Characteristics of Three-Dimensional Resonant Vibration in a MEMS Silicon Beam Resonator

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A silicon beam resonator has been fabricated by using the bulk surface micromachining, and mechanical beam vibrations have been directly evaluated with the laser-Doppler technique. The in-plane vibration, caused by the electrostatic force exerted on a gap between the beam and the drive electrode, and the out-of-plane vibration, caused by the asymmetrical electric field around the beam, have been compared with each other. The measured resonant frequencies have well agreed with those calculated by a simulator. The air damping effect has been measured under various vacuum conditions. The result suggests the fabricated resonators should be packaged under 500 Pa for the air-damping-free vibration. The electrical characterization using an impedance analyzer has shown that the impedance and capacitance have depended on the operating bias voltage, while the resonant frequency has been slightly varied by the bias voltage. These electrical characteristics have been compared with the mechanical vibration behaviors. It has indicated that the qualitative similarity between them has been shown, although the 4 to 5% resonant frequency increase has been observed.

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