Nitrogen incorporation and lattice constant of strained dilute Ga As 1 − x N x layers on GaAs (001): An ab initio study

Various nitrogen-related defects in $\mathrm{Ga}{\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ are studied within the framework of the density-functional theory using a plane-wave pseudopotential method. We use a biaxially strained periodic 64-atom supercell corresponding to coherent growth on a GaAs (001) substrate, containing up to four N atoms. The (001) lattice constants ${a}_{\ensuremath{\perp}}$, strain coefficients $\ensuremath{\alpha}$, and formation energies of the following configurations are calculated: substitutional ${\mathrm{N}}_{\mathrm{As}}$, N interstitials, N clusters on one As site, and N clusters on two nearest-neighbor Ga-As sites. We analyze the available experimental evidence for deviations from the linear decrease of the lattice constant with increasing N concentration (Vegard's rule). Our results suggest that negative deviations (faster than linear decrease) can be due to substitutional N and to vacancy-containing defect complexes stabilized by hydrogen. Positive deviations (slower than linear decrease) are attributed to N interstitials and clusters.