Silicon Beam Resonator Utilizing the Third-Order Bending Mode

Abstract

A silicon beam resonator utilizing the third-order bending mode is designed and fabricated. It has three driving electrodes for increasing the amplitude of the third-order mode. The mechanical vibration modes of the beam are measured using a laser-Doppler vibrometer, and the electrical characteristic is evaluated with a network analyzer. Because the in-plane vibration is caused by the electrostatic force exerted on a gap between the beam and each driving electrode, the amplitude of the third-order mode in the in-plane vibration can be enhanced by placing three driving electrodes along a resonant beam. The measured resonant frequencies well agree with the simulated ones. From the measurement of the third-order mode in the in-plane vibration with a network analyzer, it has been shown that resonant frequency decreases by 2.3 kHz as DC voltage increases from 30 to 70 V owing to the spring softening effect. The DC bias dependence agrees well between the electrical and mechanical measurements. Finally, the mechanism of inducing an out-of-plane vibration is discussed from a viewpoint of the influence of the electric field generated on a substrate.