Auger release of a deeply trapped carrier in a quantum dot

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We have studied the process of Auger-induced release of an electron deeply trapped in a semiconductor quantum dot (QD). The importance of this release mechanism in connection with the termination of a dark state of the photoluminescence (PL) has not been investigated earlier. The considered release mechanism is caused by the optical illumination of the QD in the course of observations and is due to an alternative (with respect to the usual Auger process) recombination channel of a newly created electron-hole pair with the recombination energy transferred to the trapped electron. In the studied QDs of CdSe/CdS type, where the hole ground state is confined to the CdSe core while the electron ground state is extended over both the core and CdSe shell, this Auger process is characterized by the F\"orster dependence $\ensuremath{\sim}1/{r}_{0}^{6}$ of the energy transfer rate on the trap distance ${r}_{0}$ from the QD center. The efficiency of this release mechanism is comparable with the one of the usual Auger recombination, if the deep trap is located nearby the QD core. On the contrary, the release probability is small for a distant trap, so that the QD can participate in many acts of the optical creation and subsequent Auger recombination before the trapped electron is released. If there are several traps within the QD shell, their spatial distribution results in a distribution of the release rates (and therefore of PL ``off times''). We have considered several models of the trap population distribution and calculated the corresponding ``off time'' distributions. In particular, for a homogeneous spatial distribution of traps and the ``F\"orster''-like dependence ($\ensuremath{\sim}1/{r}_{0}^{6}$) of the trapping probability, the distribution of the PL off times is the power law $\ensuremath{\sim}1/{t}_{\mathrm{off}}^{\ensuremath{\alpha}}$ with the exponent $\ensuremath{\alpha}=3/2$.