Adaptive gradient-based source and mask co-optimization with process awareness

Yijiang Shen; Fei Peng; Xiaoyan Huang; Zhenrong Zhang

doi:10.3788/COL201917.121102

Journals >Chinese Optics Letters >Volume 17 >Issue 12 >Page 121102 > Article

Chinese Optics Letters
Vol. 17, Issue 12, 121102 (2019)

Adaptive gradient-based source and mask co-optimization with process awareness

Yijiang Shen^1、*, Fei Peng¹, Xiaoyan Huang¹, and Zhenrong Zhang²

Author Affiliations

¹School of Automation, Guangdong University of Technology, Mega Education Center South, Guangzhou 510006, China

²Guangxi Key Laboratory of Multimedia Communications and Network Technology, School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China

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DOI: 10.3788/COL201917.121102 Cite this Article Set citation alerts

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 Copy Citation Text

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

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

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

I_{02}

in Fig. 4(c).

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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

I_{02}

in Fig. 4(c) illuminated by the annular source in Fig. 4(a).

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Fig. 4. (a) Annular source

J_{0}

with

σ_{i n} = 0.6

and

σ_{o u t} = 0.9

. (b), (c) The desired target patterns

I_{01}

I_{02}

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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

I_{01}

and

I_{02}

illuminated by the annular source in Fig. 4(a).

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Fig. 6. Simulation results with

I_{01}

as the target pattern. Columns from left to right: the synthesized source pattern

\hat{J}

, the synthesized mask pattern

\hat{M}

, the EPE images, and the PV Band images illuminating

\hat{M}

\hat{J}

. Rows: proposed approach (a) with

γ_{1}

and (b) with

γ_{2}

, SGD (c) with

γ_{1}

and (d) with

γ_{2}

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Fig. 7. Randomly initialized masks within the range

(0, 1)

; (a)

M_{01}

and (b)

M_{02}

. (c)

ω_{1}

and (d)

ω_{2}

are the transformed parameters.

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Fig. 8. Simulation results with

I_{01}

and

I_{02}

as the target pattern and weight

γ_{2}

. Rows: (a) and (c) proposed approach with

ω_{1}

and

ω_{2}

, (b) and (d) SGD with

ω_{1}

and

ω_{2}

as initial masks.

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Fig. 9. Convergence of (a)

S

, (b)

S_{pe}

of the simulations in Fig. 8, (c)

S_{pe}

of the simulations in Figs. 8(a) and 8(b), and (d)

S_{pe}

of the simulations in Figs. 8(c) and 8(d).

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Layer	Index	Thickness (nm)
Incident medium	(1.45, 0)
Top anti-reflection	(1.55, 0.0)	35
Photoresist	(1.8, 0.02)	100
Bottom anti-reflection	(1.72, 0.33)	87
Substrate	(0.833, 2.778)

Table 1. Wafer Stack Parameters

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	Fig. 5	Fig. 6
	row $I_{01}$	(a)	(b)	(c)	(d)
$S_{pe}$	4494	614	540	586	490
$S_{epe}$	1158	172	175	174	143
$S_{pv}$	2347	2246	1834	2211	1885

Table 2. Spe, Sepe, and Spv of the Simulations in Figs. 5 and 6

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	Fig. 5	Fig. 8		Fig. 5	Fig. 8
	row $I_{01}$	(a)	(b)	row $I_{02}$	(c)	(d)
$S_{pe}$	4494	567	n.a.	5193	468	n.a.
$S_{epe}$	1158	178	n.a.	1512	96	n.a.
$S_{pv}$	2347	1867	n.a.	3965	2472	n.a.

Table 3. Spe, Sepe, and Spv of the Simulations in Figs. 5 and 8

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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