Validity of Vegard’s rule for Al1−x_{1−x}Inx_xN (0.08 < xx < 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.Funding by FCT Portugal grants PTDC/FIS/65233/2006 and PTDC/FIS-NAN/0973/2012 is gratefully acknowledged. SM thanks FCT for his post-doc grant SFRH/BPD/98738/2013 and KL for her grant as ‘Investigador FCT’. RAO and FT acknowledge funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 279361 (MACONS). The LEAP 5000 XR was funded by the EPSRC grant EP/M022803/1

Validity of Vegard’s rule for Al₁₋ₓ Inₓ N (0.08

In this work, comparative x-ray diffraction (XRD) and Rutherford backscattering spectrometry (RBS) measurements allow a comprehensive characterization of Al1-xInxN thin films grown on GaN. Within the limits of experimental accuracy, and in the compositional range 0.08 &lt; x &lt; 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 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 Al1-xInxN films studied allowed furthermore a detailed investigation of the composition leading to lattice-matching of Al1-xInxN/GaN bilayers