J. Phys. Chem. C 2008, 112, 4813-4817
4813
Simple Surface-Trap-Filling Model for Photoluminescence Blinking Spanning Entire CdSe Quantum Wires John J. Glennon, William E. Buhro, and Richard A. Loomis* Department of Chemistry and Center for Materials InnoVation, Washington UniVersity in St. Louis, One Brookings DriVe, CB 1134, Saint Louis, Missouri 63130 ReceiVed: October 16, 2007; In Final Form: December 24, 2007
The mechanism for synchronous photoluminescence intensity fluctuations, blinking, spanning entire micrometerlong CdSe quantum wires (Glennon, J. J.; Tang, R.; Buhro, W. E.; Loomis, R. A. Nano Lett. 2007, 7, 3290) is likely different than that commonly cited for semiconductor quantum dots. We present a simple model for the intensity blinking in quantum wires that is based on the dynamic, transient filling of surface-trap sites by photogenerated excitons and the emptying of these occupied trap sites. The model implements a kinetic Monte Carlo scheme and a dynamic photoluminescence quantum yield that depends on the fraction of trap sites filled. When a majority of the surface traps are filled, one-dimensional excitons are formed and a high emission efficiency is realized. Autocorrelation analysis of both experiment and simulation reveal the nonergodic kinetics governing the blinking phenomenon.
I. Introduction We recently reported that the photoluminescence (PL) spanning the entire lengths of individual CdSe quantum wires (QWs) can undergo synchronous intensity fluctuations, or blinking, with continuous illumination.1 A few percent of the QWs synthesized using the solution-liquid-solid (SLS) method are observed to blink between “dark” and “bright” states with the PL quantum yields, Φ, increasing from a background level of ≈0.5% to as high as 20% within the temporal resolution of the measurement, 30 ms. The duration of the whole-wire “dark” and “bright” events are found to be as long as 60 and 20 s, respectively. Similar, “on”/“off” PL intensity blinking has been investigated in numerous semiconductor quantum dots (QDs)2-6 and quantum rods (QRs).7 Blinking at localized regions on single CdSe QWs was also carefully characterized by the Kuno group,8 and statistics similar to those of the QDs were measured. In all of these previous reports, the observed spatial extent of the blinking was less than the spatial resolution of the measurement. In stark contrast, the whole-wire blinking is observed to span lengths as long as 15 µm at room temperature. Several models widely implemented for simulating blinking in QDs9-12 assert that the “off” events in QDs are the result of an electron becoming temporarily localized outside of the semiconductor core of the QD, leaving behind a positively charged core. Subsequently photogenerated electron-hole pairs undergo three-body, nonradiative Auger recombination with the charge in the core of the QD. The PL is restored to an “on” state when the QD is neutralized either by an electron returning to the core of the QD, whereupon the electron and hole recombine, or by the ejection of the hole from the QD during the aforementioned Auger process. A typical PL intensity-time trace for a blinking QD consists of “off” periods during which no PL is observed, and the PL intensity often reaches a common maximum intensity level when the properly passivated QD is * To whom correspondence should
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in an “on” state for a duration that is longer than the integration time of each measurement.4,6 The PL intensity-time traces for blinking CdSe QWs exhibit several significant differences from those of QDs,1 some of which are noticeable in Figure 1, parts a and b. The blinking CdSe QWs have a weak, continuous PL signal during “dark” periods; the background PL counts in Figure 1, parts a and b, are ≈28 000 counts per 50 ms bin width and are typically between 10 000 and 60 000 counts when using similar conditions. The “bright” events appear as spikes in the PL intensity with durations as long as seconds, but the maximum intensity levels fluctuate from event to event. There is also an induction period, typically ranging from 40 to 60 s, before the PL blinking is observed for QWs, whereas the blinking is nearly instantaneous for QDs. Even after a QW is observed to be blinking, if the irradiation is turned off, an additional time period is needed before the onset of the synchronous PL intensity fluctuations are again detected once irradiation is resumed. Last, the statistics for QD blinking seem to be independent of illumination power density,4,6 whereas with power densities of >500 W cm-2 the blinking QWs appear to remain in a constant “bright” state. Because of these differences the mechanism outlined above to explain blinking in QDs cannot reproduce the experimental observations of QW blinking. For QDs the maximum PL intensity levels achieved during an “on” event as well as for ensembles of QDs suspended in solution are highly sensitive to surface passivation.13-16 Additionally, the nonradiative relaxation rate, knrad, of excitons in CdSe nanocrystals has been shown to decrease in a reversible manner with irradiation,17 and this reversible behavior was attributed to a change in the surface-trap environment. The measured Φ values for ensembles of QWs in solution, (#), results that decreases as the number of filled trap sites, #, increases. A dynamic PL quantum yield that explicitly depends on # results, Φ*(#) ) krad/{krad + k/nrad(#)}. Although the details of the trap sites are not deduced from first principles, the simple distribution of trap energies implemented in the model reproduces quite well the experimental CdSe QW blinking data. The agreement between the data and the simulations supports the proposed model, and the observed PL intensity spikes occur during times when most of the trap sites are occupied and the QW is “dark” with a low Φ when anything less than most are filled. II. Model Details We use a kinetic Monte Carlo scheme to simulate the timedependent trajectory of the PL intensity of a single CdSe QW. To do so, probability distributions for every event are defined; specifically, separate distributions for emission, exciton trapping, trap emptying, and nonradiative decay are included. The pathways included in this model are illustrated in Figure 2. Absorption events that excite the system from the ground state, |g〉, to an excitonic state, |e〉, are assumed to occur at an average absorption rate, kexc, that is based on the estimated absorption cross section of a 1 µm long, 7 nm diameter QW (σ ≈ 2 × 10-11 cm-2)8 and a typical experimental, irradiation power density of 25 W cm-2. After the absorption of a photon, the exciton can recombine radiatively or nonradiatively, or it can become temporarily trapped in a surface-trap site. The low ensemble quantum yields for the QWs indicate that nonradiative recombination is the dominant pathway, and we assume that there exists only a small, finite probability, δ, that the exciton will become temporarily trapped. Although it is possible for excitons, electron-hole pairs, or single charge carriers, either electrons or holes, to become trapped in surface-trap sites, and a complete theory should account for the probabilities for each, we have chosen to include only the trapping of excitons in this model for a couple of reasons. The binding energies of the photogenerated 1D excitons are quite large in CdSe QWs, >100 meV,24,25 and a significant amount of energy would be necessary to separate the electron-hole pairs even at room temperature. Additionally, previous studies indicate that continued charging with irradiation does not occur in CdSe QWs; the total steadystate electron density on single CdSe QWs with continuous irradiation has been estimated to be at most 0.45-1.2 µm-1 along the length of the QW.26 This indicates that at most only
Model for PL Blinking in Quantum Wires a few additional charge carriers are photogenerated, especially considering that these QWs were found to have permanent mobile charges on the surface of the QW.26 Thus, Auger recombination either from charge-exciton or exciton-exciton collision events should be minimal at this power density.27 Therefore, under the conditions where PL blinking is observed the dominant nonradiative pathway is assumed to be from exciton recombination at surface-trap sites. Absorption events in these CdSe QWs are assumed to form 1D excitons that can sample the entire volume of the QW and interact with any of the unoccupied surface-trap sites. By keeping δ small, 0.004-0.01, the model maintains that most excitons will recombine nonradiatively when encountering a surface-trap site, and it is a rare event for an exciton to become temporarily trapped. In those events when an exciton does become trapped, # is increased by one, and subsequently formed excitons will encounter a smaller number of unoccupied trap sites, and a decrease k/nrad(#) and thus an increase in Φ*(#) will result. Since δ is so small, introducing a #-dependent δ would not significantly affect the simulation results, and we keep δ constant for simplicity. We assume the surface traps are not homogeneous, and thus the recombination rate of the trapped excitons, k/rec, represents a distribution of rates that correspond to the different types and characteristics of the surface traps present. In order to mimic a distribution of rates, the time each exciton remains in a trap site is drawn from a power-law distribution with the same parameters as the power-law distribution used by Verberk et al.28 in simulating the trapping of charge carriers and coreshell QD blinking. A parameter, sc, scales the power-law distribution to an average observed trap time, and a second parameter, γ, represents the ratio of the potential barriers for an exciton to go from the core to a trap site to that for a carrier to go from a trap site back to the core. Since we presume that the trap sites are lower in energy than the excited state, γ < 1. For our simulations, γ is held between 0.65 and 0.80 on the basis of the results of Verberk et al.28 The parameters sc and γ that govern the distribution of occupied surface traps in the simulations were defined by Verberk et al.28 and were systematically varied to investigate their role in the simulations. As mentioned above, the probability distribution curve for the time that excitons remain in a surface trap follows a power law with every time an exciton can remain trapped, t, assigned a probability, P(t). By increasing sc by a factor c, the probability of P(t) also increases by c. So simulations with larger sc values yield longer “bright” events because the excitons remain trapped for a longer average time. The values of sc utilized ranged from 1000 to 27 000. The experimental data were best reproduced with sc in the middle of this range, near 15 000. Given a constant set of all other simulation parameters, only negligible differences arise when sc is increased or decreased by a few thousand about this value. The simulations are much more sensitive to the value of γ, which was varied from 0.65 to 0.8 with the larger value representing an increased propensity for a carrier to return from a trap site to the semiconductor core. For a given scaling factor, sc, smaller values of γ produce higher intensity spikes superimposed on a slightly higher and noisier background PL level. In contrast, for the smallest values of γ no intensity spikes are observed because the surface traps empty slowly, and the Φ*(#) of the QW is always very high. If the value of γ is increased, the simulated data have a smaller, less noisy background PL level and lower intensity spikes. A change of γ from 0.77 to 0.75 results in an increase in the background PL intensity of
J. Phys. Chem. C, Vol. 112, No. 13, 2008 4815 ≈1500 counts in a 50 ms bin width. The intensities of the spikes relative to the background signal also increase by nearly 5×. If the algorithm randomly determines that an exciton does not become trapped, which is >99% of the time, then the current value of Φ*(#) determines whether relaxation is radiative or nonradiative. Radiative recombination of the exciton or electronhole pair occurs after a time drawn from an exponential distribution with a decay rate krad ) 4 × 108 s-1 ) (τ)-1 ) (2.5 ns)-1. The radiative lifetime for CdSe QWs is currently not known, but PL decay curves were fit to double-exponential decays with a short-time component of ≈200 ps and a longtime component of ≈2.5 ns, which would be closer to the radiative lifetime.27 Nevertheless, lifetime values spanning from 700 ps to 10 ns were used, and no significant changes were noticeable in the data. The experimental excitation is at 488 nm, far above the band gap of the QW, ≈690 nm, and thus stimulated emission does not occur and is not considered. Additionally, intraband relaxation occurs on time scales, ≈3 ps,27 that are much faster than the other Poisson processes, and it is not explicitly included. The first-order radiative decay events are mapped onto the (0, 1) uniform distribution for use in a random number generating algorithm to determine the precise timing of each emitted photon. As mentioned, the low ensemble Φ of the CdSe QWs,
