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Thermoelastic Damping in Micromechanical Resonators with a Proof Mass and a Network of Suspension Beams

Predicting thermoelastic damping is crucial for the design of high Q micromechanical resonators. In the past, for microresonators which consist of a proof mass and a network of suspension beams, some experiments showed that Zener's model [Phys. Rev. 52 (1937) 230; Phys. Rev. 53 (1938) 90] and Lifshitz and Roukes' model [Phys. Rev. B 61 (2000) 5600] can give a reasonable prediction, and others experiments showed that the two models fail to give a reasonable prediction. Few works give a reasonable and detailed explanation for this phenomenon. In this paper, a general proof is presented that shows Lifshitz and Roukes' model is valid for microresonators with a proof mass support by a network of suspension beams if all suspension beams are operated at pure bending vibration and all suspension beams have the same thickness. The accuracy of Lifshitz and Roukes' model is verified by comparing its results with the experimental results available in the literature.