870 000 $Q$ -Factor Capacitive Lamé Mode Resonator With Gap Closing Electrodes Enabling 4.4 k $\Omega$ Equivalent Resistance at 50 V

This work presents a Lamé mode resonator featuring a novel gap closing mechanism, which employs electrostatic force to reduce the capacitive transduction gaps to submicrometer values in order to overcome fabrication technology critical spacing limitations. This leads to significant resonator loss and motional resistance reduction while maintaining high Q-factor even in air. Prototypes were fabricated in two commercial siliconon-insulator processes. Upon the application of a dc voltage of 55 V between the resonator structure and the electrodes, the gaps sizes are reduced to as low as 200 nm. A resonance frequency of 18 MHz with Q-factors as high as 866000 was observed under 1 mtorr vacuum and as high as 32000 at atmospheric pressure. A loss of 33 dB was measured at 55 V, which corresponds to an equivalent resistance of 4.4 kΩ, more than 60 times lower than that of a similar design without a gap closing mechanism at the same voltage. This significantly reduces the complexity of the oscillation sustaining circuitry. The frequency tuning range is also increased significantly as a result of the gap reduction, which can be useful for overcoming ambient conditions and fabrication variations.