Local Level Set Based Mask Optimization with Semi-Implicit Discretization

Fig. 3. Lithographic imaging performance with multi-density mask pattern I₀. (a) Simulation results without OPC and I₀ as illuminated mask; (b) conventional level-set MO; (c) semi-implicit MO; (d) localized semi-implicit MO

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Fig. 4. Pattern error versus simulation time for desired pattern I₀

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Fig. 5. Simulation experiment running time

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Fig. 6. Optimization of monitoring pixels. (a) Begin; (b) end

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Fig. 7. Monitoring pixel counting in x and y coordinates with respect to iteration

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Fig. 8. Time to solve linear system of equations in semi-implicit and localized semi-implicit MO approaches with respect to iteration

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Table 1. Main work flow of proposed approach

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Table 1. Main work flow of proposed approach

Mask synthesis with semi-implicit discretization
Input is target pattern I₀
Output is synthesized mask M
1. Initialize M as I₀, ω=arccos(2\|M\|-1), according to Eq. (3)
2. Set K as maximum iteration number
3. Start iteration with k=0
4. While k<K
5. Construct partial differential equation according to Eq. (5)
6. Label pixels in x coordinate with $\|ω_{x}\|$ >e_thr as monitoring pixels
7. Compute linear system of equations [E-2τA_x(ω^k)]u^k⁺¹=ω^k for u^k⁺¹
8. Label pixels in x coordinate with $\|ω_{y}\|$ >e_thr as monitoring pixels
9. Compute linear system of equations [E-2τA_x(ω^k)]v^k⁺¹=ω^k for v^k⁺¹
10. Average ω^k⁺¹=0.5(u^k⁺¹+v^k⁺¹)
11. Update \|M^k⁺¹\|= $\frac{1 + \cos (ω^{k + 1})}{2}$ according to Eq. (3)
12. k=k+1
13. end while
14. Return M=M^k⁺¹

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Yijiang Shen, Xiaopeng Wang, Yanzhou Zhou, Zhenrong Zhang. Local Level Set Based Mask Optimization with Semi-Implicit Discretization[J]. Acta Optica Sinica, 2021, 41(9): 0911004

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Paper Information

Category: Imaging Systems

Received: Jul. 22, 2020

Accepted: Dec. 2, 2020

Published Online: May. 8, 2021

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

DOI:10.3788/AOS202141.0911004

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology