Long-lived excitons in GaN/AlN nanowire heterostructures

GaN/AlN nanowire heterostructures can display photoluminescence (PL) decay times on the order of microseconds that persist up to room temperature. Doping the GaN nanodisk insertions with Ge can reduce these PL decay times by two orders of magnitude. These phenomena are explained by the three-dimensional electric field distribution within the GaN nanodisks, which has an axial component in the range of a few MV/cm associated to the spontaneous and piezoelectric polarization, and a radial piezoelectric contribution associated to the shear components of the lattice strain. At low dopant concentrations, a large electron-hole separation in both the axial and radial directions is present. The relatively weak radial electric fields, which are about one order of magnitude smaller than the axial fields, are rapidly screened by doping. This bidirectional screening leads to a radial and axial centralization of the hole underneath the electron, and consequently, to large decreases in PL decay times, in addition to luminescence blue shifts.

Figure 1

(a) HAADF STEM image of the GaN/AlN NW heterostructures. The AlN barriers (darker) and GaN disks (brighter) have nominal thicknesses of 4 nm. (b) Zoom into the squared region in (a) displayed in temperature color code. (c) HRTEM image of the first three GaN:Ge disks (near the GaN stem). (d) HRXRD $\omega -2\theta$ scan around the (0002) reflection of sample N3, together with a simulation. The simulation is down shifted for clarity.

Figure 2

(a) Normalized PL spectra of samples N1–N4 measured at low temperature $(T=5\mathrm{K})$. The spectra are normalized and vertically shifted for clarity. The dotted vertical line indicates the location of the GaN band gap. (b) Normalized integrated PL intensity of the samples shown in (a) as a function of temperature. Solid lines are fits to Eq (3). Inset: Simplified three-level model of the PL dynamics.

Figure 3

(a) Time-resolved PL spectra of sample N3. The red stripe follows the intensity maximum as a function of time. (b) Evolution of the PL spectra as a function of time. The time of maximum intensity is taken as $t=0$. The spectra are acquired with a time integration window of 0.4 ns. (c) Evolution of the PL peak intensity as a function of time. The dashed line is an exponential fit to the PL decay for times longer than 60 ns.

Figure 4

(a) PL decay for samples N1–N4 measured at low temperature $(T=10\mathrm{K})$. The decays were taken following the method described in Fig. 3. (b) PL decay characteristic times extracted from the exponential part of the PL decays [similar to Fig. 1], plotted as a function of temperature. The emission wavelengths are indicated in the figure. Superimposed, PL decay times of an NID GaN/AlN quantum well (labeled NID QW) emitting at approximately the same wavelength that N1.

Figure 5

(a) Schematic representation of three GaN/AlN nanodisks in the center of the nanowire heterostructures, as they are described in the input file for NEXTNANO3. The structure is viewed along the [1−100] plane. White areas correspond to GaN and yellow areas correspond to AlN. (b) Calculation of the ${\varepsilon }_{xx}$ strain component (strain along [11−20]) for these same disks. (c) Calculation of the ${\varepsilon }_{zz}$ strain component (along [000–1]). (d) Calculation of the ${\varepsilon }_{xz}$ shear strain component.

Figure 6

(a)–(d) Calculation of the conduction and valence band profiles and first electronic levels of electrons and holes. (a), (b) Conduction and valence band profiles along [000−1] taken at the center of the NW, for (a) undoped nanodisks and (b) Ge-doped nanodisks (sample N3). The ground electron and hole levels are indicated by dashed lines. In (a), the ground hole level is not indicated because the value of the squared wave function along the center of the NW is zero. (c), (d) Radial conduction and valence band profiles for the (c) undoped and (d) Ge-doped nanodisk in the center of the stack. Note that the conduction band was taken at the bottom of the disk, while the valence band was taken at the top of the disk. The squared wave functions of the ground electron and hole states are indicated in the figures.

Figure 7

Calculation of the electric field along [11−20] at the top of the nanodisk for various doping concentrations in the nanodisks, (a) neglecting surface charges, and (b) with surface charges at a concentration of $\sigma =-2\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$. With higher doping levels, the electric field in the disk is attenuated. Positive electric field implies that it points in the [11−20] direction. The sign of the electric field sees a crossover at a dopant concentration of (a) $\sim 2\times {10}^{19}\mathrm{c}{\mathrm{m}}^{-3}$, and (b) $\sim 4\times {10}^{19}\mathrm{c}{\mathrm{m}}^{-3}$. The magnitude of the radial electric field is (a) 0.42 MV/cm, and (b) 0.58 MV/cm. A null electric field was seen (a) 14 nm and (b) 17 nm from the center of the wire.