X-ray diffraction analysis of features of the crystal structure of GaN/Al$_{0.32}$Ga$_{0.68}$N HEMT-heterostructures by the Williamson–Hall method

The fitting of $\theta$/2$\theta$ and $\omega$ peaks in X-ray diffraction curves is shown to be most accurate in the case of using an inverse fourth-degree polynomial or probability density function with Student's distribution (Pearson type VII function). These functions describe well both the highest-intensity central part of the experimental peak and its low-intensity broadened base caused by X-ray diffuse scattering. The mean microdeformation $\varepsilon$ and mean vertical domain size $D$ are determined by the Williamson–Hall method for layers of GaN ($\varepsilon\approx$ 0.00006, $D\approx$ 200 nm) and Al$_{0.32}$Ga$_{0.68}$N ($\varepsilon$ = 0.0032 $\pm$ 0.0005, $D$ = 24 $\pm$ 7 nm). The $D$ value obtained for the Al$_{0.32}$Ga$_{0.68}$N layer is most likely to result from the nominal thickness of this layer, which is 11 nm.