Dislocation correlations in GaN epitaxial films revealed by EBSD and XRD
Correlations between dislocations in crystals reduce the elastic energy via screening of the strain by the surrounding dislocations. We study the correlations of threading dislocations in GaN epitaxial films with dislocation densities of $5\times10^{8}$ cm$^{-2}$ and $1.8\times10^{10}$ cm$^{-2}$ by X-ray diffraction (XRD) in reciprocal space and by high-resolution electron backscatter diffraction (HR-EBSD) in real space, where the strain is derived from a cross-correlation analysis of the Kikuchi patterns. The measured XRD curves and HR-EBSD strain and rotation maps are compared with Monte Carlo simulations within one and the same model for the dislocation distributions. The screening of the dislocation strains is modeled by creating pairs of dislocations with opposite Burgers vectors, with the mean distance between dislocations in a pair equal to the screening distance. The pairs overlap and cannot be distinguished as separate dipoles. The HR-EBSD-measured autocorrelation functions of the strain and rotation components follow the expected logarithmic law for distances smaller than the screening distances and become zero for larger distances, which is confirmed by the Monte Carlo simulations. The kink in the plot of the autocorrelation function allows a robust and accurate determination of the screening distance without making any simulation or fit. Screening distances of 2 $μ$m and 0.3 $μ$m are obtained for the samples with low and high dislocation densities, respectively. The dislocation strain is thus screened by only 4 neighboring dislocations. In addition, an anisotropic resolution of the HR-EBSD measurements is observed and quantified. In this version, an error in the processing of the HR-EBSD maps of the Si wafer is specified.