5 July 2000 Predictive and corrective model for bulk heating distortion in photomasks
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Abstract
Finite element (FE) numerical models were proposed to simulate and predict substrate thermal expansion in photomask substrates and were found to be computationally expensive and dependent on the mask-writing strategy. The present work describes a newly developed model that predicts and corrects for the substrate heating effects in the photomask. This prosed model provides a practical way of predicting in-plane distortions during real-time patterning that is not limited to nay writing strategy or pattern density distribution. The main advantage of this model is that it significantly reduces the computational time by using the linear superposition theory. By adopting the concept of linear superposition, pattern placement errors of mask substrate scan be determined at any time during writing using lookup tables from precomputed FE models. IF the thermal distortion of the substrate at the time during writing using lookup tables from, precomputed FE models. IF the thermal distortion of the substrate at the time of writing is known, beam deflection can be introduced to correct for the distorted substrate. The result predicted by the linear superposition FE model showed a difference of less than 10 percent compared with those predicted using a real-time calculated Fe mode, in a worst case scenario. The accuracy of the linear superposition FE model was found to be partially dependent on the size of the simulated patterning field. The results presented in this paper illustrate the effect of other parameters on the performance of the newly developed model, such as the shape of the patterning fields and pattern coverage uniformity. The overview of this work focuses on fused silica mask substrate materials.
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Bassam Shamoun, Bassam Shamoun, David Trost, David Trost, Frank Chilese, Frank Chilese, } "Predictive and corrective model for bulk heating distortion in photomasks", Proc. SPIE 4000, Optical Microlithography XIII, (5 July 2000); doi: 10.1117/12.389053; https://doi.org/10.1117/12.389053
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