Frequency anti-crossing effect induced by hybrid modal coupling in a disk MEMS resonator

With the rapid development of micro- and nano-manufacturing technologies, microelectromechanical system (MEMS) resonators have become indispensable building blocks in high-precision sensing, time and frequency references, and quantum information systems. However, the hybrid modal coupling between same-order degenerate eigenmodes—the dominant source of quadrature error in MEMS resonators—still lacks systematic investigation on its tunable regulation mechanism and the associated frequency anti-crossing phenomenon. This paper reports the frequency anti-crossing effect induced by hybrid modal coupling in a disk MEMS resonator. Under structural stiffness mismatch, the presence of stiffness axis deflection enables simultaneous detection of orthogonal response signals from the hybrid modes. The hybrid modal coupling between same-order eigenmodes is systematically characterized through rigorous theoretical modeling and comprehensive experimental validation by tuning the device’s DC bias voltage. Results show that a distinct frequency anti-crossing effect occurs when the resonant frequencies of the two hybrid modes gradually approach each other, and the span of the anti-crossing region is directly determined by the stiffness axis deflection angle, which can quantitatively characterize the strength of hybrid modal coupling. This work reveals the inherent correlation between structural imperfections, hybrid modal coupling, and the frequency anti-crossing effect; provides quantitative design guidelines for active tuning of hybrid modal coupling in MEMS resonators; and paves the way for performance optimization of MEMS gyroscopes as well as the development of high-precision sensing and quantum electromechanical systems.