Analyses of determination conditions of n-GaN dislocation density by triple-axis X-ray diffraction

Dislocation densities of two hydride vapor phase epitaxy-grown hexagonal GaN samples, which are Si doped and unintentionally doped respectively, are determined by triple-axis X-ray diffractometry and van der Pauw variable temperature Hall-effect measurement. The dislocation densities of these two samples should be at the same level from the X-ray testing, the -FWHM (full width at half maximum) values of all corresponding reflections for these two samples are almost the same. But from the Hall-effect measurements, the dislocation density values should be different from each other remarkably, because the unintentionally doped sample belongs to Mott transition material, while the Si-doped one does not. This fact indicates that the X-ray testing is perhaps inaccurate under some conditions, although the triple-axis X-ray diffractometry is a highly suitable technique for discriminating different kinds of structural defects such as edge and screw dislocations that lead to characteristic broadening of symmetric and asymmetric Bragg reflection. The experimental result obtained so far (say, for hot-electron bolometer) shows that the dislocation density value from mobility fitting model is in good accordance with that from -FWHM fitting using Srikant method. The anomaly that the dislocation density from -FWHM fitting is much lower than that from mobility fitting for the same sample (sample 59#), indicates that dislocations located in grain boundary may not be tested by triple-axis X-ray diffractometry. According to mosaic model, the layer is assumed to consist of single crystallites, called mosaic blocks, which are assumed to be slightly misoriented with respect to each other. The out-of-plane rotation of the block perpendicular to the surface normal is of the mosaic tilt, and the in-plane rotation around the surface normal is of the mosaic twist. The average absolute values of tilt and twist angles are directly related to the FWHM values of the corresponding distributions of crystallographic orientations. So, the X-ray testing can determine the average orientation of the grains with the same interplanar distance, excluding the information about the grain boundary at which X-ray cannot interfere because of disdortion of lattice. The experimental results and calculation analyses indicate that the dislocation density value from Srikant model is accurate when the ratio of twist angle to tilt angle exceeds 2.0, or the magnitude of the lateral coherence length is larger than 1.5 m.