Penetration of electronic perturbations of dilute nitrogen impurities deep into the conduction band of ${\mathrm{GaP}}_{1-x}{\mathrm{N}}_x$

The electronic structure consequences of the perturbations caused by dilute nitrogen impurities in $\mathrm{GaP}$ are studied by means of supercell calculations using a fully atomistic empirical pseudopotential method. We find that numerous localized states are introduced by a single $\mathrm{N}$ atom and $\mathrm{N}$ clusters, not only close to the band edge but also throughout the $\mathrm{GaP}$ conduction band, up to $\sim 1\mathrm{eV}$ above the conduction band edge. These localized states suggest an alternative interpretation for a previously puzzling observation of splitting of photoluminescence excitation intensity at the $\mathrm{GaP}$ ${\Gamma }_{1c}$ energy into two features, one blueshifting and the other staying pinned in energy with increasing $\mathrm{N}$ concentration.

Figure 1

Calculated energies and character of electronic states for a large (1728 atom) cubic supercell containing (a) a single $\mathrm{N}$ atom and (b)–(e) $\mathrm{N}$ pairs separated by fourth to first nearest-neighbor distances, respectively. The dotted lines show energy positions of the unperturbed $\mathrm{GaP}$ host states. The energies are with respect to the $\mathrm{GaP}$ valence band maximum of unstrained $\mathrm{GaP}$. The solid vertical lines show the energy positions of the perturbed $\mathrm{GaP}$ host states, with the height of those lines being the $X$, $L$, $X$, and $\Gamma$ character (in percent) for the $X_{1c}$, $L_{1c}$, $X_{3c}$, and ${\Gamma }_{1c}$ perturbed host states, respectively. The isolated symbols denote N localized states (cluster states), showing their $\Gamma$, $L$, and $X$ character.

Figure 2

Energy distribution of the (a) $\Gamma$, (b) $L$, and (c) $X$ character densities for the ${\mathrm{GaP}}_{1-x}{\mathrm{N}}_x$ alloy conduction states at different $\mathrm{N}$ concentration: 0.69% (solid line), 1.27% (dotted line), and 3.47% (dashed line). Each density is averaged over 12 different random atomic configurations, using a $0.02\mathrm{eV}$ Gaussian smearing. Vertical dotted lines denote the energy positions of the critical points of the pure unstrained $\mathrm{GaP}$. The energies are with respect to the unperturbed $\mathrm{GaP}$ valence band maximum. The $\Gamma ∕L∕X$ densities are in units of the number of states weighted by percentage of their $\Gamma ∕\mathrm{L}∕\mathrm{X}$ character per $\mathrm{eV}$ per supercell atomic site $(\mathrm{Ga},\mathrm{P},\mathrm{N})$. Arrows in (a) point at a pinned peak at $2.90\mathrm{eV}$.

Figure 3

Schematic energy diagram showing how the $\mathrm{N}$ perturbation shifts and perturbs $\mathrm{GaP}$ host state energy levels (a) to produce the perturbed host states $\left(\mathrm{PHS}\right)$ (b), as well as introduces $\mathrm{N}$ cluster states (CS) (d) throughout the $\mathrm{GaP}$ conduction band, which combines with $\mathrm{PHS}$ in the resulting picture of $\mathrm{GaPN}$ alloy states (c).