CdS Quantum Rod

LETTER pubs.acs.org/NanoLett

Ultrafast Electronic Delocalization in CdSe/CdS Quantum Rod Heterostructures E. Ryan Smith, Joseph M. Luther, and Justin C. Johnson* National Renewable Energy Laboratory, 1617 Cole Boulevard, Golden, Colorado 80401, United States

bS Supporting Information ABSTRACT: Femtosecond cross-polarized transient grating (CPTG) and polarization anisotropy were used to probe the extent of electronic delocalization in CdSe/CdS quantum rod heterostructures (QRH) with a “dot-in-rod” geometry. The alignment of the bulk valence and conduction band edges of CdSe and CdS suggest a “type I” band configuration, leading to localization of both the electron and hole on the CdSe seed, but size quantization effects make the distinction less clear. Photoexcited electrons in 2.1 and 2.9 nm diameter structures have considerable excess kinetic energy above the CdS conduction band and show clear evidence of electron delocalization into the surrounding shell. However, the dependence of the CPTG decay rate on aspect ratio for 2.9 nm seeded QRHs is minimal, suggesting that the delocalization is mostly isotropic (i.e., not preferentially along the rod length). The rates for the 2.1 and 2.9 nm QRHs fall in line with expected trends based on effective exciton size. The 4.2 nm diameter structures also lack any rod length dependence of the CPTG decay and instead exhibit a biexponential decay that is indicative of coupled pathways for fine structure relaxation, likely due to anisotropic interfacial strain. CPTG is found to serve as a unique tool for determining charge transfer and delocalization in nanoheterostructures, which can rarely be predicted accurately from examination of bulk band offsets. KEYWORDS: Nanorods, heterostructures, exciton wave function, polarized transient grating

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dSe/CdS colloidal quantum dot embedded in a nanorod (“dot-in-rod”) heterostructures are useful platforms for investigating the consequences of band offsets, a concept developed for bulk semiconductors, in the regime of strong quantum confinement.1 In such quantum rod heterostructures (QRHs), the energy difference between the quantized CdSe and CdS conduction band levels can be tuned with size, resulting in exciton wave function localization in the CdSe seed2 to extensive charge transfer or delocalized wave functions.3 Quantification of the rate and degree of delocalization across an interface is essential for realizing nanoheterostructures that perform well in functional device architectures for which they are often touted. Some applications require rapid charge separation (i.e., photovoltaic or photoelectrochemical schemes4) whereas colocated charges may be beneficial to improve light-emitting efficiencies or energy transfer rates in other applications.5 Moreover, the rate of multiple exciton generation (MEG), and its reverse Auger recombination, can be manipulated by adjusting the electron
hole interaction strength.6 The relationship between fast delocalization and fast MEG must be controlled in arrays of nanostructures that are designed to take advantage of exciton multiplication for photovoltaics.7 We discuss energy level alignment here because the application of band offsets determined from bulk CdSe and CdS may be misleading: dot-in-rod structures have a nonplanar interface, increasing the role of strain,8 and they are not isotropic, which means that a charge carrier is not influenced by just one band offset but instead a continuously varying potential that depends on direction. r 2011 American Chemical Society

Works showing that the heterostructure’s radiative rate decreases with increasing rod length9 or that certain rods exhibit anomalous photoluminescence excitation spectra10 support the concept of a delocalized electronic wave function spreading into the CdS rod. Other investigations have noted the distinct polarized emission arising from these heterostructures,11 which could result from either dielectric effects or alteration of the exciton fine structure through anisotropic deformation of the excitonic wave function.12 In the latter case, both wave function delocalization and crystal field effects may induce such a fine structure perturbation, which brings the c-axis polarized transition lower in energy than those with polarization perpendicular to the c-axis (the direction of a wurtzite crystal). At sizes corresponding to nearly degenerate conduction bands of CdS and CdSe, band mixing may occur, resulting in eigenstates with hybrid character. Borys et al. found that small variations in the heterostructure shape can cause a spread in barrier heights for the near-degenerate CdS/CdSe conduction bands in a “quasitype II” regime.13 Sitt et al. used multiexciton photoluminescence intensity thresholds to argue for quasi-type II behavior for QRHs with seeds smaller than 2.8 nm.14 Despite many investigations, some disagreement persists about the degree of delocalization of the electron wave function and how it depends on size/shape of the heterostructure. Investigations Received: August 18, 2011 Revised: September 28, 2011 Published: October 19, 2011 4923

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Figure 1. Exciton fine structure of wurtzite quantum nanocrystals. Solid lines represent levels that couple to photons, and dashed lines represent optically dark levels. Double headed arrows represent pathways for fine structure relaxation, following the scheme given in ref 18 (mirror image pathways are omitted). Energy splittings are not to scale.

involving photoemission of heterostructures can often be plagued by an uncertainty about the role of strain and interface states in the emission dynamics. Interpretation of decay profiles may be complicated by a large distribution of trapping and detrapping rates that must be accounted for quantitatively.15 Techniques that are not influenced by picosecond and slower processes are preferred because they reveal the true initial excited state wave function rather than a convolution of secondary processes. Femtosecond pump
probe techniques are particularly useful in this regard, although the transient absorption features that result can be difficult to interpret.16 We instead use the four-wave mixing process cross-polarized transient grating (CPTG), which provides high signal-to-noise ratios and fast-decaying signals due to relaxation among the lowest exciton fine structure states. The CPTG decay rate is dictated by changes in the angular momentum projection of the exciton, more generally referred to as spin flip, as it relaxes through the fine structure levels. For wurtzitic nanocrystals, the exciton fine structure consists of nominally degenerate states with a total projection of the angular momentum along the crystal axis (F) of 0, ( 1, and (2.17 The rate of electron/hole spin flip can depend on both exchange and spin
orbit coupling effects, which are interactions that are sensitive to electron
hole overlap and thus size quantization. Mixing of states within the exciton fine structure manifold allows spin relaxation in which the sign of the spin is conserved (e.g., F = 0 T F = (1 or F = (1U T F = (1L) or flipped (e.g., F = (1 T F = -2). A schematic including the fine structure levels and dominant spin relaxation pathways is shown in Figure 1. In wurtzitic nanocrystals such as CdSe, the F = 0 and F = (1 states are mixed by strain, which can be due to acoustic phonons and lattice mismatch at interfaces in heterostructures.19 Large spin
orbit coupling interactions due to the heavy atom effects cause the latter process. Both of these coupling matrix elements are dependent upon 1/d2. However, the strain effects are dependent on the actual size of the nanocrystal, whereas the spin
orbit coupling depends on the exciton size.18 This distinction becomes particularly clear in the CdSe/CdS system, where the exciton wave function is likely to expand into the surrounding shell because of the relatively small conduction band offset. As a result, the CPTG rate can serve as a selective ruler for the “size” of the exciton and effective electron/hole separation. Several investigations of CdSe and CdSe/CdTe nanocrystals using CPTG have characterized how the spin flip rate depends on nanocrystal size.18,20,21 For rods and spheres, the dependence is roughly 1/d4,18 while for the type II heterostructures22 there is a distinct dependence on the CdSe shell thickness, which

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determines the conduction band offset. Separating the electron and hole in a type II structure greatly decreases the spin flip rate. A reduced CPTG decay rate is also expected as charges separate in the CdSe/CdS QRHs and should allow for a quantitative determination of electron
hole overlap. We use the CPTG decays in conjunction with emission polarization anisotropy and steady-state absorption/emission to characterize electronic delocalization in a series of QRHs with varying aspect ratio and size. Experimental Section. The CdSe seeds and CdSe/CdS rods (QRHs) were synthesized according to the procedure found in ref 23 and suspended in toluene. The size of the CdSe seed was calculated from the location of the first exciton absorption peak using the relationship found in Yu et al.24 For simplicity, the nanocrystals will be referred to by the size of the CdSe seed (2.1 nm seed or 2.1 nm QRH) used in their synthesis throughout this manuscript. Each sample was washed in total 5 times similar to ref 23, alternating the use of octylamine and nonanoic acid to produce an optically transparent solution before the addition of methanol and centrifugation. Finally the QRHs were suspended in hexane or toluene for optical experiments. QRHs with varying aspect ratios were grown seeded with 2.9 and 4.2 nm CdSe dots. The 2.9 nm QRHs with aspect ratios 2:1, 4:1, and 7:1 have extra layers of CdS deposited in the radial dimension, as evidenced by the larger absorption red shift with increasing rod length (see Supporting Information Figure S1). The concentration of 4.2 nm seeds and postinjection CdS rod growth time was carefully controlled when synthesizing batches of 4.2 nm QRHs with aspect ratios of 6:1, 10:1, and 13:1. For wurtzitic CdSe crystals, CdS rod growth occurs fastest in the direction of the crystal axis,10 therefore a low seed concentration was used to limit the growth of CdS in the radial dimension. The absorption red shift for the 4.2 nm QRHs (0.05 eV) was insensitive to the length of the rod. Transmission electron microscopy (TEM) images confirm the width of the QRH does not vary with length (Supporting Information Figure S2). All samples for transient grating experiments were placed in sealed cuvettes of 1 or 2 mm thickness in a glovebox in oxygenfree conditions. All samples were dissolved in hexane with the exception of the 2.1 nm QRHs, which were suspended in toluene. Hexane was found to have a lower saturation concentration than toluene. Thus, a precipitate would often settle out of solution a few hours after preparation, leaving the remaining solution nonscattering, but of lower optical density. The sample was still used for transient grating experiments with care taken to avoid probing or disturbing the precipitate. The optical density for each sample at the peak laser wavelength used in the experiment ranged from 0.08 to 0.18. The absorption spectrum of the seeded rods is shown in Figure 2 with the laser spectrum used in the CPTG experiment overlaid. The absorption spectrum of each sample was taken every day it was under test to check for oxidation (signified by a shift of the absorption spectrum to the blue) and aggregation (increased scattering at nonresonant wavelengths). Most samples showed no sign of oxidation after weeks in the sealed cuvettes. The CdSe exciton peak of the QRHs did not shift even after prolonged exposure to air, although those samples were not used in transient grating experiments. Detailed theory of cross-polarized transient grating experiments is described in ref 21. The experimental setup has previously been described in Johnson et al.25 Briefly, frequency-doubled pulses from a 10 kHz regenerative Ti:Sapphire amplifier (Quantronix Integra-HE, 780 nm fundamental) pumped a home-built noncollinear optical parametric amplifier (NOPA) to produce visible pulses. The output beam of 400 μJ pulses of 100
150 fs duration 4924

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Figure 2. Optical and structural characterization of CdSe/CdS quantum rod heterostructures. (Upper left) Absorption spectra of QRHs (solid) in order of increasing seed diameter (sample A = 2.1 nm, 7:1 aspect ratio; sample B = 2.9 nm, 4:1 aspect ratio; sample C = 4.2 nm, 5:1 aspect ratio) with spectra of laser used in transient grating experiment superimposed (dotted line). Panels labeled A, B, and C correspond to the TEM image of QRH samples A, B, And C, respectively. The scale bar on the TEM images is 25 nm.

passed through a 0.4 mm BBO doubling crystal, producing approximately 100 μJ pulses at 390 nm. A few microjoules of the fundamental beam were sent through a delay line and focused onto a 2 mm sapphire plate to produce a spatially uniform, stable continuum that seeds the NOPA. A pass through a 1 cm piece of glass stretched the continuum, allowing for better wavelength selectivity in the amplification stages. The doubled beam was split by an 80:20 beamsplitter with the low energy portion crossing the continuum at a 6° angle in a 1 mm BBO crystal for the first stage of amplification. Both the continuum and pump beams were focused by reflective optics, but both pump beams focused before the crystal to avoid damage and possible thermal effects. The amplified seed was again focused, crossed, and temporally overlapped with the high energy portion of the pump beam in another 2 mm BBO crystal. The visible beam was collimated and compressed by a pair of BK7 prisms separated by approximately one meter. The NOPA produced laser pulses tunable from 490 to 620 nm ranging from 50 to 25 fs in duration at the sample position. Some experiments on the 4.2 nm seed and QRH were performed using a 1 kHz Clark amplifier. The characteristics of the NOPA output did not change after replacement of the Clark amplifier with the Quantronix system despite the higher rep-rate, that is, the experiments on the 1 kHz system repeated at the higher rep-rate produced results that were identical within error. The beam was split into three copies of approximately equal power by a succession of pellicle beamsplitters with each beam traversing a delay stage followed by a half waveplate and linear polarizer. This allowed independent control of the polarization and power in each beam. Beam k1was chopped at 5 kHz (k2 at 500 Hz for the 1 kHz system). After the delay arms, the beams were set parallel to one another, and spatially arrayed in the boxcar configuration before focusing into the sample at a crossing angle of ∼3° by reflection off a curved mirror. The signal in

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the ks =
k1 + k2 + k3 direction was apertured before being recollimated, sent though a detection polarizer, and refocused onto a silicon photodiode. The signal was sent into a lock-in amplifier referenced to the chopper frequency, and the output digitized and processed using software. The delay of beams k2 and k3 could be independently step-scanned, allowing for autocorrelation of all three beams in a 0.05 mm BBO crystal at the sample position to determine temporal overlap and pulse width. For the transient grating experiment, k1 and k2 were temporally overlapped and k3 scanned. Pulse energies for transient grating measurements were typically 30
50 nJ/pulse. No dependence on pulse energy was measured for nanocrystal CPTG decay constants or amplitudes when the pulse energies were decreased by a factor of 4. Neat toluene produced a measurable nonresonant optical response that decayed much faster than most nanocrystal CPTG decays, therefore fits to data began after 50
60 fs (see below for further detail). Measurements were performed in hexane to confirm the toluene response was not obscuring the nanocrystal CPTG decays. The polarization of each of the three excitation beams and the detector polarizer could be independently set. A cuvette of CS2 placed at the sample position was used to optimize the transient grating signal. When the laser was tuned to the shortest wavelengths to probe the 2.1 nm seed and rod samples, the width of the coherence spike of the all vertical (k1 = V, k2 = V, k3 = V, ks = V) CS2 transient was used to determine the pulse width. The sample replaced the CS2 cuvette and only the k3 delay was changed. Transient grating data were taken using several different polarization configurations for each sample. A full data set at a particular polarization configuration is an average of 3
6 individual transient grating scans taken sequentially. To account for long-term drift in the laser intensity, individual scans were designed to take no more than 20 min. Scans had fixed time steps. Scans of the 2.1 nm nanocrystals, which showed the fastest dynamics, had the minimum possible time step of 2/3 fs, whereas the 2.9 nm nanocrystal scans had 4 fs time steps, and the 4.2 nm nanocrystals scans had 10 fs steps. VVVV scans were taken to measure population dynamics on the time scale of the measurement. Crossed polarized transient grating (CPTG) scans were performed using VHHV when k2 was chopped or VHVH when k1 was chopped. These two configurations convey the same information,21,26 and scans should be identical when using homodyne detection. Polarization mismatched VVVH scans were performed to measure any residual nonlinear signal that came about from imperfectly polarized pulses. Several data sets were acquired for each sample across different days. Results. In addition to cross-polarized transient grating experiments, time-resolved emission and transient absorption polarization anisotropy were measured for each sample. In all cases, the dots are found to exhibit essentially no anisotropy (0.1 ps
1) spin-flip rates in the 4.2 nm seed samples. Also, CPTG experiments on QRH samples that had 4927

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Figure 5. Spin flip rates extracted from fits to CPTG traces compared against exciton size. Exciton size is calculated using the relationship between peak exciton wavelength and diameter given in ref 24. The dotted fit line includes the fast 4.2 nm QRH rates, and the dashed line includes the 4.2 nm slow rates.

undergone size-selective precipitation to drastically reduce the number of tetrapods revealed the same behavior. Therefore, we conclude that the zinc blende/tetrapod shaped-nanocrystals are not the cause of the biexponential behavior and likely do not contribute substantially to the CPTG signal. To compare CdSe seeds to that of the QRHs, we calculated the “effective” exciton size. The term “effective” is defined as the size dictated by the first exciton peak absorption wavelength observed in the dot-in-rod referenced to the experimental first exciton wavelength vs size curve for CdSe seeds.24 Figure 5 shows an average of decay rates taken from multiple data sets for the various samples plotted against effective CdSe seed size. The predominant (fast) spin-flip rates of the QRHs fall along the same curve as the dots when using the effective exciton size for the dot in rod. A power law fit to the data including the fast 4.2 nm QRH decay leads to a 1/d4.6 dependence with exciton size. Excluding both 4.2 nm QRH decays produces the same result. Including the slow 4.2 nm QRH decays leads to 1/d1.9 dependence. A 1/d4 relationship is theoretically predicted for CdSe nanocrystals.18 It is clear from Figure 5 that spin relaxation rates, excluding the 4.2 nm QRH data points, all follow the same qualitative trend when compared against effective exciton diameter. The variation of fitting parameters is likely a result of the relative paucity of nanocrystal sizes investigated here compared to previous studies,18,20,30 and to a fundamental change in the nature of the 4.2 nm QRH exciton. In our discussion below, we attribute the low dependence of spin-flip rate as a function of rod length for the 2.9 nm QRHs to isotropic expansion of the exciton. Constraining the fit to all but the 4.2 nm QRHs to be proportional to 1/d4 predicts a spherical exciton diameter of 4.4 nm from the fast QRH decay, but the slow decay cannot be correlated to a diameter using that fit function. Rather than rely on purely statistical arguments to explain the data, in the discussion below we use physical arguments to propose that (1) the expansion of the exciton in 2.1 and 2.9 nm QRHs is isotropic and (2) the exciton distorts from spherical to oblate in the 4.2 nm QRHs, and the accompanying change in exciton fine structure causes the biexponential spin relaxation dynamics. Discussion. Cross-polarized transient grating experiments have shown that excitonic fine structure can reflect information about exciton size in homogeneous spherical and rod-shaped

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structures.21,25 Much of the discussion below will concern what conclusions can be made about the actual shape of the exciton in CdSe/CdS QRHs. When the empirical effective exciton diameter is taken into account, most QRH samples analyzed fit the same trend in spin-flip rate as the seed. Calculations of the electron and hole wave functions in CdSe/CdS core
shells show that the electron spreads significantly into the shell,31 increasing the size of the exciton. Some wave function delocalization is experimentally confirmed by comparing the continuous red-shifting of the absorption spectrum with increased shell growth,31,32 and more directly measured in the CdSe/CdS QRH by the scanning tunneling spectroscopy measurements of Steiner et al.2 The effective diameter calculated for each of the QRHs is only 1
3 CdS monolayers (0.35 nm per monolayer) larger than the diameter of the seed, suggesting that the exciton spreads in accordance with the increase of the radial diameter of the heterostructure. This conflicts with a common interpretation based on the linearly polarized emission from CdSe/CdS QRHs that the conduction electron wave function spreads out a significant distance away from the seed along the long axis of the rod.13 This interpretation proposes that encapsulation of the CdSe seed by the CdS rod, and concurrent delocalization of the electron wave function along the rod axis, changes the alignment and strength of the fine structure states. Theory predicts that the optically active fine structure state 0U (polarized along the rod axis) is energetically stabilized compared to the (1U and (1L states (polarized perpendicular to the rod) as the exciton wave function deforms from spherical to prolate. We also observe polarization anisotropy in ensemble photoluminescence experiments. We observed no trends in anisotropy as a function of CdSe seed size, and very little difference in the anisotropies of samples with different aspect ratios. Recent analysis of time-resolved photoluminescence polarization anisotropy data of CdSe/CdS QRHs has shown that electric field absorption is strongly reduced in the radial direction by dielectric effects, which depends only on the dielectric constants and shape of the particle, not the dipole moments of the fine structure manifold.11 This effect limits the information about fine structure states that can be learned from emission experiments. CPTG experiments, however, are sensitive only to dynamics that affect the nonzero spin states. From our CPTG results, we make arguments based on energetics that suggest that extended delocalization along the axis of the rod need not be invoked. Within the effective mass approximation, the kinetic energy of the lowest confined electron and hole levels of a spherical nanocrystal in a potential well, and their Coulombic interaction energy, can be calculated numerically according to Schooss et al.33 To assess the effect of the change in confinement potential upon replacing the toluene solvent with a CdS shell, we begin by calculating the degenerate 1Se (electron) and 1S3/2 (hole) levels of CdSe in a dielectric environment of toluene. The values achieved using this theory may only be qualitatively correct, but they provide some intuition about the nature of the wave function in the seed and QRH. Since the effective mass of the electron is less than that of the hole (me = 0.11, mhh = 0.45), the 1S3/2 energy is much less dependent upon the magnitude of the barrier.17,34 First, we will discuss the implications of these calculations for the smaller QRHs. Empirical calculation of QRH effective diameters suggest the exciton wave function spreads out only 1
2 monolayers (0.35 nm/CdS monolayer) beyond the seed, which corresponds to the increase in radial thickness determined with TEM. The 1Se 4928

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Figure 6. Differences in fine structure and expected spin relaxation kinetics between spherical and oblate excitons. (A) (Top) Schematic of conduction band potential (gray), kinetic energy eigenstate (dashed line), and wave function (solid black) for QRH (left) and QRH with surface strain (right). The material boundaries are marked by changes in color. (Bottom) Evolution of fine structure energy splittings upon exciton deformation. The evolution of the splitting between the (1 levels, ΔEU,L, and the rate constant for the fast spin flip process, k+,
is shown. The thickness of the line represents the oscillator strength for a level. The (2 level has zero oscillator strength. The dark 0L state is omitted from the diagram for simplicity. (B,C) CPTG signal calculations (black lines) compared against 4.2 nm seed (red dots) and 4.2 nm QRH CPTG (blue dots) data. Parameters (given in text) of model are varied according to expected changes in the fine structure manifold on going from a spherical exciton to an oblate exciton. (D) Fits to seed (red line) and QRH (blue line) CPTG data. Kinetic processes dominating the QRH CPTG signal during each differently shaded time period are overlaid on the plot.

level for the 2.1 and 2.9 nm seeds in toluene is 1.00 and 0.66 eV above the CdSe bulk conduction band, respectively. Including a coating of 1
2 monolayers of CdS in the calculations (see Tables S4
S6 in Section III of Supporting Information for a summary of these calculations) reveals that the confinement energy in that core
shell system still exceeds the 0.3 eV potential barrier at the interface by 100
400 meV. The electron and hole wave functions extend partially into the CdS shell, producing a larger effective exciton diameter. Adding the electron
hole Coulomb interaction term into the Hamiltonian produces optical bandgap energies that are within 0.1 eV of experimental values. Thus the isotropic expansion of the exciton into the surrounding shell could account for the absorption redshift. The small change in the 2.9 nm QRH spin-flip rate upon extension of the rod from an aspect ratio of 2 to 4, as seen in the inset of Figure 4A, is more consistent with the slow growth of CdS in the radial dimension than the large increase in the axial dimension. Indeed, there is spread in the spin-flip rate data that masks any systematic changes that may occur purely as a function of added CdS rod length. This suggests that electron
hole attraction overcomes the energetic stabilization that would accompany extended delocalization. The red shift of the 4.2 nm seeds is much less dependent on the aspect ratio, in accordance with the care taken to control synthesis conditions that limited the CdS growth to the axial dimension of the rod. Since we have ruled out sample inhomogeneity, which varies for different aspect ratios (Supporting Information Figure S1), as a source of the unique behavior of the 4.2 nm QRHs, we believe the two spin-flip processes to be coupled pathways intrinsic to the QRH. The calculated confinement energy of the electron in the 4.2 nm seed is 0.39 eV above the conduction band. The addition of 1
2 monolayers of CdS reduces the confinement energy equal to or below the CdS conduction band potential. The low kinetic energy relative to the confinement potential means the electron and hole wave functions are more sensitive to the actual potential energy landscape of the QRH, rather than the idealized band diagram often drawn for heterostructures. A schematic of this concept is shown in Figure 6A, in which an idealized cylindrical QRH is shown

compared against the axial and radial electronic potential energy surfaces, with projections of the spherical wave function corresponding to the 1Se state superimposed. This picture implicitly assumes perfect epitaxial growth of the CdS shell on the CdSe seed, with no lattice dislocations, alloying, or surface strain. In reality, surface strain due to lattice mismatch induces a piezoelectric polarization at the CdSe/CdS interface, causing band bending.35 Because the confinement kinetic energy is low, the electron and hole wave functions are distorted by the small changes in the potential energy surface. This is illustrated on the right side of Figure 6A, where the exciton is more confined along the axial direction of the QRH by the internal electric field and band bending. The schematic wave function shown on the top right in Figure 6A takes on more oblate character. Because of the anisotropic CdS rod growth, this effect is more perturbative than that described by Nie and co-workers8 in which isotropic compressive and tensile strain shift the conduction band of the core and shell, respectively. Other effects at the interface such as alloying may play a role in modulating the potential energy surface as well.36 Following the results of Efros et al.17 the change in splitting and strengths of wurtzitic CdSe fine structure levels between a spherical exciton and an oblate exciton is shown schematically in the bottom part of Figure 6A. As the splitting between the (1L and (2 levels becomes smaller, the rate constant for transfer between those states should increase. The kinetic scheme in Figure 1 shows two dominant pathways for evolving from a spinconserved state to a spin-flipped state: the lower pathway, (1U T (1L T -2 (green and red arrows), and the upper pathway, (1U T 0U T -1U (purple arrows). The relative influences of these pathways will be affected by changes in fine structure induced by distortion of the exciton, thus altering the observed CPTG decays. Calculations of CPTG signals, proportional to the square of the difference between conserved and flipped spins [nc
nf]2, are compared against the 4.2 nm seed and 4.2 nm QRH data and are shown in Figure 6B,C, respectively. Full detail of the kinetic scheme can be found in Figure S7 and Section IV of Supporting 4929

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Nano Letters Information. The calculations were not the result of a leastsquares fitting procedure but are shown to confirm that the simple model can recreate the basic features of the decay of the CPTG signal captured in our experiments. The rate constants k+,
, the energy gap between the (1U T ( 1L states (ΔEU,L), and the initial population in those four states (oscillator strengths) are the primary parameters that affect the CPTG decay and are known to change with exciton anisotropy. For calculations on both seed and QRH, other rate constants were held fixed at reasonable values (kU,L = 0.3 ps
1 and k0,1 = 0.001 ps
1), because it is unknown what the effect of surface strain or exciton distortion would be on these parameters. The energy gap ΔEU,L was 20 meV in the seed (spherical exciton) calculation and 30 meV in the QRH (oblate exciton) calculation. These magnitudes are physically reasonable and the increase is expected for an oblate distortion.17 This change affects the short time decay as well as the long time offset, which is determined by the rate of the upper pathway and the contribution to the signal from the 0U state, which is not included in our model because it results in a decay on a much slower time scale than we measured. Therefore, the offsets from the fits to the data in Table 1 are added to the calculations shown in Figure 6B,C for comparisons against the data. The ratio of oscillator strengths, (1U:(1L, changed from 1:1 for the seed to 0.8:1 for the QRH, which is in agreement with the expected trend.17 Finally, k+,
changed from 1.1 ps
1 in the seed calculation to 1.25 ps
1 in the QRH calculation, which would be expected if the splitting ΔE between the (1L and (2 states becomes smaller due to the oblate deformation, with k+,
being dictated by spin
orbit coupling and thus varying as 1/ΔE . Figure 6D shows the fits to the seed (red line) and QRH (blue line) CPTG data from Table 1. The kinetic modeling results lead us to conclude that the subpicosecond spin relaxation in the 4.2 nm QRH CPTG signal (shaded in dark blue) is dominated by equilibration of the (1L and -2 states. The spin relaxation is driven by the slower equilibration of the (1L and (1U states in the next few picoseconds (shaded in lighter blue). Spin relaxation from the upper pathway follows on the 10+ picoseconds time scale. These calculations show that small changes in fine structure that are consistent with an anisotropic deformation of the exciton can account for the change from mono- to biexponential behavior in the CPTG decay from 2.1 and 2.9 nm QRHs to 4.2 nm QRHs. On the basis of the lack of dependence of spin-flip rates on QRH aspect ratio, we conclude that the exciton is not delocalized over the entire QRH. Instead surface strain, which is localized around the CdSe seed, is a significant factor influencing excitonic shape and fine structure in nanocrystal heterostructures. The consistent relationship between spin-flip rate and exciton size for the 2.1 and 2.9 nm QRHs suggests that the excitons in those systems are not substantially distorted because the excess kinetic energy due to confinement is large in comparison to deformation in the potential energy surface due to interface effects. When the available kinetic energy becomes similar to or less than modulations of the interface potential as in 4.2 nm QRHs, the exciton shape becomes much more sensitive to the anisotropic nature of this potential. This work shows that cross-polarized transient grating experiments can provide information about both the size and shape of an exciton in a quantum rod heterostructure that cannot be definitively inferred using other optical techniques such as timeresolved photoluminescence, and without the instrumental complexity of scanning tunneling spectroscopy or near-field optical

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techniques. We find that for small QRHs the spin-flip rate depends on the radial diameter but is not especially sensitive to aspect ratio, leading us to conclude that the exciton wave function spreads out isotropically, not delocalizing over the entire CdSe-seeded CdS rod. For the 2.1 and 2.9 nm QRHs, although the quantum confinement kinetic energy of the 1Se state exceeds the 0.3 eV conduction band offset between CdSe and CdS, Coulombic attraction between the electron and hole is sufficient enough to center the exciton on the CdSe seed. The anomalous CPTG signals for the 4.2 nm QRH reveal that the reduced confinement energy for the 4.2 nm QRH samples not only results in confinement of the exciton closer to the seed but also distorts the exciton wave function via internal electric fields at the strained interface between CdSe and CdS. We correlate distortion of the excitonic wave function from spherical to oblate to changes in fine structure level alignment consistent with the signals observed.

’ ASSOCIATED CONTENT

bS

Supporting Information. Steady state photoluminescence, time-resolved photoluminescence anisotropy, TEM images, particle size distribution, spherical particle-in-a-well calculations, detailed description of kinetic model. This material is available free of charge via the Internet at http://pubs.acs.org.

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