Spectral Diffusion of Emissions of Excitons and Trions in Single CdSe

Sep 26, 2016 - Spectral Diffusion of Emissions of Excitons and Trions in Single CdSe/ZnS Nanocrystals: Charge Fluctuations in and around Nanocrystals...
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Spectral Diffusion of Emissions of Excitons and Trions in Single CdSe/ ZnS Nanocrystals: Charge Fluctuations in and around Nanocrystals Hiroto Ibuki, Toshiyuki Ihara,* and Yoshihiko Kanemitsu* Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan ABSTRACT: The temporal fluctuations in the photoluminescence (PL) spectra of single CdSe/ZnS nanocrystals (NCs) exhibiting PL blinking at room temperature as well as their dynamical properties were studied. In the case of large NCs, measuring the time-dependent PL intensities and lifetimes allowed us to separately characterize the degree of spectral diffusion (SD) of the exciton and trion (charged exciton) emissions. The SD properties, such as the polarizability and field fluctuation, were investigated quantitatively through comparisons with the results of numerical calculations based on a simple field fluctuation model. We found that trion emissions exhibit unique SD characteristics; i.e., their binding energies are positive and their polarizabilities are smaller than those of excitons. In addition, we observed that the exciton emissions exhibited size-dependent SD behaviors, reflecting the differences in the polarizabilities of the NCs with different sizes. Finally, the experimental data, including an analysis of the energy shifts occurring before and after the periods corresponding to the trion emissions, are discussed, based on a model that accounts for the charge redistribution in and around the NCs.

I. INTRODUCTION Over the past three decades, there have been extensive studies on the optical properties of colloidal semiconductor nanocrystals (NCs), both from a fundamental physics viewpoint and with respect to their application in practical devices.1 Since NCs exhibit high photoluminescence (PL) quantum yields and because their PL wavelengths can be tuned by changing their size, they are emerging as potential materials for various applications, including light-emitting diodes, solar cells, bioimaging labels, and single-photon sources for quantum cryptography communications.2,3 NCs are an excellent platform for fundamental studies of not only excitons (electrons and corresponding holes formed in NCs) but also exciton complexes such as trions (a negative or positive charge is added to the exciton state, also known as a charged exciton) and biexcitons (a pair of excitons) in nanoscale materials. Nonlinear optical processes such as Auger recombination and multiple exciton generation have been also studied in NCs.4−6 To elucidate these intrinsic and unique features of NCs, single NC spectroscopy is widely used.7,8 Single NC spectroscopy has revealed some very interesting phenomena, such as PL blinking (intermittency) and spectral diffusion (SD).9,10 PL blinking is the random switching between the light-emission (ON) and no-emission (OFF) or intermediate (INT or gray) states,9,11−24 while SD is a fluctuation in the PL photon energy and/or the line widths of the PL spectrum.10 Although the exact mechanism that causes PL blinking, which was first observed in 1996, is yet unknown, it is widely accepted that both PL blinking and SD are associated with temporal fluctuations in the local charge in and around the NCs.11 PL blinking is caused by the ionization of the NCs and by charge trapping in the NCsthe ON state © XXXX American Chemical Society

is attributed to the exciton state, while the INT state is attributed to the trion state.19−24 On the other hand, SD results from the quantum-confined Stark effect (QCSE) under the electric field generated by the charges around NCs, which result in a decrease in the transition energies.10,11,25−36 These temporal fluctuations in the PL intensity and PL photon energy are undesirable with respect to the use as stable light emitters. Thus, it is of prime importance to clarify how the phenomena of PL blinking and SD can be suppressed and to elucidate how these two phenomena are correlated. PL blinking is associated with the appearance of the trion state. Thus, in order to suppress PL blinking, the trion state needs to be highly emissive and/or the degree of ionization of the NC needs to be reduced. Given the advances in material design and synthesis, recent studies have succeeded in suppressing PL blinking in NCs.37−39 On the other hand, SD is characterized by the QCSE.10 In order to suppress SD, the polarizability of the NC has to be minimized and/or the electric field fluctuations have to be decreased. The polarizability is defined as a coefficient relating the decrease in the transition energy and the square of the electric field.10 To date, there have been many studies on the SD of exciton emissions, clarifying the relationship between the energy shift and the line width.10,32−36 Recently, we clarified the SD of the exciton emission using an advanced method based on simultaneous measurement of PL lifetime and spectrum.36 However, the properties of the SD in the trion emission, which should be different from that of the exciton emission, remained unclear. Received: June 21, 2016 Revised: September 23, 2016

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DOI: 10.1021/acs.jpcc.6b06220 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Detailed understanding of the SD in the trion emission is needed for clarifying the connection between SD and blinking. In this work, we studied the temporal fluctuations in the PL properties of single CdSe/ZnS NCs, exhibiting both PL blinking and SD at room temperature. The SD of the trion emissions was distinguished from that of the exciton emissions by taking into account the differences in the PL intensities and lifetimes. In order to characterize the SD of each emission, the correlation between the PL photon energy and the line width was investigated. We found that trion emissions exhibit unique SD properties; i.e., they have positive binding energies compared to excitons and have smaller polarizabilities than those of the exciton emissions. We propose a simple field fluctuation model, which allows the polarizability of trions and the fluctuations in the local electric field in an NC to be evaluated quantitatively. Further, we show that the trions in the NCs exhibit small polarizability, which can reduce the fluctuations in the PL photon energy. We also show that the exciton emissions exhibit size-dependent SD characteristics, which reflect the differences in the polarizabilities with excitons in NCs of different sizes. Finally, we also demonstrate that large shifts occur more frequently before and after the INT state than during the ON state, owing to the changes in the charge distribution before and after the INT state. This is the first study showing the differences between the SD of exciton emissions and that of trion emissions and quantitatively investigates the characteristics of the charge fluctuations at room temperature.

II. EXPERIMENT To elucidate the SD of exciton emissions as well as that of trion emissions, we used relatively large CdSe/ZnS NCs (Qdot 655; Life Technologies). Figure 1a shows a transmission electron microscopy (TEM) image of the NCs. The NCs were bulletlike in shape and typically had dimensions of φ7 × 14 nm. To study the size dependence of their properties, smaller spherical CdSe/ ZnS NCs (Qdot605 and Qdot565; Life Technologies) were also studied. The NCs were initially dissolved in decane. After diluting the NCs using toluene, which included 0.1% poly(methyl methacrylate), we spin-coated them on a cover glass. A pulsed light with a wavelength of 540 nm (530 nm, 450 nm) was used to excite the Qdot655 (Qdot 605, Qdot565) NC. The pulse was produced by introducing the output of a white-light supercontinuum pulse laser (SC400-PP; Fianium) operating at a repetition rate of 40 MHz into a monochromator with a focal length of 25 cm. The pulse duration was 40 ps, and the spectral width of the excitation light was almost 0.5 nm. An oil-immersion objective lens with a numerical aperture of 1.30 was used for both the excitation of the NCs and the detection of the emitted PL. The excitation spot size (d) was estimated to be 1−2 μm in diameter. We evaluated the excitation power density by considering d = 1.5 μm. The positions of the single NCs were monitored using an electron-multiplying chargecoupled device (CCD) camera. The PL spectra were recorded using a monochromator with a focal length of 30 cm and a liquid-nitrogen-cooled CCD camera. To measure the timeresolved PL, we changed the repetition rate of the excitation white pulse to 5 MHz and detected the spectrally integrated PL using an avalanche photodiode (APD) and a time-correlated single-photon counting (TCSPC) board (SPC-130EM; Becker & Hickl GmbH). The response function of the measurement system was almost 200 ps. We also performed photon

Figure 1. (a) TEM image of NCs (Qdot 655). (b) A result of coincident count measurement on a single NC. (c) PL spectrum of ON state (obtained at 1.22 s) of a single CdSe/ZnS NC (Qdot 655) excited at 540 nm, after background subtraction. The measurements were performed at an excitation power of 260 W/cm2 for bin times of 20 ms. The red line is a Lorentzian fitting curve. PL spectrum of (d) QCSE-modified ON state and (e) INT state (obtained at 3.06 and 5.22 s, respectively). The black lines are Lorentzian fitting curves. Time traces of the (f) PL intensity, (g) PL peak energy, and (h) line width as determined from fitting curve of the spectrum. The gray dots in (g) and (h) are the uncertainties of the peak energies and fwhm evaluated from the fitting.

correlation measurements using a pair of the APD and the TCSPC board. For this measurement, a standard HanburyBrown Twiss interferometer was utilized, as we have reported in our recent papers.24,36 As shown in Figure 1b, clear antibunching was observed, and it was confirmed that the test sample was truly a single NC. All experiments were conducted at room temperature.

III. RESULTS AND DISCUSSION A. Time Traces of PL Properties: Exciton and Trion Emissions. Figure 1c shows the PL spectrum of a single Qdot 655 NC in ON state (black curve). The excitation power was 260 W/cm2, and the data were recorded for a binning time of B

DOI: 10.1021/acs.jpcc.6b06220 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C 20 ms. The red curve is the fitting result of the PL data using a single Lorentzian function. Figures 1d and e show the representative PL spectra of the QCSE-modified ON state and that of the INT state, respectively. These spectra were also fitted by a Lorentzian function (black curve). The PL spectrum of the QCSE-modified ON state was red-shifted and was broader than that in the ON state. The red shift of the QCSEmodified ON state from the ON state changes as a function of time.10,36 The PL spectrum in the INT state was also redshifted. It is important to note that the PL intensity of the INT state was decreased significantly compared to that of the ON state. From the fitting, we obtained the PL intensity, peak energy, and line width. The temporal changes in the PL intensity, peak energy, and full-width-at-half-maximum (fwhm) line width are plotted in Figures 1f, g, and h, respectively. The uncertainties of the peak energies and fwhm evaluated from the fitting are plotted as gray dots in Figures 1g and h, respectively. The PL intensity time trace in Figure 1f shows a clear PL blinking signature, indicating random switching between the bright ON states, which have high intensities, and the gray INT states, which have low intensities. Similarly, the time traces of the PL photon energy and the line width in Figures 1g and h show clear SD signatures. As we show in the next section, the influences of QCSE on the ON states and INT states can be elucidated by analyzing the correlation between the observed PL properties. Figure 2a shows a time trace of the PL intensity measured over a period of 100 s. The PL intensity distribution histogram

region corresponds to the data plotted in green; this region appears between the ON and INT states. The signal in the green region is a mixture of PL signals of ON and INT states in a single bin time. According to early works,19−24 the main contribution to the ON state is attributed to the exciton emissions, while that of INT state is attributed to the trion emissions. Figure 2c shows a time trace of the PL intensity measured at a lower excitation power (150 W/cm2). The PL intensity distribution histogram is shown in Figure 2d. Compared to the number of trion emissions (red region, INT) observed at 260 W/cm2, a decrease was observed for 150 W/cm2. This phenomenon of trion emissions disappearing at lower excitation powers is consistent with previously reported results.23 PL lifetime measurements were also performed on a single Qdot655 NC. The PL decays corresponding to the ON (blue curve) and INT (red curve) states are shown in Figure 3a. By

Figure 3. (a) Representative PL decays for the ON and INT states of a single NC measured at an excitation power 36 W/cm2. The bin time was set at 100 ms. The excitation wavelength and repetition rate were set at 500 nm and at 5 MHz, respectively. The PL lifetime of ON state was 23.4 ns, while that of INT state was 8.41 ns. (b) The averaged PL decays for the ON and INT states. The averaged lifetimes of the ON and INT states were 20.2 and 7.06 ns, respectively. The PL lifetime was calculated from a single exponential fitting. (c) PLID plot and (d) histogram of the PL intensity.

performing a single exponential fit for all the decay curves within a bin time of 100 ms, the PL lifetime could be determined as a function of bin time step. The PL lifetimes for the ON and INT states obtained from the single exponential fits are 23.4 and 8.41 ns, respectively. Averaged PL decay curves for the ON and INT states are shown in Figure 3b, and the lifetimes are 20.2 and 7.06 ns, respectively. Figure 3c shows the PL lifetime-intensity distribution (PLID) plot, which shows the correlation between the PL lifetime and intensity. The corresponding PL intensity histogram is shown in Figure 3d; distinct ON, INT, and OFF states can be seen. The ON state (exciton emissions) has a long PL lifetime and extends from 20 to 80 ns, while the INT state (trion emissions) has a short PL lifetime with approximately 7 ns. The low PL intensity and short PL lifetime of the trion emissions can be explained by the

Figure 2. (a) Time trace and (b) histogram of the PL intensity measured at 260 W/cm2. (c) Time trace and (d) histogram of the PL intensity measured at 150 W/cm2. The blue, red, and black regions correspond to the ON, INT, and OFF states, respectively. The signal in the green region is a mixture of PL signals of ON states and that of INT states in a single bin time.

is plotted in Figure 2b. From this plot, the data are separated into four regions. The first one is related to emissions in the ON state and is represented by the blue region, which corresponds to the highest PL intensity. The second is related to emissions in the INT state and is represented by the red region; the PL intensity corresponding to this region is moderately high, and a distinct peak can be seen. The third region is in black and is attributed to the OFF state. The fourth C

DOI: 10.1021/acs.jpcc.6b06220 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C increase in the nonradiative recombination rate due to the Auger process.19−24 From the results of PL spectra and lifetime, we could distinguish explicitly three contributions; the standard exciton emission, the QCSE-modified exciton emission (with red-shifted photon energy, broader line width, and longer PL lifetime), and the trion emission (with low PL intensity, shorter PL lifetime, and red-shifted photon energy). B. QCSE and Polarizabilities of Excitons and Trions. Next, we determined the relationship between the PL photon energy and the line width for both exciton and trion emissions. Figure 4a shows the correlation between the PL photon energy

Figure 5. PL peak energy histograms of the (a) exciton and (b) trion states. The solid lines are the fitted curves described by eq 5. The exciton and trion signals are distinguished by their PL intensities (see Figure 2a). For excitons, we show two results of calculation obtained with different parameters (μ = 200 kV/cm and σ = 80 kV/cm for dotted line, and μ = 150 kV/cm and σ = 60 kV/cm for dashed line).

that the binding energies of the trions can be estimated from the obtained data, resulting in 17 meV for the studied NCs. This value of trion binding energy is almost the same as the result reported by early works.22 Note that, in Figure 5b, an occurrence can be observed on the higher-energy side of the steep edge at 1.891 eV. We believe that this was not a trion emission but an emission with a different origin. Since it appeared in the INT state, its intensity was lower than that of the exciton emissions. It is likely that this signal resulted from a phenomenon such as charge trapping or charge migration.42−44 Since these emission processes are similar to those responsible for exciton emissions, the signal appeared in the energy region where exciton emissions were observed. Next, in order to evaluate quantitatively the fluctuations in the local electric field applied to the NC and the polarizability of trions, we developed a simple field fluctuation model and compared the theoretical results with those determined experimentally. Since this model allows for quantitative estimation of the electric-field fluctuations, the combination with the previously introduced single NC spectroscopy technique36 can lead to new results of SD. In this model, the electric field applied to the NC is the sum of the electric fields generated by the charges present around the NC. To establish a model, we simply assumed that the three-dimensional electric field (εx, εy, and εz) applied to the NC changes randomly according to a Gaussian distribution f i

Figure 4. Correlations between the PL peak energy and line width, as determined from the data shown in Figures 2a and c. The excitation powers were (a) 260 W/cm2 and (b) 150 W/cm2.

and the line width, which were obtained from the data measured at 260 W/cm2 and are shown in Figures 1g and h. The exciton and trion emissions are represented by the blue and red dots, respectively. For both the exciton and the trion emissions, an increase in the PL line width was observed clearly with a red shift in the PL photon energy. This correlation between the PL photon energy and the line width is a characteristic feature of SD caused by the QCSE.10,32−36,40,41 Interestingly, the blue and red dots appeared in different regions; that is, the trion signal appeared at a lower energy than that corresponding to the exciton signal. As can be seen from Figure 4b, similar results were obtained after analyzing the data obtained at a lower excitation power (150 W/cm2). The correlation in the case of the exciton emissions was almost the same; however, the number of red dots was significantly lower than that obtained at 260 W/cm2. Using the data shown in Figures 4a and b, histograms of the PL photon energies of the exciton and trion emissions were plotted; these are shown in Figures 5a and b, respectively. Interestingly, for both the exciton and the trion emissions, the histograms of the PL photon energies were asymmetrical; that is, a steep edge was observed on the higher-energy side, while a gradual decay was seen at the lower-energy side. This asymmetry can be explained by the fact that SD caused by the QCSE always appears as red shifts in the PL photon energy. The steep edge on the higher-energy side appears at 1.908 eV in the case of the exciton emissions, while it appears at 1.891 eV in the case of trion emissions. This difference in the photon energies of the steep edges on the higher-energy side can be explained by the positive binding energies of trions. This means

fi (εi) =

⎛ (ε − μ )2 ⎞ i i ⎟ exp⎜⎜ − ⎟, 2 2 2σi ⎝ ⎠ 2πσi 1

i = x, y, z (1)

where i is the axis number, μi is the mean value, and σi is the standard deviation. μi is determined by the average amount and positions of the charges around the NC, and σi is determined by the degree of hopping of the charges around the NCs. It was assumed that, at a certain time, the electric field applied to a NC deviates in a single direction. We considered this direction to be the z-axis and set the mean values corresponding to the xand y-axes to zero. μz = μ (2) On the other hand, it was assumed that the electric field fluctuates equally in the three directions. D

DOI: 10.1021/acs.jpcc.6b06220 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C σx = σy = σz = σ

the standard deviation σ determines the width of the distribution. This result was confirmed from several NCs. We also performed a similar fit for the case of the experimental data of the trion emissions shown in Figure 5b. For this analysis, we assume that the eqs 4 and 5 are valid for trions. The fitted curve agrees well with the experimental data. From the fit, we determined α and μ value for trions while assuming that the degree of hopping of the charges around the NCs (σ ≈ 80 kV/cm) does not change for both excitons and trions. The polarizability of trions was found to be ∼2 × 10−7 eV/(kV/cm)2, while the value of μ was ∼130 kV/cm. The polarizability of trions was thus smaller than that of excitons. When we performed the same experiments using several NCs, we again found that the polarizability of trions was smaller than that of excitons in all the NCs. Next, we discuss the mechanism responsible for the difference in the polarizabilities of excitons and trions. When an exciton in an NC is located in an external electric field, the electron and the hole move in different directions. This causes a large red shift in the PL photon energy, which depends on the size of the NC with a certain exciton polarizability. In the case of trions, however, the case is different. When trions with two electrons and a hole are formed in the NC, the separation between the electrons and the hole is smaller compared to that in the case of excitons. This is because of the Coulombic repulsion between the two electrons. Since the separation between the electrons and the hole is smaller, the PL energy of trions is affected to a lower degree by the electric field than that of excitons. As a result, the polarizability of trions should be smaller than that of excitons. In the following, we show the size dependence of the correlation between the photon energy and the line width of the PL spectra of excitons. The results obtained using three types of CdSe/ZnS NCs having different radii (Qdot655, Qdot605, and Qdot565) are shown in Figures 6a, b, and c. respectively. All plots are for the exciton emissions, as shown in the insets of Figure 6. The highest photon energies (E0) were 1.908, 2.070, and 2.235 eV, respectively. The effective core radii as calculated using E0 were 4.1, 3.0, and 2.5 nm, respectively.48 Moreover, the polarizabilities of excitons, α, calculated from the radii, were 3.3 × 10−7, 1.2 × 10−7, and 0.67 × 10−7 eV/(kV/ cm)2, respectively, according to ref 47. An almost linear correlation can be seen in all three plots. The fitting curves (y = Ax + B, where x is red shift, y is fwhm, and A and B are fitting parameters) are shown in Figures 6a−c. The slope of the correlation, A, decreases with a decrease in the NC size, since the polarizability of excitons decreases. The correlation between photon energy and line width has been discussed previously.10,32,35,41 Two models have been proposed to explain the fact that the fwhm increases in proportion to ΔE 10,32 or to ΔE5/4.35 The former model assumes that a fluctuation in the amount of charge around the NC causes SD.10,32,41 This model predicts that the fwhm exhibits the following relationship

(3)

The energy shift due to the QCSE is proportional to the square of the electric field10 ΔE = αε 2 = α(εx 2 + εy 2 + εz 2)

(4)

where α is the polarizability of the system and is strongly affected by the degree of separation of the electron and the hole. The value of ΔE is defined being positive for the red shift of PL energy. We assume that, even when the NC is not spherical, the value of α can be represented by an average value. The polarizability of excitons in CdSe NCs has been measured experimentally10,45,46 and can be calculated from the core radius of the NCs.47 On the basis of the highest PL photon energy (1.908 eV), we estimated the average radius of the core to be 4.1 nm.48 Subsequently, the polarizability of the excitons in the NC was determined to be 3.3 × 10−7 eV/(kV/cm)2.47 We derived the total probability density function, g(ΔE), which is a function of the distribution of the energy shift, ΔE, from eqs 1−4. By calculating the convolution integral of the distribution functions in the three dimensions, the following equation is obtained: g (ΔE) =

2 2 ⎛ ΔE ⎞ 2 ⎟ (ασμ)−1e−μ /2σ exp⎜ − ⎝ 2ασ 2 ⎠ π ⎛ μ ΔE ⎞ sinh⎜ 2 ⎟ α ⎠ ⎝σ

(5)

The obtained function is the product of an exponential function and a hyperbolic sine function. Using this function in conjunction with the value of the exciton polarizability, we fitted the experimental results shown in Figure 5a. The black solid line in Figure 5a is the result of the fitting and fits the experimental data surprisingly well. We note that the steep edge on the higher-energy side could be reproduced well by the use of eq 1. When a different form of fluctuation is considered, it seems that the probability density function becomes strongly different. For example, when we assume one-dimensional field fluctuation, the probability density function becomes g ′(ΔE) =

2 2 ⎛ ΔE ⎞ 2 ⎟ e−μ /2σ exp⎜ − 2 ⎝ 2ασ 2 ⎠ πασ ΔE ⎛ μ ΔE ⎞ cosh⎜ 2 ⎟ α ⎠ ⎝σ

(6)

This equation shows a divergence at ΔE = 0, which is not consistent with the experimental data. As long as we use eq 5, the data is reproduced well, which means that the assumption of independent three-dimensional fluctuations is plausible for this Qdot. From the fit, we could estimate the values of μ and σ, which were found to be ∼150 and ∼80 kV/cm, respectively. The value of μ is almost equivalent to the electric field generated by one elementary charge on the surface of the NCs.35 Even in the case of the other two smaller NCs (Qdot 605 and Qdot 565), the average distances between the elementary charge and the exciton were almost equal to the radii of the NCs. In Figure 5a, we also show the calculated curves obtained with different parameters (dotted line, μ = 200 kV/cm and σ = 80 kV/cm; dashed line, μ = 150 kV/cm and σ = 60 kV/cm). The mean value μ determines the peak position of the distribution, and

fwhm ∝

αΔE ·δq

(7)

where α is the polarizability of excitons and δq is the fluctuation in the amount of charge. The latter model assumes that fluctuations in the positions of the charges around the NC cause SD.35,41 Based on this model, the fwhm exhibits the following relationship fwhm ∝ α −1/4 ·ΔE5/4 ·δr E

(8) DOI: 10.1021/acs.jpcc.6b06220 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 6. Size dependence of the correlation between the PL peak energy and line width: (a) Qdot655 (average size ≈7 × 14 nm) excited at 540 nm, (b) Qdot605 (average diameter ≈8 nm) excited at 530 nm, and (c) Qdot565 (average diameter ≈5.6 nm) excited at 450 nm. The solid lines are linear fits. The values of A in the figures are the slopes of the linear fits.

where δr is the fluctuation in the distance between the charges and the NC. Since an almost linear correlation was observed in all three plots, fluctuations in both the number of charges and their positions around the NCs should be taken into account. However, eq 8 cannot explain the increase in the slope of the curve representing the correlation for large NCs, since it includes the term α−1/4, suggesting that the slope should decrease for large NCs. On the other hand, eq 7 can explain the experimental results, since it includes the term √α. These facts suggest that the fluctuation in the number of charges contributes more to the phenomenon of SD. We believe that, by conducting similar measurements on NCs with unique morphologies, the role of fluctuations of number and location of charges will be clarified in more detail. C. Change in Electric Field before and after Appearance of a Trion. Finally, we discuss the effect of the INT state (trion state) on SD using the results of an analysis based on a method reported in a previous study.11−32 Figure 7a shows the time dependence of the PL spectra as an image map. Based on the differences in the PL intensities, the data have been separated into three groups: the data for the period corresponding to the ON state, that corresponding to the INT state, and the remaining part. Figure 7b shows the distribution of the difference in the photon energy of the first spectrum (Eistart) and that of the last spectrum (Eiend) for the ith ON state period. Figure 7c shows the distribution of the difference between the PL photon energy of the last spectrum of the ith ON state period (Eiend) and the PL photon energy of the first spectrum of the i+1th ON state period after the INT state period (Ei+1start). The black curves in Figures 7b and c are the results of Gaussian fits. The fwhm of the distribution in Figure 7b is 11.3 meV, while that of the distribution in Figure 7c is 20.9 meV. This difference in the fwhm values means that large

Figure 7. (a) Color map of the time-dependent PL spectrum of a single CdSe/ZnS NC. (b) Distribution of the difference between the peak energy of the first spectrum (Eistart) and the peak energy of the last spectrum of the ith ON state period (Eiend). (c) Distribution of the difference between the peak energy of the last spectrum of the ith ON state period (Eiend) and the peak energy of the first spectrum of the i +1th ON state period after the INT state period (Ei+1start). The PL spectra of five CdSe/ZnS NCs were also recorded. The solids lines are the Gaussian fitting curves. Schematic diagrams showing charge redistribution: (d) exciton (ON state), (e) biexciton (ON state), (f) trion (INT state), and (g) exciton (ON state) after the change in electric field. The blue and red circles are electrons and holes, respectively.

energy shifts occur more frequently before and after the INT periods than during the ON period. This can be explained on the basis of charge redistribution, that is, on the basis of the changes in the distribution of the charges in the vicinity of the NCs before and after the trion state.11 Figures 7d−g show illustrations explaining the charge redistribution process. During the ON period, a single electron and a single hole (exciton) are present in a NC, while the other charges are distributed around the NC (Figure 7d). When two photons are absorbed and two excitons are excited, a biexciton is formed in the NC (Figure 7e). Then a certain charge exits the NC, the trion state appears, and the INT period begins (Figure 7f). Conversely when the extra charge enters the NC F

DOI: 10.1021/acs.jpcc.6b06220 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

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the INT period ends, and the ON period begins again (Figure 7g). These entering and exiting processes of charges result in changes in the local electric field around the NC before and after the INT period.

IV. CONCLUSION In summary, we studied the temporal fluctuations in the PL spectra of single CdSe/ZnS NCs. We observed clear correlations between the red shifts of the PL photon energy and the line width due to SD for both exciton and trion emissions. These spectral changes can be explained by the QCSE. We found that trion emissions exhibit unique SD characteristics, indicating that their binding energies are positive and their polarizabilities are smaller than those of exciton emissions. It was found that the trion emissions are less affected by the QCSE than are exciton emissions. If the Auger recombination of trions is suppressed, the trion emissions of single NCs have the potential to be used as light sources with stable photon energies. We also evaluated the mean value and standard deviation of the electric field around the NCs and found them to be ∼150 and ∼80 kV/cm, respectively. The mean value is almost equal to an electric field generated by one elementary charge at the surface of the NC. In addition, the correlation of the PL photon energy and the line width for different sizes indicates that the fluctuations in the electric field as well as the phenomenon of SD are caused mainly by changes in the number of charges rather than by changes in their positions. Moreover, exciton emissions often exhibit large spectral jumps before and after the appearance of trion emissions. This is indicative of charge redistribution, that is, changes in the distribution of the charges around NCs before and after the appearance of the trion emissions.

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AUTHOR INFORMATION

Corresponding Authors

*Phone: +81-774-38-4513. E-mail: [email protected]. *Phone: +81-774-38-4510. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Dr. Sato for his help with TEM observation of our samples. Part of this work was supported by JSPS KAKENHI (25247052 and 16K17483) and JST-CREST.

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REFERENCES

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Article

The Journal of Physical Chemistry C

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DOI: 10.1021/acs.jpcc.6b06220 J. Phys. Chem. C XXXX, XXX, XXX−XXX