Quantitative determination of short-range ordering in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$

Short-range ordering in the form of an excess of In-N bonds with respect to the random case has been recently predicted for the dilute nitride alloy ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_{1-y}{\mathrm{N}}_y.$ This ordering induces a blue shift of the optical band gap and could represent a fundamental materials limitation. In this report we provide a quantitative determination of the effect of annealing on the short-range ordering in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_{1-y}{\mathrm{N}}_y,$ using x-ray- absorption spectroscopy and state-of-the-art analysis methods. We find that in annealed samples short-range ordering is weak, one order of magnitude smaller than predicted.