Dynamical X‐ray diffraction theory: Characterization of defects and strains in as‐grown and ion‐implanted garnet structures

Abstract

The generalized dynamical theory of X-ray diffraction by imperfect single crystals is extended to characterize structure imperfections of real single crystals with complex basis and similar crystalline films with inhomogeneous strain fields. The influence of various defects (intrinsic and extrinsic point defects, nanoclusters, and microdefects), simultaneously presented in such structures, on changing both average and fluctuating strain fields as well as structure factors are taken into account. The analytical expressions connecting immediately the coherent and diffuse components of the scattering intensity with statistical characteristics of these defects are obtained. Thus, the self-consistent description of the coherent and diffuse dynamical diffraction intensity components is provided. Some examples of the application of the developed theoretical model to treat rocking curves measured from various garnet structures by using high-resolution double-crystal X-ray diffractometer are reviewed. Possibilities for the quantitative characterization of structural defects and strain profiles in the as-grown and ion-implanted garnet single crystals and yttrium iron garnet films are demonstrated.The self-consistent dynamical description of coherent and diffuse scattering intensities from imperfect crystal structures with inhomogeneous strain fields and randomly distributed defects make it possible to determine the parameters of strain profiles and statistical characteristics of defects by analytical treating the coherent and diffuse components of rocking curves measured by the high-resolution double-crystal X-ray diffractometer with widely open detector window.

Defect‐Pattern‐Induced Fingerprints in the Electron Density of States of Strained Graphene Layers: Diffraction and Simulation Methods

“…The dynamic diffraction methods used in the studies of complex multilayer crystalline systems showed that these methods allow to determine the profiles of inhomogeneous in‐depth distribution of defects, and thus distinguish the near‐surface layer with a low defect concentration from the deep layer with a high defect concentration. At the same time, the sensitivity of dynamical diffraction methods allows detection of defects with a density of down to ≈10 10 cm −2 , which corresponds to ≈0.0001% of defects in a graphene lattice.…”

“…Above‐mentioned concepts have been already applied to carry out a nondestructive diagnostic of the structural heterogeneities for multilayer single‐crystal heterosystems: epitaxial films of yttrium iron garnet on the substrate of gadolinium gallium garnet, which are widely used in nanoindustry. However, when structures are significantly thin, especially several layers in thick as a multilayer graphene or even single layer, the use of traditional diffraction patterns is not feasible.…”

X-­ray diagnostics of the structure of near­surface layers of ion­implanted monocrystalline materials

“…In ionic implantation, created point defects that can be combined in the dislocation loops are created. According to [16], the contribution of diffuse X-ray scattering by dislocation loops is much greater than diffuse scattering by point defects. In this case, the dominant contribution in diffuse X-ray scattering is from the dislocation loops.…”

“…To analyze the experimental rocking curves for defining parameters of defects in nonimplanted and implanted monocrystals and films, the simulation of diffraction of X-rays in nonperfect crystals was used. A statistical dynamic theory of X-ray scattering was used, which makes possible to take into account the presence of specific types of defects in the structure and does not impose restrictions on the size of the defects [16]. To do this, a special program has been developed in the C++ Builder, which allowed the modeling of theoretical rocking curves using the given defects parameters of the crystal.…”

Modeling of X-ray rocking curves for layers after two-stage ion-implantation

“…The kinematical [13][14][15][16][17][18] and generalized dynamical theory [21,22] of X-ray diffraction were used in combination with the dynamical approach in case of the Takagi-Topens approximation [11,12,19,20], for the ω/2Θ scans simulation for ion implanted layers. The kinematical and the dynamical approaches are used for thin implanted layers and high-quality bulk material, respectively.…”