Evaluation of interpolations of InN, AlN and GaN lattice and elastic constants for their ternary and quaternary alloys

Structural and compositional data were collected for several high-quality strained InGaN, InAlN, AlGaN and InAlGaN layers with various compositions. Based on these results, the InN/AlN/GaN molar fractions of every film were indirectly estimated by the application of Vegard's law (Vegard 1921 Z. Phys. 5 17) to lattice and elastic constants of the binaries and by an alternative approach proposed by (Williams et al 1978 J. Electron. Mater. 7 639) (even considering possible mistakes in its application). True compositions were independently assessed by x-ray spectroscopy or Rutherford backscattering spectrometry. The results of both interpolation models are highlighted in utilizable contour and surface ternary plots of lattice constants and biaxial strain relaxation coefficients calculated for the whole compositional range. Calculated compositions from Vegard's law best fit the measured values. Finally, it is geometrically demonstrated that there are wrong assumptions in the Williams et al model, so that Vegard's law should only be used to successfully determine the compositions of ternary and quaternary III-N nitrides.