Thermoelastic damping in fine-grained polysilicon flexural beam resonators

The design and fabrication of polysilicon flexural beam resonators with very high mechanical quality factors (Q) is essential for many MEMS applications. Based on an extension of the well-established theory of thermoelastic damping in homogeneous beams, we present closed-form expressions to estimate an upper bound on the attainable quality factors of polycrystalline beam resonators with thickness (h) much larger than the average grain size (d). Associated with each of these length scales is an independent damping mechanism; we refer to them as Zener and intracrystalline thermoelastic damping, respectively. For representative polysilicon beam resonators (h = 2 μm; d = 0.1 μm) at 300 K, the predicted critical frequencies for these two mechanisms are ∼7 MHz and ∼14 GHz, respectively. The model is consistent with data from the literature in the sense that the measured values approach, but do not exceed, the calculated thermoelastic limit. From the viewpoint of the maximum attainable Q, our model suggests that single-crystal silicon, rather than fine-grained polysilicon, is the material of choice for the fabrication of flexural beam resonators for applications in the gigahertz frequency range.