Charge separation and temperature-induced carrier migration in Ga${}_{1-x}$In${}_x$N${}_y$As${}_{1-y}$ multiple quantum wells

We have investigated the photoluminescence (PL) of two carefully selected dilute nitride Ga${}_{1-x}$In${}_x$N${}_y$As${}_{1-y}$ multiple quantum well structures in magnetic fields up to 50 T as a function of temperature and excitation power. The observation of a nonmonotonic dependence of the PL energy on temperature indicates that localized states dominate the luminescence at low temperature, while magneto-PL experiments give new insights into the nature of the localization. We find that the low-temperature spatial distribution of carriers in the quantum well is different for electrons and holes because they are captured by different disorder-induced complexes that are spatially separated. A study of the thermalization of the carriers toward free states leads to the determination of the free-exciton wave-function extent in these systems and enables an assessment of the localization potentials induced by inhomogeneity in the quantum well.

Figure 1

Temperature dependence of the PL energy for samples A (triangles) and B (circles) with an excitation power density of 2.5 Wcm${}^{-2}$. The local minimum in the S shape, typical for recombination from localized states, is more pronounced and appears at higher $T$ for Sample A. Dashed lines indicate the Varshni fits to the high-$T$ data.

Figure 2

PL energy (squares) and integrated intensity (circles) as a function of excitation power density for Sample A. A clear blueshift is observed, hinting at spatially indirect recombination. The line through the PL energy data is a guide to the eye. The integrated intensity is linearly dependent on the excitation power, confirming that the recombination is excitonic. The excitation power dependence over six orders of magnitude is shown in the inset for Sample A. The blueshift, combined with a reduced importance of the low-energy broadening of the PL peak at high excitation power, is clearly noticeable.

Figure 3

Temperature dependence of the PL energy for Sample A at different excitation power densities. The local minimum in the S shape of the temperature dependence is increasingly suppressed at higher excitation power densities. The dashed line is the Varshni fit from Fig. 1.

Figure 4

The shift of the PL energy versus magnetic field at a power density of 5 Wcm${}^{-2}$. The line is a fit to the data of Sample A using the model of Ref. 10. For Sample A, a crossover from parabolic to linear behavior occurs at 8 T (indicated by the vertical arrow), whereas the data for Sample B are linear down to very low fields. The inset shows the PL spectra for both samples A (red) and B (blue) at 0 (full lines) and 48 T (dotted lines) measured at 4.2 K. The low-energy broadening is present in the data for Sample A only. The line width of the PL peak for Sample B is considerably smaller.

Figure 5

PL energy shift as a function of magnetic field for various excitation power densities at 77 K. The inset shows a summary of the magnitudes of the energy shift between 0 and 45  T for the four different excitation power densities at 77 K and the corresponding energy shift at 4 K. The larger uncertainty in the 4 K PL energy shift is due to fewer data points in the low-field regime for the measurement at this temperature.

Figure 6

Exciton wave-function extent as a function of $T$ for the DC-field measurements using 2.5 Wcm${}^{-2}$ of excitation power. At low $T$, the exciton radius in Sample B is larger than in Sample A, but as $T$ increases, the relation rapidly reverses. The lines are unconstrained exponential fits to the data. The PL energy shift as a function of DC magnetic field for Sample B at 5, 50, and 100  K is shown in the inset. The open symbols represent data points in the low-field regime, while filled symbols are used for data points at magnetic fields above the crossover point, i.e. in the high-field regime. In contrast to the pulsed field data, a small parabolic regime can clearly be observed.

Figure 7

Schematic representation of the potential landscape based on our observations. The electron and hole localization centers, due to local nitrogen and indium excess, respectively, are expected to be present in an out-of-phase spatially periodic manner (see e.g. Ref. 30). For clarity, the localization centers in the conduction band due to local indium excess are not shown. Recombination energies in the figure are derived from PL center of mass transition energies and are approximate. The average separation of N-rich and In-rich regions is estimated from our data as being 15 nm for Sample A and 18 nm for Sample B.