We study the impact that local strain effects have on the spatial distribution of In in coherent ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ grown epitaxially on GaN(0001) using an effective crystal growth modeling technique that combines a semi-grand-canonical Monte Carlo simulation with an ab initio parametrized empirical force field. Our calculations show that ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ epitaxial layers exhibit a strong tendency towards ordering, as highlighted by the formation of a vertical stack of the $\sqrt{3}\times \sqrt{3}$ patterned layers along the $\langle c\rangle$ direction. The ordering phenomena are identified as a key factor that determines lateral phase separation in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ epitaxial layers at the nanometer scale. Consequences of this nanophase separation for the enhanced radiative emission through carrier localization in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ of $x<1/3$ are discussed.

• Received 9 October 2014
• Revised 25 November 2014

DOI:https://doi.org/10.1103/PhysRevB.90.245301