators and also pushes forward the development of low-power consumption self-oscillation resonant sensors.