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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Two-Photon Absorption and Two-Photon Induced Gain in Perovskite Quantum Dots Gabriel Nagamine, Jaqueline O. Rocha, Luiz Gustavo Bonato, Ana Flavia Nogueira, Zhanet Zaharieva, Andrew A.R. Watt, Carlos H. de Brito Cruz, and Lazaro A Padilha J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01127 • Publication Date (Web): 08 Jun 2018 Downloaded from http://pubs.acs.org on June 8, 2018

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The Journal of Physical Chemistry Letters

Two-Photon Absorption and Two-Photon Induced Gain in Perovskite Quantum Dots Gabriel Nagamine,∥# Jaqueline O. Rocha,∥# Luiz G. Bonato,§# Ana F. Nogueira,§ Zhanet Zaharieva,† Andrew A. R. Watt,† Carlos H. de Brito Cruz,∥ and Lazaro A. Padilha ∥*

∥Instituto

de Fisica “Gleb Wataghin”, Universidade Estadual de Campinas, UNICAMP, P.O. Box 6165, 13083-859 Campinas, Sao Paulo, Brazil

§

Instituto de Quimica, Universidade Estadual de Campinas, UNICAMP, P.O. Box 6154, 13084-971 Campinas, Sao Paulo, Brazil

†

Department of Materials, University of Oxford, 16 Parks Road Oxford OX1 3PH, United Kingdom e-mail: [email protected]

1 ACS Paragon Plus Environment

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Abstract Perovskite quantum dots (PQDs) emerged as a promising class of material for applications in lighting devices, including light emitting diodes and lasers. In this work, we explore nonlinear absorption properties of PQDs showing the spectral signatures and the size dependence of their two-photon absorption (2PA) cross-section, which can reach values higher than 106 GM. The large 2PA cross section allows for low threshold two-photon induced amplified spontaneous emission (ASE), which can be as low as 1.6 mJ/cm2. We also show that the ASE properties are strongly dependent on the nanomaterial size, and that the ASE threshold, in terms of the average number of excitons, decreases for smaller PQDs become. Investigating the PQDs biexciton binding energy, we observe strong correlation between the increasing on the biexciton binding energy and the decreasing on the ASE threshold, suggesting that ASE in PQDs is a biexciton-assisted process.

TOC:


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Since the first report, in 2015, of the successful synthesis of completely inorganic CsPbX3 perovskite quantum dots (PQDs),1 this new class of nanomaterials has called the attention of several research groups, mainly due to its unique optical and electronic properties. In particular, these nanomaterials present narrow photoluminescence (PL) spectra, high PL quantum yield (QY), and band gap tunability covering the whole visible range, turning them into good candidates for application in lighting technologies, including LEDs2,3 and lasers.4,5 In addition to the advantageous emission properties, this class of nanomaterials has shown other unique properties, such as the strong Coulombic interactions which directly results in fast multi-exciton Auger recombination6,7 and large biexciton binding energy.6 The later can lead to low threshold amplified spontaneous emission (ASE) due to reduced absorption losses. In fact, the first reports of ASE for PQDs have indicated threshold on the order of 10´s of µJ/cm2 for excitation at 400 nm (3.1 eV). 4,8 Most recently, few studies have explored the nonlinear optical properties of CsPbBr3 PQDs, reporting on extremely large two-photon absorption (2PA) cross section, δ2PA, on this kind of nanoparticles. While Xu et.al. have shown δ2PA = 2.7 x 106 GM (1 GM = 10-50 cm4s) measured with excitation at 800 nm (1.55 eV) for CsPbBr3 PQDs of about 9 nm,9 other authors have reported values on the order of 105 GM for similarly sized PQDs at the same excitation wavelength.10,11 In addition to the large 2PA cross section, low threshold for two-photon induced ASE in CsPbBr3 PQDs have also been reported, revealing that the excitation threshold is on the order of few mJ/cm2 for 100 fs excitation at 800 nm.9,11,12 However, despite all the exciting results, one can see that most of the studies regarding the 2PA and two-photon enabled ASE (2PE-ASE) properties of PQDs are restricted to measurements at 800 nm of CsPbBr3 PQDs of nearly 9 nm. Indeed, to the best of our 3 ACS Paragon Plus Environment


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knowledge, only a recent paper discusses 2PA for different sizes of CsPbBr3 PQDs, however, the size dependence study is also restricted to 800 nm (1.55 eV) excitation,10 turning the size dependence analysis insensitive to the, typically strong, spectral dependence of 2PA. Consequently, several important questions remain unanswered regarding the optical properties of CsPbBr3 PQDs, such as: How does the 2PA spectra and magnitude depend on the PQDs size? How does 2PA cross section for CsPbBr3 PQDs compare to other visible emitting quantum dots? How does the 2PE-ASE threshold depend on the PQDs size? Finally, what are the specific physical mechanisms that allow for lowthreshold ASE and high 2PA cross section on this kind of nanomaterial. Inspired by the above questions, here we present a comprehensive study of 2PA and 2PEASE for a series of CsPbBr3 PQDs, with sizes varying from 7.4 nm to 12.5 nm. By measuring their 2PA spectra, we observe that the maximum 2PA cross section exceeds 106 GM for the sample containing the largest PQDs, while for the smallest nanoparticles, this value barely reaches 3 x105 GM, indicating clear size dependence, similar to the one observed at 800 nm by Chen et.al.10 More than that, the 2PA spectra reveals that the first 2PA transition peak is blue shifted compared to the first one-photon absorption peak, indicating that the optical transitions in these nanomaterials are restricted to the parity symmetry selection rules, similarly to previously observed for Cd-based13 and Pb-based14,15 quantum dots. Comparing the 2PA cross section for the PQDs as a function of the nanoparticle volume to other visible-emitting quantum dots, we observe that the giant 2PA cross section measured for CsPbBr3 PQDs is, indeed, a result from the large size of these nanostructures and not from any particularly large transition oscillator strength. Exploring the 2PE-ASE for all samples, we also observe a dependence on the PQDs size, so that, the


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larger the PQDs, the lower the ASE threshold in mJ/cm2. Nevertheless, we observe that this trend is inverted if we consider the ASE threshold in terms of average exciton per PQDs, 〈〉 . To explain such trends, we have investigated the biexciton binding energy for all samples, finding a strong correlation between the biexciton binding energy and the ASE threshold. This suggests that the low-threshold ASE measured for PQDs is a result of the larger than usual red-shift caused by the strong biexciton Coulombic interactions, as we have proposed in our previous paper.6 For these studies, four different samples of CsPbBr3 PQDs were synthesized with sizes varying from 7.4 nm to 12.5 nm. These highly stable PQDs were synthesized following the amine-free synthesis developed by Yassittepe et al.2 Briefly, 82 mg of Cs2CO3 (~0.25 mmol) and 380 mg of Pb(OAc)2.3 H2O (~1 mmol) were placed in a 3-necked rounded flask with 2 mL of oleic acid and 5 mL of 1-octadecene. The mixture was kept under vacuum and stirred at 100 ºC for 1 hour to form Cs(oleate) and Pb(oleate)2 precursors. After the formation of the precursors, the solution was kept under N2 flow. To obtain the Brprecursor, 550 mg of tetraoctylammonium bromide (~1mmol) was dissolved in a mixture of 1 mL of oleic acid and 1 mL of 1-octadecene, both pre-heated and vacuum degassed before using. The reaction temperature of the solution containing Cs(oleate) and Pb(oleate)2 precursors was previously adjusted before the rapid injection of the Br precursor. After the injection, it was observed the formation of a bright green solution, containing CsPbBr3 PQDs. The purification procedure was made in just one step by the addition of anhydrous methylacetate to the PQDs solution (5 mL of solvent for each 1 mL of PQDs solution) followed by the centrifugation at 12000 rpm for 5 minutes (adapted from ref. 16). After, the supernatant was discarded and the solid was re-suspended in anhydrous hexane. The PQDs



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size was controlled by the temperature of the solution containing the Cs(oleate) and Pb(oleate)2 precursors, which were 75oC, 95oC, 115oC, and 135oC. For all the spectroscopic measurements, including linear absorption, 2PA spectra, PL lifetime and multi-exciton dynamics, the samples were dispersed in hexane and loaded in sealed 1 mm spectroscopy grade quartz cuvettes. Linear optical characterization (UV-Vis absorption and PL spectra, PL quantum yield, and linear absorption cross section) was performed on all samples kept at low concentration, such that the optical density at the first absorption peak was around 0.1. The 2PE-ASE experiments were performed in drop casted films deposited in 1 mm glass slides. The linear absorption cross-section, . , was obtained by measuring the saturation of the PL intensity as a function of the excitation fluence at 3.1 eV, and fitting to a Poisson distribution as discussed in details in ref. 6. The experimental results and the fittings for the linear absorption cross section are shown in the Supporting Information. Table I summarizes the linear optical characteristics of these samples and their sizes measured by TEM. TABLE I: Linear optical properties and lateral size measured for all four PQDs.

*

Sample *

. × 10

QY **

d*** (nm)

PQD-75

8.7 ± 0.3

0.66 ± 0.07

7.4 ± 0.8

PQD-95

11.6 ± 0.5

0.60 ± 0.06

8.2 ± 0.9

PQD-115

17.9 ± 0.6

0.50 ± 0.05

11.5 ± 1.4

PQD-135

24.0 ± 1.3

0.51 ± 0.05

12.5 ± 1.5

The number in the sample identification corresponds to the reaction temperature in oC

**

QY is measured using Rhodamine B in Methanol as reference.


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***

d is the defined as the average edge size of the cubic shaped CsPbBr3 nanoparticles.

Two-Photon Absorption: Two-photon spectroscopy was performed by the two-photon excited photoluminescence technique.17 In order to certify that the measured PL was excited by two-photon absorption, for each excitation wavelength, the measurement was performed using different pump intensities. In this way, the quadratic dependence between the excitation intensity and the emitted PL could be verified. The absolute 2PA magnitude has been calculated using Rhodamine B dissolved in methanol as reference. The values for the 2PA cross section for Rhodamine B in methanol has been extracted from ref.18. More information about the two-photon excited photoluminescence measurements can been found in the Supporting Information.



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Figure 1: Linear absorption, PL and 2PA cross section spectra for the series of CsPbBr3 PQDs with lateral sizes (a) d = 7.4 ± 0.8; (b) d = 8.2 ± 0.9; (c) d = 11.5 ± 1.4; (d) d = 12. 5 ± 1.5. The insets show the TEM images for each of the samples. The upper horizontal axis corresponds to the photon energy for the 2PA excitation; the lower horizontal axis corresponds to the transition energy, which is equal to the photon energy for the 1PA process and twice the photon energy for the 2PA process.

Figure 1 shows the linear absorption, PL, and 2PA cross section spectra for all four samples (for each sample, the TEM image is shown in the inset). The values for the 2PA cross section shown in Fig. 1 are corrected by the local field penetration using the MaxwellGarnett model,10 considering $%&'( = 1.88 and $*+, = 4.96.10 In our PQDs samples, due to the large size of the nanoparticles, the linear absorption spectrum only slightly blue-shifts when the size is reduced from 12.5 to 7.4 nm. In similar way, the 2PA spectrum shape does not depend strongly on the size of the PQDs. On the other hand, different from what has been suggested in ref. 10, the 2PA spectra shown in Fig. 1 do not follow the spectral behavior of the linear absorption. This difference between linear absorption and 2PA spectra is only clear because the 2PA spectra shown in Fig. 1 are taken at small spectral steps throughout the full 2PA spectrum. Indeed, the spectral differences between the linear absorption and 2PA spectra, observed in Fig. 1, give us important information regarding the electronic structure of PQDs. For all samples, the 2PA cross-section is small under the first linear absorption peak and it rises, showing the first peak, at energies about 100 meV higher than the first linear absorption peak, similar to what has been observed for other nanomaterials, e.g., PbS15 and CdSe13 quantum dots. Because linear absorption and 2PA 8 ACS Paragon Plus Environment

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follow different parity selection rules, this result indicates that the electronic wavefunctions in PQDs have well defined parity symmetry.14 Another interesting behavior is that they all show nearly constant 2PA cross section for transitions between 3.0 and 3.5 eV (i.e., for pump from 1.50 to 1.75 eV). As the photon energy increases even further, approaching the band edge energy, the 2PA cross section increases due to the intermediate state resonant enhancement.13,

19

However, note that the 2PA spectra rise is not as steep as the linear

absorption at higher energies. This difference is possibly due to the distinct selection rules,20 and the influence of scattering in the linear absorption curve for higher photon energies. The volume dependence is similar to other nanomaterials: the smaller the PQDs, the lower the 2PA cross section. However, the most striking result is the absolute magnitude of the 2PA cross section observed in this class of nanomaterials, which can reach as much as 1,000,000 GM for the largest sample. To understand the influence of the quantum confinement on the 2PA properties, comparing the 2PA cross section at a single excitation wavelength is less than ideal, because it does not account for the spectral dependence of the 2PA. To investigate the size dependence of the 2PA cross section in this material, we take advantage of the fact that for the spectral region between 3.0 and 3.5 eV, the 2PA cross section is nearly constant for each one of the samples. Consequently, we use the average value of the 2PA cross section in this spectral region to perform the size dependence analysis. Thus, we can directly compare to the literature values, which are mostly taken with excitation at 1.55 eV. Taking this average, we observe that the 2PA cross section, near 1.55 eV excitation, goes from about 160,000 GM for the PQDs with 7.4 nm, to about 710,000 GM for the largest nanoparticles, with 12.5 nm, following a nearly linear



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dependence with the nanoparticle volume. Indeed, the large 2PA cross sections measured for these samples are in remarkable agreement with most of the results recently reported in the literature for 2PA measurements performed with excitation at 1.55 eV (3.10 eV transition energy).10,11 Our data reveals that, in the spectral region where the 2PA reaches nearly a plateau, the 2PA cross section measured for PQDs is almost one order of magnitude higher than the 2PA peak values reported for other visible emitting colloidal quantum dots, such as CdSe13,

21,22

and CdTe22. However, in order to compare the 2PA

cross section between PQDs and other visible emitting quantum dots, it is important to consider the difference in the nanoparticle volume. While the PQDs have volumes above 100´s of nm3, typical CdSe or CdTe QDs are much smaller,13, 22 with volume in the order of 10´s of nm3. Figure 2 shows a comparison of the 2PA cross section as a function of the volume for a series of different visible emitting QDs. All the data shown in Figure 2 are corrected by the Maxwell Garnett local field,10 in order to eliminate the influence of the solvent. For CsPbBr3 PQDs, in most of the literature, only values at 1.55 eV are available. For the other nanomaterials, when the full spectrum is available, the value considered is an average of the values near 1.55 eV excitation. By doing this procedure, we minimize the influence of the energy dependence of 2PA in our volume dependence comparison.


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CsPbBr3- This work

2PA (GM)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

6

10

5

10

4

CdSe - Ref 13 CdSe - Ref 22 CdTe - Ref 22 CdSe - Ref 21 CsPbBr3 - Ref 10 CsPbBr3 - Ref 11

10

1

2

10 3 Volume (nm )

10

3

Figure 2. Volume dependence of the 2PA cross section for several visible emitting nanoparticles. The values for 2PA cross section are considered for excitations at 1.55 eV or around this spectral region. The gray shaded area indicates de volume dependence for Cd based quantum dots. In ref. 22 the data is not corrected by the local field penetration, and we performed this correction for the comparison.

The shaded area in Fig. 2 represents the volume dependence of the 2PA cross section for CdSe and CdTe QDs. It is interesting to point out that, despite large, the 2PA cross section for CsPbBr3 PQDs, when the volume is taken into account, is typically lower than for other nanomaterials. The dashed line in Fig. 2 indicates the best fit of all the 2PA data for CsPbBr3 PQDs, suggesting that, for this class of nanomaterials, the 2PA cross section is about 3 to 4 times lower than for CdSe or CdTe QDs with the same volume. The lower 2PA 11 ACS Paragon Plus Environment


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cross section for PQDs is not surprising if one considers that measurements of the linear absorption cross section for PQDs have revealed that this is almost one order of magnitude lower than that for CdSe QDs with the same volume.6,7 Consequently, the fact that the 2PA cross section is, at most, a factor of 3-4 lower than for CdSe with the same volume, suggests that, despite the weaker interband transition oscillator strength, the intraband transitions in PQDs are, at least, as strong as for other nanomaterials. Two-Photon Excited ASE: A direct application of the large 2PA cross section is in twophoton pumped lasers. Indeed, up-converted ASE has been demonstrated for CsPbBr3 PQDs under two9,

11,12

and three11 photons excitation. After fully characterizing these

materials’ two-photon absorption properties, we have prepared drop casted films of CsPbBr3 PQDs deposited in glass to study how the 2PE-ASE depends on the PQDs dimensions. However, when PQDs are deposited into films, aggregation and surface traps can occur, which could affect the 2PA properties. To make sure this was not the case for our samples, we measured the PL saturation under 2PA excitation for PQDs in solution and films, and they both showed similar saturation intensity (within ~15% of our experimental error), indicating that assembling the PQDs in films does not significantly influence the 2PA properties. Consequently, it is reasonable to assume that PQDs have the same 2PA cross section in films and in solution, in agreement with has been considered in the literature.9, 11,12 To perform the ASE experiment, the 1.55 eV laser beam was focused by a cylindrical lens into a stripe of 120 µm x 2.20 mm in order to favor the ASE process. The emitted light was collected by an objective lens put at the side of the glass slide, to collect the PL and ASE signal (see Fig. 3a). At low pump fluence, the emission is dominated by the broad PL 12 ACS Paragon Plus Environment

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signal. As the excitation power increases, a narrower peak emerges and grows super linearly with the pump fluence, becoming the dominating feature, and indicating the presence of ASE (Figure 3a). Maintaining the same experimental conditions, 2PE-ASE has been tested in films made of all four PQDs samples. As it can be seen in Fig. 3b, the ASE threshold varies for the different samples, and they tend to be lower, in mJ/cm2, for larger PQDs. This result is expected because, as it has been shown in Fig. 1, the larger the nanomaterial, the higher is the 2PA cross section.

Figure 3. a) Emission spectra as a function of the pump intensity at 1.55 eV for the PQD-75. The inset displays a picture of the setup showing the ASE from the sample. b) Integrated emission spectra as a function of the pump intensity for all four samples. c) Integrated emission spectra as a



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function of the average number of excitons per PQD for all four samples. The ASE threshold is considered to be the point where the slope increases drastically.

On the other hand, it is also important to understand the ASE threshold in terms of the average number of photo-generated excitons. To do that, we consider the 2PA cross section measured at 1.55 eV (Fig. 1), and estimate number of excitons photo-generated for each of the pump fluence. For the 2PA process, in the case of degenerate photons, the number of excitons created relates to the pump fluence by 〈〉 =

-./0 1. 2

, where 3* is the 2PA cross

section in cm4s, F is the fluence in photons/cm2, and 4 is the laser pulse width (4 ≅ 50 67 − 9:1/ ? @ ~D. DB

2.3

6000

2.4 2.5

0.0

0.2

0.4 0.6

0.8

1.0

Time (ns)

b)

2.3

ASE ~0.03 ~3.80 Bi-exciton emission

5000

2.6

> ? @ ~B. CD

2.4 2.5 2.6 0.0

0.2

0.4

0.6

0.8

Time (ns)

1.0

PL and ASE (a.u.)

Energy (eV)

a)

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4000 3000 2000 1000

0 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65

Energy (eV)

Figure 4. Temporal and spectral resolved PL for PQD-75 taken under (a) low intensity excitation and (b) high intensity excitation. The red shift caused by the biexciton emission can be seen at early times in (b). (c) Comparison of the single and biexciton emission and the ASE spectra. The red shift observed for the ASE spectra and for the PL in the film can be explained by the reabsorption of the blue part of the emitted spectra.



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We observe, for all samples, that the ASE spectrum is red shifted with respect to the steady state PL peak (Fig. 4). In principle, different physical phenomena could explain the ASE red shift: inhomogeneity of the PL lifetime, re-absorption, and, in the case of biexciton assisted ASE, the biexciton binding energy. To elucidate this question, we have investigated the PL dynamics for all samples. Figure 4a shows the PL lifetime in solution for low excitation fluence. From Fig. 4a, one can see that, for the PQD solution, PL decay is nearly homogeneous throughout the spectrum, indicating that the inhomogeneity of the PL lifetime should not be the responsible for the ASE red-shift. However, by comparing the PL dynamics at low pump intensities, when multi-excitons population is negligible (Fig 4a), and high pump intensities, when most of the PQDs are populated with more than one exciton (Fig 4b), we see a red-shift at the early times, which is due to the Coulomb interaction of the biexcitons, resulting on a high biexciton binding energy (about 61 meV). This suggests that the ASE is a biexcitonic process. According to ref. 25, for biexciton assisted ASE, the average number of excitons should be higher than 1, when one considers that biexciton and single exciton emissions are nearly at the same energy level. From our data, the ASE threshold is higher than 〈〉 = 1 for most of the samples, but not for the smallest PQDs, for which 〈〉 = 0.73 ± 0.11. This means that, considering the Poisson statistics, at this population density, only about 32% of the excited nanocrystals (i.e., about 16% of all PQDs in the sample) are populated by at least 2 excitons. Meanwhile over 48% are not excited, and biexciton gain would not be possible at this population density when biexciton emission is at an energy close to the band edge. Consequently, biexciton-assisted ASE at this low threshold would only be possible if the reabsorption losses were reduced


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due to a large red-shift of the biexciton emission, caused by high biexciton binding energy. Indeed, in a recent paper, we have shown that the biexciton binding energy for PQDs can be as large as 100 meV, depending on the size of the nanocrystal.6 To investigate the influence of the biexciton binding energy on the low ASE threshold, we have calculated the biexciton binding energy for all four samples by measuring the spectral shift of the time-resolved PL, between high (with biexcitons) and low (without biexcitons) intensity excitation, as shown in Figs. 4a and 4b, respectively. The large biexciton binding energy is more evident in Fig. 4c where we show the comparison of the early times (integrated over the first 50 ps after excitation) spectra under low and high excitation. The biexciton emission spectrum is obtained from the difference between the two spectra. As discussed in details in ref. 6, the biexciton binding energy can be estimated from the difference between the PL peak at low intensity and the biexciton emission peak. One can notice that the spectral subtraction in Fig. 4c used to estimate the biexciton binding energy renders a small peak at the high energy part of the spectrum. This peak is probably due to contributions from the emission of higher excitonic populations, such as triexciton emission.26-28 The biexciton binding energies measured for all four samples, using the method of Fig. 4c, are shown in Fig. 5 together with the ASE threshold obtained from Fig. 3c. Considering the sizes of the PQDs investigated here and the exciton Bohr radius, all samples are in the weak confinement regime. As a result, the biexciton binding energy varies slightly with the PQD size, going from nearly 41 meV up to 61 meV as the PQDs gets smaller, in agreement with our previous report.

6, 8

Comparing the 2PE-ASE threshold and the biexciton binding

energy for all four samples (Fig. 5), we see strong correlation between them: the higher the 17 ACS Paragon Plus Environment


binding energy, the lower the 2PE-ASE threshold. To rationalize the correlation observed in Fig. 5, we consider that the increasing biexciton emission red-shift, caused by the growing biexciton binding energy as the PQDs becomes smaller, results on reduced absorption losses. Consequently, at the biexciton emission energy, the ratio between the rate for photon emission and the rate for photon absorption tend to increase, reducing the threshold for biexciton gain. In other words, this strongly suggests that the ASE is facilitated by a reduction on the reabsorption losses caused by the red-shift on the biexciton

1,6 60

1,5 1,4

55

1,3 1,2

50

1,1 1,0

45

0,9 0,8

40

0,7 0,6 7

8

9

10

11

12

13

14

Bi-exciton Binding Energy (meV)

emission, indicating that this is a biexciton-assisted process.

ASE (excitons/dot)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Size (nm)

Figure 5. ASE threshold in terms of population density and the biexciton binding energy are plotted as a function of the PQDs size. The inverse trend observed indicates that the larger the red shift caused by the biexciton binding energy, the lower the threshold. The dashed lines are guides to the eye.


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Another important factor that needs to be accounted for, in the case of biexcitonic ASE, is the influence of Auger recombination. Typically, for quantum dots, the Auger biexciton lifetime increases linearly with the nanoparticle volume,29 in a way that one would expect this to spoil biexcitonic ASE for smaller nanoparticles. The decreasing of 〈〉 for smaller PQDs suggests that this is not the case here. In fact, this can be explained if we consider that, for CsPbBr3 PQDs with sizes above 7 nm the Auger biexciton lifetime is about 30-40 ps and only depends weakly on the size.6,7. In conclusion, we have reported on the spectral and size dependence of 2PA and ASE in PQDs based on CsPbBr3. Our results have shown that the 2PA cross section in PQDs is typically higher than for other visible emitting nanomaterials, but this is simply due to the large volume of the PQDs. When the volume is taken into account, we verified that PQDs underperform CdSe or CdTe QDs, as expected from the lower linear absorption cross sections recently reported.6,7 Nevertheless, the extremely large values for 2PA in PQDs allow for 2PE-ASE at low threshold, which goes from 1.6-2.4 mJ/cm2. When considering the ASE threshold in terms of the average number of generated excitons, we observe that PQDs performs better for smaller samples, reaching 〈〉 = 0.73 ± 0.11. Monitoring the PL dynamics, we found strong correlation between the increasing on the biexciton binding energy, which goes from about 41 meV to 61 meV, and the decreasing on the number of excitons necessary for ASE. This indicates that the large red-shift of the biexciton emission, caused by the strong biexcitonic Coulomb interactions, reduces the absorptive losses and favors optical gain in this class of nanomaterials at low threshold, turning them into one of the most promising candidates for applications in this field.



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AUTHOR INFORMATION #

G.N., J.O.R., and L.G.B. Contributed equally to this work

Corresponding Author *

[email protected]

ACKNOWLEDGMENT This publication has received the financial support from FAPESP (Project number 2013/16911-2) and The Royal Society – Newton Advanced Fellowship (NA 150152). L.G.B acknowledge the financial support from CAPES and J.O.R. and G.N acknowledges CNPq for their scholarships.

ASSOCIATED CONTENT Supporting Information includes experimental details of the X-ray diffraction, linear absorption cross section measurements, and two-photon absorption spectroscopy.

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