Pseudopotential Theory of Auger Processes in CdSe Quantum Dots

Auger rates are calculated for CdSe colloidal quantum dots using atomistic empirical pseudopotential wave functions. We predict the dependence of Auger electron cooling on size, on correlation effects (included via configuration interaction), and on the presence of a spectator exciton. Auger multiexciton recombination rates are predicted for biexcitons as well as for triexcitons. The results agree quantitatively with recent measurements and offer new predictions.

Figure 1

Illustration of the Auger processes considered here.

Figure 2

Auger lifetimes for electron cooling, evaluated at $T=0\mathrm{K}$, with EPM-2 and within the single-particle approximation, for three values of the broadening parameter $\Gamma$ [see Eq. (4)]. The vertical arrows denote the value of the calculated cooling energy $\Delta E={ϵ}_{e_p}^0-{ϵ}_{e_s}^0$.

Figure 3

Electron cooling: Auger lifetimes at $T=300\mathrm{K}$ calculated with EPM-1 within the single-particle (SP) approximation (solid line), and with CI, both in the absence (dashed line) and in the presence (long-dashed line) of a spectator ground state exciton. The initial states include all three electron $p$ states and both hole $s$ states, and the final states $e_s$ and 30 hole states $h_n$ with energy centered around $E_{n0}={ϵ}_{h_{s1}}-{ϵ}_{e_p}+{ϵ}_{e_s}$.

Figure 4

Auger biexciton recombination lifetime ${\tau }_{e\mathrm{\text{−}}h}^{2\to 1}$ calculated with $\overline{ϵ}(\mathbf{r},{\mathbf{r}}^{\mathbf{\prime }})$ as in Eq. (3) (solid line), decomposed into its surface (long-dashed line) and bulk (dashed line) contributions, compared to ${\tau }_{e\mathrm{\text{−}}h}^{2\to 1}$ calculated with $\overline{ϵ}(\mathbf{r},{\mathbf{r}}^{\mathbf{\prime }})=1$ (dotted line). All curves were calculated at $T=0$ with EPM-1.

Figure 5

Auger multiexciton recombination lifetimes: (a) ${\tau }_{e\mathrm{\text{−}}h}^{2\to 1}$ decomposed into the ${\tau }_e$ and ${\tau }_h$ contributions [see Eq. (5)]; (b) ${\tau }_{e\mathrm{\text{−}}h}^{3\to 2}$ together with its two contributions coming from a single hole and a single electron scattering. All lifetimes were calculated at $T=0$ with EPM-2 and $\overline{ϵ}(\mathbf{r},{\mathbf{r}}^{\mathbf{\prime }})=1$.