Improved Cross-Wafer Variability in MEMS Resonators: The Advantage of Tapered Flexures

This paper presents a novel flexure design geometry that significantly reduces the sensitivity of MEMS resonators to manufacturing variability, specifically critical dimension (CD) loss. The impact of a quadratically tapered flexure, which maintains constant stress along its length, is demonstrated in mitigating fabrication imperfections. The proposed design achieves a 36.5% reduction in variability compared to traditional uniform cross-section (“straight”) flexures. Additionally, quadratically tapered flexures exhibit a 9× reduction in Af when comparing local die regions of flexure orientations in the horizontal and vertical directions. By incorporating these flexures, MEMS resonator designs demonstrate reduced cross-wafer frequency variation, benefiting MEMS inertial sensors that rely on degenerate mode operation (e.g., mode-matched gyroscopes) or require tighter resonant frequency distributions. As a result, this design is expected to improve cross-wafer yield for a given Af criterion. Finally, we show a 17% improvement in accelerometer scale factor sensitivity for nearly identical device footprints.