Methods and properties of quadratic iterative learning control for semi-conductor processes under different perturbations

Semi-conductor manufacturing is composed of a large number of processing steps, but only a very limited number of processing wafers are monitored after few critical steps of manufacturing process, because metrology is costly and requires a long measurement delay usually. The wafers are inevitably subject to various perturbations, and quality variables (QVs) are scattered around their target values. The most important mission of R2R control in semiconductor processes is to reduce the variation of QVs instead of set point tracking and/or regulation against persistent disturbances. EWMA-based methods are dominantly employed in R2R control in present semi-conductor industries although the EWMA filtering has limitations in more detailed handling of noisy signals. In this study, quadratic iterative learning control (QILC) combined with the Kalman filter has been evaluated as a replacement of EWMA R2R control for tighter reduction of QV variations. Different types of stochastic disturbance are considered in the bias in a linear static model, and QILC algorithms are derived. The performance of the QILC methods was compared with that of the EWMA R2R control method.