Exciton Dynamics within the Band-Edge ... - American Chemical Society

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Exciton Dynamics within the Band-Edge Manifold States: The Onset of an Acoustic Phonon Bottleneck Gabriele Rainò,*,†,⊥ Iwan Moreels,*,†,§,⊥ Antti Hassinen,‡,∥ Thilo Stöferle,† Zeger Hens,‡,∥ and Rainer F. Mahrt† †

IBM Research−Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland Physics and Chemistry of Nanostructures, Ghent University, Krijgslaan 281-S3, 9000 Gent, Belgium § Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy ∥ NB-Photonics, Center for Nano and Biophotonics, Ghent University, Belgium ‡

S Supporting Information *

ABSTRACT: Exciton dynamics within the band-edge state manifold of CdSe/ZnS and CdSe/CdS quantum dots (QDs) have been investigated. Low-temperature timeresolved photoluminescence (PL) experiments demonstrate that exciton relaxation is mediated by LO phonons, whereas an acoustic phonon bottleneck is observed for splitting energies lower than the optical phonon energy. This has important implications since the main source affecting exciton dephasing is considered to be a spin-flip process. Our results concur with recent observations of long exciton dephasing times in CdSe/CdS QDs and show a way to engineer nanoparticles with enhanced coherence time, a prerequisite for their use in quantum optical applications.

KEYWORDS: Colloidal quantum dots, exciton relaxation, fine structure splitting, exciton−phonon coupling

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energy splitting is on the order of 2−10 meV, where a larger splitting will in general be characteristic of smaller particles. More recently, by means of time- and spectrally resolved luminescence studies, an additional state within the fine structure has been resolved and assigned to an upper bright state.11 Again, a distinct size dependence was observed with splitting energies varying from 30 to 80 meV. Hereafter, we will label this upper bright state as BU. This probably is either the J = ±1U or the J = 0U state, but for the present manuscript its exact spin projection does not play a role. In addition to the size-dependent splitting, a novel way to tailor the fine-structure splitting has been revealed.12,13 Precise engineering of the wave function delocalization enables a significant reduction of the electron−hole exchange interaction. It has been showed that the splitting between the upper-lying bright state (BU) and the dark-bright manifold (0L − ±1L) can be reduced to values below 1 meV.13 Despite this promising progress, the exciton relaxation within this manifold of states remains elusive, and only recently have some experimental efforts tackled this issue. It has been observed that lowtemperature time-resolved PL exhibits a fast initial decay, in addition to a temperature-dependent slow decay, characteristic

olloidal nanocrystals or quantum dots (QDs) have proved to be a very versatile class of quantum nanoemitters in many fields of application. Besides being a unique platform to study fundamental quantum effects, these materials have attracted considerable interest because of their potential use in optoelectronics, photonics and optical quantum communication. Indeed, they have already demonstrated to be an excellent material system for lasing, photovoltaic devices and as a room-temperature triggered single photon source with high efficiency.1−6 However, the strong confinement of the charge carriers induces a complicated exciton band-edge fine structure.7 For example, typical splitting energies in CdSe vary from a few hundreds of microelectronvolts in the bulk material to tens of millielectronvolts in strongly confined QDs.7−10 This has driven extensive research on the connection between the band-edge fine structure and the energy, the polarization, and the coherence of photons emitted by colloidal QDs. The observed size-dependence of the fine structure energy splitting is typically interpreted within the theoretical framework proposed by Efros et al.,7 using the so-called effective mass approximation (EMA). In this model, the crystal field, the spin−orbit coupling, the shape anisotropy and the electron−hole exchange interaction give rise to a splitting of the band-edge exciton state with specific size-dependent spacings. For spherical wurtzite QDs, an optically dark exciton state with spin projection J = ±2 is observed below the optically bright exciton state with spin projection J = ±1L. The dark-bright © XXXX American Chemical Society

Received: June 27, 2012 Revised: September 24, 2012

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dx.doi.org/10.1021/nl302390b | Nano Lett. XXXX, XXX, XXX−XXX

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as recently demonstrated.20−22 In particular, smaller core/ thicker shell heterostructures exhibit a longer exciton lifetime owing to a modified delocalization of the electron wave function in the shallow potential well that is formed by the CdSe/CdS heterostructure. Consequently, wave function engineering provides a new degree of freedom to tune the electron−hole exchange interaction and the fine-structure splitting. In the case of CdSe/ZnS, the shell mainly improves the surface passivation, resulting in QDs with typical quantum yields of 15−30%. Owing to the high conduction band offset, both the electron and the hole wave function in CdSe/ZnS QDs are confined mainly in the core region, resulting in a socalled type I configuration. Quasi-type II CdSe/CdS had similar yields, and by growing and additional monolayer of ZnS we were able to maintain a high yield after ligand exchange. By using all these different types of core/shell QDs, we can cover a wide range of fine structure energy splittings, enabling us to investigate the dependence of the exciton relaxation rate on the splitting and to gain deeper insight into the underlying mechanism. Figure 1d shows the expected size-dependent energy splitting for bare quasi-spherical wurtzite QDs with an aspect ratio (AR) of 1.15:1. This slight shape anisotropy results in a reordering with respect to spherical particles.11 Here, the lowest state is the 0L, which is still optically dark. It is energetically separated from the first bright state, ± 1L, and the second bright state, 0U, by 1−5 and 20−70 meV, respectively (for a detailed description see ref 11). The exciton dynamics was investigated by low-temperature (5 K) time- and spectrally resolved PL experiments. Figure 2a reports a typical streak-camera image taken of a CdSe/ZnS sample with a core diameter of ∼2 nm. The lower part of the figure shows the PL spectra at zero delay time and at 1.5 ns, averaged over a 50 ps time window. The asymmetric PL spectrum at 0 ps, suggests that more than one state contributes. The emission peak at lower energy (spectrum taken at 1.5 ns) stems from the slow decay of excitons in states 0L and ±1L. An additional blue-shifted, superimposed, and rapidly decaying emission feature is observed around t = 0 ps. Given the inhomogeneous line broadening of ∼100 meV (full width at half-maximum), we can neglect the small splitting between the 0L and ±1L states and consider them here as one effective state. To identify the states, we fit the data at t = 0 ps with two biGaussian peak functions, assuming the same shape and width for both peaks.11 To reduce the number of free parameters, the spectral position of the lower energy peak function was kept fixed to the value characterizing the emission at long delay time (for details of the fitting procedure, see ref 11). For the sample presented in Figure 2a, we obtained an energy splitting of about 70 meV, which is in good agreement with theoretical predictions from EMA calculations (Figure 1d). Figure 2b reports the same analysis for a CdSe/CdS QDs with a core diameter of 2.7 nm. Because of a stronger delocalization of the electron wave function in the shell region and the resulting reduction of the electron−hole exchange interaction, the measured splitting is about 33 meV. This proves that we can indeed tune the energy splittings over a very wide range, by using different material systems. The measured energy splitting for all samples studied are reported in Figure 2c. The splitting energy varies from 70 down to ∼5 meV. The drastic change for CdSe/CdS QDs can be explained by considering the change in electron−hole wave function overlap in addition to the change in exciton volume.13

of the dark-bright splitting. At present, the fast component has been attributed to a thermal outflow of excess energy, that is, the initial decay arises from phonon-assisted emission within a hot QD.14 On the other hand, a size-dependent energy splitting between the rapidly decaying peak and the long-lived manifold state has been observed,11,13,15 which suggests that the fast component is related to exciton relaxation within the band-edge fine structure. In this work, by combining CdSe/ZnS, CdSe/ CdS, and CdSe/CdS/ZnS core/shell QDs, we make use of a wide range of energy splittings between the BU −dark-bright manifold to monitor the exciton relaxation. We observed a sizedependent relaxation rate with a faster relaxation occurring within QDs having a larger energy splitting. This relaxation is most probably mediated by LO phonons that are coupled via the polar Fröhlich interaction, whereas an acoustic phonon bottleneck slows down the relaxation for splitting energies lower than the LO-phonon energy. Our results elucidate the intrinsic exciton dynamics at the band-edge and show a way to design QDs with very long dephasing times. Figure 1a provides a sketch of the samples investigated. CdSe/ZnS and CdSe/CdS core/shell QDs were synthesized

Figure 1. (a) Illustration of the CdSe/ZnS and CdSe/CdS core/shell QDs. (b) Typical transmission electron microscopy (TEM) image revealing the narrow size distribution. (c) Band alignment for the CdSe/CdS core/shell QDs. Because of the small conduction band (CB) offset (ΔC ∼ 0.3 eV), tailoring the electron−hole wave function overlap is possible by suitably tuning the core or the shell thickness. As an example, the sketch depicts the expected change in electron wave function distribution by changing the core diameter. (d) Theoretical calculation of the band-edge exciton fine structure for wurzite CdSe QDs with an AR of 1.15:1. Dark states are marked by dotted lines; bright states by solid lines.

according to established procedures.16−19 Figure 1b shows a typical transmission electron microscopy (TEM) image, illustrating the narrow size dispersion. In Figure 1c, the band alignment is sketched for the case of a CdSe/CdS core/shell QD. Because of a reduced conduction band offset (ΔC ∼ 0.3 eV), the electron wave function delocalization can be controlled by the physical dimensions of the core and the shell. This strongly affects the optical properties of these nanostructures, B


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Figure 2. (a) Low-temperature (5 K) time- and spectrally resolved PL for CdSe/ZnS QDs having a core size of 2 nm (total QD size: 2.9 nm). The lower plot reports the PL spectra at zero delay time and at 1.5 ns, averaged over a 50 ps time window. At t = 0 ps, an energy splitting of ∼70 meV has been obtained from the two centers of a bi-Gaussian fit. (b) Low-temperature (5 K) time- and spectrally resolved PL for a CdSe/CdS QDs having a core size of 2.7 nm (total QD size: 5.3 nm). The measured energy splitting is about 33 meV. (c) The measured energy splitting versus emission energy for all the studied samples.

slower relaxation is observed, as can be clearly inferred from Figure 3. Several effects could influence the observed exciton dynamics. First, the contribution of charged, multiexcitons or eventually the effect of ground-state saturation can be excluded considering the very low excitation power used in the experiments (see Supporting Information for more details). Second, an energy-transfer process to the vibrational modes of the ligands has been suggested as the main physical process affecting the electron decay from the p-shell to the s-shell.23 This hypothesis can be tested by varying the coupling to the available vibrational modes by exchanging the oleic acid ligands with dodecanethiol ligands (CdSe/ZnS) and sulfur ligands (CdSe/CdS/ZnS), respectively. By means of nuclear magnetic resonance (NMR) spectroscopy, we monitored the ligand exchange on both CdSe/ZnS and CdSe/CdS/ZnS core/shell QDs (not shown here), and found that at least 85% of the oleic acid ligands are removed by the respective ligand exchange procedures. Figure 4a reports the time- and spectrally resolved measurements for CdSe/ZnS core/shell QDs before (left plot) and after (center plot) ligand exchange. The plot on the right shows the spectrally integrated PL decay traces. For the CdSe/ ZnS sample, the fast decay component is 50 ps before and 57 ps after ligand exchange. The small variation observed (within 20%) can be attributed to sample-to-sample variation or can also be due to an incomplete surface passivation after ligand exchange rather than to an effect mediated by ligand vibrational modes. Figure 4b shows the same analysis on CdSe/CdS/ZnS core/shell QDs. In this case, the organic oleic acid ligands were replaced by inorganic S2‑ ions. Again, the fast component remains nearly unchanged (within 20%). From these results, we can infer that ligand vibrational modes represent only a minor contribution to the exciton relaxation process. The difference between our observation and the dynamics reported in the

More insight into the exciton relaxation can be obtained by analyzing the spectrally integrated time-resolved PL decay traces reported in Figure 3. At low temperature, the decay is

Figure 3. Spectrally integrated time-resolved traces for samples having different energy splittings between the BU and the 0L − ± 1L manifold states. The smooth red lines are the best fits obtained using a biexponential decay function. The fast component clearly increases with decreasing energetic splitting.

nonexponential and can be well fitted to a biexponential decay function. The longer decay component is related to the radiative recombination from the 0L − ± 1L manifold. The fast component has been attributed to the exciton relaxation from the BU state.11,13 For QDs with reduced energy splitting, a C


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Figure 4. (a) Time- and spectrally resolved measurements of CdSe/ZnS core/shell QDs (core size 2.7 nm, total size 3.6 nm) before (left) and after (center) ligand exchange. The plot on the right shows the spectrally integrated time-resolved traces of the samples for which oleic acid ligands were exchanged with dodecanethiol ligands. (b) Time- and spectrally resolved measurements of CdSe/CdS/ZnS core/shell QDs (core size 2.6 nm, total size 9.1 nm) before (left) and after (center) ligand exchange (in this case, oleic acid ligands are exchanged with inorganic S2‑ ions). The plot on the right shows the spectrally integrated time-resolved traces. The small variation in lifetime before and after ligand exchange (within 20%) has to be attributed to sample-to-sample variation or to an incomplete surface passivation after ligand exchange rather than to an effect mediated by ligand vibrational modes. Note that despite their similar core diameters (2.7 and 2.6 nm), the samples in (a) and (b) exhibit strongly different lifetimes because of the reduced splitting in CdSe/CdS QDs (∼5 meV instead of the 53 meV for CdSe/ZnS QDs), which results from a different electron delocalization in the shell.

is a direct result of the particular dispersion of the acoustic phonon modes, which is almost linear for small wave vectors (i.e., at low energy).25 Note that even if it was theoretically predicted, a clear phonon bottleneck effect has not been observed so far in colloidal QDs due to the presence of additional efficient relaxation paths. The relaxation of hot excitons in QDs has remained controversial, mainly due to the difficulty to separate all the physical mechanisms that are usually involved. Early work showed a subpicosecond relaxation time which was explained considering both efficient multiphonon emission and Augertype electron−hole energy transfer.26−28 A slowed population buildup has also been observed for the lowest hole state, suggesting the appearance of a phonon bottleneck in the valence band.29 More recent works have also highlighted the importance of the surface ligands or the defects at the interface, which strongly alter the exciton relaxation rate.23,30 A comprehensive review on such a topic can be found in ref 31. It is important to note that all the works mentioned above explored the exciton dynamics by probing the relaxation between different QD excited states (usually the 1P-to-1S transition is probed), where excess energies usually exceed the LO-phonon energy. In our work, we make use of a wide range of energy splittings within the fine structure manifold states

literature could be explained by considering the difference in the energy scales involved in the process. Indeed, the typical energy splitting between the p-shell and the s-shell is on the order of 150−250 meV, which is in the same range as the onset of the vibrational modes of organic molecules23 and almost an order of magnitude larger than the energies involved in our case. Figure 5 summarizes the splitting-dependent exciton relaxation anticipated in Figure 3 for all samples studied. Specifically, the decay time of the fast component is plotted versus the measured splitting. For a large splitting, the lifetime is largely constant at about 50 ps, whereas for splittings below ∼30 meV, the lifetime progressively increases and reaches 250 ps for a splitting of about 5 meV. Having ruled out the influence of the ligands, this behavior must be intrinsic to the inorganic QD. The abrupt transition from a constant to a progressively reduced relaxation rate when the splitting energy drops below 30 meV, indicates that the relaxation is mediated by LO-phonons, which have an energy of 26−27 meV in CdSe/ CdS QDs.24 Thus, exciton relaxation below the LO-phonon energy can only take place via acoustic phonon modes, which exhibit a strongly reduced density of states and therefore constitute a bottleneck for the relaxation process. It appears that the linear increase in lifetime below the LO-phonon energy D


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Author Contributions ⊥

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank B. Mazenauer and E. Wehrli for their technical support and J. Plumhof and B. J. Offrein for stimulating discussions. The research leading to these results has received funding from the European Community’s Seventh Framework Programme under Grant 214954 (HERODOT). Z.H. acknowledges the FWO-Vlaanderen (Project No. G.0794.10) and the Belgian Science Policy (IAP 6.10, photonics@be) for funding this research.

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Figure 5. Intraband relaxation time versus measured splittings. The vertical error bars indicate the 20% sample-to-sample variation observed before and after ligand exchange. A net increase in lifetime has been observed for splittings smaller than the LO phonon energy in the CdSe/CdS material system. This behavior has been attributed to an acoustic phonon bottleneck slowing down the relaxation rates. The inset schematically shows the energy levels involved. A comprehensive analysis of the three-level system used to interpret our results is reported in the Supporting Information.

allowing to probe the exciton dynamics when the excess energy is far below the LO-phonon energy. Indeed, such low excess energy involved in the exciton relaxation unveils the peculiar behavior we observed. Obviously, a quantitative modeling of the relaxation rates requires comprehensive knowledge not only of the acoustic phonon mode density of states but also of the electron−phonon coupling strength. In addition, momentum conservation rules must be taken into consideration when assessing which phonon modes dominate the relaxation behavior. Such a quantum-mechanical description exceeds the scope of the current paper, but our insights should stimulate a theoretical assessment of phonon-mediated relaxation within the band-edge exciton fine structure. In summary, we have shown that the exciton relaxation at the band edge is mediated by an LO phonon, whereas for splittings smaller than 30 meV an acoustic phonon bottleneck slows down the relaxation rate to at least 250 ps. As the main source affecting the exciton dephasing is considered to be a spin-flip process from the bright to the dark states, our results concur with the recent observation of long spin dephasing in CdSe/ CdS QDs (with reduced dark-bright splitting).32 This is of central importance on the road to using colloidal QD as quantum nanoemitters.

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ASSOCIATED CONTENT

S Supporting Information *

Additional data on the optical properties of CdSe/ZnS-CdS nanocrystals, Figures S1−S4. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (G.R.) [email protected]; (I.W.) iwan.moreels@iit. it. E


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