Direct Observation of Electron-to-Hole Energy Transfer in CdSe Quantum Dots

We independently determine the subpicosecond cooling rates for holes and electrons in CdSe quantum dots. Time-resolved luminescence and terahertz spectroscopy reveal that the rate of hole cooling, following photoexcitation of the quantum dots, depends critically on the electron excess energy. This constitutes the first direct, quantitative measurement of electron-to-hole energy transfer, the hypothesis behind the Auger cooling mechanism proposed in quantum dots, which is found to occur on a $1\pm 0.15\mathrm{ps}$ time scale.

Figure 1

(a) Left: Luminescence spectra. Also shown is the excitation pulse (shaded area). Right: We measure the increase in intensity at the peak of the luminescence spectra (gray lines) as a function of delay $\tau$. (b) Left: The transmitted THz pulses $E_{\mathrm{THz}}(t,\tau )$ and the exciton-induced modulation thereof, $\Delta E_{\mathrm{THz}}(t,\tau )$. Right: The modulation is measured at the point marked with an arrow in the left panel ($t=1.9\mathrm{ps}$), as a function of $\tau$, giving rise to the transient hole population of the $1S_{3/2}$ level. The dynamics in both (a) and (b) are adequately described by exponential rise times determined by the carrier cooling rates (black lines in the right-hand panels).

Figure 2

Cooling times (describing the return to the cold electron and hole states) obtained from exponential fits to the THz-TDS and luminescence measurements as a function of mean particle diameter (horizontal error bars indicate size distributions). The dashed lines are the result of the model described in the text. The arrow marks the diameter for which (given the excitation energy) hot electron excitation is allowed, calculated from the energy levels in Ref. 1—i.e., only for diameters $D\gtrsim 3.3\mathrm{nm}$ must electron (as well as hole) cooling be considered, marking a clear step in the luminescence and THz rise times in the main figure.

Figure 3

Hole cooling time as a function of hole excess energy (calculated using the transitions in Ref. 1), for QDs with diameters proportional to the symbol size (2.5, 3.0, 3.2, 3.9, and 4.3 nm, respectively). Solid symbols denote particles for which the electron $1P_e$ state is optically accessible with the 3.15 eV excitation pulse; open symbols are those for which the electron is excited into its $1S_e$ state. The arrow indicates the transition occurring at $D\sim 3.3\mathrm{nm}$: Hole cooling slows down considerably when the electron is excited into the hot state. The dashed lines are the result of the model. Inset: Schematic representation of the five-level model described in text.