Erratum: “Analyzing the growth of InxGa1−xN/GaN superlattices in self-induced GaN nanowires by x-ray diffraction” [Appl. Phys. Lett. 98, 261907 (2011)

Abstract

an underestimation of the In content by approximately 30% of the given values, otherwise our findings remain valid. We derive here the correct expression that replaces Eq. (2) of the original paper. Symmetric Bragg x-ray diffraction probes the vertical (normal to the layers) lattice constants of strained layers in a heterostructure. For coherent epitaxial growth without plastic relaxation, all layers attain a common in-plane lattice parameter. In case of a planar heterostructure on a bulk substrate, all layers have the same lateral lattice parameter as the substrate. The resulting average vertical lattice parameter of the heterostructure is governed by the Poisson effect, and the well-known result is given below in Eq. (9) .I n a nanowire, however, the heterostructure is free to relax laterally, and the in-plane lattice parameter is obtained from a balance between layers. If the requirement of the stressfree side surface is satisfied on average, the Poisson effect is compensated and the average vertical lattice parameter is given by Eq. (11) below. To derive this not obvious result, let us consider a periodic superlattice stack made from two materials, 1 and 2. Material 1 is taken as a reference for all strain values and material 2 possesses an eigenstrain e0 with respect to it. We take the lateral and the vertical eigenstrain components equal to each other. Thus, the lattice constants c 0 and c 0 in the fully relaxed state are related by e0 ¼ð c 0 � c 0 Þ=c 0 . For the coherent growth considered here, the in-plane lattice parameter can be approximated to assume a constant value throughout the whole stack, so that the in-plane total strain e1xx ¼ e2xx ¼ exx. The same condition holds for the yy components, the axes x and y are in the lateral plane. For the lateral relaxation of the SL, we distinguish two cases