Shell Nanorods: Transfer

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NANO LETTERS

Multiexciton Engineering in Seeded Core/Shell Nanorods: Transfer from Type-I to Quasi-type-II Regimes

2009 Vol. 9, No. 10 3470-3476

Amit Sitt,† Fabio Della Sala,‡ Gabi Menagen,† and Uri Banin*,† The Institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew UniVersity of Jerusalem, Jerusalem 91904, Israel, and NNL-National Nanotechnology Laboratory of CNR-INFM, UniVersita` del Salento, Via per Arnesano, 73100 Lecce, Italy Received May 27, 2009; Revised Manuscript Received July 24, 2009

ABSTRACT Multiple excitations in core/shell CdSe/CdS-seeded nanorods of different core diameters are studied by quasi-cw multiexciton spectroscopy and envelope function theoretical calculations. For core diameters below 2.8 nm, a transfer from binding to repulsive behavior is detected for the biexciton, accompanied by significant reduction of the triexciton oscillator strength. These characteristics indicate a transition of the electronic excited states from type-I localization in the core to a quasi-type-II delocalization along the entire rod as the core diameter decreases, in agreement with theoretical calculations.

Colloidal core/shell semiconductor nanocrystals (NCs) have attracted considerable interest in the past few years owing to their unique optical and electrical properties, which are governed by the composition, dimensions, and shape of each of their components.1-6 By controlling the NCs’ potential profile through material choice and particle size, the spatial distribution of the electrons’ and holes’ excited state wave functions can be confined either to the core or to the shell. Consequently, the overlap between the wave functions can be controlled, affecting the band gap photoluminescence (PL) energy, the quantum yield, the lifetime, and the multiexciton (MX) properties. For example, NCs with a type-I enclosed potential profile, where both electrons and holes are confined to the same region of the NC, exhibit bright and stable fluorescence and are used for biological tagging7-9 and as emitters in light-emitting diodes,10-12 while NCs with a typeII staggered potential profile, where electrons and holes are confined to the different regions of the NC, exhibit intrinsic charge separation, which is beneficial for photovoltaic applications.5,6,13 The MX states in such systems also exhibit remarkably different behaviors and reveal intriguing manybody interactions.5,6,14,15 The biexciton (BX) state in a typeII system is characterized by a repulsive interaction leading to a blue-shifted emission peak with respect to the exciton (X), which was shown to provide advantageous lasing properties,6 while in a type-I system, the BX state is * To whom correspondence should be addressed. E-mail: banin@ chem.ch.huji.ac.il. † The Hebrew University of Jerusalem. ‡ CNR-INFM. 10.1021/nl901679q CCC: $40.75 Published on Web 08/05/2009

 2009 American Chemical Society

characterized by an attractive interaction leading to a redshifted emission peak with respect to the X peak. Recently, several types of high-quality seeded rod quantum dots (QDs), in which a CdS rod-like shell was grown onto a spherical NC, were developed.16-19 Of particular interest is the system of a CdSe core embedded in a CdS rod, which yields highly uniform NCs with very high quantum yields (reaching 70%)16,17,19 and linearly polarized photoluminescence that can be tuned by an external electric field.20,21 These high-quality heterostructures provide a benchmark for fundamental studies of optical and electronic properties in a system of mixed dimensionality where the core is a 0D dot, while the rod-shaped shell imposes a 1D confinement. Elegant optical studies on these systems, utilizing lifetime measurements accompanied by model calculations, yielded a conclusion of a flat band offset for the conduction band, resulting in a quasi-type-II system, where the electron is delocalized over the CdS nanorod while the hole is localized to the core.17,20-22 However, more direct scanning tunneling spectroscopy (STS) studies accompanied by model calculations on such NCs indicate a type-I band offset of 0.3 eV for the conduction band potential.23 To date, this difference regarding the band offsets of the system in the literature was not explained. Here, we investigate multiexciton (MX) behavior of CdSe/ CdS-seeded rods and explore its dependence on the dimensions of the system using quasi-continuous-wave MX spectroscopy24 along with theoretical modeling. On the basis of the X-BX emission spectral shifts, we analyze the nature

of the system, showing its shift from a type-I to a quasitype-II behavior while changing the CdSe core’s diameter, and show that this behavior can be explained by considering a type-I potential band offset. We also demonstrate that the quasi-typeII system MX behavior can be tuned and that the MX peak positions can be red shifted just by increasing the rod’s width. This study resolves the previous differences between optical studies and the STS work discussed above. CdSe cores of several diameters, ranging from 2.2 to 4 nm, were synthesized and encapsulated within CdS rods with diameters of ∼5 nm and lengths ranging from 45 to 100 nm, based on literature procedures (see Table S1 of the Supporting Information for the dimensions of the samples).17 In addition, for a core size of 2.2 nm, CdS rods of several widths and lengths were attained by halting the synthesis at different times after the injection of cadmium and sulfur precursors through rapid cooling of the system to room temperature using a water bath (see Table S2 of the Supporting Information for the dimensions of this set of samples). The samples were cleaned and purified through precipitation and redissolved in hexane for spectroscopic measurements. The effective dimensions of the NCs were measured by transmission electron microscopy (TEM) analysis of at least 100 particles per sample (see Figure S1 of the Supporting Information for characteristic TEM images). MX experiments were performed using the quasi-continuous-wave (qcw) excitation method,24 in which a nanosecond optical excitation pulse, long compared to the Auger lifetimes, was used. The average number of excitons per QD, 〈n〉, was determined in this regime by a steady-state ladder climbing process, where higher MX states are sequentially generated upon increasing the excitation fluence via state filling. As the MX emissions occur at different wavelengths than that of the X, it is possible to separate the instantaneous emission spectrum temporally overlapping the excitation pulse into the different components which are related to each MX state. The laser source used in our experiments is a frequency-tripled Q-switched Nd:YAG laser (355 nm) providing 5 ns pulses at 10 Hz. Pulses were weakly focused, at room temperature, to an area of 5 mm2 in a cuvette containing QDs in hexane solution with an optical density of 0.1 at the excitation wavelength. Fluorescence emission was collected by a 0.5 numerical aperture lens and directed through a monochromator onto a photomultiplier tube. The signal was detected on a digital oscilloscope triggered by a fast Si p-i-n photodiode. Transient emission spectra were obtained by scanning the monochromator wavelength over the entire emission spectral range. The absorption (Figure 1) and PL spectra (Figure 1, inset) of the CdSe/CdS dot/rod NCs show, from bottom to top, the change in the linear absorption and PL as the core diameter is increased (consecutive traces are shifted vertically for clarity). The significant increase in the absorption at wavelengths lower than 500 nm is attributed to the onset of absorption into the CdS rod transitions. The position of the CdS absorption peak is nearly the same for all measured systems, indicating a weak size dependence of the CdS Nano Lett., Vol. 9, No. 10, 2009

Figure 1. Absorption spectra of colloidal CdSe/CdS-seeded rods with different cores sizes (the core diameter, rod length, and rod diameter for each system are listed above). Consecutive spectra are shifted vertically for clarity. The inset shows a magnification of the absorption in the band gap regions (solid) and band edge emission (dashed).

electronic states, as expected for this system in the range of rod dimensions between 4.7 and 6 nm. The weak absorption peak at higher wavelengths (Figure 1, inset) is associated with the first electronic transition related to the CdSe core, which is of significantly smaller volume compared to the CdS rod. Band edge PL assigned to the X emission can be observed. Both the emission and CdSe absorption peak are red shifted as the core size is increased due to the quantum size effect. Three examples of MX emission spectra, at intensities varying from 10 nJ to 1 mJ per pulse, measured at the peak of the excitation pulse, are shown in Figure 2. Briefly, the X emission is obtained from the lowest-energy data, where, on average, less than one photon is absorbed per dot. The set of spectra measured at higher illumination intensities is fitted using three additional peaks (each with an arbitrary spectral location and spectral width), accounting for BX (in blue), a triexciton (TX) (in green), and a third peak which we shall label as CdS rod emission (in magenta). The assignment of the peaks is obtained both from their order of appearance and from the peak amplitude dependence on pump intensity. A detailed description of the fitting procedure appears elsewhere.24 Figure 2a portrays the spectra obtained for CdSe/CdSseeded rods (core diameter of 4.0 nm; rod dimensions of 45 nm × 6 nm). The amplitude of the first appearing peak at 612 nm (shown in red) is linearly dependent on the excitation intensity (inset), indicating that it involves the absorption of one photon, and thus can be assigned to the X. The second peak, which appears at a wavelength of 622 nm, (blue) follows a quadratic power law with respect to the excitation intensity, attesting that it involves the sequential absorption of two photons, and thus can be assigned to the BX. The BX peak appears significantly red shifted with respect to the X peak. This shift is attributed to the binding interaction in the BX state, which is typical for type-I systems. The third appearing peak, at 564 nm, is blue shifted with respect to the X and can be easily distinguished at high 3471

Figure 2. Transient emission spectra (solid black line) measured at the peak of the excitation pulse at increasing pulse energies ranging from 0.01 to 150 photon per dot (ppd) (a) for 4 nm diameter CdSe cores embedded in 45 nm × 6 nm CdS rods, (b) for 2.2 nm diameter CdSe cores embedded in 114 nm × 4.7 nm CdS rods, and (c) for 3.9 nm diameter ZnSe cores embedded in 50 nm × 5 nm CdS rods. Spectra sets were fitted using four peaks featuring the X (red), BX (blue), TX (green), and CdS emission (magenta). The red shift between X and BX peaks in (a) indicates an attractive interaction, while the blue shift between the peaks in (b) and (c) indicates a repulsive interaction. The insets present the pump intensity dependence of the X (red circles), BX (blue squares), TX (green triangles), and CdS (magenta diamonds) peak amplitudes compared to a linear and a quadratic fitting curve (dashed red and blue line, respectively).

excitation fluences. Due to its low intensity at low excitation fluences, it is difficult to obtain its initial growth from the data, but it is apparent that once the systems have reached an absorbance level of a single photon per dot, it shows a quadratic dependence. This implies that a sequential threephoton absorption process is required in order to obtain this state, indicating that it is the TX state emission. The last appearing peak, at 480 nm, also shows a quadratic growth. This peak, whose position is in the vicinity of the CdS absorption (Figure 1), can be attributed to states in the CdS rod, as will be discussed below. Figure 2c shows similar spectra obtained from ZnSe/CdSseeded rods (core diameter of 3.9 nm; rod dimensions of 50 nm × 5 nm). In this case, the BX peak, at 563 nm, is blue shifted with respect to the X peak, at 585 nm. This blue shift is typical to type-II systems and is attributed to the repulsive interaction in the BX state. This result agrees with the bulk band offsets and with STS experiments that were performed on this system.23 In addition, the TX peak, at 541 nm, is considerably less pronounced than that in the type-I case above. This behavior is typical to type-II systems because of the reduction in TX oscillator strength due to spatial charge separation and thus can be used as an additional signature for such systems. Again, there is a buildup of another peak at 475 nm, at the gap of the CdS 3472

absorption, which can be attributed to emission from the CdS rod states. Figure 2b shows the spectra obtained for CdSe/CdS-seeded rods with small cores (core diameter of 2.2 nm; rod dimensions of 114 nm × 4.7 nm). In this case, the BX peak, at 556 nm, is blue shifted with respect to the X peak, at 568 nm. The TX peak, at 524 nm, has a relatively low intensity and is hard to distinguish. As mentioned above, these are indicators for a type-II system, in contrast to the type-I characteristics that were obtained for the first case, for a system with the same composition but larger core size. Similar experiments and analyses were performed for a series of seeded rods of various dimensions. The measured positions of the MXs peaks as a function of the core diameter, extracted from the qcw spectra, are plotted in Figure 3a, and the extracted MX shifts with respect to the X are plotted in Figure 3c. Upon increase of the core diameter, we observe a transition of ∆BX-X (Figure 3c) from positive (repulsive binding interactions, maximal value of +43 meV), which indicates a type-II behavior, to negative (attractive binding interactions, minimal value of -33 meV), which is characteristic of a type-I system. The crossover between the attractive and repulsive BX behavior is seen for a core diameter of ∼2.75 nm. Nano Lett., Vol. 9, No. 10, 2009

Figure 3. (a) Multiexciton peak positions as a function of core diameter. Measured X (blue circles), BX (red squares), TX (green downwardpointing triangle), and CdS (magenta upward-pointing triangle) peak positions in CdSe/CdS-seeded rods. Dashed lines are a guide to the eye. (b) MX transition scheme. (c) Extracted ∆BX-X shifts; a crossover from repulsive (type-II) to attractive (type-I) BX binding energy is seen at a core diameter of ∼2.75 nm. (d) Measured intensity ratio of TX/X at an excitation flux of 100 photons per dot.

Figure 3d shows the ratio between the TX peak and the X peak intensities for different core diameters at an excitation flux of ∼100 photons per dot. For systems with core diameters lower than 2.9 nm, there is a significant drop in TX intensity under the same excitation fluence, with high correlation to the BX behavior crossover. The results show that as the core diameter increases, there is a transfer from type-II to type-I behavior. Systems with core diameters lower than ∼2.8 nm exhibit a distinctive type-II behavior, which is characterized by BX positive binding energies and low intensity of the TX emission due to small overlap between the electron and hole wave functions. For core diameters larger than ∼2.8 nm, negative BX binding energies and high intensity of the TX emission are seen, all indicative for high overlap between the excited electron and hole wave functions typical for a type-I system. The effect of the CdS rod diameter was examined for fixed core sizes of 2.2 and 4.0 nm (see Supporting Information for further details). In the large, 4 nm, core system, increasing the CdS shell width affected only the position of the CdSrelated peak but did not affect the peak positions of the X and BX. This explicitly indicates that in this system, the X and BX involve core states and therefore are not affected by the change in the rod’s dimensions. In contrast, the CdSrelated emission peak is shifted to the red as the rod diameter increases, indicating that it is related to transition from states in the CdS rod. On the other hand, for the small core system, increasing the rod’s width shifted all of the peaks to the red (see Figure S3, Supporting Information), indicating that all of them involve rod states. Nano Lett., Vol. 9, No. 10, 2009

The experimental study was accompanied by theoretical investigations using the envelope function approximation (EFA).27 The dot/rod NC was modeled as a sphere of CdSe with diameter Dc inside of a hexagonal prism of CdS of length L and diameter Ds. The center of the CdSe sphere was located at a distance D ) L/4 from the hexagonal basis.17,25,26 The experimental results were modeled by a series of simulations, with a variable core diameter (Dc). Rod dimensions were kept constant, with diameter Ds ) 6 nm and length L ) 40 nm (resembling the experimental dimensions; see Table S1, Supporting Information). The electronic and optical properties of the NCs were obtained by solving the variable effective mass Hamiltonian27,28 on a three-dimensional Cartesian grid. The effective mass parameters which were used are me ) 0.13 and mh ) 0.45 for CdSe and me ) 0.2 and mh ) 0.70 for CdS.17,25,26 The energy gaps at room temperature were taken as 1.75 eV for CdSe and 2.5 eV for CdS.29 A uniform dielectric constant of ε ) 8 was used for the entire rod. Dielectric mismatch effects15,30 will be considered elsewhere. The CdSe/ CdS conduction band offset (∆c) has been fixed to 0.3 eV, as found recently in our combined STS-theory study, which directly measures this value.23 A smaller band offset (∆c ) 0.2 eV) was also considered in order to estimated the sensitivity of this parameter. The band offset with respect to the vacuum level is fixed to 1.25 eV for both electrons and holes.31 Previous calculations have shown that this approach can correctly describe the energy levels23 and the whole absorption spectra of the seeded rods.17,26 3473

Figure 4. Computed electronic properties for CdSe/CdS core/shell NCs with different CdSe core diameters (Dc) and with L ) 40 nm and Ds ) 6 nm (∆c ) 0.3 eV). (a) Lowest seven electron eigenvalues. The CdS and CdSe conduction band edges (2.05 and 1.75 eV, respectively) are also shown. Inset: First electronic wave function along the main axis of the rod for Dc ) 2.0 and 4.8 nm. (b) Core localization for the e1, h1, e2, and h2 states and the exciton emission intensity (fX).

The MX emission energies, EMX (see Figure 3b) can be obtained from perturbation theory32-36 as follows EX ) εe1 - εh1 - Je1,h1 EBX ) EX + Je1,e1 + Jh1,h1 - 2Je1,h1 p ETX ) εe2 - εh2 + 2Jh1,h2 - Kh1,h2 + 2Je1,e2 -

(1)

Ke1,e2 - (2Je2,h1 + 2Je1,h2 + Je2,h2)

where εi is the ith single particle eigenvalue of the electron or hole, J indicates the coulomb integral, and K is the exchange integral. The coulomb and exchange integral are computed as Jab ) 〈φa|Vbb|φa〉 and Kab ) 〈φa|Vab|φb〉, respectively, where Vab(r) is the electrostatic potential of the product density φa(r)φb(r), obtained by solving the Poisson equation.25 The emission intensity of the X transition is approximated as fX ∝ |〈φe1|φh1〉|2, that is, proportional to the square of the electron-hole overlap. We note that in atomistic or multiband calculations the ground-state triexciton configuration has a non-Aufbau occupation sequence (see Figure 3b) where one hole always occupies the low-lying p-state due to reduced hole-hole coulomb interaction.37 This suggests that the single-band effective mass approximation, where the crystal field split s-type hole state is not present, can correctly describe triexcitons. In eq 1, we consider the TX emission energies originating from a p-p recombination channel.37 The s-s recombination channel will have emission energies close to excitons,37,38 in contrast with the data in Figure 3a (see also in the following). Figure 4a shows the lowest seven conduction band eigenvalues, εej, calculated for different core diameters. For the smallest cores, the first conduction state wave function φ1e(r) is not localized in the core (Figure 4a, inset); note that the eigenvalues are higher than the bottom of the CdS conduction band due to the rod quantization energy. As the core diameter increases, the first eigenvalue energy decreases. 3474

For the largest core, the φ1e(r) is localized in the core. Higher eigenvalues are already fully delocalized along the rod and thus do not present significant variation for different CdSe cores size. To better quantify the localization of the wave function, we report in Figure 4b the core localizations defined as lX ) ∫CdSe |φX(r)|2 d3r for X ) e1, h1, e2, and h2. Figure 4b shows that le1 continuously changes from 0.11 to 0.80, while lh1 is in the range of 0.68-0.96. As a consequence, the exciton emission intensity, that is, the square of the e1-h1 overlap, changes by a factor of 2.20. Figure 4b also reports the core localization for the second electron (e2) and second hole (h2) states. The e2 state is completely delocalized in the rod for Dc < 4 nm. For a larger core, it is localized in the core and assumes a p-type character (see the corresponding wave functions in Figure S5 and energies in Figure S6, Supporting Information). The h2 state is a p-type orbital with increased localization in the core for large Dc. For the smallest core radius (Dc ) 2 nm), this state delocalizes into the rod. Figure 5 reports the computed MX properties. In Figure 5a, we report the difference between the BX peak (EBX) and the X peak (EX), which corresponds to the negative of the biexction binding energy. Note that the expression in eq 1 for the biexciton energies does not include correlation contributions, yields always positive values for EBX - EX, and hence is only approximation for type-I systems.35,39 The computation of the correlation can be performed as described, for example, in refs 35 and 39, but it will be very expensive for the systems considered in this work due to the contribution of several electronic rod states. However, eq 1 should correctly describe the trends between our systems because the electronic rod states are not changing with the core diameter (see Figure 4a), and thus, the correlation contributions can be expected to be almost a constant.35,39 Figure 5a shows that for ∆c ) 0.3 eV, the biexciton binding energies Nano Lett., Vol. 9, No. 10, 2009

Figure 5. MX properties of CdSe/CdS core/shell NCs for different CdSe core diameters and with L ) 40 nm and Ds ) 6 nm with ∆c ) 0.2 eV (red circles) and ∆c ) 0.3 eV (black squares). (a) Difference between BX and X emission energies. (b) Ratio between TX and X intensities.

vary by about 50 meV for the core diameters considered in the experiments, in close agreement with the measured values in Figure 3c. In Figure 5b, we report the computed TX/X intensity. The TX emission intensity is approximated as fTX ∝ |〈φe2|φh2〉|2.39 The TX energies mainly depend on the single-particle energy gap εe2 - εh2 (see Figure S7, Supporting Information) and in particular on εh2 as εe2 does not change with Dc (see Figure 4a). For the smallest core size (Dc e 2 nm), the TX/X intensity is high because the second hole state is not localized in the CdSe core, but it is spread along the rod (see Figure S5, Supporting Information). For a Dc > 2 nm, the second hole state rapidly assumes a p-type shape and becomes localized in the CdSe (see Figure S5, Supporting Information, and Figure 4b). For a larger core size, the p-hole state does not change its shape considerably (see Figure S5, Supporting Information), while the second electronic wave function becomes more localized inside of the CdSe, increasing the overlap with the hole p-state and thus the TX/X intensity. Note that the graph in Figure 5b is on a log scale. Thus, the TX intensity can hardly be observed for small core size (i.e., quasi-type-II confinement). This is in qualitative agreement with the experimental results, showing only a very weak TX emission peak for small core diameters, and confirms that the measured triexcitons are due to a p-p recombination. From both the computational and the experimental results, it can be seen that the behavior of the CdSe/CdS system is shifted from a type-I to a quasi-type-II behavior by tuning the system dimensions. This is achieved due to the special Nano Lett., Vol. 9, No. 10, 2009

potential profile of this system and its mixed dimensionality. The bulk potential structure of the system exerts a type-I structure, where both excited electrons and holes should occupy the core. However, the conduction band offset of CdS and CdSe is relatively small (0.3 eV), thus the barrier for the electrons is relatively low, and as a result, the ability to confine the electronic states in the core is highly influenced by its diameter. For larger CdSe core diameters, the lowest conduction band state of the CdSe resides within the core. In this case, a type-I behavior is seen. For smaller core diameters, the lowest conduction band state of the CdSe rises in energy and eventually goes above the barrier, forming a CdSe-CdS mixed state, which is delocalized along the rod, forming a quasi-type-II structure. These results resolve the differences in the literature regarding the CdSe/CdS-seeded rod band structure. The STS measurements, which were done on CdSe cores with a diameter of 4 nm, indicated a type-I behavior and yielded, along with the theoretical analysis, a CB offset of 0.3 eV.23 The present results are well explained using this band offset, where the observed clear transfer from type-I to quasi-typeII was a direct consequence of reducing the core size. The previous optical spectroscopic measurements of the seeded rods reported a quasi-type-II behavior, and these indeed focused on the range of relatively small cores,17,26 for which such behavior was also observed in the MX properties measured here. We have thus demonstrated the transfer of CdSe/CdSseeded rod NCs from type-I to quasi-type-II behaviors by direct engineering of the lowest electronic state wave function and its distribution along the particle through controlling the core size and rod width. These results provide new insights into the electronic structure of these heterostructures with mixed 0D-1D dimensionality and demonstrate the utilization of the multiexciton properties as a sensitive indicator for the band structure of such systems. Supporting Information Available: (I) TEM images and dimension measurements. (II) Measured system dimensions and spectroscopic information for systems with different core diameters. (III) Measured system dimensions and spectroscopic information for systems with a fixed core diameter of 2.2 nm and varying rod dimensions. (IV) Effect of rod dimensions in the quasi-type-II regime for a fixed 2.2 nm core size. (V) Lifetime measurements for type-I and quasitype-II CdSe/CdS-seeded rods. (VI) Calculated second electronic state and second hole state wave functions along the main axis of the rod. (VII) Calculated eigenvalues of the first and second valence levels for a CdS/CdSe dot/rod with different core diameters. (VIII) Calculated TX emission energy for different core diameters. This material is available free of charge via the Internet at http://pubs.acs.org. Acknowledgment. This work was supported in part by the Israel Science Foundation Converging Technologies program (Grant No. 1704/07) and by the NanoSci-ERAnet Single Nanohybrid project. U.B. acknowledges support of the Alfred and Erica Larisch Memorial Chair in solar energy. 3475

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