NANO LETTERS
Control of Exciton Spin Relaxation by Electron-Hole Decoupling in Type-II Nanocrystal Heterostructures
2008 Vol. 8, No. 11 4007-4013
Jun He, Shun S. Lo, Jeongho Kim, and Gregory D. Scholes* Department of Chemistry, Institute for Optical Sciences, and Centre for Quantum Information and Quantum Control, UniVersity of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada Received September 2, 2008
ABSTRACT The electron spin flip relaxation dynamics in type II CdSe/CdTe nanorod heterostructures are investigated by an ultrafast polarization transient grating technique. Photoexcited charge separation in the heterostructures suppresses the electron-hole exchange interaction and their recombination, which reduces the electron spin relaxation rate in CdSe nanocrystals by 1 order of magnitude compared to exciton relaxation. The electron orientation is preserved during charge transfer from CdTe to CdSe, and its relaxation time constant is found to be ∼5 ps at 293 K in the CdSe part of these nanorods. This finding suggests that hole spin relaxation determines the exciton fine structure relaxation rate and therefore control of exciton spin relaxation in semiconductor nanostructures is possible by delocalizing or translating the hole density relative to the electron.
Colloidal semiconductor nanoparticles, known as nanocrystals (NCs) or quantum dots, have been investigated in detail such that researchers have elucidated the size tunable optical properties characteristic of many systems and have examined many fundamental questions concerning their photophysics and excited states.1-8 An area that has attracted recent interest is learning how to control the optical properties using shells of another semiconductor that has suitable band offsets9 so that the electron or hole wave function is delocalized or transferred between core and shell.10-12 As one example, Klimov et al. demonstrated single-exciton optical gain in NCs by using type II CdS/ZnSe core/shell heterostructures to delocalize the hole wave function in a particular way relative to the electron.13,14 The resulting reduction in electron-hole overlap led to strong exciton-exciton repulsion that offsets the biexciton absorption from that of the exciton. In other work, it has been suggested that type II semiconductor heterostructures display tremendous potential for applications that include photovoltaics15-18 and spintronics.19 In recent work from our laboratory, we have investigated the relaxation processes in the exciton fine structure of CdSe NCs.20-23 These relaxation processes can be associated with electron and hole spin relaxation.23 Photoexcitation creates a collective excited state, a nanoscale exciton, spanning the NC.24 That excited sate is described in terms of single excitation configurations whereby an electron can be pro* To whom correspondence should be addressed. E-mail: gscholes@ chem.utoronto.ca. 10.1021/nl802668s CCC: $40.75 Published on Web 10/08/2008
2008 American Chemical Society
moted from a 4-fold degenerate valence band to a doubly degenerate conduction band.25 Owing to the electron-hole exchange interaction, these configurations are mixed to produce an exciton fine structure.25 In recent experimental studies, we have identified various dynamic relaxation processes but found one rapid pathway dominates at room temperature. We suggested the mechanism that promotes this fast relaxation, whereby bright (F ) (1) and dark (F ) -2) excitons interconvert with a change in the sign of total angular momentum (F), is a Dresselhaus spin-orbit coupling effect. That assignment further implies that it is a hole flip that controls the exciton spin relaxation. In turn, that presents a means to use synthesis to control the rate of the electron spin relaxation. Type-II CdSe/CdTe heterostructure NCs can serve this purpose by separating the electron and hole wave functions after photoexcitation. The more we decouple the hole from the electron, then the less the hole flip will “drag” on the electron part of the wave function. Here we report an example of this prediction in a study of the electron spin flip dynamics in type II CdSe/CdTe nanorod heterostructures using the ultrafast polarization transient grating technique. In recent work, we have described the synthesis and characterization of heterostructure NC rods consisting of fused, collinear, rod-like segments of CdSe and CdTe.15 Transmission electron microscopy (TEM) images of two such CdSe/CdTe nanorod heterostructures prepared for the present study are shown in Figure 1. The band edges of CdSe and CdTe segments are offset to give a type II alignment. The
Figure 1. TEM images of CdSe/CdTe heterostructures: (a) sample 2, (b) sample 3, showing a collection of fairly uniform rod-like structures ∼9 nm long and ∼3 nm wide.
Table 1. Characterization of the CdSe/CdTe Heterostructure Samples sample
λCdSe (nm)a
λCdTe (nm)a
length (nm)b
diameter (nm)b
1 574 642 10.3 (1.8) 2.9 (0.5) 2 573 642 9.0 (1.7) 2.9 (0.5) 3 543 628 7.7 (1.8) 2.8 (0.5) a Lowest excitonic absorption peaks obtained from Gaussian fitted absorption spectra. b Average size (standard deviation) calculated from TEM measurements assuming a Gaussian distribution.
valence and conduction band energies within the CdTe segment are respectively higher than that in CdSe. As a result, it is energetically favorable to form a charge transfer (CT) state consisting of an electron in the CdSe segment and a hole in CdTe after photoexcitation. The characteristics of each of the samples are summarized in Table 1. More information on sample synthesis and characterization can be found in ref 15 and in Supporting Information. Typical absorption and photoluminescence (PL) spectra, shown in Figure 2a, demonstrate that the energies of absorption and PL features vary with sample parameters such as the rod diameter and size of each component. In the past, we have studied these parameters systematically.26 For the purpose of the present study, we simply require the electron-hole separation after photoexcitation. Three samples were studied to ensure the observations reported here are general in nature and are free from artifacts. The absorption peaks for samples 1 and 2 are located at ∼642 nm (CdTe) and ∼573 nm (CdSe), respectively, while they are more blueshifted, to ∼628 nm (CdTe) and ∼543 nm (CdSe), for sample 4008
Figure 2. (a) Representative absorption and PL spectra of the three CdSe/CdTe nanorod heterostructures. (b) CdSe seed absorption (thick solid line) spectrum and heterostructure absorption (thin solid line) fitted to Gaussian bands (dashed lines) for sample 2. The absorption bands corresponding to the lowest energy CdSe, CdTe, and CT optical transitions are labeled a1, a2, and a3, respectively.
3, owing to greater quantum confinement effects. Comparison with the absorption spectrum of the seed material indicates that the CdSe nanorods do not grow during the CdTe deposition stage. According to a recent theoretical calculation based on band-structure-corrected local density approximation,27 the lowest excitonic absorption peaks for both CdSe and CdTe segments are consistent with the TEM results. Although the absorption cross sections of the CdSe and CdTe exciton states are much higher than that of the CT state,26 the PL is dominated by the near-infrared CT state PL. Figure 2b identifies the three lowest energy electronic transitions in the heterostructures with the valence and conduction orbital energies associated with the 1Se-1S3/2 transitions of CdSe and CdTe. Over the past few years, we have developed an experimental probe of dynamics within the NC fine structure states based on an ultrafast transient polarization grating technique.28 Transient polarization grating techniques use a sequence of three ultrafast laser pulses to initiate and probe dynamics. The probe step involves interrogation using the third pulse in the sequence, but the information is obtained in a fourth direction via a third-order polarization radiated by the sample. We measure that signal using heterodyne detection, which retrieves the sign of the linearized signal (cf. the comparison of VHVH and VHHV signals) and also simplifies kinetic analysis of the transients compared to homodyne-detected data. Generally speaking, transient gratNano Lett., Vol. 8, No. 11, 2008
ing measures population decay, whereas polarization grating measures depolarization. A key result is that optical selection rules for quantum dot excitons, governed by both circularly and linearly polarized light, can be exploited in nonlinear optical experiments to examine the exciton fine structure of NCs even though these levels are completely obscured by inhomogeneous line broadening.29 The signal measured by the cross-polarized heterodyne third-order transient grating technique28,30-32 (CPH-3TG) is obtained as IHET(tp) ∝
∫
∞
0
/ dt · Re{ELO (tp, ∆φ) · Ρ(3)(0, tp, t) · [C · (n+1 C + +1 -1 n-1 C ) + C ′ · (nF + nF )]}
(1)
*
where E LO(tp, ∆φ) is the electric field of the local oscillator with phase shift relative to the probe field ∆φ, and tp is the pump-probe delay time during which the excitons equilibrate among the fine structure states, recombine to the ground state, or are dissociated into surface traps. P(3)(0, tp, t) is the induced third-order polarization, and nC+1(nC-1) and nF+1(nF-1) are the populations of conserved and flipped excitons, respectively. By this terminology, we mean that a conserved exciton in one NC within the ensemble has the same sign of its total angular momentum when it is probed as it was photoexcited into via the pump at time -tp in the past. For example, if we photoexcited an F ) +1 state, then it is conserved if we later probe F ) +1 or F ) +2. A flipped exciton means the sign of the total angular momentum has changed (because of relaxation among the fine structure states) so that, for example, F ) +1 f F ) -1 or F ) -2. The coefficients, C and C′, are rotational averaging factors that both take the value of 2/15 in a population grating experiment, for example, when all three pulses and the signal analyzer are vertically polarized in the laboratory frame (VVVV). Therefore the VVVV signal decays only with population relaxation like a normal pump-probe experiment. On the other hand, when the pulses are cross-linearly polarized (known as a polarization grating), then C and C′ have values of 2/15 (-2/15) and -2/15 (2/15) for the VHVH (VHHV) polarization sequence, respectively,29 where V and H represent the vertical and horizontal polarizations. We are thus able to measure distinct kinds of radiationless relaxation processes in NCssthe various relaxation pathways within the fine structure states of the lowest exciton band. Here we report the imaginary (absorptive) part of the CPH3TG signals of the type II CdSe/CdTe nanorod heterostructures measured using VVVV, VHVH, and VHHV polarization sequences. Typical CPH-3TG data recorded with resonant photoexcitation at the lowest CdSe exciton absorption band for sample 3 are shown in Figure 3. The VVVV 3-TG data were fit by a sum of three-exponentials according to IVVVV(tp) ) Α1 · [1 - exp(-k1 · tp)] + Α2 · exp(-k2 · tp) + Α3 · exp(-k3 · tp)
(2)
where tp is the pump-probe delay time. The fitting results are displayed in Table 2. Note all the experimental data were fitted from ∼ 60 fs after the zero time delay in order to avoid the coherent spike (nontime ordered signals).33 This fitting function captures the rise in the signal that we assign to Nano Lett., Vol. 8, No. 11, 2008
Figure 3. (a) Representative imaginary (absorptive) part of the CPH-3TG data recorded for sample 3. Data for the VVVV (dashed), VHVH (dotted), and VHHV (short-dashed) polarization sequences are shown. The solid lines are the three-exponential fits, described in the text. (b) The same 3-TG data plotted in the short time window.
Table 2. Fitting Parameters for the CPH-3TG Studies of CdSe/CdTe Heterostructures sample (expt)a
A1
k1 (ps-1)
A2
k2 (ps-1)
A3
1 (VVVV)b 0.0027 2.8 1 (VHVH)c 0.060 0.22 0.030 0.032 0.19 1 (VHHV) c -0.042 0.13 -0.076 0.023 0.15 2 (VVVV) b 0.0060 2.7 2 (VHVH)c 0.027 0.25 0.029 0.036 0.12 2 (VHHV) c -0.025 0.16 -0.040 0.035 0.080 b 3 (VVVV) 0.013 2.6 3 (VHVH)c 0.011 0.11 0.011 0.035 0.099 3 (VHHV) c -0.030 0.35 -0.025 0.036 0.088 a The polarization sequence used in the CPH-3TG experiment is given in parenthesis (V ) vertical and H ) horizontal linear polarization in the laboratory frame). b VVVV data were fitted using eq 2. We list here only the parameters for the exponential rise, assigned to the charge transfer rate constant. See Supporting Information for complete fit parameters. c VHVH and VHHV data were fitted using eq 3. k1 and k2 are assigned to electron spin relaxation rate coefficients.
charge transfer from CdTe to CdSe (see below) as well as recombination and surface trapping decay processes. A fast rise process (∼ 400 fs), exhibiting the form of exponential growth and described by the first function in eq 2, was observed in each sample. We assign this to population of the charge transfer state by electron transfer from the CdTe exciton. Because we are exciting the CdSe absorption feature, this assignment means that the CdTe exciton is mainly populated by electronic energy transfer from CdSe that is too fast for us to resolve. Some CdTe excitons are directly photoexcited. We rule out hole transfer directly from photoexcited CdSe because this hole transfer would not lead to an increased bleach or transient absorption signal at the 4009
CdSe resonance compared to the CdSe exciton. This interpretation of the kinetics does not affect the final conclusions of this paper. The slowest decay, represented by the last function in eq 2, reaches over a nanosecond time scale and reflects the dynamics of charge recombination, which is known to be highly nonexponential.34 In addition, a decay component of ∼7-8 ps is observed for samples 1 and 2 with a very small amplitude, while it completely disappears for sample 3. It is assigned to a surface trapping process.35 The negligible surface trapping evident in the CdSe signal might be due to surface passivation by CdTe overgrowth, but it more likely suggests that the electron is not rapidly trapped in surface states compared to holes.36-39 The cross-polarized signals with VHVH and VHHV polarization sequences are sensitive to exciton fine structure relaxation (EFSR) rather than recombination and therefore decay much faster than the VVVV traces; predominantly from hundreds of femtoseconds to tens of picoseconds. It is notable that initial decays of VHVH and VHHV signals have opposite signs, which is a prediction of the different rotational averaging captured by each cross-polarized signal.28 This sign difference is not obvious in the raw data for the heterostructures owing to the overlying population changes associated with the electron transfer (the rising signal), but it is clearly retrieved by the fitting procedure (vide infra). The crosspolarized signals were fit by two exponentials and an offset, multiplied by the VVVV decay function, as dictated by the theory behind the measurement:21 IVHVH(tp) ) [Α1 · exp(-ks1 · tp) + Α2 · exp(-ks2 · tp) + Α3] · IVVVV(tp)
(3)
In eq 3, ks1 and ks2 are the fast and slow decay components of EFSR decay rates, respectively, and IVVVV(tp) is the decay profile of the VVVV 3TG signal as a function of the pump-probe time delay, tp, and A3 is the amplitude of the exciton recombination dynamics contributed by F ) 0, excitons that follow the VVVV signal. The fitting results for 3TG signals using cross-polarized linear polarizations are collected in Table 2. The fitted negative amplitudes (A1 and A2) for VHHV data indicate the opposite sign of the rotational averaging factors for VHHV measurement compared to that for VHVH experiments. We focus on exciting and probing the CdSe absorption feature in the heterostructure nanorods because we have previously obtained a detailed understanding of exciton relaxation in normal CdSe nanorods.21-23 Here we investigate the relaxation of an electron once it is transferred back to CdSe from the CdTe exciton. Figure 4 summarizes the sequence of processes occurring after photoexcitation, which outlines the kinetic model we have assumed when fitting the data. According to the experimental VVVV transients, electronic energy transfer from the CdSe exciton to the CdTe exciton is too fast to resolve. The angular momentum is preserved during the energy transfer because the NCs are aligned along the wurtzite c-axis.40,41 Energy transfer, therefore, does not decay the polarization grating. Subsequently, a signal rise with a time constant of ∼400 fs is observed, which indicates the electron transfer back from the conduction band of CdTe to that of CdSe. Our estimated 4010
Figure 4. Schematic diagram that describes excitation, charge transfer and spin flip dynamics in the type II CdSe/CdTe Nanorod heterostructures.
electron transfer rate (k1 ≈ 2.7 ps-1) determined by the CPH3TG VVVV measurements is in good agreement with recent measurements (∼2 ps-1) of a similar sample by femtosecond broadband pump-probe spectroscopy.42 Another study of the size-dependent charge separation rates for CdTe/CdSe type II core-shell quantum dots, using the femtosecond fluorescence upconversion technique, reports charge separations rates of ∼1-2 ps-1.43 A remarkable observation is the rise in the VHVH and VHHV signal amplitudes concomitant with the electron transfer back to the CdSe conduction orbital. That observation demonstrates that the electron spin state is preserved from the orientation produced by photoexcitation through energy transfer and subsequent charge transfer. In the section below, we describe how the experiment measures the spin relaxation of that electron. The photoexcited electron and hole are now spatially separated, in the CdSe conduction orbital and a CdTe valence orbital, respectively. The VHVH/ VHHV signals decay as the electron in the CdSe conduction orbitalundergoesspinrelaxation.Asweknow,theelectron-hole exchange interaction for the CT state is weak in the type-II CdSe/CdTe nanorod heterostructures and the electron-hole recombination lifetime is as long as microseconds.8,15,34 We therefore expected this weak exchange interaction to decouple the electron and hole. If the hole flip is indeed the rate-limiting phenomenon in causing the exciton relaxation, as we previously postulated23 and as is familiar (for somewhat different reasons) for bulk semiconductors,44 then the electron spin flip process will be slower than the exciton spin relaxation in a similarly sized CdSe nanorod. That is indeed observed, as we discuss below. First, we describe how the CPH-3TG experiment measures this electron spin relaxation. The lowest exciton state of short CdSe NCs consist of eight configurations that are split by the electron-hole exchange interaction, intrinsic crystal field, and shape asymmetry into a fine structure with five energy levels, as shown in Figure 5a. Each fine structure state is identified by its total angular momentum, obtained by adding electron and orbital angular momentum.8,23,25 Transitions among the exciton fine structure states are promoted by a coupling matrix element and enabled through energy conservation ensured by a bath of phonon modes. We can obtain insight into how excitons Nano Lett., Vol. 8, No. 11, 2008
Figure 5. (a) Schematic showing the fine structure of the CdSe NC first excitonic state, which is obscured by inhomogeneous line broadening, but can be probed using the CPH-3TG measurement. (b) The CdSe exciton Hamiltonian matrix in standard form.
Table 3. Antisymmetrized Product Functions That Compose the Fine Structure of the Lowest Excitonic Statea hole lz
e-h product
3/2 3/2
3/2 1/2
|sR〉|h1〉 |sR〉|h2〉
-1 0
3/2
-1/2
|sR〉|h3〉
+1
3/2 3/2 3/2
-3/2 3/2 1/2
|sR〉|h4〉 |sβ〉|h1〉 |sβ〉|h2〉
+2 -2 -1
3/2
-1/2
|sβ〉|h3〉
0
l
3/2 -3/2 |sβ〉|h4〉 a Reproduced from ref 23.
total angular momentum, F
+1
antisymmetrized product function representation φ1 ) -|sa j bbj ccj| φ2 ) (2|aa j sbj ccj| j ccj|)/6 2|asbb φ3 ) (2|aa j bsccj| + 2|aa j bbj scj|)/6 φ4 ) |aa j bbj cs| φ5 ) -|sja j bbj ccj| φ6 ) (2|aa j jsbj ccj| j ccj|)/6 2|asjbb φ7 ) (2|aa j bsjccj| + 2|aa j bbj jsjc|)/6 φ8 ) |aa j bbj csj|
versus electrons (anions) are probed by considering a simple Hamiltonian to describe the exciton fine structure states.23 For the conduction electrons, we have two spin orbitals (technically serving as basis functions for the Bloch sums) s ) sR and s ) sβ, where R (β) denotes the electron as spin +1/2 (-1/2). Different from the molecules, spin-orbit coupling is strong in the valence band of NCs, so we use the following hole functions that are diagonal in the spin-orbital coupling as detailed in elsewhere.23,45 h1 ) -a
(4a)
h2 ) (2b - a¯√2) ⁄ √6
(4b)
h3 ) (2b¯ + c√2) ⁄ √6
(4c)
h4 )c¯
(4d)
The basis functions for the exciton states are now obtained as products of the electron and hole functions, as listed in Table 3. On the basis of those product functions, we write the exciton Hamiltonian in a standard form where the conduction electron spin up functions are in the upper left quadrant and the spin down functions are in the lower right Nano Lett., Vol. 8, No. 11, 2008
Figure 6. (a) Feynman diagrams showing the nonlinear response functions associated with ground-state recovery (RI + RII) and excited-state absorption (RIII) for the CdSe anion, where |g〉 and |e〉 are the neutral ground-state and exciton. |a〉 is the anion formed by photoinduced electron transfer from a CdTe exciton to the CdSe rod, while | f〉 represents excitation of the anion (a trion). (b) Illustration showing transient absorption and bleaching in the charged, spin-polarized CdSe NC segment. The upper pathway is an allowed transient absorption to form | f〉. The lower pathway shows how formation of this state is blocked, which contributes to the bleach signal.
quadrant, depicted in Figure 5b. The matrix elements within quadrants, Hij, are diagonal and are collected in ref 23 and in Supporting Information. The two quadrants are mixed by exchange interactions. The NC exciton fine structure states may be obtained by solving secular equations,
∑ (H
R ij - ERδij)λj ) 0
(5)
i
where ER is the excitation energy of state R, whose wave function is defined by the coefficients λjR. These are the states that are photoexcited by the pump pulse sequence and are those that we have considered previously with respect to exciton relaxation.20-23,28,29 The 3TG signal for excitons arises from a sum of groundstate recovery (GSR), stimulated emission (SE), and excitedstate absorption (ESA) response functions.30,33,46 Similarly, we write three related response functions, RI, RII, and RIII, to describe the present data. These are depicted as doublesided Feynman diagrams, shown in Figure 6a, where the states |e〉 are the optically bright fine structure states found by solving eq 5, |a〉 are the anion states of CdSe, and | f〉 are excited states of |a〉 (trions).47 How to interpret these response functions and the associated rotational averaging is described in more detail in ref 29. 4011
In the case of the CdSe/CdTe heterostructure, the spinpolarized electron in the CdSe conduction band will selectively allow and forbid electronic transitions to a restricted set of CdSe exciton fine structure states: those of the excitonic anion | f〉. Those states are obtained by diagonalizing just one block of the Hamiltonian of Figure 5b. The result is trivial because each block is already in diagonal form. For example, if the electron is in the spin R state, the antisymmetrized configuration state function φ8 (F ) +1, electron spin β) can be photoexcited in the presence of the electron to form an anion exciton state | f〉, or a trion state. That contributes ESA to the 3TG signal. In this same scenario, the absorption to form φ1 (F ) -1, electron spin R) is transition-forbidden owing to Pauli blocking, and that is seen in the RI + RII contribution as differential transmission, as is illustrated in Figure 6b. The corresponding rotational averaging factors, CESA (F ) +1) and CGSR (F ) -1) are analogous to the exciton relaxation case, conferring the values of -2/15 (2/15) to the response functions for the VHVH (VHHV) polarization sequences (the negative sum associated with ESA or RIII being collected with the sign of the rotational average term).29 Now, if the electron in the CdSe conduction band flips to the spin β state during the pump-probe delay tp, the state φ8 becomes blocked while φ1 is switched on. Correspondingly, the rotational average factors switch signs. Our previous work has demonstrated that the F ) 0 states provide a constant positive offset to the VHVH and VHHV signals and do not affect the measured spin flip dynamics.21 For completeness, it is worth noting that the antisymmetrized configuration state functions φ6 (F ) -1, electron spin β) and φ3 (F ) +1, electron spin R) will contribute signals opposite to that of φ8 and φ1. That leads to reduced signal amplitude compared to the picture described above, but the effect is not significant because the triplet determinants in φ6 and φ3 are optically dark. We are thus able to monitor the electron (or hole) spin flip dynamics in type II semiconductor heterostructures and charged quantum dots by using this CPH-3TG technique. The rate coefficients k1 and k2 obtained from the VHVH and VHHV measurements, fitted by eq 3 and listed in Table 2, cannot be assigned to EFSR decay rates of the CdSe nanorods. Instead, we assign them to the spin flip dynamics of the photoexcited electrons in the type-II CdSe/CdTe heterostructures. The observed slow spin flip rate, k2 (∼0.035 ps-1), could be induced by phonon scattering48 or hyperfine interaction with nuclei.49,50 We discover that the fast spin flip rate, k1 (∼0.1-0.3 ps-1), is nearly 1 order of magnitude smaller than that of excitons in pure CdSe nanorods with similar diameters (∼1.8 ps-1).21 Hence the spin relaxation time (T1 time) of an electron optically oriented and isolated in a CdSe nanocrystalline rod is ∼5 ps at room temperature (293 K). Type II heterostructures therefore provide an effective means to control the electron spin relaxation. Our experiments support our previous suggestion that hole spin relaxation determines the exciton fine structure relaxation rate23 because separating the electron and hole in the heterostructure reduced the relaxation time by 1 order of 4012
magnitude. Because the charge separation in type II semiconductor heterostructures can be tuned by material composition, size, shape, and strain, it provides a new degree of freedom to control the exciton, hole, and electron spin relaxation in semiconductor nanostructures. 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. Supporting Information Available: Description of the synthesis and characterization of nanocrystal heterostructures as well as experimental methods and supporting data. This material is available free of charge via the Internet at http:// pubs.acs.org. References (1) Alivisatos, A. P. Science 1996, 271, 933. (2) Weller, H. Angew. Chem., Int. Ed. Engl. 1993, 32, 41. (3) Gaponenko, S. V. Optical Properties of Semiconductor Nanocrystals; Cambridge University Press: Cambridge, UK, 1998. (4) Klimov, V. I. Semiconductor and Metal Nanocrystals: Synthesis and Electronic and Optical Properties; Marcel Dekker Inc: New York, 2004. (5) Burda, C.; Chen, X. B.; Narayanan, R.; El-Sayed, M. A. Chem. ReV. 2005, 105, 1025. (6) Rogach, A. L.; Eychmu¨ller, A.; Hickey, S. G.; Kershaw, S. V. Small 2007, 3, 536. (7) Klimov, V. I. Annu. ReV. Phys. Chem. 2007, 58, 635. (8) Scholes, G. D. AdV. Funct. Mater. 2008, 18, 1157. (9) Wei, S. H.; Zunger, A. Appl. Phys. Lett. 1998, 72, 2011. (10) Kim, S.; Fisher, B.; Eisler, H. J.; Bawendi, M. J. Am. Chem. Soc. 2003, 125, 11466. (11) Balet, L. P.; Ivanov, S. A.; Piryatinski, A.; Achermann, M.; Klimov, V. I. Nano Lett. 2004, 4, 1485. (12) Peng, P.; Milliron, D. J.; Hughes, S. M.; Johnson, J. C.; Alivisatos, A. P.; Saykally, R. J. Nano Lett. 2005, 5, 1809. (13) Klimov, V. I.; Ivanov, S. A.; Nanda, J.; Achermann, M.; Bezel, I.; McGuire, J. A.; Piryatinski, A. Nature 2007, 447, 441. (14) Ivanov, S. A.; Piryatinski, A.; Nanda, J.; Tretiak, S.; Zavadil, K. R.; Wallace, W. O.; Werder, D.; Klimov, V. I. J. Am. Chem. Soc. 2007, 129, 11708. (15) Kumar, S.; Jones, M.; Lo, S. S.; Scholes, G. D. Small 2007, 9, 1633. (16) Zhong, H. Z.; Zhou, Y.; Yang, Y.; Yang, C. H.; Li, Y. F. J. Phys. Chem. C 2007, 111, 6538. (17) Schrier, J.; Demchenko, D. O.; Wang, L. W.; Alivisatos, A. P. Nano Lett. 2007, 7, 2377. (18) Gross, D.; Susha, A. S.; Klar, T. A.; Como, E. D.; Rogach, A. L.; Feldmann, J. Nano Lett. 2008, 8, 1482. (19) Mino, H.; Kouno, Y.; Oto, K.; Muro, K.; Akimoto, R.; Takeyama, S. Appl. Phys. Lett. 2008, 92, 153101. (20) Huxter, V. M.; Kovalevskij, V.; Scholes, G. D. J. Phys. Chem. B 2005, 109, 20060. (21) Kim, J.; Wong, C. Y.; Nair, P. S.; Fritz, K. P.; Kumar, S.; Scholes, G. D. J. Phys. Chem. B 2006, 110, 25371. (22) Scholes, G. D.; Kim, J.; Wong, C. Y.; Huxter, V. M.; Nair, P. S.; Fritz, K. P.; Kumar, S. Nano Lett. 2006, 6, 1765. (23) Wong, C. Y.; Kim, J.; Nair, P. S.; Nagy, M. C.; Scholes, G. D. J. Phys. Chem. C. submittedfor publication. (24) Scholes, G. D.; Rumbles, G. Nat. Mater. 2006, 5, 683. (25) Efros, A. L.; Rosen, M.; Kuno, M.; Nirmal, M.; Norris, D. J.; Bawendi, M. Phys. ReV. B 1996, 54, 4843. (26) Scholes, G. D.; Jones, M.; Kumar, S. J. Phys. Chem. C 2007, 111, 13777. (27) Li, J. B.; Wang, L. W. Phys. ReV. B 2005, 72, 125325. (28) Scholes, G. D.; Kim, J.; Wong, C. Y. Phys. ReV. B 2006, 73, 195325. (29) Scholes, G. D. J. Chem. Phys. 2004, 121, 10104. (30) Mukamel, S. Principles of Nonlinear Optical Spectroscopy; Oxford: New York, 1995. (31) Fourkas, J. T.; Fayer, M. D. Acc. Chem. Res. 1992, 25, 227. (32) Goodno, G. D.; Dadusc, G.; Miller, R. J. D. J. Opt. Soc. Am. B 1998, 15, 1791. Nano Lett., Vol. 8, No. 11, 2008
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