Figure 1

(Color online) Illustration of the difference between single-NC $N$-exciton Auger lifetimes, ${\tau }_N$, and ensemble-averaged lifetime ${\tau }_{⟨N⟩}^{*}$.Reuse & Permissions

Figure 2

(Color online) (a) Auger transitions that involve excitation of either a conduction-(left) or a valence-band (right) electron; solid and open circles correspond to electrons and holes, respectively. (b) Possible conduction-to-valence band transitions in the case of Auger recombination of a symmetric $1S1S1S$ (left) or asymmetric $1S1S1P$ (right) triexciton assuming that the $S\text{−}P$ interband transitions are much weaker than the $S\text{−}S$ and $P\text{−}P$ transitions. (c) Comparison of possible energy-transfer pathways involving near-neighbor interactions during Auger recombination of a triexciton in a spherical NC (left) and an elongated quasi-1D nanorod (right).Reuse & Permissions

Figure 3

(Color online) (a) The NC-size dependence of biexciton (solid symbols) and triexciton (open symbols) Auger lifetimes for CdSe NCs from this work (diamonds), Ref. 4 (circles), Ref. 25 (triangles), and Ref. 26 (squares). Lines are fits to a power dependence ${\tau }_{2,3}\propto R^m$. (b) The size dependence of the ${\tau }_2∕{\tau }_3$ ratio for CdSe [solid diamonds (this work), open circles (Ref. 4), and solid triangles (Ref. 25)] and PbSe (squares) NCs in comparison to ratios expected for quadratic (2.25), cubic (3.375), statistical (4.5), and quantum-mechanical (2.5) scalings.Reuse & Permissions

Figure 4

(Color online) Calculated multiexciton Auger lifetimes for quadratic (open circles), cubic (open squares), and statistical (solid triangles) scalings of the ${\tau }_N$ time constants assuming a biexciton lifetime of $130\mathrm{ps}$.Reuse & Permissions

Figure 5

(Color online) (a) $1S$ bleach dynamics measured for CdSe NCs with $R=2.8\mathrm{nm}$ (symbols) for different pump fluences ($100\mathrm{fs}$, $3\mathrm{eV}$ pulses) that correspond to $⟨N_0⟩=0.56$, 1.1, 2.5, and 5.4 (increasing from bottom to top); lines are calculations assuming the state-filling model and cubic scaling of ${\tau }_N$ $({\tau }_2=130\mathrm{ps})$. Obvious disagreement between the calculated and the measured traces indicates a significant influence of non-state-filling-related mechanisms on the $1S$ bleach dynamics. Inset: early-time instantaneous $1S$ bleach relaxation time $\left({\tau }_i\right)$ as a function of initial average occupancy of the NCs. Steady decrease of ${\tau }_i$ with $⟨N_0⟩$ in the range of pump fluences that correspond to $⟨N_0⟩>2$ indicates the sensitivity of the $1S$ bleach relaxation to recombination dynamics of multiexcitons with order greater than 2; this further confirms the importance of non-state-filling-related contributions to the $1S$ signal. (b) Pump-intensity-dependent dynamics of NC average occupancies extracted from TA traces in pl (a) using the phenomenological dependence of $\Delta {\alpha }_{1S}∕{\alpha }_{0,1S}$ on $⟨N⟩$ given in Eq. (4) with $k_1=1.1$ and $k_2=1.6$. The latter is shown by the solid line in the inset together with the experimental data points (solid circles; $t=2\mathrm{ps}$) and the dependence obtained for state filling alone assuming a Poisson distribution of carrier populations (dashed-dotted line). In the same plot, we also show the dependence of the measured long-term values of $\Delta {\alpha }_{1S}∕{\alpha }_{0,1S}$ $(t=325\mathrm{ps})$ as a function of $⟨N⟩$ (open squares); see text for details. Solid lines in the main frame are calculations for the cubic scaling; traces calculated for quadratic and statistical scalings are shown by the dashed and the dashed-dotted lines, respectively.Reuse & Permissions

Figure 6

(Color online) (a) NC average population dynamics extracted from $1S$ bleach time transients measured for CdSe NCs with $R=1.7\mathrm{nm}$ (symbols) for different pump fluences ($100\mathrm{fs}$, $3\mathrm{eV}$ pulses) that correspond to $⟨N_0⟩=0.073$, 3.3, 0.8, and 2.2. Solid lines are calculations assuming quadratic scaling of ${\tau }_N$ $({\tau }_2=20\mathrm{ps})$; the transient measured for $⟨N_0⟩=2.2$ is also compared to calculations for cubic (dashed line) and statistical (dashed-dotted line) scalings. The inset on the right is the expanded view of early-time dynamics measured for $⟨N_0⟩=2.2$ in comparison to calculations (line styles are the same as in the main frame). The inset on the left is the pump-intensity dependence of the $1S$ bleach (symbols) in comparison to a fit using the phenomenological dependence given in Eq. (4) with $k_1=0.67$ and $k_2=1.13$ (line).Reuse & Permissions

Figure 7

(Color online) (a) $1S$ bleach dynamics measured for PbSe NCs with $R=4\mathrm{nm}$ (symbols) for different pump fluences ($50\mathrm{fs}$, $1.5\mathrm{eV}$ pulses) that correspond to $⟨N_0⟩=⟨N(t=0)⟩=0.35$, 1.1, 2, 2.9, 4, and 5.1 (increasing from bottom to top); lines are calculations assuming statistical scaling of ${\tau }_N$ $({\tau }_2=160\mathrm{ps})$. Inset: biexciton (circles) and triexciton (diamonds) dynamics extracted from TA traces in comparison to single-exciton dynamics (squares). [(b) and (c)] $1S$ bleach dynamics for PbSe NCs with $R=4\mathrm{nm}$ and $2\mathrm{nm}$ (initial average NC occupancies are 4 and 2, respectively) modeled assuming statistical (solid line), cubic (dashed line), or quadratic (dashed-dotted line) scalings of ${\tau }_N$. The inset in pl (b) is the expanded view of early-time dynamics, which indicates that in the case of the $4\mathrm{nm}$ sample, statistical scaling provides a better fit of experimental data than cubic scaling. The expanded view of early-time dynamics for the $2\mathrm{nm}$ sample [inset in pl (c)] shows that both cubic and statistical scalings describe experimental data better than the quadratic one. On the other hand, based on these data it is difficult to further distinguish between the statistical and the cubic scalings.Reuse & Permissions

Figure 8

(Color online) (a) $1S$ bleach dynamics for PbSe NCs with $R=4.2\mathrm{nm}$ (symbols) measured at low pump intensity $(⟨N_{\mathit{ph},0}⟩=0.1)$ and different photon energies from 2.4 to $7.8E_g$ (indicated in the figure). These measured traces are modeled (lines) using initial average multiplicities 1, 2.2, 3, 5, and 7 (from bottom to top) and assuming statistical scaling of ${\tau }_N$ time constants. The biexciton lifetime is derived from a single-exponential fit of the initial fast TA decay $({\tau }_f=260\mathrm{ps})$ measured with $3.9E_g$ photons $(⟨N_{\mathit{ph},0}⟩=0.1)$, for which CM is expected to primarily produce biexcitons (inset; solid circles); the fit of the TA trace measured using high-intensity $(⟨N_{\mathit{ph},0}⟩=1.1)$, low-photon-energy $\left(2.4E_g\right)$ excitation produces a fast decay component with a time constant of $200\mathrm{ps}$ (inset; open squares). [(b) and (c)] $1S$ TA dynamics (symbols) measured with $6.7E_g$ and $7.8E_g$ photons modeled using either cubic (dashed line) or statistical (solid line) scaling of Auger lifetimes.Reuse & Permissions