Variable gain motion control of wafer scanners

Abstract

Over the past decade, variable gain control has aided both the positioning accuracy (overlay and imaging) and the productivity (throughput) of several motion systems in wafer scanners. In the control of wafer scanners, i.e., the lithographic machinery used to produce chips, nonlinear elements are traditionally used to linearize the feedback loop. In this paper, however, nonlinearity is introduced to de-linearize the feedback loop, which is carried out with the aim to better deal with design trade-offs. For wafer scanners, an overview is given of the most relevant nonlinear control designs, which are based on variable gains. This includes posing a framework not only for stability analysis in which (measured) frequency response functions are key in providing graphical checks, but also for discussing performance via nonlinear Bode diagrams.