For example, X-ray reflectivity can reveal the electron density profile in the direction perpendicular to a thin film with a sub-nm resolution 31, 32. For decades, surface X-ray scattering techniques have been developed to interrogate substrate-supported structures, owing to their sensitivity to buried interfaces and the easiness of adapting in situ sample environments 29, 30. As a result, the X-ray coherent imaging methods, including theory, instrumentation, and applications, have been growing rapidly 25, 26, 27, 28.įor probing surface/interface structures, the transmission scattering geometry will not be applicable. The reconstruction algorithm uses iterative Fourier transforms (FT) and inverse FTs, operated over the form factors of the subject in real and reciprocal spaces 11.
#CALCULATE FLUX INTEGRAL 3D FULL#
Thanks to the weak interaction between hard X-rays and most of the materials on nano, micro, and even macro scales, conventional transmission and Bragg CDI reconstruction methods can take full advantage of kinematic analysis (or BA), as the 3D structure can be resolved but requires scanning numerous projection angles. Ptychographic X-ray computed tomography is effective in reconstructing extended samples such as integrated circuits 1, 21, 22, 23 and neuronal reconstruction 24. For isolated objects such as single nanocrystalline particles, the Bragg diffraction-based CDI (BCDI) 16, 17 can probe 3D strain distribution and dynamics during structural transformation 18, 19, 20. With the advent of coherent X-ray sources provided by modern storage-ring-based synchrotron 13 and linear-accelerator-based X-ray free-electron laser facilities 14, lensless X-ray coherent diffraction imaging (CDI) has become a popular microscopic method in materials and biological sciences 11, 15. This approach has been proven powerful in non-destructive structural characterization for vast scientific and technological applications 11, 12. The Bragg diffraction from crystals 9 and small-angle scattering 10 from non-periodical materials are usually analyzed by assuming kinematic scattering using Born approximation (BA) under weak perturbations. Probing structures and dynamics with nanometer (nm) spatial resolution usually requires X-ray scattering and imaging techniques, thanks to the short wavelength. In addition, scientific and technological applications of surface/interface fabrication and manipulation require precise determination of mesoscale 3D structures from tens micrometers down to sub-nanometers (sub-nm) in heterogeneous and non-periodical systems that control the functionality of the devices. These systems include but are not limited to, planar nanoelectronic circuits 1, hierarchical mesoscale surface structures 2, thin-film-based quantum dots 3 and photovoltaic 4, heterogeneous catalysts 5, biological membranes, and supramolecules 6, 7, 8, where observation in situ, operando, and in real-time is important. Surface/interface phenomena associated with mesoscale and low-dimensional materials are of great interest to scientists and engineers for establishing structure–function relationships.
The holographic method and simulations pave the way for single-shot structural characterization for visualizing irreversible and morphology-transforming physical and chemical processes in situ or operando. A first-principles calculation of the single-view holographic images resolves the surface patterns’ 3D morphology with nanometer resolutions, which is critical for ultrafine nanocircuit metrology. This approach further leads to the demonstration of hard-X-ray Lloyd’s mirror interference of scattering waves, resembling dark-field, high-contrast surface holography under the grazing-angle scattering conditions. We developed a 3D finite-element-based multibeam-scattering analysis to decode the heterogeneous electric-field distribution and to faithfully reproduce the complex scattering and surface features.
Here, we discovered that multibeam scattering in grazing-incident reflection geometry is sensitive to three-dimensional (3D) structures in a single view, which is difficult in conventional scattering or imaging approaches. Visualizing surface-supported and buried planar mesoscale structures, such as nanoelectronics, ultrathin-film quantum dots, photovoltaics, and heterogeneous catalysts, often requires high-resolution X-ray imaging and scattering.
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