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X-ray phase-retrieval algorithms are widely exploited in contemporary hard x-ray diffraction techniques to image at the nanoscale, less than 10–20 nm. Often reconstruction of the sample shape (image) suffices for the purpose of experiment. Identification of specimen composition requires a quantitative profiling of the complex refractive index. This Letter shows that, although such quantitative analysis is possible in many cases, there is a lower limit to variations in optical density, which can be quantitatively reconstructed using the common phase-retrieval methods.

High-resolution x-ray diffraction and imaging techniques commonly assume a well-defined plane wave incident on the sample. Experimentally, the wave-front is limited by a collimating slit. Slit imperfections, such as surface roughness on the edges, may significantly contribute to the formation of the diffraction pattern from a specimen placed behind the slit. These effects become more profound when imaging at the nano-scale. This Letter presents experimental and simulated x-ray diffraction data quantitatively demonstrating the influence of slit edge imperfections on the formation of the diffraction pattern in the far-field regime.

X-ray Fraunhofer diffraction data have been collected from a series of weakly thickness-modulated samples using a synchrotron source. Three different areas of a linear Fresnel zone structure etched in a silicon wafer each 10 μm wide were studied. Each area studied included different numbers of zones, ranging from 6 to 20. An X-ray phase retrieval technique was used to profile the complex refractive index within the areas examined. The zone structure thickness profiles were mapped with a spatial resolution of 100 nm.

X-ray Fraunhofer diffraction data have been collected from a series of weakly thickness-modulated samples using a synchrotron source. Three different 10 μm wide areas of a linear Fresnel zone structure etched in a silicon wafer were studied. Each studied area included different number of zones, ranging from 6 to 20. Phase retrieval X-ray diffractometry technique was used for the experimental data analysis. The zone structure thickness profiles were mapped with a spatial resolution of 100 nm.

An X-ray diffraction technique has recently been developed and successfully applied to comprehensively, including both phase and amplitude contrast, map the complex refractive index of non-crystalline materials with submicron spatial resolution. The methodology is based on the measurement of a high angular resolution X-ray Fraunhofer diffraction pattern with further application of the phase-retrieval formalism using a logarithmic dispersion relation. The technique is reviewed from the perspective of its ability to deliver ultra-high, order of several nanometres, spatial resolution and to uniquely determine both the real and imaginary components of the complex refractive index of the material under analysis. Potential niche of practical applications is discussed in terms of the spatial resolution and field of view achievable by the method.

Phase retrieval X-ray diffraction was used to profile the complex refractive index of a slice through an acetate filament sample with a square cross-section. High angular resolution X-ray Fraunhofer diffraction patterns and a logarithmic dispersion relation phase-retrieval formalism were used to recover the projection profile of the sample for each of several sample orientations. The tomographic reconstruction of the slice from these projections closely reproduced the refractive index, geometrical shape and size of the acetate filament, using only limited a priori knowledge of the sample.

High-angular-resolution Fraunhofer diffraction data were collected from several samples with interfaces between dissimilar metals and an artificial crack in a metal foil using synchrotron x-radiation. The refractive index profile in the vicinity of the interface and crack of each sample was reconstructed with spatial resolution of about 40-60 nm by the Phase Retrieval X-Ray Diffractometry technique, using only limited a priori knowledge of the sample. These studies have demonstrated the viability of the technique as an in-situ nondestructive method of characterization of internal interfaces within multiphase materials and crack developing under external force.

High-angular-resolution Fraunhofer diffraction data were collected from several samples with interfaces between dissimilar metals using synchrotron x-radiation. The refractive index profile in the vicinity of the interface of each sample was reconstructed with spatial resolution of about 80nm by the phase retrieval x-ray diffractometry technique, using only limited a priori knowledge of the sample. These studies have demonstrated the viability of the technique as a nondestructive method of characterization of internal interfaces within multiphase materials.

An experimental-analytical technique for the model-independent nondestructive characterization of single-crystal alloys is applied to partially strain-compensated SiGe:C∕Si single layer structures with high concentrations of Ge. The studies were performed on pre- and postannealed SiGe:C∕Si samples. X-ray Bragg diffraction profiles were collected at a synchrotron radiation source near the absorption edge of Ge. The studies have allowed the reconstruction of the complex crystal structure factor as a function of crystal depth, permitting direct observation of the effect of the thermal annealing on lattice strain and structural composition in the SiGe:C layer. The technique was shown to be applicable to the analysis of both perfect crystals and crystal structures containing a low defect concentration.

A neural network root finder approach for finding complex roots of high-degree complex polynomials was applied as part of the phase-retrieval x-ray diffractometry technique to reconstruct strain profiles in SiGe(C)∕Si(C) superlattice structures. The high spatial resolution, 5A, as a result of significantly higher degree of the complex polynomial, 1400 roots, allowed us to obtain more accurate results for the strain profile distribution in SiGe(C)∕Si(C) superlattice structures. Previously, such high quality analysis was fundamentally impossible due to the limitations imposed by conventional numerical methods of finding complex polynomial roots.