Thermoelastic damping of the in-plane vibration of thin silicon rings

This paper considers thermoelastic damping of the in-plane vibration of rings. The work was motivated by the need to gain improved understanding of energy-dissipation effects in silicon MEMS resonators, for which a high Q-factor is often a key design objective. The presented analysis is based on Zener's classical work on the modelling of thermoelastic loss in uniform beams, and on a recent refinement of Zener's analysis by Lifshitz and Roukes. A review of Zener's and Lifshitz and Roukes’ analysis is given. The paper then extends the above work by applying the thermoelastic models to the in-plane vibration of uniform rings of rectangular cross-section. Using both approaches, numerical predictions of modal Q-factors are developed and compared. The relationships between ring geometry, scale and Q-factor are explored and the ability to choose resonator dimensions to control Q-factor due to thermoelastic loss is illustrated.