J. Phys. Chem. C 2008, 112, 5423-5431
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Exciton Trapping and Recombination in Type II CdSe/CdTe Nanorod Heterostructures Marcus Jones, Sandeep Kumar, Shun S. Lo, and Gregory D. Scholes* Department of Chemistry, Institute for Optical Sciences, and Center for Quantum Information and Quantum Control, 80 St. George Street, UniVersity of Toronto, Toronto, Ontario M5S 3H6, Canada ReceiVed: NoVember 19, 2007; In Final Form: January 25, 2008
Trap states are known to influence the excited-state dynamics in nanocrystalline semiconductors, but the nature and magnitude of the exciton-trap interaction is poorly understood owing to the relative optical inactivity of carrier traps and the heterogeneity of trap-state distributions. Nanocrystal time-resolved fluorescence measurements are typically complex traces that contain information about both radiative and nonradiative processes. The interpretation of these fluorescence transients is nontrivial, and typical multi- or stretched exponential analyses yield little specific photophysical information. Here, we develop a stochastic model of nanocrystal exciton and trap-state dynamics, which is used to describe coupled excitonic and charge-transfer photoluminescence from a series of CdSe/CdTe collinear quantum rod heterostructures. In this way we evaluate the photoexcitation dynamics of core nanocrystal states: the CdTe exciton and CdSe(e-)-CdTe(h+) chargeseparated state and states associated with one or more trapped charge carriers. We describe the overwhelming influence of traps on the population dynamics and resolve population changes caused by the addition of a surface passivating ligand. Additionally, the long radiative lifetimes of the charge-separated state are reported.
1. Introduction Quantum confinement is responsible for size-tunable excitonic photoluminescence (PL) in nanocrystals, in which at least one physical dimension is smaller than the exciton Bohr radius.1,2 Relatively small changes in size and shape induce significant PL energy changes, which when coupled with the intrinsically high room-temperature quantum efficiency of nanocrystal excitonic PL, make these materials very attractive for applications in lasers,3,4 LED displays,5,6 or as biological labels.7 However, an impediment to the use of nanocrystals in these emerging technologies is their susceptibility to exciton trap states, which enhance nonradiative decay channels and can drastically reduce PL quantum efficiency, especially for longlived excitons. A major challenge, therefore, is to develop an understanding of the dynamics of exciton traps. In this work, we construct a model that enables the extraction of trap-state energies and population rates from time-resolved PL measurements on a series of novel quantum rod heterostructures. Time-domain studies of optical transients are a way to clarify the microscopic mechanisms and dynamics of radiative and nonradiative decay phenomena. Time-correlated single photon counting (TCSPC) provides a means to determine the fate of photogenerated excitons on time scales of ∼10 ps and longer; however, structural inhomogeneities, which are characteristic of excitons in nanoscale systems,8 often preclude quantitative analysis of the underlying processes that give rise to subtle changes in the shape of complex decays. An ensemble of semiconductor nanocrystals, for example, is inhomogeneous by nature: even the best synthetic methods give rise to a distribution of shapes and sizes. Additionally, these materials contain a high proportion of atoms near an interface (surface or boundary), where incomplete passivation or epitaxial strain can produce carrier traps, which interact with exciton states and * To whom correspondence should be addressed. E-mail: gscholes@ chem.utoronto.ca.
affect the dynamics of time-resolved photoluminescence. For example, while it has been shown, in a few special cases, that excitons in CdSe or CdTe quantum dots can decay with singleexponential kinetics,9,10 the vast majority of nanocrystal systems studied to date have been found to show multiexponential decays. These nonexponential kinetics are thought to be caused by the presence of trap states. Trap states in nanocrystals are usually pictured as surface atoms with a partial positive or negative charge at which an electron or hole may become temporarily localized.11,12 Deep trap sites may also refer to crystalline defects within the core of the nanocrystal. Surface traps may be reduced by encapsulation with a wide band gap material, e.g., ZnS or CdS,13-18 or by careful selection of one or more ligands that are able to bind to as many sites as possible while keeping the nanocrystals suspended in solution.19-21 Trap sites energies are likely distributed, reflecting their dispersion about the surface of nanostructures,12 and their dynamics are poorly understood due to the inherent difficulty of accessing nonradiative states. They have previously been introduced to explain PL-upconversion data in II-IV nanocrystals, and transitions between these states and the valence and conduction band edges have been shown to affect TCSPC decays.22,23 Recent work24 described the synthesis and characterization of heterostructured nanocrystals consisting of fused, collinear, rodlike segments of CdSe and CdTe. A typical transmission electron microscopy (TEM) image of these systems is shown in Figure 1, and for a detailed discussion of their structure we refer the reader to the article by Kumar et al.24 At the interface between CdTe and CdSe segments, the band edges are offset to give a type II alignment: i.e., the valence and conduction band energies within the CdTe segment are respectively higher energy than the valence and conduction bands in CdSe. As a result, it is energetically favorable to form a charge-separated (CS) state after photoexcitation. Indeed, it was found24 that measurable PL originated from two excited states: CdTe
10.1021/jp711009h CCC: $40.75 © 2008 American Chemical Society Published on Web 03/18/2008
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Figure 1. (a) TEM image of a typical CdSe/CdTe heterostructure preparation showing a collection of fairly uniform rodlike structures ∼20 nm long and ∼4 nm wide. (b) Representative PL and absorption spectra of three CdSe/CdTe heterostructure samples and of a sample of CdSe nanorods that were precursors to the heterostructure sample characterized with a solid black line.
excitonic PL and red-shifted PL from the CS states consisting of an electron in the CdSe segment and a hole in CdTe. Typical absorption and PL spectra, shown in Figure 1, demonstrate that the energies of absorption and PL features may be tuned by adjusting the size and shape of the constituent segments. They also show that while the absorption cross section of CdSe and CdTe exciton states is much higher than that of the CS state, the PL is typically dominated by the red-shifted CS state PL. Charge transfer is therefore likely to play an important role in the excitation kinetics of these heterostructures. Radiative recombination from the CS states should be very slow due to small electron-hole wavefunction overlap. Indeed, long PL decays with average lifetimes up to ∼1 µs were measured24 for the CS states. Their long lifetime is likely to make CS states susceptible to the influence of trap states. Hence, an estimate of the CS state radiative lifetime must account for both carrier recombination and trapping. An important ancillary conclusion of the present work is that surface trapping is not always an irreversible process during the excited-state lifetime, so trap states do not always diminish the PL quantum yield, at least not in a straightforward way. CS states in nanocrystals with type II band alignment could provide an effective route for extracting charge carriers from nanocrystals since their relatively long lifetimes increase the chance that diffusion-controlled electron or hole transfer will occur. Additionally, optical amplification in the single exciton regime has recently been demonstrated using core-shell quantum dots in which CS states are formed.3 It is, therefore, important to know the recombination rates of CS states and understand how their population is affected by associated trap states. We show in this paper that information about nonradiative trap states can be extracted from the careful analysis of PL transients. The energy and dispersion of trap states can be affected by the type of coordinating molecule surrounding nanocrystals, so to discern the affect on the excited-state kinetics of changing the chemistry around the nanocrystals we have looked at PL data from “as-synthesized” heterostructure samples as well as samples to which an excess of tri-octyl phosphine (TOP) has been added. We demonstrate a kinetic scheme that effectively models PL from both radiating states and hence derives the photoinduced heterostructure excitation dynamics. 2. Experimental Section 2.1. Sample Preparation and Characterization. Two nanocrystal samples were prepared and analyzed for this
Jones et al. experiment. The same general method was used to synthesize both samples, although small variations in the conditions resulted in two rather different size distributions. Sample 1 was prepared by first dissolving 124 mg of CdO in a mixture of 0.4 g of tetradecyl phosphinic acid (TDPA) and 1.6 g of tri-octylphosphine oxide (TOPO) (90% technical grade) by first evacuating at 75 °C for 2 h, followed by heating at 330 °C under an argon atmosphere. Once an optically clear solution was achieved, Se-tri-octyl-phosphine (Se-TOP) solution (20 mg in 1.5 mL of TOP) was injected rapidly at 306 °C. The nanocrystals were then allowed to grow for 4.5 min at 280 °C, and an aliquot was taken out to examine the resulting CdSe nanocrystals. Te-TOP solution (55 mg in 2 mL of TOP) was then injected rapidly at 280 °C, and the resulting nanocrystals were allowed to grow for a further 8 min at 260 °C. The reaction was terminated by removal of the heating mantle, and when the solution reached 50 °C anhydrous MeOH was added to precipitate nanocrystals. These were then cleaned twice with MeOH and redispersed in toluene. To synthesize sample 2, 128 mg of CdO was dissolved in a mixture of 1.65 g of TOPO and 0.36 g of TDPA by first evacuating at 70 °C for 2 h, followed by heating at 340 °C under an argon atmosphere. Once an optically clear solution was obtained, Se-TOP solution (31 mg of Se in 1 mL of TOP) was injected at 310 °C and grown at 280 °C for 7 min. An aliquot was taken out at this stage to analyze the seed CdSe sample. Te-TOP solution (51 mg in 1.5 mL of TOP) was then injected rapidly. The nanocrystals were allowed to grow for another 7.5 min in the temperature range of 260-270 °C. Removing the heating mantle quenched the growth of nanoparticles. At 50 °C, about 5 mL of toluene was added to extract the reaction mixture and nanoparticles were precipitated by adding methanol. The sample was twice cleaned with a methanol/butanol mixture and finally redispersed in toluene for further measurements. 2.2. Spectroscopic Measurements. Steady-state PL spectra were recorded using a Fluorolog-3 (JYHoriba) spectrometer that utilized a xenon arc light source, an R928 PMT instrument (Hamamatsu) for visible wavelengths, and a liquid-nitrogencooled InGaAs photodiode for near-IR wavelengths. PL dynamics were measured by TCSPC, using an IBH Datastation Hub system with an IBH 5000M PL monochromator and a R3809U50-cooled MCP PMT detector. The light source was a model 3950 picosecond Ti:sapphire Tsunami laser (Spectra-Physics), pumped by a Millenium X (Spectra-Physics) diode laser and frequency doubled using a GWU-23PL multiharmonic generator (Spectra-Physics). The excitation wavelength for the photon counting experiment was 450 nm. Single photon counting data were analyzed by least-squares iterative reconvolution of a model decay function with an experimentally determined instrument response. The shortest event, tmin, that the TCSPC experiment can resolve is dependent on the laser pulse width, the detector response time, and the channel width. Assuming at least 3 orders of magnitude between signal in the channel with maximum intensity and the background signal, it is usual to conservatively approximate tmin to be approximately 20% of the full width at half maximum (fwhm) of the instrument response peak.25 The fwhm of the IRF in our experiment is 330 ps, so we estimate that tmin ≈ 70 ps. 2.3. Kinetic Data Analysis. The aim of this paper is to develop a kinetic model that effectively reproduces coupled time-resolved PL decays measured on several heterostructure samples, while treating trap-state contributions in a simple and
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consistent manner to reveal useful information about radiative and nonradiative decay processes occurring in these systems. Given an arbitrary N-state kinetic scheme, the dynamics of exciton relaxation are formulated schematically in terms of probabilities, Fn(t), that the state n is populated at time t after excitation. Values of Fn(t) are determined by finding the solution to a series of rate equations:
dFn(t) dt
) -γRn Fn(t) +
NR (γNR ∑ mn Fm(t) - γnm Fn(t)) m*n
(1)
NR where γNR mn (γnm ) are the nonradiative transition rates from state m(n) to state n(m) and γRn is the radiative transition rate from NR state n. Given a rate, γNR mn , then the reverse (uphill) rate, γnm , for states m and n having energies Em and En (Em > En) is determined according to detailed balance, where kB is the Boltzmann constant:
(
)
Em - E n γmfn ) γnfm exp kBT
(2)
Equation 1 represents one of a collection of N-coupled ordinary differential equations to which it is possible to find numerical solutions using standard linear algebra methods based on the eigenvalue problem. The resulting expressions for Fn(t) are N-exponential functions from which the time-resolved PL signals for any state with a nonzero radiative rate are calculated with eq 3.
In(t) ) γRn Fn(t)
(3)
The function In(t) can be directly compared to recorded PL decays, Dn(t), after convolution with a measured instrument response curve, G(t):
Dn(t) ) sn(In(t) × (G(t) - cG)) + cD
(4)
where sn is a scaling factor and cG and cD are the background levels of the recorded instrument response and decay data. An iterative fitting procedure may then be utilized wherein some or all of the En, γnm, and sn values are varied until the recorded decays are modeled within accepted tolerances. As mentioned in the Introduction, the major advantage of performing a kinetic analysis of this kind on a type-II CdSe/ CdTe heterostructure is due to the existence of two steady-state PL peaks24 arising from the finite probability that either a CdTe exciton or a CS state may exist in a single CdSe/CdTe nanorod heterostructure. PL transients recorded at the maxima of these two peaks are therefore coupled and may be modeled simultaneously using a single kinetic scheme. Such a global analysis of two data sets reduces parameter uncertainty and thereby increases the confidence in derived values of Fn(t). 2.4. Justification of the Use of a Single Kinetic Scheme. The electronic structure of CdSe/CdTe is strongly dependent on the size and shape of the two quantum rod segments,24 and structural inhomogeneities within an ensemble cause broadening of the nanocrystal PL peaks26 and concomitant variations in radiative rates. Similarly, the energy, location, and abundance of trap states depend on many subtle factors related to synthesis methods and on the surfactants used to disperse the nanocrystals in solution. It is, therefore, important to estimate the accuracy of using a single kinetic scheme to model measurements made on an inhomogeneous ensemble system. To achieve this, we used an instrument response function, collected using the
TCSPC apparatus described above (channel width ) 119 ps), together with a Monte Carlo convolution method27 to simulate the TCSPC data generated by two series of normalized lognormal lifetime distributions, R1(τ) and R3(τ)
RN(τ) )
N
1
n)1
τσnx2π
∑
( ( ))
exp -
ln(τ/µn)
x2 σn
2
(5)
where µn and σn are the mean and the standard deviation of the nth distribution, respectively. Log-normal functions were chosen to reflect the distribution of rates in an activated process given a normal distribution of activation energies within the ensemble. The decay functions are then given by
IN(t) )
∫0∞ RN(τ) exp(- τt ) dτ
(6)
Once the simulated data were produced they were analyzed in the usual way to extract an analytical N-exponential best-fit decay function. By the repetition of this procedure for a range of σn values, it is possible to deduce the maximum standard deviations of an N-component log-normal lifetime distribution that can be modeled acceptably with an N-exponential decay function. This was done for N ) 1 with µn ) 20 ns and for N ) 3 with µn ) 2, 20, and 200 ns; for simplicity, a single value of σ was used for each distribution (σn ) σ). We have employed two statistical tests to gauge fit quality, reduced chi-squared, χ2r , and the Durbin-Watson parameter, dW, (both defined in ref 28), and the values of these tests are depicted in Figure 2A, wherein a range of σ values are highlighted within which both the N ) 1 and N ) 3 data could be modeled within accepted tolerances25 (χ2r < 1.2 and dW > 1.85). This corresponds, as shown in Figure 2B for the N ) 1 lifetime distribution, to a fwhm of up to 4.7 ns about a mean value of 20 ns and σmax ) 0.1. Also plotted for comparison in Figure 2B is the first component of the N ) 3 lifetime distribution that can be acceptably modeled (with σmax ) 0.15) and has a fwhm of 6.9 ns, which demonstrates that multiexponential decays effectively lower the resolution of single photon counting data unless the data collection time is dramatically increased. A recent study10 has shown that spontaneous emission rates in CdTe and CdSe quantum dots have a linear dependence on PL energy, as expected from Fermi’s golden rule. Corresponding lifetimes range from ∼15 ns (2.35 eV) to ∼40 ns (1.72 eV) in CdTe (∼3.5-8 nm diameter29) and from ∼18 ns (2.22 eV) to ∼36 ns (1.89 eV) in CdSe (∼3-8 nm diameter29,30). Since quantum dot syntheses typically produce a size dispersion of ∼10%, the spontaneous emission lifetime distribution within an ensemble of CdSe and CdTe quantum dots is expected to be less than 5 ns for both large and small dots. Depending on the mean lifetime, this is close to or within the bounds of the maximum log-normal lifetime distribution calculated above (4.7 ns when the mean lifetime is 20 ns but 8.3 ns at 40 ns assuming σ ) 0.1) and explains why inhomogeneous CdSe and CdTe samples can be prepared that still produce single-exponential PL decays.10 In addition, the data in Figure 2A,B indicate that increasing the number of lifetime distributions allows the σmax value to increase, which lends further credence to the assertion that inhomogeneous systems can be modeled with a simple sum of exponential function and, hence, by a single kinetic scheme. 3. Results and Discussion In this section we first introduce and characterize four CdSe/ CdTe heterostructure preparations. Absorption and steady-state
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Figure 2. Synthetic data produced using two series containing N ) 1 and N ) 3 normalized log-normal lifetime distributions and subsequently analyzed by iterative reconvolution of N-exponential functions with recorded instrument response data. (a) The quality of the exponential fit, as judged by χ2r and dW and plotted versus distribution width, σ. The thick, horizontal dashed lines represent the acceptable upper and lower limits of χ2r and dW, respectively, and the thin vertical dashed lines are the values of σmax for N ) 1 and N ) 3. (b) The log-normal distribution function at σ ) 0.1 for N ) 1 (solid line), and the shortest component of the distribution function at σ ) 0.15 for N ) 3 (dashed line).
TABLE 1: Collected Photophysical Data from Samples I and II CdSe
CdSe/CdTe
sample
lgth (nm)
diam (nm)
lgth (nm)
diam (nm)
CdTe tavg (ns)
CS tavg (µs)
χ2r
dW
γ(CdTe) (ns) R
γ(CS) R (µs)
γet (ps)
PTrap/ PCore
1a 1b 2a 2b
8.41 8.41 8.97 8.97
4.46 4.46 5.14 5.14
14.28 14.28 13.38 13.38
5.41 5.41 5.25 5.25
112 82 46 44
0.745 0.751 1.300 1.821
1.10 1.13 1.11 1.17
1.96 1.83 1.93 1.82
39.8 39.5 12.7 7.5
4.95 4.81 2.37 2.07
200 200 199 117
32.9 26.1 174.4 86.8
PL data are presented from which the energies of exciton and CS states are derived. These values are then fed into a kinetic model, which is systematically constructed in Section 3.2. We use this model in Section 3.3 to analyze PL transients measured on each of the samples and discuss how this treatment uncovers the dominance of trap states in the excitation dynamics of these materials. We shall illustrate how subtle changes in TRPL data, induced by nanocrystal surface modifications, may actually represent significant changes in trap-state population dynamics. In addition, we isolate radiative rates that are virtually invariant to surface modifications and derive estimates of the electrontransfer rate. Finally, in Section 3.4, we consider the difficulties of determining the initial populations of exciton states and judge the effect of a range of initial conditions on the derived kinetic parameters. 3.1. Sample Characterization. We report the analysis of time-resolved PL from two CdSe/CdTe heterostructure nanorod samples, denoted 1 and 2. The size and shape of each of these samples is outlined in Table 1. Each of the samples was divided into two equal amounts, and solvent was added: diluting 1 and 2 with toluene formed 1a and 2a, respectively, and the addition of a TOP/toluene mixture formed 1b and 2b. TOP binds to Se and Te (it is used to dissolve elemental Se and Te during synthesis), and its lone pair of electrons facilitates binding to Cd at the surface of the heterostructures. Excess TOP was therefore added to colloidal CdSe/CdTe in an attempt to reduce the surface trap density and thereby modify the PL dynamics. Steady-state absorption and PL spectra for each of these
Figure 3. Absorption and steady-state PL spectra recorded on two heterostructure preparations before (red lines) and after (blue lines) treatment with excess TOP solution. Inset: diagram of type II band alignment between CdSe and CdTe segments.
samples are presented in Figure 3. Consistent with previous work,24 the spectra of samples 1a and b show two distinct excitonic absorption features and a red tail corresponding to weak excitation of the CS state. Absorption to CdSe is redshifted by about 100 meV in samples 2a and b, relative to samples 1a and b and almost completely obscures the CdTe
Type II CdSe/CdTe Nanorod Heterostructures transition, which now appears as a small shoulder. PL from φCS is also dramatically red-shifted as shown for sample 2a. These differences are consistent with a relatively wider CdSe nanorod segment in samples 2a and b as evidenced by the TEM data presented in Table 1. The addition of TOP to sample 1a causes an approximately uniform blue shift of CdSe and CdTe absorption energies by ∼30 meV, consistent with a slight shrinking of the nanorods, possibly caused by coordination and subsequent solvation of surface atoms by TOP. Virtually no peak shift was observed in sample 2, although uncertainty in the peak energy of the partially obscured CdTe transition makes precise measurement difficult. The energies of CdSe and CdTe exciton states and of the CS state are estimated to be midway between the Gaussian fitted peak positions in absorption and PL spectra (the CdSe PL was recorded on a sample of seed CdSe nanorods). Photoluminescence quantum yields were measured by comparison with a dye (magnesium phthalocyanine in propanol) whose quantum yield is known to be 0.76. Each of the samples used in this study had quantum yields in the range of 5-10%. 3.2. Constructing a Kinetic Scheme. In the limit of low excitation intensity, the average generated population of electronhole pairs per heterostructure is ,1 and nonlinear processes such as Auger ionization may by disregarded. Using the simple picture of type II CdSe/CdTe quantum rod heterostructures inset in Figure 3, we consider two exciton and two CS core states, + which are, in order of increasing energy: φCS (eCdSe hCdTe), X + X + φCdTe (eCdTe hCdTe), φCdSe (eCdSe hCdSe), and φCS* (eCdTe h+ CdSe), where the superscript “X” denotes an exciton state and the dominant location of the electron and hole is indicated in the parentheses. States φXCdTe and φXCdSe are localized mainly within one segment of the heterostructure, while φCS and φCS* correspond to CS states delocalized over the both segments. As shown in Figure 3, direct photoabsorption to φCS (tail extending to the red of the excitonic features), φXCdTe and φXCdSe is easily identified, while high-energy features and light scattering obscure any transition to φCS* states. Although strong e-h exchange interactions and crystal-field anisotropies give rise to optically bright and dark exciton fine structure states,31-34 these have been ignored because the thermal population of bright states dominates these measurements. Depopulation of the core states may occur in a number of ways including radiative recombination and carrier localization at surface traps and direct coupling to phonon modes associated with the ground state. In addition, intersegment charge transfer from φXCdTe and φXCdSe can populate φCS, and φXCdTe can be formed from φXCdSe by resonant energy transfer (RET). Significantly, PL is only observed from the two lowest energy states, φCS and φXCdTe, and not from φXCdSe or φCS*. If formed, the φCS* state’s radiative recombination rate is likely to be rather slow and depopulation by charge transfer will probably occur long before PL. The lack of PL from φXCdSe could be due to fast hole transfer and/or resonant energy transfer to φXCdTe. Assuming otherwise similar radiative and nonradiative relaxation rates for φXCdSe as for φXCdTe, the observations of significant φXCdTe PL but nothing from φXCdSe requires that the rate of hole transfer is several orders of magnitude faster than that of electron transfer, which makes it unlikely that the former mechanism is wholly responsible for the lack of φXCdSe PL. Conversely, quenching of PL by RET from φXCdSe to φXCdTe requires strong coupling between φXCdSe f φGS and φGS f φXCdTe transitions. This has been dealt with from a quantum electrodynamics standpoint for two coaxially fused quantum dots,35 where it was shown that
J. Phys. Chem. C, Vol. 112, No. 14, 2008 5427 virtual photon propagation leads to the conservation of spin information during RET. Given the segments’ parallel transition dipoles36 and the large overlap between φXCdTe absorption and φXCdSe PL spectra, RET is a likely pathway for φXCdSe depopulation; however, the rate of RET depends strongly upon the extent to which the dipole coupling approximation breaks down for two conjoined nanocrystal segments.37-39 Assuming negligible absorption of 450 nm photons by φCS and φCS* because the extinction coefficient is small,40 we suggest a kinetic scheme wherein φXCdSe and φXCdTe are rapidly populated after photoexcitation. The rate of hot carrier relaxation differs for electrons, which decay via a size-dependent Auger mechanism, and holes, for which nonadiabatic transitions mediated by the surface ligands are the dominant relaxation channel.41 These ultrafast processes are predicted to be well beyond the resolution of our TRPL experiment41-46 and we have found that the resulting fits are insensitive to the precise value of the relaxation rate, as long as it is more than 0.05 ps-1. We therefore state that both the φXCdSe and φXCdTe states are populated according to a time constant of 1 ps. The proportion, F0CdSe and F0CdTe, of the total excitation relaxing to the φXCdSe and φXCdTe states, where F0CdSe + F0CdTe ) 1, is more difficult to determine. Values may be obtained from the relative extinction coefficients of the CdSe and CdTe quantum rod segments for 450 nm photons; however, the complexity of the absorption spectrum at high energies makes extraction of this information unfeasible. Instead, we have made the assumption that F0CdSe ) F0CdTe in all the calculations described in Section 3.3 and discuss, in Section 3.4, the effects on the fitted parameters when F0CdSe and F0CdTe are varied. The radiative rates of CdTe quantum dots have been reported by Wuister et al.,47,48 and their values are used as initial guesses in our analysis. Due to the extended nature of the wavefunction and the large average distance between electron and hole, the radiative decay rate of φCS is likely to be much longer than that of φXCdTe. Additionally, electron-phonon coupling in CdSe and CdTe quantum dot exciton states is weak,49-51 so it is likely that phonon-coupled nonradiative decay is a minor relaxation pathway for all the core states. For simplicity, we have, therefore, assumed no nonradiative decay from φXCdSe, φXCdTe, and φCS, but have instead considered all nonradiative recombination to originate from trap states, which may couple much more effectively with local vibrational modes. Trap states clearly have an affect on nanocrystal decay kinetics, but although there have been a few studies on the involvement of trap states in the exciton dynamics of CdSe quantum dots,52,53 trap energies and rates of carrier trapping are poorly characterized. We consider a general scheme wherein either charge carrier may become temporarily localized on the surface of the nanocrystal. One electron trap state, φeX, and one hole trap state, φhX, are defined for both φXCdSe and φCS states. In addition, we allow for the possibility that both carriers may become sequentially trapped resulting in a dual trap state, φeh X. The kinetic scheme used to model time-resolved PL is presented in Figure 4. Nine states are drawn: three core states (φXCdSe, φXCdTe, and φCS) and three trap states associated with both φXCdTe and φCS. Trap states associated with φXCdSe have been omitted for clarity. As shown, the three core states are interconnected by charge transfer (γet and γht) and resonant energy transfer (γRET) processes. Trap states are connected to the core states via an electron or hole trapping process (γ(X) e or (X) (X) γ(X) ) whence dual trap states may be formed (γ or γ h e,h h,e ). (X) Radiative decay (γR ) originates only from core states while
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X X Figure 4. Kinetic scheme used to model TCSPC data showing three band-edge states, φCdSe , φCdTe , and φCS, together with six possible trap-state configurations. Individual trap states are represented by dotted lines. Filled (open) circles are photogenerated electrons (holes). Arrows indicate transitions between states that occur with rate γXn . Other symbols include electron (e), hole (h), electron/hole transfer (et/ht), and resonant energy transfer (RET). The radiative and nonradiative transitions to the ground state are denoted by R and NR, respectively.
nonradiative recombination occurs only from trap states. For simplicity, we have defined just two nonradiative γ(CdTe) and NR X γ(CS) NR , involving trap states that are associated with φCdTe and φCS, respectively. The energies of φXCdSe, φXCdTe, and φCS, estimated from PL and absorption spectra, were held constant, together with the hot carrier relaxation rate, during the analysis, but all other state energies and rates were allowed to vary. 3.3. Analysis of PL Transients. When the time-resolved PL data recorded on each of the four samples are fitted, in the usual way, with an arbitrary multiexponential decay function shown in eq 7, average PL lifetimes, τavg, may be calculated according to eq 8.
I(t) )
( ) t
∑n Rn exp - τ
(7)
n
τavg )
∑n Rnτn2 ∑n
(8) Rnτn
These are presented in Table 1 and are found to be consistent with previously reported CdSe/CdTe TRPL measurements.24 The average PL lifetime of the φCS state is 6.7 to 41 times longer than that of the φXCdTe state; however, the addition of TOP to samples 1a and 2a causes two rather different responses. A 27% decrease in τavg(φXCdTe) is observed in sample 1, with little change in τavg(φCS), but conversely, in sample 2, τavg(φCS) increases by 40% with only slight variation in τavg(φXCdTe). While this indicates that trap-state modulation by TOP addition will change the PL dynamics, it is clear that the standard method
of analysis reveals little about the underlying photophysics. Multiexponential functions with at least five lifetime components, ranging over 3 orders of magnitude, were required to satisfactorily model the data, which indicates that the number of states (excluding the ground state) involved in the temporal evolution of the excitation is at least five; however, as suggested by the findings presented in Section 2.4, it is very likely to be many more. The time-dependent average populations of φCS and φXCdTe are reflected, by eqs 3 and 4, in the transient PL signals, ICdTe(t) and ICS(t), measured at the peaks of the CdTe and CS PL. With the use of the kinetic scheme described in the previous section and illustrated in Figure 4, the transient PL signals from all four samples have been accurately modeled. To illustrate the ability of this model to reproduce heterostructure TCSPC data, we present in Figure 5a PL transients recorded on samples 1a and b together with the fitted curves obtained using the kinetic scheme. Weighted residuals for each of the two fits (two data sets are modeled in a single fit), also shown in Figure 5, are virtually featureless and symmetric about zero: indicating an excellent reproduction of the experimental data. Values of χ2r and dW, obtained after fitting the kinetic scheme to TCSPC data from all the samples, are included in Table 1. In each case, the two statistical parameters are close to or within the acceptable range defined in Section 2.4. The fitted curves acquired for all four samples are plotted (minus the experimental data for clarity) in Figure 5b. The precise model used to fit samples 1a and b, including all the trap-state energies and transition rates, is illustrated in detail in Figure 6. It was found that, in both cases, a single CdSe trap state was required to model the PL transients; otherwise, each model is identical to the scheme outlined in Figure 4. It should be emphasized that the number of trap states
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Figure 5. (a) TCSPC data recorded at the peak of the steady-state CdTe (left) and CS PL in samples 1a (blue) and b (red). Solid black lines are fits to data obtained by application of the kinetic scheme illustrated in Figure 4. Weighted residuals from each of these fits are also presented. (b) The fitted decay functions obtained for samples 1 and 2.
Figure 6. Detailed kinetic scheme that is able to simultaneously X reproduce time-resolved PL from φCdTe and φCS states in samples 1a and 1b. All transition rates are shown, and radiative and nonradiative transitions are indicated with solid and dashed lines, respectively. The three core states are labeled and shown as thick blue horizontal lines; the trap states are red. Horizontal braces indicate that the nonradiative recombinations from all CdTe and all CS traps are each approximated by a single rate.
used in these models is simply the minimum required for an acceptable fit, and additionally, a thorough search of parameter space failed to yield any alternative solutions. It is very likely that the energies and rates calculated here represent average values of a trap-state manifold within an ensemble of heterostructures. Likewise, errors in the parameters reported in Figure 6, estimated by calculating the standard deviation of each of the parameters, must be taken into account when estimating the model’s accuracy. If the upper and lower error limits, γ( L , of
(logγ(σγ), where σ is rate parameter, γ, are defined by, γ( γ L ) 10 the standard deviation of γ, we find that, in sample 1a, the values of σγ are similar for all γ and the average is 0.060. For a process γ with a reported rate of 0.01 ps-1 (τ ) 100 ps), we therefore find 0.9 × 10-2 ps-1 < γ < 1.1 × 10-2 ps-1. Similarly, the average standard deviation of trap-state energies in sample 1a is found to be 13 meV. The calculated radiative lifetimes of the φXCdTe and φCS states in all four samples are listed in Table 1. The φXCdTe radiative lifetimes extracted for samples 1a,b and 2a,b are approximately what one might expect for CdTe nanorods of these sizes,29 and the radiative lifetime of φCS is, as previously conjectured,24 very long (>4.5 µs for samples 1a and b and >2 µs for samples 2a and b). Both radiative rates change only slightly after addition of TOP. At ∼200 ps in samples 1a and b, the electron-transfer rate appears to be virtually unaffected by the considerable change in trap-state kinetics; however, there is a marked decrease in γet for samples 2a and b. The accuracy of these values is probably somewhat low, considering the resolution of the experiment. Perhaps the most dramatic difference shown in Figure 6 between the schemes for samples 1a and b is the change in the trap states associated with φXCdTe: enhanced passivation raises the average trap-state energy by ∼100 meV. In addition, γ(CdTe) and γ(CS) NR NR increase by factors of 2.2 and 1.4, respectively. These are consistent with elimination of the lowest energy (deepest) trap states and concomitant reduction of trap density by interaction with TOP, leaving shallower traps from which carrier recombination requires smaller activation energy. In contrast, the average energy of trap states associated with either φXCdTe or φCS states in sample 2 does not change by more than 20 meV, but the recombination rate γ(CdTe) still increases by a NR factor of 2.6. The time-dependent occupation probabilities, Fn(t), for samples 1 and 2 are presented in Figure 7, where to ensure clarity, the contribution of trap states associated with φXCdTe and with φCS have been summed to give two total trap contributions: trap X Ftrap CdTe(t) and FCS (t), and contributions from φCdSe and associated traps have been omitted. The affects of TOP on the occupation dynamics of samples 1 and 2 are reflected by dramatic changes between the red (a) and blue (b) dashed curves in Figure 7: while the shapes of FCdTe(t) and FCS(t) do not trap change much upon TOP addition, Ftrap CdTe(t) and FCS (t) change significantly in both samples. This change can be
5430 J. Phys. Chem. C, Vol. 112, No. 14, 2008
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Figure 7. Excited-state occupation probability, Fn(t), for samples 1 and 2, a (red) and b (blue), plotted versus time. Core states are depicted with X and φCS states are respectively summed and are represented with dashed lines. Inset histograms solid lines while the trap states associated with φCdTe report the percent change in integrated occupation probability (Pn) observed after the addition of TOP to 1a and 2a, respectively.
quantified by considering the integrated occupation probability, Pn ) ∫ Fn(t) dt, of state n. The percent changes of Pn for each of the four excited-state occupation probability functions after the addition of TOP to samples 1a and 2a are plotted as histograms in Figure 7. The histograms reveal some important trends but also highlight the complexity of the kinetics in these systems. Perhaps the most easily rationalized change involves the CdTe trap states, whose total occupation probability, Ptrap CdTe, decreases by ∼60 and ∼25% in samples 1 and 2, respectively. Since CdTe is the dominant material near the surface of the entire heterostructure, including a thin shell over the CdSe segment, the addition of TOP effects the dynamics of the φXCdTe state most strongly, so elimination of surface trap states will limit the number of trap states into which an electron or hole may be transferred. Trap states associated with φCS appear to behave rather differently in samples 1 and 2, where Ptrap CS increases by ∼16% and decreases by ∼12%, respectively. An increase in the total φCS occupation probability, observed in both samples, would be expected to produce a parallel rise in Ptrap CS ; while this is true for sample 1, there appears to be an opposing effect in sample 2 that causes an overall decrease in Ptrap CS . A clue to what might be causing this effect comes from the TEM data presented in Table 1. The diameter of the CdSe/CdTe heterostructures is always greater than that of the CdSe seed nanorods from which they were grown, and the magnitude of this difference approximately equates to twice the thickness of the CdTe shell. In sample 1 the shell is ∼0.5 nm, but in sample 2 it is, on average, only ∼0.05 nm, which is less than one monolayer and probably indicates patchy lateral coverage of the CdTe over the CdSe. The relative proximity of the surface in sample 2 increases the probability that a CdSe-localized electron in the φCS state of sample 2 will become localized at a surface trap site. TOP-induced surface changes will therefore affect the dynamics of the φCS state in sample 2a more than in sample 1a, thereby causing the overall drop in Ptrap CS . This effect also suggests that a potentially important reaction should be added to the kinetic scheme, namely, that of the direct electron transfer from CdTe-localized to CdSe-localized Cdδ+ electron trap sites. In fact, the distinction between φeCS and φeCdTe (and hence e+h between φe+h CS and φCdTe) is likely to be somewhat blurred when the thickness of the CdTe shell is small. Unfortunately, the limited number of samples precludes accurate consideration of this effect. Significantly, when we evaluate the total occupation probability of core states (φXCdSe, φXCdTe, and φCS), PCore, versus trap
states, PTrap, where PCore/Trap ) ∑Core/Trap Pn, we find that in all samples the total probability of finding a heterostructure in an excited trap state is, as shown in Table 1, much larger than the likelihood of seeing a core excited state. Even though the addition of TOP to samples 1a and 2a has the effect of reducing the relative probability of trap state occupation, they still appear to dominate the excited-state dynamics. We note that the PL quantum yields were measured between ∼5 and 10%, and despite the high level of occupation of nonradiative trap states, the PL quantum yields calculated exactly from the kinetic schemes for samples 1a and b were 1.3 and 1.7%, respectively, and for samples 2a and b they were 1.55 and 2.0%, both fairly close to the measured values. Note that in both cases, the addition of excess TOP caused the PL quantum yield to increase. In Section 2.4, we justified using a single kinetic scheme to analyze ensemble data; however, one scenario in which the arguments presented in Section 2.4 may break down concerns an inhomogeneous distribution of trap states whose energies are close to a radiative state. The reverse trapping rate is strongly dependent on the energy gap between trap state and radiative state (eq 2), so the quantum yield calculated for a model with just four discrete trap states could be rather different from the yield calculated on a more realistic system in which a continuous distribution of trap states is considered. This may explain why the calculated yields are slightly lower than the measured values. 3.4. Initial Population Distributions. As discussed in Section 3.2, it is extremely difficult to uncover the initial relative occupation probabilities, F0CdSe and F0CdTe, so in the previous section we simply assumed that F0CdSe ) F0CdTe. To justify this assumption we have repeated the analysis of PL transients in samples 1a and 2a for a wide range of F0CdTe values between 0 and 1. With the use of the parameters derived for the case when F0CdTe ) 0.5 as a starting point, calculations were performed iteratively by slowly increasing or decreasing F0CdTe. The ranges over which F0CdTe could be varied while maintaining an acceptable fit to the PL transients were 0.1 > F0CdTe > 0.6 and 0.3 > F0CdTe > 0.7 for samples 1a and 2a, respectively. Over these ranges, it was found that both γ(CdTe) and γ(CS) remained R R essentially unchanged in both samples; however, the recovered electron-transfer rate was found to increase significantly in the analysis of sample 1a from ∼200 ps at F0CdTe ) 0.6 to ∼500 ps at F0CdTe ) 0.1. A corresponding but smaller increase was observed in sample 2a. Importantly, varying F0CdSe and F0CdTe did not strongly affect the ratio, PTrap/PCore, which decreased, for example, in sample
Type II CdSe/CdTe Nanorod Heterostructures 1a from ∼33 at F0CdTe ) 0.1 to ∼29 at F0CdTe ) 0.6. This indicates that whatever the initial excitation conditions, trap states dominate the kinetics of carrier recombination. 4. Conclusions The preceding discussion demonstrates a clear dependence of the photogenerated excitation dynamics in CdSe/CdTe nanorod heterostructures on the energy and distribution of surface trap states. We have shown that a relatively simple kinetic scheme is able to model coupled PL transients and demonstrated that subtle variances in PL decays may be caused by significant changes in trap-state population dynamics. Although the schemes almost certainly do not constitute an exact representation of the excited-state kinetics in these systems, they are the simplest models that could successfully reproduce the experimental data and, as such, they capture the essence and relative importance of the exciton and trap-state processes that are occurring in the nanocrystals. Importantly, these schemes confirm that the energy and distribution of trap states have a dominant effect on the population of radiative states: even after treatment with a passivating ligand, the total integrated occupation probability of trap states in either sample exceeded the total probability of finding a core excitation by more than an order of magnitude. This is a remarkable result considering the relative paucity of attention directed toward understanding the dynamics of nanocrystalline carrier traps. Acknowledgment. The Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged for support of this research. G.D.S. acknowledges the support of an E.W.R. Steacie Memorial Fellowship. References and Notes (1) Brus, L. J. Phys. Chem. 1986, 90, 2555. (2) Efros, A. L.; Efros, A. L. SoViet Phys. Semicond. 1982, 16, 772. (3) Klimov, V. I.; Ivanov, S. A.; Nanda, J.; Achermann, M.; Bezel, I.; McGuire, J. A.; Piryatinski, A. Nature 2007, 447, 441. (4) Klimov, V. I.; Mikhailovsky, A. A.; Xu, S.; Malko, A.; Hollingsworth, J. A.; Leatherdale, C. A.; Eisler, H. J.; Bawendi, M. G. Science 2000, 290, 314. (5) Ganesh, N.; Zhang, W.; Mathias, P. C.; Chow, E.; Soares, J. A. N. T.; Malyarchuk, V.; Smith, A. D.; Cunningham, B. T. Nat. Nano 2007, 2, 515. (6) Coe, S.; Woo, W. K.; Bawendi, M.; Bulovic, V. Nature 2002, 420, 800. (7) Medintz, I. L.; Uyeda, H. T.; Goldman, E. R.; Mattoussi, H. Nat. Mater. 2005, 4, 435. (8) Scholes, G. D.; Rumbles, G. Nat. Mater. 2006, 5, 920. (9) Fisher, B. R.; Eisler, H. J.; Stott, N. E.; Bawendi, M. G. J. Phys. Chem. B 2004, 108, 143. (10) van Driel, A. F.; Allan, G.; Delerue, C.; Lodahl, P.; Vos, W. L.; Vanmaekelbergh, D. Phys. ReV. Lett. 2005, 95. (11) Califano, M.; Franceschetti, A.; Zunger, A. Nano Lett. 2005, 5, 2360. (12) Lifshitz, E.; Dag, I.; Litvitn, I. D.; Hodes, G. J. Phys. Chem. B 1998, 102, 9245. (13) Creti, A.; Anni, M.; Rossi, M. Z.; Lanzani, G.; Leo, G.; Della Sala, F.; Manna, L.; Lomascolo, M. Phys. ReV. B: Condens. Matter Mater. Phys. 2005, 72. (14) Li, J. J.; Wang, Y. A.; Guo, W. Z.; Keay, J. C.; Mishima, T. D.; Johnson, M. B.; Peng, X. G. J. Am. Chem. Soc. 2003, 125, 12567. (15) Lifshitz, E.; Glozman, A.; Litvin, I. D.; Porteanu, H. J. Phys. Chem. B 2000, 104, 10449. (16) Jones, M.; Nedeljkovic, J.; Ellingson, R. J.; Nozik, A. J.; Rumbles, G. J. Phys. Chem. B 2003, 107, 11346.
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