Displacement sensing based on resonant frequency monitoring of electrostatically actuated curved micro beams

The ability to control nonlinear interactions of suspended mechanical structures offers a unique opportunity to engineer rich dynamical behavior that extends the dynamic range and ultimate device sensitivity. We demonstrate a displacement sensing technique based on resonant frequency monitoring of curved, doubly clamped, bistable micromechanical beams interacting with a movable electrode. In this configuration, the electrode displacement influences the nonlinear electrostatic interactions, effective stiffness and frequency of the curved beam. Increased sensitivity is made possible by dynamically operating the beam near the snap-through bistability onset. Various in-plane device architectures were fabricated from single crystal silicon and measured under ambient conditions using laser Doppler vibrometry. In agreement with the reduced order Galerkin-based model predictions, our experimental results show a significant resonant frequency reduction near critical snap-through, followed by a frequency increase within the post-buckling configuration. Interactions with a stationary electrode yield a voltage sensitivity up to ≈560 Hz V^-1 and results with a movable electrode allow motion sensitivity up to ≈1.5 Hz nm^-1. Our theoretical and experimental results collectively reveal the potential of displacement sensing using nonlinear interactions of geometrically curved beams near instabilities, with possible applications ranging from highly sensitive resonant inertial detectors to complex optomechanical platforms providing an interface between the classical and quantum domains.