Highly decoupled single-crystal silicon resonators: an approach for the intrinsic quality factor

Abstract

Special attention has been paid in this work to use all possible means to measure an intrinsic quality factor (Q) for silicon beam resonators realized on SOI wafers. Specifically, this work points to the energy dissipation into the support; a model is given and a high insulating system for clamped–clamped and clamped-free configurations has been studied, preserving the resonating element from support damping. Finite element analysis on these structures evidences values of Qsupport higher than 107. Out-of-plane and in-plane vibration Q values up to 1.0 × 105 have been measured under a high vacuum using, respectively, laser Doppler vibrometry and stroboscopic optical microscopy combined with image processing. The results have shown good agreement with thermoelastic theory. However, the observed agreement on the resonator dimension dependences is limited to quality factors lower than 3.0 × 104. Beyond these values, a physical limitation is evidenced in both cases (in-plane and out-of-plane) which does not match with the surface and clamping models listed. The role of the SOI wafer's oxide layer is discussed as a possible source of dissipation.

Design strategies for controlling damping in micromechanical and nanomechanical resonators

“…Support losses can be reduced by using analytical and numerical models for stresswave radiation to guide the selection of materials, structures, dimensions, modes, and frequencies. Alternately, the generation and propagation of elastic waves can be disrupted by contacting the resonator at its nodal points using anchors or tethers [26][27][28][29][30][31] and incorporating phononic band-gap structures [32][33][34][35], acoustic reflectors [36,37], and vibration isolators [38,39]. In each case, well-established models from vibrations and elasticity are available to guide design.…”

Les microsystèmes électromécaniques optiques

“…Sa valeur a un impact direct sur la résolution, la sensibilité et la stabilité des oscillateurs et des micro-capteurs résonants. Les micro-résonateurs basse fréquence en silicium ou en GaAs monocristallin peuvent présenter des facteurs de qualité sous vide très élevé (>10 5 ) si les résonateurs sont dimensionnés de façon appropriée et si les pertes d'énergie via les ancrages sont minimisées [3,4]. Le coefficient de qualité des micro-résonateurs est cependant fortement dégra dé lorsqu'ils sont intégrés dans des microsystèmes élec -tromé caniques en raison de la nécessité de les recouvrir d'électrodes pour réaliser l'actionnement et la détection des vibrations.…”

Effect of die attachment on key dynamical parameters of micromachined gyroscopes

“…Support loss is considered as energy propagation into the supporting structure. Analytical model and experimental study for support loss in clamped-free and clamped-clamped micromachined beam resonators have been proposed in published literatures (Judge et al 2007;Hao et al 2003;Foulgoc et al 2006). Yang et al (2002) and Yasumura et al (2002) have studied surface loss in beam resonators.…”