20060
2005, 109, 20060-20063 Published on Web 10/07/2005
Dynamics within the Exciton Fine Structure of Colloidal CdSe Quantum Dots Vanessa M. Huxter, Vitalij Kovalevskij,† and Gregory D. Scholes* Lash-Miller Chemical Laboratories, 80 St. George Street, Center for Quantum Information and Quantum Control, and Institute for Optical Sciences, UniVersity of Toronto, Toronto, Ontario, M5S 3H6 Canada ReceiVed: August 17, 2005; In Final Form: September 22, 2005
Evidence for an interaction between the quantum dot exciton fine structure states F ) (1 is obtained by measuring the dynamics of transitions among those states, exciton spin relaxation or flipping. An ultrafast transient grating experiment based on a crossed-linear polarization grating is reported. By using the quantum dot selection rules for absorption of circularly polarized light, it is demonstrated that it is possible to detect transitions between nominally degenerate fine structure states, even in a rotationally isotropic system. The results for colloidal CdSe quantum dots reveal a strong size dependence for the exciton spin relaxation rate from one bright exciton state (F ) (1) to the other in CdSe colloidal quantum dots at 293 K, on a time scale ranging from femtoseconds to picoseconds, depending on the quantum dot size. The results are consistent with an interaction between those states attributed to a long-range contribution to the electron-hole exchange interaction.
The size-dependent optical properties of semiconductor quantum dots have been widely studied in recent years.1 Clear optical absorption features ascribed to the 1S3/21Se, 2S3/21Se, and so forth, exciton states are evident in ensemble spectra. Beyond that, it has been ascertained that each of those absorption bands is split into a fine structure by crystal asymmetry effects and the exchange interaction.2,3 However, there is a dearth of experimental studies of that manifold of states, because it spans only tens of millielectronvolts and is consequently hidden by the inhomogeneous broadening of the spectrum arising from the sample size distribution. According to calculations, the fine structure of CdSe consists of eight states, five of which are optically bright.3-6 Of these, one state with total angular momentum F ) 0 has a linearly polarized transition moment, and four states, those with F ) (1, obey selection rules for absorption of circularly polarized light. Experimental studies of the exciton fine structure states in colloidal quantum dots have hitherto concentrated on the splitting between dark (F ) (2) and bright states (F ) (1), which is effected by the short-range part of the electron-hole exchange interaction.7-9 It has been predicted that, for quantum dots with an anisotropic shape, a further interaction arises between the F ) (1 exciton states mediated by the long-range part of the exchange interaction.10 At low temperatures, particularly in the presence of a strong magnetic field, that asymmetry-induced exchange interaction is seen as a splitting of the bright exciton transitions.11 In the present report, we show that the zero-field long-range exchange interaction promotes transitions from one bright exciton state to the other on a time scale ranging from femtoseconds to picoseconds, depending on the quantum dot size. * Send correspondence to:
[email protected]. † Present address: Institute of Physics, Savanoriu Av. 231, 02300 Vilnius, Lithuania.
10.1021/jp0546406 CCC: $30.25
Optical pumping of exciton states, such as the F ) (1 quantum dot states, using circularly polarized light can establish exciton spin polarization (orientation) in oriented crystals by projecting photon angular momentum onto an exciton state.12-14 Hence, in oriented systems, transitions between the F ) (1 states can be monitored by circular-polarization photoluminescence anisotropy decays, for example, as has been reported for quantum wells.15-17 However, investigations of exciton orientation and relaxation in rotationally isotropic systems, such as an ensemble of colloidal quantum dots, have been impeded, because it is not evident how selection rules for optical excitation can be exploited. To capture the dynamics of transitions between the degenerate exciton fine structure levels, a new approach was recently proposed.18 That method, based on measuring the decay of a transient polarization grating, is sensitive to exciton-state history rather than excited-state population. In other words, the signal decays proportionally to the number of quantum dots probed in a different exciton state to that prepared by the optical pump. We report here results of application of that method to measure transitions from F ) +1 to F ) -1 exciton fine structure states and vice versa for CdSe quantum dots. High-quality CdSe colloidal quantum dots passivated with trioctylphosphine oxide were prepared using the usual organometallic route.19 Those samples were dispersed in optical-quality polymer films, which were maintained under vacuum for the experiments at 293 K. We have ascertained that the physics we report here is independent of sample preparation, including passivating ligands and host matrix. Ultrafast laser pulses of 20-36 fs duration were generated using a setup described previously.20 Measurements were undertaken using third-order transient grating (3-TG) spectroscopy, similar in principle to the ubiquitous pump-probe method. However, the pump pulse is split into a pair of beams that have different wavevectors, k1 and k2, which arrive simultaneously to photoexcite the sample © 2005 American Chemical Society
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Figure 1. Plots of 3-TG data recorded using various polarization sequences for 5.0 nm diameter CdSe, 293 K in poly(butyl methacrylate). Polarization sequences for pulses 1-3 and the analyzer in the signal path (if included) are indicated in the inset, where V ) vertical, H ) horizontal, and M ) magic angle. In those tables, s and r refer to data recorded in either the ks or kr phase-matched signal directions, respectively (ks ) -k1 + k2 + k3 and kr ) k1 - k2 + k3). The information is listed in the same order (top to bottom) as the curves in the corresponding plot. (a) Population gratings. (b) Polarization gratings.
at a crossing angle of a few degrees (in the theory, they are assumed to be collinear). A probe beam, with wavevector k3, monitors the evolution of ground and excited-state density as a function of time delay tp. 3-TG signals are seen in the phasematched directions ks ) -k1 + k2 + k3 and kr ) k1 - k2 + k3, which facilitates spatial isolation of background-free signals. Detection of those signals on a photodiode yields the homodynedetected 3-TG signal intensity as a function of the pump-probe time delay, IHOM(tp). The bandwidth of the pulses accommodates possible inelasticity in the four-wave mixing process. An important difference between 3-TG and ultrafast pumpprobe measurements is that the polarization of each of the three laser beams as well as an analyzer in the signal path can be independently arranged. In the present work, we discuss permutations of orthogonal linear polarizations, labeled vertical (V) and horizontal (H). For the majority of linear or circular polarization conditions, the 3-TG signal is expected to decay according to exciton cooling and recombination kinetics.18 We find that to be the case, as shown in Figure 1a. However, if the pump pulse pair are cross-polarized (e.g., vertical/horizontal ) V/H), and likewise for the probe/analyzer pair, then a completely different kind of kinetics is predicted to be measured by the decay of the signal.18 That prediction is consistent with the experimental results shown in Figure 1b. Counterintuitively, that experiment directly records the rate of transitions among F ) (1 exciton states in quantum dots.18 It is worth mentioning that we are not observing an optical Kerr effect in these data. Furthermore, we
J. Phys. Chem. B, Vol. 109, No. 43, 2005 20061 note that a similar experiment cannot be devised using circularly polarized pulses (see Table 2 of ref 18). The polarization grating established by the pump pulse pair in our experiment is analogous to that discussed previously, for example, to measure sodium vapor velocity distributions.21 But because the selection rules for optical excitation of quantum dot excitons involve complex transition moments, the readout of the polarization grating decay by the probe is important. A qualitative understanding of the experiment can be garnered by considering the polarization grating properties and decay, as discussed by Fourkas et al.22 A cross-polarized linear excitation (e.g., VH) forms a transient population grating with a spatially varying polarization along each fringe, changing from left-hand circular to elliptical to linear to elliptical to right-hand circular, and so on. The diffracted intensity of the probe beam decays if any process disrupts that spatial polarization modulation, for example, rotational diffusion of a transition dipole. In the present case, the modulation is diminished when the circularly polarized transition moment flips concomitantly with transitions between the F ) +1 and F ) -1 exciton states. When the quantum dot c-axis is antiparallel to the k-vector of the incident radiation, light-handed circularly polarized light excites the states with total angular momentum F ) +1, while left-handed circularly polarized light excites states with F ) -1. A general microscopic description of the phenomenon was elucidated previously by evaluating rotational averaging for the coherent 3-TG spectroscopy.18 A rotational average for any third-order nonlinear spectroscopy is obtained by considering the action of a sequence of laser pulses, polarized in the laboratory frame according to the tensor Sabcd, on the internal selection rules acting in the nanocrystal frame, which respond as TRβγδ.23-25
〈P(3)(τ, tp, t)〉 ) CP(3)(τ, tp, t)
(1)
where C ) Sabcd mTRβγδ I(4) and P(3)(τ, tp, t) is the third-order induced polarization radiated by the sample. The tensor I(4) relates space-fixed to nanocrystal-fixed frames via rotationally averaged direction cosines. The field part, Sabcd, provides the polarization sequence of the three impinging laser pulses and the signal field radiated in the phase-matched direction. The susceptibility part TRβγδ is given by the response of the quantum dot according to transition moments for the relevant transitions. The superscript m labels the various pathways for generating a signal, for example, ground-state recovery or excited-state absorption. The result of such an analysis is simply a scalar that determines the signal intensity, for example, C ) 1/5 for the VVVV polarization sequence. The principle of the cross-polarized 3-TG experiment with a VHVH polarization sequence is that the sign of this rotational averaging factor changes if the exciton fine structure state changes (e.g., from F ) +1 to F ) -1) during the delay time tp between pump and probe. Such a sign change in C is equivalent to a π phase shift of the radiated signal field P(3)(τ, tp, t). Immediately after the pump pulse sequence, aside from nanocrystals excited to an F ) 0 state, half of the excited nanocrystals in the ensemble, n+1, will initially be in a state with F ) +1, while the other half, n-1, will have been photoexcited to a state with F ) -1. Dark states are not observed. Under those conditions, the rotational averaging contributes a factor of C ) 2/15. However, if the exciton fine structure state for some population of quantum dots changes during tp, then n+1 and n-1 decrease with concomitant increases in n′-1 and n′+1, where the prime indicates the change in exciton state. The latter population is spectroscopically indis-
20062 J. Phys. Chem. B, Vol. 109, No. 43, 2005
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tinguishable from the initially excited population, except that the rotational averaging factor changes sign for the signal associated with the population of quantum dots that are in the opposite |F| ) 1 exciton fine structure state to that initially excited by the pump pulse; C′ ) -2/15. That sign change provides a means of detecting transitions F ) +1 T F ) -1, that we call exciton spin relaxation to be consistent with similar dynamics known for quantum wells.17 The intensity of the homodyne-detected 3-TG signal therefore evolves according to
IHOM(tp) ∝
∫0∞ dt|P(3)(0, tp, t) ×
[152 (n
+1
+ n-1) -
|
2 2 (n′-1 + n′+1)] (2) 15
where P(3)(0, tp, t) is the induced third-order polarization as a function of pulse delay time between the temporally overlapped pump sequence and the probe, tp, radiated by the sample over time t. Because the exciton spin relaxation dynamics are faster than other contributions to the signal decay, I(tp) decays as the F ) (1 population evolves toward the equilibrium ks
n+1 + n-1 y\z n′-1 + n′+1
(3)
The rate of exciton spin relaxation can therefore be determined, because the cross-polarized 3-TG ensemble polarization decays as exp(-2kstp). For homodyne-detected signals, the measured intensity decays approximately as exp(-4kstp), where ks is the exciton spin relaxation rate. The F ) 0 exciton state population, that follows selection rules for linearly-polarized light, always contributes a positive-signed signal, therefore providing a background decaying according to the exciton recombination kinetics. In Figure 2a, we compare polarized 3-TG data collected in the ks phase matching direction using ultrafast laser pulses of 23 fs duration, centered on resonance with the lowest-energy exciton transition. The sample is 5.0 nm mean diameter nanocrystalline CdSe. The VVVV (all vertical) polarization sequence reveals the relatively long exciton recombination time as well as associated cooling dynamics, as is well-known from pump-probe studies.26 The VHVV trace is smaller by 2 orders of magnitude. Theoretically, that signal should be zero, but in practice, it provides a measure of the baseline signal arising from imperfect polarization conditions. The VHVH signal is initially as intense as the VVVV signal, but decays rapidly to an effective baseline determined by the signal from the population of quantum dots initially excited to the F ) 0 state. Marked quantum beats with the frequency ωLO ) 25.8 meV, corresponding to the LO-phonon, are evident in these data. Similar quantum beats are known, for example, from the work of Mittleman et al.27 The decay of the VHVH 3-TG signal derives from a distinctly different mechanism than those used in usual ultrafast spectroscopies, where the decay of signal intensity is proportional to exciton recombination or spectral diffusion. Such methods are insensitive to exciton spin relaxation dynamics because of the degeneracy of the states, the large inhomogeneous broadening that obscures the fine structure, and the fact that circularly polarized selection rules do not yield a suitable anisotropy experiment for an isotropic ensemble. The VHVH 3-TG experiment relies on an interference of polarizations from an ensemble to effect the measured intensity decay; the signal polarization changes sign after any exciton spin flip. Thus, the measurement is unaffected by inhomogeneous line broadening. However, the exciton spin relaxation rate is strongly size-
Figure 2. (a) Comparison of 3-TG data [5.0 nm diameter CdSe, 293 K in poly(butyl methacrylate)] for the VVVV, VHVH, and VHVV polarization sequences. For perfect polarization of the pulses, there would be no signal for the VHVV sequence. (b) VHVH 3-TG data in the ks phase matched signal direction (points) for CdSe nanocrystals, labeled according to their average radii. The solid lines correspond to fits using eq 4.
dependent, so we actually measure a distribution of rates according to the overlap of the laser pulse spectrum with the absorption band. Such a distribution appears as a single exponential in a curve-fitting procedure.28 Figure 2b shows the decay of the VHVH 3-TG data for CdSe quantum dots of various sizes. The VHVH 3-TG signals contain a long time decay contribution associated with exciton recombination, but the decay is dominated by ks. The marked size dependence of this exciton spin relaxation rate ks is evident. To analyze these data, input parameters for a nonlinear leastsquares analysis were obtained using a Hankel singular value decomposition algorithm. For the VHVH 3-TG signals, the exciton recombination rate k∞ was also a fixed parameter. Analysis of the VHVH 3-TG data retrieved fits according to
IHOM(tp) ≈ A1 e-4kstp + ALO e-2kLOtp cos(ωLOt + φ) + A3 e-k∞tp (4) shown as the solid lines. Here, kLO is the damping rate for quantum beats assigned to the LO-phonon frequency and φ is the phase of the oscillations. This is the usual way to obtain an approximate fitting of homodyne-detected transient grating data.29 For the fastest-decaying homodyne-detected signals, the
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J. Phys. Chem. B, Vol. 109, No. 43, 2005 20063 opportunities for using resonance energy transfer to transmit exciton spin states through space.31 Acknowledgment. The authors acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada, Canada Foundation for Innovation, Ontario Innovation Trust and Research Corporation. G.D.S. thanks the Alfred P. Sloan Foundation. V.M.H. and V.K. contributed equally to this work. Supporting Information Available: More details on the experimental setup, sample absorption spectra, and laser pulse profiles, as well as 3-TG data for a model dye control system, CdSe quantum dots with amine capping groups, and a sample in solution. This material is available free of charge via the Internet at http://pubs.acs.org.
Figure 3. Plot of the exciton spin relaxation rate (symbols) vs mean radii of the quantum dots. A point obtained from heterodyne-detected data30 is marked with an asterisk. The dashed line is a calculation of the rate assuming a Fermi Golden rule expression for the rate (see text) and an empirical R-3 form of the long-range exchange interaction.
first exponential in the fit actually represents a cross term between the exciton reoriention term and damping of the LOphonon.30 We have verified that by reconstructing homodynedetected data from the real and imaginary parts of heterodynedetected data.30 It was necessary to correct for those entangled kinetics in the results for the two smallest quantum dots. Detailed modeling of the kinetics shows their precise relationship to the measured signals, as will be reported elsewhere along with heterodyne-detected data.30 The rates of exciton spin relaxation versus mean diameter of the quantum dots are plotted in Figure 3. Examination of these data suggests that the exciton spin relaxation rate ks depends on quantum dot radius R with an attenuation going as ∼R-4 to R-6. Considering a Fermi golden rule rate expression, ks ) (2π/p)|VLR|2 FF, where VLR is the long-range exchange interaction and FF is the density of final states, that result is consistent with the anticipated size dependence of the long-range contribution to the exchange interaction for approximately spherical quantum dots. Tagakahara10 estimates that size dependence of VLR to follow ∼R-3, while a dependence closer to R-2 is predicted by the atomistic calculations reported by Franceschetti et al.4 We estimate that VLR is on the order of ∼1 meV, though we are still working on quantifying this interaction more accurately. In conclusion, we have shown that it is possible to probe the next level of detail underlying quantum dot exciton states, interactions between the quantum dot exciton fine structure states F ) (1, by measuring the dynamics of transitions among those states: exciton spin relaxation. That was possible by using an ultrafast transient polarization grating method and making use of the quantum dot selection rules for absorption of circularly polarized light. Significantly, it was demonstrated that such an experiment is possible, even in a rotationally isotropic system. The results for colloidal CdSe quantum dots revealed a strong size dependence for the exciton spin relaxation, consistent with its origin being attributed to a long-range contribution to the electron-hole exchange interaction. A ramification of these observations is that internal exciton spin relaxation proceeds more rapidly than resonance energy transfer between small quantum dots, thus influencing orientation factors and hampering
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