J. Gronkowski

Propagation of X-rays in distorted crystals under dynamical diffraction

Abstract The basic equations of the dynamical theory of X-ray diffraction for distorted crystals (the Takagi-Taupin equations) are derived and reviewed in two most useful forms. Numerical methods of their solution for a general deformation and for the case of depth-depending strain gradients are discussed. Applications of simulation techniques for studies of physical effects accompanying propagation of X-ray beams in distorted crystals (curved trajectories, interbranch scattering, Fraunhofer diffraction, spherical-wave interferences, standing waves) are reviewed.

A study of defects generated in Czochralski-grown Si during two-step annealing

A variety of oxygen-related micro-defects (spherical and octahedral precipitates, their agglomerations, dislocations and dislocation loops) with dimensions in the range 0.1-100 mu m were revealed using X-ray topography and transmission electron microscopy after two-step annealing of Czochralski-grown silicon. The defects are distributed in a non-uniform way across the samples with the gradient of their density normal to the crystal surface.

X-ray diffuse scattering characterization of microdefects in highly Te-doped annealed GaAs crystals

Diffuse scattering of x-rays is applied to studies of microdefects in annealed highly doped crystals of GaAs:Te. X-ray diffraction reciprocal space mapping was performed by high-resolution x-ray diffractometry in the triple-axis mode. The most characteristic feature of the experimental maps is the lack of the zero-intensity lines for all high-symmetry reflections. Owing to this aspect of measured maps it was possible to determine the type of microdefects. The computer simulations performed for point defects with orthorhombic symmetry in annealed crystals of GaAs fit very well to the patterns of measured iso-intensity contours. The experimental data obtained so far give the possibility of determining the displacement field outside the defect core but are not sufficient to obtain information about the interior of the defect. The mean radius of microdefects was estimated to be smaller than 0.2 m.

X-ray Diffraction Study of Composition Inhomogeneities in Ga1-xInxN Thin Layers

Inhomogeneities due to alloy fluctuations in MOCVD grown Ga 1-x In x N thin films in the compositional range 0 < x ≤ 0.093, deposited on GaN sublayers grown on c sapphire plane, are investigated. InGaN films are analyzed by x-ray diffraction profiles and reciprocal space maps in the triple-axis mode. Films grown with the lower In content (x ≤ 0.085) reveal compositional inhomogeneity as a single extra peak in the diffraction rocking curve which can be attributed to local bilayer growth of the ternary. Films grown with the higher In content exhibit both a smearing of diffraction profiles (quasi-continuous compositional changes) and development of multiple peaks that corresponds to local-domain growth. Non-uniform epitaxial growth results in a composition distribution of the ternary, derived by x-ray measurements, which is compatible with the value of composition obtained from RBS characterization.

X-ray section topographs under various coherence properties of the primary beam

The aim of this work is to study to what extent a typical section-topography setup can supply information about the degree of coherence of the incident x-ray beam. In real experiments, the incident beam is partially coherent, with the degree of coherence described by the shape of the correlation function. In this paper the correlation functions for the outgoing beam are calculated by solving the Takagi-Taupin equations, assuming a truncated Gauss correlation function for the incident beam with the correlation length determined by the van Cittert-Zernike theorem. Its influence on the measured intensity of the diffracted beam in section topography is investigated.

Strain relaxation in Ga1−xInxN thin layers grown on GaN sublayers

Abstract The strain ratio ec/ea versus crystallographic orientation is measured for 25–80-nm thick MOCVD ternary layers of Ga1−xInxN deposited on 3-μm thick buffer layer of GaN grown on the c-plane of sapphire. High resolution X-ray maps and diffraction profiles were measured for all basic crystallographic directions. Atomic force microscopy (AFM) measurements and simulations of the measured X-ray diffraction peaks are included. An analysis of the positions of diffraction maximums in the maps shows that no relaxation can be observed. A striking feature is the anisotropy of the values of the ratio ec/ea measured for different crystallographic configurations.

X-ray topography studies of microdefects in silicon

X–ray topography has been successfully applied to study microdefects with the sizes in the range from well below standard topographic resolution to tenths of micrometers, thus effectively widening applicability of the Lang section topography. The lower value is set by the application of high order asymmetric reflection. Disappearance of the Kato fringes on the section topography is a clear indication of the existence of defects, which are otherwise not detectable as the standard contrast features. The presence of the defects with such sizes was also confirmed by transmission electron microscopy. Microdefects in the higher end of the size spectrum are well covered by Lang traverse and section topography where detailed contrast study is possible for individual defects. Lang traverse and section topography was applied to study specific case of oxygen related defects in silicon crystals.

HIGH-RESOLUTION CHARACTERIZATION OF MICRODEFECTS BY X-RAY DIFFUSE SCATTERING

Highly tellurium–doped GaAs samples were investigated by high–resolution X–ray diffractometry in the triple–axis mode. Different reciprocal maps, depending on the technological process, are presented and interpreted as caused by different microdefects. Computer simulations allow us to determine the type of microdefects, namely the orthorhombic defects and dislocations loops. A theoretical approach for defects composed of several atoms is proposed. Alternative descriptions of pairs of defects as uniform distributions of such paired defects or non–uniform distributions of single–defect components are presented.

X-ray topographic study of defects in annealed silicon

X-ray topography was applied to characterize defects in silicon subjected to thermal treatments. In one group of Czochralski-grown (CZ) samples numerous precipitates and dislocation loops were generated by making scratches with metallic contaminants (Ni, Fe, Cu) on one surface. Rapid thermal annealing (RTA) was performed at 1150 degrees C for 300 s in an oxidation atmosphere. Far away from the damaged regions no structural defects were detected in any of the samples. In other CZ samples small precipitates of nonuniform density were produced after two-step annealing (TSA) at 900 degrees C (for 75 min) and 1150 degrees C (for 8 h) in an oxygen atmosphere.

X-ray diffraction pictures for Fourier-transformed narrow incident beams

Influence of the Fourier transform of the incident beam on the measured diffracted intensity in X-ray diffraction is analysed. The theory presented is a more rigorous physical picture of X-ray diffraction in the case of a narrow incident beam than the usually assumed spherical-wave theory. The shape of diffracted beam amplitude depends on the FT of the incident beam which is fully determined by experimental conditions. The proposed methods may be used for direct calculations of the correlation function for electromagnetic fields and studies of the coherence degree of X-ray radiation.