Fractional-order filters for active damping in a lithographic tool

In a lithographic tool used in semiconductor manufacturing, vibrations in the projection lens reduce image contrast and can limit the system's resolution. Active damping by direct velocity feedback can reduce this effect, but requires sufficient amplitude roll-off for higher frequencies in the open-loop transfer function. Ongoing mass decoupling, however, tends to increase the transfer function magnitude. Stability is endangered by phase lag induced by control loop components and non-collocation of the actuator or sensor. Conventional lowpass filtering is not possible because of the minimum induced 90° phase shift. This paper introduces the usage of fractional-order filters with an order smaller than one in the feedback controller. The filter's reduced phase lag allows amplitude reduction for higher frequencies without stability risk. Implementation of 1/2-order and 2/3-order filters, and their effect in an active damping system for a lithographic tool's projection lens, are shown.