Effect of phonon interactions on limiting the f.Q product of micromechanical resonators

We discuss the contribution of phonon interactions in determining the upper limit of f.Q product in micromechanical resonators. There is a perception in the MEMS community that the maximum f.Q product of a microresonator is limited to a “frequency-independent constant” determined by the material properties of the resonator [1]. In this paper, we discuss that for frequencies higher than ωτ= 1/τ, where τ is the phonon relaxation time, the f.Q product is no longer constant but a linear function of frequency. This makes it possible to reach very high Qs in GHz micromechanical resonators. Moreover, we show that 〈100〉 is the preferred crystalline orientation for obtaining very high Q in bulk-acoustic-mode silicon resonators above ∼750 MHz, while 〈100〉 is the preferred direction for achieving high-Q at lower frequencies.