Analytical Modeling of a Novel High- $Q$ Disk Resonator for Liquid-Phase Applications

To overcome the detrimental effects of liquid environments on microelectromechanical systems resonator performance, the in-fluid vibration of a novel disk resonator supported by two electrothermally driven legs is investigated through analytical modeling and the effects of the system's geometric/material parameters on the dynamic response are explored. The all-shear interaction device (ASID) is based on engaging the surrounding fluid primarily through shearing action. The theory comprises a continuous-system, multimodal model, and a single-degree-of-freedom model, the latter yielding simple formulas for the fundamental-mode resonant characteristics that often furnish excellent estimates to the results based on the more general model. Comparisons between theoretical predictions and previously published liquid-phase quality factor (Q) data (silicon devices in heptane) show that the theoretical results capture the observed trends and also give very good quantitative estimates, particularly for the highest Q devices. Moreover, the highest Q value measured in the earlier study (304) corresponded to a specimen whose disk radius-to-thickness ratio was 2.5, a value that compares well with the optimal value of 2.3 predicted by the present model. The insight furnished by the proposed theory is expected to lead to further improvements in ASID design to achieve unprecedented levels of performance for a wide variety of liquid-phase resonator applications.