Temperature Dependence of the Luminescence Lifetime of Single $\mathrm{C}\mathrm{d}\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}$ Quantum Dots

We study the temperature dependence of the luminescence decay of single $\mathrm{C}\mathrm{d}\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}$ quantum dots between 2 and 140 K. For the first time, we observe a biexponential decay which was completely hidden in ensemble measurements. We find that the long time component strongly depends on temperature. This demonstrates that the band edge luminescence arises from two thermally mixed fine structure states, the dark ground state and the lowest bright one. To interpret our results, we derive the analytical expressions for the decay using a three level model. Fitting the experimental data leads directly to the lifetime of the states as well as their energy splitting.

Figure 1

Typical luminescence decay curves of $\mathrm{C}\mathrm{d}\mathrm{S}\mathrm{e}/\mathrm{Z}\mathrm{n}\mathrm{S}$ QDs. (a) An ensemble measurement (at 16 K) gives a multiexponential decay. (b) A single QD decay is biexponential at 16 K. The short time is within our time resolution and the long decay time is around 73 ns. (c) A single QD decay is monoexponential at 140 K with a typical lifetime of 19 ns. Inset: The three-state model. $|G⟩$ is the zero exciton ground state. The “bright” state $|A⟩$ and the “dark” state $|F⟩$ are the two lowest states of the band edge exciton with respective lifetimes ${\Gamma }_A^{-1}$ ($\sim 10\mathrm{n}\mathrm{s}$) and ${\Gamma }_F^{-1}$ ($\sim 1\mu \mathrm{s}$). ${\gamma }_0\sim 10{\mathrm{n}\mathrm{s}}^{-1}$ is the zero temperature $|A⟩\to |F⟩$ relaxation rate. ${\gamma }_{\mathrm{t}\mathrm{h}}$ is the thermalization rate due to the interaction with an acoustic phonon mode.

Figure 2

Histograms of the long component decay time ${\tau }_L$ built from about a hundred single QDs at various temperatures (between 2.3 and 140 K). The mean ${\tau }_L$ values are 865 ns at 2.3 K, 209 ns at 5.7 K, 85 ns at 16 K, 51 ns at 77 K, and 19 ns at 140 K.

Figure 3

(a) Evolution with temperature of the mean decay rate ${\tau }_L^{-1}$ deduced from the histograms of Fig. 2. The continuous curve is theoretical rates of Eq. (2), plotted with ${\Gamma }_A=0.13{\mathrm{n}\mathrm{s}}^{-1}$, ${\Gamma }_F=2\mu {\mathrm{s}}^{-1}$, and $\Delta E=3.5\mathrm{m}\mathrm{e}\mathrm{V}$. (b) Inset: luminescence decay curves of a single QD, recorded at temperatures 2.7, 10, 12, 15, 18, and 28 K. For clarity, the first 10 ns of the curves are not presented and the data are normalized. (b) Main figure: Temperature dependence of the long component rate, for three single QDs with different radius (circles for the “red” QD, radius 5.6 nm; squares for the “yellow” QD, radius 1.9 nm; triangles for the “green” QD, radius 1.5 nm). The experimental points are well fitted with the expression of ${\tau }_L^{-1}$ deduced from the thermal mixing model. The fits give ${\Gamma }_F=5.4\mu {\mathrm{s}}^{-1}$, ${\Gamma }_A=57\mu {\mathrm{s}}^{-1}$, $E_{AF}=2.1\mathrm{m}\mathrm{e}\mathrm{V}$ for the “red” QD; ${\Gamma }_F=1.4\mu {\mathrm{s}}^{-1}$, ${\Gamma }_A=92\mu {\mathrm{s}}^{-1}$, $E_{AF}=3.8\mathrm{m}\mathrm{e}\mathrm{V}$ for the “yellow” QD; ${\Gamma }_F=2.0\mu {\mathrm{s}}^{-1}$, ${\Gamma }_A=82\mu {\mathrm{s}}^{-1}$, $E_{AF}=5.0\mathrm{m}\mathrm{e}\mathrm{V}$ for the “green” QD.