Ultrafast intraband Auger process in self-doped colloidal quantum dots

Abstract

•Self-doped β-HgS QDs, a platform to monitor the electron dynamics only•The intraband Auger process occurring in the conduction band•Mechanism of electron relaxation processes in n-type self-doped β-HgS CQDs Excess charge accumulation in quantum dots is unavoidable when running electronic devices. Since it is an instant phenomenon happening randomly, there have not been many systematic approaches to investigate it. Also, the excess charge-accumulated state is an adequate model for exploration of higher quantum states. n-Type self-doped quantum dots provide an excellent platform from which to study the electron-accumulated state in the conduction band. In combination with femtosecond mid-infrared spectroscopy, we were able to selectively photoexcite the excess electrons in the lowest energy state of the conduction band and monitor the electron dynamics that have never been directly and experimentally measured. In particular, ultrafast electron dynamics are revealed by this method such as the intraband Auger process, helping us to comprehend the blinking of single quantum dots, disproportionate charging in light-emitting diodes, and hot electron dynamics in higher quantum states coupled to surface states of colloidal quantum dots. Investigating the separate dynamics of electrons and holes has been challenging, although it is critical for the fundamental understanding of semiconducting nanomaterials. n-Type self-doped colloidal quantum dots (CQDs) with excess electrons occupying the low-lying state in the conduction band (CB) have attracted a great deal of attention because of not only their potential applications to infrared optoelectronics but also their intrinsic system that offers a platform for investigating electron dynamics without elusive contributions from holes in the valence band. Here, we show an unprecedented ultrafast intraband Auger process, electron relaxation between spin-orbit coupling states, and exciton-to-ligand vibrational energy transfer process that all occur exclusively in the CB of the self-doped β-HgS CQDs. The electron dynamics obtained by femtosecond mid-infrared spectroscopy will pave the way for further understanding of the blinking phenomenon, disproportionate charging in light-emitting diodes, and hot electron dynamics in higher quantum states coupled to surface states of CQDs. Investigating the separate dynamics of electrons and holes has been challenging, although it is critical for the fundamental understanding of semiconducting nanomaterials. n-Type self-doped colloidal quantum dots (CQDs) with excess electrons occupying the low-lying state in the conduction band (CB) have attracted a great deal of attention because of not only their potential applications to infrared optoelectronics but also their intrinsic system that offers a platform for investigating electron dynamics without elusive contributions from holes in the valence band. Here, we show an unprecedented ultrafast intraband Auger process, electron relaxation between spin-orbit coupling states, and exciton-to-ligand vibrational energy transfer process that all occur exclusively in the CB of the self-doped β-HgS CQDs. The electron dynamics obtained by femtosecond mid-infrared spectroscopy will pave the way for further understanding of the blinking phenomenon, disproportionate charging in light-emitting diodes, and hot electron dynamics in higher quantum states coupled to surface states of CQDs. High-energy electron dynamics (e.g., Auger recombination and hot electron process), blinking phenomenon, charge trapping, multi-exciton generation, trion formation, and unbalanced charge injection are of great interest in the colloidal quantum dot (CQD) research field.1Pan J.L. Reduction of the Auger rate in semiconductor quantum dots.Phys. Rev. B Condens. Matter Mater. Phys. 1992; 46: 3977-3998Crossref Scopus (21) Google Scholar, 2Park Y.S. Bae W.K. Pietryga J.M. Klimov V.I. Auger recombination of biexcitons and negative and positive trions in individual quantum dots.ACS Nano. 2014; 8: 7288-7296Crossref PubMed Scopus (179) Google Scholar, 3Pandey A. Guyot-Sionnest P. 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Reversible charging of CdSe nanocrystals in a simple solid-state device.Adv. Mater. 2002; 14: 1068-1071Crossref Scopus (73) Google Scholar, 14Anikeeva P.O. Halpert J.E. Bawendi M.G. Bulović V. Electroluminescence from a mixed Red−Green−Blue colloidal quantum dot monolayer.Nano Lett. 2007; 7: 2196-2200Crossref PubMed Scopus (386) Google Scholar Therefore, understanding how charge carriers move through discrete energy states in the CB and exploiting each carrier relaxation pathway are essential to addressing the aforementioned challenging problems and developing novel CQDs for various applications.10Chattarji D. The Theory of Auger Transitions. Academic Press, 1976Google Scholar, 11Alivisatos A.P. Semiconductor clusters, nanocrystals, and quantum dots.Science. 1996; 271: 933-937Crossref Scopus (10568) Google Scholar, 12Efros A.L. Kharchenko V.A. Rosen M. 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Direct measurement of auger electrons emitted from a semiconductor light-emitting diode under electrical injection: identification of the dominant mechanism for efficiency droop.Phys. Rev. Lett. 2013; 110: 177406Crossref PubMed Scopus (513) Google Scholar, 18Chen H.Y. Chen T.Y. Son D.H. Measurement of energy transfer time in colloidal Mn-doped semiconductor nanocrystals.J. Phys. Chem. C. 2010; 114: 4418-4423Crossref Scopus (58) Google Scholar, 19Hendry E. Koeberg M. Wang F. Zhang H. De Mello Donegá C. Vanmaekelbergh D. Bonn M. Direct observation of electron-to-hole energy transfer in CdSe quantum dots.Phys. Rev. Lett. 2006; 96: 057408Crossref PubMed Scopus (196) Google Scholar For intrinsic CQDs with empty CB states, interband photoexcitation is indispensable for a detailed investigation of electron dynamics in the CB, which inevitably creates a hole in the valence band (VB). Due to the differences in energy gaps between neighboring states in each band and the characteristic effective masses, a hole in the VB and an electron in the CB exhibit different dynamics.1Pan J.L. Reduction of the Auger rate in semiconductor quantum dots.Phys. Rev. B Condens. Matter Mater. Phys. 1992; 46: 3977-3998Crossref Scopus (21) Google Scholar,10Chattarji D. The Theory of Auger Transitions. Academic Press, 1976Google Scholar,12Efros A.L. Kharchenko V.A. Rosen M. Breaking the phonon bottleneck in nanometer quantum dots: role of Auger-like processes.Solid State Commun. 1995; 93: 281-284Crossref Scopus (383) Google Scholar Furthermore, the quantum confinement in CQDs enhances the interaction between the electron and hole, which leads to the interband Auger recombination. Consequently, the hole dynamics in the VB unavoidably affect the electron dynamics in the CB and vice versa. Often, hole dynamics in the VB are fast and dominate the charge-carrier relaxation processes,19Hendry E. Koeberg M. Wang F. Zhang H. De Mello Donegá C. Vanmaekelbergh D. Bonn M. Direct observation of electron-to-hole energy transfer in CdSe quantum dots.Phys. Rev. Lett. 2006; 96: 057408Crossref PubMed Scopus (196) Google Scholar,20Guyot-Sionnest P. Shim M. Matranga C. Hines M. Intraband relaxation in CdSe quantum dots.Phys. Rev. B Condens. Matter Mater. Phys. 1999; 60: R2181-R2184Crossref Scopus (347) Google Scholar which hampers the selective study of state-to-state transition, electron-electron collision, and electron-phonon dissipation of electrons in the CB. Recently, n-type self-doped CQD systems were found to be of use for studying such electron dynamics in the CB without interband photoexcitation. Two electrons occupy the lowest energy state of the CB (1Se) via the non-stoichiometry of the material and the surface dipole moment.21Kim J. Choi D. Jeong K.S. Self-doped colloidal semiconductor nanocrystals with intraband transitions in steady state.Chem. Commun. (Camb.). 2018; 54: 8435-8445Crossref PubMed Google Scholar, 22Jeong K.S. Deng Z. Keuleyan S. Liu H. Guyot-Sionnest P. Air-stable n-doped colloidal HgS quantum dots.J. Phys. Chem. Lett. 2014; 5: 1139-1143Crossref PubMed Scopus (87) Google Scholar, 23Park M. Choi D. Choi Y. Shin H.B. Jeong K.S. Mid-infrared intraband transition of metal excess colloidal Ag2Se nanocrystals.ACS Photon. 2018; 5: 1907-1911Crossref Scopus (31) Google Scholar, 24Deng Z. Jeong K.S. Guyot-Sionnest P. Colloidal quantum dots intraband photodetectors.ACS Nano. 2014; 8: 11707-11714Crossref PubMed Scopus (118) Google Scholar, 25Choi D. Park M. Jeong J. Shin H.B. Choi Y.C. Jeong K.S. Multifunctional self-doped nanocrystal thin-film transistor sensors.ACS Appl. Mater. Interfaces. 2019; 11: 7242-7249Crossref PubMed Scopus (8) Google Scholar, 26Jeong J. Yoon B. Kwon Y.W. Choi D. Jeong K.S. Singly and doubly occupied higher quantum states in nanocrystals.Nano Lett. 2017; 17: 1187-1193Crossref PubMed Scopus (27) Google Scholar, 27Yoon B. Jeong J. Jeong K.S. Higher quantum state transitions in colloidal quantum dot with heavy electron doping.J. Phys. Chem. C. 2016; 120: 22062-22068Crossref Scopus (23) Google Scholar Thus, the self-doped CQD system renders the conditions under which to study ultrafast carrier dynamics of electrons in well-defined CB energy states by using mid-infrared (IR) pulses resonant with the transition between the two states, 1Se and 1Pe, in the CB. Here, we present the electron dynamics taking place in the CB of the self-doped β-HgS CQD, using femtosecond mid-IR pump-probe electronic (IR PP) spectroscopy. IR PP spectroscopy with various pump-pulse energy densities reveals not only the dynamics of a hot electron in a one-exciton state but also ultrafast electron-electron dynamics in a biexciton state. Unexpectedly, in addition to inter-sublevel transition (IST) and energy transfer to ligand vibrations, we found direct evidence of a picosecond intraband Auger process (IAP) in CQDs, a new type of Auger process exclusively occurring in the CB.28Melnychuk C. Guyot-Sionnest P. Auger suppression in n-type HgSe colloidal quantum dots.ACS Nano. 2019; 13: 10512-10519Crossref PubMed Scopus (19) Google Scholar These experimental findings along with the result of density functional theory (DFT) calculation for the CB electronic states provide invaluable information for understanding the excited electron dynamics within the CB manifold.25Choi D. Park M. Jeong J. Shin H.B. Choi Y.C. Jeong K.S. Multifunctional self-doped nanocrystal thin-film transistor sensors.ACS Appl. Mater. Interfaces. 2019; 11: 7242-7249Crossref PubMed Scopus (8) Google Scholar Figure 1A is a schematic illustration of the energy levels and electron populations in the CB and VB of the β-HgS CQDs in a steady state. The broad absorption peak at ∼2,650 cm−1 (Figure 1B), which is energetically much lower than the usual band-gap transition, corresponds to the intraband transition from 1Se to 1Pe in the mid-IR frequency range. We found no band-gap absorption peak (1Sh-1Se) at ∼9,700 cm−1, which shows that the 1Se state is fully occupied by two electrons (see Figure S1 for the Fourier transform infrared [FTIR] spectrum). Furthermore, no absorption bands in the low-frequency side of the FTIR spectrum other than the main peak associated with 1Se-1Pe transition indicate that the 1Pe state is empty. The full-width-at-half-maximum values of the intraband transition peaks of β-HgS CQDs passivated with dodecanethiol (DDT) and oleylamine (OLAm) are 1,024 and 1,121 cm−1, respectively. Such broad absorption linewidths can be attributed to the non-degenerate 1Se-1Pe transitions, i.e., 1Se-1Pe3/2 and 1Se-1Pe1/2, where 1Pe3/2 and 1Pe1/2 are the two spin-orbit coupling states, and the shape asymmetry, as well as the size heterogeneity (Figures 1, S2, and S3).29Kovalenko M.V. Manna L. Cabot A. Hens Z. Talapin D.V. Kagan C.R. Klimov V.I. Rogach A.L. Reiss P. Milliron D.J. et al.Prospects of nanoscience with nanocrystals.ACS Nano. 2015; 9: 1012-1057Crossref PubMed Scopus (826) Google Scholar Gaussian fitting analyses of the intraband IR absorption spectra of both β-HgS-DDT and β-HgS-OLAm, show that the energy differences between 1Pe3/2 and 1Pe1/2 states are 313 and 413 cm−1, which are similar to those of HgTe and HgSe CQDs.28Melnychuk C. Guyot-Sionnest P. Auger suppression in n-type HgSe colloidal quantum dots.ACS Nano. 2019; 13: 10512-10519Crossref PubMed Scopus (19) Google Scholar,30Hudson M.H. Chen M. Kamysbayev V. Janke E.M. Lan X. Allan G. Delerue C. Lee B. Guyot-Sionnest P. Talapin D.V. Conduction band fine structure in colloidal HgTe quantum dots.ACS Nano. 2018; 12: 9397-9404Crossref PubMed Scopus (31) Google Scholar The intraband 1Se-1Pe transition frequency of β-HgS CQD is in excellent agreement with the DFT calculations with Perdew-Burke-Ernzerhof (PBE) density functional and projector-augmented-wave (PAW) pseudopotentials (see Data S1; Figures S4 and S5).4Bae W.K. Park Y.S. Lim J. Lee D. Padilha L.A. McDaniel H. et al.Controlling the influence of Auger recombination on the performance of quantum-dot light-emitting diodes.Nat. Commun. 2013; 4: 2661Crossref PubMed Scopus (493) Google Scholar The calculated energies of the three 1Pe states indicate the breaking of degeneracy into three 1Pe states. Their intraband transition energies (1Se-1Pe), 2,524, 2,581, and 2,702 cm−1, are close to the absorption maximum of the IR spectrum. Figure 1E depicts the frontier molecular orbitals (electronic states) of 1Sh in the VB and 1Se and three 1Pe states in the CB that are near the band gap of β-HgS CQDs. The 1Pe states resemble the H-atomic p-orbitals, and the 1Se state appears to be more isotropic and spherically symmetric, much like the H-atomic s-orbital. Interestingly, 1Se, 1Pe, and high-lying states in the CB are substantially delocalized on the surface of β-HgS CQD compared with those in the VB. This characteristic morphology of the CB states turns out to be important because their energies and the relaxation processes of electrons in those states are found to be affected by surface ligands spatially close to these states. To elucidate the mechanism of electronic relaxation processes in the CB, we used femtosecond mid-IR pulses centered at 2,650 cm−1, resonant with the intraband transition (1Se-1Pe), which do not induce any interband (VB-to-CB) transitions. Note that the pump frequency should be at least higher than ∼12,400 cm−1 for such an interband transition. This center frequency of mid-IR pulse was selected to avoid any absorptions by tetrachloroethylene (TCE) solvent or ligand molecules. Figure 2A depicts the time profiles of the normalized IR PP signals of β-HgS-DDT CQDs (see Figure S6 for the whole set of frequency-resolved IR PP signals). The intraband absorption spectrum associated with the 1Se-1Pe transition is much broader than the spectral width (∼250 cm−1) of our femtosecond IR pulse (Figure S3 and Data S2). Therefore, only a subensemble of CQDs was optically selected, and mainly the 1Pe3/2 state was populated by the pump field-CQD interaction, resulting in the negligible frequency dependence of IR PP signals (Figure S7). Since the IR PP signals do not show significant polarization dependence due to the bulky nature of β-HgS CQDs, the isotropic PP signals provide information on the electron population relaxation processes (see Figure S8 for isotropic PP signals at different probe frequencies). With an increase in the excitation energy density from 56 to 747 μJ cm−2, the relaxation rate of electrons in the β-HgS-DDT CQDs becomes faster. It converges to a constant (Figure 2A) when the pump energy density is higher than 378 μJ cm−2. We first carried out multi-exponential fitting analyses of the isotropic PP signals of β-HgS-DDT CQDs to identify the time scales of involved electronic relaxation processes in the CB (solid lines in Figure 2A). We found that at least three exponentially decaying components are needed to fit the decay of the PP signal (Figures 2A and S9), indicating that at least three distinguishable electronic relaxation pathways should be taken into consideration to establish the kinetic scheme for the electronic population relaxation mechanism. First of all, we could rule out the possibility that these relaxations originate from radiative recombination processes. In the case of our β-HgS CQDs, the radiative recombination rate can be approximately estimated by using the following equation (in cgs unit),kR=TR−1=(3ϵmϵHgS+2ϵm)22e2ω1Se1Pe2fn3m0c2,(Equation 1) where ϵHgS and ϵm are the relative permittivity of β-HgS and that of the solvent medium, respectively, e is elementary charge, ω1Se1Pe is transition frequency, f is oscillator strength, n is refractive index, m0 is the mass of a free electron, and c is the speed of light. From Equation 1, the calculated radiative recombination lifetime is ∼0.9 μs. Assuming that the quantum yield (QY = kR/(kR + kNR)) is in the range of ∼1.0 × 10−3–10−4 and using the calculated radiative lifetime of ∼0.9 μs, the non-radiative lifetime of the excitons is estimated to be in the range from ∼90 to 900 ps.22Jeong K.S. Deng Z. Keuleyan S. Liu H. Guyot-Sionnest P. Air-stable n-doped colloidal HgS quantum dots.J. Phys. Chem. Lett. 2014; 5: 1139-1143Crossref PubMed Scopus (87) Google Scholar Indeed, the decay constants of the slow component (∼400 ps) is in this range, suggesting that the observed electronic relaxation corresponds to the non-radiative processes. The measured IR PP signals show a clear dependence on the excitation energy density. Figure 2B is the plot of the three exponential decay time constants with respect to the excitation energy density. The fast and intermediate components have decay time constants of around 1 ps (black) and 12 ps (red), respectively, and are not strongly dependent on the pump intensity. On the other hand, the decay constant of the slow component (blue) decreases from ∼400 to ∼250 ps with an increase in the excitation energy density. Since the three exponential decay time constants are fitting parameters not the rate constants associated with different relaxation pathways, they could depend on the excitation energy density. We shall return to this issue later in this paper with a proposed kinetic model and numerical simulation results. The relative amplitudes of these three components also exhibit strong pump power dependences (Figure 2C). They all reach asymptotic values as the excitation energy density increases, indicating saturation of the absorption of the IR pump beam by CQDs with large oscillator strengths. At high pump powers, a significant population of the biexciton state, which results from two-photon absorption by a single nanocrystal, is created. In the saturation regime at an excitation energy density higher than 378 μJ cm−2, the time constants of the three decaying components do not change with excitation energy density (Figure 2B). Figure 2C shows that the fast component with a decay time constant of 1 ps contributes more to the PP signal at high excitation energy densities, which is manifest in the rapidly decaying PP signal upon increasing the excitation energy density (Figure 2A). Our experimental findings that the decay time constant (τfast) of the picosecond component does not depend on the excitation energy density and that the corresponding amplitude (Afast) increases with the pump energy density suggest that this fast component is associated with the IAP of the biexciton state resulting from two-photon absorptions by the two electrons in the 1Se state, which creates two electrons in the 1Pe3/2 state and two holes in the 1Se state (Figure 3A). The Auger recombination process is known to be one of the ultrafast non-radiative relaxation processes of excited electrons through which the excitation energy is transferred to create another exciton. Unlike the cases of the interband excitonic CQD, this IAP in n-type self-doped CQDs has not been observed before, and even its possibility strictly within the CB states has been a matter of doubt or controversy. For undoped CQDs, e.g., CdSe, the ultrafast intraband dynamics was studied by employing a pump-push-probe method.19Hendry E. Koeberg M. Wang F. Zhang H. De Mello Donegá C. Vanmaekelbergh D. Bonn M. Direct observation of electron-to-hole energy transfer in CdSe quantum dots.Phys. Rev. Lett. 2006; 96: 057408Crossref PubMed Scopus (196) Google Scholar,20Guyot-Sionnest P. Shim M. Matranga C. Hines M. Intraband relaxation in CdSe quantum dots.Phys. Rev. B Condens. Matter Mater. Phys. 1999; 60: R2181-R2184Crossref Scopus (347) Google Scholar,31Rabouw F.T. Vaxenburg R. Bakulin A.A. Van Dijk-Moes R.J.A. Bakker H.J. Rodina A. Lifshitz E. Efros A.L. Koenderink A.F. Vanmaekelbergh D. Dynamics of intraband and interband Auger processes in colloidal core-shell quantum dots.ACS Nano. 2015; 9: 10366-10376Crossref PubMed Scopus (40) Google Scholar The optical pumping of electrons from one of the VB states to a CB state, which produces both a hole in the VB and an electron in the CB, had to be proceed before probing the relaxation processes of both particles. The hole in the VB is then involved in the Auger recombination process, whereby the high-energy electron loses its energy and simultaneously a high-energy hole is created in a low-lying VB state, and vice versa. Therefore, in the intrinsic CQD with filled VB states and vacant CB states, such a fast Auger recombination process involving relaxation dynamics of the hole taking place in the VB states makes it complicated to interpret experimental results from the pump-push-probe measurements. In contrast, the relaxation processes of excited electrons in the 1Pe state of our self-doped β-HgS CQDs occur within the CB states only, so that elusive hole dynamics in the VB does not interfere with the observed PP signals that purely reflect electron dynamics in the CB. Quite unexpectedly, the IAP is found to be much faster than the interband Auger process found in various intrinsic CQDs. For example, the scaling coefficient of the intraband biexciton lifetime (p=τBXr3=1 ps(1.6 nm)3) and the intraband Auger coefficients (CA=V2τBX) are 0.24 ps nm−3 and 3.82 × 10–31 cm6 s−1, respectively. Here, r, τBX, and V are the nanocrystal radius, intraband biexciton lifetime, and nanocrystal volume, respectively. These values are approximately one order of magnitude smaller than those reported for the undoped CQDs such as CdSe CQDs (p = 5.5 ps nm−3) and HgTe CQDs (p = 1.9 ps nm−3).20Guyot-Sionnest P. Shim M. Matranga C. Hines M. Intraband relaxation in CdSe quantum dots.Phys. Rev. B Condens. Matter Mater. Phys. 1999; 60: R2181-R2184Crossref Scopus (347) Google Scholar,30Hudson M.H. Chen M. Kamysbayev V. Janke E.M. Lan X. Allan G. Delerue C. Lee B. Guyot-Sionnest P. Talapin D.V. Conduction band fine structure in colloidal HgTe quantum dots.ACS Nano. 2018; 12: 9397-9404Crossref PubMed Scopus (31) Google Scholar, 31Rabouw F.T. Vaxenburg R. Bakulin A.A. Van Dijk-Moes R.J.A. Bakker H.J. Rodina A. Lifshitz E. Efros A.L. Koenderink A.F. Vanmaekelbergh D. Dynamics of intraband and interband Auger processes in colloidal core-shell quantum dots.ACS Nano. 2015; 9: 10366-10376Crossref PubMed Scopus (40) Google Scholar, 32Melnychuk C. Guyot-Sionnest P. Slow Auger relaxation in HgTe colloidal quantum dots.J. Phys. Chem. Lett. 2018; 9: 2208-2211Crossref PubMed Scopus (20) Google Scholar Thus, our experimental observation suggests that a self-doping of the HgS CQDs makes the overall carrier relaxation much faster than in undoped cases, which can be attributed to the higher collision probability of the carriers, both electrons and holes, in the CB states that are surface-delocalized.32Melnychuk C. Guyot-Sionnest P. Slow Auger relaxation in HgTe colloidal quantum dots.J. Phys. Chem. Lett. 2018; 9: 2208-2211Crossref PubMed Scopus (20) Google Scholar Furthermore, the relative amplitude of the IAP component at the lowest excitation energy density of 56 μJ cm−2 is not zero but 0.29 for β-HgS-DDT CQDs, indicating that the population of the biexcitonic CQDs is not negligibly small even at such a low excitation energy density. This is again consistent with the fact that the oscillator strength of the 1Se-1Pe3/2 transition of β-HgS CQD is high.24Deng Z. Jeong K.S. Guyot-Sionnest P. Colloidal quantum dots intraband photodetectors.ACS Nano. 2014; 8: 11707-11714Crossref PubMed Scopus (118) Google Scholar Next, we provide explanations and interpretations of the intermediate and slow components. Because there are no other exciton or phonon modes that can accept the energy of an excited electron in the one-excitonic CQDs, the one-exciton relaxation rate could be slow compared with that of a biexciton. The initial decay of the PP signal in 1 ps results from the filling (or quenching) of the hole in the 1Se state after the 1-ps IAP (Figure 3A). Among a few possible scenarios for the assignments of the intermediate and slow components, we can ignore electron transfers between neighboring CQDs because the average distance between nearest neighboring CQDs is large enough. We found it very useful to adopt the kinetic scheme recently suggested by the Guyot-Sionnest group.28Melnychuk C. Guyot-Sionnest P. Auger suppression in n-type HgSe colloidal quantum dots.ACS Nano. 2019; 13: 10512-10519Crossref PubMed Scopus (19) Google Scholar They studied n-doped HgSe CQDs with time-resolved emission spectroscopy and showed that the IST rate from 1Pe3/2 state to 1Pe1/2 state is approximately 5–30 ps. The slow (>100 ps) component found in their time-dependent emission signals was assigned to the energy transfer from the 1Se-1Pe1/2 exciton-to-ligand vibrational modes. In our cases of β-HgS-DDT CQDs, we also identified two 1Pe states (1Pe3/2 and 1Pe1/2), which results from the spin-orbit coupling. Therefore, the intermediate component (τinter) in the decay of our PP signal can be similarly attributed to the electronic relaxation from the high-lying 1Pe3/2 state to the low-lying 1Pe1/2 state (Figure 3B). Unlike the time-resolved emission spectroscopy, the electron transferred to the low-lying 1Pe1/2 state does not contribute to the PP signal because our probe beam with a center frequency of 2,650 cm−1 is not resonant with the 1Se-1Pe1/2 transition with a frequency of ∼2,250 cm−1. The slow population relaxation of one-exciton states in the range from 250 to 400 ps could be explained in terms of a phonon-bottleneck effect. To further confirm that this slow component is associated with electronic-to-ligand vibrational energy transfer (electronic-to-vibrational energy transfer [EVET], exciton-to-vibrational energy transfer, near-field energy transfer), we carried out the same set of experiments with β-HgS CQDs passivated by amine ligand molecules, OLAm. If this slow component can be attributed to the EVET, its relaxation rate would be dependent on the ligand. Our DFT calculations show that the frontier orbitals (states), both 1Se and 1Pe, are significantly surface-delocalized (Figures 1E and S5), implying that the EVET, unlike IAP and IST, would exhibit a notable dependence on the nature of passivating ligands. The mid-IR PP signals of β-HgS-OLAm CQDs, which exhibit a triexponential decaying pattern, are similar to those of β-HgS-DDT CQDs (Figure 4A). The lengthy aliphatic chain of OLAm makes electron transfers between neighboring nanocrystals inefficient and provides the same solvation environment as that around each β-HgS-DDT CQD. Indeed, the ligand exchange from DDT to OLAm does not make any significant difference in the fast and intermediate components (Figures 4B and 4C; Table S1). Furthermore, the decay time constant of the fast component of β-HgS-OLAm CQDs does not depend on pump energy density either. Its relative amplitude Afast increases with the excitation energy density, where the saturation excitation energy density is around 136 μJ cm−2, significantly lower than that of the β-HgS-DDT at 378 μJ cm−2. This result infers that the carrier density of the β-HgS-OLAm is higher than that of the β-HgS-DDT and is consistent with the previous finding that the second intraband transition (1Pe-1De) is observed only for β-HgS-OLAm.27Yoon B. Jeong J. Jeong K.S. Higher quantum state transitions in colloidal quantum dot with heavy electron doping.J. Phys. Chem. C. 2016; 120: 22062-22068Crossref Scopus (23) Google Scholar In contrast to the fast and intermediate components, the decay time constant of the slow component substantially increases from ∼400 to ∼500 ps, and the relative amplitude decreases from 0.17 to 0.1 for CQDs with OLAm ligands (Figures 4B and 4C; Table S1). In HgS-DDT CQDs, the decay time of the slow component, in contrast, decreases from ∼400 to ∼250 ps as the excitation energy density increases (see the dashed line in Figure 4B). The amplitude fractions of the intermediate and slow components of both CQDs decrease when the excitation pump becomes stronger. However, the slow components for CQDs with OLAm account for more fractions compared with that for HgS-DDT CQDs. These experimental results on the ligand effect support the hypothesis that the slowly decaying component is associated with the relaxation of hot electrons via energy transfer to ligand vibrations. This observation is consistent with the expectation from our DFT calculation results that the interactions of the surface-delocalized 1Pe and high-lying states with ligand molecules can induce the slow EVET process, and the decay rate of IAP-produced electrons in such high-energy states would be highly dependent on the ligand nature and strength of the CQD-ligand interactions. Time-resolved IR PP measurements of two different β-HgS CQDs with varying pump energy densities provided critical information on the time scales and origins of electronic relaxations in the CB (Data S3). However, to extract quantitative data on the state-to-state transition rates, simple multi-exponential fitting analysis is not useful because such an analysis assumes that the fitted exponential components represent completely independent relaxation processes. To shed light on the intricately correlated electronic relaxations in β-HgS CQDs, we need a kinetic model to describe the entire electronic relaxation pathway. Our proposed kinetic scheme involving both the one-exciton and biexciton relaxations is shown in Figure 5. The ground state is denoted as 1Se(2)1Pe(0), where the number in parentheses represents the number of electrons in the corresponding state. The interactions of CQDs with incident IR pump beam can produce either one-exciton state (1Se(1)1Pe3/2(1)) or biexciton state (1Se(0)1Pe3/2(2)). Here, we considered the electronic excitation from 1Se to 1Pe3/2 state only because the center frequency of our IR pump beam is 2,650 cm−1 and also because the oscillator strength associated with the 1Se-1Pe3/2 transition is much higher than that with the 1Se-1Pe1/2 transition at this frequency (Figure 1B). At a low pump power, one-exciton state 1Se(1)1Pe3/2(1) is significantly populated, which will undergo an IST to 1Se(1)1Pe1/2(1) via energy (∼400 cm−1) transfer to QD phonon modes. In our IR PP measurements, the state 1Se(1)1Pe1/2(1) produced by this IST is dark because the IR pump or probe beam is not resonant with the transition between1Pe1/2 and 1Se states. As a consequence, the intermediate state 1Se(1)1Pe1/2(1) contributes to the IR PP signal as ground-state bleaching (GSB) term only. The non-radiative relaxation of the intermediate state 1Se(1)1Pe1/2(1) requires an energy transfer of approximately 2,000 cm−1 to bath degrees of freedom. However, due to the lack of QD phonon modes with such high frequencies, the relaxation from 1Se(1)1Pe1/2(1) to the ground state 1Se(2)1Pe(0) is not efficient, which is known as a phonon-bottleneck effect. However, Melnychuk and Guyot-Sionnest recently showed that the energy transfer to ligand vibrations could occur on a time scale of a few hundred picoseconds.32Melnychuk C. Guyot-Sionnest P. Slow Auger relaxation in HgTe colloidal quantum dots.J. Phys. Chem. Lett. 2018; 9: 2208-2211Crossref PubMed Scopus (20) Google Scholar,33Pandey A. Guyot-Sionnest P. Slow electron cooling in colloidal quantum dots.Science. 2008; 322: 929-932Crossref PubMed Scopus (436) Google Scholar Therefore, we believe that the recovery of the ground state hole via the relaxation from 1Se(1)1Pe3/2(1) or 1Se(1)1Pe1/2(1) to 1Se(2)1Pe(0) is related to the slow component in the IR PP signal caused by the EVET process. We next consider the relaxation of the biexciton state denoted as 1Se(0)1Pe3/2(2). This biexciton state contributes to the IR PP signal as two stimulated emissions and two GSBs. Due to the ultrafast IAP, the intermediate state (1Se(1)1Pe3/2(0)1Xe(1)) is created after ∼1 ps. Here, spatial confinement of the two excited electrons in 1Pe3/2 state and the two holes in 1Se state in a single nanocrystal with a diameter of about 3.2 nm would enhance the Auger interaction, which causes a rapid intraband (not interband) Auger recombination. The resulting state, 1Se(1)1Pe3/2(0)1Xe(1), contributes to the PP signal as one GSB term. Now, the electron in the high-lying 1Xe(1) state could dump approximately 2,500 cm−1 energy to either CQD phonons or ligand vibrations more effectively not only because the 1Xe state is highly surface-delocalized (Figure S5) but also because there exist other electronic states between 1Xe and 1Pe states that could assist cascading-type internal conversion (IC) processes. After this IC, the resulting one-exciton states can be either 1Se(1)1Pe3/2(1) or 1Se(1)1Pe1/2(1), which would then relax back to the ground state 1Se(2)1Pe(0) slowly via the EVET process. An additional aspect that should not be ignored is a local heating effect on the IR PP signal. Strong light-matter interactions followed by excess energy dissipations cause an increase in local temperature around each CQD, which could affect the IR PP spectrum. We measured the temperature-dependent FTIR spectra of CQDs (Figure S11). The absorbance of β-HgS CQDs decreases within our spectral window as temperature increases. Therefore, the decreased PP signal at substantially long delay times (∼microseconds) can be safely attributed to this local heating effect, which contributes to the IR PP signal as a constant offset. We numerically solved the kinetic equations determined by four rate constants, τIAP, τIST, τIC, and τEVET, using a finite-difference method. We then used the resulting time-dependent populations of all the states to calculate the IR PP signals directly for varying pump energy densities (Data S2). As can be seen in Figures 6A and 6B , our proposed kinetic mechanism reproduces not only the multi-exponentially decaying patterns of the IR PP signals but also the pump power-dependent electron dynamics of the two different β-HgS CQDs almost perfectly, which supports the validity of the kinetic scheme in Figure 5. The decay time constants τIAP, τIST, and τIC depend on neither the pump power nor the surface ligand (Figure 6C). This result is consistent with the interpretation that the IST and IC processes are mainly induced by electron-QD phonon couplings, not electron-ligand vibration couplings. Unlike the IAP, IST, and IC decay time constants, that associated with the EVET depends on the surface ligand; the EVET rate of β-HgS-DDT is faster than that of β-HgS-OLAm, which is consistent with the fact that the interaction between the thiol group of DDT and QD is usually stronger than that between the amine group of OLAm and QD.34Martell A.E. Smith R.M. Critical Stability Constants. Plenum Press, 1974Google Scholar,35Wright J.G. Natan M.J. MacDonnel F.M. Ralston D.M. O’Halloran T.V. Mercury (II)—Thiolate chemistry and the mechanism of the heavy metal biosensor MerR.Prog. Inorg. Chem. 1990; 38: 323-412Crossref Google Scholar The weakly interacting ligand makes the EVET rate slow, which is an important clue of use for designing a CQD with a longer lifetime in its one-exciton state. Furthermore, τEVET unexpectedly shows a dependence on the excitation energy density. One of the possible explanations for this notable deviation is that there could be a contribution from the radiative recombination process to the PP signals at very long pump-probe delay times. Unfortunately, the scanning range of pump-probe delay time is limited (<300–400 ps) due to the use of a mechanical translational stage. Note that the time scale of the radiative recombination process could be on the order of a few microseconds for IR materials. Thus, our experimental data (PP signals up to 300 ps) are not sufficient enough to resolve such a slow process. Therefore, the estimated rate constants for the EVET in the HgS-OLAm system (Figure 6C) could include both the EVET and slow radiative recombination processes, making the estimated τEVET value dependent on the pump energy density. It will be of great interest to investigate the ligand effects on the EVET and radiative recombination processes for various CQDs with different passivation layers. From the kinetic analysis, we were able to estimate the branching fractions of one-exciton (x) and biexciton state (1 − x) upon the pump excitations (Figure 6D). The fraction x of the one-exciton state in β-HgS-OLAm CQDs is smaller than that in β-HgS-DDT CQDs, which indicates that the electronic transition probability increases upon ligand exchange from DDT to OLAm, reflecting the higher carrier density of β-HgS-OLAm than that of β-HgS-DDT. We carried out time-resolved IR pump-probe studies of n-type self-doped β-HgS CQDs, where the electronic transition from 1Se to 1Pe states in the CB is in the mid-IR frequency range. The decaying patterns of the IR pump-probe signals provided critical information on the electronic relaxation processes of carrier particles in the CB state manifold only. From quantitative analyses of the IR PP signal for varying pump energy densities, we showed that the IAP of biexciton occurs unexpectedly rapidly on a time scale of ∼1 ps. The rate of the IST from 1Pe3/2 to 1Pe1/2 states is approximately 10 ps. The electron-phonon coupling-induced IC from high-lying excited states in the CB to the 1Pe state occurs on a time scale of 60 ps irrespective of thiol or amine ligand. The slow component with a decay time constant of a few hundred picoseconds reflects the electron relaxation from 1Pe to 1Se state via the EVET process, and its rate strongly depends on the binding strength of ligand molecules on the surface of CQD. We show here that the possibility of creating biexcitons with mid-IR light could open a new avenue for developing novel efficient photovoltaic devices operating in a relatively low photon energy regime. From this work, we anticipate that the insights into the electron relaxation dynamics of self-doped CQDs found here could be of use to elucidate the previously unresolved observations such as blinking of quantum dots, disproportionately charged quantum dots in a light-emitting diode, and hot electron dynamics occurring in high-lying CB states that are coupled to nanocrystals’ surface states.