Transport of dipolar excitons in (Al,Ga)N/GaN quantum wells

We investigate the transport of dipolar indirect excitons along the growth plane of polar (Al,Ga)N/GaN quantum well structures by means of spatially and time-resolved photoluminescence spectroscopy. The transport in these strongly disordered quantum wells is activated by dipole-dipole repulsion. The latter induces an emission blue shift that increases linearly with exciton density, whereas the radiative recombination rate increases exponentially. Under continuous, localized excitation, we observe continuously decreasing emission energy, as excitons propagate away from the excitation spot. This corresponds to a steady-state gradient of exciton density, measured over several tens of micrometers. Time-resolved microphotoluminescence experiments provide information on the dynamics of recombination and transport of dipolar excitons. We account for the ensemble of experimental results by solving the nonlinear drift-diffusion equation. Quantitative analysis suggests that in such structures, exciton propagation on the scale of 10 to 20 $\mu m$ is mainly driven by diffusion, rather than by drift, due to the strong disorder and the presence of nonradiative defects. Secondary exciton creation, most probably by the intense higher-energy luminescence, guided along the sample plane, is shown to contribute to the exciton emission pattern on the scale up to 100 $\mu m$. The exciton propagation length is strongly temperature dependent, the emission being quenched beyond a critical distance governed by nonradiative recombination.

Figure 1

Calculated electronic band structures showing energy and wave functions of electrons and holes in a polar single quantum well (sample C) at (a) low and (b) high exciton density, respectively, and at $T=4$ K. $E_{\text{AlGaN}}$ is the energy gap in the barrier, $E_0$ $\left(E_X\right)$ is the exciton recombination energy in the zero (high) density limit, and $E_{\text{BS}}$ is the population-induced blue shift $E_{\text{BS}}=E_X-E_0$.

Figure 2

Calculated dependence of radiative lifetime (a) and transition energy (b) versus exciton density, for samples A, B, and C found by solving Schrödinger-Poisson equations (triangles, circles, and squares, respectively). Continuous lines show the approximations by exponential [lifetimes (a)] and linear laws [energies (b)].

Figure 3

Color map of the PL intensity taken at $T=4$ K on (a) sample A, (b) sample B, and (c) sample C. The abscissa $r$ corresponds to the distance from the excitation spot. The ordinate corresponds to the energy spectrum. The color map (d) shows the PL peak wavelength as a function of the position in the $\left(x,y\right)$ plane of sample B. The excitation spot is located at the center of the map.

Figure 4

Grayscale map of the PL intensity taken on sample A for different temperatures: (a) 4, (b) 20, (c) 50, and (d) 80 K. The solution of the diffusion equation with constant diffusion coefficient $D$ and recombination rate $R$ such that $\sqrt{D/R}=12\mu m$ is displayed in (a) as a red dotted line.

Figure 5

Time evolution of the PL intensity $I_0$ for sample A, taken at $T=4$ K and at (a) 4, (b) 6, (c) 16, and (d) 60 $\mu \mathrm{m}$ away from the excitation spot. The grayscale map indicates the intensity of emission at a given energy (horizontal scale) and at a given time (vertical scale). Red curves show the calculated change of transition energy, with time, for each distance.

Figure 6

Grayscale map of the PL intensity calculated using Eq. (3) at different temperatures: 4, 20, 50, and 80 K as a function of the distance $r$ from the excitation spot, and emission energy. The drift current given by Eq. (6) is taken into account. A phenomenological Gaussian broadening of the blue shift with a standard deviation of 70 meV has been introduced.

Figure 7

Grayscale map of the PL intensity, calculated as in Fig. 6 except that only the diffusion current $J_{\mathbf{diff}}$ [Eq. (4)] is taken into account, whereas the drift current $J_{\mathbf{drift}}$ [Eq. (6)] is neglected.

Figure 8

Illustration of the modeling assumptions for sample A. Diffusion coefficient (a) and exciton lifetime $\tau$ (b) as a function of the blue shift at $T=4$ K (red solid line) and $T=80$ K (red dashed line). Radiative and nonradiative components ${\tau }_{\text{rad}}$ and ${\tau }_{\text{nrad}}$ are shown by blue and green lines, respectively.