Adaptive feedforward for a wafer stage in a lithographic tool

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The wafer stage and reticle stage in a lithographic tool, used to manufacture integrated circuits (ICs), operate at nanometer accuracy during a scanning motion. The position accuracy and settling time after accelerating to the scanning velocity are largely determined by the feedforward controller. The feedforward controller calculates the required force for the stage to move according to its position profile by multiplying the reference acceleration with the known stage mass. Two effects limit the accuracy directly after the acceleration phase. First, the actual stage acceleration in response to the controller-calculated force depends on the position of the stage in its working range. A variation of 0.1% is observed. Second, dynamic resonances in the stage response require a higher-order feedforward model. Combined, these effects result in a 20–30 nm peak position error. This brief investigates online adaptation of the feedforward mass parameter, with the aim of reducing the position-dependent stage behavior. Adaptation of only the feedforward mass is shown not to be able to compensate for stage dynamics, additionally requiring a higher-order feedforward element. From the control force and the measured motion response, the feedforward mass parameter is estimated on line. Least-squares estimation is fast enough to update the mass parameter during the acceleration phase, which takes less than 100 ms. This brief addresses a number of practical aspects and shows that adaptive feedforward estimation in combination with higher-order feedforward reduces the peak position error consistently by creating position-independent behavior.
Original languageEnglish
Pages (from-to)875-881
Number of pages7
JournalIEEE Transactions on Control Systems Technology
Issue number3
Publication statusPublished - 2013


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