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.

A silicon microelectromechanical systems (MEMS) resonator utilizing the torsional-to-transverse vibration conversion is designed, fabricated and evaluated. The resonant frequency for the torsional modes mostly depends on only beam length, providing a large tolerance in the fabrication process. It has been, however, a critical issue to investigate the mechanism for generating the torsional vibration and the reduction of motional resistance. We propose a new beam structure, in which four torsion beams are vibrated by twist force generated by a transverse beam. The novel process for fabricating resonators provides a narrow gap surrounded by flat surfaces, which can reduce the motional resistance. The fabricated resonators are measured with a laser-Doppler (LD) vibrometer. The scanning function of the LD vibrometer confirms the torsional-to-transverse vibration conversion has been successfully achieved. The measured resonant frequency, 10.96 MHz, is in good agreement with the simulated one. The Q-factor has been also measured to be as high as 2.2 ×104 in vacuum. The electrical characteristic is evaluated with an impedance analyzer. At the resonant frequency, the extracted motional resistance for the 0.5-µm-gap resonator is 2.0 MΩ, which is greatly reduced, owing to the narrow gap effect, from that of the 1-µm-gap resonator. The temperature coefficient of the resonant frequency between -40 and 85 °C, has been measured to be -24.4 ppm/deg. The resonant frequency linearly decreases as the temperature rises.

No abstract