Light Absorption Coefficient of CsPbBr3 Perovskite Nanocrystals - The

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials 3

On the Light Absorption Coefficient of CsPbBr Perovskite Nanocrystals Jorick Maes, Lieve Balcaen, Emile Drijvers, Qiang Zhao, Jonathan De Roo, André Vantomme, Frank Vanhaecke, Pieter Geiregat, and Zeger Hens J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01065 • Publication Date (Web): 23 May 2018 Downloaded from http://pubs.acs.org on May 23, 2018

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The Journal of Physical Chemistry Letters

On the Light Absorption Coefficient of CsPbBr3 Perovskite Nanocrystals Jorick Maes,†,‡ Lieve Balcaen,¶ Emile Drijvers,†,‡ Qiang Zhao,§ Jonathan De Roo,k André Vantomme,§ Frank Vanhaecke,¶ Pieter Geiregat,†,‡ and Zeger Hens∗,†,‡ Physics and Chemistry of Nanostructures (PCN), Ghent University, Krijgslaan 281-S3, 9000 Gent, Belgium, Center for Nano and Biophotonics, Ghent University, Technologiepark-Zwijnaarde, 9052 Gent, Belgium, Atomic and Mass Spectrometry (A&MS), Ghent University, Krijgslaan 281-S12, 9000 Gent, Belgium, Instituut voor Kern-en Stralingsfysica, KU Leuven, Leuven, Belgium, and Department of Chemistry, Columbia University, New York, United States E-mail: [email protected]

∗

To whom correspondence should be addressed Physics and Chemistry of Nanostructures (PCN), Ghent University, Krijgslaan 281-S3, 9000 Gent, Belgium ‡ Center for Nano and Biophotonics, Ghent University, Technologiepark-Zwijnaarde, 9052 Gent, Belgium ¶ Atomic and Mass Spectrometry (A&MS), Ghent University, Krijgslaan 281-S12, 9000 Gent, Belgium § Instituut voor Kern-en Stralingsfysica, KU Leuven, Leuven, Belgium k Department of Chemistry, Columbia University, New York, United States †

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The Journal of Physical Chemistry Letters 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

Abstract Inductively coupled plasma mass spectrometry (ICP-MS) was combined with UV-VIS absorption spectroscopy and transmission electron microscopy to determine the size, composition and intrinsic absorption coefficient µi of 4 to 11 nm-sized colloidal CsPbBr3 nanocrystals (NCs). The ICP-MS measurements demonstrate the nonstoichiometric nature of the NCs, with a systematic excess of lead for all samples studied. Rutherford backscattering measurements indicate that this enrichment in lead concurs with a relative increase of the bromide content. At high photon energies, µi is independent of the nanocrystal size. This makes that the nanocrystal concentration in CsPbBr3 nanocolloids can be readily obtained by a combination of absorption spectroscopy and the CsPbBr3 sizing curve.

Graphical TOC Entry µi = A ln 10 fxL

intrinsic absorption coefficient (µi)

µi ~ cte

edge length CsPbBr3 NCs

2


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The concentration of colloidal nanocrystals (NCs) is a key characteristic for any quantitative study on nanocrystals, involving, for example, their use as biolabels, 1 the assessment of NC toxicity, 2,3 the modeling of NC-based opto-electronic devices 4 or the investigation of their surface chemistry. 5 Nanocrystal concentrations are typically determined by means of spectrophotometry, where absorbances can be recalculated into volume fractions or molar concentrations by means of Lambert-Beer’s law if the intrinsic absorption coefficient µi or the molar absorption coefficient is known, respectively. For various semiconductor NCs, it was found that µi is a size-independent quantity at photon energies well above the NC band-edge transition that concurs with a theoretical absorption coefficient calculated using Maxwell-Garnet theory and bulk optical constants. 6–8 Interestingly, this approach also applies to more complex NCs, such as core/shell heteronanocrystals, 9,10 quantum rods 11,12 or nanoplatelets, 13,14 and it proved a solid starting point for studies into the mechanism and kinetics of nanocrystal synthesis, 15,16 single nanocrystal photoluminescence, 17 or the evaluation of the optical gain characteristics of such materials. 4 In recent years, nanocrystals of hybrid and all-inorganic lead halide perovskites (APbX3 ) have been put forward as a novel, most promising solution-processable semiconductor for nextgeneration photovoltaic 18,19 and lighting applications. 20,21 In particular, CsPbBr3 NCs have been widely studied as they are easy to synthesize and exhibit near-unity photoluminescence quantum yield 22,23 and low optical gain thresholds. 24,25 At present, the concentration of CsPbBr3 NCs is typically quantified by means of an absorption coefficient or cross section obtained from photoluminescence saturation 24,25 or by thermogravimetric analysis; 26 two methods that are not accurate and need benchmarking by direct quantification methods. Such a quantitative analysis was presented by De Roo et al., 27 who determined the absorption coefficient of ∼ 8 nm CsPbBr3 NCs by combining inductively coupled plasma mass spectrometry (ICP-MS) and absorption spectrophotometry. No other studies on absorption coefficients of CsPbBr3 NCs have been reported. Hence, it remains unclear as to how absorption coefficients depend on the dimensions of the CsPbBr3 NCs, in particular in the sub 7 nm size range, where

3



A)

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B)

10 nm

10 nm

C)

D)

20 nm

20 nm

Figure 1: A)-D) Bright-field TEM images of selected fractions of CsPbBr3 NCs. The nanocrystals have average edge lengths of (A) 5.1, (B) 6.5, (C) 10.6 and (D) 12.7 nm. quantization effects become important. 22 We combined absorption spectrophotometry and elemental analysis by ICP-MS and Rutherford backscattering spectrometry (RBS) to determine the absorption coefficient of CsPbBr3 NCs with sizes ranging from 4 to 11 nm. The CsPbBr3 NCs were synthesized according to De Roo et al., 27 and we used an optimized post-synthesis size-selective precipitation to separate the polydisperse crude synthesis product into distinct, monodisperse fractions. For each fraction, the edge length of the NCs was determined by means of Transmission Electron Microscopy (TEM), where we analyzed bright-field images as displayed in Figure 1A-D. The detailed NC synthesis protocol, additional TEM images and sizing histograms are presented in the Supporting Information, Section S1 and S2. Figure 2A displays the size-dependent absorbance spectrum of 9 such CsPbBr3 NC fractions. One sees that all spectra exhibit a well-resolved absorption onset that shifts to shorter wavelength with decreasing NC size. We identify the first absorbance feature with the NC Table 1: Parameters yielding the best fit of the experimental Eg versus d data to an analytical sizing curve as expressed by Equation 1.

Eg (∞) (eV) 29 2.25

α (eV−1 ) β (nm−1 · eV−1 ) -1.26

0.996

4


γ (nm−2 · eV−1 ) -0.0324

A)

norm. abs. (a.u.)

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


B)

335 nm 2 d 1

band gap (eV)

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2.70 2.60 2.50 2.40 2.30

0 300 400 500 wavelength (nm)

2 x rB

Protesescu et al. Brennan et al. this work

bulk

5 10 15 edge length (nm)

Figure 2: (A) UV-Vis absorption spectra different fractions of CsPbBr3 NCs in n-hexane. The absorbance is normalised at 335 nm. (B) Representation of (full markers) experimental (Eg , d) data points as obtained by combining UV-Vis absorbance spectroscopy and TEM imaging. The full line represents the best fit to Equation 1 and the vertical line twice the Bohr radius (rB ) of CsPbBr3 . 22 The open markers represent two literature data sets. 22,28 band-edge transition, and correlating the thus obtained band-gap energy Eg with the NC edge length d yields the sizing curve shown in Figure 3B. To have an analytical expression for Eg as a function of d, we fitted the experimental sizing curve to the following expression: 7

Eg (d) = Eg (∞) +

1 α + β · d + γ · d2

(1)

Table 1 lists the parameter values that yield the best fit of the experimental data to Equation 1, and the resulting Eg (d) curve has been included in Figure 2B. One sees that this approach provides a reliable interpolation of the experimental datapoints, such that Equation 1 can be used to obtain a NC diameter from the energy of the band-edge transition as obtained from the absorbance spectrum. In addition, sizing data by Protesescu et al. 22 and Brennan et al. 28 are plotted in Figure 2. Most of the data points lie within the standard deviation of our measurements which indicates a good agreement between all data sets. The intrinsic absorption coefficient µi of a given set of CsPbBr3 NCs can be calculated from the absorbance A and optical path length L of the sample once the CsPbBr3 volume fraction

5



B) 335 nm 400 nm

5 0

C) 3

a b c d e 300 400 500 wavelength (nm)

Pb

backscattered yield (a.u.)

10

Br Cs

nPb/nCs

A) norm. abs. (a.u.)

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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1.2 1.1 1.0

0 1.25 1.50 energy (MeV)

4

6

8 10

cube length (nm)

Figure 3: (A) Representation of the UV-Vis absorbance spectra of the CsPbBr3 NCs used for elemental analysis by (samples a-e) ICP-MS and (samples a, b, d) RBS spectrometry. The absorbance is normalised at 335 nm. The average edge length of the CsPbBr3 NCs in the different samples are (a) 10.8 nm, (b) 8.3 nm, (c) 7.3 nm, (d) 5.8 nm, (e) 4.1 nm. (B) RBS spectrum recorded on sample b. The 3 signals are assigned to backscattering from Br, Cs and Pb, as indicated. (C) Pb:Cs ratio as obtained by (•) ICP-MS and (◦) RBS for the different samples analyzed.

f is known: 8 µi =

A ln 10 fL

(2)

To determine f , we made a detailed analysis of the composition of a selection of CsPbBr3 samples. As outlined in the Supporting Information, section S3, this involved the determination of absolute concentrations of Cs and Pb in the given samples by means of ICP-MS, and of the Cs:Pb:Br stoichiometry by means of RBS. We preferred this combination since the necessary dissolution of the samples in nitric acid prior to ICP-MS analysis may result in an uncontrolled loss of bromine through HBr formation. Five CsPbBr3 NC fractions, with edges ranging from 4.1 to 10.8 nm, were selected for ICP-MS (samples a-e), and a further subset of three fractions was analyzed by RBS (samples a, b and d). Figure 3A represents the absorption spectra of these 5 samples, where the multiple features in the spectra attest to the high quality of the fractionation. In addition, we used in all cases four purification cycles involving the successive addition of a non-solvent to the sample, centrifugation, decantation and the redispersion of the obtained pellet in a solvent. No excess of ligands was added after the last precipitation step. Moreover, before elemental analysis, the purity of the samples was analyzed by means of solution nuclear magnetic resonance spectroscopy (NMR) and the structural integrity of the 6


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Table 2: Elemental ratios as determined by RBS. The statistical error on the atomic ratios is estimated to be 1-2%. sample a b d

NC edge length (nm) 10.8 8.3 5.8

elemental ratios of Cs : Pb : Br 1.00 : 1.04 : 3.00 1.00 : 1.09 : 3.11 1.00 : 1.16 : 3.25

NCs by x-ray diffraction (see Figure S4). In agreement with observations reported by Zhang et al., 30 we observed that residual PbBr2 co-precipitated with the fractions containing NCs with a mean edge length of 9 to 10 nm (see Figure S1). Therefore, these sizes where excluded from the elemental analysis. Figure 3B shows, as an example, the RBS spectrum of 8.3 nm CsPbBr3 NCs (sample b). Three signals show up atop an almost zero-intensity background – a result that confirms once more the high purity of the samples analyzed – that can be assigned to backscattering of He from Br (1.29 MeV), Cs (1.39 MeV) and Pb (1.45 MeV). For all samples analyzed, the Pb:Cs ratio as obtained from the RBS spectra and the ICP-MS analysis are displayed in Figure 3C. First, one sees that both methods yield consistent results. Second, it follows that smaller NCs exhibit an excess of Pb, with the Pb:Cs ratio exceeding 1.2 for the smallest NCs analyzed (sample e). The NC stoichiometry as determined by RBS indicates that this enrichment in Pb of the NCs comes with a relative increase of the Br content too (see Table 2). Whereas the largest NCs are close to stoichiometric, the smallest sample analyzed by RBS (sample d) has a Pb:Cs ratio of 1.16 and a Br:Cs ratio of 3.25. This suggests that the surface of the smallest NCs is partially terminated by lead bromide (see Figure 4), or, viewed differently, that surface caesium ions are replaced by oleylammonium ions. 31 These results agree with previous reports were lead halide termination is observed and even promoted by (post-)synthesis methods to improve the stability and optical properties. 32,33 The structure model derived from the elemental analysis is visualised in Figure 4. Here, the highly dynamic surface stabilisation is adopted from De Roo et al. 27 We calculated the CsPbBr3 volume fraction by assigning to each element a volume that corre-

7



R NH2

O

HO

HBr

R R

Br R

H 3N

CsPbBr3

NH3

O bromide

lead

O R

Figure 4: Cartoon illustrating the lead bromide surface termination and the dynamic surface stabilisation by oleylammonium bromide, oleylammonium oleate and oleylamine, according to De Roo et al. 27 B)

5

335 nm

1

60

-1

-1

2 x rB

~d

40

3

-1

5 2x102

ε (cm µM )

A) µi (10 cm )

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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400 nm

20 0

4 8 12 edge length (nm)

0 4 8 12 edge length (nm)

Figure 5: A) The size-independent intrinsic absorption coefficient µi for CsPbBr3 NCs dispersed in n-hexane, where rB denotes the Bohr radius 22 and B) the related molar attenuation coefficient . sponds to the product of its ionic volume fraction φ in the CsPbBr3 unit cell and the volume of that unit cell (see Supporting Information, Section S4). Hence:

f = NA a3 (φCs .cCs + φP b .cPb + φBr .cBr )

(3)

Here, NA denotes Avogadro’s number, and a represents the lattice paramater for bulk CsPbBr3 crystals (0.587 nm). For this calculation, the molar concentrations of caesium cCs and lead cPb were directly taken from the ICP-MS analysis, whereas the bromide concentration cBr was obtained from the RBS stoichiometry (see Supporting Information, Section S4). Figure 5A shows the intrinsic absorption coefficient µi at wavelengths of 335 and 400 nm of the

8


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Table 3: Experimental values for the CsPbBr3 NC intrinsic absorption coefficient µi and molar extinction coefficient at λ = 335 nm and 400 nm. d denotes the edge length in nm. wavelength 335 nm 400 nm

solvent n-hexane toluene n-hexane toluene

µi (cm−1 ) (1.59 ± 0.05) × 105 (1.79 ± 0.06) × 105 (7.7 ± 0.8) × 104 (8.7 ± 0.9) × 104

(cm−1 · µM−1 ) (4.20 ± 0.04) × 10−2 × d3 (4.74 ± 0.04) × 10−2 × d3 (1.98 ± 0.04) × 10−2 × d3 (2.42 ± 0.04) × 10−2 × d3

different CsPbBr3 NC dispersions analyzed, where we used n-hexane as a solvent. For both wavelengths, it can be seen that the absorption coefficients lie randomly around an average value, without showing a pronounced size dependence. However, in the case of 335 nm, the relative standard deviation is smallest (see Table S4), possible because all NC absorption spectra are largely featureless around this wavelength (see Figure 3A). As summarized in Table 3, the mean intrinsic absorption coefficient µi, 335 nm amounts to:

µi, 335 nm = (1.59 ± 0.05) × 105 cm−1

(4)

The molar absorption coefficient of a given set of CsPbBr3 NCs is obtained as the product of the intrinsic absorption coefficient µi and the volume of 1 mole of NCs:

=

NA d3 µi ln 10

(5)

Clearly, as µi is size-independent, will increase with the cube of the edge length, as shown in Figure 5B. A numerical expression for in n-hexane is given in Table 3. A drawback of analyzing CsPbBr3 NC dispersions at 335 nm is the possible contribution of residual ligands to the absorbance, which can be especially problematic in crude solutions or ill-purified dispersions (see Supporting Information, Section S5). In such cases, it is better to use the mean absorption coefficient or the molar extinction coefficients at 400 nm, and we have included the corresponding figures in Table 3 as well. When CsPbBr3 NCs are transferred from n-hexane to toluene, we observed a pronounced 9



absorbance increase of about 13 % (see Figure S5). From the data determined for n-hexane dispersions, we thus calculated an intrinsic absorption coefficient in toluene of 1.79×105 cm−1 at 335 nm (see Table 3). This value is close to the figure of 2.0×105 cm−1 reported by De Roo et al. 27 for CsPbBr3 NCs in toluene. Interestingly, while such a solvent-dependence of the intrinsic absorption coefficient is expected from a direct application of Maxwell-Garnett theory, 8 it is rarely observed in practice. In the case of CdSe QDs, for example, hardly any variation of the absorption coefficient was observed when comparing different apolar solvents. 6,34,35 Possibly, this difference reflects the dilute, dynamic ligand shell of CsPbBr3 NCs, 27 which makes that solvent molecules can reach the QD surface more easily. Importantly, the absorption coefficients obtained here deviate strongly from the ones reported by luminescence saturation experiments. 24,25 For example, Castaneda et al. deduce a value of about 0.5×104 cm−1 at 400 nm, which is about 15 times smaller than the value of 7.7×104 cm−1 we obtain by normalizing the absorption spectra at 335 nm using µi, 335 nm . This suggests that the state-filling argumentation, originally developed for strongly confined colloidal QDs, does not hold for the CsPbBr3 NCs studied by Castaneda et al.. The large deviation demonstrates the importance of an assumption-free method to determine absorption coefficients of perovskite nanocrystals, which is key to any quantitative analysis of the optical properties of such materials after photo-excitation.

In conclusion, we determined the intrinsic absorption coefficient µi of CsPbBr3 NCs by combining elemental analysis and absorption spectroscopy. Although we find that the composition of the NCs depends on their size, we find that µi is size independent within the 4–11 nm size range analyzed here. Importantly, we observe that the intrinsic absorption coefficient shows a pronounced dependence on the refractive index of the solvent, which necessitates a proper recalculation when measurements involve solvents other than n-hexane or toluene as studied here. As µi can be readily converted into the molar absorption coefficient or the absorption cross section of CsPbBr3 NCs, our results show that the intrinsic absorption coefficient is a

10


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most convenient quantity to quantify light absorption by CsPbBr3 NCs.

Acknowledgement ZH acknowledges support by the European Commission via the Marie-Sklodowska Curie action Phonsi (H2020-MSCA-ITN-642656) and the Marie Sklodowska-Curie Action Compass (H2020 MSCA-RISE-691185). ZH acknowledges the Research Foundation Flanders (project 17006602), IWT-Vlaanderen (SBO-MIRIS) and Ghent University (GOA no. 01G01513). PG acknowledges the FWO-Vlaanderen for a fellowship and an equipment grant (12K8216N). ED acknowledges IWT-Vlaanderen for financial support.

Supporting Information Available The Supplementary Information contains synthesis, purification and size-selective precipitation methods, along with XRD and NMR spectra of size-selective precipiated fractions; size histograms, used to construct the sizing curve and a alternative sizing curve; and details about the elemental analysis and the calculation of the absorption coefficients.

This material is available free of charge via the Internet at http://pubs.acs.org/.

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Light Absorption Coefficient of CsPbBr3 Perovskite Nanocrystals - The

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