Design and Optimal Control of a Magnet Assisted Scanning Stage for Precise and Energy Efficient Positioning

Abstract

Scanning stages are characterized by repeated back and forth motions and are widely used in advanced manufacturing processes like photo-lithography, laser-scribing, inspection, metrology, 3D printing, and precision parts assembly, many of which are closely related to the semiconductor (i.e., integrated circuit) manufacturing industry. In order to deliver more high- performance semiconductor chips, i.e., to keep up with predictions made by Moore’s Law, the scanning stages employed by the industry need to move faster while maintaining nanometer-level precision. Achieving these two goals simultaneously requires extensive use of thermal and vibration-induced error mitigation methods, because the motors, and subsequently the surrounding stage components, become heated and flexible parts of scanning stages are easily excited by their aggressive motions (with high acceleration/deceleration). Most of the available solutions tackle the heat and vibration mitigation problems separately, even though the two problems originate from one source, i.e., the large inertial loads generated by the scanning stage’s actuators. Much benefit (e.g., size and cost reductions) can be achieved by considering the two problems simultaneously by addressing their root cause.

This dissertation proposes a design-based approach to simultaneously mitigate thermal and vibration-induced errors of scanning stages. Exploiting the repeated back-and-forth motions of scanning, permanent magnet (PM) based assist devices are designed to provide assist force needed during the motion reversal portions of scanning trajectories. The PM-based assist devices store the kinetic energy of the moving table during deceleration and release the stored energy when the table accelerates. Consequently, the force requirements of the primary actuator decrease, thus lowering its heat generation due to copper (resistive) losses. Moreover, the reaction forces borne by the PM assistive devices are channeled to the ground, bypassing the vibration isolated base upon which the scanning stage rests, thus reducing unwanted vibration. To increase the force density of the PMs, a 2D Halbach arrangement is adopted in a prototype scanning stage. Moreover, an efficient and low-cost servo system, optimized for versatility, is integrated into the scanning stage for automatic positioning of the PMs.

The designed magnet assisted scanning stage is an over-actuated system, meaning that it has more control inputs than outputs. For the best utilization of its actuators, a feedforward approach for optimal allocation of control efforts to its actuators is developed. The stage, controlled with the optimal feedforward control inputs, achieves significant reductions of actuator heat and vibration-induced errors when applied to typical scanning motions used in semiconductor manufacturing (silicon wafer processing). To further improve the positioning accuracy of the stage, an Iterative Learning Control (ILC) approach for over-actuated systems is developed, exploiting the repeated motion of scanning stages. The optimal ILC update law is designed, considering model and input force uncertainties, for robust monotonic convergence of tracking errors, and the resultant control force is efficiently allocated to multiple actuators. Applied to the magnet assisted scanning stage, the proposed ILC approach additionally reduces tracking errors arising from the mismatch between the model and actual system, thus significantly improving the positioning accuracy of the stage.