Stacking faults as quantum wells in nanowires: Density of states, oscillator strength, and radiative efficiency

We investigate the nature of excitons bound to $I_1$ basal-plane stacking faults $\left[(I_1,X)\right]$ in GaN nanowire ensembles by continuous-wave and time-resolved photoluminescence spectroscopy. Based on the linear increase of the radiative lifetime of these excitons with temperature, they are demonstrated to exhibit a two-dimensional density of states, i.e., a basal-plane stacking fault acts as a quantum well. From the slope of the linear increase, we determine the oscillator strength of the $(I_1,X)$ and show that the value obtained reflects the presence of large internal electrostatic fields across the stacking fault. While the recombination of donor-bound and free excitons in the GaN nanowire ensemble is dominated by nonradiative phenonema already at 10 K, we observe that the $(I_1,X)$ recombines purely radiatively up to 60 K. This finding provides important insight into the nonradiative recombination processes in GaN nanowires. First, the radiative lifetime of about 6 ns measured at 60 K sets an upper limit for the surface recombination velocity of $210{\mathrm{cm}\mathrm{s}}^{-1}$ considering the nanowires mean diameter of 50 nm. Second, the density of nonradiative centers responsible for the fast decay of donor-bound and free excitons cannot be higher than $6\times {10}^{16}$ ${\mathrm{cm}}^{-3}$. As a consequence, the nonradiative decay of donor-bound excitons in these GaN nanowire ensembles has to occur indirectly via the free exciton state.

Figure 1

Continuous-wave PL spectra of the GaN nanowire ensemble under consideration for various temperatures as indicated in the figure. The spectra are shifted vertically for clarity. The major transitions are labeled according to their origin.

Figure 2

Superposition of scanning electron micrographs (gray scale) and monochromatic CL maps (false color) taken at 10 K at the emission energy of (a) the $(D^0,X)$ and (b) the $(I_1,X)$. The scale bar corresponds to 1 µm. (c) Same as (a) and (b) but taken at 300 K at the FX emission energy. (d) CL intensity of the $(D^0,X)$ and $(I_1,X)$ transitions at 10 K and of the FX line at 300 K along the nanowire highlighted by the yellow rectangle in (b).

Figure 3

(a) FX (squares) and $(I_1,X)$ (circles) emission energies as a function of $T$. The solid line is a fit to the free exciton emission energy using the expression derived by Pässler [32]. $\Delta E=54$ meV is the energy difference between the FX and the delocalized $(I_1,X)$. (b) Sum of the FX and $(D^0,X)$ emission intensities (squares) and $(I_1,X)$ emission intensity (circles) as a function of $T$, displayed on a double logarithmic scale. The black solid line is a fit to the total FX and $(D^0,X)$ intensity assuming that the nonradiative lifetime of FX is a constant and that its radiative lifetime increases with $T^{3/2}$. The blue solid line is the result of an Arrhenius fit to the $(I_1,X)$ emission intensity accounting for a nonradiative recombination channel with an activation energy $E_{\mathrm{A}}=54\pm 3$ meV.

Figure 4

(a) PL intensity transients of the FX, $(D^0,X)$, and $(I_1,X)$ transitions at 10 K. The temporal resolution was set to 20 ps. The vertical arrows indicate the time at which each transient reaches its maximum intensity. The effective lifetime ${\tau }_{\mathrm{eff}}^{\mathrm{X}}=190$ ps has been obtained from an exponential fit to the $(D^0,X)$ transient. (b) PL intensity transients of the $(I_1,X)$ transition at 10, 20, and 55 K. The temporal resolution was set to 160 ps. An exponential fit of these transients yields ${\tau }_{\mathrm{eff}}^{\mathrm{BSF}}=1.6$, 2.9, and 5.6 ns for $T=10$, 20, and 55 K, respectively. (c) Temperature dependence of ${\tau }_{\mathrm{eff}}^{\mathrm{BSF}}$ (squares). The solid lines show the result of the fits using Eq. (2) for $n=1$ ($A=0.666$ ${\mathrm{ns}\mathrm{K}}^{-1/2}$), $n=2$ ($A=0.110$ ${\mathrm{ns}\mathrm{K}}^{-1}$), and $n=3$ ($A=0.017$ ${\mathrm{ns}\mathrm{K}}^{-3/2}$).

Figure 5

Top-view scanning electron micrographs of samples (a) A, (b) B, and (c) C. (d) PL spectra at 10 K for samples A, B, and C. The spectra are vertically shifted for clarity. $R$ is the ratio between the spectrally integrated intensities of the $(I_1,X)$ transition and the sum of the $(D^0,X)$ and FX transitions. (e) Decay time of the $(I_1,X)$ band as a function of $T$ for samples A, B, and C.