Jones pupil decomposition and its lithographic imaging impacts

Zhiyuan Niu; Zhiyuan Niu; Ming Ding; Junhai Jiang; Hongbo Shang; Hongbo Shang; Siyu Zhu; Siyu Zhu; Fang Zhang; Weijie Shi; Aijun Zeng; Aijun Zeng; Huijie Huang; Huijie Huang; Huijie Huang

doi:10.1364/AO.414144

Applied Optics
Vol. 60,
Issue 5,
pp. 1357-1365
(2021)
•https://doi.org/10.1364/AO.414144

Jones pupil decomposition and its lithographic imaging impacts

Zhiyuan Niu, Ming Ding, Junhai Jiang, Hongbo Shang, Siyu Zhu, Fang Zhang, Weijie Shi, Aijun Zeng, and Huijie Huang

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Zhiyuan Niu, Ming Ding, Junhai Jiang, Hongbo Shang, Siyu Zhu, Fang Zhang, Weijie Shi, Aijun Zeng, and Huijie Huang, "Jones pupil decomposition and its lithographic imaging impacts," Appl. Opt. 60, 1357-1365 (2021)

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- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: November 5, 2020
- Revised Manuscript: January 12, 2021
- Manuscript Accepted: January 13, 2021
- Published: February 9, 2021

Abstract

The Jones pupil is a full description of imaging properties of projection lenses in optical lithography. The decomposition of the Jones pupil into components with clear physical meanings was studied previously; however, the decomposition method has not been studied systematically. To generalize the existing decomposition method, this work is aimed at finding all the decomposition methods and analyzing the lithographic imaging impacts. In this work, six decomposition methods are proposed, and the lithographic imaging impacts of the Jones components are studied and compared for all the decomposition methods. The results demonstrate that, although the decomposition methods are different, their lithographic impacts are identical. To be specific, apodization has a dominant impact on the critical dimension with a magnitude of 1.3 nm, and the impact of diattenuation is 0.3 nm. In contrast, the impacts of the other Jones components of aberration, birefringence, rotator, and ellipticity are negligible. This work gives a complete understanding of the imaging impacts of the Jones pupil.

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Name	Value/Description
Wavelength (nm)	193. Wavelength of illuminated light.
Numerical aperture	1.35. NA of the projection lens.
Illumination type	Freeform illumination with intensity map shown in Fig. 9. The intensity map is plotted as function of the pupil coordinates.
Polarization	XY. The polarization type is XY, which is a widely used polarization mode in modern lithography.
Mask	6% attenuated phase shifting mask (attPSM), dark field. The mask has 100% transmission and no phase change for the pattern areas, and has 6% transmission and phase change of 180° for the other areas (called background or field areas).
Patterns	Through pitch patterns with line $L = 45 n m$ , pitch $P = 90 - 400 n m$ . The patterns are corrected with OPC (optical proximity correction) to print size to target. The pattern is shown in Fig. 10. Due to diffraction, the shape of mask image is usually far different from that of mask. OPC is a technique to optimize the mask pattern’s shape to get good image quality and the desired pattern shape.
Resist model	Pure optical model with threshold at which the pattern L45P90 is printed to 45 nm at wafer. The resist information is not taken into account. CDs calculated by this kind of model are called optical CDs.
Jones pupil	Original Jones pupil and 17 reconstructed ones.

Components	Max. CD Difference [nm]
(Apodization)	1.32
$d$ (diattenuation)	0.32
$Φ$ (aberration)	0.08
$δ_{1}$ of $J_{H 1}$ (ellipticity)	0.00
$δ_{2}$ of $J_{H 2}$ (ellipticity)	0.00
$τ$ in $J = J_{H 1} J_{U 1}$ (ellipticity)	0.01
$τ$ in $J = J_{U 1} J_{H 2}$ (ellipticity)	0.01
$J_{r e t} (ϕ, γ)$ in $J = J_{H 1} J_{U 1}$ (birefringence)	0.07
$J_{r e t} (ϕ, γ)$ in $J = J_{U 1} J_{H 2}$ (birefringence)	0.07
$J_{r e t} (φ, β)$ in $J = J_{H 1} J_{U 2}$ (birefringence)	0.08
$J_{r e t} (φ, β)$ in $J = J_{U 2} J_{H 2}$ (birefringence)	0.08
$J_{r o t} (α)$ in $J = J_{H 1} J_{U 2}$ (rotator)	0.01
$J_{r o t} (α)$ in $J = J_{U 2} J_{H 2}$ (rotator)	0.01
$J_{r o t} (ϑ)$ in $J = J_{H 1} J_{U 3}$ (rotator)	0.04
$J_{r o t} (ϑ)$ in $J = J_{U 3} J_{H 2}$ (rotator)	0.04
$J_{r e t} (ρ)$ and $J_{r e t} (σ)$ in $J = J_{H 1} J_{U 3}$ (birefringence)	0.07
$J_{r e t} (ρ)$ and $J_{r e t} (σ)$ in $J = J_{U 3} J_{H 2}$ (birefringence)	0.07

Name	Value/Description
Wavelength (nm)	193. Wavelength of illuminated light.
Numerical aperture	1.35. NA of the projection lens.
Illumination type	Freeform illumination with intensity map shown in Fig. 9. The intensity map is plotted as function of the pupil coordinates.
Polarization	XY. The polarization type is XY, which is a widely used polarization mode in modern lithography.
Mask	6% attenuated phase shifting mask (attPSM), dark field. The mask has 100% transmission and no phase change for the pattern areas, and has 6% transmission and phase change of 180° for the other areas (called background or field areas).
Patterns	Through pitch patterns with line $L = 45 n m$ , pitch $P = 90 - 400 n m$ . The patterns are corrected with OPC (optical proximity correction) to print size to target. The pattern is shown in Fig. 10. Due to diffraction, the shape of mask image is usually far different from that of mask. OPC is a technique to optimize the mask pattern’s shape to get good image quality and the desired pattern shape.
Resist model	Pure optical model with threshold at which the pattern L45P90 is printed to 45 nm at wafer. The resist information is not taken into account. CDs calculated by this kind of model are called optical CDs.
Jones pupil	Original Jones pupil and 17 reconstructed ones.

Components	Max. CD Difference [nm]
(Apodization)	1.32
$d$ (diattenuation)	0.32
$Φ$ (aberration)	0.08
$δ_{1}$ of $J_{H 1}$ (ellipticity)	0.00
$δ_{2}$ of $J_{H 2}$ (ellipticity)	0.00
$τ$ in $J = J_{H 1} J_{U 1}$ (ellipticity)	0.01
$τ$ in $J = J_{U 1} J_{H 2}$ (ellipticity)	0.01
$J_{r e t} (ϕ, γ)$ in $J = J_{H 1} J_{U 1}$ (birefringence)	0.07
$J_{r e t} (ϕ, γ)$ in $J = J_{U 1} J_{H 2}$ (birefringence)	0.07
$J_{r e t} (φ, β)$ in $J = J_{H 1} J_{U 2}$ (birefringence)	0.08
$J_{r e t} (φ, β)$ in $J = J_{U 2} J_{H 2}$ (birefringence)	0.08
$J_{r o t} (α)$ in $J = J_{H 1} J_{U 2}$ (rotator)	0.01
$J_{r o t} (α)$ in $J = J_{U 2} J_{H 2}$ (rotator)	0.01
$J_{r o t} (ϑ)$ in $J = J_{H 1} J_{U 3}$ (rotator)	0.04
$J_{r o t} (ϑ)$ in $J = J_{U 3} J_{H 2}$ (rotator)	0.04
$J_{r e t} (ρ)$ and $J_{r e t} (σ)$ in $J = J_{H 1} J_{U 3}$ (birefringence)	0.07
$J_{r e t} (ρ)$ and $J_{r e t} (σ)$ in $J = J_{U 3} J_{H 2}$ (birefringence)	0.07

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Applied Optics