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X-ray diffraction is one of the most popular experimental methods employed for determination of dislocation densities, as it can recognize both the strain fields and the local lattice rotations produced by dislocations. The main challenge of the quantitative analysis of the dislocation density is the formulation of a suitable microstructure model, which describes the dislocation arrangement and the effect of the interactions between the strain fields from neighboring dislocations reliably in order to be able to determine the dislocation densities precisely. The aim of this study is to prove the capability of X-ray diffraction and two computational methods, which are frequently used for quantification of the threading dislocation densities from X-ray diffraction measurements, in the special case of partially bunched threading dislocations. The first method is based on the analysis of the dislocation-controlled crystal mosaicity, and the other one on the analysis of diffuse X-ray scattering from threading dislocations. The complementarity of both methods is discussed. Furthermore, it is shown how the complementarity of these methods can be used to improve the results of the quantitative analysis of bunched and thus inhomogeneously distributed threading dislocations and to get a better insight into the dislocation arrangement. [ABSTRACT FROM AUTHOR]

The intensity of x-ray diffraction from a polycrystalline multilayer in a grazing-incidence scattering geometry is modulated by a standing wave created by the interference of the radiation transmitted through the multilayer stack with the wave field specularly reflected from the superlattice interfaces. Similarly, the radiation being diffracted from the polycrystalline structure is reflected specularly from the interfaces and a standing-wave interference pattern results as well. This effect is demonstrated by a series of diffraction measurements on C/Ni periodic multilayers; the experimental data have been modeled using the distorted-wave Born approximation and a very good correspondence with the experiments was achieved. The method was used for the study of the profiles of the crystallite sizes and strains in multilayers. [ABSTRACT FROM AUTHOR]

A simple approach for the analysis of mosaic epitaxial layers is proposed, based on a Patterson-like analysis of the reciprocal-space distribution of the scattered intensity. Within this approach, the mosaic-block-shape function P and the deformation correlation function are determined. The method is used for the analysis of relaxed PbTe epitaxial layers on Si(111). The sizes of the mosaic blocks determined by this method are compared with the results of conventional Williamson-Hall-type analyses of the width of the diffraction maxima. The block sizes compare well with the mean distances of threading dislocations penetrating the PbTe layers. [ABSTRACT FROM AUTHOR]

Coplanar high-resolution x-ray diffraction has been used for the characterization of size, chemical composition, and strain of Ge/Si (001) islands in a three-dimensional island crystal grown using self-assembly on a prepatterned (001) Si substrate. The measured diffusely scattered intensity is simulated using the kinematical approximation and the parameters of model islands are fitted. These simulations require calculations of the strain fields within the islands and the spacer layers. For this purpose, an analytical approach to solve the continuum elasticity equations has been extended to a full three-dimensional calculation. The Ge content in the islands is found to be on the average 40%, and the island shape does not change dramatically during capping. [ABSTRACT FROM AUTHOR]

Lateral composition modulation in InAs/AlAs short-period superlattices was investigated by x-ray grazing-incidence diffraction and coplanar x-ray diffraction at a “normal” wavelength and at an anomalous wavelength, for which diffraction from the (200) planes does not exhibit a chemical contrast. The experimental data were compared with theoretical simulations assuming that the interfaces consist of a periodic sequence of monoatomic steps. The displacement field in the superlattice was calculated by continuum elasticity and using a valence-force field method. From the fit of the experimental data to the theory, the lengths of individual atomic terraces were determined. [ABSTRACT FROM AUTHOR]

Presents a study that described x-ray diffraction in thin layers containing small randomly placed defects by means of the kinematical diffraction theory and optical coherence formalism. Calculation of both the diffracted intensity and angular distribution; simulation of double crystal and triple crystal x-ray diffractometry experiments; Application of the theory to experimental data obtained from diffractometry measurements of an epitaxial zinc-tellurium layer with mosaic structure.

X-ray nanodiffraction was used for the investigation of basal stacking faults in a-GaN microcrystallites. The method made it possible to find the positions of individual stacking faults in a chosen crystallite, and the resulting positions were compared with the observation of individual faults by electron channeling contrast in scanning electron microscopy. The x-ray diffraction data revealed that the faults occur in closely positioned pairs; the stacking faults in a pair have opposite displacement vectors. [ABSTRACT FROM AUTHOR]

Abstract: For the first time self-organized epitaxially grown semiconductor islands were investigated by a full three-dimensional mapping of the scattered X-ray intensity in reciprocal space. Intensity distributions were measured in a coplanar diffraction geometry around symmetric and asymmetric Bragg reflections. The 3D intensity maps were compared with theoretical simulations based on continuum-elasticity simulations of internal strains in the islands and on kinematical scattering theory whereby local chemical composition and strain profiles of the islands were retrieved. [Copyright &y& Elsevier]

The use of a combination of X-ray scattering techniques for the complete characterization of ultra-low-energy ( E < 5 keV) implanted Si is discussed. Grazing incidence diffuse X-ray scattering (GI-DXS) reveals the properties of the defects confined within thin crystalline layers with depth resolution. Due to the weak diffuse intensity arising from such defects, the high brilliance of synchrotron radiation is required. GI-DXS proved to be particularly well suited for the investigation of the so-called `end-of-range' defects. In a complementary way, X-ray diffraction (XRD) in the vicinity of the 004 Bragg reflection is sensitive to the distribution of the strain in the Si lattice in the direction perpendicular to the sample surface. The structural characterization is complemented by the electron density profile of the near-surface amorphous region provided by specular reflectivity (SR). It will be shown that only by merging the results obtained with GI-DXS, XRD and SR, is it possible to obtain the detailed structural characterization of the implanted Si samples. [ABSTRACT FROM AUTHOR]

Abstract: Anomalous X-ray scattering from self-assembled PbSe quantum dots embedded in Pb1−x Eu x Te was used for the study of their structure. The measured reciprocal-space distributions of diffracted intensity were compared with simulations based on kinematical scattering theory and continuum elasticity. From the comparison, the mean chemical composition of the dots and their aspect ratio (height/width) were estimated. [Copyright &y& Elsevier]

Atomic force microscopy and grazing incidence x-ray diffraction measurements have revealed the presence of ripples, aligned along the [formula] direction on the surface of (Ga,Mn)As layers grown on GaAs(001) substrates and buffer layers, with periodicity of about 50 nm in all samples that have been studied. These samples show the strong symmetry breaking uniaxial magnetic anisotropy normally observed in such materials. We observe a clear correlation between the amplitude of the surface ripples and the strength of the uniaxial magnetic anisotropy component suggesting that these ripples might be the source of such anisotropy. [ABSTRACT FROM AUTHOR]

We used high-resolution x-ray reciprocal space mapping in noncoplanar grazing-incidence geometry for the determination of the density of edge threading dislocations in c-oriented GaN epitaxial layers and we compared the measured intensity distributions with results of numerical Monte Carlo simulations of diffuse scattering. We demonstrated that a combination of diffraction data taken in coplanar symmetric and noncoplanar grazing-incidence geometries makes it possible to obtain the densities of screw and edge threading dislocations. [ABSTRACT FROM AUTHOR]

Densities of Mn ions in epitaxial layers of (Ga,Mn)As were determined by anomalous x-ray diffraction, i.e., by a measurement of the dependence of the intensity of weak diffraction 002 on the photon energy around the Mn K absorption edge. From the measured data it was possible to determine the density of Mn ions in substitutional positions and the difference in the Mn densities in two possible interstitial positions in the GaAs lattice. The data demonstrate that the rate of the out-diffusion of the Mn interstitials from the Ga tetrahedrons significantly exceeds that from the As tetrahedrons. [ABSTRACT FROM AUTHOR]

The intensity of x-ray diffraction from a polycrystalline multilayer in a grazing-incidence scattering geometry is modulated by a standing wave created by the interference of the radiation transmitted through the multilayer stack with the wave field specularly reflected from the superlattice interfaces. This effect is used for the structure investigation of Nb/Si periodic multilayers. The experimental data have been modeled using the distorted-wave Born approximation and a good correspondence with the experiments was achieved, and it was possible to determine the thicknesses of crystalline and amorphous parts of the Nb layers as well as the mean size of the crystallites. [ABSTRACT FROM AUTHOR]

Anomalous x-ray diffraction is used to investigate self-organized ordering of PbSe/PbEuTe quantum dot superlattices in which different ordered structures form for different PbSe dot layer spacings. Using a theoretical dot ordering model, the different ordering parameters are determined from the x-ray spectra. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The lateral composition modulation in (InAs)[sub n]/(AlAs)[sub m] short-period superlattices was studied by means of synchrotron x-ray diffraction. By choosing specific diffraction vectors having a large component closely parallel to the modulation direction, we are able to observe a number of lateral satellite peaks around the zero-order short-period superlattice peak. A model, incorporating both composition and strain, is used to simulate the intensities of these satellites. Our results provide a quantitative fit and permit the evaluation of the composition amplitude. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present tensile and compressive strains realized within the same Si capping layer on an array of SiGe islands grown on pit-patterned (001) Si substrates. The strain distributions are obtained from synchrotron X-ray diffraction studies in combination with three-dimensional finite element calculations and simulations of the diffracted intensities. For barn-shaped islands grown at 720 °C with average Ge contents of 30%, the Si cap layer is misfit- and threading-dislocation free and exhibits compressive strains as high as 0.8% in positions between the islands and tensile strains of up to 1% on top of the islands. [ABSTRACT FROM AUTHOR]

We present investigations on the strain properties of silicon capping layers on top of regular SiGe island arrays, in dependence on the Si-layer thickness. Such island arrays are used as stressors for the active channel in field-effect transistors where the desired tensile strain in the Si channel is a crucial parameter for the performance of the device. The thickness of the Si cap was varied from 0 to 30 nm. The results of high resolution x-ray diffraction experiments served as input to perform detailed strain calculations via finite element method models. Thus, detailed information on the Ge distribution within the buried islands and the strain interaction between the SiGe island and Si cap was obtained. It was found that the tensile strain within the Si capping layer strongly depends on its thickness, even if the Ge concentration of the buried dot remains unchanged, with tensile strains degrading if thicker Si layers are used. [ABSTRACT FROM AUTHOR]

The rearrangement of SiGe islands during the deposition of Si was studied by a combination of scanning tunneling microscopy, transmission electron microscopy and high-resolution X-ray diffraction. With increasing silicon capping of the islands, an increasing flattening accompanied by a rising intermixing could be determined. Using a finite element calculation, which served as an input for X-ray simulations, the strain distribution within the islands was obtained. [Copyright &y& Elsevier]

The elastic strain relaxation in a series of dry-etched periodic multilayer Si/SiGe wire samples with different etching depths was investigated systematically by means of grazing incidence diffraction (GID). The samples were patterned by holographic lithography and reactive ion etching from a Si/SiGe superlattice grown by molecular beam epitaxy. Scanning electron microscopy and atomic force microscopy were employed to obtain information on the shape of the wires. The inhomogeneous strain distribution in the etched wires and in the non-etched part of the multilayers was derived by means of finite element calculations which were used as an input for simulations of the scattered X-ray intensities in depth dependent GID. The theoretical calculations for the scattered intensities are based on distorted-wave Born approximation. The unperturbed scattering potential was chosen with a reduced optical density corresponding to the ratio of wire width and wire period, in order to reflect the main interaction between the incident X-rays and the patterned samples. The calculations are in good agreement with the experimental data demonstrating the variation of strain relaxation with depth. [Copyright &y& Elsevier]

A thorough investigation is presented of the magnetic and structural properties of Mn-doped Bi 2 Se 3 topological insulators grown by molecular beam epitaxy on top of insulating BaF 2 (111) substrates. The magnetic properties have been studied in the temperature range from 2 K to 300 K in magnetic fields up to 7 T. The systems were further characterized by means of high-resolution X-ray diffraction, electron-microprobe analysis, and X-ray photoemission spectroscopy. Samples with the atomic concentration of Mn up to about 0.06 exhibit an almost perfect crystalline structure while, for higher Mn concentrations, diffuse scattering from defects is observed. Photoemission results suggest a localized non-metallic Mn 3d 5 ground state which is weakly or intermediately coupled to the Bi 2 Se 3 environment. The exchange interaction between the Mn moments leads to a ferromagnetic phase at low temperatures with a roughly linear relation between the Curie temperature and the atomic concentration of Mn. [ABSTRACT FROM AUTHOR]

We report on the structure and arrangement of particles created in the Fe2O3/TiO2+SiO2 multilayers. X-ray diffraction and extended X-ray absorption fine structure spectroscopy reveal the presence of crystalline rutile-TiO2 while the iron oxide remains either amorphous or forms very small clusters of Fe2O3. The Fe3+ oxidation state of iron atoms has been confirmed by Mössbauer and X-ray spectroscopy. The degree of the particle ordering has been studied by grazing-incidence small-angle X-ray scattering. It was demonstrated that with increasing temperature partially ordered nanoparticles are created and grow up to a critical temperature when the ordering is destroyed. Both particle sizes and inter-particle distances depend strongly on the thickness of the Ti/Fe containing layer. [ABSTRACT FROM AUTHOR]

Highlights: [•] Composition and strain of two InGaN phases formed by spinodal decomposition. [•] The phases could be attributed to morphological features. [•] The well-ordered GaN cap seems to be most promising for applications. [•] The In-rich phase is expected to reduce the device performance. [Copyright &y& Elsevier]

Abstract: We investigated the size and crystal structure of nanometer-sized ω inclusions in single crystals of β-Ti alloys by X-ray diffraction pole-figure measurements and reciprocal space mapping. We studied the topotactical relation of the β and ω crystal lattices, and from the positions and shapes of the diffraction maxima of the ω lattice determined the mean size of the ω inclusions and the misfit of the inclusion lattice with respect to the host lattice, as well as their changes during ageing. The lattice of the ω inclusions exhibits a large positive misfit already before ageing and the misfit is subsequently reduced during the ageing process. Using the theories of elasticity and X-ray scattering we simulated diffuse X-ray scattering around the β diffraction maxima and demonstrated that the diffuse scattering is caused mainly by local elastic strains in the β host phase around the ω inclusions. [Copyright &y& Elsevier]

Coherent x-ray diffractive imaging is extended to high resolution strain analysis in crystalline nanostructured devices. The method now enables reconstruction of elastic strain distribution in layered nanowires or dots. The application potential is demonstrated by determining the strain distribution in (Ga,Mn)As/GaAs nanowires. By separating diffraction signals in reciprocal spaces, individual parts of the device could be reconstructed independently by our inversion procedure. We demonstrate the method to be effective for material specific reconstruction of strain distribution in highly integrated devices. [ABSTRACT FROM AUTHOR]

We present an experimental and theoretical study of magnetocrystalline anisotropies in arrays of bars patterned lithographically into (Ga,Mn)As epilayers grown under compressive lattice strain. Structural properties of the (Ga,Mn)As microbars are investigated by high-resolution x-ray diffraction measurements. The experimental data, showing strong strain relaxation effects, are in good agreement with finite element simulations. Magnetization measurements are performed using a superconducting quantum interference device to study the control of magnetic anisotropy in (Ga,Mn)As by the lithographically induced strain relaxation of the microbars. Microscopic theoretical modeling of the anisotropy is performed based on the mean-field kinetic-exchange model of the ferromagnetic spin-orbit coupled band structure of (Ga,Mn)As. Based on the overall agreement between experimental data and theoretical modeling, we conclude that the micropatterning induced anisotropies are of magnetocrystalline, spin-orbit coupling origin. [ABSTRACT FROM AUTHOR]

The paper reports on implantation damage accumulation, Ag distribution and the interior morphology in different crystallographic orientations of implanted samples of cubic yttria-stabilised zirconia (YSZ). (100)-, (110)- and (111)-oriented YSZ was implanted with 400-keV Ag+ ions at ion fluences from 5 × 1014 to 5 × 1016 cm−2. Rutherford backscattering spectrometry (RBS) in the channelling mode (RBS-C), as well as X-ray diffraction (XRD), were used for the quantitative measurement of the lattice disorder and Ag distribution. The defect propagation and Ag accumulation were observed using transmission electron microscopy (TEM) with the energy-dispersive X-ray spectroscopy (EDX). Although similar damage evolution trends were observed along with all channelling directions, the disorder accumulation is lower along the <110> direction than along the <100> and <111> direction. The damage extends much deeper than the theoretically predicted depths. It is attributed to long-range defect migration effects, confirmed by TEM. At the ion fluence of 5 × 1016 cm−2, nanometre-sized Ag precipitates were identified in the depth of 30–130 nm based on the Ag concentration–depth profiles determined by RBS. • Ion-beam channelling in YSZ using RBS-C. • 2D channeling patterns of the normalised angular backscattering yields around the three main directions in YSZ. • The normalised yield observed around the three main directions in the Zr-sublattice. • The progressive shift of the damage layer in the case of higher fluences. • The formation of the Ag NPs is independent on the crystallographic orientations. [ABSTRACT FROM AUTHOR]