Study on thermoelastic dissipation in bulk mode resonators with etch holes

This paper aims to investigate the primary cause for marked drops in quality factor (by over 98%) of a bulk mode resonator as a result of introducing etch holes into the structure. We show that thermoelastic damping (TED) appears to be the dominant cause of energy dissipation. The resonator is fabricated in single-crystal silicon (SCS). According to finite-element (FE) analysis, the uniform isochoric property of the Lamé mode is no longer preserved when etch holes are introduced. This results in marked drop in quality factor (Q) by 98.5% for the Lamé mode and 75.7% for the extensional from measurements. FE analysis based on coupled thermoelastic equations is used to compute the the thermal gradients that give rise to TED when etch holes are added to the resonator.