Prediction of lens heating induced aberration via particle filter in optical lithography

In optical lithography, lens heating induced aberrations of a projection lens lead to degradation of imaging quality. In order to accurately compensate for thermal aberrations by integrated manipulators in projection lens, it is crucial to apply an accurate method for thermal aberration prediction. In this paper, an effective and accurate method for thermal aberration prediction is proposed. Double exponential model is simplified in respect of the timing of exposure tools, and particle filter is used to adjust the parameters of the double exponential model. Parameters of the simplified model are updated recursively pursuant to the aberration data measured during the exchange of wafers. The updated model is used to predict thermal aberrations of the lens during the following exposure of wafer. The performance of the algorithm is evaluated by simulation of a projection lens for ArF lithography. Maximum root mean square (RMS) value of perdition error of thermal aberration under annular illumination and dipolar illumination are reduced by 68.3% and 76.1%, respectively. The proposed method is also of well adaptability to different types of aberration measurement error.