Cross-axis bending-torsion coupled dynamic model for thermal-induced frequency drift of 2D MEMS micromirrors

Thermal-induced frequency drift poses significant threats to the performance and long-term reliability of microelectromechanical systems (MEMS) micromirrors. Unlike uniaxial micromirrors, cross-axis two-dimensional (2D) micromirrors exhibit the substantially different bending-torsion coupled dynamic behaviors due to mutually perpendicular beams. Therefore, it is interesting yet challenging to reveal the coupling effect on the cross-axis bending-torsion coupled dynamic behaviors of 2D micromirrors. Here, a temperature-dependent cross-axis bending-torsion coupled dynamic model is developed to elucidate the thermal-induced frequency drift of 2D micromirrors. The proposed model explains the intricate multimodal coupling relationships of cross-axis 2D micromirrors, indicating that the thermal-induced frequency drift of fast-scanning mode is influenced not only by the torsional stiffness of fast-axis beam, but also by the bending stiffness of slow-axis beam. Consequently, by introducing the temperature-dependent cross-axis bending-torsion coupled stiffness matrix, the prediction error of thermal-induced frequency drift is reduced by 88.7 %. Furthermore, a package optimization method for low thermal-induced frequency drift is presented based on the proposed model. As a result, the temperature coefficient of frequency (TCF) is decreased by 62.4 % at the temperature difference of 120 K, which significantly improves the frequency stability of cross-axis 2D micromirrors. This work helps to better comprehend the cross-axis bending-torsion coupled dynamic behaviors of MEMS devices, as well as provides general design guidelines for the low thermal-induced frequency drift and crosstalk-free 2D MEMS micromirrors.