Lithographic Stepping Trajectory Planning for Residual Vibration Suppression: An Asymmetric S-Curve Method

During the lithographic process, stepping motion enables a rapid switch from one die to another. To meet the throughput requirement of nowadays high-end lithography equipment, the settling time is limited to only several milliseconds, which requires extremely little residual vibration. The design of the traditional symmetric S-curve through the pole-zero placement theory has the ability to eliminate the residual vibration caused by the zero-damping flexible mode. However, the nonzero damping ratio and the imprecisely known resonant frequency will lead to performance degradation. To tackle this issue, this paper further proposes an asymmetric S-curve planning method, which enhances the robustness. This is accomplished by introducing an additional design parameter at the deceleration phase, which adds one more zero to compensate for the pole of the flexible mode. The proposed method has one preferable feature compared to the existing asymmetric S-curve planning method: the method can be utilized to design not only the 3rd order S-curve but also higher order S-curves. Simulation results verify the effectiveness of the proposed method.