V. I. Punegov

Analysis of the mosaic structure of an ordered (Al,Ga)N layer

The mosaic structure of an (Al,Ga)N layer grown on (0001) sapphire showing natural ordering was studied by high-resolution X-ray diffraction (HRXRD) reciprocal-space mapping. The direction-dependent mosaicity of the layer has been elaborated using maps of symmetrical and asymmetrical reflections. The reciprocal-lattice points show significant broadening depending on the direction in reciprocal space, the diffraction order and the reflection type (fundamental or superstructural). The evaluation followed two paths: (i) a procedure based on the Williamson–Hall plot and (ii) a new approach based on the statistical diffraction theory (SDT). Here, the transformed Takagi equations were implemented for the simulation of the reciprocal-space maps (RSM) for symmetrical and asymmetrical reflections. The reconstruction comprised the mosaic block size, their average rotation angle and the spatial distribution of some components of the microdistortion tensor. The results based on the SDT modelling agree well with those obtained by the Williamson–Hall method, while providing a higher degree of precision and detail.

The statistical kinematical theory of X-ray ­diffraction as applied to reciprocal-space mapping

The statistical kinematical X-ray diffraction theory is developed to describe reciprocal-space maps (RSMs) from deformed crystals with defects of the structure. The general solutions for coherent and diffuse components of the scattered intensity in reciprocal space are derived. As an example, the explicit expressions for intensity distributions in the case of spherical defects and of a mosaic crystal were obtained. The theory takes into account the instrumental function of the triple-crystal diffractometer and can therefore be used for experimental data analysis.

Statistical dynamical theory of X-ray diffraction in the Bragg case: application to triple-crystal diffractometry

The statistical dynamical theory of X-ray diffraction is developed for a crystal containing statistically distributed microdefects. Fourier-component equations for coherent and diffuse (incoherent) scattered waves have been obtained in the case of so-called triple-crystal diffractometry. New correlation lengths and areas are introduced for characterization of the scattered volume.

Coherent and diffuse X-ray scattering in crystals modulated by a surface acoustic wave

Equations describing the coherent and diffuse scattering in a crystal modulated by a surface acoustic wave (SAW) are derived using the dynamical X-ray diffraction theory. The effect of depth attenuation of the Rayleigh surface wave amplitude on the crystal rocking curve profiles is investigated. Results of the numerical simulation of the dynamical diffraction in a mosaic crystal modulated by a SAW, taking into account a block size distribution, are presented. It is shown that the diffuse scattering is distributed in the reciprocal space not only in the vicinity of the main diffraction peak but also about the satellite diffraction peaks, and this distribution depends on the size fluctuations of the crystal defects. Theoretical reciprocal space maps and rocking curves are compared with the corresponding experimental results.

The equations of the statistical dynamical theory of X-ray diffraction for deformed crystals

Using the statistical approach to dynamical X-ray diffraction, the equations for coherent and diffuse scattered waves in a general case of a deformed crystal are obtained.

X-Ray diffraction analysis of multilayer InAs-GaAs heterostructures with InAs quantum dots

Multilayer InAs-GaAs structures with an array of vertically aligned InAs quantum dots in a GaAs matrix, grown by molecular-beam epitaxy, were investigated by crystal truncation rods and high-resolution x-ray diffractometry methods. It was shown that the formation of scattering objects such as vertically aligned quantum dots in the structures strongly influences the mechanism of diffraction scattering of x-rays and changes the spatial distribution of the diffracted radiation. This is explained by the appearance of additional long-range order in the lateral arrangement of the scattering objects in the periodic structures, by the curving of the crystallographic planes in the periodic part of the structure, and by the quasiperiodicity of the deformation profile due to the vertically coupled quantum dots. The observed spatial distribution of the diffracted intensity can be explained qualitatively on the basis of a new model where the scattering layers with quantum dots consist of defect-free, coherently coupled, InAs and GaAs clusters.

High-Resolution Synchrotron Diffraction Study of Porous Buffer InP(001) Layers

X-ray reciprocal space mapping was used for quantitative investigation of porous layers in indium phosphide. A new theoretical model in the frame of the statistical dynamical theory for cylindrical pores was developed and applied for numerical data evaluation. The analysis of reciprocal space maps provided comprehensive information on a wide range of the porous layer parameters, for example, layer thickness and porosity, orientation, and correlation length of segmented pore structures. The results are in a good agreement with scanning electron microscopy data.

Paracrystalline model in statistical theory of X-ray diffraction on epilayers with quantum dots

A statistical theory of kinematical X-ray diffraction on nanostructured crystalline systems with quantum dots (QDs) has been developed with allowance for a spatial correlation of QDs. The lateral distribution of QDs in an epilayer is described using a two-dimensional paracrystalline model. The angular distribution of diffuse X-ray scattering intensity was numerically simulated and analyzed depending on the degree of lateral ordering of QDs.

Theory of X-ray diffraction in nanoporous crystals with lateral quasi-periodicity

A theory of X-ray scattering from nanoporous crystals in the presence of a short-range structural order of the scattering elements (crystallites) has been developed within the framework of a statistical approach. It is shown that the angular distribution of the scattering intensity is determined by the coherence of the lateral quasi-periodicity of the porous material. Structural characteristics of a porous indium phosphide are determined using by fitting the results of theoretical calculations to the available experimental data.

Diffuse X-Ray scattering from crystalline systems with ellipsoidal quantum dots

A theory of diffuse X-ray scattering from a semiconductor system with ellipsoidal quantum dots (QDs) has been developed. The elastic strains outside a QD are calculated using the method of multipole expansions. An expression for the lattice displacement field is presented accurate to within the quadrupole term of expansion. Using the proposed approach, an analytical solution for the diffuse scattering from a crystalline medium with ellipsoidal inclusions is obtained. Reciprocal-space maps of the scattering intensity distribution are obtained by numerical calculations for QDs with various ratios of the height to lateral radius.