Research on Packaging Reliability and Quality Factor Degradation Model for Wafer-Level Vacuum Sealing MEMS Gyroscopes

MEMS gyroscopes are widely applied in consumer electronics, aerospace, missile guidance, and other fields. Reliable packaging is the foundation for ensuring the survivability and performance of the sensor in harsh environments, but gas leakage models of wafer-level MEMS gyroscopes are rarely reported. This paper proposes a gas leakage model for evaluating the packaging reliability of wafer-level MEMS gyroscopes. Based on thermodynamics and hydromechanics, the relationships between the quality factor, gas molecule number, and a quality factor degradation model are derived. The mechanism of the effect of gas leakage on the quality factor is explored at wafer-level packaging. The experimental results show that the reciprocal of the quality factor is exponentially related to gas leakage time, which is in accordance with the theoretical analysis. The coefficients of determination (R²) are all greater than 0.95 by fitting the curves in Matlab R2022b. The stable values of the quality factor for drive mode and sense mode are predicted to be 6609.4 and 1205.1, respectively, and the average degradation characteristic time is 435.84 h. The gas leakage time is at least eight times the average characteristic time, namely 3486.72 h, before a stable condition is achieved in the packaging chamber of the MEMS gyroscopes.