A High-Sensitivity Micromechanical Electrometer Based on Mode Localization of Two Degree-of-Freedom Weakly Coupled Resonators

This paper reports a high-sensitivity resonant electrometer based on the mode localization of two degree-of-freedom weakly coupled resonators (WCRs). When charges are applied to the input electrodes, the effective stiffness of a specific resonator of the WCRs will be perturbed, leading to a drastic change in mode shape owing to the mode localization phenomenon. By measuring the shift of the amplitude ratio, the small charge fluctuation can be accurately sensed. The theoretical mode of the electrometer is established based on the transfer functions of the WCRs. In particular, we establish the design rules of the coupling factor according to the-3-dB bandwidth, amplitude ratio measurement errors, and frequency misalignment between the resonators. The experimental results show that the amplitude ratio-based sensitivity is $\sim 2151$ times higher than the frequency-based sensitivity. The amplitude ratio-based resolution of the electrometer is approximately 1.269 fC.