Yefanov O. Dynamical X-Ray Diffraction in Multilayered Structure

The thesis is devoted to investigation of X-ray diffraction in multilayered structures. A new approach for calculation of N-beam dynamical diffraction in planar multilayers is developed and its applications for experimental data analysis are shown. The main features of proposed model are: plane waves are considered; propagation equation, derived from Maxwell equations, and boundary conditions are solved without simplifications; suitable for any geometry (Bragg, Laue, Bragg-Laue); 3D simulation in reciprocal and 1D in real space; covers the whole angular range, including grazing angles, backscattering and specular reflection; precise calculation of any polarization with information about diffracted and reflected beams polarization; no principal limitation on quantity of reciprocal lattice points taken part in diffraction; arbitrary layers thickness (valid for both thick and thin layers); all calculation are carried out for x,y,z projections of wave vectors, diffraction vectors and electric field. The examples of developed approach application, such as diffraction curves (DC), reflection curves, Renninger scan and reciprocal space maps are shown. One more method for N-beam diffraction in multilayers calculation is presented. This method is less common and is suitable only for coplanar case and only sigma polarization, but it is faster then 3D algorithm described above. Dispersion equation for 2, 3, 4 and N-beam diffraction are numerically solved and dispersion surfaces for these cases are drawn. For two-beam case the simplified (quadratic) and exact (quartic) equations are solved analytically. Absorption is taken into account and different geometries as well. For many-beam cases (more than two) the way for avoiding numerical problems is shown. These problems arise if the wave vectors are expressed in Cartethian coordinates with the origin in (000) point. This is explained by the fact that there could be many origins of wave vectors near the same Lorentz point, so the precision of computer calculations is not enough to distinguish the difference between solutions (its order is about $10^{-5}$) while the value of these roots is about $1$. That's why the origin of coordinate system must be placed in Lorentz point. The influence of composition gradient on boundaries between GaAs and InGaAs layers in 8-period superlattice is analyzed. Four type of gradient functions were considered: sharp, linear, quadratic and quadratic-hyperbolic. With the last function the best coincidence between simulated and experimental DC near substrate peak was achieved. But for good intensity correlation on the far tails of DC different parameters of composition gradient must be set for each boundary in superlattice. For this reason autofit procedure was used and this gave better results. Anisotropic deformations investigation was done with the help of measuring azimuthaly dependent diffraction curves. It allows to explain satellite peaks period dependence on azimuthal angle and shift of the zero satellite. The first fact is well known tobe explained by the structure diffraction vector misorientation to the surface normal, while the latter is more interesting and is explained by local InGaAs layers misorientation. A new method of structure analysis via calculation of two-dimensional maps of azimuthal dependent intensity distribution is presented (one axis is usual $