Figure 1

(a) II and (b) AR processes. Electrons (filled red circles), holes (empty red circles), conduction band (labeled C) and valence band (labeled V). (c) Immediately following high photon-energy excitation ($\hslash \omega /E_g>3$ in our measurements), highly excited excitons form in some NCs. A fraction of these ($n_{xx}$) undergo II to create biexcitons, while others simply cool to the band edge, remaining as single excitons ($n_x$). Biexcitons that form via II next undergo AR to produce a single exciton at long time. (d) Representative time-resolved data in which carrier populations are monitored in the pump intensity regime of $N_{e\mathrm{\text{−}}h}<1$ for low (red line) and high (blue line) pump photon energy (here below or above $3E_g$, respectively). The fast relaxation component in the blue trace is due to AR of biexcitons that have been generated via II. Its amplitude provides a direct measure of II efficiency: ${\eta }_{ii}=n_{xx}/(n_x+n_{xx})=(A-B)/B$.Reuse & Permissions

Figure 2

(a) Photoexcitation at 1.55 eV produces a change of absorption ($\Delta \alpha$) at the $A_1$ absorption maximum (here 0.86 eV) that is linear up to $N_{e\mathrm{\text{−}}h}\approx 3$. (b) Carrier relaxation dynamics monitored at the $A_1$ absorption feature (0.86 eV) using 1.55 eV photoexcitation, for which II cannot occur. At $N_{e\mathrm{\text{−}}h}=0.6$ (red line), primarily slow relaxation dynamics are observed. At $N_{e\mathrm{\text{−}}h}=1.6$ (black line), $\Delta \alpha$ becomes larger and a fast relaxation component becomes well pronounced; this component (shown in the inset after isolation from the slow component [9]) corresponds to rapid AR of biexcitons. (c) The lifetime of the fast relaxation component depends linearly upon the NC volume (red squares), which is indicative of AR of biexcitons. (d) A TA trace recorded with $N_{e\mathrm{\text{−}}h}=0.25$ using 3.10 eV pump photon energy (blue line), for which II is possible, shows a fast, “biexcitonic” relaxation component when monitoring the $A_1$ absorption feature. The extracted fast component (inset) is nearly identical to the inset shown in (b). For comparison, a trace of single exciton relaxation dynamics recorded using 1.55 eV photoexcitation with $N_{e\mathrm{\text{−}}h}=0.6$ has been replotted from (a) (red line). The NC-volume dependence of the relaxation constant of the fast component, observed in the II regime [blue circles in (c)] closely agrees with the biexciton lifetimes measured using 1.55 eV excitation [red squares in (c)].Reuse & Permissions

Figure 3

(a)–(c) The $A_1$ feature relaxation dynamics, normalized at long time delay, measured for PbSe NCs having three different values of $E_g$ are shown using photoexcitation at 3.10 (blue lines) and 1.55 eV (red lines) with $N_{e\mathrm{\text{−}}h}<0.5$. These studies show that II efficiency is dependent upon the photogenerated exciton excess energy. The inset in (b) shows the measurable buildup of the TA signal for 3.10 eV excitation (blue line) and an autocorrelation of the pump pulse (black line). (d) II efficiencies as a function of pump photon energy are compared for two cases: (1) the pump photon energy is fixed and the $E_g$ of the NCs is changed (black squares); (2) $E_g$ is fixed and the pump photon energy is changed (red circles). (e) For a fixed NC energy gap ($E_g=0.94\mathrm{eV}$), a tunable pump laser source was used to vary the pump photon energy and the efficiency of II was measured. All traces are normalized at long delay.Reuse & Permissions

Figure 4

Calculated power conversion efficiencies of single stage solar cells as a function of material $E_g$ for different efficiencies and onsets of II. (a) For a $3E_g$ II onset, a 10% increase (to 48.3%) in conversion efficiency is calculated for ${\eta }_{ii}=100\%$ (at $E_g=0.8\mathrm{eV}$) relative to the 43.9% efficiency that can be obtained without II (${\eta }_{ii}=0\%$). (b) The power conversion efficiency, shown for different onsets of II for ${\eta }_{ii}=100\%$, can increase conversion efficiency by 37% (to 60.3%), if the onset is decreased to $2E_g$.Reuse & Permissions