Fig. 4: Grazing-incidence X-ray holography of the substrate-supported single-bar surface pattern.
a Schematic of surface holography near the substrate (not to scale). The scattered X-rays from the sample at low exit angles (close to or below the critical angles) can propagate towards the detector via the two pathways—the direct Path A and reflected Path B. They have a path length difference of approximately \(2d{{\sin }}({\alpha }_{f})\) and an incident angle-dependent reflection phase shift. When αf is lower than or close to the substrate critical angle, the direct and reflected scattering intensities are comparable, creating a situation similar to Lloyd’s mirror and Young’s double-slit with an effective slit spacing of 2d and the additional variable phase shift due to the reflection. b The two-path interference period along the αf direction is invariable for incident angles (0.4, 0.6, and 0.8°) above the substrate critical angle of 0.22°. The fringes from experimental images correspond to 2d of 114.4 nm (see text for details). The error bars are estimated from the uncertainty (about 3 detector pixels) of the interference period along the αf-direction. c The holography-based first-principles calculation generates a simulated pattern (left panel) that well matches the experimental data (right). d Line scans along the center of the arc (\({q}_{x}=0\)) from \({\alpha }_{f}=0^\circ\) (horizon) to 0.3° (black dashed line in panel c), showing the first-principles Lloyd’s mirror calculation is validated by both the experimental data and full-fledged FE-DWBA simulation at the low exit angles. e Line scan of the scattering profile along the white dashed line in panel c, containing the information of the form factor of thin-film surface pattern, more specifically, the length of the bar along the X-ray beam. The oscillation period indicates the bar length is 70.0 µm precisely. The first-principles calculation indicates that the single-incident angle scattering pattern contains the precise sample structural information in 3D.
