J. Borowski

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.

High resolution X-ray diffraction defect structure characterization in Si-doped and undoped GaN films

Abstract The effect of Si doping ( N Si ∼3×10 18 cm −3 ) on crystalline quality of GaN epitaxial layers grown on sapphire c face was studied by high resolution X-ray diffraction including several Bragg reflections in different scan directions, reciprocal space maps, radial scans, and measurements of radii of curvature. Elastic and hydrostatic strain components were derived taking into account strains introduced in the sapphire substrate by the highly mismatched GaN layer. Si-doped and undoped GaN layers were grown by atmospheric pressure MOCVD technique using the same growth conditions. All the layers were under compression but with slightly higher stress in the undoped layer, while the hydrostatic strain component remained unchanged. It was found that doping of GaN by Si decreased edge dislocation density and increased screw dislocation density. It could be concluded that edge-type threading dislocation arrangement, piled up in small-angle columnar grain boundaries, dominated in both samples.

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.

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 diffuse scattering simulations in the Huang region for Si crystals with microdefects of orthorhombic symmetry

Abstract A numerical program written in the Mathemathica 2.1.1 package to simulate the symmetrical part of X-ray diffuse scattering is presented. This program can be used to determine the type of any point defect in any crystal by comparing X-ray triple crystal measurements with simulations. Simulations for point defects with the orthorhombic symmetry in a Si crystal, calculated for the first time to the authors knowledge, are presented.

Numerical calculations of the Bessel functions for complex argument and application to X-ray diffraction

A numerical procedure for calculating the Bessel functions for complex argument is proposed. An asymptotic expansion is used to calculate the Bessel function for large modulus of the argument. Application to X-ray diffraction is presented.

Orthorhombic microdefects in Si crystals

In the present paper the orthorhombic microdefects detected in a Si single-crystal sample are analysed on the basis of theoretical simulations exactly matching the experimental x-ray diffuse scattering map. The mean radius of microdefects is estimated to be smaller than 0.1 µm.

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.

X-ray diffuse scattering from extended microdefects of orthorhombic symmetry for Si single crystals

The displacement field of a crystal lattice, in the continuous media approximation, caused by extended microdefects of rectangular parallelepiped shape, is considered. X-ray diffuse scattering from the defect core as well as the long-range displacement field is analyzed. A theoretical expression for the intensity of X-ray diffuse scattering resulting from randomly distributed microdefects of orthorhombic symmetry is presented using the kinematical approximation of X-ray statistical diffraction theory. The computer simulations of the isointensity contours for two sets of defect parameters are performed. A way of obtaining the defect parameters by fitting the computer simulations to the experimental data is proposed.