Virginie Chamard

Three-dimensional high-resolution quantitative microscopy of extended crystals

Hard X-ray lens-less microscopy raises hopes for a non-invasive quantitative imaging, capable of achieving the extreme resolving power demands of nanoscience. However, a limit imposed by the partial coherence of third generation synchrotron sources restricts the sample size to the micrometer range. Recently, X-ray ptychography has been demonstrated as a solution for arbitrarily extending the field of view without degrading the resolution. Here we show that ptychography, applied in the Bragg geometry, opens new perspectives for crystalline imaging. The spatial dependence of the three-dimensional Bragg peak intensity is mapped and the entire data subsequently inverted with a Bragg-adapted phase retrieval ptychographical algorithm. We report on the image obtained from an extended crystalline sample, nanostructured from a silicon-on-insulator substrate. The possibility to retrieve, without transverse size restriction, the highly resolved three-dimensional density and displacement field will allow for the unprecedented investigation of a wide variety of crystalline materials, ranging from life science to microelectronics.

Inversion of the diffraction pattern from an inhomogeneously strained crystal using an iterative algorithm

The displacement field in highly nonuniformly strained crystals is obtained by addition of constraints to an iterative phase retrieval algorithm. These constraints include direct space density uniformity and also constraints to the sign and derivatives of the different components of the displacement field. This algorithm is applied to an experimental reciprocal space map measured using high-resolution x-ray diffraction from an array of silicon lines, and the obtained component of the displacement field is in very good agreement with the one calculated using a finite element model.

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.

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.

High resolution three dimensional structural microscopy by single angle Bragg ptychography

Coherent X-ray microscopy by phase retrieval of Bragg diffraction intensities enables lattice distortions within a crystal to be imaged at nanometre-scale spatial resolutions in three dimensions. While this capability can be used to resolve structure-property relationships at the nanoscale under working conditions, strict data measurement requirements can limit the application of current approaches. Here, we introduce an efficient method of imaging three-dimensional (3D) nanoscale lattice behaviour and strain fields in crystalline materials with a methodology that we call 3D Bragg projection ptychography (3DBPP). This method enables 3D image reconstruction of a crystal volume from a series of two-dimensional X-ray Bragg coherent intensity diffraction patterns measured at a single incident beam angle. Structural information about the sample is encoded along two reciprocal-space directions normal to the Bragg diffracted exit beam, and along the third dimension in real space by the scanning beam. We present our approach with an analytical derivation, a numerical demonstration, and an experimental reconstruction of lattice distortions in a component of a nanoelectronic prototype device.

Evidence of stacking‐fault distribution along an InAs nanowire using micro‐focused coherent X‐ray diffraction

InAs nanowire samples grown by metal-organic chemical vapor deposition present a significant amount of wurtzite structure, while the zincblende lattice is known to be the stable crystal structure for the bulk material. The question of the wurtzite distribution in the sample is addressed using phase-sensitive coherent X-ray diffraction with a micro-focused beam at a synchrotron source. The simultaneous investigation of the wurtzite 10\bar{1}0, 20\bar{2}0 and 30\bar{3}0 reflections performed on a bunch of single wires shows unambiguously that the wurtzite contribution is a result of stacking faults distributed along the wire. Additional simulations lead to adjustments of the wire structural parameters, such as the wurtzite content, the strain distribution, the wire diameters and their respective orientations.

Nanobeam x-ray scattering : probing matter at the nanoscale

INTRODUCTION X-RAY DIFFRACTION PRINCIPLES -Introduction -Beam Coherence -Specific Properties of Different Sources: Laboratory vs Synchrotron vs FEL FOCUSING OF X-RAYS -Beam Propagation and Modeling -Focusing Principles Available for the Hard X-Ray Regime -Clasic Microfocusing Devices -Practical Issues SCATTERING EXPERIMENTS USING NANOBEAMS -From the Ensemble Average Approach Towards the Single Nanostructure Study -Diffraction from Single Nanostructures -Scanning X-Ray Diffraction Microscopy -Other Types of Contrast -Local X-Ray Probe Experiments from Organic Samples -Local X-Ray Probe Experiments from Biological Samples NANOBEAM DIFFRACTION SETUPS -Beam Positioning on the Nanoscale -Stability Issues: Maintaining the Spot on the Sample During Scanning Angles, Vibrations -Active Systems to Maintain the Beam Position on the Sample Constant -Restriction of Different Setups -Detector Issues: Resolution in Real and Reciprocal Space, Dynamic Range, Time Resolution SPECTROSCOPIC TECHNIQUES USING FOCUSED BEAMS -Micro/Nano-EXAFS, XANES. Fluorescence -A Side Glance on Soft X-Ray Applications COHERENT DIFFRACTION -More on Coherence Properties of Focused X-Ray Beams -The Use of Phase Retrieval Instead of Modeling Approaches -Different Retrieval Algorithms -Shape Determination of Single Structures (Retrieving the Modulus of Electron Density) -Strain Determination (Retrieving the Phase of Electron Density) -Fresnel Coherent Diffractive Imaging -Holographic Approaches (Using a Reference Wave Instead of Numerical Phase Retrieval) -Ptychography (For Extended Objects with Nanoscale Structure) -Particular Advantages and Problems when Using Coherent Diffraction Imaging in the Bragg Case THE POTENTIAL AND THE LIMITS OF THE METHOD -Limits in Beam Size -Limits in Intensity/Brilliance -Resolution Limits in Real and Reciprocal Space -Combinations with Other Local Probe Techniques FUTURE DEVELOPMENTS -Detector Developments -Beamlines at Third Generation Synchrotron Sources -The Role of Free Electron Lasers

Imaging the displacement field within epitaxial nanostructures by coherent diffraction: a feasibility study

We investigate the feasibility of applying coherent diffraction imaging to highly strained epitaxial nanocrystals using finite-element simulations of SiGe islands as input in standard phase retrieval algorithms. We discuss the specific problems arising from both epitaxial and highly strained systems and we propose different methods to overcome these difficulties. Finally, we describe a coherent microdiffraction experimental setup using extremely focused x-ray beams to perform experiments on individual nanostructures.

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.

Investigation of shape, strain, and interdiffusion in InGaAs quantum rings using grazing incidence x-ray diffraction

The formation of nanoscopic InGaAs ring structures on a GaAs(001) substrate takes place when InAs quantum dots, grown by Stranski-Krastanov self-organization, are covered by a thin layer of GaAs. The shape transformation into rings is governed by strain, diffusion, and surface tension, physical parameters which are of importance to monitor the magneto-optical and electronic properties of the rings. In this work we report on the characterization of morphology and structure of the rings in three dimensions (such as strain and chemical composition). To this end we apply grazing incidence small angle x-ray scattering (GISAXS) and grazing incidence diffraction (GID). From GISAXS the shape is found to be of circular symmetry with an average outer radius of 26nm, a height of about 1.5nm, and a hole in the middle, in good agreement with atomic force microscopy measurements. Information about strain and interdiffusion is derived from intensity mappings in reciprocal space close to the (220) and (22¯0) reflections ...