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Accepted: Aug. 6, 2019

Posted: Dec. 3, 2019

Published Online: Dec. 3, 2019

The Author Email: Yijiang Shen (yjshen@gdut.edu.cn)

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Yijiang Shen, Fei Peng, Xiaoyan Huang, Zhenrong Zhang. Adaptive gradient-based source and mask co-optimization with process awareness[J]. Chinese Optics Letters, 2019, 17(12): 121102

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Fig. 1. (a) Schematic of forward lithography. (b) Reflection from and transmission through a stratified medium.

Fig. 2. (a) EPE measurement illustration. (b) Numerical superposition region. (c) Pattern edge set (PES). (d) Edges of target pattern $I02$ in Fig. 4(c).

Fig. 3. PV Band demonstration. (a)–(c) Printed images under different process conditions. (d) Computed PV Band. (e) PV Band of the printed images with $I02$ in Fig. 4(c) illuminated by the annular source in Fig. 4(a).

Fig. 4. (a) Annular source $J0$ with $σin=0.6$ and $σout=0.9$. (b), (c) The desired target patterns $I01$, $I02$.

Fig. 5. Printed wafer images with (a) PE 4494 and (d) PE 5193, EPE images with (b) EPE 1158 and (e) EPE 1512, PV Band images with (c) PV Band 2347 and (f) PV Band 3965 with respect to target patterns $I01$ and $I02$ illuminated by the annular source in Fig. 4(a).

Fig. 6. Simulation results with $I01$ as the target pattern. Columns from left to right: the synthesized source pattern $J^$, the synthesized mask pattern $M^$, the EPE images, and the PV Band images illuminating $M^$ by $J^$. Rows: proposed approach (a) with $γ1$ and (b) with $γ2$, SGD (c) with $γ1$ and (d) with $γ2$.

Fig. 7. Randomly initialized masks within the range $(0,1)$; (a) $M01$ and (b) $M02$. (c) $ω1$ and (d) $ω2$ are the transformed parameters.

Fig. 8. Simulation results with $I01$ and $I02$ as the target pattern and weight $γ2$. Rows: (a) and (c) proposed approach with $ω1$ and $ω2$, (b) and (d) SGD with $ω1$ and $ω2$ as initial masks.
Fig. 9. Convergence of (a) $S$, (b) $Spe$ of the simulations in Fig. 8, (c) $Spe$ of the simulations in Figs. 8(a) and 8(b), and (d) $Spe$ of the simulations in Figs. 8(c) and 8(d).