Abstract
Understanding multipleexciton generation (MEG) in quantum dots (QDs) requires indepth measurements of transient exciton dynamics. Because MEG typically faces competing ultrafast energyloss intraband relaxation, it is of central importance to investigate the emerging timescale of the MEG kinetics. Here, we present ultrafast spectroscopic measurements of the MEG in PbS QDs via probing the groundstate biexciton transients. Specifically, we directly compare the biexciton spectra with the singleexciton ones before and after the intraband relaxation. Early emergence of MEG is evidenced by observing transient Stark shift and quasiinstantaneous linewidth broadening, both of which take place before the intraband relaxation. Photondensitydependent study shows that the broadened biexciton linewidth strongly depends on the MEGinduced extraexciton generation. Long after the intraband relaxation, the biexciton broadening is small and the singleexciton state filling is dominant.
Introduction
The limiting factor for improving solarcell efficiency lies in the simple physics that singlephoton absorption generates one electronhole pair^{1}. The possibility of generating multiple charge carriers per photon, known as carrier multiplication (CM) or multiple exciton generation (MEG), is of crucial importance for developing efficient solarcell devices^{2,3,4,5,6,7,8}. Semiconductor quantum dots (QDs) represent welldefined structures to explore the quantum limit of harnessing solarconversion efficiency^{9,10,11,12,13}. By engineering the sizes of QD composites, it has been demonstrated that not only the optical properties^{14,15}, but also the MEG efficiency in QDs can be modified^{16}. MEG in a photoexcited QD system is a prominent route for enhancing the conversion efficiency because carriers confined in spatial dimensions that are smaller than the bulk exciton Bohr radius lead to the formation of discrete excitonic states such that efficient MEG is possible either by suppressing the ultrafast electronphonon relaxation^{4,17,18} or by enhancing the Coulomb interactions via reduced dielectric screening at the QD surface^{19}.
Numerous investigations have shown that the kinetic origin of MEG dynamics in QDs is intrinsically complex because the photogenerated single exciton initially suffers from extremely fast intraband relaxation^{20,21,22}, whose interaction timescale is typically in the range of a few ps^{6}. To enhance the MEG efficiency, it is desirable to circumvent the ultrafast energyloss intraband process^{23,24}. Recent studies suggest that the MEG is an instantaneous phenomenon occurring before the intraband energy relaxation^{25} via virtual single excitonic^{26} or biexcitonic optical transition^{27} or coherent superposition among multiexciton states^{12}. Other investigation suggests that the intraband relaxation rate competes with the MEG formation rate^{6}.
The above mentioned photophysical complexity of MEG is largely due to the nature of intrinsic multiparticle (or multiexciton) interaction^{28}. When more than two excitons are created under highenergy excitation condition, the lowest lying energy state is not the single exciton; the mutual interaction between two excitons results in the formation of a Coulombcorrelated two excitonic state, called biexciton^{29,30,31,32,33}. The biexciton is energetically more stable than the single exciton such that it exists below the singleexciton state^{32,34}. Recent studies have reported that the final biexciton density strongly influences the solarconversion efficiency^{25,26,35}. Although it is important to study the impact of the MEG on the transient biexciton spectra, no experimental investigations have been provided to compare the MEGinduced biexciton dynamics with the intraband relaxation dynamics.
The key experimental observation in this study is that the opticallyinduced MEG is an extremely fast process, arising before the intraband relaxation. By exploring the lowest observable biexciton dynamics, we directly measure that the biexciton bleaching comes from early emergence of the photoinduced MEG, in which the effect of extraexciton generation is manifested by the increased broadening of the biexciton linewidth via multiexciton interaction. Note that, in contrast to the conventional singleexciton MEG spectroscopy^{11,36,37,38,39}, our ultrafast timeresolved experiments were performed both in the MEG and in the nonMEG regimes via photonenergy and densitycontrolled measurements on the single and biexciton spectra.
Results
Singleexciton 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 pumpprobe measurements (See method for the detailed description of sample preparation and ultrafast spectroscopy). The lowest singleexciton bandgap energy E_{x} is identified as 0.93 ± 0.01 eV, and the groundstate biexciton energy E_{xx} is estimated to be 0.87 ± 0.03 eV^{30,31,32,33}.
Before the discussion on the biexciton dynamic, it is instructive to present detailed measurements on the intraband relaxation dynamics because the linewidth broadening of single excitons and biexcitons is necessary related to the competing relaxation rate between the MEG and the intraband dynamics, in which the time scale of the intraband 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 pumpphoton energy E_{pump} with 1.55 eV and 3.10 eV, and the average number of initially photogenerated excitons per QD 〈N_{0}〉, 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 intraband relaxation rate, we measured the E_{x} dynamics in a short Δt range between −1 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 pumpprobe delay Δt = 1 ps for 1.66E_{x} excitation (nonMEG regime) and Δt = 2 ps for 3.3E_{x} excitation (MEG regime). This 2 ps time constant is consistent with prior experimental studies of hotcarrier 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} ( = 1.66E_{x}). The observed steplike signals with a small A/B ratio (amplitude ratio of the early to late pumpprobe delay Δt) 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} ( = 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 Δt (denoted by B in Fig. 2c and d) provides a scaling factor for calculating the exciton multiplicity 〈N_{x}〉 = A/B, where A is the amplitude of singleexciton population immediately after pump excitation (denoted by A in Fig. 2c and d). By comparing the measured A/B ratios in the limit of 〈N_{0}〉 → 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 Δt with controlled excitations from 〈N_{0}〉 = 0.22 to 〈N_{0}〉 = 2.2. Immediately after pump excitation, the photoinduced absorption (PA) exhibits rapid bleaching at E_{xx} within the first Δt = 400 fs with a much larger PA peak for the 3.3E_{x} pump than the 1.66E_{x} pump. While both signals decay nonexponentially, 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 Δt = 2 ps.
In a strong quantumconfinement regime, the pumpcreated 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 photogenerated 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 carrierinduced Stark shift and by the absorption linewidth Γ that leads to a broader feature^{46,47}. As discussed later, this broadened Γ directly determines the effect of MEG on the biexciton dynamics through extraexciton generation.
It is expected that high E_{pump} excitation, larger than E_{x}, enhances the Γ broadening due to the extraexciton generation. Immediately after the pump (Δt = 400 fs), we clearly observe that the biexciton Γ is broader for the 3.3E_{x} excitation case than for the 1.66E_{x} one, as shown in Figs. 3d and e with two different excitations of 〈N_{0}〉 for each E_{pump} excitation. Thus, the observed transient PA dynamics can be understood by combined effects of both the carrierinduced transient Stark shift and the MEGinduced biexciton Γ broadening. We additionally notice that the spectrallyintegrated areas of the broadened biexciton absorption remain the same regardless of 〈N_{0}〉 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 excitonexciton collisioninduced broadening rather than the phasespace filling argument^{46}.
Quantitative analysis of the MEGinduced biexciton broadening and the early emergence of MEG
The entire pumpinduced 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, Δ_{XX} is the biexciton binding energy, and μ_{X} and μ_{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 groundstate E_{xx}. For the PA dynamics measured at Δt = 400 fs (Figs. 3d and e), because the intraband relaxation time (2 ps) is longer than Δt of 400 fs, the absorption change measured at E_{x} was not induced by the singleexciton state filling. In addition, Auger recombination and impact ionization (Auger processes) can be neglected because the timescale of Auger processes is much slower (100 ~ 200 ps) than the intraband relaxation. On the other hand, the difference in Γ, obtained from a fit of equation (1) to the measured PA spectra, shows that the broadening is associated with the MEGinduced biexciton broadening.
For quantitative analysis, the biexciton Γ is plotted as a function of the average number of total excitons per QD 〈N_{x}〉, and the results are displayed in Fig. 3g. Here, we note that the definition of 〈N_{x}〉 (obtained from the measured A/B ratios in Fig. 2c) differs from that of 〈N_{0}〉 in a sense that 〈N_{x}〉 includes both the average number of initially photogenerated excitons and the MEGinduced excitons per QD; 〈N_{0}〉 is the average number of photogenerated exciton per QD^{11}. In other words, the biexciton broadening is directly related to the total number of excitons 〈N_{x}〉, not by the initial exciton occupancy 〈N_{0}〉. By plotting the Γ as a function of 〈N_{x}〉, we obtain a linear relationship of where γ ( = 6.8 meV per exciton) is the Γ broadening parameter per exciton. Because Γ(0) represents the linewidth broadening in the absence of photogenerated 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 ± 5 meV, well corroborated with the fitted Γ(0) = 98 meV of the biexciton broadening. The characteristic broadening of Γ with increasing 〈N_{x}〉 entails the effect of MEG, i.e. as more excitons are injected, more broaden feature of biexciton Γ is expected.
Discussion
The early emergence of the MEG is substantiated by measuring the single and biexciton spectra before/after the intraband relaxation of 2 ps. It is expected that Γ should be large if Δt is shorter than the intraband relaxation time, i.e. if the MEGinduces excitonexciton scattering occurs earlier than the intraband relaxation, Γ before the intraband relaxation is larger than Γ after intraband relaxation. Figures 4 (a) and (b) show the PA signals at Δt = 1 ps. As expected, the Γ broadening at Δt = 1 ps is smaller than at Δt = 400 fs, but larger than at Δt = 2 ps. Figures 4c and d show the spectra at Δt = 2 ps for the 1.66E_{x} pump and for the 3.3E_{x} pump, respectively. The Γ at 2 ps for 3.3E_{x} with 〈N_{0}〉 = 2.2 is 110 meV while the Γ at Δt = 400 fs with same condition is 123 meV. Indeed, we clearly see that Γ at Δt = 2 ps is smaller than that of before intraband relaxation both for the two 〈N_{0}〉 excitations (see Fig. 3e and Figs. 4b and d).
Long after the intraband relaxation finishes, the carrierinduced Stark shift becomes weak, and the singleexciton 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 singleexciton 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 intraband relaxation) are distinguishable in comparing the MEGinduced biexciton lineshape and the singleexcitondominated one. There is a possibility that significant reshaping of singleexciton spectra can be observed at longer Δt, which may occur when as many as 50% of QDs are occupied by multiple electronhole pairs (i.e. 〈N_{0}〉 < 1). This scenario can be excluded in our investigation because the PA peaks at Δt = 2 ps show negligible energy shifts^{48} even when 〈N_{0}〉 > 1.
To investigate the effect of Auger and singleexciton recombination on Γ, we compare the PA spectra at Δt of 10 ps and 500 ps. We noted that the singleexciton 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” singleexciton recombination (referred to as excitonic background^{6}). Figures 4e and f display the PA spectra at Δt = 10 ps. Because the Auger recombination is not completed, Γ at Δt = 10 ps is smaller than Γ at Δt = 2 ps. After the Auger recombination is finished, 〈N_{x}〉 at Δt = 500 ps approaches one both for the 1.66E_{x} and 3.3E_{x} pump cases. Because nearly one exciton is left at Δt = 500 ps, Γ for both E_{pump} (Figs. 4g and h) is identical with Γ of 100 meV, representing negligible effect of singleexciton recombination on Γ.
The measured data are summarized in Fig. 4j. Two main aspects are addressed. First, Γ at Δt = 400 fs is the largest compared to the Γ at Δt > 400 fs, providing an evidence for the large biexciton Γ broadening in early Δt. Second, by observing the fact that the decreasing slope of Γ with Δt for 3.33E_{x} excitation is steeper than the 1.66E_{x} excitation up to Δt = 2 ps, we can find that the effect of MEG on Γ is strongly influenced by extraexciton generation before the intraband relaxation.
To conclude, we have investigated the transient dynamics of biexciton, located below the singleexciton 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 intraband relaxation time. We additionally have presented quantitative analysis that the broadening parameter Γ per exciton increases linearly with increasing the total number of excitons. For detailed timeresolved spectral analysis, the PA spectra are compared with singleexciton ones at Δt = 400 fs and longer delays. The comparison underscores that Γ broadening before Δt = 2 ps is larger than the Γ after Δt = 2 ps, corroborating that the MEG indeed occurs before the intraband 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 airfree 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 1octadecene (ODE) are placed in a flask and heated to 100°C under vacuum, and then nitrogen was introduced. The temperature was controlled to the appropriate injection temperature (100 to 150°C) 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 3mm cell contained in the toluene liquid with two opticallytransparent MgO windows, and the samples are actively stirred using a magnetic stirrer to ensure that photocharging does not occur during the measurements (Fig. 1b)^{50}. Using a 250 kHz Tisapphire 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 photodynamics. 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 wavelengthtunable optical parametric amplifier (Coherent OPA 9850).
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Acknowledgements
The work at Yonsei was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF20110013255, NRF2011220D00052, NRF20110028594, NRF20090083512, NRF2012R1A1A2043180) and the LG Display Academic Industrial Cooperation Program. S. C. Lim and Y. H. Lee at SKKU are grateful for the support by Institute for Basic Science (grant number EM 1304).
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Affiliations
School of Electrical and Electronic Engineering, Yonsei University, Seoul 120749, Republic of Korea
 Younghwan Choi
 , Sangwan Sim
 & Hyunyong Choi
IBS Center for Integrated Nanostructure Physics, Institute for Basic Science (IBS), Daejon 305701, Republic of Korea
 Seong Chu Lim
 & Young Hee Lee
Department of Energy Science, Sungkyunkwan University, Suwon, 440746, Republic of Korea
 Seong Chu Lim
 & Young Hee Lee
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Contributions
H.C. and Y.H.L. developed the original experimental ideas. Y.C. and S.S. performed the ultrafast pumpprobe measurements. Y.C. and S.C.L. prepared the colloidal QD samples and analyzed the data. The manuscript was written through contributions of all authors.
Competing interests
The authors declare no competing financial interests.
Corresponding authors
Correspondence to Young Hee Lee or Hyunyong Choi.
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Nature Physics (2015)
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