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

Ostwald ripening of faceted two-dimensional islands

We study Ostwald ripening of two-dimensional adatom and advacancy islands on a crystal surface by means of kinetic Monte Carlo simulations. At large bond energies the islands are square-shaped, which qualitatively changes the coarsening kinetics. The Gibbs--Thomson chemical potential is violated: the coarsening proceeds through a sequence of `magic' sizes corresponding to square or rectangular islands. The coarsening becomes attachment-limited, but Wagner's asymptotic law is reached only after a very long transient time. The unusual coarsening kinetics obtained in the Monte Carlo simulations are well described by the Becker--Döring equations of nucleation kinetics. These equations can be applied to a wide range of coarsening problems

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

Bunches of misfit dislocations on the onset of relaxation of Si0.4_{0.4}Ge0.6_{0.6}/Si(001) epitaxial films revealed by high-resolution x-ray diffraction

The experimental x-ray diffraction patterns of a Si$_{0.4}$Ge$_{0.6}$/Si(001) epitaxial film with a low density of misfit dislocations are modeled by the Monte Carlo method. It is shown that an inhomogeneous distribution of 60$^\circ$ dislocations with dislocations arranged in bunches is needed to explain the experiment correctly. As a result of the dislocation bunching, the positions of the x-ray diffraction peaks do not correspond to the average dislocation density but reveal less than a half of the actual relaxation

Dynamic coalescence kinetics of facetted 2D islands

We study the coalescence of 2D islands on a crystal surface by atomic-scale kinetic Monte Carlo simulations on an ensemble of meandering islands. The Brownian motion of islands is due to the motion of atoms within the islands, with the escape of atoms from islands prohibited by the presence of a step edge barrier. We find that the diffusion of individual islands and their size distribution qualitatively change for large bond energies or low temperatures, when the islands develop straight edges (facets). The island diffusion coefficient becomes size-independent and the size distribution becomes monotonously decreasing. The results of the kinetic Monte Carlo simulations are supported by numerical solutions of the Smoluchowski equations. We derive the kernel of the Smoluchowski equations for the 2D case taking into account the screening effects and find that the screening essentially alters the island size distribution