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Letter

Size and Wavelength Dependent Two-Photon Absorption Cross-Section of CsPbBr Perovskite Quantum Dots 3

Junsheng Chen, Karel Žídek, Pavel Chabera, Dongzhou Liu, Pengfei Cheng, Lauri Nuuttila, Mohammed J. Al-Marri, Heli Lehtivuori, Maria E Messing, Keli Han, Kaibo Zheng, and Tõnu Pullerits J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 08 May 2017 Downloaded from http://pubs.acs.org on May 9, 2017

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The Journal of Physical Chemistry Letters

Size and Wavelength Dependent Two-Photon Absorption Cross-Section of CsPbBr3 Perovskite Quantum Dots Junsheng Chen,1, 2

e

de ,1,3 Pavel Chábera,1 Dongzhou Liu,4, 8 Pengfei Cheng,2 Lauri Nuuttila,5

Mohammed J. Al-Marri,7 Heli Lehtivuori,5 Maria E. Messing,6 Keli Han, *, 2 Kaibo Zheng, *, 1,7 and e i *, 1 1

Department of Chemical Physics and NanoLund, Lund University, P.O. Box 124, 22100

Lund, Sweden 2

State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical

Physics, Chinese Academy of Sciences Dalian, 116023, China 3

Regional Centre for Special Optics and Optoelectronic Systems (TOPTEC), Institute of

Plasma Physics, Academy of Sciences of the Czech Republic, Za Slovankou 1782/3, 182 00 Prague 8, Czech Republic. 4

College of Science, Agricultural University of Hebei, Lingyusi 289, 071001, Baoding, Hebei,

China 5

University of Jyväskylä, Department of Physics, Nanoscience Center, P.O. Box 35, 40014

Jyväskylä, Finland 6

Solid State Physics and NanoLund, Lund University, Box 118, 22100 Lund, Sweden

7

Gas Processing Center, College of Engineering, Qatar University, PO Box 2713, Doha,

Qatar 8

College of Physics Science & Technology, Hebei University, East of Wusi 180, 071002,

Baoding, Hebei, China

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Abstract All-inorganic colloidal perovskite quantum dots (QDs) based on cesium, lead and halide have recently emerged as promising light emitting materials. CsPbBr3 QDs have been also demonstrated as stable two-photon-pumped lasing medium. However, the reported two photon absorption (TPA) cross-sections for these QDs differ by an order of magnitude. Here we present an in-depth study of the TPA properties of CsPbBr 3 QDs with mean size ranging from 4.6 nm to 11.4 nm. By using femtosecond transient absorption (TA) spectroscopy we found that TPA cross section is proportional to the linear one photon absorption. The TPA cross section follows a power law dependence on QDs size with exponent 3.3±0.2. The empirically obtained power-law dependence, suggests that the TPA process through a virtual state populates exciton band states. The revealed power-law dependence and the understanding of TPA process are important for developing high performance nonlinear optical devices based on CsPbBr3 nanocrystals.

TOC


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Hyb id o g ic−i o g ic h ide perovskites have attracted broad research interest as promising material for solar cells,1-3 light emitting diodes (LED),4-6 lasing,7-9 and photodetector10-12 applications owing to their broadband absorption, easily tunable optical band gap, efficient charge generation and transportation, as well as their luminescence properties13-15 . Recently all-inorganic cesium lead halide perovskite colloidal quantum dots (CsPbX3 QDs, X = Cl, Br, I) with enhanced emission have been reported by Kovalenko and coworkers.16 The QDs are stable and have very high photoluminescence (PL) quantum yield (QY) PL up to 90%, narrow PL emission band and large optical gain.14,

17

Furthermore, the emission is

spectrally tunable over the whole visible range by changing the composition and the QD size. 5, 10, 13, 16, 18, 19

Recently CsPbBr3 QDs have been suggested as a material for two-photon-pumped laser development because of their strong two-photon absorption (TPA) and ease of achieving population inversion.20, 21 Two-photon-pumped laser has been considered as an alternative for frequency up-conversion21, 22 and nanoscale laser7, 23, that can be used in biomedical photonics owing to their

spatially highly confined excitation and relaxed phase-matching

requirements.22 Moreover, compared to the one-photon linear absorption and emission, the two-photon induced emission enables longer excitation penetration depth. Such TPA materials can be also utilized for three-dimensional material micro-fabrication,24 information technology25 and bio-imaging.26,

27

For developing and applying any of these techniques,

understanding of the physical processes behind TPA cross-section of the materials and knowing the precise values is essential.25 Recent reports of TPA cross-sections of CsPbBr3 QDs suggest that the TPA can be over two orders of magnitude stronger in this material compared to the conventional CdSe and CsTe semiconductor QDs.20, 21, 28, 29 At the same time, the reported TPA cross-sections of



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CsPbBr3 QDs differ by over one order of magnitude, from 1.2 × 105 GM 20 up to 2.7 × 106 GM

21

for the same material. The usual TPA evaluation protocol for colloids involves

one-photon linear absorption (OPLA) as a reference. Essentially it means that the OPLA cross-section is used to determine the concentration of the nanoparticles. Consequently the possible uncertainties in OPLA cross-sections spill over to the TPA. Indeed the reported OPLA cross-sections of CsPbBr3 QDs are also spread over a wide range (10-14~10-13 cm2 ) 17, 21, 30-32

14,

.

Another important factor influencing the cross-sections is the QD size. It has been reported that the OPLA cross-sections of CsPbBr3 QDs show size dependence.32 Also the TPA crosssection in CdSe,28,

29, 33

CdTe,28 CdS34 and PbS35 QDs depends strongly on the QD size

whereas the dependence has allowed to identify the physical process behind the TPA. The particle size dependence of the TPA cross-section of perovskite QDs has not been reported so far. In this work we determine the OPLA cross-section of CsPbBr3 QDs by utilizing femtosecond transient absorption (TA) spectroscopy and using statistical analyses of the saturation of the long time signal intensity-dependence. The OPLA cross-section is then used as a reference to obtain the TPA cross-section from TA measurements. This is different from the previous studies where the TPA cross-section of CsPbBr3 QDs was obtained by Z-scan technique, which requires careful measurement of the amount of two-photon absorbed light.29, 36, 37

Since TPA is weak, high excitation intensities are need and the method can be easily

affected by the thermo-optical effects and strong background.

29, 36, 37

Our measurements

provide the TPA cross-section of CsPbBr3 QDs (9.4 nm) 1.8±0.1×105 GM, which is close to the value reported by Sun, et al. 20 The contradicting TPA cross-section values in the previous studies20, 21 partially originate from different OPLA cross-sections of the CsPbBr 3 QDs used in these studies. We have systematically studied the size dependence of TPA cross-section of 4 ACS Paragon Plus Environment

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CsPbBr3 QDs and found proportionality to the 3.3th power of the size. In addition, we report the excitation wavelength dependence of TPA cross-section of CsPbBr3 QDs and found it to be proportional to the OPLA cross-section. Based on this result we draw conclusion that the photophysical process of TPA in CsPbBr 3 QDs is mediated by a virtual state and populates an exciton band states. CsPbBr3 colloidal QDs were prepared by using a method developed by Kovalenko and coworkers.16, 38 0.814 g Cs2CO3 (Sigma-Aldrich, 99%) was mixed with 40 mL 1-octadecene (ODE, Sigma-Aldrich, 90%) and 2.5 mL oleic acid (OA, Sigma-Aldrich, 90%), and heated up to 120 ℃ for 1hour under vacuum. The mixture was heated up to 150 ℃ for 30 mins under N2 atmosphere. The obtained Cs-oleate was kept in glove box and heated up to 100 ℃ before using. 0.689 g PbBr2 (Sigma-Aldrich, 99.999%) and 10 mL ODE were heated up to 120 ℃ under vacuum for 1 hour, afterwards 0.5 mL dry oleylamine (OAm, Sigma-A d ich, 80−90%) and 0.5mL OA were added and heated up to 120 ℃ under N2 atmosphere. To control the QD size, the temperature was increased to different levels between 140 ℃ and 200 ℃, then 0.4 mL Cs-oleate solution was rapidly injected. After injection the mixture solution was immediately cooled by ice-water bath. The injection temperature was set at 140 ℃, 150 ℃, 160 ℃, 180 ℃ and 200 ℃ to obtain particles with mean size of 4.6, 5.2, 6.9, 9.4 and 11.4 nm, respectively. The detailed information about isolation, purification and transmission electron microscopy (TEM) size characterization of CsPbBr3 QDs, and steady-state spectroscopy is provided in SI. TA experiments were performed by using a femtosecond pump-probe setup.39 Laser pulses (800 nm, 120 fs pulse length, 1 kHz repetition rate) were generated by a regenerative amplifier (Spitfire XP Pro) seeded by a femtosecond oscillator (Tsunami, both Spectra Physics). For the OPLA experiments, the pump pulses at 400 nm were generated by a BBO crystal as a second harmonic of the laser. For the two photon absorption experiments the 5 ACS Paragon Plus Environment


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pump pulses at 800 nm were obtained directly from the regenerative amplifier whereas the pulses at 675 nm, 725 nm, 870 nm and 950 nm were generated by an optical parametric amplifier (Topas, Light Conversion). For the probe we used either the super-continuum generation from a thin CaF2 plate (TA spectra measurements) or the Topas to obtain pulses with central wavelength tuned from 470 to 513 nm (TA kinetic measurements). The mutual polarization between pump and probe beams was set to the magic angle (54.7°) by placing a Berek compensator in the pump beam. In order to avoid photo-damage, the sample was moved to a fresh spot after each time delay point. The kinetics of the different scans stay the same for both OPLA and TPA experiment showing no sign of degradation (SI Figure S6). The absorption spectrum of the sample was recorded after each scan. No changes were detected. Excitation power and spot size measurements were used to determine the excitation fluence with uncertainty within 20% of the fluence value. The detailed information is provided in SI. QDs with 5 different sizes were prepared. Due to the quantum confinement16 the absorption edge and the emission peak of the QDs are blue-shifted with decreasing size (diameters d from 11.4 nm to 4.6 nm, Figure 1A, 1B and Table S1). One can also notice that the 1S exciton transition peak in absorption spectra becomes more pronounced for smaller QDs.


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Figure 1. (A): Absorption and photoluminescence spectra (λex=430nm) of CsPbBr3 QDs with different sizes. (B) High-resolution TEM images. An important part of the TPA cross-section evaluation is obtaining reliable OPLA crosssection  (1) .40-42 (SI S4). The OPLA cross-section is often evaluated from mass spectrometry.20, 21, 32 Time-resolved spectroscopy offers an alternative approach based on the intensity dependent signal saturation curve. 17, 30, 43-45 The reported OPLA cross-sections vary in a broad range,

14, 17, 21, 30, 32, 46

due to different experimental conditions. For example,

excitation fluence is a critical factor for calculating OPLA cross-sections by using timeresolved spectroscopy. Here we determined the excitation fluence with uncertainty within



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20%, and applied TA spectroscopy to quantify  (1) for 9.4 nm QDs - see SI S5 for details of the experiment. Briefly, we assume that the initial multiple exciton population follows a Poisson distribution. After a rapid Auger process there will be only one excitation in all excited QDs. Therefore the amplitude of the long time (t≥1ns) TA signal saturates with increasing excitation fluence, and the saturation behavior is controlled by  (1) . Hence,  (1) can be quantified by measuring the long time scale TA signal saturation as a function of the excitation fluence. The analyses provides  (1) value (7.0±1.4)×10-14cm2 (Figure S3), which agrees well with some of the previous reports14 and with an empirical expression proposed in 32

(eq. S3). Therefore, in the following, we have applied the eq. S3 to calculate  (1) of

different size CsPbBr3 QDs (Table S2). We have measured the TPA-induced GSB signal amplitude at the lowest 1S exciton energy (2.42eV~2.64eV, 470nm~513nm, depending on the QD size). TA data can be found in SI, Figures S4 and S5. The ratio between –ΔA (i.e. GSB signal amplitude) and the linear absorbance of QDs (A) at exciton transition energy (-ΔA/A) quantifies the number of photogenerated excitons in QDs within excitation optical path. Below the saturation threshold31, 47, the signal amplitude is proportional to the exciton population in the QDs. The population depends on the excitation fluence in a linear fashion for the OPLA (Figure 2A) and quadratically for the TPA (Figure 2B):









 C1  400

(1)

2  C2  800

(2)

In eq.1 and 229 , 400 and 800 denote the excitation fluences at 400nm and 800nm, respectively. C1 is obtained from the linear fit to the fluence dependence of the experimental data with 400nm light excitation (with χ(2)≈0.99, Figure S7 and Table S3). In a similar fashion, 8 ACS Paragon Plus Environment

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C2 is obtained from a quadratic fit to the fluence dependence of -ΔA/A with 800nm light excitation (with χ (2)≈0.99, Figure S7 and Table S3). The quadratic dependence is a direct evidence of TPA process in CSPbBr3 QDs with 800nm excitation.

Figure 2. Excitation fluence dependent GSB signal normalized with absorbance at 1S exciton transition energy (-ΔA/A) for CsPbBr3 QDs with different size (plotted in a log-log scale). GSB signals have been taken from early-time (t~2ps). The excitation densities were kept well below the GSB saturation threshold. A: 400nm excitation; B: 800nm excitation.



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Figure 3. Wavelength dependent absorption cross sections of the 9.4 nm size QDs. Black line, OPLA cross section  (1) , which is calculated from absorption spectrum based on the OPLA cross-section  (1) at 400 nm (7.87×10-14cm2 , Table S2). Yellow dots, excitation wavelength dependent TPA cross-section  (2) (1 GM corresponds to 10-50 cm4 s/photon) at 675 nm, 725 nm, 800 nm, 870 nm and 950 nm- see SI S9 for details of the experiment. TPA cross-sections  (2) of CsPbBr3 QDs can be now calculated from QD concentration together with the factors C1 and C2 . (SI S4 and S7, and Table S4). For CsPbBr 3 QDs with 9.4±0.5 nm size, we obtained the value  (2) = 1.8±0.2×105 GM at 800 nm (Figure 3), which agrees well with previous results by Sun et al.20 (  (2) ~1.2×105 GM for 9 nm size CsPbBr3 QDs) but is significantly smaller than in ref 21 (Figure 4A). As discussed by Xiao et al,21 such divergence can emerge from uncertainty in OPLA cross-section  (1) . Here, we have obtained

 (1) by using TA spectroscopy and analytic expression (eq. S3) giving for the 9.4 nm size QDs at 400 nm (Figure S3) the value (7.0×10-14cm2). Similar values have recently been reported in a number of other articles (8.0×10-14cm2 and 7.9×10-14cm2).14, 32 In ref. 21 a larger 10 ACS Paragon Plus Environment

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value 1.2×10-13 cm2 was used for the OPLA which partially explains the very different outcome of the TPA cross-section in that study.

Figure 4. (A)  (2) dependence of QD size d (average of length and width of QDs) in a loglog scale. Black dots: TPA cross section  (2) at 800 nm (values listed in Table S4); orange dots: TPA cross section  (2) at adjusted wavelength (values listed in Table S10) and the data are fitted by using a power-law (  (2)  Cd  ,C=111±55,  =3.3±0.2, χ(2)≈0.97, red dot line). Results from earlier reports21 (green triangle) and (blue square) 20 are included for comparison. The error bar for the size d is calculated from the QD size distribution. The error bar for the TPA cross-section  (2) is propagated from the error of excitation fluence, -ΔA/A, size d, and molar extinction coefficient. (B) Schematic diagram of the mechanism of TPA in CsPbBr3 QDs. Because of the quantum confinement the electronic structure of the different size QDs is not the same. In order to account for these changes, we have measured the TPA for the 9.4 nm size QDs at five different wavelengths (Figure 3). The wavelength dependence of TPA cross section follows well the trend of linear absorption spectrum. Even though TPA and OPLA follow different dipolar parity selection rules, both  (1) and  (2) can be seen as a multiplication of the density of states by the corresponding electronic transition matrix element at a certain transition energy (wavelength). Similar wavelength dependent trend of 11 ACS Paragon Plus Environment


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 (1) and  (2) can be ascribed to the same density of the accepting states and similar wavelength dependence of the two electronic transition matrix elements, even though the matrix elements correspond to qualitatively different processes. TPA is generally described in terms of an intermediate state in resonance with single photon energy which can be either a virtual state or a real state with negligible single-photon absorption. Such sub-band gap states can occur in QDs but would lead to nonradiative decay channels. The very high fluorescence QY in our QDs (45-70%, Table S2) speaks against such scenario and we argue that the TPA occurs via a virtual state leading to quadratic dependence of two photon excited PL intensity on excitation intensity (Figure S13). Analogous quadratic dependence in CsPbBr3 QDs has been reported by Sun and co-workers.20 In order to describe the TPA Chou and co-workers28 have used a simple model where the QD volume is divided to a large number of interacting units. The exciton states of the system were described by a Hückel approach. They found that in such model the calculated size dependence of the TPA cross section  (2) is determined by the nature of the final state. If the final state of the TPA process in QDs is an exciton state then  (2) has a third order power-law dependence on the QD size (  (2)  d 3 ), whereas  (2) shows a sixth order power-law dependence on the size (  (2)  d 6 ) if the final state is a nonexcitonic defect state.28 Following the above described experimental protocol we have measured the TPA cross section with 800 nm light for a series of QDs with different sizes (Figure 4A). Here we have used the 9.4 nm results as a reference and rescaled the 400 nm two-photon energies for other size QDs following the CdSe QD work by Norris and Bawendi 48, where the electronic energies above the lowest transition (band-edge) scale close to linearly with the lowest transition energy (SI S9). After such rescaling we found that the TPA cross section  (2) of CsPbBr 3 follows the (2) 3.3 power law dependence on the size of the QDs with the exponential factor 3.3:   d


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(Figure 4A). This is close to third orders power-law predicted for the excitonic final state. The small deviation from d 3 can be due to the approximations used in Chou and co-worker’s model.28 Similar power-law dependence has been reported in CdSe QDs28, 33 and CdS QDs34 . We conclude that the TPA process in CsPbBr3 QDs proceeds through a virtual level and the final state is an exciton band state and not a defect state (Figure 4B). The initially excited hot state will relax in sub-ps timescale to the band edge.21, 31, 49, 50 Finally the e ec o −ho e p i recombine though radiative (photoluminescence emission) and nonradiative processes.31 We used transient absorption spectroscopy to measure two-photon absorption cross-section of CsPbBr3 QDs of different sizes (4.6~11.4 nm). The TPA cross-section reaches 1.8×105 GM for CsPbBr3 QDs with d ~ 9 nm size. The inconsistency in the previously published results is partially ascribed to the uncertainty in one photon absorption cross-sections which are used in such studies. The TPA cross-section of CsPbBr3 QDs shows a power-law size dependence

 (2)  d 3.3 and follow the OPLA cross section  (1) wavelength dependence. Clearly, the two photon absorption coefficient can be significantly tuned by the size of the QDs. The TPA proceeds via a virtual state, the power law dependence and wavelength dependence allow us to assign the final state to an exciton state. The revealed detailed understanding of the TPA in CsPbBr3 nanocrystals can open ways for developing new high performance non-linear optical materials and devices. ASSOCIATED CONTENT AUTHOR INFORMATION Corresponding Author *[email protected]

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*[email protected]

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Tel: +46 46 222 8131 13

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*[email protected]

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Notes The authors declare no competing financial interests.

Acknowledgements This work was financed by the Swedish Research Council (VR), the Knut and Alice Wallenberg Foundation, and NPRP grant # NPRP7-227-1-034 from the Qatar National Research Fund, Interreg Öresund-Kattegat-Skagerrak, european regional development fund, and the Program of Study Abroad for Young Teachers by Agricultural University of Hebei. We acknowledge collaboration within NanoLund. We thank Dr. Torbjörn Pascher for help regarding transient absorption spectroscopy measurements. Supporting Information Isolation and purification of CsPbBr3 QDs, size Characterization and steady-state spectroscopy, excitation fluence determination in TA spectroscopy, determine TPA crosssection from TPA coefficient and QDs concentration, OPLA cross-section and concentration calculation, TA spectroscopy signal, parameters C1 and C2 fitting, TPA coefficient calculation, calculated TPA cross-section, wavelength dependent TPA cross-section, excitation intensity dependent PL and

A coefficie

β.

References: (1) Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050-6051.


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(2) Lee, M. M.; Teuscher, J.; Miyasaka, T.; Murakami, T. N.; Snaith, H. J. Efficient Hybrid Solar Cells Based on Meso-Superstructured Organometal Halide Perovskites. Science 2012, 338, 643-647. (3) Zhou, H. P.; Chen, Q.; Li, G.; Luo, S.; Song, T. B.; Duan, H. S.; Hong, Z. R.; You, J. B.; Liu, Y. S.; Yang, Y. Interface Engineering of Highly Efficient Perovskite Solar Cells. Science 2014, 345, 542-546. (4) Dohner, E. R.; Jaffe, A.; Bradshaw, L. R.; Karunadasa, H. I. Intrinsic White-Light Emission from Layered Hybrid Perovskites. J. Am. Chem. Soc. 2014, 136, 13154-13157. (5) Li, X. M.; Wu, Y.; Zhang, S. L.; Cai, B.; Gu, Y.; Song, J. Z.; Zeng, H. B. CsPbX3 Quantum Dots for Lighting and Displays: Room-Temperature Synthesis, Photoluminescence Superiorities, Underlying Origins and White Light-Emitting Diodes. Adv. Funct. Mater. 2016, 26, 2435-2445. (6) Li, G. R.; Tan, Z. K.; Di, D. W.; Lai, M. L.; Jiang, L.; Lim, J. H. W.; Friend, R. H.; Greenham, N. C. Efficient Light-Emitting Diodes Based on Nanocrystalline Perovskite in a Dielectric Polymer Matrix. Nano. Lett. 2015, 15, 2640-2644. (7) Zhang, W.; Peng, L.; Liu, J.; Tang, A. W.; Hu, J. S.; Yao, J. N. A.; Zhao, Y. S. Controlling the Cavity Structures of Two-Photon-Pumped Perovskite Microlasers. Adv. Mater. 2016, 28, 4040-4046. (8) Xing, G. C.; Mathews, N.; Lim, S. S.; Yantara, N.; Liu, X. F.; Sabba, D.; Gratzel, M.; Mhaisalkar, S.; Sum, T. C. Low-Temperature Solution-Processed Wavelength-Tunable Perovskites for Lasing. Nat. Mater. 2014, 13, 476-480. (9) Deschler, F.; Price, M.; Pathak, S.; Klintberg, L. E.; Jarausch, D. D.; Higler, R.; Huttner, S.; Leijtens, T.; Stranks, S. D.; Snaith, H. J.; et al. High Photoluminescence Efficiency and Optically Pumped Lasing in Solution-Processed Mixed Halide Perovskite Semiconductors. J. Phys. Chem. Lett. 2014, 5, 1421-1426.



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Figure 1. (A): Absorption and photoluminescence spectra (λex=430nm) of CsPbBr3 QDs with different sizes. (B) High-resolution TEM images. 150x141mm (300 x 300 DPI)


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Figure 2. Excitation fluence dependent GSB signal normalized with absorbance at 1S exciton transition energy (-∆A/A) for CsPbBr3 QDs with different size (plotted in a log-log scale). GSB signals have been taken from early-time (t~2ps). The excitation densities were kept well below the GSB saturation threshold. A: 400nm excitation; B: 800nm excitation. 415x194mm (300 x 300 DPI)



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Figure 3. Wavelength dependent absorption cross sections of the 9.4 nm size QDs. Black line, OPLA cross section σ(1), which is calculated from absorption spectrum based on the OPLA cross-section σ(1) at 400 nm (7.87×10-14cm2, Table S2). Yellow dots, excitation wavelength dependent TPA cross-section σ(2) (1 GM corresponds to 10-50 cm4 s/photon) at 675 nm, 725 nm, 800 nm, 870 nm and 950 nm- see SI S9 for details of the experiment. 182x127mm (300 x 300 DPI)


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Figure 4. (A) σ(2) dependence of QD size d (average of length and width of QDs) in a log-log scale. Black dots: TPA cross section σ(2) at 800 nm (values listed in Table S4); orange dots: TPA cross section σ(2) at adjusted wavelength (values listed in Table S10) and the data are fitted by using a power-law (σ(2)=Cdα,C=111±55, α=3.3±0.2, χ(2)≈0.97, red dot line). Results from earlier reports21 (green triangle) and (blue square) 20 are included for comparison. The error bar for the size d is calculated from the QD size d distribution. The error bar for the TPA cross-section σ(2) is propagated from the error of excitation fluence, -∆A/A, size d, and molar extinction coefficient. (B) Schematic diagram of the mechanism of TPA in CsPbBr3 QDs. 114x55mm (300 x 300 DPI)


Perovskite Quantum Dots - ACS Publications - American Chemical

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