Support loss in the radial bulk-mode vibrations of center-supported micromechanical disk resonators

This paper presents a comprehensive analysis of support loss, the dominant loss mechanism, in center-supported micromechanical disk resonators operating in their radial bulk-modes. Through separation and coupling between the three components (disk, support beam, and support structure) of a disk resonator, support loss is evaluated quantitatively and the closed-form expression is obtained for support quality factor (Qsupport) of a center-supported disk resonator. The comparison between theoretical analysis and experimental data shows good agreement. This work provides significant insights into the geometrical design and choice of materials in high-Q center-supported disk resonant structures. To minimize support loss, a quarter wavelength rule exists for the height of the support beam in a center-supported disk resonator, similar to the length of torsion support beams of a free–free flexural beam resonator.