Diffuse x-ray scattering from statistically inhomogeneous distributions of threading dislocations beyond the ergodic hypothesis

Diffuse x-ray scattering from threading dislocations in epitaxial structures is simulated numerically by a Monte Carlo method. The method allows one to simulate diffraction curves for dislocation types, where macroscopic approaches fail. That includes dislocation types for which analytical ensemble averaging is not feasible as well as microdiffraction curves from small sample volumes. In the latter case, the degree of statistic fluctuation of characteristic features is determined. The Monte Carlo method makes it possible to correlate quantitatively the widths of the microdiffraction curves to the densities of various dislocation types. The potential of the method has been demonstrated by a quantitative estimation of the density distribution of edge and screw threading dislocations in laterally overgrown epitaxial GaN structures, which is investigated by a full-field microdiffraction imaging technique. Measuring the asymptotic behavior of the microdiffraction curves allows one to conclude on the prevailing type of threading dislocations.