Three-dimensional x-ray Fourier transform holography: the Bragg case

Imaging Ultrafast Dynamical Diffraction Wave Fronts in Strained Si with Coherent X Rays

Dynamical diffraction effects in thin single crystals produce highly monochromatic parallel x-ray beams with a mutual separation of a few microns and a time delay of a few femtoseconds-the so-called echoes. This ultrafast diffraction effect is used at X-Ray Free Electron Lasers in self-seeding schemes to improve beam monochromaticity. Here, we present a coherent x-ray imaging measurement of echoes from Si crystals and demonstrate that a small surface strain can be used to tune their temporal delay. These results represent a first step toward the ambitious goal of strain tailoring new x-ray optics and, conversely, open up the possibility of using ultrafast dynamical diffraction effects to study strain in materials.

Confocal Bragg ptychography for bulk specimens: a numerical demonstration

We report on a new X-ray imaging method, which generalizes Bragg ptychography to 3D mapping of embedded crystalline volumes within thick specimens. The sample is probed by a pencil X-ray beam. The diffracted beam is magnified by an objective and passes through a slit in the image plane to be monitored by a 2D detector in the far-field of the image plane. The dimensions of the incoming beam and the slit opening define a confocal Bragg volume. Scanning the sample with respect to this probe volume, an iterative oversampling routine is used to reconstruct the shape and projected displacement field of extended internal volumes. This routine takes into account the pupil function and known aberrations of the lens. We demonstrate the method by a numerical study of a 3.5 µm grain comprising a wall of edge dislocations. With a probe volume of ∼0.12 µm³ and a compound refractive lens with a numerical aperture of 0.49×10^-3 as the objective, the dislocations are fully resolved with a displacement sensitivity of ∼10 pm. The spatial resolution is 26×27×123 nm³ (rms), with the poor resolution along the optical axis being limited by the probe size. With a four times larger numerical aperture, the resolution becomes 16×8×123 nm³ (rms). The lens aberrations are found to be not critical.

Revealing crystalline domains in a mollusc shell single-crystalline prism

Biomineralization integrates complex processes leading to an extraordinary diversity of calcareous biomineral crystalline architectures, in intriguing contrast with the consistent presence of a sub-micrometric granular structure. Hence, gaining access to the crystalline architecture at the mesoscale, that is, over a few granules, is key to building realistic biomineralization scenarios. Here we provide the nanoscale spatial arrangement of the crystalline structure within the 'single-crystalline' prisms of the prismatic layer of a Pinctada margaritifera shell, exploiting three-dimensional X-ray Bragg ptychography microscopy. We reveal the details of the mesocrystalline organization, evidencing a crystalline coherence extending over a few granules. We additionally prove the existence of larger iso-oriented crystalline domains, slightly misoriented with respect to each other, around one unique rotation axis, and whose shapes are correlated with iso-strain domains. The highlighted mesocrystalline properties support recent biomineralization models involving partial fusion of oriented nanoparticle assembly and/or liquid droplet precursors.

Deterministic Bragg Coherent Diffraction Imaging

A deterministic variant of Bragg Coherent Diffraction Imaging is introduced in its kinematical approximation, for X-ray scattering from an imperfect crystal whose imperfections span no more than half of the volume of the crystal. This approach provides a unique analytical reconstruction of the object's structure factor and displacement fields from the 3D diffracted intensity distribution centred around any particular reciprocal lattice vector. The simple closed-form reconstruction algorithm, which requires only one multiplication and one Fourier transformation, is not restricted by assumptions of smallness of the displacement field. The algorithm performs well in simulations incorporating a variety of conditions, including both realistic levels of noise and departures from ideality in the reference (i.e. imperfection-free) part of the crystal.

Strain in a silicon-on-insulator nanostructure revealed by 3D x-ray Bragg ptychography

Progresses in the design of well-defined electronic band structure and dedicated functionalities rely on the high control of complex architectural device nano-scaled structures. This includes the challenging accurate description of strain fields in crystalline structures, which requires non invasive and three-dimensional (3D) imaging methods. Here, we demonstrate in details how x-ray Bragg ptychography can be used to quantify in 3D a displacement field in a lithographically patterned silicon-on-insulator structure. The image of the crystalline properties, which results from the phase retrieval of a coherent intensity data set, is obtained from a well-controlled optimized process, for which all steps are detailed. These results confirm the promising perspectives of 3D Bragg ptychography for the investigation of complex nano-structured crystals in material science.

Reconstruction of crystal shapes by X-ray nanodiffraction from three-dimensional superlattices

Quantitative nondestructive imaging of structural properties of semiconductor layer stacks at the nanoscale is essential for tailoring the device characteristics of many low-dimensional quantum structures, such as ultrafast transistors, solid state lasers and detectors. Here it is shown that scanning nanodiffraction of synchrotron X-ray radiation can unravel the three-dimensional structure of epitaxial crystals containing a periodic superlattice underneath their faceted surface. By mapping reciprocal space in all three dimensions, the superlattice period is determined across the various crystal facets and the very high crystalline quality of the structures is demonstrated. It is shown that the presence of the superlattice allows the reconstruction of the crystal shape without the need of any structural model.

Perfect crystals grown from imperfect interfaces

The fabrication of advanced devices increasingly requires materials with different properties to be combined in the form of monolithic heterostructures. In practice this means growing epitaxial semiconductor layers on substrates often greatly differing in lattice parameters and thermal expansion coefficients. With increasing layer thickness the relaxation of misfit and thermal strains may cause dislocations, substrate bowing and even layer cracking. Minimizing these drawbacks is therefore essential for heterostructures based on thick layers to be of any use for device fabrication. Here we prove by scanning X-ray nanodiffraction that mismatched Ge crystals epitaxially grown on deeply patterned Si substrates evolve into perfect structures away from the heavily dislocated interface. We show that relaxing thermal and misfit strains result just in lattice bending and tiny crystal tilts. We may thus expect a new concept in which continuous layers are replaced by quasi-continuous crystal arrays to lead to dramatically improved physical properties.

Noise models for low counting rate coherent diffraction imaging

Coherent diffraction imaging (CDI) is a lens-less microscopy method that extracts the complex-valued exit field from intensity measurements alone. It is of particular importance for microscopy imaging with diffraction set-ups where high quality lenses are not available. The inversion scheme allowing the phase retrieval is based on the use of an iterative algorithm. In this work, we address the question of the choice of the iterative process in the case of data corrupted by photon or electron shot noise. Several noise models are presented and further used within two inversion strategies, the ordered subset and the scaled gradient. Based on analytical and numerical analysis together with Monte-Carlo studies, we show that any physical interpretations drawn from a CDI iterative technique require a detailed understanding of the relationship between the noise model and the used inversion method. We observe that iterative algorithms often assume implicitly a noise model. For low counting rates, each noise model behaves differently. Moreover, the used optimization strategy introduces its own artefacts. Based on this analysis, we develop a hybrid strategy which works efficiently in the absence of an informed initial guess. Our work emphasises issues which should be considered carefully when inverting experimental data.

Nano-X-ray absorption spectroscopy of single Co-implanted ZnO nanowires

We report on the local structure of single Co-implanted ZnO nanowires studied using a hard X-ray nanoprobe. X-ray fluorescence maps show uniform Zn and Co distributions along the wire within the length scale of the beam size. The X-ray fluorescence data allow the estimation of the Co content within the nanowire. Polarization dependent X-ray absorption near edge structure shows no structural disorder induced neither in the radial nor axial directions of the implanted nanowires after subsequent annealing. Co2+ ions occupy Zn sites into the wurtzite ZnO lattice. Extended X-ray absorption fine structure data reveal high structural order in the host lattice without distortion in their interatomic distances, confirming the recovery of the radiation damaged ZnO structure through thermal annealing.

Coherent x-ray wavefront reconstruction of a partially illuminated Fresnel zone plate

A detailed characterization of the coherent x-ray wavefront produced by a partially illuminated Fresnel zone plate is presented. We show, by numerical and experimental approaches, how the beam size and the focal depth are strongly influenced by the illumination conditions, while the phase of the focal spot remains constant. These results confirm that the partial illumination can be used for coherent diffraction experiments. Finally, we demonstrate the possibility of reconstructing the complex-valued illumination function by simple measurement of the far field intensity in the specific case of partial illumination.

Three-dimensional diffraction mapping by tuning the X-ray energy

Three-dimensional reciprocal-space maps of a single SiGe island around the Si(004) Bragg peak are recorded using an energy-tuning technique with a microfocused X-ray beam with compound refractive lenses as focusing optics. The map is in agreement with simulated data as well as with a map recorded by an ordinary rocking-curve scan. The energy-tuning approach circumvents both the comparatively large sphere of confusion of diffractometers compared with nanostructures and vibrations induced by motors. Thus, this method offers new possibilities for novel combinations of three-dimensional micro- and nano-focused X-ray diffraction with complex in situ sample environments such as scanning probe microscopes.