Size-Dependent Biexciton Quantum Yields and Carrier Dynamics of

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Size-Dependent Biexciton Quantum Yields and Carrier Dynamics of Quasi-Two-Dimensional Core/Shell Nanoplatelets Xuedan Ma,*,† Benjamin T. Diroll,† Wooje Cho,§ Igor Fedin,§ Richard D. Schaller,†,‡ Dmitri V. Talapin,†,§ Stephen K. Gray,† Gary P. Wiederrecht,† and David J. Gosztola† †

Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States ‡ Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States §

S Supporting Information *

ABSTRACT: Quasi-two-dimensional nanoplatelets (NPLs) possess fundamentally different excitonic properties from zero-dimensional quantum dots. We study lateral size-dependent photon emission statistics and carrier dynamics of individual NPLs using second-order photon correlation (g(2)(τ)) spectroscopy and photoluminescence (PL) intensity-dependent lifetime analysis. Room-temperature radiative lifetimes of NPLs can be derived from maximum PL intensity periods in PL time traces. It first decreases with NPL lateral size and then stays constant, deviating from the electric dipole approximation. Analysis of the PL time traces further reveals that the single exciton quantum yield in NPLs decreases with NPL lateral size and increases with protecting shell thickness, indicating the importance of surface passivation on NPL emission quality. Secondorder photon correlation (g(2)(τ)) studies of single NPLs show that the biexciton quantum yield is strongly dependent on the lateral size and single exciton quantum yield of the NPLs. In large NPLs with unity single exciton quantum yield, the corresponding biexciton quantum yield can reach unity. These findings reveal that by careful growth control and core− shell material engineering, NPLs can be of great potential for light amplification and integrated quantum photonic applications. KEYWORDS: CdSe/CdS nanoplatelets, biexciton, radiative lifetime, second-order photon correlation function, exciton coherent motion area, quasi-2D exciton

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interaction compared to kinetic energy leads to uncorrelated electrons and holes as well as an exciton oscillator strength that is proportional to the square of the electron−hole wave function overlap.14,15 In NPLs, electrons and holes are bound in the form of excitons by Coulomb interaction with exciton binding energies of up to a few hundreds of meV,16 and the exciton oscillator strength increases with the area of the exciton coherent motion, leading to the so-called giant oscillator effect.17 Therefore, a monotonic increase in the radiative decay rate with the NPL lateral size should be expected for certain size ranges where the exciton coherent motion area is equivalent to the NPL lateral size. However, it remains unknown to what extent the lateral size would affect the oscillator strength because for large NPLs, the exciton emission

uasi-two-dimensional (2D) II−VI semiconductor nanoplatelets (NPLs) with atomically controlled thickness are promising candidates for potential applications in areas such as lasing,1−4 light-emitting diodes,5,6 and photovoltaics7−9 due to their giant oscillator strength,10,11 exceptionally narrow spectral features, and large lateral carrier mobility.12 Their electric-field tunable photoluminescence (PL)13 and lifetime-limited line width11 make them appealing for integrated photonic applications in quantum information processing. The thickness of NPLs can be controlled with atomic-layer precision to be a few monolayers (MLs), while their lateral size can be extended to a few tens of nanometers by tuning the reaction time. Therefore, compared to 0D quantum dots (QDs), excitons in NPLs are strongly confined only in the thickness direction due to their much larger lateral dimensions than the exciton Bohr radius. Such an increase in the lateral size and a weakening in the in-plane confinement has significant effects on the excitonic properties. First, in QDs, where the strong confinement approximation applies, the small Coulomb © 2017 American Chemical Society

Received: June 5, 2017 Accepted: August 8, 2017 Published: August 8, 2017 9119

DOI: 10.1021/acsnano.7b03943 ACS Nano 2017, 11, 9119−9127

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ACS Nano wavelength in the NPLs becomes comparable to the lateral size, and the electric dipole approximation may break down due to the so-called retardation effect, as was previously observed in large QDs.15,18 Additionally, the exciton coherent motion area may also be dependent on temperature due to exciton−phonon scatterings.19 Other factors such as local potential minimainduced exciton localization may also reduce the exciton coherent motion area and consequently the radiative decay rate20 in large NPLs, considering the fact that the probability of creating such local potential traps increases with the lateral size. Homogeneous broadening effects, in which several excited excitonic states are overlapped within the homogeneous line width of the lowest exciton state due to the small energy spacing of the excitonic levels in large nanocrystals,21,22 may also play a role in the size-dependent radiative decay rates. Second, the weak in-plane confinement facilitates spatial spreading of excitons in the NPL lateral plane, which can potentially reduce the Auger recombination effects3,8,9 and lead to the emission of multiple photons. This effect, however, may be compensated by the increased concentration of spatially confined trapping states in large NPLs23,24 in which the rapid Auger recombination can lead to significant exciton−exciton annihilation.25,26 Overall, the lateral size of NPLs has complex effects on the carrier dynamics and photon emission statistics of NPLs, two of the most important properties of excitons in NPLs for their applications in optoelectronic devices and entangled photon-pair generation. To address these open issues, we systematically study carrier dynamics and photon emission statistics of individual NPLs with different lateral sizes at room temperature. Second-order photon correlation (g(2)(τ)) studies and PL intensity-dependent lifetime analysis of individual NPLs show an increase in biexciton quantum yield and a decrease in single exciton quantum yield with the increase of NPL lateral size. This suggests that reduction in Auger recombination due to spatial spreading of excitons in large NPLs outpaces trapping state induced exciton−exciton annihilation. Additionally, instead of a monotonic decrease, we observe that the radiative decay lifetime first decreases and then flattens out with the increase of NPL lateral size, which deviates from the electric dipole approximation. Our results directly reveal changes in the excitonic properties of semiconductor nanomaterials in the transition from 0D to 2D systems and indicate the promising applications of NPLs in entangled photon-pair generation and light amplification by careful control of size and surface trapping states.

Figure 1. (a, b) Absorption (a) and PL spectra (b) of NPLs with different lateral sizes. (c−g) TEM images of NPLs with different lateral sizes. NPLs in samples NPL1 (c), NPL2 (d), NPL3 (e), and NPL4 (f) have 2 ML CdS shells, and those in sample NPL5 (g) have 4 ML CdS shells.

Compared to these of the core NPLs, PL spectra of the NPLs with 2 ML thick shells are red-shifted with emission peaks at ∼620 nm (Figure 1b, black, red, green, and blue). Similar to previous studies,24,29 no drastic spectral shift was observed with the increase of the NPL lateral size, mainly due to the weak quantum confinement in the lateral dimensions. The largest NPLs with 4 ML CdS shells (Figure 1b, orange) have a red-shifted emission peak at ∼656 nm compared to the 2 ML CdS shell counterparts, likely caused by the extension of the carrier wave functions into the two additional CdS shells. However, our carrier wave function calculations in the strongly confined thickness direction indicate that these additional 2 ML CdS shells have negligible influence on the radiative lifetimes of the NPLs (Supporting Information S2). The average lateral sizes of the NPLs estimated from TEM images are 15.9 ± 2.8 nm by 4.4 ± 0.6 nm (Figure 1c, denoted as NPL1), 19.9 ± 3.1 nm by 7.8 ± 1.6 nm (Figure 1d, NPL2), 16.2 ± 2.0 nm by 11.1 ± 1.3 nm (Figure 1e, NPL3), 30.3 ± 3.6 nm by 8.8 ± 1.1 nm (Figure 1f, NPL4), and 33.4 ± 3.8 nm by 13.0 ± 2.8 nm (Figure 1g, NPL5), respectively. Detailed dimensions and shell thicknesses of the five different samples are listed in Table 1. Table 1. Lateral Sizes, Shell Thicknesses, Average Single Exciton Quantum Yields Q1X, Average Biexciton Quantum Yields Q2X, and Average Radiative Lifetimes τrad of the Five NPL Samples

RESULTS/DISCUSSION CdSe/CdS core/shell NPLs of the same thickness but various lateral sizes were synthesized following a previously published method with slight modifications (see the Methods section).27,28 Briefly, 4 ML thick (∼1.2 nm) CdSe NPLs with different lateral sizes were synthesized, followed by the growth of 2 ML CdS conformal shells on the core NPLs using a colloidal atomic layer deposition technique. To investigate the influence of shell thickness, CdSe core NPLs with the largest lateral size were coated with a 4 ML CdS shell. CdSe core NPLs with different lateral sizes have similar absorption and PL spectra, with the former exhibiting two distinct peaks at 511 and 480 nm and the latter a single narrow peak at 515 nm (Supporting Information S1). Figure 1 shows absorption and PL spectra and transmission electron microscope (TEM) images of the synthesized CdSe/CdS core/shell NPLs.

sample name

lateral size (nm2)

shell thickness (ML)

Q1X (%)

Q2X (%)

τrad (ns)

NPL1 NPL2 NPL3 NPL4 NPL5

69.1 155.5 180.3 266.3 434.9

2 2 2 2 4

48.3 27.3 26.2 26.7 36.2

9.9 19.6 18.7 20.5 32.6

20.1 8.8 8.8 8.6 9.1

Size-Dependent Q2X/Q1X Values. We perform secondorder photon correlation (g(2)(τ)) studies using the time-tagged time-resolved mode on individual NPLs of different lateral sizes and shell thicknesses. In this mode, each single photon count event is time tagged with respect to the beginning of the experiment and the synchronization pulses. This allows us to perform PL intensity-dependent lifetime analysis, as we will discuss in the next section. In this study, the laser excitation power was kept sufficiently low so that the average absorbed 9120

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stacking, we apply a time gating technique38 to the g(2)(τ) measurements to separate these two factors. Because biexcitons decay much faster than single excitons,31 by setting the beginning of the time gate to be much longer than the biexciton lifetime, contributions from biexciton emission can be excluded, and only photon emission of the single excitons will be used to construct the g(2)(τ) traces. In this work, only those NPLs that show gated R values of zero are considered as single NPLs and are further investigated. The second and third curves in Figure 2a show g(2)(τ) traces of the NPL by rejecting photons in the first 17 and 25 ns of time delay. The corresponding R values decrease from the initial 0.09 to 0.03 and 0, respectively. The detailed dependence of R values on the applied gate delay time is further illustrated in Figure 2c. The fact that R approaches zero after certain gate delay time clearly indicates that the photon emission is indeed from a single NPL, and biexciton emission was the sole contribution to the nonzero center peak. For a Poissonian absorption process, in which the probability of absorbing n photons with an average absorbed photons per Nn pulse of N is Pn = n ! e−N , the amplitude of the coincidence feature in the g(2)(τ) trace in the limit of N → 0 is related to the biexciton (Q2X) and single exciton quantum yield (Q1X) by RN→0 = Q2X/Q1X.39 Since N values in this study are kept below 0.14, Q2X/Q1X values can be directly extracted from the g(2)(τ) traces. This is further verified by performing pump-dependent g(2)(τ) measurements of single NPLs at an excitation power of only 10% of that corresponding to N = 0.14 (Supporting Information S5). No reduction in the R value is observed with the decrease of excitation power, indicating that the assumption of RN→0 = Q2X/Q1X is valid in our study. Our analysis of 47 individual NPLs in sample NPL1 results in an average Q2X/Q1X value of 0.24. In stark contrast, g(2)(τ) measurements of the individual NPL from sample NPL4 give a much higher R value of 0.94 (Figure 2b, top curve). Time gating of the NPL photon emission also leads to the vanishing of the center peak in the g(2)(τ) trace (Figure 2b,d), indicating that the emission indeed originates from a single NPL. We determine an average Q2X/Q1X value of 0.75 from analysis of 49 individual NPLs in sample NPL4. The lateral size-dependent average Q2X/Q1X values are plotted in Figure 5a, and in general an increase is observed with the size, although the changes for samples from NPL2 to NPL4 are less significant (Supporting Information S6). A similar sizedependent trend of the R value has been observed by Tessier et al. in core/crown NPLs.40 For sample NPL5, an average Q2X/Q1X value as large as 0.93 is observed, indicating that quantum yields of biexcitons in these large NPLs are almost comparable to those of single excitons. Another interesting effect of the NPL lateral size is that, in contrast to the case of small NPLs, typically a much longer gate delay time is required for the large NPLs in order to have the R value reach zero (Figure 2c,d). This behavior is likely related to a slower biexciton decay process in large NPLs, which has been observed by Li et al. using pump-dependent transient absorption spectroscopy.41 Our pump-power-dependent PL measurements of NPL thin films further confirms that the Auger process in NPLs is suppressed because no apparent PL intensity saturation is observed even when N is great than 1 (Supporting Information S7). Size-Dependent Carrier Dynamics. To determine the values of Q2X, Q1X values of the NPLs are required. The inherent heterogeneity of the NPLs42 or their environment

photons per pulse determined from the NPL absorption cross sections30−32 (Supporting Information S3) was below ∼0.14. The top curves in Figure 2a,b show representative g(2)(τ) traces of two individual NPLs from samples NPL1 and NPL4,

Figure 2. (a, b) Gate delay time (tTG)-dependent g(2)(τ) traces of small (a) and large (b) NPLs from samples NPL1 and NPL4, respectively. The applied gate delay time is indicated in the center of the traces. (c, d) Gate delay time (tTG)-dependent R values (RTG) of the small (c) and large (d) NPLs. The flat RTG values in the first 15 ns correspond to the time before the sync pulse. The red curves are exponential fittings to the data. The circles highlight data points that correspond to the time-gated g(2)(τ) traces in (a) and (b).

respectively. We define the area ratio between the center peak (τ = 0) and that of the side peaks of the g(2)(τ) trace as R. The disappearance of the center peak (R → 0) corresponds to the so-called photon antibunching, indicating that the probability of the detection of two or more photons per excitation pulse is low. For the g(2)(τ) trace of the small NPL in Figure 2a (top curve), a R value of 0.09 is obtained. Aside from influences from background and crosstalk between two single photon avalanche diodes, which are negligible in this study, this nonzero R value could have two contributions: (1) excitation of multiple NPLs in the excitation laser beam due to effects such as NPL stacking, which is commonly observed both in solutions and solid films;33,34 and (2) quantum cascade emission of multiple photons from single NPLs due to the generation of multiexciton states.35−37 To study the biexciton emission efficiency in single NPLs and exclude the effect of NPL 9121

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Figure 3. (a, e) PL time traces of a small NPL from sample NPL1 (a) and a large NPL from sample NPL4 (e) with the background subtracted. The time bin is set to 100 ms. (b, f) PL intensity distributions extracted from (a) and (e). (c, g) PL intensity-dependent decay lifetimes τs determined by fitting the corresponding PL decay curves with stretched exponential functions. Here the y-axis is the corresponding bin center. Uncertainties in the fitted lifetime values are plotted in orange. Insets: Schemes of a three-level model with the nonradiative recombination of the trapped charge (c, dashed red arrow) or trapped charge recovery (g, solid blue arrow) being the dominating process, respectively. |G⟩: ground state; |E⟩: excited state; |T⟩: charge trapping state. Thicknesses of the curves represent the probability of the optical transitions. (d, h) Decay rate distributions of the small (d) and large (h) NPLs constructed from the stretched exponential fitting results in (c) and (g). The color coding of the rate distribution curves is consistent with the colored circles in (c) and (g).

exponential fitting functions. A smaller PL intensity is correlated to a shorter decay lifetime, as was previously observed in CdSe NPLs at 20 K42 and CdSe/ZnS core/shell QDs.50,51 We thus attribute the continuous PL intensity distribution and intensity-dependent decay lifetimes to a similar mechanism: a distribution of trapping states in the NPLs. The broadening of the decay rate distributions at low PL intensities (Figure 3d, red and blue) further confirms this speculation. Most importantly, we obtain that at the highest PL intensities (above 90% of the maximum PL intensity Imax), the PL decay curve of the NPL is almost single exponential (Supporting Information S8) with a β value of 0.89 (Figure 3d, gray). A similar phenomena is observed in over 91% of the 47 studied NPLs from sample NPL1, with the photons emitted during the maximum PL intensity periods giving β values larger than 0.80. This single exponential decay behavior at the highest PL intensity is consistent with previous studies of single QDs showing unity quantum yields during the “on” periods.51,52 This effect and the above-mentioned reduction in lifetime with PL intensity lead us to the conclusion that the highest PL intensity lifetimes correspond to the radiative lifetimes of the NPLs. This conclusion is further verified by comparing the excitation and emission rates of the NPLs. Excitation rates of the NPLs are estimated by γexc = ρ × Cabs, where ρ is the pump fluence and Cabs is the absorption cross section. By taking the detection efficiency of the microscope into consideration, the estimated detected PL intensities of NPLs with unity singleexciton quantum yield are compared to the experimentally determined average maximum PL intensity values of the five NPL samples (Figure 4a), and a good agreement between the two data sets can be observed. This confirms that the maximum PL intensity periods have unity single exciton quantum yields and the corresponding lifetimes are solely contributed by the radiative recombination process. For the specific NPL in Figure 3a−d, a radiative lifetime of 16.7 ns is obtained. An average radiative lifetime of 20.1 ns is determined for sample NPL1, as is shown in Figure 5b and Table 1. We perform similar carrier dynamic studies on the other NPL samples. Figure 3e presents a PL intensity time trace of the same large NPL from sample NPL4 shown in Figure 2b. Drastic PL fluctuations can be observed, which leads to a broad, continuous PL intensity distribution with no clear on state

means that the Q1X values of each individual NPLs are different. The potential existence of dark NPLs, as was previously observed in colloidal QDs43 and semiconductor carbon nanotubes,44 further implies that single NPL quantum yields are most likely different from those of the ensemble solutions. In this context, we determine Q1X values of each single NPL by studying their PL intensity-dependent carrier dynamics using the time-tagged time-resolved method, as was described above. PL time traces of single NPLs are recorded. For the same small NPL from sample NPL1, shown in Figure 2a,c, PL blinking can be observed in the time trace (Figure 3a), and despite the broad, continuous intensity distribution (Figure 3b), two distinct peaks can be clearly observed, commonly referred to as the “on” and “off” states. Such on−off blinking behavior has been observed in other quantum emitters and is commonly attributed to charge carrier trapping at surface and/or core/ shell interface states.42,45−47 Li et al. using transient absorption spectroscopy have confirmed the existence of hole trapping at the core/crown interfaces of NPLs.48 The excess charge carriers in the NPLs could result in a nonradiative Auger recombination process, by which the subsequent absorbed exciton energy is transferred to the extra charge carrier without emitting photons. Since the Auger recombination process is typically much faster than the radiative recombination process, the PL could be strongly suppressed in a charged NPL until this excess charge carrier is neutralized. We then extract PL decay curves at different PL intensities, and each decay curve is fit with a stretched exponential function: I(t) = I0 exp(−t/τs)β, with β (0 < β ≤ 1) being a constant that determines the rate distribution. A small β indicates a broad decay rate distribution, while β = 1 corresponds to a single exponential decay. From the β and τsvalues, an average lifetime of τs can be determined from the fitting. The reason that stretched exponential functions are chosen to fit the decay curves is that the complex multiexponential behavior of the decay curves makes it challenging to assign each exponential component to a certain physical meaning, while stretched exponential functions can be considered as a superposition of simple exponentials,45,49 from which the decay rate distribution can be extracted by a direct inverse Laplace transformation of the fitting function: I0 exp(−t/τs)β = ∫ ∞ 0 exp(−t/τ)ρ(τ)dτ. Figure 3c presents the PL intensity-dependent lifetimes τs calculated from the stretched 9122

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potentially undergo one of two possible processes: (1) being released by the trapping state back to the bright state and recombine with the hole,23 and (2) remaining trapped until it recombines nonradiatively.55 In both cases, as long as the electron is trapped, the NPL will remain dark because subsequent absorption of photons will lead to an Auger effect. However, in the first scenario, once the electron is released, the exciton can resume the original cycle and decay to the ground state. In this case, in a certain observation time (e.g., a time bin of 100 ms), an increase in the observed lifetime should be expected due to the extra time the electron stays in the trapping state, which would lead to a reduction in the emission quantum yield and consequently the PL intensity. In contrast, in the second scenario, both a reduction in lifetime and PL intensity should be expected because charge trapping simply leads to an additional nonradiative recombination channel to the overall exciton decay process. While it is difficult to determine if one or both effects exist in the NPLs from our data, we can conclude from the different PL intensity-dependent lifetime behavior of the NPLs shown in Figure 3c,g that the nonradiative recombination process weighs more in the small NPLs (Figure 3c, inset), and recovering of the trapped charges happens more often in the large ones (Figure 3g, inset). This size dependence may be attributed to the Coulomb attraction induced electron localization in the vicinity of the hole in large NPLs.55 The decay rate distributions of the large NPL show a similar trend as that of the small one. The PL decay curve of the NPL constructed from photons emitted during the highest PL intensity periods (above 90% of the maximum PL intensity Imax) is single exponential (Supporting Information S8) with a β value of 0.81 and τs value of 11.2 ns (Figure 3h, gray). The rate distribution broadens at low PL intensities (Figure 3h, red and blue), revealing the contributions from many trapping states. We assign the highest PL intensity lifetime of the NPL to its radiative lifetime. Applying the same method, radiative lifetimes of NPLs with different lateral sizes are determined from their corresponding maximum PL intensity decay curves, and the average values determined from more than 45 single NPLs from each sample are plotted in Figure 5b and listed in Table 1. When the NPL lateral size is increased from ∼70 nm2 to 156 nm2, the average radiative lifetime τrad decreases from ∼20 to 8.8 ns. Further increase in the lateral size does not cause significant changes in the radiative lifetime, which remains constant at ∼8.8 ns. This radiative lifetime value of the large NPLs is in agreement with that estimated by Rabouw et al.23 In the electric dipole approximation, for a weakly confined system such as large QDs and NPLs, the optical transition oscillator strength increases with QD or NPL volume V. Therefore, the radiative decay rate, which is proportional to the oscillator strength, is γred ∝ V (Figure 5b, red curve).14 However, our data point to the possibility that after a certain lateral size, the area of the exciton coherent motion becomes independent of the NPL size, indicating that in large NPLs, exciton wave function is spatially confined to a scale much smaller than the NPL lateral size. From the radiative lifetime and lateral size of NPL1, we can derive this spatially confined area to be ∼160 nm2. This kind of excitonic behavior has been observed in several other material systems such as large GaN/ AlN QDs,56 InGaAs QDs,20 and GaAs QDs,57 and it has been attributed to two possible causes: (1) local potential minima caused by material inhomogeneities induced during growth which strongly confine excitons;20,57 (2) breakdown of the electric dipole approximation in such large semiconductor

Figure 4. (a) Estimated PL intensities of NPLs with unity singleexciton quantum yield calculated from the excitation rate (gray squares) together with the experimentally determined average maximum PL intensity values (red spheres). Uncertainties in the theoretically estimated PL intensity values are determined by assuming a 20% uncertainty in the collection efficiency of the microscope. (b−e) Probability densities of “on” (left) and “off” (right) time intervals of the time traces shown in Figure 3a,e plotted on a log−log scale. The red lines are linear fits to the data.

(Figure 3f). Different from the small NPL shown in Figure 3a,b, the large NPL stays mostly in a “gray” state with a low emission intensity. A typical NPL could have a distribution of trapping states, and the properties of each trapping state may fluctuate over time. The continuous distribution of PL intensities observed in Figure 3f could be attributed to the migrations of charge carriers among the different trapping states50 or fluctuations of the trapping state properties.47 Depending on the exact trapping states that the charge carriers are in, and the ratio between the Auger and radiative recombination rates,46 different PL intensities could be obtained in a certain time bin. Probability densities of on- and off-/gray-state duration times P(t) = t−m are calculated from the corresponding time traces, and a power-law distribution that is commonly observed in QDs46,53,54 is obtained for the different NPL samples (Figure 4b−e) and Supporting Information S10), with the m value varying between 1.0 and 2.2. Analysis of the PL intensitydependent lifetimes of the large NPL by fitting the decay curves with stretched exponential functions shows that instead of a monotonic decrease in the lifetime with PL intensity, a small increase in the lifetime is observed following an initial decrease (Figure 3g). This phenomena is observed more often in the large NPLs (NPL4:68%) than in the small ones (NPL1:35%, see Supporting Information S9 for more examples) and can be explained based on a three-level reversible charge trapping model (Figure 3c,g, insets). When one of the charge carriers of an exciton, say the electron, is trapped at a trapping state, it can 9123

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excitons in quantum disks into consideration, Stobbe et al.18 predicted a similar radiative decay lifetime saturation for large disk radii, consistent with our finding. Takagahara, instead, considered the influence of temperature on radiative lifetimes.22,60 He predicted that as the size of a QD increased, energy spacing between excitonic levels decreased. Eventually when the energy spacing became so small, the thermal excitation from the lowest to higher excitonic states became possible. In this situation, redistribution of excitons among these excitonic states happened and the higher excitonic states also contributed to the radiative decay process, which could lead to a radiative lifetime saturation. We evaluate the influence of temperature on radiative lifetimes by taking exciton−phonon scattering into consideration. In general, the coherent motion area of quasi-2D excitons is limited by exciton−phonon scattering rates. With the increase of temperature, a reduction in exciton coherent motion area is expected due to the increasing effect from exciton−phonon scatterings. To verify the influence of phonon scattering at room temperature on the exciton coherent motion areas, we adapt a method developed by Feldmann et al. within the effective-mass approximation,19 in which the transition oscillator strength of a 1s quasi-2D exciton is calculated by summarizing the oscillator strengths of all the unit cells that contribute to the optical transition. Therefore, the transition oscillator strength and radiative decay rate are proportional to the exciton coherent motion area. The exciton coherent motion area Ac at a specific temperature T is then calculated by Ac = 4h2/Δ(T)M, where Δ(T) is the spectral line width at temperature T, and M = me + mh. From our experimentally determined room-temperature spectral line width of ∼70 meV and me = 0.13 m0 and mhh = 0.9 m0,10 we get Ac = 167 nm2. However, due to exciton−phonon scattering, only the fraction of excitons r(T) within the spectral width can contribute to the recombination. We thus define the “effective” exciton coherent motion area as Ac,eff = Acr(T), with r(T) = 1 − exp(−Δ(T)/ kT).19 At room temperature, the effective exciton coherent motion area of our samples is estimated to be Ac,eff = 156 nm2, which is in excellent agreement with our experimental result shown in Figure 5b, where saturation of the radiative decay lifetime is observed at a lateral size of ∼160 nm2. We further estimate the value of Ac,eff at 5 K. The spectral line width at this temperature is ∼0.7 meV,11 from which we estimate the effective exciton coherent motion area to be ∼12700 nm2. This significant reduction in the exciton coherent motion area with temperature is a direct result of exciton−phonon scattering, and our observed radiative lifetime saturation in the large NPLs is likely due to a reduced exciton coherent motion area at room temperature. Determination of Single Exciton (Q1X) and Biexciton (Q2X) Quantum Yields. From the PL intensity-dependent lifetime analysis, we determine that photons emitted during the maximum PL intensity periods have negligible influence from nonradiative recombination and a unity single exciton quantum yield. Therefore, we approximate the single exciton quantum yield of a NPL (Q1X) during the measurement time by Q1X = Iavg/Imax, with Iavg being the time-averaged PL intensity determined from the PL time trace, and Imax the average PL intensity of photons emitted during the above 90% of the maximum PL intensity Imax periods. For the small NPL from NPL1 shown in Figures 2a and 3a−d, and the large NPL from NPL4 in Figures 2b and 3e−h, Q1X values of 55% and 25% are determined, respectively. From the Q1X and the Q2X/Q1X values

Figure 5. (a) NPL lateral size-dependent Q 2X/Q1X values determined from the second-order photon correlation (g(2)(τ)) traces. (b) Lateral size-dependent average radiative decay lifetimes τ⟨rad⟩ determined from more than 45 individual NPLs in each sample. The red curve is derived from the electric dipole approximation by assuming τrad ∝ V−1 and the smallest NPLs still follow the electric dipole approximation. (c) Size-dependent single exciton (Q1X, black) and biexciton (Q2X, red) quantum yields. The apparent increase in the Q1X and Q2X values of the largest NPLs is likely due to the extra two MLs of CdS shells. (d) Q2X plotted as a function of the corresponding Q1X values of single NPLs from sample NPL1 (black) and NPL5 (red). The blue line indicates equal Q1X and Q2X values.

systems due to the retardation effect.15,18,58 Although the distribution of excitons in the bright and dark states, which have recombination lifetimes differing by 2 orders of magnitude, may be affected by a lateral size induced change in the splitting energy of the two states, at room temperature such effect on the radiative lifetime can be negligible due to the small dark-bright splitting energy (typically a few meV) compared to the thermal energy and rapid exciton spin relaxation dynamics resulting from thermodynamic equilibrium between the two states.59 Additionally, due to the controlled separate growth of the CdS shell materials at relatively low temperature in our study, formation of alloys at the core−shell interface is quite unlikely, although the influence of larger amounts of defect states in large NPLs cannot be ruled out. However, if defect state induced reduction in exciton coherent motion area is the sole reason for the deviation of the radiative lifetime from the electric dipole approximation, a similar trend in the sizedependent Q1X values should be observed (see Supporting Information S11 for a detailed explanation). As shown in Figure 5b,c, this is not the case. The electric dipole approximation is valid only if variation of the electromagnetic field is negligible over the span of the emitter. For a CdSe/CdS core/shell NPL with a length L of 20 nm and emission wavelength of 620 nm, the value of |k|L = 0.29, with k being the optical wave vector of the emission and by assuming the dielectric constant of the surrounding medium (mainly ligands and residual solvents) to be 2.0.16,31 This in principle justifies the fulfillment of the basic criterion of |k|L ≪ 1 for the electric dipole approximation even in such large NPLs. However, the growth of the CdS shells may further complicate the optical field in the NPLs. By taking nonlocal interaction between light and spatially extended 9124

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ACS Nano determined from the g(2)(τ) traces in the first section, we derive Q2X values of 4.7% and 23% for the small and large NPLs, respectively. Size-dependent Q1X and Q2X values averaged over more than 45 individual NPLs from each sample are plotted in Figure 5c and listed in Table 1. The Q1X value decreases with the increase of lateral size from NPL1 to NPL2 due to the increasing probability of finding trapping states in large NPLs,24 but remains mostly constant from NPL2 to NPL4. The slight increase of Q1X value for NPL5 is most likely due to the thicker 4 ML CdS shell, which reduces the amount of trapping states at the NPL surface. As mentioned above, two factors can have opposite effects on the biexciton quantum yields of NPLs with the increase of the lateral size. The weak in-plane confinement can lead to spatial spreading of exciton wave function, as inferred by the decreased radiative lifetimes in the large NPLs shown in Figure 5b. It can thus reduce exciton−exciton annihilation effects and lead to coexistence of multiple excitons in a single NPL. However, increase in NPL lateral size also introduces more trapping states, which can induce exciton−exciton annihilations in these states and prevent the emission of multiple photons. The overall biexciton quantum yield is determined by the interplay of these two factors. In Figure 5c, an apparent increase in the biexciton quantum yield is observed from sample NPL1 to NPL2, revealing that spatial spreading of excitons outpaces the introduction of trapping states and dominates in determining the biexciton quantum yield. However, a further increase in the lateral size from NPL2 to NPL4 causes no apparent change in the Q2X value. This trend is the same as is observed for the Q1X value, and we attribute it to the limited effective exciton coherent motion area at room temperature (Ac,eff = 156 nm2). Specifically, when the NPL size is already larger than Ac,eff, a further increase in the NPL lateral size (provided that other parameters remain the same) will lead to no change in the emission properties because the excitons are effectively confined to lateral areas as large as Ac,eff. Determination and rational control of Q2X values are critical for light amplification applications and entangled photon pair generation. Figure 5d displays influences of NPL size and quality on the Q2X values. For NPLs from sample NPL1 (Figure 5d, black), the Q2X value is below 25% regardless of the NPL quality (Q1X value). However, the Q2X value can reach unity in some NPLs from sample NPL5 (Figure 5d, red), although it is limited by the Q1X values of the NPLs. Overall, to achieve unity Q2X values, NPLs with large lateral size and high emission quality are required. Additionally, we observe that for samples NPL2 and NPL3, which have similar lateral areas but different lateral dimensions, identical carrier dynamics and exciton quantum yields are obtained, indicating that for the quasi-2D NPLs with weak lateral confinements, morphology does not seem to play a significant role in determining these optical properties.

decreases with NPL lateral size, indicating the significant contribution of trapping states in large NPLs. Coating the CdSe NPLs with thick CdS shells can reduce influence from these trapping states. Moreover, with the increase of the NPL lateral size, the biexciton quantum yield also increases, reaching an average value of 33% in the largest NPLs. This value is affected by both the quality of the NPLs (Q1X) and NPL lateral size. With careful growth control and core/shell heterostructure design, biexciton quantum yields in NPLs can reach unity. This finding has significant implication toward applications of NPLs in light amplification and quantum information processing. Specifically, due to the surrounding low dielectric medium, the estimated large biexciton binding energy in NPLs3 compared to those in epitaxially grown quantum wells makes it, in principle, possible to energetically resolve single photon and biexciton emission, rendering NPLs potentially interesting materials for single photon-pair generation. Additionally, high biexciton quantum yield can dramatically reduce the amplified spontaneous emission threshold.2,4 By coupling to proper photonic microcavities, it may even enable ultracompact nanolasers capable of thresholdless lasing at room temperature.61

METHODS Nanoplatelet Synthesis. Materials. Selenium powder (99.99%), cadmium nitrate tetrahydrate (>99.0%), sodium myristate (>99%), octadecene (90%), oleylamine (70%), oleic acid (90%), Nmethylformamide (99%), methylcyclohexane (99%), ammonium sulfide solution (40−48 wt % in water), and cadmium acetate dihydrate (98%) were purchased from Sigma-Aldrich. Cadmium propionate (anhydrous) was purchased from MP Biomedicals. All solvents used were ACS grade or higher. Synthesis Methods. The synthesis of 4 ML thick CdSe NPLs followed literature procedures.3 Briefly, 12 mg of selenium powder, 170 mg of cadmium myristate, made by precipitation from methanolic solutions of sodium myristate and cadmium nitrate,62 and 15 mL of octadecene were combined into a 50 mL three-neck flask and evacuated at room temperature for 1 h. Under nitrogen, the reaction contents were heated to 240 °C. At 195 °C, 40 mg of finely ground cadmium acetate was added to the flask by counterflow addition. Once reaching 240 °C, the reaction temperature was maintained for 30 min to synthesize the largest NPLs used in this study. To obtain intermediate sizes of NPL, the temperature was maintained for 2 or 5 min. To make the smallest NPLs in this study, the reaction was stopped at 225 °C after cadmium acetate addition. The narrowest NPLs (TEM in Figure 1c) were made by adding the equivalent amount (48 mg) of cadmium propionate instead of acetate at 195 °C and running the reaction for 5 min at 240 °C. Purification of all samples involved injection of 2 mL of oleic acid and 15 mL of hexanes as the samples cooled, followed by centrifugation to isolate NPLs in a solid pellet. The pellet was dispersed and stored in methylcyclohexane. Synthesis of core/shell NPLs followed the colloidal atomic layer deposition method developed in earlier work with minor modifications.3,28 1 mL core NPL stock (1/8 of the reaction product) was precipitated with ethanol and redispersed in hexanes as a biphasic system with 0.5 mL N-methylformamide (NMF) subphase. Ten μL ammonium sulfide solution was added to the subphase, and the mixture was shaken to induce phase transfer. The hexanes phase was extracted, and the NMF phase was washed two more times with clean hexanes. The NPLs in NMF were then precipitated with toluene (1 mL), redispersed NMF, and precipitated again with toluene. Then, the NPLs were redispersed in a solution of 0.15 M cadmium acetate in NMF and precipitated with toluene. NPLs were dissolved in NMF and then transferred back into hexanes using a biphasic mixture with 20 μL of oleylamine and 20 μL of oleic acid. Finally, NPLs in hexanes were precipitated with ethanol and redispersed in hexanes, completing the formation of 1 ML of CdS. To achieve thicker shells, this process was repeated for the desired number of times.

CONCLUSIONS We investigate lateral size-dependent carrier dynamics and photon emission statistics of NPLs. We find that similar to QDs,51,52 photons emitted during the maximum PL intensity periods of NPLs have negligible influence from nonradiative recombination processes. This allows us to estimate the radiative decay rate of the NPLs. We find that with the increase of the NPL size, the radiative lifetime first decreases and then flattens out, in contrast with expectations from the electric dipole approximation. We estimate the single exciton quantum yield of the NPLs from PL time traces and find it 9125

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ACS Nano Single Nanoplatelet Optical Measurements. For single NPL measurements, diluted samples were drop cast onto precleaned glass cover slides and loaded onto a home-built confocal laser microscope. A pulsed diode laser with a wavelength of 400 nm and a repetition frequency of 1 MHz was focused onto the samples by a microscope objective (60×, NA = 1.40). PL from the NPLs was collected by the same objective, split by a beam splitter, and focused onto two identical single photon avalanche diodes in a Hanbury−Brown and Twiss geometry. Time-resolved photon measurements were performed with HydraHarp electronics (PicoQuant).

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ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b03943. Absorption and PL spectra of CdSe core NPLs; carrier wave function calculations of the NPLs; method for determination of average absorbed photons per pulse; contribution of biexciton emission to the overall PL intensity at low excitation powers; pump-dependent g(2)(τ) measurements; size-dependent Q2X/Q1X values; pump-power-dependent PL measurements; maximum PL intensity decay curves and fittings; examples of PL intensity-dependent lifetime analysis; probability densities of on- and off-state duration times; influence of defects on the effective exciton coherent motion area (PDF)

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

Xuedan Ma: 0000-0002-3163-1249 Benjamin T. Diroll: 0000-0003-3488-0213 Richard D. Schaller: 0000-0001-9696-8830 Dmitri V. Talapin: 0000-0002-6414-8587 Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was performed, in part, at the Center for Nanoscale Materials, a U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences User Facility under contract no. DE-AC02-06CH11357. We also acknowledge support from NSF DMREF Program under awards DMR-1629601 and DMR-1629383. REFERENCES (1) Guzelturk, B.; Kelestemur, Y.; Olutas, M.; Delikanli, S.; Demir, H. D. Amplified Spontaneous Emission and Lasing in Colloidal Nanoplatelets. ACS Nano 2014, 8, 6599−6605. (2) Li, M.; Zhi, M.; Zhu, H.; Wu, W.-Y.; Xu, Q.-H.; Jhon, M. H.; Chan, Y. Ultralow-Threshold Multiphoton-Pumped Lasing from Colloidal Nanoplatelets in Solution. Nat. Commun. 2015, 6, 8513. (3) She, C.; Fedin, I.; Dolzhnikov, D. S.; Dahlberg, P. D.; Engel, G. S.; Schaller, R. D.; Talapin, D. V. Red, Yellow, Green, and Blue Amplified Spontaneous Emission and Lasing Using Colloidal CdSe Nanoplatelets. ACS Nano 2015, 9, 9475−9485. (4) Grim, J. Q.; Christodoulou, S.; Stasio, F. D.; Krahne, R.; Cingolani, R.; Manna, L.; Moreels, I. Continuous-Wave Biexciton Lasing at Room Temperature Using Solution-Processed Quantum Wells. Nat. Nanotechnol. 2014, 9, 891−895. 9126

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