Extreme ultraviolet phase defect characterization based on complex amplitudes of the aerial images

Wei Cheng; Wei Cheng; Sikun Li; Sikun Li; Sikun Li; Xiangzhao Wang; Xiangzhao Wang; Xiangzhao Wang; Zinan Zhang; Zinan Zhang

doi:10.1364/AO.425941

Applied Optics
Vol. 60,
Issue 17,
pp. 5208-5219
(2021)
•https://doi.org/10.1364/AO.425941

Extreme ultraviolet phase defect characterization based on complex amplitudes of the aerial images

Wei Cheng, Sikun Li, Xiangzhao Wang, and Zinan Zhang

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Wei Cheng, Sikun Li, Xiangzhao Wang, and Zinan Zhang, "Extreme ultraviolet phase defect characterization based on complex amplitudes of the aerial images," Appl. Opt. 60, 5208-5219 (2021)

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Abstract

The profile deformation of a phase defect in an extreme ultraviolet (EUV) mask blank is the key factor to simulate its optical effects accurately and to compensate for it precisely. This paper provides a new, to the best of our knowledge, profile characterization method based on complex amplitudes of the aerial images for phase defects in EUV mask blanks. Fourier ptychography is adopted to retrieve the complex amplitudes of the aerial images and improve the lateral resolution. Both amplitude and phase impacted by the defect are taken into consideration to reconstruct the defect profile parameters (the height and the full width at half maxima of the defect’s top and bottom profiles). A conformal convolutional neural network model is constructed to map the amplitudes and phases of aerial images to the defect profile parameters. The Gaussian-shaped defect models with the mapped profile parameters can be used to simulate the amplitude and phase properties of the defects when compensating for them. The proposed method is verified to reconstruct the defect profile parameters of both bump defects and pit defects accurately. The involvement of both the amplitude and phase information makes the reconstructed defect profile parameters more appropriate to simulate the optical effects of the defects.

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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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Simulation Object	Submodule	Parameters
Optics	Illumination	Wavelength: 13.5 nm Chief ray angle: 6°
	Projection	$900 \times$ magnification, ${N A}_{o b j} = 0.0825$
Mask	Multilayer	40 pairs of Mo/Si bilayers Mo/Si thickness: 2.78 nm/4.17 nm Refractive index: Mo: 0.9238–0.006435j, Si: 0.9990–0.0018265j
	Substrate	${S i O}_{2}$ thickness: 20 nm

Truncation Order	14	13	12	11	10	9
Time(s)	16064.5	9541.6	5708.8	3380.5	1986.9	1158.4
Accuracy	/reference	2.1e-5	4.2e-5	6.7e-5	9.2e-5	0.00011
Truncation Order	8	7	6	5	4
Time(s)	595.0	284.7	147.5	75.5	36.6
Accuracy	0.00014	0.00019	0.00050	0.0016	0.0030

Illumination Angle	$l_{1}$	$l_{2}$	$l_{3}$	$l_{4}$	$l_{5}$	$l_{6}$	$l_{7}$	$l_{8}$	$l_{9}$
$θ_{r} (^{\circ})$	0	2.03	2.03	2.03	2.03	2.84	2.84	2.84	2.84
$φ (^{\circ})$	0	0	90	180	–90	45	135	–135	–45

Defect Type	Inputs	MAE (nm)	ARE (%)	MAE (nm)	ARE (%)	MAE (nm)	ARE (%)	MAE (nm)	ARE (%)
		$h_{t o p}$		$ω_{t o p}$		$h_{b o t}$		$ω_{b o t}$
Bump	Amplitude and phase	0.050	2.75	0.24	0.47	0.42	3.49	0.51	1.75
Pit	Amplitude and phase	0.055	3.71	0.12	0.24	0.28	2.32	0.43	1.28
Bump	Amplitude	0.11	5.68	0.45	0.91	0.88	7.18	0.94	3.66
Pit	Amplitude	0.089	5.50	0.44	0.82	0.51	4.18	0.38	1.23

Defect Type	Noise Type	SNR (dB)	MAE (nm)	ARE (%)	MAE (nm)	ARE (%)	MAE (nm)	ARE (%)	MAE (nm)	ARE (%)
			$h_{t o p}$		$ω_{t o p}$		$h_{b o t}$		$ω_{b o t}$
Bump	without noise	/	0.050	2.75	0.24	0.47	0.42	3.49	0.51	1.75
Bump	Gaussian	47.2	0.058	2.96	0.27	0.55	0.87	6.89	0.80	3.02
Bump	Gaussian	42.2	0.077	4.56	0.41	0.88	1.33	10.66	1.19	4.54
Bump	Gaussian	37.2	0.11	6.20	0.56	1.17	1.89	16.27	1.74	6.67
Bump	Poisson	37.7	0.088	5.26	0.46	0.97	1.24	10.41	1.22	4.56
Pit	without noise	/	0.055	3.71	0.12	0.24	0.28	2.32	0.43	1.28
Pit	Gaussian	47.2	0.055	3.71	0.15	0.31	0.37	3.04	0.50	1.48
Pit	Gaussian	42.2	0.056	3.70	0.17	0.35	0.53	4.02	0.64	1.85
Pit	Gaussian	37.2	0.063	4.12	0.26	0.54	0.77	5.92	0.96	2.72
Pit	Poisson	37.7	0.059	3.85	0.20	0.40	0.60	4.68	0.71	2.06

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Applied Optics