Detection Methods for Multi-Modal Inertial Gas Sensors.

We investigate the rich potential of the multi-modal motions of electrostatically actuated asymmetric arch microbeams to design higher sensitivity and signal-to-noise ratio (SNR) inertial gas sensors. The sensors are made of fixed-fixed microbeams with an actuation electrode extending over one-half of the beam span in order to maximize the actuation of asymmetry. A nonlinear dynamic reduced-order model of the sensor is first developed and validated. It is then deployed to investigate the design of sensors that exploit the spatially complex and dynamically rich motions that arise due to veering and modal hybridization between the first symmetric and the first anti-symmetric modes of the beam. Specifically, we compare among the performance of four sensors implemented on a common platform using four detection mechanisms: classical frequency shift, conventional bifurcation, modal ratio, and differential capacitance. We find that frequency shift and conventional bifurcation sensors have comparable sensitivities. On the other hand, modal interactions within the veering range and modal hybridization beyond it offer opportunities for enhancing the sensitivity and SNR of bifurcation-based sensors. One method to achieve that is to use the modal ratio between the capacitances attributed to the symmetric and asymmetric modes as a detector, which increases the detection signal by three orders of magnitude compared to a conventional bifurcation sensor. We also present a novel sensing mechanism that exploits a rigid arm extending transversely from the arch beam mid-point and placed at equal distances between two side electrodes. It uses the asymmetry of the arch beam motions to induce rotary motions and realize a differential sensor. It is found to increase the detection signal by two orders of magnitude compared to a conventional bifurcation sensor.