Evolution of superclusters and delocalized states in GaAs${}_{1-x}$N${}_x$

The evolution of individual nitrogen cluster bound states into an extended state infinite supercluster in dilute GaAs${}_{1-x}$N${}_x$ was probed through temperature and intensity-dependent, time-resolved and magnetophotoluminescence (PL) measurements. Samples with compositions less than 0.23$\%$ N exhibit PL behavior that is consistent with emission from the extended states of the conduction band. Near a composition of 0.23$\%$ N, a discontinuity develops between the extended state PL peak energy and the photoluminescence excitation absorption edge. The existence of dual localized/delocalized state behavior near this composition signals the formation of an N supercluster just below the conduction band edge. The infinite supercluster is fully developed by 0.32$\%$ N.

Figure 1

PL spectra taken under low- and high-pulsed excitation fluences (solid lines) and the corresponding PLE spectrum (dashed lines) are shown for samples with (a) 0.12$\%$ N, (b) 0.23$\%$ N, and (c) 0.32$\%$ N. The horizontal arrows marked “PLE” indicate the spectral regions that were detected for PLE; “1” and “2” are the regions over which TRPL decay curves were measured. The extracted 2-K PLE band gap energies and 80-K PL $A$ or $B$ peak energies (Ref. 7) are shown in (d).

Figure 2

PL spectra measured over the temperature range 5–80 K for samples with N concentrations of (a) 0.04$\%$ N, (b) 0.12$\%$ N, (c) 0.23$\%$ N, and (d) 0.32$\%$ N. The spectra measured under excitation powers of 3 mW (solid lines) and 75 mW (dashed lines) are not displayed on the same scale. Arrows indicate the energies of peaks $A$ and $B$ measured under pulsed excitation (Fig. 1) at 2 K for each sample.

Figure 3

PL spectra measured under a range of applied magnetic fields (0–30 T) for samples with N concentrations of (a) 0.04$\%$ N, (b) 0.12$\%$ N, (c) 0.23$\%$ N, and (d) 0.32$\%$ N. The magnetodispersion curves of the peaks labeled $A$ and $B$ are shown in (e).

Figure 4

PL decay curves measured at localized N cluster states over the spectral region marked with a horizontal arrow labeled “2” in Fig. 1 for samples with N concentrations of 0.12$\%$, 0.23$\%$, and 0.32$\%$. Measurements were performed at 1 μJ/cm${}^2$.

Figure 5

PL decay curves for N concentrations of 0.12$\%$, 0.23$\%$, and 0.32$\%$ measured under excitation fluence of (a) 1 μJ/cm${}^2$ and (b) 20 μJ/cm${}^2$. All decay curves were measured in the spectral regions indicated by the horizontal arrows labeled “1” in Fig. 1. The insets show the decay times extracted from the single-exponential fits that are plotted as black lines in the main figures.

Figure 6

Theoretical population decay curves for carriers in the percolated N supercluster and localized N cluster states calculated from Eqs. (1, 2, 3). The time-integrated laser excitation into the conduction band is equal to 2.5$n_{\mathrm{s}}$ for the dashed curves and 50$n_{\mathrm{s}}$ for the solid curves. A schematic of the relative energy positions of the three sets of states is shown in the inset.