Understanding and controlling modal coupling in micro/nanomechanical devices is integral to the design of high-accuracy timing references and inertial sensors. However, insight into specific physical mechanisms underlying modal coupling, and the ability to tune such interactions is limited. Here, we demonstrate that tuneable mode coupling can be achieved in capacitive microelectromechanical devices with dynamic electrostatic fields enabling strong coupling between otherwise uncoupled modes. A vacuum-sealed microelectromechanical silicon ring resonator is employed in this work, with relevance to the gyroscopic lateral modes of vibration. It is shown that a parametric pumping scheme can be implemented through capacitive electrodes surrounding the device that allows for the mode coupling strength to be dynamically tuned, as well as allowing greater flexibility in the control of the coupling stiffness. Electrostatic pump based sideband coupling is demonstrated, and compared to conventional strain-mediated sideband operations. Electrostatic coupling is shown to be very efficient, enabling strong, tunable dynamical coupling.

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Mode-localized sensors have attracted attention because of their high parametric sensitivity and first-order common-mode rejection to temperature drift. The high-fidelity detection of resonator amplitude is critical to determining the resolution of mode-localized sensors where the measured amplitude ratio in a system of coupled resonators represents the output metric. Operation at specific bifurcation points in a nonlinear regime can potentially improve the amplitude bias stability; however, the amplitude ratio scale factor to the input measurand in a nonlinear regime has not been fully investigated. This paper theoretically and experimentally elucidates the operation of mode-localized sensors with respect to stiffness perturbations (or an external acceleration field) in a nonlinear Duffing regime. The operation of a mode-localized accelerometer is optimized with the benefit of the insights gained from theoretical analysis with operation in the nonlinear regime close to the top critical bifurcation point. The phase portraits of the amplitudes of the two resonators under different drive forces are recorded to support the experimentally observed improvements for velocity random walk. Employing temperature control to suppress the phase and amplitude variations induced by the temperature drift, 1/f noise at the operation frequency is significantly reduced. A prototype accelerometer device demonstrates a noise floor of 95 ng/√Hz and a bias instability of 75 ng, establishing a new benchmark for accelerometers employing vibration mode localization as a sensing paradigm. A mode-localized accelerometer is first employed to record microseismic noise in a university laboratory environment.

This paper demonstrates a resonant accelerometer employing weakly coupled resonators for inertial force transduction. An ultra-low virtual mode coupling is established by employing the parametric pump in the coupled resonators to enhance the parametric sensitivity. This paper proposes that the amplitude of the driven resonator can be used for monitoring the input acceleration in a limited linear range around the veering point. In addition to the high-sensitivity improvement, the measurement complexity is also considerably reduced compared to the previous amplitude ratio readout sensors. The sensitivity is adjustable by changing the parametric pumping amplitude. The experimental results show that the noise power spectral density is ∼230 ng/√Hz, which is the best reported noise floor for resonant accelerometers based on weakly coupled resonators.