Effects of Inhomogeneous Shell Thickness in the Charge Transfer

Article pubs.acs.org/JPCC

Effects of Inhomogeneous Shell Thickness in the Charge Transfer Dynamics of ZnTe/CdSe Nanocrystals Zhong-Jie Jiang and David F. Kelley* University of California, Merced, 5200 North Lake Road, Merced, California 95343, United States S Supporting Information *

ABSTRACT: ZnTe/CdSe core/shell nanocrystals with varying ZnTe core sizes and CdSe shell thickness have been synthesized. The absorption onset and photoluminescence (PL) wavelengths vary from the mid-visible to the near-infrared range. The conduction and valence band energies as well as bandgap and electron−hole overlap are accurately described by an effective mass approximation model. These particles are type-II, with the hole confined to the ZnTe core. PL quenching dynamics of ZnTe/ CdSe nanocrystals having various shell thicknesses by hole acceptors are studied. A model has been developed to describe the interfacial charge transfer of the core-confined holes to adsorbed acceptors. This model considers a Poisson distribution of acceptor numbers and includes shell thickness variability. The shell thickness variability occurs on each particle and corresponds to surface roughness. The shell local thickness is assumed to have a Poisson distribution of numbers of layers.

■

INTRODUCTION Colloidally synthesized semiconductor nanocrystals, also referred to as quantum dots, are nanoscale crystalline particles surrounded by a layer of organic ligand molecules.1,2 The electronic and optical properties of these nanocrystals are tunable by simply changing their size, shape, and composition.3−6 The presence of organic capping ligands, which can also be manipulated through ligand exchange, allows them to be soluble in aqueous or organic solvents, facilitating their potential uses as light-absorbing species and chromophores suitable for a wide range of applications, including lightemitting diodes (LEDs),7,8 lasers,9,10 and optical labels.11,12 Recently, a great deal of attention has been put on the synthesis of core/shell nanocrystal heterostructures, which consist of two or more semiconductor components in a single particle.13−18 Core/shell heterostructures exhibit properties of each semiconductor component as well as new, collective phenomena based on the strong electronic coupling between nanoscale units. Core/shell semiconductor nanocrystal heterostructures are typically classified as type-I or type-II.13,16,19−21 In the case of type-I, electron and hole pairs generated from the photoexcitation are localized in the same region of the nanocrystal.13,22,23 This enhances the probability of radiative recombination, leading to high photoluminescence (PL) © 2012 American Chemical Society

quantum yields, which is beneficial for biological tagging applications12 and for applications such as light-emitting diodes.8,24 In the type-II case, the lowest conduction and valence band edges of the nanocrystal heterostructures are in different semiconductors.22,25−28 Therefore, a staggered energy band alignment exists at the interface of two semiconductors, which tends to spatially separate photogenerated electrons and holes. The resulting absorption band edge is red-shifted compared to that of the core and shell material alone, making type-II structures particularly attractive for photovoltaic applications.25,27,29−31 Spatial separation of the electrons and holes can facilitate electron and hole transfer to their respective acceptors.25,27,28,32−34 Type-II nanocrystals exhibit lower oscillator strengths, which provides greater potential to completely transfer the electron and hole prior to radiative recombination.18,24,32,35 Type-II nanocrystal heterostructures therefore have great potential as photon absorbers in quantum dot sensitized solar cells. To improve the utilization of photogenerated electrons and holes in photovoltaic devices, it is generally expected to use Received: April 6, 2012 Revised: May 18, 2012 Published: May 21, 2012 12958

dx.doi.org/10.1021/jp303307r | J. Phys. Chem. C 2012, 116, 12958−12968

The Journal of Physical Chemistry C

Article

same, and the shells on each individual nanocrystal are assumed to have a Poisson distribution of numbers of layers. The molecular quenchers are taken to be stochastically adsorbed on these core/shell nanocrystals. The model is successfully applied to the hole quenching dynamics in the type-II ZnTe/CdSe in the presence of phenothiazine, a commonly used molecular hole quencher.

semiconductor nanocrystals with a higher conduction band edge which could provide a greater energetic driving force for electron transfer. Among the II−VI semiconductors, ZnTe has conduction and valence band edges at relatively high energies, 3.0 and 5.25 eV, respectively, with respect to vacuum. (These values are determined from the known band edges of CdSe and the CdSe−ZnTe valence (0.66 eV) and conduction (1.17 eV) band offsets.36−38) These energetics make ZnTe particularly attractive as a component in a type-II heterostructure.21,29,39,40 However, relatively little work has been done on ZnTe nanocrystals, and little has been reported on the electron and hole dynamics in high-quality ZnTe-based nanostructures. ZnTe has a type-II band alignment and small lattice mismatch with CdSe, making this choice of materials an obvious one for the study of dynamical behavior type-II systems. Unlike the inverse CdSe/ZnTe core/shell particles for which the synthesis is straightforward,25,41 the difficulty of preparing high-quality ZnTe/CdSe particles perhaps contributes to the relative lack of previous studies.16 The practical implementation of type-II nanocrystals in photovoltaic devices requires that photogenerated charges within them can be transferred to external electrodes. However, charge transfer often competes with several other exciton processes, such as nonradiative recombination, surface trapping, and biexciton Auger processes,42−44 leading to a decrease in the efficiency of photovoltaic devices. Understanding the dynamics of interfacial charge transfer is therefore very important for the design of semiconductor photovoltaic devices. In most cases, interfacial charge transfer dynamics are elucidated through investigation of charge transfer to adsorbed molecular electron or hole acceptors, which offers a simple model system to understand ultrafast interfacial charge transfer involved in the photovoltaic processes. Interfacial charge between singlecomponent semiconductor nanocrystals and molecular acceptors has been extensively studied.45−49 The observed charge transfer rates are typically quite inhomogeneous, which is often understood in terms of a Poisson distribution of the number of molecular acceptors on each nanocrystal. Although there has been some work on interfacial charge transfer in the core/shell nanocrystals,14,48,50−52 these dynamics are still not well understood. In most of the published work, it is generally assumed that the shell thickness is uniform on each core particle. This is often a poor approximation, as can be seen in the TEM images reported for most core/shell nanocrystals.53−55 To further understand interfacial charge transfer dynamics in core/shell nanocrystals, the inhomogeneity of shell thicknesses must be taken into account. In this work, ZnTe/CdSe core/shell nanocrystals are synthesized using a method similar to that previously reported.16 These nanocrystals exhibit a type-II carrier confinement in which photogenerated electrons are localized in the CdSe shell and holes are confined in the ZnTe core. The spectroscopic properties can be understood in terms of electron and hole wave functions that are calculated using an effective mass approximation model. The calculated electron−hole overlaps permit prediction of the relative spectral intensities and radiative lifetimes, which are in good agreement with measured values. These calculations also predict the excited state redox potentials of the particle. Interfacial hole transfer quenching dynamics are also studied. A model is described in which the role of shell thickness variability is taken into account in the interfacial charge transfer dynamics. In this model, the average shell thicknesses on each particle are taken to be the

■

EXPERIMENTAL SECTION Chemicals. Diethyl zinc (Zn(Et)2, 96%), tellurium (Te, 99.8%), oleic acid (90%), selenium (Se, 99%), and chloroform (CHCl3, 99.8%) were obtained from Alfa Aesar. Cadmium oxide (CdO, 99.5%), trioctylphosphine (TOP, 97%), octadecene (ODE, 90%), methanol (MeOH, 98%), toluene (99%), phenothiazine (PTZ, 98%), and hexadecylamine (HDA, 90%) were obtained from Aldrich. HDA was recrystallized from toluene before use. TOP and ODE were purified by vacuum distillation. Oleic acid was dried by vacuum distillation with molecular sieves. Methanol, toluene, and chloroform were purified by distillation from appropriate drying agents. All other chemicals were used as received. Precursors for Shell Growth. The 0.1 M cadmium precursor solution used for the CdSe shell growth was prepared by dissolving 0.3204 g of CdO in a mixture of 6.18 g of oleic acid and 18 mL of ODE at 250 °C. The 0.1 M selenium precursor solution was prepared by dissolving 0.1580 g of Se in 5 mL of TOP and 15 mL of ODE. Synthesis of ZnTe Cores and ZnTe/CdSe Core/Shell Nanoparticles. In a typical reaction, a reaction flask loaded with 3 g of HDA and 4 g of ODE was heated to 280 °C under N2 flow. A solution of 0.50 mmol of Te and 0.50 mmol of Zn(Et)2 in 2 mL of TOP was quickly injected into the reaction flask. Following injection, the reaction temperature was set to 270 °C to allow nanoparticles to grow for 3 min. This produced ZnTe nanoparticles with a diameter of 2.6 nm. Larger particles are produced by further dropwise addition of the Te and Zn(Et)2 mixture in TOP, until the desired sized nanoparticles are obtained. For the growth of the CdSe shell, the above reaction mixture was cooled to 240 °C. An amount of 1.0 mL of the cadmium precursor stock solution (described above) was added dropwise, followed by addition of the same amount of the Se precursor, also added dropwise. The reaction was then run for 15 min. Subsequent shell growth is accomplished by the dropwise addition of the same amounts of cadmium and selenium shell precursors alternately. Aliquots were taken for measurements after each set of cadmium and selenium injections. Before spectroscopic analysis, the samples were precipitated by the addition of methanol and subsequently washed by several cycles of suspension in toluene, followed by precipitation by methanol and centrifugation. The washed nanocrystals were then dispersed in CHCl3. Hole Quenching. Samples used for the PTZ quenching studies were prepared by adding excess PTZ dissolved in CHCl3 to the CHCl3 solution of ZnTe/CdSe nanocrystals. Before spectroscopic measurements, the samples were allowed to sit for more than 3 h to ensure that the quenchers were well adsorbed to the surface of ZnTe/CdSe nanocrystals. Instrumentation. Static fluorescence spectra were obtained using a Jobin-Yvon Fluorolog-3 spectrometer. The instrument consists of a xenon lamp/double monochromator excitation source and a CCD detector. Time-resolved luminescence measurements were obtained by time-correlated single-photon 12959



Article

respectively. ZnTe is a direct band gap semiconductor with a bulk band gap of 2.25 eV (550 nm), indicating that the ZnTe nanocrystals produced in this work are in the strong quantum confinement regime. These organically capped ZnTe nanocrystals are not emissive, presumably due to the presence of many surface defects, which trap the carriers and thereby quench the luminescence from the band edge state. ZnTe nanocrystals produced by a similar procedure were also reported to show no luminescence.16,39 Due to the small lattice mismatch between CdSe and ZnTe (about 0.3%),16,56,57 CdSe can be easily deposited on the surface of ZnTe nanocrystals, forming ZnTe/CdSe core/shell nanocrystals. The shell growth reaction is nearly quantitative, and controlling the amounts of shell precursors gives good control of the CdSe shell thickness. Figure 1B shows a typical TEM image of ZnTe/CdSe nanocrystals with a shell thickness of 1.8 on a 2.6 nm diameter core. The initial cores and the core/shell nanocrystals have approximately spherical shapes and exhibit a high degree of monodispersity. There is no evidence of small CdSe nanoparticles resulting from homogeneous nucleation in either the spectroscopic or TEM results. Shell thicknesses are determined from TEM images of the core/shell particles. These images and histograms of the particles sizes are in the Supporting Information. The absorption spectra in Figure 2a show that upon the deposition of the CdSe shell the lowest-energy absorption peak shifts to the red and loses intensity, typical of type-II semiconductor heterostructures.19,25,58,59 This is due to the lowest exciton transition taking on increasing charge transfer character across the ZnTe−CdSe interface, in which the hole is localized in the ZnTe valence band and the electron is localized in the CdSe conduction band. PL measurements show that nanocrystals with less than a 0.7 nm thick CdSe (about two monolayers) shell are not emissive. Such a thin shell likely leaves some areas of the ZnTe cores uncoated and therefore not well passivated. Further shell deposition produces emissive nanocrystals with luminescence wavelengths that continuously shift to the red with increasing shell thicknesses, as shown in Figure 2b. Consistent with previous reports on type-II core/shell nanocrystals,16,25,39 the relative PL intensities undergo an initial increase with shell thickness due to the improved surface passivation, followed by a subsequent decrease. The type-II behavior of these heterostructures is also evident in the luminescence decays shown in Figure 3. In all cases, the PL decay can be fit to a triexponential, I(t) = ∑3i=1Aie−t/τi. The

counting (TCSPC), using a PicoQuant PMD 50CT SPAD detector and a Becker-Hickel SP-630 board. The light source was a cavity dumped Ti:sapphire laser (Coherent Mira) operating at 410 nm with a 1 MHz repetition rate. In all cases, the fluorescence was focused through a 0.25 m monochromator with a 150 groove/mm grating. Transmission Electron Microscopy (TEM) images were obtained with a FEI Tecnai 12 transmission electron microscope with an accelerating voltage of 100 kV in the Electron Microscope Laboratory (EML) at UC Berkeley.

■

RESULTS AND DISCUSSION Synthesis and Spectroscopic Properties of ZnTe and ZnTe/CdSe Nanocrystals. Several attempts were made to synthesize ZnTe nanocrystals from zinc carboxylates, rather than the more commonly used diethylzinc. Although ZnTe particles can be obtained, we find that only the organometallic is sufficiently reactive to obtain high quality, monodisperse nanocrystals. The ZnTe nanocrystals in the present work are synthesized with a high-temperature pyrolysis method by injecting the reaction precursors, diethylzinc and elemental selenium dissolved in purified TOP, into a mixture of octadecylamine and octadecene at 280 °C. The high temperature involved in this preparation enables the synthesis of ZnTe nanocrystals with a high degree of crystallinity. The ZnTe nanocrystals show a narrow size distribution with an average size of 2.6 nm and exhibit a sharp absorption band edge with an onset at 2.75 eV (450 nm), as shown in Figures 1a and 2a,

Figure 1. TEM images of (A) 2.6 nm core ZnTe nanocrystals and (B) ZnTe/CdSe core/shells with a CdSe shell of 1.8 nm on a 2.6 nm ZnTe core.

Figure 2. Absorption (a) and PL (b) spectra of 2.6 nm ZnTe core and ZnTe/CdSe core/shell nanocrystals. The CdSe shell thicknesses are given in the legends. Luminescence spectral widths (fwhm) are 221, 164, 159, 183, 200, and 208 meV for the particles with 0.8−1.95 nm shells, respectively. 12960



Article

The longest decay component obtained by triexponential fitting of the decay curves in Figure 3 is often assigned to the radiative lifetime. These lifetimes increase dramatically with shell thickness. For nanocrystals with thicker shells, the longest components are over 100 ns, which is significantly longer than the lifetimes typically observed for single component, type-I, or alloyed nanocrystal quantum dots. The trends in the absorption spectra and PL decay kinetics can be quantitatively understood in terms of calculated electron−hole overlaps, as discussed below. The band gap of bulk ZnTe is 2.25 eV,60,61 having the conduction and valence band edges at −1.52 and +0.73 V vs NHE,16,25 respectively. Bulk CdSe has a band gap of 1.74 eV,16,62and its respective conduction and valence band edges are at −0.30 and +1.44 V vs NHE.37,63,64 This gives conduction and valence band offset energies of Ue = 1.22 eV and Uh = 0.71 eV, respectively, and an energy alignment that favors the localization of photogenerated electrons in the CdSe shell and the holes in the ZnTe core. Using these energetics and the known electron and hole effective masses16,57 (me = 0.12 and mh = 0.60 for ZnTe and me = 0.13 and mh = 0.45 for CdSe), electron and hole wave functions and energies can be calculated. Zeroth-order electron and hole wave functions and energies are first calculated using these potentials. Following the calculation of the electron and hole wave functions, electron−hole interactions are considered as a perturbation. These calculations give the optical properties and redox energies associated with these core/shell structures. The details of the calculations are discussed in previous papers.64,65 The calculated results are compared to the absorption spectra shown above and the redox properties, which are discussed later. Figure 4a shows a comparison of the calculated band gaps with the absorption onsets and emission peaks for different shell thicknesses (determined from TEM images) on the 2.6 nm cores. These quantities are chosen (rather than the first exciton maxima) because they can in all cases be determined very accurately. The agreement with the observed absorption onsets is quite good. We note that this shows that the particles contributing to the luminescence spectrum have the same average size as the entire ensemble, seen in the absorption spectrum. Figure 4b shows the changes of the calculated conduction (1Se) and valence (1Sh) band edges of the ZnTe/

Figure 3. Normalized PL decay curves of the ZnTe/CdSe nanocrystals with different CdSe shell thicknesses on 2.6 nm ZnTe cores.

lifetimes and amplitudes of the triexponential decay components are collected in Table 1. The fits are quite good, and the Table 1. Lifetime Data Extracted from a Triexponent Fit to the PL Decays for ZnTe/CdSe Nanocrystals Having Different Shell Thicknesses

a

shell (nm)

A1

τ1 (ns)

A2

τ2 (ns)

A3

τ3 (ns)

0.8 1.0 1.3 1.6 1.8 1.95 1.25a

0.67 0.39 0.38 0.29 0.23 0.13 0.40

0.37 1.06 1.47 2.00 2.09 2.41 1.40

0.23 0.18 0.19 0.18 0.18 0.13 0.18

4.5 11.2 12.3 16.4 16.9 22.4 12.5

0.11 0.43 0.43 0.53 0.59 0.74 0.42

29 57 76 96 105 125 75

Different batch of particles.

statistical uncertainties of the fitting parameters are very small, in all cases, less than a percent. We have repeated these measurements with particles from several different syntheses and found the reproducibility to be good, typically within a few percent. This is probably limited by the reproducibility of specific shell thicknesses. Figure 3 and Table 1 show that the relative amplitudes and decay rates of the shorter components decrease with increasing shell thickness, indicating better surface passivation.

Figure 4. (a) Comparison of the band gaps calculated using an effective mass approximation with the absorption onsets and emission peaks obtained from the spectra of the ZnTe/CdSe particles. Error bars reflect the standard deviations of the means, obtained from Figure S2 (Supporting Information). (b) Calculated lowest conduction (1Se) and valence (1Sh) band edges of the ZnTe/CdSe nanocrystals as a function of shell thickness. The straight line in the figure indicates the PTZ oxidation potential. 12961



Article

absorbances is problematic because the particle concentrations are generally not known. To avoid this problem, the absorption spectra have been normalized to an absorbance at a wavelength far to the blue of the excitonic features, in this case, 320 nm. The (wavelength) integrated absorbances, ∫ ε(λ)dλ, of the lowest energy transitions are obtained by fitting Gaussians to the red edges of the absorption spectra (see Figure 2), and these plots are shown in Figure 6. The central question regarding the use of this type of normalized spectra is how the 320 nm absorption intensity varies with particle size. Two extreme assumptions could be made: that the absorbance scales linearly with particle volume or that the absorbance is independent of particle volume. The former assumption is commonly made for type-I (and in some cases type-II) semiconductor nanoparticles and is justified by the argument that near-UV excitation generates an electron−hole pair with both particles having sufficient energy above the band edge that quantum confinement effects are unimportant.66,67 However, the validity of this assumption has not been experimentally demonstrated for type-II particles, and simple energetic considerations suggest that when there is a large valence band offset it is not correct. Consider the present case of a ZnTe with a CdSe shell. In the simplest approximation, the relative amounts of energy that photoexcitation puts in the electron and hole scale with the inverse of each particle’s effective mass. The ZnTe electron and hole effective masses are 0.12 and 0.60 in units of the electron mass, respectively.68,69 ZnTe has a 2.25 eV bandgap, and 3.87 eV (320 nm) excitation puts about 1.35 and 0.27 eV in the electron and hole, respectively. However, the CdSe valence band is at a potential that is 0.71 eV further positive than that of ZnTe. This is greater than the hole energy (0.27 eV) following 3.87 eV excitation. Furthermore, if the shell is sufficiently thin, then CdSe localized excitons also cannot be formed. Thus, deposition of a thin CdSe shell results in essentially no increase in the effective excited volume. These energetic considerations indicate that how the 3.87 eV extinction coefficient scales with the shell thickness is somewhat complicated, and a simple linear scaling with total volume does not apply to the thin shell limit. However, as the shell gets thicker, excitation occurs into both the core and shell regions, and in this case the excitation volume increases with shell thickness. Because of these uncertainties, we treat this scaling empirically. We find reasonable overall agreement with the experimental results is obtained with an assumption that is intermediate between the two extreme possibilities, specifically that the 320 nm absorbance scales as V1/2. With this assumption, plots of S2λ2CT/V1/2 (where λ2CT is the absorption maximum of the charge transfer band) can be compared to experimental plots of the integrated absorbance. We emphasize that this scaling with the volume is purely empirical and is not the main point to be made here. The main point is that the electron−hole overlap decreases dramatically with increasing shell thickness. Analogous behavior is seen in the dependence of the PL kinetics on shell thickness. The PL decays are fit to a triexponential, and in the absence of slow nonradiative processes, the slowest decay component may be taken to be the radiative lifetime. These values are plotted in Figure 6. Calculated values of 1/τrad are taken to be proportional to S2/ λ2CT.70 Figure 6 shows that the agreement between these values and the longest decay component is reasonably good, with a discrepancy occurring only at the smallest rates. Figure 6 also shows that inclusion of a small nonradiative decay rate constant

CdSe as a function of shell thickness. The hole oxidation potential is given by Eh = Evb + Ehqc, where Evb is the energy of the bulk ZnTe valence band and Ehqc is the hole quantum confinement energy. Similarly, the electron potential is Ee = Ecb − Eeqc + Ee‑h, where Ecb is the energy of the bulk CdSe conduction band; Eeqc is the electron quantum confinement energy; and Ee‑h is the electron hole attraction energy. The quantum confinement energies scale inversely to the effective masses, and the electron−hole interaction energy is much smaller. The bandgap energy is given by Eg = Evb − Ecb + Ehqc + Eeqc − Ee‑h. We note that in these type-II particles the hole is confined to the core and the electron to the shell. Thus, if electron transfer occurs to an absorbed acceptor, this greatly increases the electron−hole distance. However, this is not the case for hole transfer. On the basis of this consideration, the Ee‑h term is omitted from the hole potential. With these approximations, the bandgap energy is simply given by Eg = Eh − Ee. The hole energies in ZnTe/CdSe nanocrystals are strongly dependent upon the size of the core and are less affected by the thickness of the shell, while the opposite is true for the electron energies. This is consistent with the photoexcited electrons being primarily localized in the CdSe shell, while the holes are mainly confined in the ZnTe core. Increasing shell thickness or the core size results in further separation of the electron and hole. The confinement of the holes in the core and the localization of electrons in the shell are also shown in the calculated electron (Ψe) and hole (Ψh) radial wave functions for the ZnTe/CdSe nanocrystals (see Figure 5). For type-II

Figure 5. Band alignment (upper) and radial distribution functions (lower) for electron and hole levels of the ZnTe/CdSe core/shell nanocrystals with a ZnTe core diameter of 2.6 nm and a CdSe shell thickness of 1.3 nm. The magnitude of the hole wave function in the vicinity of the shell surface is shown in the lower panel inset.

semiconductor nanocrystals, the integrated absorption coefficient of the low-energy charge transfer transition depends upon the extent of electron and hole overlap. The electron− 2 hole overlap integral is defined as S = ∫ ∞ 0 r drΨeΨh and is related to the integrated absorption coefficient by ∫ ε(ω)dω = ∫ ε(λ) (2πc/λ2)dλ ∝ S2f 0, where f 0 is the lowest exciton transition oscillator strength when the electron and hole wave functions completely overlap. Obtaining relative charge transfer 12962



Article

Figure 6. (Left panel) Comparison of the lowest energy transition integrated areas of the normalized absorption spectra (solid black squares) with calculated electron−hole wave function overlap integrals, S2λ2/V1/2. (Right panel) Observed longest PL decay components (black solid squares). Also shown are calculated relative radiative rates based on calculated electron−hole wave function overlap integrals and PL wavelengths (solid red circles) and calculated relative radiative rates considering a small (4.2 μs−1) intrinsic nonradiative recombination rate (open green circles).

analysis can be reversed to give the sample size inhomogeneity from the spectral width. The measured spectral width gives a σh value of 0.154 nm, about 0.5 CdSe monolayer. Along with the core variability, this indicates overall particle diameters of 5.22 ± 0.40 nm. We suggest that the small difference between spectral and TEM inhomogeneities arises because TEM imaging and optical spectroscopy examine different quantities. The optical experiment sees only the subset of particles that are luminescent. This consideration indicates that the particles that contribute to the luminescence spectrum are slightly more uniform than the ensemble as a whole. The inhomogeneity derived from the optical experiment is more relevant because the quenching studies described below examine only this subset of the particles. We conclude that these particles have an average shell thickness of 4.2 CdSe monolayers, and by this estimate the standard deviation of shell thickness between particles is about 0.5 monolayer. Hole Quenching by Phenothiazine. The type-II band offsets of the ZnTe/CdSe core/shell result in little hole density at the particle surface and hole transfer rates that are very sensitive to the shell thickness. Phenothiazine (PTZ) is a commonly used hole acceptor,37,45,71,72 having an oxidation potential of +0.83 V vs NHE.73 Figure 4 shows that the ZnTe/ CdSe nanocrystals with a 2.6 nm diameter core have a hole potential at ∼0.97 eV vs NHE, making hole transfer to adsorbed PTZ energetically favorable. Figure 7 shows the absorption and PL spectra of nanocrystals with a core diameter of 2.6 nm and an average shell thickness of 1.25 nm in chloroform with different concentrations of PTZ. Increasing PTZ concentration results in an increased absorbance at 280− 350 nm, assigned to free, solution-phase PTZ. The PTZ extinction coefficient is 4700 L·mol−1·cm−1,74 and the solution PTZ concentrations calculated from the absorption spectra very accurately match the PTZ concentrations calculated from dilution of known amounts of PTZ used to make the solutions. The experimental results in Figure 7 show that the luminescence from the bandgap state is quenched by adsorbed PTZ. Consistent with the steady-state PL spectra, Figure 8 shows that PL lifetimes become progressively shorter with increasing PTZ concentration. Analysis of the PL decay curves shows the presence of very fast and much slower decays: the PTZ quenching process is quite heterogeneous. Figure 8a also shows

(corresponding to a decay time of 240 ns) to all of the decays eliminates this discrepancy. This relatively slow nonradiative recombination could be due to residual defects which act as recombination centers, or it could reflect an intrinsic recombination rate. These particles are, of course, somewhat inhomogeneous. The particle to particle variation in shell thickness can be derived in either of two independent ways: from the luminescence spectral widths in Figure 2 or directly from the histograms of diameters measured from TEM images (see the Supporting Information). We compare these approaches, focusing on the particle having 1.3 nm thick shells, for which we present quenching results. The TEM results indicate that the ZnTe cores have diameters of 2.6 ± 0.25 nm and that these core/shell particles have diameters of 5.22 ± 0.48 nm. If the shell thickness is independent of core size, then these measured parameters are related to the variation in shell thickness by (σ2h + σ2c )1/2 = σp, where σp is the standard deviation of the particle radius (= 1/2 0.48 nm = 0.24 nm); σc is the standard deviation of the core radius (= 1/2 0.25 nm = 0.125 nm); and σh is the standard deviation of the shell thickness. We get that σh = 0.205 nm. The spectral width is given by ⎡ ⎛ ∂Eg ⎞2 ⎛ ∂Eg fwhm = 2.355⎢σc2⎜ ⎟ + σh2⎜ ⎣ ⎝ ∂rc h ⎠ ⎝ ∂h

rc

⎞2 ⎤1/2 ⎟⎥ ⎠⎦

where ∂Eg ∂rc

and h

∂Eg ∂h

rc

relate the luminescence energy to the core radius and shell thickness, respectively. From Figure 4, we get that (∂Eg/∂h)|rc = −0.43 eV/nm, evaluated at a shell thickness of 1.3 nm. The type-II nature of these particles, along with the hole effective mass being much greater than that of the electron, cause the exciton energy to be relatively insensitive to the core size. Calculations analogous to those in Figure 4 give (∂Eg/∂rc)|h = −0.17 eV/nm. This gives a predicted luminescence spectral fwhm of 0.21 eV, which is only slightly greater than the measured value of 0.164 eV (see Figure 2b). Alternatively, this 12963



Article

shell; APTZ is the surface area occupied by an adsorbed PTZ; and ANC is the particle surface area. The model has two adjustable parameters, Kads and k, which are chosen to fit the long time decays in Figure 8b. The Langmuir isotherm also accounts for saturation effects; when the number of adsorbed PTZs is ANC/APTZ, the surface is completely covered. In the present case, these effects are small but not completely negligible. The best fits to the concentration-dependent long decay amplitudes are obtained if the surface is taken to be 40% covered at the highest (5 mM) concentration, corresponding to about 16 adsorbed PTZs. The fits are only weakly sensitive to saturation effects, so the 40% saturation value is necessarily very approximate. Figure 8b shows that although adequate fits to the long time results are obtained for all concentrations, the calculated PL decay curves do not accurately fit the experimental results at short times. The presence of fast decay components in the PL decay curves compared to the calculated curves in Figure 8b indicates the presence of fast charge transfer in some fraction of the ensemble. We suggest that this results from shell thickness inhomogeneity, i.e., surface roughness. This is an inhomogeneity on each particle and does not reflect differences of shell thicknesses comparing one particle to another. The PL peaks shown in Figure 2b are quite narrow, indicating that the extent of type-II behavior and hence the average shell thickness is close to the same on all of the particles in the ensemble. The role of particle to particle variability is quantitatively considered later. Below we develop a model based on Marcus theory which incorporates shell thickness inhomogeneity and the variation of PTZ numbers. Shell Thickness Dependent Quenching Rates. The Marcus theory rate for a nonadiabatic electron transfer process is given by75−77

Figure 7. PTZ concentration-dependent absorption and PL spectra of ZnTe/CdSe nanocrystals with a ZnTe core of 2.6 nm and a CdSe shell of 1.25 nm.

decay curves calculated with the assumption that the nanocrystals have a uniform shell thickness and the same number of PTZs. These decay curves are calculated as I(t) = ∑3i=1Aie−t/τie−t/τq, where the Ai and τi constants are taken from Table 1. The PTZ quenching time, τq, is taken to be proportional to the PTZ concentration and is chosen so that the calculated curves match the long-time decays. The agreement with the experimental results is obviously very poor. Better (but still not adequate) agreement with the experimental results is obtained if the nonuniformity of the number of the adsorbed PTZ on each nanocrystal is also considered. In this case, a Poisson distribution of PTZs on each nanocrystal is considered, and the rates from each of the adsorbed PTZs are taken to be additive. Specifically, the concentration-dependent PL decay is given by m

I (t ) =

∑ m

kET(d) =

3

⟨m⟩ −⟨m⟩ −mkt e e ∑ Aie−t /τi m! i=1

(1)

2π ℏ

⎡ (λ + ΔG)2 ⎤ |H |2 exp⎢ − ⎥ 4λkBT ⎦ ⎣ 4πλkBT

(2)

where H is the donor−acceptor electronic coupling; ΔG is the energetic driving force; kB is Boltzmann’s constant; T is the temperature; and λ is the reorganization energy. In the case of hole quenching by electron transfer from an adsorbed molecular quencher to a hole confined in the core of the core/shell nanocrystal, the reorganization energy is determined by the electron−phonon coupling in the nanocrystal core, bond length changes in the molecular quencher, and the solvent. It

where m is the number of adsorbed PTZs and k is the quenching rate for a single adsorbed PTZ. The average number of PTZs adsorbed on the nanocrystal is denoted as . This average depends on the PTZ concentration through the Langmuir isotherm. It is given as ⟨m⟩ = (ANC/ APTZ)·((APTZKads[PTZ])/(1 + APTZKads[PTZ])), where Kads is the equilibrium constant for adsorption onto a unit area of the

Figure 8. Experimental PL decays as a function of PTZ concentration as indicated. Also shown are (a) PL decay curves calculated assuming the particles have a uniform CdSe shell and the same number of PTZs and (b) PL decay curves calculated assuming the particles have a uniform CdSe shell and a Poisson distribution of the number of PTZs. The same data are presented in (a) and (b), and data and corresponding calculated curves are the same color. 12964



Article

3, kn = k0e−β(n·0.31nm). The numbers of adsorbed PTZs at each shell thickness (the values of mn in eq 5) are sampled independently from a Poisson distribution, P(m) = [(m)/(m!)]e− for all m = mn. The averages of each of these n distributions are given by a Langmuir isotherm

should thus remain essentially constant when the same quencher and the nanocrystals with the same core size are used and the experiments are done in the same solvent environments, even if these nanocrystals have a different shell thicknesses. Furthermore, in quantum dot systems, the intraband hole relaxation is extremely fast (less than a few picoseconds),78,79 and hole quenching mainly occurs on the band edge 1Sh state. Therefore, the energetic driving force ΔG for the hole quenching can be expressed as the Gibbs free energy change for the quencher oxidation and the nanocrystal reduction, i.e., ΔG = −e(V(NC*/NC−) − V(q/q+)). In the core/shell nanocrystals with holes confined in the core, the energetics of the band edge 1Sh state are mainly determined by the size of the core and only slightly influenced by the shell thickness (see Figure 4b). This indicates that ΔG also remains essentially constant as the shell thickness is varied. The important point is that from eq 2 the hole transfer rate is proportional to the square of the electronic coupling. In the case that the charge acceptor binds to the surface of the core/ shell nanocrystals, the electronic coupling can be taken to be proportional to the density of the carrier wave function at the surface.13,64 Specifically, kd ∝ |Ψ1h(d)|2, where d is the shell thickness. This can also be expressed as kd = k 0 |Ψ1h(d)|2 /|Ψ1h(0)|2

⟨mn⟩ = Nnfλ (n)

λ n −λ e n!

I(t ) = I(0) ·∑ (Ai exp( −t /τi)) ·exp(−kqt ) i

∑ mnkn n

(7)

As in eq 1, values of Ai and τi are taken from Table 1. Equation 7 is summed over the distribution of quenching rates. The final result is calculated PL decays having a wide range of decay rates. The two adjustable parameters of the model, Kabs and k0, are evaluated by fitting the PL quenching decay curves, as shown in Figure 9. The data are fit using k0 = 28.5 ns−1 and Kads

(3)

Figure 9. Experimental PL decays as a function of PTZ concentration as indicated (same data as in Figure 8). Also shown are calculated curves generated from eq 7. The PTZ concentrations and average numbers of PTZs adsorbed on each particle are indicated.

(4)

= 0.15 nm−2 mM−1. The value of k0 comes from the decay kinetics and is determined quite accurately, probably within 5− 10%. The 5 mM PTZ solution results in about 16 adsorbed PTZs per particle, which is well below the estimated saturation value of about 40. As a result, quencher saturation effects are small in this concentration range, and the calculated fits are minimally sensitive to any assumption about the area occupied by an adsorbed PTZ, APTZ. However, since the value of Kads depends on the estimated number of PTZs needed to saturate the particle, the result of this consideration is that Kads is probably not determined to better than ±30%. Figure 9 shows that PL decay curves calculated in this way accurately fit the experimental results over the entire range time range at all PTZ concentrations. It is important to note that the entire set of decay curves is calculated with the same values of Kabs and k0.

where fλ(n) is the probability of a section of the surface having n monolayers of shell material and λ is the average number of shell monolayers. The values of λ are controlled by the number of SILAR cycles of shell deposition and experimentally determined from TEM images. The final shell thickness is the product of λ and the thickness of a ZnSe layer, about 0.31 nm. In the present case of a 1.25 nm thick shell, λ = 4.0. The total quenching rate for each particle can be expressed as

kq =

(6)

where Nn is the number of PTZs that can adsorb on the part of the shell having a thickness of n layers, Nn = 4π(R + n·0.31nm)2/APTZ. This is analogous to the definitions following eq 1, and the constant Kads is also defined the same way as following eq 1. The values of Kads and k0 are adjustable parameters in the calculation. Repeated Monte Carlo sampling of Poisson distributions for each term in eq 5 generates a distribution of rate constants, kq. For each calculated value of kq, we get a PL decay curve described as

where k0 is the hole quenching rate for the bare core and |Ψ1h(0)|2 is the hole wave function density at the bare core/ quencher interface. We find that the dependence of kd/k0 on shell thickness calculated from the effective mass approximation described above can be accurately described by a simple exponential dependence, kd = k0e−βd, with β having a value of 6.0 nm−1. An exponential distance dependence of tunneling rates is commonly found for nonadiabatic charge transfer processes.48,80 We have performed analogous calculations for the electron wave function density of CdSe/ZnS nanocrystals. These calculations give a β value of 3.7 nm−1, which is in good agreement with the experimental result of 3.5 nm−1 previously reported.48 The larger β value in the case of hole transfer in ZnTe/CdSe particles makes sense in terms of the larger hole effective mass. These relative hole transfer rates can be used to assess the effects of the variability of the shell thickness on the overall hole transfer dynamics. We use a simple model to describe surface roughness, that the shell thicknesses on each nanocrystal have a Poisson distribution

fλ (n) =

APTZK ads[PTZ] 1 + APTZK ads[PTZ]

(5)

where mn is the number of PTZs adsorbed on the part of the particle having a shell thickness of n layers and kn is the quenching rate of each of the acceptors, defined in terms of eq 12965



Article

The extent to which the average shell thickness varies from particle to particle can be assessed from the widths of the luminescence peaks in Figure 2b and the analysis described above. This also gives some insight into the distance scale on which the shell roughness occurs. The Poisson distribution has a standard deviation equal to the square root of the mean. For particles having a Poisson distribution of shell thickness averaging 4.0 monolayers, the sigma value σP = 2.0. This can be compared to the average shell thickness variability, σs = 0.5, derived above, from the luminescence spectral width. This comparison indicates that if the Poisson distribution of thicknesses was due to particle to particle differences the width of the luminescence peak (Figure 2b) would be 4 times larger than is observed. This analysis also addresses the “domain size” on which roughness occurs. If shell thicknesses are uncorrelated both within and between particles, then the particle shell thickness variability derived from the spectra is essentially a standard deviation of the mean of the shell thickness Poisson distribution. This is given by σs = σP/√N, where N is the number of Poisson sampled thicknesses on an individual particle. With the above values of σs and σP, we get that N = 16. The numerical values in this analysis have considerable uncertainty but suggest that there are on the order of 16 thickness domains on an average particle. On the basis of a simple ball-and-stick model of an approximately spherical particle, this is about the number of facets that one would expect for a 2.6 nm core particle. This result suggests that under that condition of this synthesis the thicknesses of each of the facets are independent. The model also semiquantitatively describes the effects of varying the average shell thickness. On a smooth surface, the average number of adsorbed quenchers should scale with the surface area. Alternatively, if the shell is sufficiently rough, then acceptors can be adsorbed essentially everywhere throughout the shell, and the number of adsorbed acceptors will scale with the shell volume. The experimental results and both scalings (shell area and shell volume) are shown in Figure 10. These two possible scalings are limiting cases, and the experimental results are intermediate between these extremes. This result is also consistent with the idea that the surface roughness occurs on the scale of the different exposed crystal facets. The above results and analyses indicate that the shell surface is very rough, and this has profound consequences on the

interfacial charge transfer dynamics. Comparison of Figures 8b and 9 shows that surface roughness effects are extremely important in describing the interfacial charge transfer dynamics and that this simple model captures the essence of these effects. It is of interest to speculate about whether all core/shell particles are this rough and what factors control the extent of surface roughness. The most obvious factor which could be involved is the core−shell lattice mismatch. It is well known that in two-dimensional epitaxially grown layered systems lattice mismatch results in island formation and is characterized as being Stranski−Krastanov or Volmer−Weber growth.81,82 The same considerations might be expected to be relevant here. However, we note that ZnTe and CdSe have nearly identical lattice parameters, and one might expect very little lattice strain. Core−shell interdiffusion complicates this simple consideration. Shell deposition at 240 °C may result in considerable cation but very little anion diffusion.83 It may be that the radial composition of these core/shell particles is best described as ZnTe - Zn,CdTe - Cd,ZnSe - CdSe. Significant lattice mismatch would be expected at the Te−Se interface, and this may be involved in producing shell thickness variability. Surface roughness increases the particle entropy, and we also speculate that entropy effects may also enter into or dominate the extent of surface roughness.82,84,85 In this case, the shell deposition temperature could have large effects on the morphology. Further studies examining these speculations are currently underway.

■

CONCLUSIONS Several specific conclusions can be drawn from the results and analysis presented above. (1) ZnTe/CdSe core/shell nanocrystals with different core sizes and shell thicknesses can be prepared by a hightemperature pyrolysis method. The bare ZnTe nanocrystals and the ZnTe/CdSe nanocrystals with a thin shell show no luminescence due to the presence of surface defects, while the ZnTe/CdSe core/shells with a thicker shell show intense luminescence with a wavelength that is tunable with both core size and shell thickness. (2) The electron and hole energies in these type-II particles can be tightly bracketed by redox reactions and the optical spectra. These energies are accurately calculated using a simple effective mass approximation model. (3) Although the photogenerated holes are confined in the core, the luminescence of ZnTe/CdSe nanocrystals can still be quenched by hole scavengers, such as PTZ. The quenching rate is strongly dependent on the shell thickness. (4) A model has been developed to describe the charge transfer dynamics of hole confined in the core of the core/shell nanocrystals to adsorbed acceptors. In this model, acceptors are assumed to be randomly adsorbed on the particle surface. The core to surface charge transfer rate is taken to be proportional to the density of the wave function at the surface, and the thickness of shell is assumed to have a Poisson distribution.

■

Figure 10. Shell thickness dependence of the number of adsorbed PTZ acceptors at a solution concentration of 5 mM (black dots). Also shown are calculated relative values of the shell area (blue curve) and the shell volume (red curve).

ASSOCIATED CONTENT

S Supporting Information *

TEM images and size histograms. This material is available free of charge via the Internet at http://pubs.acs.org. 12966



■

Article

(30) Lo, S. S.; Mirkovic, T.; Chuang, C.-H.; Burda, C.; Scholes, G. D. Adv. Mater. 2011, 23, 180−197. (31) Bang, J.; Chon, B.; Won, N.; Nam, J.; Joo, T.; Kim, S. J. Phys. Chem. C 2009, 113, 6320−6323. (32) Chuang, C.-H.; Lo, S. S.; Scholes, G. D.; Burda, C. J. Phys. Chem. Lett. 2010, 1, 2530−2535. (33) Zhu, H.; Song, N.; Lian, T. J. Am. Chem. Soc. 2011, 133, 8762− 8771. (34) Zhu, H.; Song, N.; Rodríguez-Córdoba, W.; Lian, T. J. Am. Chem. Soc. 2012, 134, 4250−4257. (35) Kaniyankandy, S.; Rawalekar, S.; Verma, S.; Ghosh, H. N. J. Phys. Chem. C 2011, 115, 1428−1435. (36) Wei, S.-H.; Zunger, A. Appl. Phys. Lett. 1998, 72, 2011−2013. (37) Song, N.; Zhu, H.; Jin, S.; Lian, T. ACS Nano 2011, 5, 8750− 8759. (38) Pearton, S. J. Wide Bandgap Semiconductors; William Andrew Publishing: New York, 2000. (39) Bang, J.; Park, J.; Lee, J. H.; Won, N.; Nam, J.; Lim, J.; Chang, B. Y.; Lee, H. J.; Chon, B.; Shin, J. Chem. Mater. 2010, 22, 233−240. (40) Acharya, K. P.; Khnayzer, R. S.; O’Connor, T.; Diederich, G.; Kirsanova, M.; Klinkova, A.; Roth, D.; Kinder, E.; Imboden, M.; Zamkov, M. Nano Lett. 2011, 11, 2919−2926. (41) Chen, C.-Y.; Cheng, C.-T.; Yu, J.-K.; Pu, S.-C.; Cheng, Y.-M.; Chou, P.-T.; Chou, Y.-H.; Chiu, H.-T. J. Phys. Chem. B 2004, 108, 10687−10691. (42) Radychev, N.; Lokteva, I.; Witt, F.; Kolny-Olesiak, J.; Borchert, H.; Parisi, J. J. Phys. Chem. C 2011, 115, 14111−14122. (43) Semonin, O. E.; Luther, J. M.; Choi, S.; Chen, H.-Y.; Gao, J.; Nozik, A. J.; Beard, M. C. Science 2011, 334, 1530−1533. (44) Htoon, H.; Malko, A. V.; Bussian, D.; Vela, J.; Chen, Y.; Hollingsworth, J. A.; Klimov, V. I. Nano Lett. 2010, 10, 2401−2407. (45) Huang, J.; Huang, Z.; Jin, S.; Lian, T. J. Phys. Chem. C 2008, 112, 19734−19738. (46) Sharma, S. N.; Pillai, Z. S.; Kamat, P. V. J. Phys. Chem. B 2003, 107, 10088−10093. (47) Dooley, C. J.; Dimitrov, S. D.; Fiebig, T. J. Phys. Chem. C 2008, 112, 12074−12076. (48) Boulesbaa, A.; Huang, Z.; Wu, D.; Lian, T. J. Phys. Chem. C 2010, 114, 962−969. (49) Boulesbaa, A.; Issac, A.; Stockwell, D.; Huang, Z.; Huang, J.; Guo, J.; Lian, T. J. Am. Chem. Soc. 2007, 129, 15132−15133. (50) Dworak, L.; Matylitsky, V. V.; Breus, V. V.; Braun, M.; Basché, T.; Wachtveitl, J. J. Phys. Chem. C 2011, 115, 3949−3955. (51) Guchhait, A.; Rath, A. K.; Pal, A. J. Chem. Mater. 2009, 21, 5292−5299. (52) Rawalekar, S.; Kaniyankandy, S.; Verma, S.; Ghosh, H. N. J. Phys. Chem. C 2010, 114, 1460−1466. (53) Manna, L.; Scher, E. C.; Li, L.; Alivisatos, A. P. J. Am. Chem. Soc. 2002, 124, 7136−7145. (54) Pal, B. N.; Ghosh, Y.; Brovelli, S.; Laocharoensuk, R.; Klimov, V. I.; Hollingsworth, J. A.; Htoon, H. Nano Lett. 2012, 12, 331−336. (55) Chen, Y.; Vela, J.; Htoon, H.; Casson, J. L.; Werder, D. J.; Bussian, D. A.; Klimov, V. I.; Hollingsworth, J. A. J. Am. Chem. Soc. 2008, 130, 5026−5027. (56) Simashkevich, A. V.; Tsiulyanu, R. L. J. Cryst. Growth 1976, 35, 269−272. (57) Gashin, P. A.; Sherban, D. A.; Simashkevich, A. V. J. Lumin. 1977, 15, 109−113. (58) Chen, C.-Y.; Cheng, C.-T.; Lai, C.-W.; Hu, Y.-H.; Chou, P.-T.; Chou, Y.-H.; Chiu, H.-T. Small 2005, 1, 1215−1220. (59) He, J.; Lo, S. S.; Kim, J.; Scholes, G. D. Nano Lett. 2008, 8, 4007−4013. (60) Luqman, M. M.; Brown, W. D.; Hajghassem, H. S. J. Electron. Mater. 1987, 16, 123−126. (61) Yim, J. W. L.; Chen, D.; Brown, G. F.; Wu, J. Nano Res. 2009, 2, 931−937. (62) Nanda, J.; Ivanov, S. A.; Achermann, M.; Bezel, I.; Piryatinski, A.; Klimov, V. I. J. Phys. Chem. C 2007, 111, 15382−15390. (63) West, A. R. Basic Solid State Chemistry; Wiley: Chichester, 1988.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This work was supported by a grant from the Department of Energy, Grant No. DE-FG02-04ER15502. REFERENCES

(1) Puzder, A.; Williamson, A. J.; Zaitseva, N.; Galli, G.; Manna, L.; Alivisatos, A. P. Nano Lett. 2004, 4, 2361−2365. (2) Smith, A. M.; Nie, S. Acc. Chem. Res. 2010, 43, 190−200. (3) Li, L. L.; Hu, J.; Yang, W.; Alivisatos, A. P. Nano Lett. 2001, 1, 349−351. (4) Liu, L.; Zhuang, Z.; Xie, T.; Wang, Y.-G.; Li, J.; Peng, Q.; Li, Y. J. Am. Chem. Soc. 2009, 131, 16423−16429. (5) Shieh, F.; Saunders, A. E.; Korgel, B. A. J. Phys. Chem. B 2005, 109, 8538−8543. (6) Regulacio, M. D.; Han, M.-Y. Acc. Chem. Res. 2010, 43, 621−630. (7) Schreuder, M. A.; Xiao, K.; Ivanov, I. N.; Weiss, S. M.; Rosenthal, S. J. Nano Lett. 2010, 10, 573−576. (8) Zhao, J.; Bardecker, J. A.; Munro, A. M.; Liu, M. S.; Niu, Y; Ding, I.-K.; Luo, J.; Chen, B.; Jen, A. K.-Y.; Ginger, D. S. Nano Lett. 2006, 6, 463−467. (9) Saba, M.; Minniberger, S.; Quochi, F.; Roither, J.; Marceddu, M.; Gocalinska, A.; Kovalenko, M. V.; Talapin, D. V.; Heiss, W.; Mura, A. Adv. Mater. 2009, 21, 4942−4946. (10) Kazes, M.; Lewis, D. Y.; Banin, U. Adv. Funct. Mater. 2004, 14, 957−962. (11) Ray, P. C. Chem. Rev. 2010, 110, 5332−5365. (12) Deka, S.; Quarta, A.; Lupo, M. G.; Falqui, A.; Boninelli, S.; Giannini, C.; Morello, G.; Giorgi, M. D.; Lanzani, G.; Spinella, C. J. Am. Chem. Soc. 2009, 131, 2948−2958. (13) Zhu, H.; Song, N.; Lian, T. J. Am. Chem. Soc. 2010, 132, 15038− 15045. (14) Zhang, Y.; Jing, P.; Zeng, Q.; Sun, Y.; Su, H.; Wang, A.; Kong, X.; Zhao, J.; Zhang, H. J. Phys. Chem. C 2009, 113, 1886−1890. (15) Yu, Z.; Guo, L.; Du, H.; Krauss, T.; Silcox, J. Nano Lett. 2005, 5, 565−570. (16) Xie, R.; Zhong, X.; Basché, T. Adv. Mater. 2005, 17, 2741−2745. (17) Reiss, P.; Bleuse, J.; Pron, A. Nano Lett. 2002, 2, 781−784. (18) Rawalekar, S.; Kaniyankandy, S.; Verma, S.; Ghosh, H. N. ChemPhysChem 2011, 12, 1729−1735. (19) Zhong, H.; Zhou, Y.; Yang, Y.; Yang, C.; Li, Y. J. Phys. Chem. C 2007, 111, 6538−6543. (20) Talapin, D. V.; Mekis, I.; Gotzinger, S.; Kornowski, A.; Benson, O.; Weller, H. J. Phys. Chem. B 2004, 108, 18826−18831. (21) Rawalekar, S.; Kaniyankandy, S.; Verma, S.; Ghosh, H. N. J. Phys. Chem. C 2011, 115, 112335−12342. (22) Balet, L. P.; Ivanov, S. A.; Piryatinski, A.; Achermann, M.; Klimov, V. I. Nano Lett. 2004, 4, 1485−1488. (23) Zavelani-Rossi, M.; Lupo, M. G.; Tassone, F.; Manna, L.; Lanzani, G. Nano Lett. 2010, 10, 3142−3150. (24) Makhal, A.; Yan, H.; Lemmens, P.; Pal, S. K. J. Phys. Chem. C 2010, 114, 627−632. (25) Kim, S.; Fisher, B.; Eisler, H.-J.; Bawendi, M. G. J. Am. Chem. Soc. 2003, 125, 11466−11467. (26) 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, 11708−11719. (27) Sitt, A.; Sala, F. D.; Menagen, G.; Banin, U. Nano Lett. 2009, 9, 3470−3476. (28) Gross, D.; Susha, A. S.; Klar, T. A.; Como, E. D.; Rogach, A. L.; Feldmann, J. Nano Lett. 2008, 8, 1482−1485. (29) Reiss, P.; Protiere, M.; Li, L. Small 2009, 5, 154−168. 12967



Article

(64) Jiang, Z.-J.; Kelley, D. F. J. Phys. Chem. C 2011, 115, 4594− 4602. (65) Jiang, Z.-J.; Kelley, D. F. Nano Lett. 2011, 11, 4067−4073. (66) Donega, C. d. M.; Koole, R. J. Phys. Chem. C 2009, 113, 6511− 6520. (67) Donegá, C. d. M. Phys. Rev. B 2010, 81, 165303−165323. (68) Rogach, A. L.; Kornowski, A.; Gao, M.; Eychmuller, A.; Weller, H. J. Phys. Chem. B 1999, 103, 3065−3069. (69) Masumoto, Y.; Sonobe, K. Phys. Rev. B 1997, 56, 9734−9737. (70) Struve, W. S. Fundamentals of Molecular Spectroscopy; Wiley: New York, 1989. (71) Jiang, Z.-J.; Kelley, D. F. ACS Nano 2010, 4, 1561−1572. (72) Jiang, Z.-J.; Leppert, V.; Kelley, D. F. J. Phys. Chem. C 2009, 113, 19161−19171. (73) Montalti, M.; Murov, S. L. Handbook of photochemistry; 3rd. ed.; CRC Press, Taylor & Francis Group: New York, 2006. (74) Ghosh, H. N.; Sapre, A. V.; Palit, D. K.; Mittal, J. P. J. Phys. Chem. B 1997, 101, 2315−2320. (75) Marcus, R. A. J. Chem. Phys. 1965, 43, 679−701. (76) Marcus, R. A. J. Chem. Phys. 1956, 24, 966−978. (77) Marcus, R. A. Annu. Rev. Phys. Chem. 1964, 15, 155−196. (78) Ferlat, G.; Xu, H.; Timoshevskii, V.; Blase, X. Phys. Rev. B 2002, 66, 85210−85216. (79) Klimov, V. I.; McBranch, D. W.; Leatherdale, C. A.; Bawendi, M. G. Phys. Rev. B 1999, 60, 13740−13749. (80) Artés, J. M.; Díez-Pérez, I.; Sanz, F.; Gorostiza, P. ACS Nano 2011, 5, 2060−2066. (81) Eaglesham, D. J.; Cerullo, M. Phys. Rev. Lett. 1990, 64, 1943− 1946. (82) Williams, R. S.; Medeiros-Rebeiro, G.; Kamins, T. I.; Ohlberg, D. A. A. Acc. Chem. Res. 1999, 32, 425−433. (83) Shaw, D. J. Cryst. Growth 1988, 86, 778. (84) Williams, R. S.; Medeiros-Rebeiro, G.; Kamins, T. I.; Ohlberg, D. A. A. J. Phys. Chem. B 1998, 102, 9605−9609. (85) Rudd, R. E.; Briggs, G. A. D.; Sutton, A. P.; Medeiros-Ribeiro, G.; Williams, R. S. Phys. Rev. Lett. 2003, 90, 146101−146104.

12968


Effects of Inhomogeneous Shell Thickness in the Charge Transfer

Recommend Documents