LETTER pubs.acs.org/NanoLett
Surface Charge and Piezoelectric Fields Control Auger Recombination in Semiconductor Nanocrystals Zhong-Jie Jiang and David F. Kelley* University of California, Merced, Merced, California 95343, United States
bS Supporting Information ABSTRACT: The dynamics of biexcitons in CdSe nanoparticles are examined as a function of the magnitudes of internal electric fields. We show that the presence of strong internal fields results in rapid Auger recombination. The strengths of the electric fields and hence the Auger recombination rates are controlled in several different ways: specifically, by varying the dielectric constant of the surrounding solvent, by changing the particle surface stoichiometry and hence the magnitude of surface charges, and by inducing a piezoelectric field through the deposition of a lattice-mismatched shell material. Auger recombination is a momentum forbidden process. Fourier transformation of calculated spatial wave functions shows that higher conduction band states have large momentum components that relax the momentum conservation constraints. Relative Auger recombination times depend upon the extent to which the internal electric fields mix conduction band levels, which is easily calculated. Comparison with calculations of valence band states suggests that the excited particle in biexciton Auger recombination is the other electron. The experimental results can therefore be understood in terms of mixing of higher conduction band states with the lowest state from which recombination occurs. KEYWORDS: Nanocrystal, Auger, piezoelectric, state mixing
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ultiexcitons in semiconductor nanocrystals can be produced by absorption of two or more photons, or from absorption of a single high energy photon followed by carrier multiplication13 (CM, also referred to as multiple exciton generation). In the case of high energy photon absorption followed by CM, generation of two or more excitons suggests the possibility of fabricating very high efficiency nanoparticlebased photovoltaics. Luminescence from biexciton states is red shifted from that of singly excited states and the nanoparticle ground-state absorption. This greatly diminishes the extent of luminescence self-absorption, and therefore facilitates the fabrication of nanoparticle-based lasers.4 The lifetimes of multi- or biexcitons are often limited by Auger recombination (AR), a process in which an electron and hole nonradiatively recombine, transferring the energy to a remaining electron or hole. CM and AR are inverse processes of each other and therefore are controlled by the same physics. Auger dynamics of charged particles or particles having a surface trapped carrier are also thought to be involved in fluorescence intermittency, “blinking” in quantum dots.5 A mechanistic understanding of the particle characteristics that control AR rates may therefore shed light on all of these phenomena. When biexciton AR occurs, the energy is deposited in the remaining electron or hole. Current understanding of AR rates in nanocrystals is based on several considerations: the extent of electronhole Coulombic interaction, the density of final states and momentum conservation.6 The magnitude of the Coulombic interaction depends on particle size,7 which is held close to constant in the present studies. The results presented here focus r 2011 American Chemical Society
on the role of momentum conservation in determining the AR rates. Since the excited electron or hole has a large momentum and the electrons and holes at the band edge have low momenta, AR is nominally a momentum forbidden process. It becomes “allowed” only when the lowest electron or hole state has high momentum components.8 The high momentum components needed to make the process allowed are due to rapid spatial variations of the lowest energy conduction or valence band wave function and are therefore absent in bulk semiconductors. These momentum components can be calculated from the spatial wave function by Fourier transformation. The lowest energy wave functions vary smoothly over the nanoparticle (having no nodes) and the high momentum components can result from the wave function truncation at the NP surface.6,8 Higher energy levels vary less smoothly in the particle interior and hence have a more abrupt variation at the particle surface, resulting in larger momentum components. To the extent that the lowest level is “mixed” with higher energy levels, it takes on these higher momentum characteristics. Internal electric fields can mix these levels and therefore play a major role in determining the AR dynamics. In this Letter, we present experimental results indicating that the presence of internal electric fields and the accompanying state mixing have a large effect on the biexciton AR rate. Internal electric fields can have several different origins and be altered by Received: March 29, 2011 Revised: August 23, 2011 Published: September 14, 2011 4067
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Figure 1. Plots of squared momentum representations of the electron (black) and hole (red) wave functions. The dotted curves correspond to the electron and hole functions in the absence of an electric field. The vertical lines indicate the electron (black) and hole (red) momenta associated with the biexciton Auger recombination process, calculated on the basis of the effective mass approximation.
variation of several different factors. Fields can be caused by partial surface charges associated with metal or chalcogenide termination and by particle strain and resulting piezoelectric fields. The factors controlling the magnitudes of these fields include the extent to which different facets are metal or chalcogenide terminated, the dielectric constant of the surrounding media, and the thickness of a larger bandgap semiconductor shell. In these studies, we systematically vary several of these factors. We vary the surrounding dielectric constant by varying the solvent polarity. The surface stoichiometries and hence the surface charges are controlled by deposition of a metal-rich single layer of CdS or ZnS. Varying thicknesses of CdS or ZnS shells are deposited, resulting in different amounts of surface strain and different extents of separation of the core particle from the surface charges. Prior to the experimental results, we first present the results of calculations that are used in the quantitative interpretation of the solvent-dependent results. The calculations also address the question of whether the electron or the hole is the excited particle in the Auger process. Electron versus Hole Excitation. We have performed calculations that allow the prediction of relative AR rates as the solvent dielectric constant and hence the magnitude of internal electric fields is varied. The basic idea is that presented by Cragg and Efros.8 We first calculate the spatial electron and hole wave functions, Ψ(r), then Fourier transform these wave functions to get the corresponding momentum representation, ψ(k). The AR rate is taken to be proportional to |ψ(ka)|2, where ka is the electron or hole wavevector corresponding the bandgap energy (this follows directly from eq 9 of ref 8). The proportionality constant contains the magnitude of the electronhole Coulombic interaction and the density of final states. These factors remain constant as the solvent dielectric constant is varied. Calculation of Ψ(r)and ψ(k) is done in the following way. The spatial functions are calculated using an effective mass approximation and the appropriate CdSe valence and conduction band potentials. The finite depth of the conduction band well is taken into account by considering the particle to be surrounded by a shell at the ionization potential. This is done by
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expanding the particle/vacuum conduction band potential in the spherical Bessel functions. Diagonalization of the conduction band levels gives the 1Se, 1Pe, and so forth states, and this calculation gives the correct extent to which the electron wave functions spill out of the particle. Calculation of the hole wave functions is complicated by valence band degeneracies. In this case, the analogous valence band potentials are expanded in the set of S-D mixed states.5 The full set of mixed and appropriately normalized S-D functions, as well as the P functions are calculated. A dipolar electric field mixes P states with the S and D components of the lowest state. For both the conduction and valence bands, the mixing between the lowest state and the higher lying P states are calculated by first order perturbation theory. Electronhole interaction energies are also included and calculated by first order perturbation theory. The total (mixed) wave functions are then FourierBessel transformed to give ψ(k)for both the conduction and valence band. Plots of |ψ(k)|2 with and without an internal electric field are shown in Figure 1. In the plots where mixing from an electric field is included, the field is taken to be 1.6 108 V/m, which is a realistic value (discussed below). It is important to note that independent of whether the electron or hole is the excited particle, the electric field dependence of the calculated wave functions shows that most of the large momentum components result from electric field mixing of the S and P states. In the absence of SP mixing, the Auger rate with electron excitation is about a factor of 5 lower (compare solid and dotted black curves in Figure 1). Despite similar qualitative behavior, there are significant differences between the electron and hole functions, both without and especially with an electric field. Because of S-D mixing in the degenerate valence band and the larger effective mass, the field-free hole states (dotted red curves in Figure 1) have somewhat larger amplitudes at high momentum than the corresponding electron states. This difference becomes larger with an increasing electric field. Valence band levels are closer together and because of the smaller energy denominators, an electric field causes more SP mixing in the valence band, resulting in larger high-momentum components in the presence of the field. This results in a very large effect on the calculated Auger rate for wavevectors less than about 4 nm1. We note that the pure S functions have nodes at larger wavevectors. The same effect was observed in the calculations reported by Cragg and Efros.8 The electric field dependence at larger wavevectors (>4 nm1) is therefore more complicated. Biexciton Auger recombination produces an electron or hole with a wavevector given by ka ¼
ð2mEg Þ1=2 p ¼ p p
ð1Þ
where Eg is the bandgap energy and m* is the effective mass of the excited carrier. Electron versus hole excitation can be considered in this context. The CdSe electron and hole effective masses are very different: m*e = 0.11 and m*h = 0.44 in units of free electron mass. Thus the value of ka corresponding to the hole being the excited particle is a factor of 2 larger than in the case of the electron. As shown in Figure 1, the value of |ψ(ka)|2 for the hole is about 2 orders of magnitude smaller than in the case of the electron, strongly implying that the electron is the excited particle in this Auger process. However, there are two important caveats to this calculation. First, in addition to being proportional 4068
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Figure 2. Power dependent transient absorption kinetics for 3.2 nm CdSe spheres in chloroform. The data are normalized to the same absorbance change at long times, >100 ps. Also shown are fit decay curves corresponding to 600, 17, and ∼2 ps components. The lowest power curves have no 2 ps component and very small 17 ps component.
to |ψ(ka)|2 the Auger rate is also proportional to the density of final states, and it could be argued that the density of states in the valence band is greater than in the conduction band. Density of states considerations may therefore favor the hole excitation, partially offsetting the momentum overlap considerations. Second, and perhaps more importantly, an effective mass approximation is used in calculating the respective electron and hole values of ka used in eq 1. This approximation may not accurately describe highly excited electrons and holes, and the relative momentum overlap values calculated this way may not be reliable. We also note that some experimental evidence on positively charged particles has determined the “trion” recombination rates.9 These studies suggest that in CdSe particles, biexciton AR occurs with excitation of the hole, rather than the electron. Because of these uncertainties, the solvent dependence and hence electric field dependence of the Auger rates are analyzed in terms of both electron and hole excitation. We find that a better fit to the experimental results is obtained assuming it is the electron that is excited (see below). However, given the simplicity of this model, both fits would have to be considered satisfactory. Thus, the experimental results presented here are not capable of distinguishing between electron and hole excitation. We emphasize that the main point of this paper, that the Auger rates are largely controlled by electric field induced state mixing, is independent of whether the electron or the hole is the excited particle. Biexciton Auger Recombination Times. In the results presented here, we have used transient absorption (TA) spectroscopy to measure the biexciton AR rates for CdSe particles dissolved in liquid solutions. In these studies, biexcitons are formed by absorbing two (or more) photons from an ultrafast laser pulse. Formation of a biexciton fills the lowest conduction band level and thereby diminishes the intensity of the 1Sh1Se absorption. The presence of a single exciton diminishes this absorption to a lesser extent. Thus, the 1Sh1Se band-edge absorption partially recovers as AR occurs and the kinetics of this absorption give the biexciton AR times. In general, the bleach decay of the 1Sh1Se band-edge absorption exhibits a very fast (few picoseconds), slower (on the order of 1020 ps) and very
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slow (hundreds of picoseconds to nanoseconds) components. Figure 2 shows the power-dependent TA kinetics for 3.2 nm wurtzite CdSe spheres in chloroform. All of the decay curves in Figure 2 are fit to decays having 23, 17, and 600 ps components. The relative magnitudes of these components depend on the pump power, that is, the number of excitons per particle. At the lowest powers almost all of the decay is the 600 ps component with only a very small 17 ps component and no 2 ps component. The relative magnitudes of the 17 ps component and especially the 2 ps component increases with pump power. Thus, the slowest component is assigned to single exciton nonradiative decay. The 17 ps component is assigned to the biexciton decay, and the 2 ps component assigned to the decay of multiexcitons. Klimov et al. also report biexciton AR times for several sizes of CdSe nanoparticles.10 Interpolation of those results gives a AR time for 3.2 nm particles of 18 ps, which is in essentially exact agreement with these results. We note literature reports indicate that upon intense UV irradiation, a significant fraction of the particles can become charged, and the presence of charged particles can confuse the transient absorption kinetics in both CdSe and PbSe nanoparticles.1113 This is particularly true if the samples are not stirred, which rapidly refreshes the sample volume. In the present studies, a relatively large sample volume (10 mL) is rapidly stirred. We find that the observed kinetics do not change with sample age or stirring rate, ensuring that particle charging is not occurring. The experimental methods are described in detail in Supporting Information. Internal Electric Fields and Solvent Polarity Effects. Internal electric fields are inherent to stoichiometric (having equal number of metal and chalcogenides atoms) IIVI semiconductor nanocrystals, such as CdSe.14,15 Different crystal facets may be either cadmium or selenium terminated. Because of the difference in electronegativity, the cadmiums and seleniums in CdSe are somewhat positively and negatively charged, respectively. These net surface charges result in the particle having a net dipole and internal electric fields. These fields are not small dielectric dispersion measurements by Shim and Guyot-Sionnest indicate the presence of permanent dipole moments that require electric fields with magnitudes on the order of 108 V/m and electric potential differences across the particles of several tenths of a volt.15 CdSe nanoparticles can be synthesized in either wurtzite or zincblende crystal structures with the former being thermodynamically slightly favored.1621 The wurtzite structure is inherently polar and the zincblende is not. One might therefore expect to observe electric fields only in wurtzite particles. However, comparison of the dipole moments of CdSe (wurtzite) and ZnSe (zincblende) nanoparticles indicates the presence of strong electric fields in both cases, albeit somewhat stronger in the CdSe (wurtzite) case.15 The conclusion is that surface charges, rather than the intrinsic crystal polarity, are the dominant source of internal electric fields in unstrained nanoparticles. The particles used here are 3.2 nm diameter wurtzite spheres, synthesized by standard methods and ligated with stearic acid and octadecylamine. This synthesis produces particles having a Cd/Se ratio of 1:1,22 and therefore equal amounts of cadmiumand selenium-terminated facets. The surface charges associated with these differently terminated facets result in internal electric fields, and the magnitude of the internal field depends on the solvent dielectric constant. The particles are dissolved in octane (ε = 2.0), chloroform (ε = 4.8), and methylene chloride (ε = 9.1). Fitting the decay curves yields biexciton AR times of 13 ps 4069
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Figure 3. (A) Transient absorption kinetics for the 1Sh1Se transition for CdSe nanocrystals in octane, chloroform, and methylene chloride. Fit curves corresponding to triexponential decays are also shown. The decay time of the intermediate component is indicated and is assigned to the biexciton AR times. (B) Calculated internal electric field intensities (red dotted curve) and relative AR times (black dotted curves) as a function of external dielectric constant. The solid and open black dotted curves correspond to assuming electron and hole excitation, respectively. Also shown are the experimentally determined AR times (large black dots). The error bars reflect estimates of the uncertainties in fitting the decay curves.
(octane), 16 ps (chloroform), and 21 ps (CH2Cl2), as shown in Figure 3A. Figure 3A shows that the relative amplitudes of the long-lived and faster (bi- and triexciton) components are slightly different. Larger differences are seen in core/shell particles, discussed below. Throughout these experiments, the excitation power density and sample absorbance at the first exciton peak are held constant. Differences in the relative amplitudes of the fast and slow components may be understood in terms of the solvent dielectric constant and other spectroscopic and experimental considerations. These considerations do not affect the biexciton times obtained from fitting the decay curves, and are discussed in the Supporting Information. The dependence of the AR time on the solvent can be understood in terms of momentum conservation and electric field mixing of the 1Se and 1Pe states. The magnitude of the internal electric field in octane is taken to be that determined by Shim and Guyot-Sionnest in hydrocarbon solvent from dielectric dispersion measurements.15 The dependence of the internal electric field on the solvent dielectric constant is obtained by solving the electrostatic problem with the appropriate boundary conditions, which is detailed in the Supporting Information. Dielectric dispersion measurements15 give the magnitude of the dipolar component of the field for which the free charge distribution on the surface of the particle is given by σf = σ1 cos θ, where σ1 is a constant. The value of σ1 is taken to be that needed to give the observed particle dipole moment. This approach is taken because it easily generalizes to charge distributions given by the Legendre polynomials. This treatment must also account for the ligands (primarily octadecylamine molecules) bound to the particle surface. These molecules are Lewis bases and bind selectively to the surface cadmium atoms. Since the cadmium-terminated facets correspond to half of the particle surface, the effective dielectric constant of this surface layer is taken as the average of octadeclyamine dielectric constant (ε = 2.7) and that of the surrounding solvent. The thickness of this shell is taken to be that of an extended octadecylamine molecule, about 1.9 nm. The electrostatic problem is solved with the above parameters to obtain the magnitude of the internal electric field. The exact values of the ligand dielectric constant and the ligand shell thickness turn out not to be critical. Internal electric field strengths
calculated from this simple model are shown in Figure 3B. The dipolar component of the electric field mixes the S and P wave functions, as discussed above, and the AR time is taken to be proportional to |ψ(ka)|2. The constant that scales all of the AR times is an adjustable parameter in this calculation, so the calculation only gives the variation of the AR time with solvent dielectric constant. Experimental and calculated relative AR times assuming the electron or hole is the excited particle are shown in Figure 3B. Better agreement is obtained assuming that the electron is the excited particle, but despite the simplicity of this model reasonable agreement is obtained in both cases. Although a dipolar field mixes the S state with only the P states, higher electric multipole components mix S states with D, F, and so forth states. The solvent dependence of these electric fields is qualitatively similar and therefore difficult to distinguish from that of dipolar mixing; see the Supporting Information. The agreement in Figure 3 therefore does not suggest that mixing from other multipole field components is insignificant. AR Dynamics in Core/Shell Particles. Addition of a CdS shell greatly slows biexciton Auger recombination in CdSe nanoparticles. This is a large and persistent effect, consistently observed for AR in CdSe/CdS nanocrystals. It has been previously reported in “giant” CdSe/CdS nanoparticles,2325 and similar results are seen in CdSe/CdS dot/rod structures.26 We have observed this in CdSe/CdS and CdSe/ZnS nanorods,27 and single particle blinking studies are also consistent with this result.28,29 The slowing is much larger than predicted by a simple volume effect, even when electronhole overlap is considered,25 and this has been qualitatively explained in terms of momentum conservation.8,25 The idea is that the interface potential between CdSe and CdS is softened by SeS interdiffusion, resulting in smaller values of |ψ(ka)|2. However, calculations analogous to those in Figure 1 give similar values of |ψ(ka)|2 for core and core/ shell particles, suggesting this not the dominant effect. We suggest that slow biexciton AR in core/shell particles is primarily brought about by several effects related to the magnitude of the internal electric fields. Part of the decrease comes because the synthetic method used in shell deposition diminishes the extent of surface charges, and hence the magnitude of all of the electric field components. The magnitude of the internal 4070
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Figure 4. Transient absorption kinetics for the 1Sh1Se transition for (A) zincblende and (B) wurtzite CdSe nanocrystals dissolved in chloroform. Kinetics are for bare stoichiometric particles and for particles with a metal-rich monolayer of CdS or ZnS, as indicated. Also shown are fit curves analogous to those in Figures 2 and 3A.
electric fields depends upon the extent to which there are different charges on different crystal facets. Previous studies have shown that prior to any further processing, syntheses using cadmium oleate and excess trioctylphosphine selenium yield equal amounts of cadmium- and selenium-terminated faces.22,30 The magnitudes of the internal electric fields can be minimized by terminating all the facets with either cadmium or selenium, which can be accomplished by subsequent chemical treatment. In the present studies, cadmium-terminated surfaces are obtained by a SILAR method31 that deposits a very thin shell (1 monolayer) of cadmium-terminated CdS onto the CdSe particle. XPS studies show that cadmium-terminated surfaces are obtained if the final SILAR reaction mixture has cadmium in excess.30 Figure 4 compares the TA kinetics for the same particles before and after this deposition. It shows that AR is slower following the deposition of a uniform cadmium-rich surface. We also find that the same effect is observed when CdSe nanocrystals are simply reacted with a cadmium oleate precursor. We suggest that the magnitudes of multipolar internal electric fields also decrease upon CdS or ZnS shell deposition. There are two interrelated reasons for this. First, larger particles have more faceted surfaces (they are closer to being spherical), and hence more of the internal electric field is in the form of higher multipole components. Second, as shell/core radius ratio increases, the magnitude of fields of higher order than dipolar are diminished, as indicated by solving the electrostatic problem; see Supporting Information. Piezoelectric Effects. To elucidate the role of crystal structure in the internal electric fields, we have synthesized comparably sized (very slightly smaller, 3.0 versus 3.2 nm in diameter) zincblende CdSe nanocrystals, following the procedure described by Mohamed et al.16 Figure 4 shows that the bare zincblende particles show a slightly faster biexciton AR time, (11 versus 15 ps) as expected on the basis of the difference in their sizes and volume scaling arguments.7 Figure 4 also shows that deposition of a cadmium-terminated CdS shell results in AR slowing in both cases. This observation is consistent with a decrease in surface charge and previous reports that the internal electric fields are not crystal structure specific and due to surface charges.15 The decrease in AR rates is larger in the case of the wurtzite particles. This may be inherent to the different crystal
structures or may be due to differences in the surface ligands present from the different syntheses used to make each type of particle. It is important to note that in the case of zincblende particles, slowing of AR is also observed following a monolayer of ZnS deposition. In this case the effect is somewhat smaller than what is observed with a CdS shell. There is a large lattice mismatch between CdSe and ZnS,32 about 12%. The smaller change in AR rate in the ZnS-shell case is probably due to irregular ZnS shell growth and therefore incomplete particle coverage, caused by the large lattice mismatch. Deposition of a ZnS shell on wurtzite CdSe nanoparticles has the opposite effect; AR is faster following ZnS shell deposition, which can be understood in terms of internal piezoelectric fields. Zincblende and wurtzite crystals have different electromechanical tensors and therefore exhibit very different piezoelectric behavior when strained. Wurtzite CdSe exhibits large piezoelectric fields upon compressive strain along the unique c axis. Zincblende crystals exhibit relatively weak piezoelectric fields only upon shear strain; uniaxial compressive strain results in no piezoelectric field.33 CdSe has a relatively small mismatch with CdS and a much larger mismatch with ZnS.32 How the deposition of a lattice mismatched shell on a wurtzite semiconductor nanocrystal produces piezoelectric fields can be understood in terms of the following considerations. Deposition of a smaller lattice parameter material on a core particle produces compressive strain on the core particle and expansive strain in the shell.34,35 The CdSe and ZnS a0 and c0 lattice parameters differ by very close to the same amount, 12.8 and 12.6%, respectively. Thus, the deposition of a uniform ZnS shell on a spherical CdSe would result in an isotropic strain on both the core and shell. An isotropic strain changes the a0 and c0 lattice parameters by very nearly the same amount and therefore results in no crystal distortion and no piezoelectric fields. However, previous studies have shown that ZnS shell deposition is not uniform. Deposition of ZnS onto wurtzite CdSe particles (rods or nearly spherical particles) increases the particle aspect ratio, indicating that shell growth occurs preferentially on the facets normal to the c axis, the (0001) facets.3638 This difference in reactivity is often exploited to synthesize “dot-in-a-rod” and “rodrod” structures.39,40 The above considerations indicate that deposition of a small amount of ZnS will result in a thicker 4071
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Figure 5. Normalized transient absorption kinetics for bare (solid symbols) and three layer ZnS coated (open symbols) CdSe nanorods. Also shown are fit curves corresponding to decays of 2.5, 10, and 200 ps (bare) and 180 and 500 ps (Zn-coated). The 10 ps (bare) and 180 ps (ZnS-coated) components are assigned to biexciton AR. Also shown are the decays of CdSe nanorods having 9 layer ZnS shells. Nearly identical decays are obtained in chloroform (crosses) and octane (plusses).
ZnS layer on the (0001) facets compared to the rest of the particle. The thicker ZnS layer on these facets results in a differential strain normal, compared to along the c axis and therefore a net lattice distortion (rather than a simple isotropic compression) and hence a piezoelectric field. Figure 4 shows that in both zincblende and wurtzite CdSe particles, deposition of a CdS shell increases the AR time, due to the reduction of surface charges described above. The same is true for the deposition of ZnS on the zincblende nanocrystals. However, deposition of ZnS on wurtzite particles results in a decrease in the AR time, and this result is interpreted in terms of strong piezoelectric fields. As in the zincblende case, the presence of the ZnS shell must also diminish the magnitude of the surface charge fields. However, the decrease in AR time (15 ps decreasing to 11 ps) indicates that the presence of the piezoelectric field more than offsets the loss of surface charge fields, in terms of mixing the conduction band states. Figure 3 shows that to produce this large a change in the AR time, the piezoelectric field must be very large, on the order of 108 V/m. We infer a potential drop across the particle on the order of 0.5 V. This is comparable to the calculated piezoelectric potential differences (about 0.5 V) for a spherical CdSe particle embedded in a CdS rod.41,42 While the magnitudes of the calculated electric fields and the fields inferred from these results are comparable, two other effects go in opposite directions, making quantitative comparisons impossible. First, ZnS has a much larger lattice mismatch than does CdS, 12% versus 4%, and larger fields are expected in CdSe/ZnS core/shell particles. (Indeed, we suggest that the smaller lattice mismatch is why piezoelectric effects are not obvious when a CdS shell is deposited). Second, in the present studies we deposit only a single monolayer of ZnS, resulting in limited lattice strain and smaller fields. ZnS is known to grow epitaxially on CdSe for only about two unit cells,36,4345 limiting the magnitude of the interfacial strain. We have measured AR times for several different ZnS shell thicknesses. We find that the largest decreases in AR times is for 12 ZnS monolayers. Particles having shell thicknesses of 35 monolayers show progressively smaller
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decreases in the AR times. Consistent with limited epitaxial growth, further ZnS deposition degrades the interfacial coherence, and we observe that deposition of thick ZnS shells results in slower AR times. Core/Shell Nanorods. The electric field effects described above can be clearly seen in the comparison the above results with analogous results on CdSe/ZnS nanorods. CdSe nanorods grow in a wurtzite crystal structure with the rod axis corresponding to the crystallographic c axis. The core CdSe nanorods have dimensions of 3.2 17 nm. Upon shell deposition, ZnS is preferentially deposited on the ends of the rods, increasing the particle aspect ratio.27,37 Unlike the case of wurtzite spheres, Figure 5 shows that deposition of a thin (3 monolayers) ZnS shell results in a dramatic increase in the AR times. We find that AR in these nanorods gets monotonically slower as the shell thickness is increased. This contrast between wurtzite sphere and rod AR kinetics upon shell deposition indicates the lack of strong piezoelectric fields in wurtzite rods. This result can be understood in terms of differential strain along and normal to the crystallographic c axis. In the case of spheres, the two (0001) facets are separated by twice the particle radius, close enough so that strain on these surfaces results in a differential strain throughout the particle. This is not the case for a nanorod having a large aspect ratio. In the case of relatively long nanorods, most of the particle feels little effect of strain caused by ZnS deposition on the ends. Thus, in the case of nanorods ZnS deposition results in little piezoelectric field. Deposition of a zincrich ZnS shell does, however diminish the extent of surface charges. It also separates the surface charges from the CdSe core. Decay curves obtained from nominally identical CdSe nanorods having a thick (9 layers) shell are also shown in Figure 5. The presence of a thick shell slightly reduces the AR rate compared to the thinner ZnS shell. More importantly, the AR rates in octane and in chloroform are close to identical, indicating that the presence of the thick shell has diminished the magnitude of higher order multipole field components. We conclude that because of the diminished effects of surface charges in the thick-coated particles, the polarity of the solvent (octane versus chloroform) has very little effect on the biexciton AR dynamics.
’ ASSOCIATED CONTENT
bS
Supporting Information. Experimental section and additional information. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported by a grant from the U.S. Department of Energy, Grant DE-FG02-04ER15502. The authors would also like to thank Professor Kevin Mitchell for helpful discussions. ’ REFERENCES (1) Nozik, A. J. Nano Lett. 2010, 10, 2735. (2) McGuire, J. A.; Joo, J.; Pietryga, J. M.; Schaller, R. D.; Klimov, V. I. Acc. Chem. Res. 2008, 41, 1810. (3) Klimov, V. I. Annu. Rev. Phys. Chem. 2007, 58, 635–73. 4072
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