Influence Function Measurement Technique Using the Direct and Indirect Piezoelectric Effect for Surface Shape Control in Adaptive Systems

Since the introduction of adaptive systems for corrective measures, static and dynamic disturbances have been reduced through the manipulation of surface shape in a well-controlled manner. One important application where adaptive systems are highly needed is in the future photo-lithography machines, particularly the wafer table where disturbances affect overlay and focus performance. To reduce overlay and focus errors, a dense array of actuators must be integrated into the wafer table to apply both in- and out-of-plane corrective deformations to the wafer surface. To realize a certain wafer shape, influence functions are linearly superimposed. Accurate models of the influence functions result in an accurate prediction of the final wafer shape. To reduce calibration errors, the influence function of every actuator needs to be determined. Here, we propose a technique to rapidly measure the influence function: the influence function measurement (IFM) technique. Using the actuate-sense property of piezoelectric materials, the influence function is determined by activating one piezo-actuator and measuring the charge induced on the neighboring piezo-actuators. The measured charges are compared to the results of finite element simulations and the absolute difference of 0.3 % is reported for the inter-actuator charge coupling parameters. This clearly indicates the potential of the proposed technique.