On characterization of a generic lithography machine in a multi-directional space

In this paper, we present a dynamics modeling approach for lithographic machines. These machines consist of N-open chains with multiple stages in each chain. A stage can suppress or exert motion in specific directions. The stages affect each other through the structural connections available within a chain or various chains. We want to capture the energy transfer in the machine to better realize the design requirements. A specific application will be the optical lithography wafer-scanner machine. In such machines, step-and-scan motion profiles demand synchronization between the chains end-effectors. The rapid production rates requirements are projected onto the design space as high-acceleration profiles that will cause vibration based on the energy paths available. Various positioning errors will take place during the production of one complete substrate. Characterizing the machine dynamics due to jointly motion and vibration helps in providing better ways to synthesis the controllers for each stage. To minimize the positioning errors, we also propose replacements of specific stages where actively controlled fine positioning stages are used. The presented machine characterization provides a means to design and optimize such stages as will be illustrated through simulation examples.