Contribution of Acoustic Losses in the Quality Factor of a Micromechanical Resonator

A semi-analytical study of the acoustic radiation losses associated with various transverse vibration modes of a micromechanical (MEMS) annular resonator is presented. The quality factor, Q, of such resonators is of interest in many applications and depends on structural geometry, interaction with the external environment, and the encapsulation method. Resonators with at least one surface exposed to air can display losses through acoustic radiation even at micro meter dimensions. Published experimental results suggest the dominance of acoustic losses in the Q of a MEMS drum resonator. In this study, a well established mathematical techniques to analytically model resonator vibration modes and fluid-structure interaction are used, and a semi-analytical procedure for computing Q due to acoustic radiation losses, Qac, in any vibrational mode outlined. Present technique includes calculation of the exact mode shape and its utilization in computing Qac. The dependence of Qac on the first 15 mode shapes is computed. Results are compared for the lowest 2 modes of a solid circular resonator using exact mode shapes to those of Lamb's approximate mode shapes. Comparison to published experimental results validates the predictive utility of the technique, especially for higher modes where acoustic radiation seems to be the dominant constituent of Q.