Study on Mechanical Cross-Axis Coupling for Non-Follow-Up Tip-Tilt Vertical Comb-Drive Micromirror

This paper presents a quantitative analysis of mechanical cross-axis coupling in tip-tilt (TT) scanning of vertical comb-drive (VCD) micromirror in detail. In the proposed non-follow-up (NFU) TT VCD micromirror design, one set of vertical combs (VCs) is fixed on the wiring substrate, while the other VC set can rotate along with the gimbal, the springs, and the reflective mirror. Such design brings not only high fabrication feasibility but also convenience for driving signal fan-out of micromirror array (MMA). The fabrication process is adopted on a double-silicon-on-insulator (D-SOI) wafer and a hollow copper (Cu) through-silicon-via (TSV) wiring substrate through bulk silicon micromachining. Based on this, a mechanical cross-axis coupling model is developed by introducing mechanical cross-axis coupling factors and plugging the deflection-dependent VC capacitance expressions into TT scanning angle solution, in order to evaluate influence from VCD actuators and series springs of gimbaled scanning structure. The calculation indicates that inner-axis rotation has little influence on outer-axis rotation, while the opposite is in direct relation to the number of VC units that contribute to VC capacitance calculation. A comparison between calculation with measured results obtained from fabricated devices is also conducted, which shows a good agreement. Additionally, we have investigated the decoupling method of the proposed model to evaluate its capability of biaxial driving voltage estimation. Furthermore, to overcome the drawbacks of the NFU TT scanning structure, a simplified calibration methodology is proposed as the extended application of the proposed model, featuring both lowering calibration workload and guaranteeing TT scanning accuracy. [2024-0214]