Micromachined Snap-In Resonators

Abstract

MEMS resonators have many applications, including micromachined gyroscopes, resonating pressure sensors and RF devices. Typically, MEMS resonators consist of a proof mass and suspension system that allows the proof mass motion in one or two directions. Micromachined actuators provide kinetic energy to the proof mass, usually at its resonant frequency. In the simplest resonators, the actuators are driven with an AC signal at or near the resonant frequency. In more complex resonators, the actuator-proof mass system is placed in an amplifier feedback circuit so that the electromechanical system self-resonates. MEMS parallel plate actuators (PPAs) are simple to realize, yet complex nonlinear variable capacitors. If a DC voltage is applied in attempt to move the proof mass greater than 1/3 of the electrode rest gap distance, the device becomes unstable and the electrodes snap into contact. A current limiting resistor is often placed in series with the PPA to limit short circuit current due to a snap-in event. Consider the effect of placing a large resistor, on the order on 10 meg-Ohms, in series with the PPA. Then apply a DC voltage across the resistor-PPA pair of sufficient voltage to cause snap-in. Once the electrostatic force (ES) exceeds the spring force (SF), the electrodes will accelerate toward each other. The capacitance between the electrodes swells as the separation distance shrinks. Since the large resistor limits the charging rate of the capacitor, the voltage across it drops. Once the SF exceeds the EF, the momentum of the movable electrode brings it into contact with the fixed electrode, discharging the capacitor. The movable electrode then accelerates away from the fixed electrode while the resistor slowly allows recharging. After recharging, the cycle repeats resulting in stable oscillation. This resonator requires only a DC power supply, a resistor and a MEMS PPA.