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20 July 2022 Cascade and cluster of correlated reactions as causes of stochastic defects in extreme ultraviolet lithography (Erratum)
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Abstract

The erratum corrects an error in parameter unit in the original article.

This article [H. Fukuda, J. Micro/Nanolith. MEMS MOEMS 19(2), 024601 (2020), doi: https://doi.org/10.1117/1.JMM.19.2.024601] was originally published online on 12 May 2020 with an incorrect parameter unit in Table 1.

The parameter unit in Table 1 was incorrectly labeled as “eV” rather than “keV.”

Original Table 1:

Table 1

Typical values and/or definitions of model parameters.

VariablesValues and definitions
Numerical aperture0.33∼0.55
Simulation area2000 nm × 20∼32 nm (for L/S)
Resist thickness20 nm
Resist photo absorption0.004  nm1 (for CAR), 0.02  nm1 (for MOx)
SE energy0.015 eV (with 10% standard deviation)
SE blur1.5 nm (mean free path of SE determined as a result of Monte Carlo simulation and dependent on density of PAGs or ligands)
Voxel size1 nm (for MOx), 2 nm (for CAR)
PAG density0.30.7  nm3 (for CAR)
Acid diffusion blur2∼5 nm (for CAR)
Turn over number (TON)Number of acid catalytic reactions per acid: 3∼10 (for CAR)
Quencher levelquencher density/PAG density: usually set at 0.2 in this paper
Acid quencher mutual diffusion length4 nm (for CAR)
Ligand density14  nm3 (for MOx)
Reaction densityDensity of acid-catalytic reactions in CAR or reactions at ligands in MOx
Threshold reaction density DcRReaction density required for flipping the solubility of polymers or molecules, DcR=NcR/voxelsize3
Reaction site densityDensity of reaction sites in resist matrix at which solubility changing reactions take place, such as protected moieties in CAR or ligands in MOx. Usually set at 2DcR.
Potential reaction densityPossible maximum reaction density under no restriction in PAG and reaction site densities, approximated by (photon irradiation density) × (photo absorption) × (# of SEs/# of photon absorptions) × (# of acid generations/# of SEs) × TON
NmaxMaximum number of voxel through thickness, Nmax = resist thickness/voxel size
NSFVdefectNumber of solubility flipped voxel through thickness required for spot pattern formation: set at 0.8Nmax UOS in this paper.
NSFVdefectNumber of solubility flipped voxel through thickness required for spot defect generation: set at 0.5Nmax UOS in this paper.

Corrected Table 1:

Table 1

Typical values and/or definitions of model parameters.

VariablesValues and definitions
Numerical aperture0.33∼0.55
Simulation area2000 nm × 20∼32 nm (for L/S)
Resist thickness20 nm
Resist photo absorption0.004  nm1 (for CAR), 0.02  nm1 (for MOx)
SE energy0.015 keV (with 10% standard deviation)
SE blur1.5 nm (mean free path of SE determined as a result of Monte Carlo simulation and dependent on density of PAGs or ligands)
Voxel size1 nm (for MOx), 2 nm (for CAR)
PAG density0.30.7  nm3 (for CAR)
Acid diffusion blur2∼5 nm (for CAR)
Turn over number (TON)Number of acid catalytic reactions per acid: 3∼10 (for CAR)
Quencher levelquencher density/PAG density: usually set at 0.2 in this paper
Acid quencher mutual diffusion length4 nm (for CAR)
Ligand density14  nm3 (for MOx)
Reaction densityDensity of acid-catalytic reactions in CAR or reactions at ligands in MOx
Threshold reaction density DcRReaction density required for flipping the solubility of polymers or molecules, DcR=NcR/voxelsize3
Reaction site densityDensity of reaction sites in resist matrix at which solubility changing reactions take place, such as protected moieties in CAR or ligands in MOx. Usually set at 2DcR.
Potential reaction densityPossible maximum reaction density under no restriction in PAG and reaction site densities, approximated by (photon irradiation density) × (photo absorption) × (# of SEs/# of photon absorptions) × (# of acid generations/# of SEs) × TON
NmaxMaximum number of voxel through thickness, Nmax = resist thickness/voxel size
NSFVpatternNumber of solubility flipped voxel through thickness required for spot pattern formation: set at 0.8Nmax UOS in this paper.
NSFVdefectNumber of solubility flipped voxel through thickness required for spot defect generation: set at 0.5Nmax UOS in this paper.

The results were obtained using the parameters in the correct units, and this error did not impact the results reported in the article. The corrected paper was republished on 13 July 2022.

© 2022 Society of Photo-Optical Instrumentation Engineers (SPIE)
Hiroshi Fukuda "Cascade and cluster of correlated reactions as causes of stochastic defects in extreme ultraviolet lithography (Erratum)," Journal of Micro/Nanopatterning, Materials, and Metrology 21(3), 039802 (20 July 2022). https://doi.org/10.1117/1.JMM.21.3.039802
Published: 20 July 2022
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KEYWORDS
Absorption

Diffusion

Extreme ultraviolet lithography

Monte Carlo methods

Stochastic processes

Computer simulations

Molecules

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