Determination of the composition of In(x)Ga(1-x)N from strain measurements

The use of incorrect GaN and InN anisotropic elastic constants and unstrained lattice constants, or the erroneous interpolation of InGaN elastic coefficients, have led to several errors in the calculations of compositions of ternary alloys based on strain measurements. To avoid this, statistically estimated elastic constants are used to calculate the correct coefficients at any composition assuming they follow Vegard's law as happens for relaxed lattice constants. In consequence, a general equation to extract x from experimentally determined a and c cell parameters in biaxial strained wurtzite InxGa1-xN is proposed. The validity of this equation is confirmed: inputting structural parameters deduced from fine electron diffraction of non-phase-segregated epilayers (0.4 < x < 0.8) gives outputs that are in agreement with compositions directly measured by energy-dispersive X-ray analysis in a scanning transmission electron microscope; high-resolution X-ray diffraction analysis also supports these findings. The proposed elastic behavior of InGaN correlates well with other experiments in the literature.