X-ray diffraction from dislocation half-loops in epitaxial films

X-ray diffraction from dislocation half-loops consisting of a misfit segment and two threading arms extending from it to the surface is calculated by the Monte Carlo method. The diffraction profiles and reciprocal space maps are controlled by the ratio of the total lengths of the misfit and the threading segments of the half-loops. A continuous transformation from the diffraction characteristic of misfit dislocations to that of threading dislocations with increasing thickness of an epitaxial film is studied. Diffraction from dislocations with edge and screw threading arms is considered and the contributions of both types of dislocations are compared

Small-angle X-ray scattering from GaN nanowires on Si(111): facet truncation rods, facet roughness and Porod's law

Small-angle X-ray scattering from GaN nanowires grown on Si(111) is measured in the grazing-incidence geometry and modelled by means of a Monte Carlo simulation that takes into account the orientational distribution of the faceted nanowires and the roughness of their side facets. It is found that the scattering intensity at large wavevectors does not follow Porod's law I(q) ∝ q-4. The intensity depends on the orientation of the side facets with respect to the incident X-ray beam. It is maximum when the scattering vector is directed along a facet normal, reminiscent of surface truncation rod scattering. At large wavevectors q, the scattering intensity is reduced by surface roughness. A root-mean-square roughness of 0.9 nm, which is the height of just 3-4 atomic steps per micrometre-long facet, already gives rise to a strong intensity reduction. open access

Crystal truncation rods in kinematical and dynamical x-ray diffraction theories

Crystal truncation rods calculated in the kinematical approximation are shown to quantitatively agree with the sum of the diffracted waves obtained in the two-beam dynamical calculations for different reflections along the rod. The choice and the number of these reflections are specified. The agreement extends down to at least $\sim 10^{-7}$ of the peak intensity. For lower intensities, the accuracy of dynamical calculations is limited by truncation of the electron density at a mathematically planar surface, arising from the Fourier series expansion of the crystal polarizability

Small-angle X-ray scattering from GaN nanowires on Si(111): facet truncation rods, facet roughness and Porod's law

Small-angle X-ray scattering from GaN nanowires grown on Si(111) is measured in the grazing-incidence geometry and modelled by means of a Monte Carlo simulation that takes into account the orientational distribution of the faceted nanowires and the roughness of their side facets. It is found that the scattering intensity at large wavevectors does not follow Porod's law I(q) ∝ q-4. The intensity depends on the orientation of the side facets with respect to the incident X-ray beam. It is maximum when the scattering vector is directed along a facet normal, reminiscent of surface truncation rod scattering. At large wavevectors q, the scattering intensity is reduced by surface roughness. A root-mean-square roughness of 0.9 nm, which is the height of just 3-4 atomic steps per micrometre-long facet, already gives rise to a strong intensity reduction. open acces

X-ray scattering study of GaN nanowires grown on Ti/Al2_{2}O3_{3} by molecular beam epitaxy

GaN nanowires (NWs) grown by molecular beam epitaxy on Ti films sputtered on Al$_{2}$O$_{3}$ are studied by X-ray diffraction (XRD) and grazing incidence small-angle X-ray scattering (GISAXS). XRD, performed both in symmetric Bragg reflection and at grazing incidence, reveals Ti, Ti$_{3}$O, Ti$_{3}$Al, and TiO$_x$N$_y$ crystallites with in-plane and out-of-plane lattice parameters intermediate between those of Al$_{2}$O$_{3}$ and GaN. These topotaxial crystallites in Ti film, formed due to interfacial reactions and N exposure, possess fairly little misorientation with respect to Al$_{2}$O$_{3}$. As a result, GaN NWs grow on the top TiN layer possessing a high degree of epitaxial orientation with respect to the substrate. The measured GISAXS intensity distributions are modeled by the Monte Carlo method taking into account the orientational distributions of NWs, a variety of their cross-sectional shapes and sizes, and roughness of their side facets. The cross-sectional size distributions of the NWs and the relative fractions of $(1\bar{1}00)$ and $(11\bar{2}0)$ side facets are determined

Thermal roughening of an SOS-model with elastic interaction

We analyze the effects of a long-ranged step-step interaction on thermal roughening within the framework of a solid-on-solid model of a crystal surface by means of Monte Carlo simulation. A repulsive step-step interaction is modeled by elastic dipoles located on sites adjacent to the steps. In order to reduce the computational effort involved in calculating interaction energy based on long-ranged potentials, we employ a multi-grid scheme. As a result of the long-range character of the step interaction, the roughening temperature increases drastically compared to a system with short-range cutoff as a consequence of anti-correlations between surface defects