Optimal thermal actuation for mirror temperature control

The latest generation wafer scanners use extreme ultraviolet light to project a pattern of electronic connections onto a silicon wafer. A significant part of the projection light is absorbed by the mirrors in the projection system. This causes the mirrors to heat up and expand, which leads to a significant reduction in the imaging quality of the wafer scanner. The imaging quality can be improved by applying an additional actuation heat load to the mirrors. Because the wafer scanner can be used with a large number of different illumination settings (which lead to different load cases) and the number of thermal actuators is limited, designing an effective actuation heater layout is an important but nontrivial task. To assist this design process, this paper proposes a computational framework to optimize a small number of spatial actuation heat load shapes with their corresponding intensities for a large number of load cases. It is guaranteed that the obtained actuation heat load shapes can keep the steady-state temperature in the optical surface of the mirror sufficiently close to a desired temperature in all considered load cases. The proposed computational framework is applied to a representative three-dimensional finite element model of a mirror. The obtained actuation heat load shapes and their corresponding intensities provide insights for the design of a thermal actuation layout for mirror heating.