Nitrogen isoelectronic trap in $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{P}}_x$: II. Model calculation of the electronic states $N_{\Gamma }$ and $N_X$ at low temperature

A semiphenomenological theory of the isolated N isoelectronic trap in $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{P}}_x$ is presented, based on an extended (multisite), one-band Koster-Slater model of the electron-impurity interaction, including the effects of both the central-cell atomic pseudopotential difference and the spatially extended lattice distortion surrounding the substitutional nitrogen impurity. The alloy host is treated in a virtual-crystal approximation. The parameters of the model are determined by fitting low-temperature photoluminescence data from ion-implanted materials of two compositions selected near $x\approx 0.35$. The model yields both a spatially localized $N_X (or A)$ state which evolves continuously with decreasing $x$ from the $A$ line of GaP, and a spatially-diffuse state $N_{\Gamma }$ which is present in near-direct and direct-band-gap alloys ($0.3\lesssim x\lesssim 0.5$). The theory quantitatively describes the energies of these luminescence lines as a function of alloy composition $x$. In addition, good agreement with the data is found for the following calculated quantities: (i) the composition dependences of the $N_{\Gamma }$ and $N_X$ luminescence intensities, (ii) the pressure dependences of the $N_{\Gamma }$ and $N_X$ intensities, (iii) the composition dependence of the $N_X$ lifetime, and (iv) the binding energy of N${\mathrm{N}}_1$ pairs in GaP. The model leads to a tentative interpretation of $N_{\Gamma }$ luminescence as originating, at least in part, from excitonic molecules.