Diffuse X-ray scattering from threading dislocations in epitaxial structures was simulated numerically by using a Monte Carlo method. This method permitted the simulation of diffraction curves for dislocation types, where macroscopic approaches failed. This included dislocation types for which analytical ensemble averaging was not feasible, as well as for micro-diffraction curves from small sample volumes. In the latter case, the degree of statistical fluctuation of the characteristic features was determined. The Monte Carlo method made it possible to correlate quantitatively the widths of the micro-diffraction curves with the densities of various dislocation types. The potential of the method was demonstrated by making a quantitative estimation of the density distribution of edge and screw threading dislocations in laterally overgrown epitaxial GaN structures, which was investigated by using a full-field micro-diffraction imaging technique. Measuring the asymptotic behaviour of the micro-diffraction curves permitted the determination of prevailing type of threading dislocation.

Diffuse X-Ray Scattering from Statistically Inhomogeneous Distributions of Threading Dislocations beyond the Ergodic Hypothesis. V.Holý, T.Baumbach, D.Lübbert, L.Helfen, M.Ellyan, P.Mikulík, S.Keller, S.P.DenBaars, J.Speck: Physical Review B, 2008, 77[9], 094102