Translational-symmetry alternating phase shifting mask grating mark used in a linear measurement model of lithographic projection lens aberrations

Zicheng Qiu; Xiangzhao Wang; Qunyu Bi; Qiongyan Yuan; Bo Peng; Lifeng Duan

doi:10.1364/AO.48.003654

Applied Optics
Vol. 48,
Issue 19,
pp. 3654-3663
(2009)
•https://doi.org/10.1364/AO.48.003654

Translational-symmetry alternating phase shifting mask grating mark used in a linear measurement model of lithographic projection lens aberrations

Zicheng Qiu, Xiangzhao Wang, Qunyu Bi, Qiongyan Yuan, Bo Peng, and Lifeng Duan

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Zicheng Qiu, Xiangzhao Wang, Qunyu Bi, Qiongyan Yuan, Bo Peng, and Lifeng Duan, "Translational-symmetry alternating phase shifting mask grating mark used in a linear measurement model of lithographic projection lens aberrations," Appl. Opt. 48, 3654-3663 (2009)

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Abstract

A linear measurement model of lithographic projection lens aberrations is studied numerically based on the Hopkins theory of partially-coherent imaging and positive resist optical lithography (PROLITH) simulation. In this linearity model, the correlation between the mark’s structure and its sensitivities to aberrations is analyzed. A method to design a mark with high sensitivity is proved and declared. By use of this method, a translational-symmetry alternating phase shifting mask (Alt-PSM) grating mark is redesigned with all of the even orders, $\pm 3$ rd and $\pm 5$ th order diffraction light missing. In the evaluation simulation, the measurement accuracies of aberrations prove to be enhanced apparently by use of the redesigned mark instead of the old ones.

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Linearity	a	b
$Z_{7} - IPE$	$pitch = 0.90 λ / NA$	0.804	0
$Z_{7} - IPE$	$pitch = 1.15 λ / NA$	1.163	0
$Z_{14} - IPE$	$pitch = 0.90 λ / NA$	$- 0.083$	0
$Z_{14} - IPE$	$pitch = 1.15 λ / NA$	$- 0.600$	0
$Z_{9} - BFS$	$pitch = 0.90 λ / NA$	2.886	$- 4.356 E - 05$
$Z_{9} - BFS$	$pitch = 1.15 λ / NA$	5.704	$- 3.168 E - 05$
$Z_{16} - BFS$	$pitch = 0.90 λ / NA$	$- 1.900$	1.247E-05
$Z_{16} - BFS$	$pitch = 1.15 λ / NA$	$- 2.818$	$- 3.069 E - 05$
$Z_{12} - {BFS}_{hv}$	$pitch = 0.90 λ / NA$	1.208	$- 5.4 E - 05$
$Z_{12} - {BFS}_{hv}$	$pitch = 1.15 λ / NA$	4.268	$- 3.2 E - 05$

Zernike Coefficient	Measurement Mark	Maximum Sensitivity	Minimum Sensitivity	Variation Range	Measurement Accuracy (nm)
$Z_{7}$	Ordinary Alt-PSM	1.96	0.04	1.92	0.52
$Z_{7}$	Optimized Alt-PSM	2.21	0.01	2.20	0.45
$Z_{7}$	Translational-Symmetry Alt-PSM	3.65	$- 0.11$	3.76	0.27
$Z_{14}$	Ordinary Alt-PSM	0.32	$- 1.97$	2.29	0.44
$Z_{14}$	Optimized Alt-PSM	0.35	$- 2.67$	3.02	0.33
$Z_{14}$	Translational-Symmetry Alt-PSM	0.67	$- 4.11$	4.78	0.21
$Z_{9}$	Ordinary Alt-PSM	12.55	$- 0.89$	13.44	0.74
$Z_{9}$	Optimized Alt-PSM	13.84	$- 0.40$	14.24	0.70
$Z_{9}$	Translational-Symmetry Alt-PSM	16.34	0.49	15.85	0.63
$Z_{16}$	Ordinary Alt-PSM	0.29	$- 13.65$	13.94	0.72
$Z_{16}$	Optimized Alt-PSM	1.69	$- 23.11$	24.80	0.40
$Z_{16}$	Translational-Symmetry Alt-PSM	0.69	$- 27.70$	28.39	0.35
$Z_{12}$	Ordinary Alt-PSM	10.96	$- 2.39$	13.35	0.75
$Z_{12}$	Optimized Alt-PSM	13.54	$- 1.40$	14.94	0.67
$Z_{12}$	Translational-Symmetry Alt-PSM	15.94	$- 0.20$	16.14	0.62

Linearity	a	b
$Z_{7} - IPE$	$pitch = 0.90 λ / NA$	0.804	0
$Z_{7} - IPE$	$pitch = 1.15 λ / NA$	1.163	0
$Z_{14} - IPE$	$pitch = 0.90 λ / NA$	$- 0.083$	0
$Z_{14} - IPE$	$pitch = 1.15 λ / NA$	$- 0.600$	0
$Z_{9} - BFS$	$pitch = 0.90 λ / NA$	2.886	$- 4.356 E - 05$
$Z_{9} - BFS$	$pitch = 1.15 λ / NA$	5.704	$- 3.168 E - 05$
$Z_{16} - BFS$	$pitch = 0.90 λ / NA$	$- 1.900$	1.247E-05
$Z_{16} - BFS$	$pitch = 1.15 λ / NA$	$- 2.818$	$- 3.069 E - 05$
$Z_{12} - {BFS}_{hv}$	$pitch = 0.90 λ / NA$	1.208	$- 5.4 E - 05$
$Z_{12} - {BFS}_{hv}$	$pitch = 1.15 λ / NA$	4.268	$- 3.2 E - 05$

Zernike Coefficient	Measurement Mark	Maximum Sensitivity	Minimum Sensitivity	Variation Range	Measurement Accuracy (nm)
$Z_{7}$	Ordinary Alt-PSM	1.96	0.04	1.92	0.52
$Z_{7}$	Optimized Alt-PSM	2.21	0.01	2.20	0.45
$Z_{7}$	Translational-Symmetry Alt-PSM	3.65	$- 0.11$	3.76	0.27
$Z_{14}$	Ordinary Alt-PSM	0.32	$- 1.97$	2.29	0.44
$Z_{14}$	Optimized Alt-PSM	0.35	$- 2.67$	3.02	0.33
$Z_{14}$	Translational-Symmetry Alt-PSM	0.67	$- 4.11$	4.78	0.21
$Z_{9}$	Ordinary Alt-PSM	12.55	$- 0.89$	13.44	0.74
$Z_{9}$	Optimized Alt-PSM	13.84	$- 0.40$	14.24	0.70
$Z_{9}$	Translational-Symmetry Alt-PSM	16.34	0.49	15.85	0.63
$Z_{16}$	Ordinary Alt-PSM	0.29	$- 13.65$	13.94	0.72
$Z_{16}$	Optimized Alt-PSM	1.69	$- 23.11$	24.80	0.40
$Z_{16}$	Translational-Symmetry Alt-PSM	0.69	$- 27.70$	28.39	0.35
$Z_{12}$	Ordinary Alt-PSM	10.96	$- 2.39$	13.35	0.75
$Z_{12}$	Optimized Alt-PSM	13.54	$- 1.40$	14.94	0.67
$Z_{12}$	Translational-Symmetry Alt-PSM	15.94	$- 0.20$	16.14	0.62

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Applied Optics