Curvature and bow of bulk GaN substrates

We investigate the bow of free standing (0001) oriented hydride vapor phase epitaxy grown GaN substrates and demonstrate that their curvature is consistent with a compressive to tensile stress gradient (bottom to top) present in the substrates. The origin of the stress gradient and the curvature is attributed to the correlated inclination of edge threading dislocation (TD) lines away from the [0001] direction. A model is proposed and a relation is derived for bulk GaN substrate curvature dependence on the inclination angle and the density of TDs. The model is used to analyze the curvature for commercially available GaN substrates as determined by high resolution x-ray diffraction. The results show a close correlation between the experimentally determined parameters and those predicted from theoretical model.