Radiative lifetime of a single electron-hole pair in $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ quantum dots

Wurtzite $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ quantum dots (QDs) are studied by time-resolved photoluminescence. Careful measurements allow us to reach the regime of a single electron-hole pair per dot, evidenced by a monoexponential decay of the luminescence and a stop of the time-dependent shift of the emission energy. The transition energy and the radiative lifetime of the QD ground state are measured in the absence of any electric field screening effect, for a wide range of QD heights. These results are analyzed within an envelope function model for the electron and hole confinement. The effective electric field, averaged over the strain distribution in the dots, is determined to be of $9.0\pm 0.5\mathrm{MV}∕\mathrm{cm}$.

Figure 1

(a) PL spectra of $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ QDs (height: $3.3\mathrm{nm}$), $0.23\mu \mathrm{s}$, $1.8\mu \mathrm{s}$, and $22\mu \mathrm{s}$ after the excitation pulse. The fringes are due to interferences in the buffer layer and remain constant for all times. (b) PL peak energy versus the delay after excitation, obtained from a Gaussian fit to the spectrum. The error on the determination of the energy is estimated to $\pm 50\mathrm{meV}$. The dashed line is a guide for the eye. The sketches present the potential felt by electrons and holes, and their ground states, with (left) and without (right) screening of the electric field.

Figure 2

Spectrally integrated intensity of the PL ($3.3\mathrm{nm}$ QDs, same as Fig. 1) versus the delay after excitation, on log-log scale (a). The data from the dashed square are presented on a linear scale (b). The plain line is a mono-exponential fit of the decay between 20 and $80\mu \mathrm{s}$.

Figure 3

Measured radiative lifetime (circles) versus measured energy of PL peak for the different QD samples. Solid lines show the calculated value of lifetime as a function of energy of the fundamental transition for an effective electric field of respectively 7, 9, and $11\mathrm{MV}∕\mathrm{cm}$ and $A=90$ (see text). The calculated QD height corresponding to the transition energies for a $9\mathrm{MV}∕\mathrm{cm}$ electric field is reported on the top axis. The electron and hole energy levels and wave functions are sketched in the regimes dominated by Stark effect (left) and quantum confinement (right).