Dislocation correlations in GaN epitaxial films revealed by EBSD and XRD

TL;DR

This study jointly uses XRD and HR-EBSD to quantify how dislocation strain fields in GaN epitaxial films are screened by surrounding dislocations. A unified Monte Carlo model with opposite-Burgers-pair screening reproduces both reciprocal-space XRD profiles and real-space strain-rotation maps, enabling direct extraction of the screening distance $R$ from strain autocorrelations. The results show robust, material- and density-dependent screening: $R\approx$ $2~\mu$m for a low density film ($\varrho\approx5\times10^{8}$ cm$^{-2}$) and $R\approx0.3~\mu$m for a high-density film ($\varrho\approx1.8\times10^{10}$ cm$^{-2}$), corresponding to roughly four dislocations participating in screening, with a strongly anisotropic HR-EBSD resolution observed. The findings unify real- and reciprocal-space analyses, clarify the effective dislocation densities inferred by XRD, and highlight the sensitivity limits and resolution anisotropy of HR-EBSD for surface-localized strain studies.

Abstract

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.

Figures (19)

• Figure 1: (a,b) Panchromatic cathodoluminescence intensity maps of GaN samples 0 and 1 and (c) scanning electron micrograph of sample 2.
• Figure 2: (a,b) X-ray diffraction curves of samples 1 and 2 (thick gray lines) and their Monte Carlo simulations (thin black lines). (c,d) Dislocation density and the screening distance $R$ obtained in the fits of the experimental (full symbols) and the simulated (open symbols) curves. The fits for different reflections are made independently and presented as a function of the angle $\Psi$ between diffraction vector and surface. The parameters for sample 1 are presented by black symbols, and for sample 2 by blue symbols. Dashed lines in (d) mark the values of screening distances obtained in the analysis of EBSD maps.
• Figure 3: HR-EBSD maps of the strain component $\varepsilon_{22}$ (a--c) in GaN samples 0, 1, and 2 and (d) in a Si(001) wafer, and (e,f) Monte Carlo simulation of the $\varepsilon_{22}$ maps for samples 1 and 2. Note that the strain obtained for Si(001) is an order of magnitude lower than in the GaN samples. The $y$ axis is chosen in the direction of the tilt of the electron beam.
• Figure 4: Top row: probabilities of (a) normal strain component$\varepsilon_{22}$ and (b) shear strain component $\varepsilon_{13}$ in samples 1 and 2, as well as in the reference dislocation free GaN sample (sample 0) and a silicon wafer, obtained from the maps in Figs. \ref{['fig:mapsEps22']}(a--d). Bottom row: probabilities of (c) normal strain component$\varepsilon_{22}$ and (d) shear strain component $\varepsilon_{13}$ in the Monte Carlo simulated maps in Figs. \ref{['fig:mapsEps22']}(e,f) and SM3, SM4. The probabilities are scaled by their maxima.
• Figure 5: Strain--strain correlation functions of (a,b) samples 1 and 2 and (c,d) their Monte Carlo simulations. The vertical red arrows point out to the screening distances taken as input of the Monte Carlo simulations (2 µ m and 0.3 µ m for samples 1 and 2 respectively).