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(Multi)exciton Dynamics and Exciton Polarizability in Colloidal InAs Quantum Dots Joep J. H. Pijpers,† Maaike T. W. Milder,† Christophe Delerue,‡ and Mischa Bonn*,† FOM Institute for Atomic and Molecular Physics, Science Park 104, 1098 XG, Amsterdam, The Netherlands, and De´partement ISEN, Institut d’Electronique de Microe´lectronique et de Nanotechnologie (UMR CNRS 8520), 41 BouleVard Vauban, F-59046 Lille Cedex, France ReceiVed: December 17, 2009; ReVised Manuscript ReceiVed: March 3, 2010
We report steady state and dynamic properties of (multi)excitons in InAs quantum dots using femtosecond time-resolved transient absorption and time-resolved terahertz spectroscopy. The polarizability of confined excitons in the ground state is found to be of the order of 104 Å3, increasing sharply with quantum dot radius as R3. The size-dependence of the exciton polarizability can be quantitatively reproduced by using multiband tight binding calculations. Following the generation of a single exciton with excess electronic energy, electron intraband relaxation from the 1Pe f 1Se level occurs on a time scale of 0.8 ps for particles of 2.2 nm radius, whereas hot hole cooling occurs faster than 150 fs. The intraband relaxation dynamics are consistent with an Auger process involving electron-hole energy transfer, indicating an electron-hole coupling time of 0.8 ps. Finally, when multiple excitons are generated through multiphoton absorption, multiexciton recombination dynamics occurs on 1-100 ps time scales. We illustrate the challenges associated with reliably extracting the time constants of multiexciton recombination from our data, which are helpful for elucidating the multiexciton recombination mechanism. Our results demonstrate that the exciton dynamics in InAs quantum dots are governed by the relatively low dielectric constant of InAs (resulting in strong carrier-carrier interactions) and the low energy spacing between valence levels (resulting from the relatively high value of the hole effective mass, and allowing for rapid phonon-mediated hole relaxation). Introduction Colloidal quantum dots absorbing and emitting in the infrared (IR QDs) have received much attention over the past decade.1 The development of sophisticated synthesis procedures has brought many potential applications close to realization. First, IR QDs have interesting properties for the optical telecommunication market, where most IR components operate at wavelengths ranging from 1200 to 1600 nm. Since the emission of IR QDs can be easily controlled over this spectral range by varying the particle diameter, QDs can be used for optical switching, wavelength change, or optical amplification outside the conventional erbium-doped-fiber amplifier window.1,2 Another promising application is the use of IR QDs as fluorescent biological labels. Human tissue absorbs little light in the nearinfrared region (NIR, 650-900 nm), allowing NIR-emitting probes to be used for in vivo imaging.3 However, only a few NIR-emitting dye molecules are available, which are furthermore sensitive to photobleaching. The emission of IR QDs can be easily tuned over the 650-900 nm region and they have proven to be a robust fluorescent probe for in vivo diagnostics.4,5 Finally, IR QDs can be applied in electro-optic devices, such as IR lightemitting diodes6 and QD solar cells.7–9 In contrast to silicon solar cells, IR QD sensitizers can absorb IR light, which makes up approximately 20% of the total energy of the solar spectrum.10 For all the above-mentioned applications, it is important to understand the interaction between IR QDs and light, and the dynamics of photogenerated carriers. Therefore, we report three * To whom correspondence should be addressed. Phone: +31 (0)20 7547100. Fax: +31 (0)20 7547290. E-mail:
[email protected]. † FOM Institute for Atomic and Molecular Physics. ‡ Institut d’Electronique de Microe´lectronique et de Nanotechnologie.
topics in this paper: (i) the polarizability of confined carriers (excitons), i.e., the exciton response to an externally applied DC electric field, (ii) the dynamics of electron intraband relaxation from the 1Pe f 1Se level, and (iii) the recombination dynamics of multiexcitons. We study these topics in colloidal InAs QDs using terahertz time-domain spectroscopy (THzTDS). The energy gap of InAs QDs can be tuned between 600 and 1600 nm, making them in principle suitable for all applications mentioned above. First, we determine the exciton polarizability (Rexc) as a function of QD size. Values of Rexc have previously been reported for CdSe and PbSe QDs11,12 and we find that the magnitude of the InAs exciton polarizability is comparable to that of CdSe QDs. The experimentally obtained values for the polarizability Rexc agree well with theoretically predicted values, as obtained from perturbative multiband tight binding calculations. Next, we combine THz-TDS with femtosecond transient absorption (TA) to study electron and hole intraband relaxation. In bulk semiconductors, the conduction and valence bands consist of densely spaced energy levels and relaxation of “hot” carriers occurs via sequential emission of longitudinal optical (LO) phonons. In the case of InAs QDs, the energy difference between the 1Se and 1Pe level ranges from ∼300 meV (3.0 nm radius) to ∼550 meV (1.5 nm radius),13 much larger than that of typical LO phonon energies (∼30 meV). Intraband relaxation in CdSe and InP QDs, materials with similar characteristics, has been reported to occur via an Auger process, in which the excess energy of the “hot” electron is transferred to a “cold” hole.14–16 The resulting hot hole can subsequently relax via phonon emission since the energy difference between valence levels is of the order of typical LO phonon energies. Our findings on 1Pe f 1Se relaxation in InAs QDs are consistent with this Auger process, characterized by an electron-hole
10.1021/jp911948z 2010 American Chemical Society Published on Web 03/17/2010
Colloidal InAs Quantum Dots coupling time of ∼0.8 ps, which is very similar to previous reports on coupling times in CdSe14,15,17,18 and InP16 QDs. Whereas the single exciton state in InAs QDs is very longlived (ca. nanoseconds),19 we observe recombination of multiexcitons to a single exciton state within tens of picoseconds. This finding is in agreement with earlier observations on CdSe and PbSe QDs.20–23 The most widely accepted mechanism for multiexciton recombination (MER) is again a nonradiative Auger process, in which the recombination energy is transferred to a third particle, either an electron or a hole. The Auger mechanism was proposed in refs 20, 22, and 23 based on the experimentally observed ratios between τ2, τ3, and τ4, the recombination rates of the biexciton, triexciton, and four-exciton state, respectively. Conclusions on the MER mechanism based on the value of the τ2/τ3 ratio should be made with care, however. The initial assumption that a τ2/τ3 ratio of 2.27 corresponds to an Auger mechanism20 was later refined by taking into account the symmetry of the multiexciton states.22 Furthermore, the value of the τ2/τ3 ratio is increasing with QD size.22,23 Another indication of an Auger-like mechanism would be a decreased recombination rate for decreasing overlap between hole and electron wave functions. However, trapping of holes at the surface or localization in an additional shell has been reported to have a negligible effect on τ2, contradicting the Auger hypothesis.21 Our approach was to investigate the mechanism of MER by inferring the τ2/τ3 ratio from transient THz data. We demonstrate the difficulties in extracting reliable numbers for τ3 from transient spectroscopy data. These difficulties are primarily due to the uncertainty in the initial distribution of excitons at high excitation fluences. An additional complication is that, for both THz and TA the magnitude of the transient signal does not necessarily increase linearly with the number of excitons per QD. Experimental Section Samples. Colloidal InAs QDs were synthesized as reported elsewhere.24,25 For the intraband relaxation experiments, we used trioctylphospine (TOP) passivated InAs cores (1.25 or 2.2 nm radius). The QDs for the polarizability and multiexciton recombination experiments were TOP passivated (2.0 nm radius) or passivated with CdSe/ZnSe shells (2.45 and 2.72 nm radius InAs core). These core/shell QDs consist of InAs cores onto which one atomic layer of CdSe and four layers of ZnSe are deposited. Samples are prepared by suspending the QDs in toluene in a 1 mm path length cuvette. The core/shell structure leads to a significantly improved quantum yield (∼50%) as compared of the TOP-passivated QDs (∼2.5%).25 This increase in fluorescence efficiency is caused by the effective removal of surface defects, leading to less emission quenching via nonradiative decay channels. Time-Resolved Spectroscopy. THz-TDS has previously been successfully applied to determine exciton polarizability and hole dynamics in CdSe and PbSe QDs.11,12,18 The experimental configuration of the optical-pump/THz probe setup has been described previously.26 This technique uses a weak electromagnetic field (∼1 kV/cm) to probe the sample response at low energies (∼4 meV) following photoexcitation with 110 fs, 800 nm laser pulses from an amplified Ti:sapphire system. To study exciton polarizability in InAs QDs, we first measured the electric field waveform ETHz(t) through the unexcited sample. Next, the modulation in the THz waveform, ∆ETHz(t), was measured by chopping the excitation pulse and monitoring the differential THz signal. ∆ETHz(t) was measured at a pump-probe delay τ of 20 ps in order to ensure that all excitons were in the ground
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Figure 1. Transmitted THz pulse ETHz(t,τ) and the exciton-induced modulation thereof, ∆ETHz(t,τ). For monitoring the transient hole population, ∆ETHz(t,τ) is measured at the point marked with an arrow (t ) 2.1 ps), as a function of τ. The dashed line corresponds to a model in which the real part of the susceptibility is finite, with a frequencyindependent value.
state. Furthermore, low excitation fluences were used (2). Quantifying the recombination time scales is relatively straightforward when the initial excitation distribution is known. However, the nonlinear scaling of the THz signal with the number of excitons per QD (discussed above) makes it difficult to directly infer the initial distribution of excitations from the magnitude of the THz signal. A solution would be to assume a Poissonian distribution for this initial excitation distribution.20,22,40 However, it has been argued that the excitation distribution is non-Poissonian when Neh > 1 (Neh is the average
J. Phys. Chem. C, Vol. 114, No. 14, 2010 6323 number of excitons per QD immediately following photoexcitation).41 For the high fluence data traces, Neh > 1, as a result of which the assumption of Poissonian statistics is not justified. For the 0.94 µJ/mm2 data trace, the excitation levels are sufficiently low that the decay is predominantly caused by biexciton and triexciton recombination. The data were fitted with the same three-level model in which we fixed τ2 to 38 ps. The amplitudes, however, were let free since the initial excitation distribution was not known exactly. The goal was to find a ratio for τ2/τ3 in order to gain insight into the MER mechanism. However, this analysis results in a seemingly unphysically large value of the τ2/τ3 ratio of 10 (see Figure 4b,c), with, however, a significant error bar. An alternative approach to extract MER time constants from transient data, following ref 20, was equally inconclusive. This procedure20;“subtractive” procedure to analyze TA data;has previously been applied to CdSe QDs. In this procedure, the transients at various fluences are normalized so that the long-time decay values match. The low pump intensity trace (Neh , 1) is considered to show only single exciton dynamics and is subtracted from a trace recorded with sufficient pump intensity to excite biexcitons. This procedure is assumed to yield purely biexciton dynamics and is repeated for traces with higher pump fluences, making it possible to extract also τ3 and even τ4. We attempted to implement this procedure for our THz traces at low fluences (0.25 and 0.94 µJ/mm2 in Figure 4a), for which the nonlinearity of the THz signal is expected to be modest. However, we experienced that the outcome of this procedure is very sensitive to the exact value of the pump-probe delay at which the data are normalized. Therefore, it is conceivable that our THz data are more reliably analyzed with the multilevel model of coupled rate equations. The above analysis illustrates that the extraction of τ3 from THz data, and presumably also from TA data, is challenging. In contrast, the radiative emission from mono-, bi-, and triexciton states can be spectrally resolved by transient photoluminescence measurements, as was shown in CdSe QDs.23 To draw conclusions on the MER mechanism in InAs QDs from the τ2/τ3 ratio, time-resolved photoluminescence spectroscopy seems to be the more suitable technique, since the decay of the triexciton state is spectrally separated from the mono- and biexciton states. Conclusions The polarizability of excitons in strongly quantum-confined InAs QDs was found to be of the order of ∼10 000 Å3 and increases with the QD radius to the fourth power. These findings are in excellent agreement with previous THz studies on CdSe and PbSe QDs.11,12 Furthermore, intraband electron relaxation from the 1Pe level to the 1Se level was found to take place on subpicosecond time scale and our observations are consistent with the currently accepted Auger mechanism for intraband relaxation. Finally, the measured biexciton recombination (MER) rates were found to vary between 10 and 40 ps, depending on the QD size. Extraction of triexciton rates from THz-TDS data, required for insight in the mechanism of MER, is challenging. A more straightforward determination of triexciton rates in InAs QDs is expected from time-resolved photoluminescence measurements. All findings reported in this article can be qualitatively explained by the low dielectric constant of InAs (resulting in strong carrier-carrier interactions) and the low energy spacing between valence levels (resulting from the relatively high value of the hole effective mass). For application of QDs in telecommunication or opto-electronic devices, material properties like the dielectric constant and the carrier effective masses are hence crucial design parameters.
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Acknowledgment. We thank David Mocatta and Uri Banin of the Hebrew University of Jerusalem for providing us with InAs QDs. This work is part of the Joint Solar Programme (JSP) of the Stichting voor Fundamenteel Onderzoek der Materie FOM, which is supported financially by Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). The JSP is cofinanced by gebied Chemische Wetenschappen of NWO and Stichting Shell Research. Supporting Information Available: Figure S1 showing the absorption spectra and energy diagram of the QDs used in the intraband relaxation experiment, Figure S2 showing the model and differential equation used to fit the TA data of the intraband relaxation experiment, Figure S3 showing the model and differential equation used to fit the THz data of the intraband relaxation experiment, and Figure S4 showing the model and differential equation used to fit the THz data of the multiexciton recombination experiment. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Rogach, A. L.; Eychmuller, A.; Hickey, S. G.; Kershaw, S. V. Small 2007, 3, 536–557. (2) Harrison, M. T.; Kershaw, S. V.; Burt, M. G.; Rogach, A. L.; Kornowski, A.; Eychmuller, A.; Weller, H. Pure Appl. Chem. 2000, 72, 295–307. (3) Weissleder, R. Nat. Biotechnol. 2001, 19, 316–317. (4) Bruchez, M.; Moronne, M.; Gin, P.; Weiss, S.; Alivisatos, A. P. Science 1998, 281, 2013–2016. (5) Zimmer, J. P.; Kim, S. W.; Ohnishi, S.; Tanaka, E.; Frangioni, J. V.; Bawendi, M. G. J. Am. Chem. Soc. 2006, 128, 2526–2527. (6) Tessler, N.; Medvedev, V.; Kazes, M.; Kan, S. H.; Banin, U. Science 2002, 295, 1506–1508. (7) Yu, P. R.; Zhu, K.; Norman, A. G.; Ferrere, S.; Frank, A. J.; Nozik, A. J. J. Phys. Chem. B 2006, 110, 25451–25454. (8) Cui, D. H.; Xu, J.; Zhu, T.; Paradee, G.; Ashok, S.; Gerhold, M. Appl. Phys. Lett. 2006, 88, 3. (9) Jiang, X. M.; Schaller, R. D.; Lee, S. B.; Pietryga, J. M.; Klimov, V. I.; Zakhidov, A. A. J. Mater. Res. 2007, 22, 2204–2210. (10) Santbergen, R.; van Zolingen, R. J. C. Sol. Energy Mater. Sol. Cells 2008, 92, 432–444. (11) Wang, F.; Shan, J.; Islam, M. A.; Herman, I. P.; Bonn, M.; Heinz, T. F. Nat. Mater. 2006, 5, 861–864. (12) Dakovski, G. L.; Lan, S.; Xia, C.; Shan, J. J. Phys. Chem. C 2007, 111, 5904–5908. (13) Banin, U.; Cao, Y. W.; Katz, D.; Millo, O. Nature 1999, 400, 542– 544. (14) Klimov, V. I.; McBranch, D. W. Phys. ReV. Lett. 1998, 80, 4028– 4031.
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