<p>With the development of the semiconductor industry below the 7 nm scale, critical dimension small-angle X-ray scattering (CD-SAXS) has emerged as a powerful tool for quantitatively measuring nanoscale deviations. In this study, the effects of X-ray beam size and photon energy on the accuracy of critical dimension measurements were investigated. Critical dimensions measured using beams with different spot sizes showed different deviations from the expected values. Beam sizes that were either too large or too small did not improve confidence intervals. As the incident energy increased, the X-ray transmission rate increased, while the scattering cross section decreased, resulting in a gradual decrease in the signal-to-noise ratio of the diffraction peaks, which reduced the accuracy of the CD-SAXS measurements. An optimal accuracy was obtained at 12 keV with a smaller beam size. Using an effective trapezoid model, the results yielded an average pitch of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$100.4 \pm 0.2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>100.4</mn> <mo>±</mo> <mn>0.2</mn> </mrow> </math></EquationSource> </InlineEquation> nm, width of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$49.8 \pm 0.2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>49.8</mn> <mo>±</mo> <mn>0.2</mn> </mrow> </math></EquationSource> </InlineEquation> nm, height of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$130.0 \pm 0.2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>130.0</mn> <mo>±</mo> <mn>0.2</mn> </mrow> </math></EquationSource> </InlineEquation> nm, and a sidewall angle below <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$1.1^\circ \pm 0.1^\circ$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>.</mo> <msup> <mn>1</mn> <mo>∘</mo> </msup> <mo>±</mo> <mn>0</mn> <mo>.</mo> <msup> <mn>1</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>. These results provide crucial guidance for the future development of CD-SAXS laboratories and the construction of X-ray machines as well as robust support for research in related fields.</p>

Impacts of X-ray energy and beam size on CD-SAXS measurement precision

期刊论文
发表日期：

2026年2月2日

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Xu-Yang Qin,
Bing Guo,
Nan Pan,
Xin-Hao Gao,
Shu-Min Yang,
Chun-Xia Hong,
Ying Wang,
Xiu-Hong Li,
Chun-Ming Yang,
Feng-Gang Bian

摘要

With the development of the semiconductor industry below the 7 nm scale, critical dimension small-angle X-ray scattering (CD-SAXS) has emerged as a powerful tool for quantitatively measuring nanoscale deviations. In this study, the effects of X-ray beam size and photon energy on the accuracy of critical dimension measurements were investigated. Critical dimensions measured using beams with different spot sizes showed different deviations from the expected values. Beam sizes that were either too large or too small did not improve confidence intervals. As the incident energy increased, the X-ray transmission rate increased, while the scattering cross section decreased, resulting in a gradual decrease in the signal-to-noise ratio of the diffraction peaks, which reduced the accuracy of the CD-SAXS measurements. An optimal accuracy was obtained at 12 keV with a smaller beam size. Using an effective trapezoid model, the results yielded an average pitch of $100.4 \pm 0.2$ $100.4 \pm 0.2$ nm, width of $49.8 \pm 0.2$ $49.8 \pm 0.2$ nm, height of $130.0 \pm 0.2$ $130.0 \pm 0.2$ nm, and a sidewall angle below $1.1^\circ \pm 0.1^\circ$ $1 . 1^{\circ} \pm 0 . 1^{\circ}$ . These results provide crucial guidance for the future development of CD-SAXS laboratories and the construction of X-ray machines as well as robust support for research in related fields.