Sampling-based imaging model for fast source and mask optimization in immersion lithography

Yiyu Sun; Yanqiu Li; Guanghui Liao; Miao Yuan; Pengzhi Wei; Yaning Li; Lulu Zou; Lihui Liu

doi:10.1364/AO.437655

Applied Optics
Vol. 61,
Issue 2,
pp. 523-531
(2022)
•https://doi.org/10.1364/AO.437655

Sampling-based imaging model for fast source and mask optimization in immersion lithography

Yiyu Sun, Yanqiu Li, Guanghui Liao, Miao Yuan, Pengzhi Wei, Yaning Li, Lulu Zou, and Lihui Liu

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Yiyu Sun, Yanqiu Li, Guanghui Liao, Miao Yuan, Pengzhi Wei, Yaning Li, Lulu Zou, and Lihui Liu, "Sampling-based imaging model for fast source and mask optimization in immersion lithography," Appl. Opt. 61, 523-531 (2022)

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- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: July 13, 2021
- Revised Manuscript: November 24, 2021
- Manuscript Accepted: December 14, 2021
- Published: January 5, 2022

Abstract

Current source and mask optimization (SMO) research tends to focus on advanced inverse optimization algorithms to accelerate SMO procedures. However, innovations of forward imaging models currently attract little attention, which impacts computational efficiency more significantly. A sampling-based imaging model is established with the innovation of an inverse point spread function to reduce computational dimensions, which can provide an advanced framework for fast inverse lithography. Simulations show that the proposed SMO method with the help of the proposed model can further speed up the algorithm-accelerated SMO procedure by a factor of 3.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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1.	Input a target pattern shown as Fig. 3(a).
2.	Initialize mask pattern the same as the target pattern, and calculate initial $Θ_{M}$ according to Eq. (17), which are shown as Figs. 3(b) and 3(c).
3.	Create random distortions with range from zero to $π$ in contour area of initial mask pattern, shown as Fig. 3(d).
4.	Add random distortions with initial $Θ_{M}$ as the proposed initial $Θ_{M}$ , shown as Fig. 3(e).
5.	Calculate the proposed initial mask pattern using Eq. (17), shown as Fig. 3(f).

SMO Methods	Runtime per Iteration (s)	Total Runtime (s)
Traditional SMO method	3.16	315.73
Proposed SMO method	1.05	92.12

$S_{J}$	40	45	50	55	60
Traditional SMO	788	768	788	858	816
Proposed SMO	630	760	460	492	1260
$S_{M}$	100	300	400	500	1000
Traditional SMO	788	778	788	798	774
Proposed SMO	910	466	460	482	528
$γ_{q}$	$1 \times 10^{- 5}$	$1 \times 10^{- 4}$	$5 \times 10^{- 5}$	$1 \times 10^{- 3}$	$1 \times 10^{- 2}$
Traditional SMO	788	788	788	788	788
Proposed SMO	460	460	460	460	466
$γ_{w}$	$1 \times 10^{- 5}$	$1 \times 10^{- 4}$	$2 \times 10^{- 4}$	$1 \times 10^{- 3}$	$1 \times 10^{- 2}$
Traditional SMO	788	788	788	788	788
Proposed SMO	460	460	460	460	466
$α$	0.3	0.35	0.4	0.45	0.5
Proposed SMO	1412	1188	460	868	1040

SMO Methods	Runtime per Iteration (s)	Total Runtime (s)
Traditional SMO method	3.15	69.21
Proposed SMO method	0.81	12.22

1.	Input a target pattern shown as Fig. 3(a).
2.	Initialize mask pattern the same as the target pattern, and calculate initial $Θ_{M}$ according to Eq. (17), which are shown as Figs. 3(b) and 3(c).
3.	Create random distortions with range from zero to $π$ in contour area of initial mask pattern, shown as Fig. 3(d).
4.	Add random distortions with initial $Θ_{M}$ as the proposed initial $Θ_{M}$ , shown as Fig. 3(e).
5.	Calculate the proposed initial mask pattern using Eq. (17), shown as Fig. 3(f).

Abstract

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Equations (45)

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