Predictor of thermal aberrations via particle filter for online compensation

Abstract. In optical lithography, aberrations induced by lens heating effects of a projection lens lead to degradation of imaging quality. In order to compensate for thermal aberrations, it is crucial to apply an accurate method for thermal aberration prediction. An effective and accurate method for thermal aberration prediction is proposed. A double exponential model is modified in respect of the timing of exposure tools, and a particle filter is used to adjust the double exponential model. Parameters of the model are updated recursively pursuant to the aberration data measured during the exchange of wafers. The updated model is used to predict thermal aberrations during the following exposure of wafers. The performance of the algorithm is evaluated by the simulation of a projection lens for argon fluoride lithography. Simulation results show that predictive errors of primary defocus and astigmatism are significantly reduced, and the mean value of wavefront error in the whole field of view is reduced by about 30% in a vertical line/space pattern. The proposed method is easily adaptable to different types of aberration measurement error.