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.