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Ultrafast biexciton spectroscopy in semiconductor quantum dots: evidence for early emergence of multiple-exciton generation

Understanding multiple-exciton generation (MEG) in quantum dots (QDs) requires in-depth measurements of transient exciton dynamics. Because MEG typically faces competing ultrafast energy-loss intra-band relaxation, it is of central importance to investigate the emerging time-scale of the MEG kinetics. Here, we present ultrafast spectroscopic measurements of the MEG in PbS QDs via probing the ground-state biexciton transients. Specifically, we directly compare the biexciton spectra with the single-exciton ones before and after the intra-band relaxation. Early emergence of MEG is evidenced by observing transient Stark shift and quasi-instantaneous linewidth broadening, both of which take place before the intra-band relaxation. Photon-density-dependent study shows that the broadened biexciton linewidth strongly depends on the MEG-induced extra-exciton generation. Long after the intra-band relaxation, the biexciton broadening is small and the single-exciton state filling is dominant.

The key experimental observation in this study is that the optically-induced MEG is an extremely fast process, arising before the intra-band relaxation. By exploring the lowest observable biexciton dynamics, we directly measure that the biexciton bleaching comes from early emergence of the photo-induced MEG, in which the effect of extra-exciton generation is manifested by the increased broadening of the biexciton linewidth via multi-exciton interaction. Note that, in contrast to the conventional single-exciton MEG spectroscopy 11,[36][37][38][39] , our ultrafast time-resolved experiments were performed both in the MEG and in the non-MEG regimes via photon-energy and density-controlled measurements on the single-and biexciton spectra.

Results
Single-exciton MEG dynamics. Figure 1a shows data for the broadband optical absorption of the colloidal semiconductor PbS QDs and Fig. 1b shows a schematic for the ultrafast pump-probe measurements (See method for the detailed description of sample preparation and ultrafast spectroscopy). The lowest single-exciton bandgap energy E x is identified as 0.93 6 0.01 eV, and the ground-state biexciton energy E xx is estimated to be 0.87 6 0.03 eV [30][31][32][33] .
Before the discussion on the biexciton dynamic, it is instructive to present detailed measurements on the intra-band relaxation dynamics because the linewidth broadening of single excitons and biexcitons is necessary related to the competing relaxation rate between the MEG and the intra-band dynamics, in which the time scale of the intra-band relaxation is typically a few ps 16,40,41 , comparable with the MEG time scale. In the experiment, the colloidal semiconductor PbS QD sample was pumped by two different pump-photon energy E pump with 1.55 eV and 3.10 eV, and the average number of initially photo-generated excitons per QD AEN 0 ae, or initial exciton occupancy, was controlled from 0.1 to 2.2 to investigate the photon densitydependent E x dynamics.
In order to determine the intra-band relaxation rate, we measured the E x dynamics in a short Dt range between 21 ps and 7 ps as shown in Figs. 2a and b. By examining the rising edge of the E x peak, we show that the relaxation process is completed at pump-probe delay Dt 5 1 ps for 1.66E x excitation (non-MEG regime) and Dt 5 2 ps for 3.3E x excitation (MEG regime). This 2 ps time constant is consistent with prior experimental studies of hot-carrier MEG dynamics in PbS quantum dots, where the reported value of intraband relaxation is in the range of 2-2.5 ps 16,40,41 . Figure 2c shows the E x transients excited by low E pump (5 1.66E x ). The observed step-like signals with a small A/B ratio (amplitude ratio of the early to late pump-probe delay Dt) are not attributed to the MEG transients, because the MEG typically requires E pump greater than a few E x . When the QDs are excited by high E pump (5 3.3E x ), we observed fast (90 ps) and slow decay (,100 ns) components with a large A/B ratio, as depicted in Fig. 2d. The experimentally determined A/B ratio of the QD occupancy was modelled via Poisson statistics (Fig. 2e) 42 . Since multiple excitons generated by the MEG decay via Auger recombination, the amplitude at long Dt (denoted by B in Fig. 2c and d) provides a scaling factor for calculating the exciton multiplicity AEN x ae 5 A/B, where A is the amplitude of single-exciton population immediately after pump excitation (denoted by A in Fig. 2c and d). By comparing the measured A/B ratios in the limit of AEN 0 ae R 0, a strong indication of the MEG for the 3.3E x pump was identified 43 . As reported previously 16,36,38,40,44 , these observations confirm that the typical MEG dynamics are observable via probing the E x dynamics.
Transient Stark shift and biexciton linewidth broadening. The central issue to address in this paper is to investigate how the biexciton dynamics is influenced by the early formation of MEG. Figures 3a and b display the biexciton transients for the 1.66E x pump and 3.3E x pump as a function of Dt with controlled excitations from AEN 0 ae 5 0.22 to AEN 0 ae 5 2.2. Immediately after pump excitation, the photo-induced absorption (PA) exhibits rapid bleaching at E xx within the first Dt 5 400 fs with a much larger PA peak for the 3.3E x pump than the 1.66E x pump. While both signals decay non-exponentially, the signals pumped by 1.66E x decay to zero after a few ps, and the transients pumped by 3.3E x change their signs from positive to negative near Dt 5 2 ps.
In a strong quantum-confinement regime, the pump-created local electric field induces a large transient shift of absorption, a phenomenon known as transient Stark shift 42,45 . This effect is more considerable with increasing photo-generated carriers, which in turn produces a stronger local field and complicates the ultrafast PA spectra as schematically shown in Fig. 3c. Note that the increased carrier density is reflected both by the carrier-induced Stark shift and by the absorption linewidth C that leads to a broader feature 46,47 . As discussed later, this broadened C directly determines the effect of MEG on the biexciton dynamics through extra-exciton generation.
It is expected that high E pump excitation, larger than E x , enhances the C broadening due to the extra-exciton generation. Immediately after the pump (Dt 5 400 fs), we clearly observe that the biexciton C is broader for the 3.3E x excitation case than for the 1.

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Stark shift and the MEG-induced biexciton C broadening. We additionally notice that the spectrally-integrated areas of the broadened biexciton absorption remain the same regardless of AEN 0 ae as shown Fig. 3f. This constraint indicates that the broadening is determined by the number of excitons, and it ensures that the biexciton PA peak is reduced by the exciton-exciton collision-induced broadening rather than the phase-space filling argument 46 .
Quantitative analysis of the MEG-induced biexciton broadening and the early emergence of MEG. The entire pump-induced changes of the absorption spectra can be faithfully fit via the following thirdorder susceptibility function 31,33 , where E L is the electric field of the pump, D XX is the biexciton binding energy, and m X and m XX are the transition dipole moments from the ground state to E x and to E xx , respectively. The first term represents the bleaching at E x and the second term represents the PA at ground-state E xx . For the PA dynamics measured at Dt 5 400 fs (Figs. 3d and e), because the intra-band relaxation time (2 ps) is longer than Dt of 400 fs, the absorption change measured at E x was not induced by the single-exciton state filling. In addition, Auger recombination and impact ionization (Auger processes) can be neglected because the time-scale of Auger processes is much slower (100 , 200 ps) than the intra-band relaxation. On the other hand, the difference in C, obtained from a fit of equation (1) to the measured PA spectra, shows that the broadening is associated with the MEG-induced biexciton broadening. For quantitative analysis, the biexciton C is plotted as a function of the average number of total excitons per QD AEN x ae, and the results are displayed in Fig. 3g. Here, we note that the definition of AEN x ae (obtained from the measured A/B ratios in Fig. 2c) differs from that of AEN 0 ae in a sense that AEN x ae includes both the average number of initially photo-generated excitons and the MEG-induced excitons per QD; AEN 0 ae is the average number of photo-generated exciton per QD 11 . In other words, the biexciton broadening is directly related  to the total number of excitons AEN x ae, not by the initial exciton occupancy AEN 0 ae. By plotting the C as a function of AEN x ae, we obtain a linear relationship of where c (5 6.8 meV per exciton) is the C broadening parameter per exciton. Because C(0) represents the linewidth broadening in the absence of photo-generated excitons, the value should corresponds to the E x broadening in Fig. 1a. A simple Gaussian fit shows that the E x broadening in Fig. 1a is 100 6 5 meV, well corroborated with the fitted C(0) 5 98 meV of the biexciton broadening. The characteristic broadening of C with increasing AEN x ae entails the effect of MEG, i.e. as more excitons are injected, more broaden feature of biexciton C is expected.

Discussion
The early emergence of the MEG is substantiated by measuring the single-and biexciton spectra before/after the intra-band relaxation of 2 ps. It is expected that C should be large if Dt is shorter than the intra-band relaxation time, i.e. if the MEG-induces exciton-exciton scattering occurs earlier than the intra-band relaxation, C before the intra-band relaxation is larger than C after intra-band relaxation. Figures 4 (a) and (b) show the PA signals at Dt 5 1 ps. As expected, the C broadening at Dt 5 1 ps is smaller than at Dt 5 400 fs, but larger than at Dt 5 2 ps. Figures 4c and d show the spectra at Dt 5 2 ps for the 1.66E x pump and for the 3.3E x pump, respectively. The C at 2 ps for 3.3E x with AEN 0 ae 5 2.2 is 110 meV while the C at Dt 5 400 fs with same condition is 123 meV. Indeed, we clearly see that C at Dt 5 2 ps is smaller than that of before intra-band relaxation both for the two AEN 0 ae excitations (see Fig. 3e and Figs. 4b and d).
Long after the intra-band relaxation finishes, the carrier-induced Stark shift becomes weak, and the single-exciton state filling is dominant (Figs. 4e-h). As schematically shown in Fig. 4i, the weak Stark shift is rendered as the absence of PA signals at 0.85 eV, but the effect is not completely vanished; negative PA peaks appear at 0.97 eV instead of the single-exciton energy of 0.93 eV in Fig. 1a. Because the PA peak is proportional to the generated exciton numbers, the magnitude of bleaching is larger for the case of 3.3E x pump than the 1.66E x pump case. We note that the chosen two E pump (1.66E x and 3.3E x ) set the below and upper limit on the occurrence of MEG such that the observed two dynamics (before and after the intra-band relaxation) are distinguishable in comparing the MEG-induced biexciton lineshape and the single-exciton-dominated one. There is a possibility that significant re-shaping of single-exciton spectra can be observed at longer Dt, which may occur when as many as 50% of QDs are occupied by multiple electron-hole pairs (i.e. AEN 0 ae , 1). This scenario can be excluded in our investigation because the PA peaks at Dt 5 2 ps show negligible energy shifts 48 even when AEN 0 ae . 1.
To investigate the effect of Auger and single-exciton recombination on C, we compare the PA spectra at Dt of 10 ps and 500 ps. We noted that the single-exciton decay dynamics consists of two relaxation components (see Figs. 2c and d): one is ''fast'' Auger recombination (known as biexcitonic relaxation component 6 ) and another is ''slow'' single-exciton recombination (referred to as excitonic background 6 ). Figures 4e and f display the PA spectra at Dt 5 10 ps. Because the Auger recombination is not completed, C at Dt 5 10 ps is smaller than C at Dt 5 2 ps. After the Auger recombination is finished, AEN x ae at Dt 5 500 ps approaches one both for the 1.66E x and 3.3E x pump cases. Because nearly one exciton is left at Dt 5 500 ps, C for both E pump (Figs. 4g and h) is identical with C of 100 meV, representing negligible effect of single-exciton recombination on C.
The measured data are summarized in Fig. 4j. Two main aspects are addressed. First, C at Dt 5 400 fs is the largest compared to the C at Dt . 400 fs, providing an evidence for the large biexciton C broadening in early Dt. Second, by observing the fact that the decreasing slope of C with Dt for 3.33E x excitation is steeper than the 1.66E x excitation up to Dt 5 2 ps, we can find that the effect of MEG on C is strongly influenced by extra-exciton generation before the intraband relaxation.
To conclude, we have investigated the transient dynamics of biexciton, located below the single-exciton energy, and have explored the impact of MEG on the biexciton spectra. Our ultrafast spectroscopy shows that the linewidth broadening of the biexciton spectra provides direct evidence on the early emergence of the MEG compared to the intra-band relaxation time. We additionally have presented quantitative analysis that the broadening parameter C per exciton increases linearly with increasing the total number of excitons. For detailed time-resolved spectral analysis, the PA spectra are compared with single-exciton ones at Dt 5 400 fs and longer delays. The comparison underscores that C broadening before Dt 5 2 ps is larger than the C after Dt 5 2 ps, corroborating that the MEG indeed occurs before the intra-band relaxation.

Methods
Synthesis of PbS quantum dots. Our PbS colloidal quantum dots are capped using eleic acid and dispersed in toluene. The synthesis of the sample followed a procedure that used standard air-free solution based technique 49 . In a typical synthesis, 2.0 mmol of PbO (0.445 g), 8.0 mmol (2.25 g) of oleic acid (OA), and 9.9 mmol (2.5 g) of 1-octadecene (ODE) are placed in a flask and heated to 100uC under vacuum, and then nitrogen was introduced. The temperature was controlled to the appropriate injection temperature (100 to 150uC) to obtain the desired particle size. The sulfur precursor was prepared by mixing bis(trimethylsilyl)sulfide with ODE. Removal of excess ligand was completed by repeated the followings: precipitation in acetone, centrifugation of the particles, and dispersion in toluene.
PbS QDs and ultrafast spectroscopy. The sample used in this experiment is semiconductor colloidal PbS QDs dispersed in toluene with an average diameter of approximately 5.1 nm. The broadband optical absorption is measured by a Fourier transform infrared (FTIR) spectrometer (Bomem DA8). For the ultrafast pumpprobe spectroscopy, the colloidal PbS QDs are maintained in a 3-mm cell contained in the toluene liquid with two optically-transparent MgO windows, and the samples are actively stirred using a magnetic stirrer to ensure that photo-charging does not occur during the measurements (Fig. 1b) 50 . Using a 250 kHz Ti-sapphire regenerative amplifier (Coherent RegA 9050), the samples are excited by 50 fs pulses with a pumpphoton energy E pump of 1.55 eV and its second harmonic E pump of 3.10 eV for investigating the MEG photo-dynamics. A fraction of the amplifier output is used as a probe pulse with photon energy E probe of 0.93 eV for the lowest E x and 0.87 eV for the E xx . Both probe pulses are delivered from wavelength-tunable optical parametric amplifier (Coherent OPA 9850).