Capacitive microbeam resonator design

Abstract

Resonant clamped-clamped microbeams sealed in a hard vacuum cavity are classified as transducers, which can measure physical variables by converting them into axial strain using an appropriate silicon microstructure. These devices can be constructed, using surface micromachining technology, on a single-crystal silicon substrate. They have fundamental resonant frequencies with high sensitivity to strain. Such devices use resonant frequency changes by variables such as pressure, temperature, force, and acceleration to measure these quantities. Electrostatically driven and sensed microbeam resonators may be used for sensor applications. In order to design such microbeam resonators it is useful to use electrical network theory. This requires that the mechanical parameters for the resonator are converted to electrical equivalents. For electrostatically driven and sensed microbeam resonators the drive voltage must contain a dc bias and a small amplitude sinusoid in order to drive the resonators at the resonant frequency. The effects of these dc biases and parasitics on the resonant frequency and the quality factor are clarified here with theoretical calculations using the electrical equivalents of electrostatic microbeam resonators and experimental results. As a result the dc bias and parasitics are dominant factors in determining the performance of capacitive microbeam resonators, especially effecting the resonant frequency and quality factor. The maximum vibration amplitude requirements for pure sinusoidal operation with low power dissipation in the capacitive microbeam resonator have also been identified.