Compositionally Graded AlGaN Nanostructures: Strain Distribution and X-ray Diffraction Reciprocal Space Mapping

The strain distribution in compositionally graded AlGaN planar structures, pillars, and nanowires (NWs) has been studied by three-dimensional (3D) strain calculations based on a numerical finite element method (FEM) and X-ray diffraction reciprocal space mapping. First, new fitting analyses of the reciprocal space maps (RSMs) are demonstrated to evaluate the depth profiles of strain and Al concentration, the film thickness, and the density of threading dislocation in compositionally graded AlGaN planar heterostructures. A good correlation between calculated and experimental RSMs for graded AlGaN thin film grown epitaxially on a GaN(0001) substrate was obtained. Second, by performing an FEM simulation of 3D strain distribution, we determined the influence of the surface-to-volume ratio of compositionally graded AlGaN nanostructures of different diameters and on different substrates on the effectiveness of strain relaxation. The results show a faster strain decay with an increasing surface-to-volume ratio from NWs to pillars. The AlGaN NWs, 40 nm in diameter on Si(111) substrate, are almost fully relaxed, implying a strong strain relaxation on the NWs side facets and a weak influence of the NW/substrate interface on strain distribution. Finally, the influence of strain inhomogeneity in the AlGaN nanostructures on the distribution of X-ray scattered intensity in reciprocal space is studied