Calibrating the Z-magnification of atomic force microscope below 10 nm by single-atom steps

He, Bo-Ching; Fu, Wei‐En; Wu, Chung-Lin; Chien, Yun-San; Liou, Huay-Chung

doi:10.1016/j.tsf.2015.01.019

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…Atomic force microscopy (AFM), widely used for dimensional measurements in the semiconductor industry, is the focus of our study. About 8 nm was for many years the smallest commercially available step-height standard, but sub-nanometer standards have been produced and measured using metrological atomic force microscopes [1][2][3][4][5][6][7]. These are a new type of standard based on monoatomic steps and make it possible to create standards with the height of a step defined by the lattice constant.…”

Section: Introductionmentioning

confidence: 99%

Study of uncertainties of height measurements of monoatomic steps on Si 5 × 5 using DFT

Campbell

Jelı́nek

Klapetek

2017

Meas. Sci. Technol.

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The development of nanotechnology gives rise to new demands on standards for dimensional measurements. Monoatomic steps on, e.g. silicon are a suitable length standard with a very low nominal value. The quantum-mechanical nature of objects consisting of only a few atomic layers in one or more dimensions can no longer be neglected and it is necessary to make a transition from the classical picture to a quantum approach in the field of uncertainty analysis. In this contribution, sources of uncertainty for height measurements using atomic force microscopy (AFM) in contact mode are discussed. Results of density functional theory (DFT) modeling of AFM scans on a monoatomic step on silicon are presented. Van der Waals forces for the interaction of a spherical tip and an infinite step are calculated classically. Height measurements in constant force mode at different forces are simulated. In our approach, we model the tip apex and the monoatomic step as systems of individual atoms. As interatomic forces act on the sample and the tip of the microscope, the atoms of both relax in order to reach equilibrium positions. This leads to changes in those quantities that are finally interpreted as the resultant height of the step. The presence of van der Waals forces induces differences between the forces acting on atoms at different distances of the step. The behavior of different tips is studied along with their impact on the resulting AFM scans. Because the shape of the tip apex is usually unknown in real experiments, this variance in the height result due to different tips is interpreted as a source of uncertainty.

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Section: Introductionmentioning

confidence: 99%

Study of uncertainties of height measurements of monoatomic steps on Si 5 × 5 using DFT

Campbell

Jelı́nek

Klapetek

2017

Meas. Sci. Technol.

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show abstract

“…Metrological traceability is a prerequisite for obtaining reliable measurement results to control manufacturing processes and ensure product quality. 12) Hence, dimensional artifacts that can be directly traced to natural constants are receiving increasing attention from researchers, most typically critical-dimension standards 13,14) and step height standards 15,16) based on the Si lattice constant. The Si lattice spacing as a secondary realization of the meter has been recommended at the 26th General Conference of Weights & Measures (CGPM).…”

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confidence: 99%

Two-dimensional sub-200 nm pitch Si gratings with natural orthogonality

Tang,

Zhao,

Deng

et al. 2023

Appl. Phys. Express

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As a standard for length and angle, two-dimensional (2D) grating reference materials can be used for performance verification and calibration of various microscopes and 2D stages. This paper proposes a 2D nanoscale reference grating manufactured by combining laser-focused atomic deposition (LFAD) and extreme ultraviolet interference lithography. The theoretical pitch of the 2D grating is 150.46 nm, which is only √2/2 times the pitch of the Cr grating manufactured by LFAD that can be traceable to the resonance transition frequency of Cr. Moreover, the angle between two periodic directions of the 2D nanograting has natural orthogonality.

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“…For example, the Si lattice constant has already been intensively used to fabricate selftraceable critical-dimension standards [9][10][11][12] (CD) and stepheight standards. [13][14][15] The merit of this approach to realize a high accuracy is the development of a direct traceability chain between the nanostructures and International-System (SI) units. Similarly, if a perpendicular angle is obtained from the ideal orthogonality inside a geometric shape, an almostperfect orthogonality of 2D nanogratings could be achieved.…”

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confidence: 99%

Natural square ruler at nanoscale

Xiao¹,

Liu²,

Zhu³

et al. 2018

Appl. Phys. Express

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Perfectly orthogonal two-dimensional gratings are crucial components in the calibration of scanning microscopes and displacement measurements of planar encoders. In this study, we propose a new approach to achieve self-traceable orthogonality by utilizing perpendicular diagonals inside a rhombus shape. Two-step laser-focused Cr atomic deposition is used to fabricate a rhombus array of dots with good uniformity, repeatability, accuracy, and stability. A theoretical analysis indicates that the non-orthogonality uncertainty budget is as low as 0.0027° for the two-dimensional Cr nanogratings with a self-traceable pitch of 212.8 nm, which makes the fabricated two-dimensional gratings promising as a natural square ruler with an extremely low uncertainty at the nanoscale.

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Calibrating the Z-magnification of atomic force microscope below 10 nm by single-atom steps

Cited by 6 publications

References 14 publications

Study of uncertainties of height measurements of monoatomic steps on Si 5 × 5 using DFT

Study of uncertainties of height measurements of monoatomic steps on Si 5 × 5 using DFT

Two-dimensional sub-200 nm pitch Si gratings with natural orthogonality

Natural square ruler at nanoscale

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