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Coulomb-Enhanced Radiative Recombination of Biexcitons in Single Giant-Shell CdSe/CdS Core/Shell Nanocrystals Nao Hiroshige, Toshiyuki Ihara, Masaki Saruyama, Toshiharu Teranishi, and Yoshihiko Kanemitsu J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b00547 • Publication Date (Web): 12 Apr 2017 Downloaded from http://pubs.acs.org on April 18, 2017

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The Journal of Physical Chemistry Letters

Coulomb-Enhanced Radiative Recombination of Biexcitons in Single Giant-Shell CdSe/CdS Core/Shell Nanocrystals Nao Hiroshige, Toshiyuki Ihara, Masaki Saruyama, Toshiharu Teranishi, and Yoshihiko Kanemitsu* Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan

AUTHOR INFORMATION Corresponding Author: *[email protected]

ACS Paragon Plus Environment

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ABSTRACT

Giant-shell CdSe/CdS core/shell nanocrystals have attracted much attention due to their unique quasi type-II band alignment, where a large valence band offset confines holes strongly to the core, but electrons are delocalized due to a small conduction band offset. Here, we report the observation of the relative enhancement in the radiative recombination rate of a biexciton compared to that of an exciton in giant-shell CdSe/CdS nanocrystals. We found a clear correlation between the shell thickness of the CdSe/CdS nanocrystals and the ratio between the radiative recombination rates of biexciton and exciton. Our finding can be explained by a picture in which the biexciton emission efficiency is enhanced through the electron localization around the core due to the strong Coulomb potential of the two holes confined in the core.

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Semiconductor nanocrystals (NCs) have unique optical properties, including NC-sizedependent photoluminescence (PL) wavelength and high PL quantum yield (QY), making them potential candidates for various optoelectronic applications.1–3 In these nanostructures, photogenerated carriers are strongly confined within a nanoscale volume, and many kinds of interesting multicarrier processes such as time-dependent PL intermittency (so-called PL blinking4,5), spectral diffusion,6,7 Auger recombination8–12 and multi-exciton generation13,14 have been investigated using optical spectroscopy on single NCs. In recent years, especially with respect to the charged-exciton emission (emission from a charged exciton, i.e., electron–hole pair with one additional charge carrier), the influence of Coulomb interactions on the emission processes in single NCs has been intensively investigated.12,15–22 It has been revealed that the spatial distribution of carriers is influenced by Coulomb interactions in various NC structures such as dot-in-rod samples.15,16 However, information on how Coulomb interactions influence the wave function of biexcitons (which consist of two electron–hole pairs) in single NCs is still rare. Further investigation of the radiative recombination dynamics of biexcitons in single NCs in relation to Coulomb interactions provide us with new insights for achieving efficient biexciton emission. An important aspect for studying the influence of Coulomb interactions on radiative processes in NCs is the asymmetric spatial distribution of electrons and holes. Such an asymmetry can be observed for example in giant-shell CdSe/CdS core/shell nanocrystals (for simplicity hereafter referred to as giant nanocrystals; g-NCs), consisting of a small CdSe core and a thick CdS shell. The band alignment of these g-NCs is quasi type-II, which is characterized by a small conduction band offset and a large valence band offset between the two materials. In the quasi type-II band alignment, the hole of an exciton is localized in the core because of the


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large valence band offset, while the electron of an exciton is delocalized over the whole shell because of the small conduction band offset.10,12,15,16,23 It has been reported that in the type-I band alignment the electron–hole overlap is usually not strongly influenced by Coulomb interactions,24,25 but this is not the case if the electron and hole are distributed asymmetrically. The shallow confinement potential for electrons means that their wave functions can be easily affected by the Coulomb potential from the core. Clarification of the relationship between the wave functions of biexcitons and their radiative recombination efficiencies enables design of new types of hetero nanostructures with high luminescence efficiencies for biexcitons. In this work, we report the observation of efficient radiative recombination of biexcitons in single g-NCs with thick shells due to localization of two electrons as a result of the strong Coulomb potential from the two holes confined in the core. We performed simultaneous measurements of second-order photon correlation, g(2), and PL-decay curves for four kinds of single g-NCs with different shell thickness and then determined the following three values: (i) the QY ratio of the biexciton to the exciton emissions, (ii) the PL lifetime of the biexciton, and (iii) that of the exciton. From these values, we evaluated the ratio between the radiative recombination rates of the biexciton and the exciton, β, for 43 single g-NCs. Interestingly, a positive correlation between β and the shell thickness of the single g-NCs was observed. We show that this relative enhancement of the radiative recombination rate of a biexciton (compared to that of an exciton) for thicker shells is a result of the increasing spatial overlap integral between electron and hole wave functions of a biexciton. To explain the increasing overlap despite the shell volume, we propose that for a biexciton the Coulomb potential of the two holes, which are strongly confined to the core, attracts the two electrons toward the core.


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We synthesized four kinds of g-NCs with different shell thickness for this work. CdSe core NCs were synthesized by a previously reported method.26 The details of g-NCs synthesis are described in Supporting Information. The diameter of the CdSe core was 3.2 nm. The four g-NCs types were prepared with CdS shell thickness of 10, 13, 23, and 33 monolayers (ML). The largest shell was around 10 nm thick (equivalent to 33 MLs). The transmission electron microscope (TEM) images of these g-NCs are presented in Supporting Information. The g-NCs were diluted in toluene and spin coated on a glass substrate with poly methyl methacrylate (PMMA). Afterwards the samples were characterized optically with light pulses, as explained below. From the measured PL properties (second-order photon correlation, lifetime), we calculated the ratio of the radiative recombination rate of biexciton ( ) and exciton ( ), / (= β). For the

determination of β, we used

=

∙ ,

(1)

where and are the QYs of a biexciton and an exciton, respectively. Using a similar notation, we define the PL lifetime of the biexciton with and that of the exciton with . Equation (1) is derived from the following two equations defining and .

= ∙ ,

(2)

= ∙ .

(3)

and

The above two relations are helpful for understanding of our model, but Eq. (1) is the more practical equation. We note that Eq. (1) is a general valid equation with no assumption about the magnitude of . From the view point of fundamental physics, the value of β provides us with


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important intrinsic properties of radiative recombination dynamics of a biexcitons in a single NC. Its absolute value determines how efficiently radiative recombination of a biexciton occurs compared to that of an exciton. Therefore, focusing on the value of β enables us to study radiative processes of biexcitons excluding the influence of non-radiative process such as Auger recombination. For determination of β, precisely measured values for / and / are required. So far, g(2) measurements have been widely used for evaluating / ,9,10,25,27–29 however, when two-photon cascade emission probabilities are high, non-linear effects such as PL saturation and non-negligible two-photon emission rates should be considered in evaluating / via g(2) measurements. To avoid this problem, we used a technique based on simultaneous measurements of g(2) curves and PL-decay curves for single NCs, which allows us to take into account for these non-linear effects and determine / precisely.30 The experimental details of simultaneous measurements of g(2) and PL-decay curves are provided in Supporting Information.

Figure 1. (a) PL intensity and PL lifetime of a single g-NC with shell thickness of 33 ML as a function of measurement time. (b) Corresponding correlation between PL intensity and PL lifetime for the total measurement range of 200 s.


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First, we show representative data of a single g-NC whose shell thickness is 33 ML and explain how β was evaluated experimentally. Figure 1a shows the time dependence of the PL intensity and PL lifetime. The PL lifetime was determined by applying a single exponential fit to the decay curves in each bin.29 The fitting range was 10 ~ 80 ns. This range is suitable because the contribution of the fast decay component becomes negligible after 10 ns. PL intensities with count rates around 70 kHz were frequently observed. The relationship between PL intensity and PL lifetime, which is known as the fluorescence lifetime-intensity distribution (FLID), is shown in Fig. 1b. The y-axis unit is 10 cts/bin. The color scale quantifies how frequently a combination of a certain PL intensity and lifetime occurs. The points are clearly distributed around a single center (PL intensity ~ 4000 cts/bin, lifetime 40 ~ 60 ns), which means that this gNC exhibits only one dominant emissive state attributed to the exciton emission and it appears to be free from blinking as previous works reported.10,31 The time-tag mode measurements enables us to extract the photon detection events from any region of the FLID.29 In Figs. 2a,b, we plotted the PL decay curve and g(2) curve obtained from analyzing the data located in the yellow rectangle in Fig. 1b. This advanced analysis is free from the disturbing influence of the time-dependent PL fluctuation.


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Figure 2. Result of simultaneous measurement of (a) PL-decay curve (black dots) and (b) g(2) curve. The red solid line is a double-exponential fitting function. The g(2) curve and PL-decay curve is obtained using the data located in the yellow rectangle in Fig. 1b.

In Fig. 2a, fast and slow decay components are observed. The red solid line is a doubleexponential fit to the PL-decay curve, from which we find that the lifetime of the fast decay component is 0.82 ns, and that of slow decay component is 51 ns. These fast and slow decay components are attributed to the biexcitons and excitons emissions, respectively. Note that the PL decay curve in Fig. 2a were obtained from the integration of the data that correspond to the data points inside the yellow rectangle of the FLID in Fig. 1b. This means that only the luminescence of the long living neutral exciton was extracted, and the luminescence of the charged exciton, which is weaker in intensity and has a shorter lifetime than that of the exciton, was therefore suppressed. As a result, the fast-decay component in the PL decay is not a signal from the charged biexciton. Furthermore, if the triexciton could be detected and the triexcitonbiexciton-exciton cascade emission would be dominant, the PL decay should be tripleexponential, but the experimental result is double-exponential. It is believed that triexcitons were not detected. The biexciton lifetime becomes short in our sample with a small core radius, because nonradiative Auger recombination rate of biexcitons depends on the core size and the core/shell interface structure in g-NCs.32–34 We conclude that the fast PL decay is due to the biexciton emission. Figure 2b shows the g(2) curve. The side peaks correspond to the count rates of two-photon detection caused by two excitons generated by the two different excitation pulses,27 but the


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assignment of the center peak is more difficult, since in general it may have contributions from both biexcitons and excitons.27 In order to verify the physical meanings of the decay components and to achieve a precise evaluation of / , we perform two additional sophisticated analyses, which have been reported in our previous work.30 The first one is the time-gated g(2) analysis,35,36 and the second one is the first photon decay analysis.9,10 The results of the time-gated g(2) analysis are shown in Fig. 3a. For this analysis, we chose 10 ns as the threshold for the time gate, which means that only the data after 10 ns was used for calculating the g(2) curve, removing any influence from the fast biexciton response. Compared to Fig. 2b, a g(2) center peak cannot be observed any more, which means that the g(2) center peak which appeared in Fig. 2b originated from a biexciton-exciton cascade emission. Figure 3b shows the result of the first photon decay analysis. This decay curve consists of the first photon detection events from the two-photon emission processes counted in the g(2) center peak, which means that this decay curve represents the first photon during a radiative biexciton recombination. The first photon decay curve is described by a single exponential function, and thus the fast PL decay is due to the biexciton lifetime. Since the g(2) side and center peak intensities could be clearly assigned to the exciton and biexciton emission rates, / was evaluated to be 0.15. Here, it has been reported that the average exciton number can be obtained from simultaneous measurements of the PL decay curve and the g(2) spectrum.29,30 We evaluated ~ 0.6 in Fig. 2. Considering a Poisson distribution for the photon population in the incident pulse, the excitation probabilities of excitons and biexcitons Px and Pxx can be written in the following forms: = 1 − exp−〈〉 and = 1 − exp−〈〉 − 〈〉 exp−〈〉. We obtained the values of

, independent of the excitation

fluence. Further, we confirmed that the lifetime of the fast decay component, 0.82 ns, was that of


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the biexciton, , and lifetime of slow decay component, 51 ns, was that of the exciton, . By inserting these values into Eq. (1), the value of β was determined to be 9.3.

Figure 3. (a) The result of the time-gated g(2) analysis. The threshold for the time gate was 10 ns. (b) The result of the first photon decay analysis. The red solid curve is a single exponential function with lifetime of 0.78 ns.

Next, we show the complete results of the same analysis performed on 43 single g-NCs, which contain g-NCs with shell thickness of 10, 13, 23, and 33 ML. In Fig. 4a, we plot β as a function of shell thickness and we find a clear increase of β with increasing shell thickness. For g-NCs with relatively thin shell such as 10 and 13 ML, the value of β is around 4. Interestingly, for the case of g-NCs with thicker shell, such as 23 and 33 ML, much larger values of β are observed for many particles. For 23 ML, we obtained β = 10 on average, and for 33 ML we found an average value of β = 15. These results confirm the relative enhancement of the radiative recombination rate of a biexciton compared to that of an exciton in g-NCs.


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Figure 4. (a) β plotted as a function of shell thickness. Black solid squares are the average value of β calculated for single g-NCs with same shell thickness. (b) plotted as a function of under the assumption of ~ 1.

Similar to our experimental results for 10 and 13 ML, other groups have also reported β ~ 4 for CdSe/CdS NCs with shell thickness around 16 ML.10,25 This value is consistent with the theoretical model, the so-called statistical scaling law, which suggests that the radiative recombination rate is proportional to the number of possible recombination pathways in a multi carrier state.9,10,25,37 According to the statistical scaling law,37 is four times larger than

because a biexciton has four radiative recombination pathways while an exciton has one, which is equivalent to β = 4. We would like to emphasize that our experimental results for 23 and 33 ML cannot be explained by considering only the number of charges and recombination pathways. It is important to note that the value of β is only dependent on and . Earlier works reported that and directly represent the degree of the overlap integral of biexcitons and

excitons, respectively.38 The value of β thus reflects how much the electrons of a biexciton overlap with the holes compared to that of an exciton. As for an exciton, in a g-NC with quasi


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type-II band alignment, the electron is delocalized over the whole shell due to the small conduction band offset, while the hole is confined to the core due to the large valence band offset.10,15,16,20–23 This means that the electron–hole overlap integral is reduced with increasing shell thickness, leading to a decrease of . using To understand the details of the overlap integral of the biexciton, we evaluated

Eq. 3 with the assumption of ~ 1, which has been assumed frequently in previous works using single-dot spectroscopy.9,27 In Fig. 4b, we plot as a function of for each single g-NC. ) are all within a relatively narrow Although the values of and scatter, their ratios (=

range [0.1~0.3, as indicated by the linear curves in Fig. 4b]. Approximately equivalent values of are obtained even with different shell thickness. Despite the largely different shell thicknesses, an almost constant was observed in thick shell g-NCs. This means that the

electron wave function of the biexciton is almost independent of shell thickness even in quasi type-II band alignment with small conduction band offset. The decreased and almost constant in thick shell g-NCs show that for a biexciton the increase of the spatial overlap integral

between the electron and the hole compared to that of an exciton resulted in the enhancement of β in g-NCs with thick shells. We propose that the increase of spatial overlap integral for a biexciton in g-NCs with thicker shell compared to that of an exciton can be explained by considering the influence of Coulomb interaction on the electron wave function as illustrated in Fig. 5. With regard to the biexciton, each electron is subject to the Coulomb potential of the two holes confined in the core, which means that the electrons of a biexciton experience a stronger Coulomb potential from the core than those of an exciton. As a consequence, the electrons of the biexciton are still confined to the core even in samples with thick shells, leading to similar values of for all four types of


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g-NCs. This effect explains why the value of β increases for thicker shells. In the ideal case, where the spatial distribution of the electrons and holes of the exciton and biexciton are of the same degree, β should be 4. A value of β larger than 4 means that the electrons of the biexciton are more confined to the core than those of the exciton as illustrated in Fig. 5. Thus, we conclude that the strong Coulomb potential of the two holes confined to the core, which attracts the electron toward the core, increases the spatial overlap integral between the electron and hole wave function of the biexciton for g-NCs.

Figure 5. Schematics of spatial distribution of exciton (left) and biexciton (right) in quasi type-II band alignment. The electron wave function of the biexciton is more localized around the core than that of the exciton due to the larger Coulomb potential from the core (illustrated with the broken curve).

Our experiment evidenced that the value of β for g-NCs with shell thickness of 33 ML is about four times larger than the value predicted by the statistical scaling law. This can be quantitatively interpreted with a 1.2 ~ 1.3 (~ 41/6) times larger electron wave function for the exciton compared to that of the biexciton, under assumption that the electron wave function in g-


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NCs is spherically. This calculation is plausible because (and ) are proportional to the

volume integral of the spatial overlap of electron and hole.38 Here, we also provide another point of view for understanding this experimental result. The difference of the charge distribution between exciton and biexciton in quasi type-II band alignment is analogous to the difference of the electron radii in hydrogen and helium atom. The charge distribution of an exciton, where the hole is localized to the core while the electron is delocalized over the shell is similar to that of the hydrogen atom. Consequently, the charge distribution of the biexciton is similar to that of the helium atom. In addition, the effective mass of the hole is larger than that of the electron,12 which resembles the relationship between nucleus and electron. Our model is supported by the fact that the radius of the helium atom is smaller than that of the hydrogen atom and that in a helium atom, the attraction between nucleus and electron is stronger than the repulsion between the two electrons. For type-I band alignment, the spatial distributions of electrons and holes are determined mainly by the confinement potential, so both wave functions are similar and hardly influenced by Coulomb interaction.21,22 Different from type-I band alignment, the electrons in quasi type-II band alignment experience only a small confinement potential at the core.10,15,16,23–25 Therefore, the electron localization degree can be easily influenced by the Coulomb potential of the biexciton, which is significantly stronger than that of the exciton. Even for exciton, negative trion and positive trion, the calculation predicts that the wave functions of electrons are modified by Coulomb interaction.20 Similar to these states, the electron wave functions of biexcitons are also expected to be modified by Coulomb interaction. Earlier works reported that electron–electron repulsion enhances delocalization of the electrons for negative trions, which leads to a suppressed Auger recombination for quasi type-II


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band alignment such as is found in g-NCs10,23,25 and in dot-in-rod structures.15,16 The observation of reduced PL blinking for single g-NCs in our measurements is consistent with earlier works, and means that in our samples negative trions are more delocalized than excitons. On the other hand, we observed a localization for the electrons of the biexcitons because of Coulomb attraction from the two holes in the core, leading to an increased radiative recombination rate of the biexciton compared to that of the exciton. Our results regarding the negative trion and the biexciton indicate that Coulomb interaction can play an important role in efficient emission from multi-carrier states by controlling the distribution of the carrier wave function. In summary, we found that, in CdSe/CdS g-NCs, a biexciton shows the relative enhancement of the radiative recombination rate compared to an exciton to Coulomb interaction. The electrons of the biexciton are localized around the core due to the strong Coulomb potential of the two holes confined to the core while the electron of the exciton is more delocalized. Our work revealed the relationship between Coulomb interaction and radiative recombination dynamics of the biexciton and will lead to new strategies for engineering wave function and obtaining efficient biexciton emission in various hetero nanostructures.

ASSOCIATED CONTENT Supporting Information. The following files are available free of charge. TEM images of giant nanocrystals (g-NCs), Nanocrystals synthesis, Single dot spectroscopy (PDF)

AUTHOR INFORMATION


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Corresponding Author: *[email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The authors would like to thank H. Tahara, T. Handa, and T. Yamada for their help. Part of this work was supported by JST-CREST (JPMJCR16N3) and JSPS KAKENHI (16K17483).

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