Phase Retrieval X-ray Diffractometry Research Articles

X-ray diffraction profiling of metal-metal interfaces at the nanoscale

Several samples containing interfaces between dissimilar metals were examined using diffraction of synchrotron radiation. The complex refractive index profile in the vicinity of the interface for each sample was reconstructed with spatial resolution of about 40 nm by the phase retrieval x-ray diffractometry technique. A series of computer simulations related to the analysis of various configurations of interfaces between dissimilar materials were performed. A practical algorithm of experimental data collection for a detailed examination of internal interfaces was suggested. An estimation of the minimal size of the interface structure modulations, which can be analyzed by the phase retrieval x-ray diffractometry technique, was suggested from the results of computer simulations. It was shown that interface modulations of about 50-100 nm in bimetals can be readily reconstructed by the technique.

Nanoresolution profiling of metal-metal interfaces from x-ray Fraunhofer diffraction data

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.

Application of phase-retrieval x-ray diffractometry to carbon doped SiGe(C)∕Si(C) superlattice structures. II. High resolution reconstruction using neural network root finder technique

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, 5Å, 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.

Nano-resolution profiling of micro-structures using quantitative X-ray phase retrieval from Fraunhofer diffraction data

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.

High-resolution X-ray diffraction imaging of non-Bragg diffracting materials using phase retrieval X-ray diffractometry (PRXRD) technique

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.

X-ray Bragg diffraction profiles from unstrained layered single-crystal structures: theoretical considerations, simulation and reconstruction using phase-retrieval X-ray diffractometry

The X-ray Bragg diffraction intensity profile for a model strain-compensated single-crystal structure consisting of a thin alloy layer grown on a thick substrate is derived using a Laplace transform interpretation of the kinematical approximation of X-ray diffraction theory, assuming a step-like attenuation depth-profile. The effects of the model physical parameters on the measurable Bragg diffraction intensity profile are discussed. The intensity profiles for model SiGe:C/Si perfectly unstrained layer thicknesses of 50 and 100 nm are simulated for three characteristic X-ray radiation wavelengths (0.05–0.15 nm). The simulations are performed near the absorption edge of Ge to maximise the observable diffraction contrast. The complex structure factor profiles are then reconstructed from the simulated intensity distributions using phase-retrieval X-ray diffractometry (PRXRD) method.

Quantitative tomographic X-ray profiling of non-Bragg diffracting materials using phase retrieval X-ray diffractometry

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.

Application of phase-retrieval x-ray diffractometry to carbon doped SiGe(C)/Si(C) superlattice structures

An experimental-analytical technique for the model-independent nondestructive characterization of single crystal alloys is applied to SiGe(C)/Si(C) superlattice structures with different positions of substitutional carbon. The technique is based on the retrieval of the phase of the diffracted x-ray wave via a logarithmic dispersion relation, with subsequent determination of the complex crystal structure factor utilizing limited a priori knowledge of the superlattice structure. High-resolution, x-ray Bragg diffraction profiles were collected using a rotating anode source. The studies have allowed the reconstruction of the complex crystal structure factor as a function of crystal depth, permitting direct observation of strain relaxation in individual layers of the superlattice structure.

Unambiguous x-ray phase retrieval from Fraunhofer diffraction data

An unambiguous inverse solution from Fraunhofer diffraction data has been achieved for an amorphous sample of low-molecular weight. The complex scattering amplitude has been reconstructed with submicron spatial resolution using the phase retrieval x-ray diffractometry technique. The technique relies on a logarithmic dispersion relation to determine the x-ray wave phase from the scattered intensity profile. Successful experimental localization of the zeros of the complex scattering amplitude was achieved by utilizing two data sets taken at different incident x-ray energies, permitting a unique solution.

An application of phase retrieval x-ray diffractometry torefraction/small-angle scattering data

A recently developed experimental-analytical x-ray diffractionmethod for the direct, comprehensive, non-destructive characterization ofcrystalline materials is applied to analyse x-ray scattering data fromamorphous materials. High-resolution refraction/small-angle scatteringintensity profiles from a homogeneous, non-crystalline sample were collectedat the 1 km long beamline, SPring-8, Japan. A logarithmic dispersion relationis used to determine the x-ray phase. A priori knowledge of the samplestructure is utilised to reconstruct the physical characteristics of thesample with a resolution of 0.25 µm. These studies have demonstrated theviability of the technique as a new characterization method for amorphousmaterials.

Application of the Phase-Retrieval X-Ray Diffractometry to an Ultra-High Spatial Resolution Mapping of SiGe Films near the Absorption Edge of Ge

A recently developed new experimental analytical X-ray diffraction method for the direct non-destructive characterization of single-crystal alloys is applied to map the complex structure-factor of SiGe layers with an ultra-high spatial resolution of 5.8 Å. The technique is based on analytical measurements of X-ray phase and amplitude changes in a narrow polychromatic region of synchrotron radiation near the absorption edge of the alloy impurity. These atomic spatial resolution studies have allowed observation and preliminary analysis of surface and interface nanoscale sublayers, where the crystal structure-factor may noticeably differ from the bulk material.

Phase-Retrieval X-Ray Diffractometry in the Case of High- or Low-Flux Radiation Source

An experimental-analytical technique for X-ray phase retrieval in the case of high- or low-flux radiation source is considered. Experimentally measurable reflectivity magnitudes, using a rotating anode or conventional X-ray tube source, affect the directly reconstructed profile of the complex crystal structure factor. Thermal and point defect diffuse scattering contaminates the tails of the Bragg diffracted intensity. A numerical procedure developed for the regularization of the directly reconstructed complex structure factor allows one to eliminate parasitic fringes in the resulting crystal-lattice strain profiles. The stability of the phase-reconstruction technique to experimental intensity measured in a different range of reflectivity values is discussed.