Correlated Theory of Cross-Axis Interference of MEMS Devices Based on Parallel Plate and Squeeze Film Air Damping Induced Suppression

Owing to inevitable errors of the material and fabrication process, the cross-axis sensitivity commonly exists in a large number of MEMS devices based on parallel plate structures. Such cross-axis interference results in the non-negligible rotation of the plate that deteriorates the performance of MEMS devices. Therefore, suppressing the cross-axis sensitivity is extremely critical in the device design. This paper proposes a novel theory to identify the interplay between the cross-axis interference and squeeze film air damping, and further develops a correlated theory of the damping induced suppression. The model of tilting plate with a tiny amplitude is set up by exploiting the Reynolds equation coupled with the equations of the mass deflection, and the analytical expressions of corresponding properties are derived to elucidate the suppression mechanism and its characterization. The analytical calculation and numerical simulation analysis demonstrate that the damping induced improvement effect exists objectively and is remarkable in the condition of a large mass and a small air film thickness. The cross-axis sensitivity rendered by the tilt angle quantitatively declines 80% in terms of the air damping. The theoretical underpinning can be utilized to elaborate the ubiquitous interplay between squeeze film air damping and cross-axis interference in non-vacuum MEMS devices, which is of paramount importance for achieving high performance and stability. More importantly, it is not an exclusive method that can be combined with other methods to minimize the cross-axis interference fully.