Effect of substrate thickness on quality factor of mechanical resonators

This paper investigates effect of substrate thickness on energy drift from anchor of mechanical resonators. A finite element (FE) method is utilized to capture energy loss from the anchor. To eliminate wave reflection from the outer boundaries of the resonator substrate model, a perfectly matched layer is used. This artificial layer absorbs waves before they reach to the outer boundaries of truncated computational regions. Simulation results reveal that the resonators, which are connected to the thicker substrates show higher quality (Q) factor. It is found that among the modes, torsional mode is the most sensitive one to the substrate thickness. Such that as substrate thickness is increased 18 times, the Q-factor of the torsional mode is increased 6587 times. The results demonstrate that the Q-factor of the out-of-plane mode is also highly sensitive to the substrate thickness. However, the Q-factor of in-plane type modes is not as sensitive as other modes. The agreement between the simulation results and experimental data for anchor loss of cantilever type resonators validates the simulation method.