Validity of Vegard’s rule for Al$_{1−x}$In$_x$N (0.08 < $x$ < 0.28) thin films grown on GaN templates

In this work, comparative x-ray diffraction (XRD) and Rutherford backscattering spectrometry (RBS) measurements allow a comprehensive characterization of Al$_{1-x}$In$_x$N thin films grown on GaN. Within the limits of experimental accuracy, and in the compositional range 0.08 < $x$ < 0.28, the lattice parameters of the alloys generally obey Vegard's rule, varying linearly with the InN fraction. Results are also consistent with the small deviation from linear behaviour suggested by Darakchieva $\textit{et al}$ (2008 Appl. Phys. Lett. 93 261908). However, unintentional incorporation of Ga, revealed by atom probe tomography (APT) at levels below the detection limit for RBS, may also affect the lattice parameters. Furthermore, in certain samples the compositions determined by XRD and RBS differ significantly. This fact, which was interpreted in earlier publications as an indication of a deviation from Vegard's rule, may rather be ascribed to the influence of defects or impurities on the lattice parameters of the alloy. The wide-ranging set of Al$_{1-x}$In$_x$N films studied allowed furthermore a detailed investigation of the composition leading to lattice-matching of Al$_{1-x}$In$_x$N/GaN bilayers.