Fast influence function measurement technique using the direct and in-direct piezoelectric effect for accurate and dynamic surface shape control in adaptive systems

Ever 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 application where adaptive systems have been implemented is in photo-lithography, particularly the wafer table where disturbances affect the overlay and focus performance. In order to reduce the overlay and focus errors, a dense array of actuators is 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 function results in an accurate prediction of the final wafer shape. To reduce modelling errors, the influence function of each wafer prior to exposure needs to be determined. More-so, in-plane influence functions are hard to measure. Here, we propose a technique to quickly measure the in-plane and out-of-plane influence function for each exposure step, the fast influence function measurement (FIFM) 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 charges are then computed into actuator displacements and fitted using solutions to the Bi-harmonic plate equation with Winkler foundation.