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Iterative Methods for High Precision Motion Control with Application to a Wafer Scanner System

  • Author(s): Stearns, Hoday Margaret
  • Advisor(s): Tomizuka, Masayoshi
  • et al.

Advances in photolithography are one of the key driving factors in the continuing expansion in capacity and decrease in cost of semiconductors. Extending this trend into the future necessitates the development of next-generation lithography technologies in order to overcome the fundamental challenges of improving critical dimension and overlay control, and lowering the total cost-of-ownership. As feature sizes become smaller and smaller, performance requirements for wafer scanner machines will become more stringent; with regards to motion control, requirements for the wafer stage include sub-nanometer positioning precision under high scan velocities and accelerations. Advanced control algorithms are needed to meet these requirements in the face of disturbances such as vibrations, noise, force ripple and friction, as well as model uncertainty.

This dissertation focuses on using the repetitiveness of the stage's motion in the photolithography process to improve control precision. Similar to many manufacturing processes, the step-and-scan motion used to expose a wafer is very repetitive, on a die-to-die and also wafer-to-wafer level. By using data gathered from past runs, the control effort for future runs may be improved, thereby exploiting the repetitiveness of the process to increase control precision.

In this research, \textit{iterative learning control} (ILC) and \textit{iterative feedback tuning} (IFT) were applied to reduce tracking error of the wafer stage. In ILC, a feedforward control signal for the system is incrementally adjusted to achieve better tracking performance using error signals from previous runs. ILC is an attractive method for high-precision control because of its simplicity and data-based nature. In this research, ILC algorithm design specifically for attenuating high frequency vibrations is investigated. Through careful design of the ILC update law, fast learning convergence and small final error is achieved. One drawback of ILC is that a feedforward signal learned through ILC is only applicable to the training trajectory; learning must be restarted when the trajectory is changed. A method is presented for making ILC results applicable to any trajectory within a class of scan trajectories; this is accomplished by using ILC as a training method for feedforward signal patterns. In IFT, controller parameters are fine-tuned incrementally using only data collected in experimental runs. IFT is applied to tune fixed-structure feedforward, feedback, and force-ripple compensator controllers. The performance of IFT is also compared with ILC in the context of iterative methods for designing feedforward control. All results are verified through computer simulations and experiments done on a wafer stage testbed system.

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