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

Abstract

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 &#x0025; is reported for the inter-actuator charge coupling parameters. This clearly indicates the potential of the proposed technique. <i>Note to Practitioners</i>&#x2014;A critical step during the integrated-circuit lithographic fabrication process is the exposure. A particular practical challenge in this step is to correct for the mismatch between the optical image plane and the wafer surface, caused by wafer deformations. The mismatch negatively impacts the overlay and focus performance. To reduce the mismatch, actuators can be embedded into the wafer table to counteract wafer deformations, where the overall wafer surface shape is a superposition of each actuator&#x2019;s influence function. As part of the calibration for the embedded actuators, their influence functions are measured and stored. However, errors arise when influence functions are not measured for every actuator. Additionally, for different wafers, the influence functions vary hence the calibration should be done per wafer. This calibration process takes time and should not influence throughput. Our paper presents a viable approach that reduces the calibration time of active wafer tables, which is also relevant for other adaptive systems such as deformable mirrors. Since the technique requires the actuators to be mechanically coupled, it is limited to continuous surfaces. The proposed technique is numerically tested and experimentally verified to demonstrate performance.