Structural Design of a Low-Frequency In-plane Torsional Mode Wheel-Shaped Resonator

Abstract In low-frequency vibrating MEMS resonators, device structures typically vibrate in flexural mode and torsional mode. The mechanical stiffness in the motion direction of the bending mode is often strongly correlated with the device’s equivalent stiffness, while torsional mode generally use piezoelectric actuation and usually have a low Q factor. These factors limit the application of low-frequency resonators in some high-reliability scenarios. This paper proposes a low-frequency wheel-shaped resonator vibrating in the in-plane torsional mode. By using the torsional vibration of the wheel-shaped mass instead of translational vibration, and adopting an in-plane capacitive structure for driving and sensing, the device maintains high in-plane stiffness while vibrating at low frequencies. At the same frequency, its in-plane stiffness is 10² orders of magnitude higher than that of the flexural mode. Simulations on the anti-overload performance of the device structure show that under a 100g static load, the frequency drifts in the X-axis and Z-axis directions are 21.67 ppb and 60.39 ppb, respectively. Under 10000g impact loads in the X-axis and Z-axis directions, the maximum in-plane stresses are 24.7 MPa and 45.7 MPa, with maximum displacements of 0.111 µm and 0.137 µm, respectively—values far lower than the maximum allowable stress of silicon material and the minimum line width of the device. This demonstrates that the structure has high frequency stability and anti-overload performance.