An Investigation of Structural Dimension Variation in Electrostatically Coupled MEMS Resonator Pairs Using Mode Localization

If a pair of MEMS resonators is electrostatically coupled together, the vibration amplitude ratios at the resonant frequencies of the resulting coupled system are sensitive to stiffness perturbation. An imbalance between the two resonators causes the confinement of vibration energy when the system is resonating, an effect known as mode localization. The degree of localization can be determined by extracting the amplitude ratio of the resonators through capacitive transduction. In this paper, we have fabricated MEMS devices, using a dicing-free silicon-on-insulator process, consisting of pairs of closely spaced microresonators. Each resonator consists of a clamped-clamped beam with a wider section in the middle, which is the location of the electrostatic coupling, instituted through the dc biasing of the resonators. Several devices have been fabricated, with the length of the anchor beams being varied, which influences the frequency of resonance. Stiffness imbalance between the resonators has been introduced through electrostatic spring softening, with the sensitivity of the amplitude ratio of the resonant-mode shape being greater for the higher frequency, shorter anchor devices. The sensitivities of the devices in this paper have been found to be nine times greater than the state-of-the-art two-degree-of-freedom mode-localized sensors.