An investigation of structural dimension variation in electrostatically-coupled MEMS resonator pairs using mode-localization

If a pair of MEMS resonators are 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 study have been found to
be 9 times greater than state-of-the-art two-degree-of-freedom
mode-localized sensors.