Elisabetta Neri
email: eneri@uliege.be

Caroline Bouvier

Laurence De Viguerie

Alain Brunelle

Nesrine Nasr

Fathi Béjaoui

François Baratte

Philippe Walter

Wax finishing in Roman polychrome statuary

Keywords: beeswax, ganosis, statues, TOF-SIMS 13

The material evidence for the wax finish on ancient marble statues, known as ganosis, is scarce and 3 controversial, although Greek and Latin sources describe the recipes and cultural value of this treatment. 4

The surface treatment of a colossal Roman head from the Roman theatre of Dougga (Tunisia), dated to the end 5 of the second century CE, is studied by a multi-analytical protocol (video-microscope, cross section, and time-6 of-flight secondary ion mass spectrometry of one sample). The results of this physico-chemical analysis and the 7 comparison with ancient recipes, prove the use of ganosis on a Roman statue and explore, for the first time, the 8 application of the recipes described in ancient sources. This result shows the potential of the Time-of-Flight 9 Secondary Ion Mass Spectrometry analysis, detecting at the same time organic and inorganic materials and their 10 stratigraphy, to study the ancient recipes.

11 12

1.

Introduction

16 17
The polychromy of Roman statues is increasingly documented thanks to remarkable work 18 carried out in the last 20 years, which has revealed the original appearance of painted statues

19
thanks to the analysis of the pigments [START_REF] Abbe | Polychromy[END_REF][START_REF] Østergaard | Polychromy of Greek and Roman sculptural[END_REF]. Conversely, the binders are less well employed and the recipes followed for the application of the wax on the wall and on the 27 statues, and these have been long interpreted and debated [START_REF] Stacey | Ancient encaustic: An experimental exploration of 313 technology, ageing behaviour and approaches to analytical investigation[END_REF][START_REF] Freccero | Wax paint and Punic wax -research and experiment[END_REF][START_REF] Omarini | Encausto: Storia, Tecniche e Ricerche = Encaustic: History, Technique 319 and Research[END_REF]. Pliny distinguishes two 28 older methods (Naturalis Historia, 35, 41) and one invented by Carthaginians for ships, the 29 so-called "Punic wax". The first two methods consist in applying the hot wax in its molten 30 state using a kind of broad-ended iron spatula-like tool (cauterium) or a punch (cestrum). The 31 third method requires the application of the cold wax as a saponified emulsion. According to 32 the recipe for the preparation of this emulsion (Naturalis historia, 21, 149), the wax is made 33 soluble by boiling it in sea water with nitrum, a sodium carbonate. The process for its 34 application on the statues is referred to in Vitruvius (De architectura, 7, 9, 3-4) and repeated 35 by Pliny (Naturalis Historia 33, 122): punic wax and oil were mixed and applied with a 36 brush, then charcoal was used to heat the surface and partially melt the coating to guarantee a 37 better penetration and, finally, it is polished using candles and a white cloth. Greek sources 38 attribute a ritual importance to the act of covering statues with wax [START_REF] Leka | La thérapéia des scultpures en Grèce ancienne : le témoignage des sources 321 textuelles[END_REF]. Some sources, such as both inorganic and organic materials from the analysed surface on a sub-micrometre scale.

94

The mass spectrum allows identification, and in addition the imaging spatially separates the 95 information, which gives the localisation of the identified compounds. Combining the two, we 96 can then access the individual composition of each layer in a stratigraphy. The recorded ion 97 images reveal spatial information with a 390 nm pixel size [START_REF] Sanyova | Unexpected 363 materials in a Rembrandt painting characterized by high spatial resolution cluster-TOF-SIMS 364 imaging[END_REF][START_REF] Richardin | Identification of different 366 copper green pigments in Renaissance paintings by cluster-TOF-SIMS imaging analysis[END_REF] and the mass spectra are 98 generated with a mass resolution (that is M/M, FWHM) of a few thousands thanks to the 99 delayed extraction of secondary ions with which the instrument is equipped [START_REF] Vanbellingen | Time-369 of-flight secondary ion mass spectrometry imaging of biological samples with delayed 370 extraction for high mass and high spatial resolutions[END_REF]. Micrometre 100 size pigment grains can be identified [START_REF] Noun | 373 High mass and spatial resolution mass spectrometry imaging of Nicolas Poussin painting 374 cross-section by cluster-TOF-SIMS[END_REF], and layers thinner than 10 µm are adequately 101 resolved so their composition can be discriminated in the spectral data using regions of 102 interest (ROIs).

103

The TOF-SIMS analyses were performed on a TOF-SIMS IV (IONTOF GmbH, Germany) in The GCIB was used to clean the sample surface in the instrument chamber prior to analysis.

111

The source was tuned to emit a beam of 2000 Ar atoms clusters with a total kinetic energy of which is lost when using BA+DE. In this latter case, the mass calibration is refined by using 125 known heavy ions peaks from the marble, like CamOn + in positive ion mode and CanOm -in 126 negative ion mode (m>n).

127

Two areas (see Fig. 3) were imaged with TOF-SIMS, spanning all the stratigraphy: marble, 128 pigmented red layer, first finishing layer, second finishing layer. To help identify which 129 secondary ions are to be sought in the sample spectra in order to then identify the ingredients, 130 reference compounds were analysed in the same analytical conditions: modern beeswax,

131
The visual examination shows the remains of colours in lips (red), hair (black), nose (yellow).

147

These traces of colour could also be observed with the video-microscope: black in the eyes 153

The micro-sample taken between the lips shows a red layer above the marble layer, and two 154 white layers on top of this one, slightly fluorescent (fig. 3).

155

The TOF-SIMS data give access to the chemical composition and the stratigraphy of the 156 different layers in the two areas analysed, which were chosen so as to include all the layers, 157 from the marble to the uppermost surface. Their composition, identified by the detection of 158 characteristic ions,attested also in the modern standard references with wellknown 159 compositions, are described in Table 1.

160
The hematite is identified through iron peaks, the pure beeswax is identified through the The analysis indicates that the marble is covered by a layer made of grains of haematite with 169 "Punic wax" as the binder (fig. 4). In the superficial white layers calcium and lead are not 170 detected, which rules out the presence of white paint in these two layers. The red pigment 171 layer is covered with a layer of "Punic wax" which is in turn covered with a layer of pure 172 beeswax.

Comparing the reference mass spectra with those extracted from the different layers of the 174 samples, as shown in Fig. 4 al. [START_REF] Regert | Chemical alteration and use of 376 beeswax through time: accelerated ageing tests and analysis of archaeological samples from 377 various environmental contexts[END_REF], whose study aimed at understanding the composition of ancient beeswax residues, 193 make no mention of the apparition of such sodium-containing compounds, so another 194 explanation could be that the wax used had a slightly different composition than the 195 references, or that the natron contained some impurities.

196

The comparison between the negative ion mass spectra extracted from the two superficial The analysis of this sample not only confirms the use of wax as a binder and a protecting

Click here to access/download;Figure

Click here to access/download;Figure

Click here to access/download;Figure

20 documented

 20 ; egg, proteinaceous and beeswax binders are rarely detected on the statues[START_REF] Brecoulaki | Characterization 304 of organic media in the wall-paintings of the "Palace of Nestor" at Pylos, Greece: evidence 305 for a secco painting techniques in the Bronze Age[END_REF][START_REF] Brøns | 308 Painting the Palace of Apries I: ancient binding media and coatings of the reliefs from the 309 Palace of Apries, Lower Egypt[END_REF] 21 although many Greek and Latin written sources (Plutarch, Quaest. Rom., 287 b-d; Ovid, Fasti 22 III, 831; Lucian, Imagines 23; Eusebius, Vita Costantini, I, 13) describe the use of wax, and a 23 technique called ganosis. This wax finishing was specifically employed to fix a chromatic 24 rendering, offering a weather-resistant protection for the statues which frequently stood out of 25 doors. In particular, Pliny the Elder and Vitruvius offer further details about the type of wax26

39

  Plutarch (Moralia, 287b-c et d), consider it as a ritual procedure (therapeia) reserved to 40 statues which are part of religious rites, and carried out before religious holidays. However,41Vitruvius and Pliny, referring to the application of ganosis to wall painting, do not specify 42 whether this practice was still ongoing as part of ritual care. 43 Despite this specific ancient literature and the detailed descriptions, material evidence relating 44 to the use of Punic wax on statues has not been recognised with any certainty. The use of 45 encaustic painting with Punic wax, widely documented in the series of portraits of the Fayum and UV light. A micro-sample was taken from the lips, embedded in an epoxy resin polished 89 and observed with a Nikon Eclipse LV100ND microscope under different light conditions. 90 This sample was analysed by TOF-SIMS to investigate the nature of the pigments and binders 91 in the different layers. Each layer can be examined independently thanks to the imaging 92 abilities of the TOF-SIMS technique, giving simultaneous localisation and identification of 93

104the

  Laboratory of Molecular and Structural Archaeology (LAMS, CNRS -Sorbonne 105 University, Paris, France). The raw data were acquired using SurfaceLab 6.7 software 106 (IONTOF GmbH, Germany) and processed with SurfaceLab 7.0. The instrument is equipped 107 with two ion sources. A Liquid Metal Ion Gun (LMIG) serves as the primary ion source for 108 analysis purposes, while an argon Gas Cluster Ion Beam (GCIB) allows one to gently sputter 109 the surface without damaging the underlying layers.

  110

112 10 keV

 10 , and the sputtered area was a square more than twice the size of the analysed area, to 113 avoid border effects of the cleaning step. The contaminants on the surface were sputtered, as 114 shown by the decrease of the signal associated to the SiC3H9 + ion (m/z 73.05) coming from 115 the recurring surface plastic additive polydimethylsiloxane (PDMS). After that step, the 116 cleaned surface was analysed using the LMIG tuned to emit a bismuth cluster pulsed ion 117 beam of 25 keV kinetic energy (Bi3 + ), impacting the surface at an angle of 45°. A low energy 118 electron flood gun neutralizes the residual charges on the surface between the various steps of 119 the analysis. 120 The analyses were carried out with the so-called "burst alignment with delayed extraction" 121 (BA+DE) focusing mode of the LMIG beam, giving the best spatial resolution on this 122 instrument. The focusing mode termed "high current bunched" (HCBU) was used in parallel 123 to calibrate the mass spectra, thanks to the linearity between the time-of-flight and the m/z, 124

148

  and the eyebrows, red partially superimposed on yellow on the lips, brown and black in the 149 hair with some blue points between the nape and the hair (fig.2). The skin displayed a yellow 150 treatment. A slight fluorescence was observed under UV illumination in the skin, lips, hair 151 and in the forehead. Some parts of the statue were particularly accentuated, such as the eyes, 152 lips and hair.

197

  layers and the reference mass spectra of beeswax, saponified wax and pure natron (fig. 5a) 198 allows one to discriminate the localisation of the Punic wax in the stratigraphy, thanks to the 199 characteristic ions detected in the Punic wax and not in beeswax. These ions are detected in 200 the paint layer and the one above it, while only the beeswax markers are detected in the 201 uppermost layer. 202 The spatial distribution of the components corresponds to the stratigraphy observed in the 203 cross section (marble, painting and two white layers) (fig. 3; fig. 5e), showing the localisation 204 of Punic wax and beeswax respectively in the lower and upper white layer. The analysis 205 suggests the use of Punic wax as the binder, since it is mixed with haematite in the paint layer, 206 and as a protecting agent, notably in the surface. The presence and the distribution of Punic 207 wax in these two layers are corroborated by the distribution of the markers of the sodium 208 carbonate reference. The distribution of sodium-containing ions has in fact the same shape as 209 these red and white layers superimposed on the marble. The use of hematite in the lower layer 210 is consistent with the shadowing using brown-red pigments, as formerly observed by Delaney 211 et. al on ancient techniques [26].212 213

263 Fig. 1 :

 2631 Fig. 1: The context of the discovery of the statue analysed: the theatre of Dougga. (a) Plan

Fig. 2 :Fig. 3

 23 Fig. 2: (a) Head of male statue from Dougga (Inv. 010326 14) in its actual state of

  280

Fig. 4 :Fig. 5 :

 45 Fig. 4: Mass spectra from the analysed areas of the statue sample, and reference compounds:

Figure 4 (

 4 Figure 4 (a, b, c)

  , the spectra from both analysed areas (showing positive ions for 175 area A and negative ions for area B), are comparable to the reference spectra of pure beeswax, 176 haematite-rich ochre (Kremer Pigmente) and dolomite marble (Kremer Pigmente), in the 177 positive ion mode; and pure beeswax, saponified wax and sodium carbonate (dehydrated Other ions like those at m/z 473, 509, 557 and 767 are detected in the sample but not in the 180 reference. As described by Stacey et al. [5], compounds like sodium carboxylate are formed in 181 the preparation processes both in cases of Punic wax and alkali-treated wax, but the 182 composition of the media is dependent on the treatments made. It is therefore difficult to link 183 the detection of a compound to a specific processing technique. In this work, we show that the 184 two layers containing wax are however distinguishable through the detection of sodium 185 carbonate characteristic ions, only present in the deeper layer, suggesting a difference in 186 preparation. As free fatty acids are also detected, it can suggest that the wax was not fully

	178
	natron), in the negative ion mode.

179 187 saponified, explaining why we are able to detect natron characteristic ions as well.

188

However, these ions mentioned in the previous paragraph can be attributed to the adducts of 189 the beeswax characteristic ion C24H57O2 -with several sodium-containing ions. Such 190 compounds could be explained by a long-term degradation process due to the reaction 191 between wax molecules and natron, consistent with their absence in the reference.

Regert et 192

  with beeswax candles is performed. A change in the application 218 technique can be deduced from the comparison between this treatment and the two other 219 Hellenistic statues in which the presence of wax is attested[START_REF] Sargent | The Technical Investigation of Sculptural Polychromy 330 at the Ny Carlsberg Glyptotek 2009-2010 -An Outline[END_REF][START_REF] Bourgeois | Re)peindre, dorer, cirer. La thérapéia en acte dans la sculpture grecque 334 hellenistique[END_REF][START_REF] Balcar | Caracterisation d'une cire d'abeille sur un 337 portrait en marbre antique dit de Berenice II[END_REF]. If the wax is applied 220 hot in the two Hellenistic statues, in the Dougga head it is the cold technique that is employed 221 with the Punic wax. This proves that the recipe transmitted by the Roman Imperial written In the colossal head of Dougga the act of covering the painted surface of first covering the 225 painted surface with Punic wax, and then again with Punic wax before a final polish with 226 beeswax, is a remarkable effort, because paintings with wax were highly prized[25, p. 67].

	222
	223	sources is not only a literary tradition, but that the recipe is actually followed in practice at
		least until the end of second century CE.
	227
	228	Moreover, the finishing with wax has undoubtedly a practical function, as a fixing and
		protecting agent for the colour.

214

agent, but also shows that the recipes described by Vitruvius and Pliny (De architectura, 7, 9, 215 3-4; Naturalis Historia 33, 122) are applied to this second-third-century African statue.

216

According to the recipes, the Punic wax is applied at first with a brush on the pigment, and 217 secondly a polishing 224

Table 1 :

 1 Table1for wax (red), and for natron (blue). The images on the right 293 are their overlays. Images have a 50 µm side for zone A and a 100 µm side for zone B. The Characteristic ions from reference mass spectra and detected in the sample.

	296
	297
	298

294

layers are delineated with dotted white lines to guide the eye. 295

Table 1 :

 1 Characteristic ions from reference mass spectra and detected in the sample

	Measured m/z			Detected in…
	: standard deviation (ppm)	Characteristic ions for positive polarity (tentative assignments)	Reference	Sample
	m/z	 (ppm)
	39.96	15	Ca +
	56.96 79.94	-51 -15	H(CaO) + and associated H(CaO)n + (n=2-7) m/z 112.92, 168.88, 224.84, 280.79, 336.75, 392.71 Mg(CaO) + and associated Mg(CaO)n + (n=2-7) m/z 135.90, 191.85, 247.83, 303.76, 359.73, 415.68	Marble Kremer Pigmente n°58740	Layer
	95.92	40	Ca(CaO) + and associated Ca(CaO)n + (n=2-5) m/z 151.88, 207.84, 263.80, 319.74
	55.93 111.87 72.94	-50 30 -14	Fe + Fe2 + FeOH + and associated H(FeO)n + (n=2-3) m/z 144.87, 216.80	Hematite Kremer Pigmente n°40510	Layer (particles below 5 µm)
	257.26	8	C15H31CO2H2 +
	285.26	-30	C15H31CO2HC2H5 +
	355.29	-93	C15H31CO2H(CH2)6CH3 +
	369.34	-79	C15H31CO2H(CH2)7CH3 +
	383.32	-99	C15H31CO2H(CH2)8CH3 +
	353.35 367.32 381.35 395.39		C15H31CO2(CH2)n +	n=7 or m=23 n=8 or m=24 n=9 or m=25 n=10 or m=26	Beeswax (pure)	Layer Layer Layer
	409.41		or	n=11or m=27
	423.38		O(CH2)mCH3 +	n=12 or m=28
	437.40		n=13 or m=29 (C30H61O + )
	451.41			n=14
	465.43			n=15
	Measured m/z			Detected in…
	: standard deviation (ppm)	Characteristic ions for negative polarity (tentative assignments)	Reference	Sample
	m/z	 (ppm)
	297.26			n=3 or m=19
	311.28			n=4 or m=20
	325.30			n=5 or m=21
	339.32			n=6 or m=22
	353.34			n=7 or m=23
	367.36			n=8 or m=24
	381.37 395.39 409.46 423.41		C15H31CO2(CH2)n -or O(CH2)mCH3 -	n=9 or m=25 n=10 or m=26 n=11or m=27 n=12 or m=28	Beeswax (pure)	Layer Layer Layer
	437.44		n=13 or m=29 (C30H61O + )
	451.45	55		n=14
	465.47	7		n=15
	479.48	83		n=16
	493.48	-88		n=17
	507.51	2		n=18
	673.67	78	C15H31COOC30H58 -

Table 1

 1 Click here to access/download;Table;Table 1.docx

	82.98	37	NaCO3 -
	137.96	30	Na2CO5 -
	154.97	63	Na2CO6H -
	162.96 178.96 188.95	35 37 30	NaO5CO3 -Na2(CO2)3H -Na3(CO3)2 -	Beeswax (saponified) *	Layer Layer
	294.90	-11	Na5(CO3)3 -
	334.91	25	Na6(CO3)3OH
	356.88	25	Na7(CO3)3O -
	66.98	7	NaCO2 -and associated NanCOm -(n=1-2 ; m=2-5) m/z 82.98, 89.98, 98.97, 105.97, 121.96, 137.96
	156.95	-18	Na3(CO2)2 -
	268.91 308.91	43 4	Na7CO6 -Na3(CO3)4 -	Natron (pure)	Layer Layer
	334.90	-25	Na6(CO3)3OH
	356.89	-32	Na7(CO3)3O -
	400.87	5	Na7(CO3)4 -

139-141, n° 116, pl. 143-144].

la Recherche (France, grant ANR-2015-CE29-0007 DEFIMAGE). This project has received funding from the

European Union's Horizon 2020 research and innovation programme (grant agreement "PolyCRomA: No.

to EN). The funding organisation had no influence in the study design, data collection and analysis, 258 decision to publish, or preparation of the manuscript.

Acknowledgements

248

Faouzi Mahfoudh, director of INP at Tunis, and Fatma Nait Yghil, director of Bardo museum, are warmly

Polychromy and Greek and Roman Sculpture in the Ny Carlsberg Glyptotek. Report


domain: spi chim phys

text:
Villamil Franco

Benoit Mahler

Christian Cornaggia

Thomas Gustavsson

Author Names Carolina

Benoît Mahler

Elsa Cassette

Auger Recombination And Multiple Exciton Generation In Colloidal Two-Dimensional Perovskite Nanoplatelets: Implications For Light-Emitting Devices

Keywords: Halide perovskite, quantum confinement, Auger recombination, multiple exciton generation, 2D nanoplatelets

Auger recombination and multiple exciton generation in colloidal two-dimensional perovskite nanoplatelets: Implications for light-emitting devices

Carolina

INTRODUCTION

By combining strong photoluminescence, color purity and enhanced stability with easy and cheap solution-processing fabrication, two-dimensional (2D) halide perovskites have taken a central role in the development of electroluminescent diodes (LEDs), laser gain media or singlephoton sources. 1 3 For all these various light-emitting devices, understanding the excitonexciton annihilation process, which ultimately limits the exciton density in these materials, is essential in order to control the device performances. For example, lasing threshold and LED efficiency are affected by the rapid non-radiative Auger recombination (AR) rate that limits the maximum electron-hole pair density in the photoactive material. [START_REF] She | Low-Threshold Stimulated Emission Using Colloidal Quantum Wells[END_REF] It is well established that AR is the dominant recombination process that occurs in semiconductor nanostructures under highexcitation density. [START_REF] Klimov | Multicarrier Interactions in Semiconductor Nanocrystals in Relation to the Phenomena of Auger Recombination and Carrier Multiplication[END_REF][START_REF] Klimov | Spectral and Dynamical Properties of Multiexcitons in Semiconductor Page 27 of 33 ACS Paragon Plus Environment ACS Applied Nano Materials Nanocrystals[END_REF] Over the last few years, AR has been the subject of several investigations in weakly-confined colloidal perovskite nanocrystals (NCs). 7 9 However, studies in strongly confined 2D perovskite samples are limited to a few cases: methylammonium lead iodide (MAPI) 2D layered thin films [START_REF] Delport | Exciton-Exciton Annihilation in Two-Dimensional Halide Perovskites at Room Temperature[END_REF][START_REF] Deng | Long-Range Exciton Transport and Slow Annihilation in Two-Dimensional Hybrid Perovskites[END_REF] and 5 monolayers (MLs) CsPbBr 3 nanoplatelets (NPLs). [START_REF] Li | Size-and Morphology-Dependent Auger Recombination in CsPbBr 3 Perovskite Two-Dimensional Nanoplatelets and One-Dimensional Nanorods[END_REF][START_REF] Vale | Biexciton, and Hot Exciton Dynamics in CsPbBr3 Colloidal Nanoplatelets. Page 28 of 33[END_REF] While an increase of the AR rate is expected with the increase of the Coulomb interactions in confined systems, a surprisingly slow bimolecular AR rate of a few 10 -4 and 10 -3 cm 2 /s was reported in 2D perovskite films in the strong confinement regime (1 to 5 MLs), leading to effective AR times on the order of hundreds of picoseconds to nanoseconds. [START_REF] Delport | Exciton-Exciton Annihilation in Two-Dimensional Halide Perovskites at Room Temperature[END_REF][START_REF] Deng | Long-Range Exciton Transport and Slow Annihilation in Two-Dimensional Hybrid Perovskites[END_REF] Interestingly, in a recent publication a decrease from 78 ps to 18 ps was reported in the effective biexcitonic recombination time of weakly-confined CsPbI 3 NCs (size 12.1 nm) compared to in morestrongly confined ones (6.2 nm). [START_REF] Cong | Carrier Multiplication and Hot-Carrier Cooling Dynamics in Quantum-Confined CsPbI3 Perovskite Nanocrystals[END_REF] Depending on the nature of the photoexcited species (free charge carrier or excitons), the AR process will follow third-or second-order kinetics. [START_REF] Pelant | Luminescence Spectroscopy of Semiconductors[END_REF][START_REF] Klimov | Nanocrystal Quantum Dots -2nd Edition[END_REF] Besides, the anisotropic geometry of a system like the 2D quantum wells can induce further Page 3 of 33 ACS Paragon Plus Environment ACS Applied Nano Materials modifications in the measured kinetics such as asymmetric exciton-exciton interactions [START_REF] Klimov | Scaling of Multiexciton Lifetimes in Semiconductor Nanocrystals[END_REF] and diffusion-limited recombination. [START_REF] Deng | Long-Range Exciton Transport and Slow Annihilation in Two-Dimensional Hybrid Perovskites[END_REF][START_REF] Li | Exciton Spatial Coherence and Optical Gain in Colloidal Two-Dimensional Cadmium Chalcogenide Nanoplatelets[END_REF] Here, we studied the multiple exciton dynamics in strongly-confined lead iodide colloidal NPLs of 2 and 3 MLs by varying the excitation fluence from less than one to tens of μJ/cm 2 . We found a fast intrinsic AR rate with a corresponding effective recombination time of less than 10 ps at high exciton density (> 5×10 11 cm -2 ) while exciton diffusion slows down the AR process to hundreds of ps when the initial exciton density is low.

We also studied the formation of multiple excitons in these NPL samples by observing the AR that occurs after high photon energy and low fluence excitation. So far, multiple exciton generation (MEG) has only been observed in weakly-confined iodide-based perovskite nanocrystals, CsPbI 3, and FAPbI 3 , using transient absorption spectroscopy. [START_REF] Cong | Carrier Multiplication and Hot-Carrier Cooling Dynamics in Quantum-Confined CsPbI3 Perovskite Nanocrystals[END_REF][START_REF] Li | Low Threshold and Efficient Multiple Exciton Generation in Halide Perovskite Nanocrystals[END_REF][START_REF] De Weerd | Efficient Carrier Multiplication in CsPbI 3 Perovskite Nanocrystals[END_REF] These measurements are always very sensitive to photo-charging effects and/or a misinterpretation as a result of a too high excitation fluence. [START_REF] Smith | Multiple Exciton Generation in Colloidal Nanocrystals[END_REF] Surprisingly, Klimov and coworkers did not observed any MEG signatures in Cs-based perovskite NCs using time-resolved photoluminescence (TR-PL) techniques. [START_REF] Makarov | Spectral and Dynamical Properties of Single Excitons, Biexcitons, and Trions in Cesium Lead-Halide Perovskite Quantum Dots[END_REF] Here, we show that MEG induces a fast AR rate in 3 ML-thick NPLs due to the proximity of the two geminate excitons, that can be easily isolated from other nonradiative recombinations.

EXPERIMENTAL SECTION

Perovskite Nanoplatelets synthesis. All the commercially available chemicals used for the synthesis of colloidal perovskite nanostructures are listed in the Supporting Information (SI). Thin perovskite nanoplatelets were synthesized at room temperature by precipitation by injecting the precursor solution into a non-polar solvent, here the toluene (see full details in the SI). Time-correlated single photon counting (TCSPC). We used a mode-locked Ti:Sapphire (MIRA 900, Coherent) pumped by a solid state laser (VERDI V10, Coherent) and providing 120 fs pulses tunable between 720 and 950 nm (about 2 W at 800 nm), at 76 MHz repetition rate. The rate was reduced to 200 kHz using a pulse picker (Model 9200, Coherent). The output pulse train was subsequently frequency-doubled, providing 400 nm pulses. The polarization of the excitation beam was controlled by a Fresnel rhomb (EKSMA) and set parallel to the detection. The fluorescence was collected on a monochromator (HR250, Jobin-Yvon). A Schott WG 420 filter was positioned in front of the entrance slit in order to cut the diffused excitation light. The fluorescence was detected with a microchannel plate photomultiplier (R1564 U, Hamamatsu). The temporal resolution is about 60 ps with a time window < 100 ns. To avoid photodegradation, the samples were continuously refreshed using a circulating system and a stirred bar in a 3 mm quartz cell.

Transient Absorption (TA). All measurements of the colloidal perovskite nanostructures were carried out at room temperature in a 1 mm-thick flow cell connected to a peristaltic pump in order to refresh the sample at the focus position to avoid photodamage and photocharging effects. Flexible and organic solvent compatible F-5500-A fluoroelastomer (Saint-Gobain®) tubing and Teflon adaptors were used to build the flow system. The employed sample solutions were prepared with optical density (OD) below 0.3 at the excitation wavelength and above in anhydrous toluene (or chloroform). We used a home-built TA fs spectrometer with an initial Ti:Sa laser source at 3 kHz, 40 fs and about 2 W to generate a tunable excitation in the 500-650 nm range with a non-collinear optical parametric amplifier (NOPA) and a white-light (WL) continuum for the probe. The output of the NOPA, after a temporal compression involving chirped mirror pair and a double-prism compressor, can be frequency doubled using a set of lens, a BBO crystals and polarizers to filter out the residual visible beam. The temporal resolution is about 100 fs in the visible and about 300 fs for the UV experiments. The maximum pump-probe time delay that can be reached is about 3.2 ns using a long delay line with a retroreflector mounted on a motorized stage (60 cm long, minimum step 200 nm, IMS600CCHA from Newport). The continuum probe beam was filtered to remove the fundamental 800 nm and reduced in intensity by a neutral density filter. Both pump and probe were set vertical in polarization using broadband half-waveplates. The repetition rate of the pump is reduced to half (1.5 kHz) to block one pulse out of two, allowing for measures with and without the pump.

The continuum spectrum was registered at 3 kHz by a commercial spectrograph (IsoPlane 160, Princeton Instruments) coupled to a CCD camera (ProEM-HS 1024B, Princeton Instruments).

To measure a spectrum of 1024 pixels at 3 kHz with the CCD camera (3000 frames/s), we use a fast-custom acquisition mode with a vertical binning of 64 pixels (13 µm each) over the region of interest (ROI) closest to the chip and an exposure time of 1 µs. The TA signal was calculated as follow:

, with I(λ,t) the WL spectrum measured

( , ) = - 1 ∑ -1 = 0 2 ( , ) - ( ) 2 + 1 ( , ) - ( )
at a pump-probe time delay t with the pump ON for a pulse 2k (even) and the pump OFF for exfoliation procedures used in previously reported hybrid colloidal NPLs, [START_REF] Hintermayr | Accelerated Carrier Relaxation through Reduced Coulomb Screening in Two-Dimensional Halide Perovskite Nanoplatelets[END_REF][START_REF] Levchuk | Brightly Luminescent and Color-Tunable Formamidinium Lead Halide Perovskite FAPbX 3 (X = Cl, Br, I) Colloidal Nanocrystals[END_REF] the direct solution approach allows a more well-defined population (i.e. number of monolayers) in thinner NPLs. The steady-state absorption and photoluminescence (PL) spectra of the synthesized NPLs dispersed in toluene are shown in Figure 1. For each sample, the energy corresponding to the first exciton transition matches the previous reports of strongly confined 2D NPLs and thin films 25 27 . Except for CsPI n=2, all NPL samples present lateral dimensions from hundreds of nanometers to a few micrometers (see SI) and thus confinement in these dimensions can be The constant value of the long component τ 3 for all excitation fluences shows that the PL signal detected at several ns is mainly associated to mono-exciton recombination. Indeed, recombination of free charge carriers will lead to bimolecular recombination, as previously observed in bulk halide perovskites. [START_REF] Johnston | Hybrid Perovskites for Photovoltaics: Charge-Carrier Recombination, Diffusion, and Radiative Efficiencies[END_REF] The amplitudes associated with this long component saturate much faster than the total amplitudes (i.e. intensity at time t=0), as seen in Figure S3 in the SI for MAPI n=3. This means that while a high excitation fluence can generate several excitons within a single NPL, multiexciton recombinations are efficient enough to reduce the dynamics (Figure 2b), in line with previous reports. 8,31 33 The decrease of the corresponding effective multiexciton decay times τ 1 and τ 2 with the initial number of created excitons is expected for quadratic multi-exciton recombination (see discussion below). As these time constants are on the order of hundreds to tens of ps, they correspond to non-radiative AR rather than radiative biexcitonic recombination (see discussion in SI). Here, trion dynamics, which corresponds to another kind of Auger recombination can be neglected since the samples were circulated within the 3 mm-cell and the repetition rate decreased to 200 kHz to prevent from photo-charging and photo-degradation effects. [START_REF] Klimov | Multicarrier Interactions in Semiconductor Nanocrystals in Relation to the Phenomena of Auger Recombination and Carrier Multiplication[END_REF][START_REF] Binks | Multiple Exciton Generation in Nanocrystal Quantum Dots -Controversy, Current Status and Future Prospects[END_REF] If the main excited species are excitonic, AR follows bimolecular recombination kinetics: [START_REF] Pelant | Luminescence Spectroscopy of Semiconductors[END_REF] [1] = -( ) [START_REF] Zhang | Advances in Small Perovskite-Based Lasers[END_REF] with ñ(t) the time-dependent exciton density and β the bimolecular AR rate. For highly asymmetric 2D nanostructures, the exciton density is surfacic (number of excitons N per NPL surface, in cm -2 ), such as β is typically displayed in cm 2 /s. We note that a factor ½ should normally be added in front of β because, for relatively low excitation photon energy, the reexcited exciton is not ionized and relax back to the band-edge at a cooling rate expected much higher than the AR rate. We note however that this factor was not taken into account previously so for a fair comparison we intentionally omit it.

The bimolecular Auger recombination requires a sufficiently high density of excitons to occur since it involves short-range exciton-exciton interactions that are described either by a collision process or a Förster energy transfer which scales as (1/d X-X ) [START_REF] Klimov | Spectral and Dynamical Properties of Multiexcitons in Semiconductor Page 27 of 33 ACS Paragon Plus Environment ACS Applied Nano Materials Nanocrystals[END_REF] , where d X-X is the distance between the excitons (one exciton transfers its energy to re-excite the other exciton). [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF] In the two limiting cases of immobile excitons (e.g. self-trapped excitons) [START_REF] Kirm | Exciton-Exciton Interactions in CdWO 4 Irradiated by Intense Femtosecond Vacuum Ultraviolet Pulses[END_REF] and large exciton delocalization length in the 2D plane (the wavefunction of the exciton center-of-mass motion extends well beyond [START_REF] Kunneman | Bimolecular Auger Recombination of Electron-Hole Pairs in Two-Dimensional CdSe and CdSe/CdZnS Core/Shell Nanoplatelets[END_REF]  is constant in time and the solution to the Equation 1 has the analytical form: [START_REF] Pelant | Luminescence Spectroscopy of Semiconductors[END_REF] Page 11 of 33

d x-x 2 ),
ACS Paragon Plus Environment ACS Applied Nano Materials [2] ( ) = (0) 1 + (0)
with ñ(0), the initial exciton density.

The measured PL intensity is proportional to the averaged instantaneous number of excitons N(t) and thus to the corresponding density ñ(t). We thus use the Equation 2 to fit the isolated multiexciton PL decay traces, by fixing the initial exciton density ñ(0) calculated from the excitation fluence and the linear absorption coefficient of the sample (Figure S4a in SI). The early-time TR-PL decay were well reproduced by the fit and we obtained an effective bimolecular AR rate β decreasing from 8.2 × 10 -2 to 1.1 × 10 -2 cm 2 /s with increasing excitation fluence from 0.15 to 15 μJ/cm 2 . These bimolecular AR rate values, listed in the first column of Table S6 in the SI, are plotted against the exciton density in Figure 3 (black squares). It is here worthwhile to note that the β values are orders of magnitude lower when using Equation S2 in the SI to fit the full PL decay, including both multi-and single-exciton dynamics (second column of Table S6 in SI), as reported by Huang and co. and Garrot and co.. [START_REF] Delport | Exciton-Exciton Annihilation in Two-Dimensional Halide Perovskites at Room Temperature[END_REF][START_REF] Deng | Long-Range Exciton Transport and Slow Annihilation in Two-Dimensional Hybrid Perovskites[END_REF] However, it is clear from the corresponding fits (Figure S4b), that these values are not representative of the multiexciton dynamics as the early time dynamics are not well reproduced. That is why we found important to fit the isolated multiexciton dynamics to extract the β values.

The experimental dynamics become faster when increasing the initial exciton density ñ(0), which is in agreement with the effective linear AR rates, extracted from the multi-exponential fit, increasing with the excitation fluence (Figure 3, red dots). This expresses a super-linear dependency of the kinetics related to multi-exciton dynamics depending on the exciton density.

As expected for a pure bimolecular recombination (cf Equation 1 and 2), the dynamics indeed become faster when increasing the initial exciton density. However, the corresponding bimolecular AR rate β should remain constant. The fact that the experimental β values extracted by bimolecular fits using Equation 2, decrease with the initial exciton density ñ(0), shows that the isolated multi-exciton dynamics deviate from bimolecular kinetics. In particular, it shows that the experimental kinetic dependency on ñ is sub-quadratic. This trend can be understood if the bimolecular AR rate β in Equation 1 is time-dependent. This is for example the case if the bimolecular AR is limited by the exciton diffusion in the 2D plane. In that case, the diffusion process reduces the dependency of the AR kinetics on the exciton density ñ. Indeed, excitons initially separated by distances larger than the typical reaction radius (i.e. moderated ñ(0)) will diffuse and eventually encounter, leading to an effective recombination.

Several works on the exciton-exciton annihilation at moderate excitation fluence in molecular systems presenting highly-limited delocalization length have included the random walk motion (diffusion) of the excitons before collision and resulting exciton-exciton recombination, at moderate excitation fluence. [START_REF] Deng | Long-Range Exciton Transport and Slow Annihilation in Two-Dimensional Hybrid Perovskites[END_REF][START_REF] Gösele | Anisotropic Diffusion, Long-Range Energy Transfer and Bimolecular Exciton Recombination Kinetics[END_REF] For example, in one-dimensional systems such as linear Jaggregates, the bimolecular rate β(t) is predicted to have a t -1/2 dependency. [START_REF] Burgel | The Ultrafast Dynamics of Aggregate Excitons in Water[END_REF] Excitons in 2D halide perovskites are expected to be much more spatially delocalized than their counterparts in molecular systems. However, due to the ionic nature of the perovskite structure, excitons in 2D perovskite structures might present reduced delocalization length along the 2D plane compared to transition metal dichalcogenides (MoS 2 , WSe 2 , etc&) or II-VI semiconductors such as CdSe. To the best of our knowledge, the effect of the exciton diffusion on the excitonexciton annihilation process in perovskite nanostructures has only been discussed by Li et al.

and Deng et al.. [START_REF] Deng | Long-Range Exciton Transport and Slow Annihilation in Two-Dimensional Hybrid Perovskites[END_REF][START_REF] Li | Size-and Morphology-Dependent Auger Recombination in CsPbBr 3 Perovskite Two-Dimensional Nanoplatelets and One-Dimensional Nanorods[END_REF] The former study did not investigate the evolution of the AR times with the excitation fluency but extracted the biexciton dynamics from transient absorption measurements on n=5 CsPbBr 3 NPLs with different lateral areas and found it very fast but sensitive to the NPL geometry (recombination time: 14 to 70 ps). [START_REF] Li | Size-and Morphology-Dependent Auger Recombination in CsPbBr 3 Perovskite Two-Dimensional Nanoplatelets and One-Dimensional Nanorods[END_REF] The latter work reported a transient absorption microscopy study of 2D layered (n=1 to 5) perovskite thin films. By comparing the diffusion constant and the AR rate extracted from their analysis, the authors concluded that the AR is reaction-limited and not diffusion-limited. [START_REF] Deng | Long-Range Exciton Transport and Slow Annihilation in Two-Dimensional Hybrid Perovskites[END_REF] Exponential functions are commonly used to fit the AR dynamics. [START_REF] Makarov | Spectral and Dynamical Properties of Single Excitons, Biexcitons, and Trions in Cesium Lead-Halide Perovskite Quantum Dots[END_REF][START_REF] Castañeda | Efficient Biexciton Interaction in Perovskite Quantum Dots Under Weak and Strong Confinement[END_REF][START_REF] Li | Size-and Morphology-Dependent Auger Recombination in CsPbBr 3 Perovskite Two-Dimensional Nanoplatelets and One-Dimensional Nanorods[END_REF][START_REF] Vale | Biexciton, and Hot Exciton Dynamics in CsPbBr3 Colloidal Nanoplatelets. Page 28 of 33[END_REF] In the absence of accurate analytical formula to describe the Equation 1 with time-dependent bimolecular AR rate, we found that the multiexponential fit was adapted to effectively fit the decay traces with high quality. In order to relate the AR rate in s -1 extracted from the multiexponential fit with the bimolecular AR rate in cm 2 /s, we introduce an effective AR rate, τ Auger, eff , which is the instantaneous rate that can be approximated by using the initial exciton density ñ(0), according to τ Auger,eff = 1/[β × ñ(0)]. The effective Auger recombination times are plotted against the initial exciton density for the four NPL samples in Figure S5 in the SI. It should be noted that τ Auger,eff calculated from β using Equation 2 cannot be uniquely identified with a specific term in the multiexponential fit. It describes the dynamics occurring over a broad range, from tens to hundreds of picosecond, that are described separately by τ 1 and τ 2 in the case of the multiexponential fit. For moderate exciton fluence, the results in Figure 3 clearly show a diffusion-limited excitonexciton annihilation process with decreasing bimolecular AR rate and increasing corresponding linear rate with ñ 0 . Furthermore, the values of the bimolecular AR rates in the order of 10 -2 cm 2 /s are consistent with the exciton diffusion constant reported by Prins and co. in the case of 2D lead iodide perovskite thin film based on butylammonium ligands. [START_REF] Seitz | Exciton Diffusion in Two-Dimensional Metal-Halide Perovskites[END_REF] From the trend of the effective linear and bimolecular AR rates, we found it more appropriate to use the multiexponential fit, clearly showing faster dynamics occurring at larger initial exciton density. We further note that the AR time is increasing in NPL samples with larger dimensionality: MAPI n=3 NPLs seem to present a much-reduced effective linear AR rate than FAPI and MAPI n=2

(Figure S5). Moreover, CsPI n=2 NPLs presenting a lateral confinement show the fastest AR dynamics at low exciton density, i.e. this latter sample displays an effective linear rate that is less diffusion-limited. We can conclude from these results that the diffusion constant is higher, or the exciton wavefunction delocalization in the 2D plane is larger, in more strongly-confined NPLs.

At higher excitation fluences, τ 1 and the effective AR lifetimes match. However, they attain asymptotically a limiting value that is comparable to the temporal resolution of our TCSPC setup (IRF about 60 ps). To determine the intrinsic AR rate (i.e. not diffusion-limited), we need to access the high fluence dynamics with a much higher temporal resolution. shows that the AR process can be described by a collision process (or a short-range energy transfer) without involving a recombination probability per collision. We further note that this sub-10 ps component is much faster compared to other nanomaterials such as II-VI and III-V semiconductors that typically have an AR time on the order of a few hundreds of picoseconds.

The second time component (τ 2 ) on the order of hundreds of ps is assigned to a diffusion-limited Auger recombination process. To further address how the multiexciton recombination rate depends on the exciton density in the two-dimensional perovskite structures, the corresponding inter-exciton distance d X-X can be calculated. In the case of MAPI n=3 NPLs, an additional component with a time constant on the order of hundreds of ps appears at excitation fluences as low as 1.3 µJ/cm 2 , corresponding to an initial exciton density of 3 × 10 10 cm -2 (calculation in the SI). This leads to an average inter-exciton distance d x-x ≈ 57 nm (center to center distance, see SI). In the same manner, we estimated the exciton-exciton distance from the excitation fluence where an ultrafast component as short as 10 ps becomes predominant (> 40 % in amplitude at 25 ± 4 µJ/cm 2 ). For this initial exciton density of (6 ± 2) × 10 11 cm -2 , d x-x ≈ 13 nm. For this distance only four to six times larger than the exciton Bohr radius a B reported for MAPbI 3 perovskite (a B < 3 nm 41 ), the excitons must overlap spatially as they recombine efficiently. Assuming an isotropic exciton delocalization in the 2D plane, we can estimate the coherent exciton radius a x (i.e. the characteristic size of the extent of delocalization of the exciton center-of-mass motion [START_REF] Li | Exciton Spatial Coherence and Optical Gain in Colloidal Two-Dimensional Cadmium Chalcogenide Nanoplatelets[END_REF] to be about d x-x,min /2 = 6.5 nm. For d x-x much larger than the delocalization length, we can only assume that the multiexciton AR rate is limited by the exciton diffusion in the 2D plane. In that case, the effective AR time depends strongly on the sample geometry. This could explain the range of AR rates reported by Li et al. in 5 ML-thick CsPbBr 3 NPLs with different lateral sizes, without the need of invoking a different AR probability per exciton collision. [START_REF] Li | Size-and Morphology-Dependent Auger Recombination in CsPbBr 3 Perovskite Two-Dimensional Nanoplatelets and One-Dimensional Nanorods[END_REF] It also means that the mono-exponential decay usually extracted for discrete biexcitonic to mono-excitonic recombination process in semiconductor nanostructures is not the intrinsic biexcitonic rate in anisotropic perovskite samples such as 2D NPLs. The intrinsic AR rate can only be obtained at high excitation fluence where the initial photogenerated excitons overlap before diffusion takes place (reaction-limited AR).

Multiple exciton generation in 2D NPLs. So far, the exciton-exciton interactions were probed at high excitation fluences, where each absorbed photon creates a unique electron-hole pair and TA dynamics (ΔA from PIB signal around 0.5 × 10 -3 ). The corresponding exciton density for 250 nm excitation was for example calculated to be less than 10 11 cm -2 (see SI with the full absorption spectrum of the sample Figure S8). The extracted PIB dynamics measured at the band-edge and normalized at long times are displayed in Figure 5a for six different excitation wavelengths. The corresponding fit parameters are in the The sum of amplitudes of the extra dynamics relative to the long one can be plotted versus the excitation energy relative to the optical bandgap one (hν/E 1exc ). This leads to an apparent number of excitons generated by a single photon (exciton generation quantum yield, QY), seen in Figure 5b (black squares), as previously reported for perovskite nanocrystals [START_REF] Cong | Carrier Multiplication and Hot-Carrier Cooling Dynamics in Quantum-Confined CsPbI3 Perovskite Nanocrystals[END_REF][START_REF] Li | Low Threshold and Efficient Multiple Exciton Generation in Halide Perovskite Nanocrystals[END_REF] and other semiconductor nanostructures. 42 44 From this plot, it seems that more than one exciton starts to be generated just below the theoretical threshold (1.98 ×E 1exc ) and the maximum MEG First, several experiments were performed to check that the short picosecond component did not arise from a solvent effect. The reason is that toluene starts to absorb light below 290 nm.

Attempts to re-disperse the n=3 NPLs or to synthesize them directly in chloroform (CHCl 3 ) solvent with negligible absorption in the whole UV range of interest, were unsuccessful.

Nevertheless, liquid scintillation experiments reveal that no emission could be detected from the perovskite NPLs after excitation of the toluene molecules, showing the absence of efficient energy transfer (see discussion in the SI). Furthermore, the direct synthesis of thinner MAPI n=2 NPLs in chloroform was possible and TA measurements on this sample do not show any picosecond component when exciting at 250 nm, even at higher excitation fluence (Figure S10a in SI). From our point of view, the MEG threshold was not reached in these materials excited under similar conditions to those used for MAPI n=3 NPLs, since they have a higher optical bandgap.

Instead, these NPLs show an intermediate component characterized by a time constant on the order of hundreds of ps after excitation at 250 nm, but having a much-reduced amplitude compared to the same NPLs dispersed in toluene (Figure S10a in SI). We interpret this result by the enhanced stability of the NPLs in chloroform versus toluene, which leads to a reduction of the intermediate component due to non-radiative pathways induced at high photon energy exposition. Similarly to the NPL n=3 sample in toluene, we found a much higher proportion of Reported observations of MEG in colloidal semiconductor nanostructures have often been controversial. That is essentially because the MEG process is not directly observed and the measurements are subject to artefacts, such as photo-charging effects leading to other Auger recombination process (trion-related). [START_REF] Klimov | Multicarrier Interactions in Semiconductor Nanocrystals in Relation to the Phenomena of Auger Recombination and Carrier Multiplication[END_REF] In addition, experiments should be performed as substantially lower excitation fluence to avoid the direct generation of multiple excitons via multiphoton absorption. Here, the smooth evolution between 260 and 270 nm of the toluene absorption (Figure S8) and of the MAPI n=3 NPL absorption cross section, cannot explain why the few picosecond component is only observed at 260 nm under similar excitation condition.

In perovskite NPLs, the strong dependence of the AR rate on the average inter-exciton distance due to the limited exciton delocalization length allows us to unambiguously rule out the possibility that the short ps component could result from an excessive excitation fluence.

Indeed, even if the low excitation fluencies used here can still generate more than one exciton per NPL (assuming a Poisson distribution [START_REF] Klimov | Nanocrystal Quantum Dots -2nd Edition[END_REF] ), the resulting Auger recombination rate will be at least one order of magnitude slower (diffusion-limited AR, see above). The calculated exciton density obtained for the 250 nm excitation of MAPI n=3 NPLs is found to be 10 11 cm -2 at maximum (see SI), which is an order of magnitude lower than the density needed to obtained the sub-10 ps component in the case of one photon generates a single exciton. On the contrary, multiple excitons photogenerated from a single high-energy photon will be spatially very close, Here, the limited exciton delocalization length in the 2D plane of the perovskite NPLs and their highly anisotropic shape allows to isolate the contribution of MEG-induced AR by its characteristically fast decay rate. Finally, we can notice that the measured threshold for MEG in n=3 NPLs is well above the theoretical limit of 2×E 1exc . This can explain why no biexciton generation could be observed in the n=2 NPL samples with larger confinement effects.

CONCLUSIONS

Page 4 of 33 ACS

 33 Paragon Plus Environment ACS Applied Nano Materials Steady-state optical characterization. Absorption measurements were carried out with a UV/Vis Lambda 850 spectrophotometer (Perkin Elmer) covering the 175-900 nm spectral range. Photoluminescence was carried out with a Fluorolog 3-22 spectrofluorometer (HORIBA JOBIN-YVON) equipped with a R928P photomultiplier tube detector (200-870 nm) and a CW Xenon arc lamp (450 W, 250-2500 nm). A UV enhanced silicon photodiode reference detector monitores and compensates for variation in the Xenon lamp intensity.

L 2 [

 2 Scheme 1. Schematics of the lead iodide perovskite NPL samples and their colloidal synthesis

Figure 1 .

 1 Figure 1. Absorption (full line) and photoluminescence (dashed line) spectra of colloidal perovskite NPLs of two monolayers (CsPI, FAPI, MAPI n=2) and three monolayers (MAPI

Page 8 of 33 ACS

 33 Paragon Plus Environment ACS Applied Nano Materials neglected. The CsPI sample, however, might display some degree of confinement in one of the lateral dimensions (nanoribbons with a width of 17 ± 3 nm and a length of several hundreds of nm, see FigureS1in SI). While the small blue shift in the spectrum of Cs-based perovskite samples compared to MA-and FA-based ones is typical,[START_REF] Eperon | Formamidinium Lead Trihalide: A Broadly Tunable Perovskite for Efficient Planar Heterojunction Solar Cells[END_REF] here it might be the consequence of the extra confinement effects, which could affect the AR rate.[START_REF] Li | Size-and Morphology-Dependent Auger Recombination in CsPbBr 3 Perovskite Two-Dimensional Nanoplatelets and One-Dimensional Nanorods[END_REF] Time resolved photoluminescence experiments. TR-PL is a standard method to study multiexciton dynamics in colloidal nanostructures. Since the PL signal is proportional to the average number of bound electron-hole pairs in the excited nanoparticles, which allows to distinguish different kinetic recombination processes.29 Here, we employ the time-correlated single-photon counting (TCSPC) technique (see EXPERIMENTAL SECTION) with an instrument response function (IRF) of about 60 ps, to record luminescence decays of the four colloidal perovskite NPLs at the band-edge after excitation at 400 nm. By varying the excitation fluence from 40 nJ/cm 2 to 15 µJ/cm 2 , multiexciton interactions may be revealed.

Figure 2 .

 2 Figure 2. Fluence-dependent PL decay traces of the perovskite NPLs excited at 400 nm (bandedge detection). (a) Experimental data (full lines) and fit (dashed lines) for MAPI n=3 NPLs. (b) Experimental data and fit of the four different NPL samples normalized at long time to highlight the extra decay at early time at high excitation fluence.

  dynamics at long times to single exciton recombination. The larger value of τ 3 for the n=3 NPL sample can be explained by its larger fluorescence quantum yield (see SI). The consistency of the long time dynamics due to mono-exciton recombination allows us to normalize the PL decay traces at a long time and to isolate the extra faster decay component appearing at larger excitation densities. We assigned this faster component to multiple exciton Page 10 of 33 ACS Paragon Plus Environment ACS Applied Nano Materials

1 )Figure 3 .

 13 Figure 3. Evolution of the effective bimolecular AR rate β (black squares) and of the effective

  Visible femtosecond transient absorption (TA). TA is a spectroscopic technique providing a much higher temporal resolution than TCSPC. Excitation fluence-dependent TA experiments were carried out on the four NPL samples using band-edge excitation to avoid the effect of cooling in the early time dynamics. A detailed description of our TA setup with pump energy Page 15 of 33 ACS Paragon Plus Environment ACS Applied Nano Materialstunable with a visible non-collinear optical parametric amplifier (NOPA) is given in the EXPERIMENTAL SECTION. The NPLs were refreshed within the cuvette using a peristaltic pump with adapted tubing to prevent from photo-degradation and photo-charging effects. The transient absorption signal ΔA we focus on in this study corresponds to the photo-induced bleach (PIB) coming from the saturation of the band-edge transition due to the presence of excitons generated by the pump in the lowest energy levels.[START_REF] Klimov | Optical Nonlinearities and Ultrafast Carrier Dynamics in Semiconductor Nanocrystals[END_REF] From a global fit analysis of the TA data, we found that the line-shapes where conserved within the time-range of interest (ps-ns), including no significant spectral shift in the PIB of the bandedge transition (FigureS6in SI). Consequently, the kinetic trace at the PIB maximum averaged over a few nanometers can be fitted directly. The sign of the negative PIB signal was inverted in order to facilite comparisons with TR-PL analysis and the PIB decays were normalized at long time to highlight the extra faster decay component appearing at high excitation fluence. The data are shown in Figure 4a for MAPI n=3 NPLs and Figure S7 in the SI for the three n=2 NPL samples. Similarly with TR-PL dynamics, the TA decays were fit by a multiexponential function. The resulting fit parameters are given in TableS7-S10 in the SI.

Figure 4 .

 4 Figure 4. (a) Band-edge PIB traces of MAPI n=3 NPLs normalized at long time for different excitation fluences (squares) and multiexponential fit (dashed lines). (b) Early-time AR time constants τ 1 extracted from the TA data of MAPI n=3 NPLs at three different fluences and in the highest excitation fluence TA decay traces of MAPI, FAPI, and CsPI n=2 NPLs.

Page 18 of 33 ACS

 33 Paragon Plus Environment ACS Applied Nano Materials multiple excitons within a single NPL decay predominantly through the Auger recombination process. We now investigate the case of high photon energy, which can potentially lead to multiexciton generation, even in the case of low excitation fluence.

Figure 5 .

 5 Figure 5. (a) PIB traces at low fluence of MAPI n=3 NPLs (band-edge detection, normalized at 500 ps) for different excitation photon energies (corresponding to 500, 310, 290, 270, 260

  photon energy.

  photon, depending on the mechanism 45 ), while at high excitation density, the Auger process is

  ABBREVIATIONS

  Table S12 in SI.While for a visible excitation the PIB dynamics can be well described by a mono-exponential decay with a long-time component of about 10 ns (represented in black in Figure5a, excitation at 1.23 × E 1ex corresponding to 500 nm), extra decay components with time constants ranging between few and hundreds of ps emerge for UV excitation. We also observe a coherent artifact at times below 300 fs. This is taken into account in the exponential fit but not considered any further. Similar to the previous analysis, the faster components can be isolated from the longtime single-exciton dynamics after normalization at long times (FigureS9in SI). This faster dynamics could be interpreted as the indirect observation of MEG, since the excitation fluence was reduced to a minimum while exciting the NPLs with high-energy photons. We should note that here, per opposition with visible TA experiments, we expected at most two excitons per NPL (for low enough excitation fluence). The component characterized by a time constant on the order of hundreds of ps is directly observed at relatively low energy excitation (1.98 ×E 1exc and 2.11 ×E 1exc ) with a relatively low amplitude. However, it becomes much more pronounced starting from 2.26 × E 1exc (270 nm in wavelength). At E ≥ 2.35 × E 1exc , an additional component of a few picoseconds appears. It should be kept in mind that this time constant is much longer than the temporal resolution (< 300 fs for UV excitation).

  this intermediate component when exciting at 250 nm compared to 310 nm (FigureS10bin SI). If this component was due to MEG, it would lead to a QY of about 134 % when excited at 250 nm (corresponding to an energy of 2.28 ×E 1exc ).

	Page 21 of 33	ACS Applied Nano Materials
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perovskite structures. In particular, the fast AR rates and efficient MEG make the NPLs promising for applications in single photon sources and photodetectors, respectively. ASSOCIATED CONTENT Supporting Information. This includes the synthesis and characterization of the NPL samples, additional TR-PL and TA data, table of the fitting parameters, details of the calculation of the exciton density, discussion on the time scale of the radiative biexciton rate and on the liquid scintillation experiments. The following files are available free of charge.

AUTHOR INFORMATION

Corresponding Author

*Corresponding author: elsa.cassette@cea.fr ORCID Carolina Villamil Franco: 0000-0002-8738-9842 Benoît Mahler: 0000-0001-5471-5608 Thomas Gustavsson : 0000-0001-7030-6812 Elsa Cassette: 0000-0002-1471-6558

Notes

The authors declare no competing financial interest.