How dislocations screen each other in GaN: direct evidence from real and reciprocal space

Threading dislocations are a defining feature of many GaN epitaxial films and play a central role in determining their structural and functional properties. From a fundamental perspective, a single straight dislocation produces a long-range elastic strain field whose elastic energy would diverge with increasing crystal size. Real crystals avoid this divergence because dislocations are not independent: correlations between dislocations screen long-range strain, limiting the elastic energy to a finite value. The key length scale governing this process is the screening distance, beyond which dislocation-induced strain correlations vanish.

While the existence of dislocation screening is well established theoretically and inferred indirectly from line shapes in X-ray diffraction (XRD), its direct determination in real space remains challenging. XRD provides access to strain statistics integrated over large sample volumes, but extracting screening distances relies on model-dependent fitting. Spatially resolved strain mapping, in contrast, offers the possibility to observe dislocation correlations directly—provided sufficient sensitivity and spatial resolution are available.

In this work, threading dislocation correlations in GaN(0001) epitaxial films are investigated by combining laboratory XRD with high-resolution electron backscatter diffraction (HR-EBSD). The study examines films with threading dislocation densities differing by orders of magnitude and benchmarks both experimental techniques against Monte Carlo simulations based on one consistent model of dislocation distributions and strain fields. This unified approach allows reciprocal-space and real-space observations to be interpreted within the same physical framework.

HR-EBSD provides maps of all components of the strain and lattice rotation tensors near the surface, obtained from cross-correlation analysis of Kikuchi patterns. Rather than focusing on individual dislocations, the analysis centers on spatial autocorrelation functions of the measured strain and rotation components. Because the strain field of a dislocation decays as 1/r with distance r, the strain–strain correlations are expected to decrease logarithmically with separation as long as dislocation strains are not screened. Once screening sets in, correlations should drop to zero beyond the screening distance. When plotted as a function of the logarithm of separation, this behavior produces a characteristic kink marking the transition from logarithmic decay to zero correlation.

This kink provides a direct and robust measure of the screening distance, without requiring fitting or assumptions about the detailed form of dislocation correlations. Using this method, screening distances of approximately 2 µm and 0.3 µm are obtained for GaN films with lower and higher threading dislocation densities, respectively. Despite the large difference in dislocation density, both values correspond to screening by only about four neighboring dislocations, demonstrating that long-range dislocation strain fields in GaN are very effectively cancelled by a small local ensemble.

XRD line-profile analysis yields dislocation densities and screening distances consistent with the HR-EBSD results, though with larger scatter and uncertainties in the screening distance across different reflections. Monte Carlo simulations show that while dislocation densities can be extracted reliably from XRD, the screening distance is more accurately determined from real-space correlation analysis. The simulations further enable a quantitative assessment of HR-EBSD measurements, revealing a strongly anisotropic spatial resolution with reduced resolution along the direction of the inclined incident electron beam, and identifying shear strain components that appear as uncorrelated noise and provide a practical estimate of measurement accuracy.

By directly revealing dislocation strain screening in real space with HR-EBSD and linking it quantitatively to the reciprocal-space determination with XRD, this work establishes strain correlation analysis as a robust tool for determining screening distances in crystalline materials. The approach is applicable beyond GaN to more complex dislocation ensembles, where direct modeling of strain fields may be difficult, and provides a valuable benchmark for combining diffraction and microscopy in the study of crystal defects.

Title: Dislocation correlations in GaN epitaxial films revealed by EBSD and XRD
Authors: V. Kaganer, D. Spallek, P. John, O. Brandt, J. Lähnemann
Source: Acta Mater., 297, 121357 (2025)
DOI: 10.1016/j.actamat.2025.121357

Core Research Area (CReA): Nitride Semiconductors