Evidence of Band-Edge Hole Levels Inversion in Spherical CuInS2

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Evidence of Band-Edge Hole Levels Inversion in Spherical CuInS2 Quantum Dots Gabriel Nagamine, Henrique B Nunciaroni, Hunter McDaniel, Alexander L. Efros, Carlos H. de Brito Cruz, and Lazaro A Padilha Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b02707 • Publication Date (Web): 07 Sep 2018 Downloaded from http://pubs.acs.org on September 8, 2018

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Nano Letters

Evidence of Band-Edge Hole Levels Inversion in Spherical CuInS2 Quantum Dots

Gabriel Nagamine,∥ Henrique B. Nunciaroni,∥ Hunter McDaniel,# Alexander L. Efros, ¥ Carlos H. de Brito Cruz,∥ and Lazaro A. Padilha ∥*

∥Instituto

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

#

UbiQD, Inc., 134 Eastgate Drive, Los Alamos, NM, 87544, United States ¥

Center for Computational Materials Science, Naval Research Laboratory, Washington DC 20375, USA *e-mail: [email protected]

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Abstract CuInS2 (CIS) quantum dots (QDs) have emerged as one of the most promising candidates for application in a number of new technologies, mostly due to their heavy-metal-free composition and their unique optical properties. Among those, the large Stokes shift and the long lived excited state are the most striking ones. Although the importance of these properties, the physical mechanism that originates them is still under debate. Here, we use two-photon absorption spectroscopy and ultrafast dynamics studies to investigate the physical origin of those phenomena. From the two-photon absorption spectroscopy, we observe yet another unique property of CIS QDs, a two-photon absorption transition below the one-photon absorption band edge, which has never been observed before for any other semiconductor nanostructure. This originates from the inversion of the 1S and 1P hole level order at the top of the valence band, and results on a blue-shift of the experimentally measured one photon absorption edge by nearly 100 to 200 meV. However, this shift is not large enough to account for the Stokes shift observed, 200-500 meV. Consequently, despite the existence of the below band gap optical transition, photoluminescence in CIS QDs must originate from trap sites. These conclusions are reinforced by the multi-exciton dynamics studies. From those, we demonstrate that biexciton Auger recombination behaves similarly to negative trion dynamics on these nanomaterials, which suggests that the trap state is an electron donating site.

Keywords: Nonlinear absorption; nanomaterials; Stoke shift; Auger recombination; biexciton; trions.


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Colloidal semiconductor quantum dots (QDs) have emerged, beginning over three decades ago, as a promising new class of materials that could be employed in a number of novel optoelectronic devices,1 renewable energy generation,2 and medicine,3 among others. Different applications of CdSe or PbSe based nanocrystals have already been demonstrated, including, light-emitting diodes (LED),4 solar cells,5 neuron monitoring,6 and label for invivo imaging.7 However, the presence of heavy metals in their composition turns them less than ideal for application in daily life technologies. As an alternative, in recent years, a class of, heavy metal free, ternary and quaternary nanomaterials have arisen.8 Among those, CuInS2, CuInSeS, and CuInSe2 have attracted attention of the scientific community because they show unique photophysical properties, including, high emission efficiency (over 80% is achieved in core shell structures), high photo stability, and tunability from the visible to the near infrared region.9, 10 The most striking characteristic shown by these materials is the large Stokes shift, which goes from 200 to 500 meV, depending on the nanomaterial size and composition.11-13 The large Stokes shift reduces the chances of a process known as reabsorption, in which a portion of the light emitted by the material that overlaps with the absorption band can be reabsorbed by it, limiting, for example, the amount of light that can travel throughout a device. Consequently, with this class of nanomaterials, in principle, it is possible to achieve better efficiencies in several technologies that involves light emission, including LEDs14 and luminescent solar concentrators (LSC).15 Indeed, recent studies by Bergren et al. showed that CuInS2 based LSCs have far better performance than any other LSC technology,15,

16

including those based on giant CdSe/CdS quantum dots17. Furthermore, added to the low toxicity, the large Stokes shift could favor applications of CIS QDs as label for imaging for 3 ACS Paragon Plus Environment

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biological tissues. In fact, if large two-photon absorption (2PA) cross section is present in this material, one could envision applications also in nonlinear optical enabled 3-D bioimaging. Nevertheless, there is a lack of understanding of the nonlinear optical behavior of this class of nanomaterials. Furthermore, despite the importance of the large Stokes shift on most of the, so far, demonstrated applications, its origin is still unclear and object of intense debate in the literature. It is well established that, in bulk CuInS2, the photoluminescence (PL) originates from a donor-acceptor pair (DAP) recombination from point defects such as In and Cu vacancies or an interstitial In.18, 19 However, the strong size dependence of the PL spectra in CIS nanomaterials revokes the hypothesis that this is also the case for QDs.12 Alternatively, several groups have proposed models that involve the recombination between one well localized carrier from a trap site with a quantized state from the QD, either from the valence or the conduction band, to describe the observed behavior.12,

20-22

Omata et.al.

20

have

proposed that the emission is due to the recombination from localized electronic defects, due to In impurities, to quantized valence band states. Meanwhile, Knowles et.al.22 and Li et.al.21 have suggested that the photoluminescence comes from the recombination from a quantized state in the conduction band to a Cu defect near the valence band. Additionally, singleparticle studies performed at room temperature by Zang et.al. have shown that the single CIS/ZnS particle has emission bandwidth on the order of 60 meV, much narrower than for the ensemble (~400 meV), suggesting that in this case emission linewidth is mostly defined by a heterogeneity on the distribution of hole trap sites, and not by vibronic effects.23 Recently, calculations by Shabaev et.al. have shown that, for spherical chalcopyrite CuInS2 nanocrystals, the optical transition from the higher state in the valence band , which 4 ACS Paragon Plus Environment

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has P-symmetry character, to the lowers 1Se state in the conduction band is parity forbidden by one photon absorption.24 Consequently, the first allowed optical transition would be at higher photon energy. Indeed, the model proposed in ref

24

expect a shift up to 300 meV

between the first allowed and first forbidden transitions, for the smallest nanoparticles. Following this approach, emission results from the formally forbidden transition. This way, the long PL lifetime and the large Stokes shift could be explained without the need of evoking defect states.24 In this paper, we perform two-photon absorption (2PA) spectroscopy in a series of CuInS2 nanocrystals, showing that the 2PA cross-section can reach values as high as 15,000 GM for QDs emitting in the near infrared region. Our results show experimentally, for the first time, that spherical CIS QDs present an unique below band-gap 2PA transitions, as predicted in the model proposed in Ref.

24

. This 2PA transition below the one-photon

absorption band edge has never been observed in other types of nanomaterials, organic or inorganic. It originates from the unique inversion of the parity symmetry of the top of the valence band, which has a P-symmetry for the spherical CIS QDs.24 However, the selection rules responsible for this phenomena in spherical nanocrystals can be broken when the shape deviates from spherical. We demonstrate strong correlation between the nanomaterial shape and the presence of this below bandgap 2PA peak. Indeed, in the samples where most of the quantum dots are most pyramidally shaped, little to no 2PA peak below the band edge is observed. Furthermore, analyzing the large Stokes shift of this material in light of this parity inversion, we see that the shift caused by the forbidden state in spherical nanocrystals is not large enough to account for the total measured Stokes shift. That suggests that the emission does not originate from the parity forbidden transition and, instead, it involves a localized 5 ACS Paragon Plus Environment

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trap site. This is in accordance with what has been recently proposed in the literature, where the most accepted model is that the photoluminescence is from a transition involving the quantized state in the conduction band and Cu impurities.21, 23, 25 We also observe that the Auger decay time of biexcitons is consistently longer in CuInS2 than in other nanocrystals, behaving similar to negative trion-like, and this can also be explained as a result of the fast hole trapping, as proposed by the Cu impurity model. Results CuInS2/ZnS (CIS) Quantum Dots Synthesis. In this study, a series of commercially available CuInS2/ZnS quantum dots (CIS) produced by UbiQD, Inc. were utilized. According to the company, these nanomaterials are manufactured using a simple, low-cost, heat-up method, based on the methods reported in Refs.

21, 26

. Given that these materials are

commercially available from Strem Chemicals, we suggest they can be considered commercially standard. As shown in Fig. 1, the emission peak of the investigated samples spans from 1.7 eV to 2.2 eV, representing almost one order of magnitude variation on the core volume based on the empirical model proposed by Booth et.al.27 The nanocrystal shape varies from sample to sample, due to variations in the ZnS shelling procedure. Some of the batches presents mostly spherical quantum dots, while others are dominated by pyramidal nanomaterials (Fig. 2 insets). The use of ZnS shell drastically suppresses surface traps, increasing the PL lifetime and quantum yield.21, 28 Consequently, we do not consider emission from surface trap in our analysis. CuInS2/ZnS (CIS) Two-Photon Absorption. To investigate the 2PA spectra, we have employed the two-photon excited photoluminescence technique,29 as described in details in


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the Supporting Information. In total, seven CIS samples with different shapes and sizes have been investigated. Figure 2 shows the linear absorption and 2PA spectra for the CIS QDs samples together with their TEM images (insets). In order to rule out the influence of any other nonlinear optical processes on the detected signal, the emitted signal is measured as a function of several pump intensities and the quadratic dependence (See Supporting Information). To identify the 2PA transition peaks, we fit the 2PA data with multiple Gaussians (two or three Gaussians are necessary to best fit the data for all samples), shown as dashed curves in Fig. 2a-2g. Note, however, that the high-energy 2PA peak is typically broader than the fitting curve for the largest samples (Fig. 2f and 2g). This originates from the fact that at high energy, several two-photon absorption transitions may be spectrally overlapped, in particular for the largest samples (Fig. 2f and 2g) and a simple Gaussian fit cannot accommodate all the data. Consequently, the peak position measured for the high-energy transition for these two samples has a larger uncertainty. The first characteristic observed on the 2PA data is that the maximum 2PA cross section varies from about 750 GM (1GM = 10-50cm4s) for the smallest sample to over 14,000 GM for the largest one. This strong size dependence would be expected from simple volume arguments, however, the variation with volume measured here (see Supporting Information for details), is stronger than the one observed for other nanomaterials, including CdSe,30, 31 PbS,32 and CsPbBr333 QDs. Moreover, the most striking characteristic shown by these data in Fig. 2 is the presence of a non-negligible first 2PA peak at energies below the first linear absorption


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transition. This unique property of CIS QDs has not yet been observed in any other organic or inorganic nanomaterial. In fact, in organic dyes, the HOMO-LUMO transition is allowed by 1PA transition, but it is only allowed for 2PA in asymmetric molecules. 34-36 Meanwhile, in typical semiconductor nanocrystals the first 2PA peak occurs at the 1S-1P transition, at higher energy than the 1PA band edge, typically 1S-1S transition.30-32, 37 Furthermore, this feature is not evident for all samples. It is evident for the samples in Fig. 2a – 2c, but for samples in Fig. 2d-2g this below-bandgap 2PA peak is either inexistent or much weaker than for others. Besides, for the samples in which the below-bandgap 2PA transition is not evident, the first apparent transition is at the same energy as the 1PA transition. Comparing the samples morphology, we notice that the below-bandgap feature is more evident for those samples composed by mostly spherical nanomaterials (Fig. 2b and 2c, note that no TEM is available for sample in 2a). Indeed, the theory developed in Ref. 24, which predicts the belowbandgap 2PA transition, considers spherical nanocrystals and, a change on the shape reflects on a change on the optical transition selection rules. One need to break the inversion symmetry to allow the 1PA and 2PA transition between the same states.37 This can explain the 2PA characteristics observed for the pyramidal samples. Different shapes of our nanoparticles are caused by the shelling process and it could result in changes in the nanocrystal electronic fine structure due to strain effects as it was recently reported by Fan et.al.38 However, the splitting of the energy levels by strain is expected to be much smaller than the distance between quantum confined levels which are studied in our paper, ruling out the influence of strain effects in our analysis. It is important to point out that, even for spherical samples, the below bandgap 2PA peak is about 5 times weaker than the high energy one. Two main reasons can explain this 8 ACS Paragon Plus Environment

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difference in magnitude. First, according to the theory in Ref.

24

, the second 2PA peak is

composed by the sum of three transitions, increasing the total magnitude, while the first 2PA peak is composed by only one. Also, from perturbation theory, 2PA transition rate, for degenerate photons, between an initial, |𝛹𝑖 >, and a final, |𝛹𝑓 >, state is proportional to39

𝑀𝑖,𝑓 = ∑ 𝑗

< 𝛹𝑓 |𝐞. 𝐩|𝛹𝑗 >< 𝛹𝑗 |𝐞. 𝐩|𝛹𝑖 > 𝐸𝑗 −𝐸𝑖𝑛𝑖 − ℏ𝜔

Where |𝛹𝑗 > is the intermediate state, given by all the 1PA allowed transition from |𝛹𝑖 >, and 𝐞. 𝐩 is the light-matter interaction Hamiltonian. Due to the energy detuning, ∆= 𝐸𝑗 −𝐸𝑖𝑛𝑖 − ℏ𝜔 (ℏ𝜔 is de photon energy), typically, the first allowed 1PA transition is the term that contribute the most for the 2PA, and the energy detuning is larger for the below bandgap transition than to the high energy one. Figure 3 compares the 2PA transitions predicted by the theory form Ref.

24

with the

2PA transitions measured in this work. As one can see, the transitions predicted by the theory agrees with the one measured experimentally, in particular for the spherical samples. Despite the fact that the theory predicts the existence of a 2PA transition at energy similar to the first 1PA transition, this is only clearly observed for the pyramidal samples, suggesting that the parity allowed 2PA transition oscillator strength is weaker in that region, for spherical nanocrystals, than the other observed ones. Addressing the origin of the large Stokes shift. The unusual band alignment in spherical CIS QDs, which results in the unique below-bandgap 2PA transition, has been suggested to be responsible for the large Stokes shift observed in these nanomaterials.24 In Figure 3, together with the measured 2PA transitions, the peak positions for the PL are shown. From 9 ACS Paragon Plus Environment

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these data, it is clear that there is still an energy gap on the order of 200 meV between the first 2PA transition and the energy of the PL peak. It is interesting to note that this shift is much larger than the LO-phonon energy for CIS QDs, ~40 meV,40 which is another indication that this energy difference cannot be addressed to vibronic effects. Furthermore, we do not observe any systematic dependence on the Stokes shift on the shape of the nanocrystals, in other words, we do not see evidence that the Stokes shift depends on the fact whether the below-bandgap 2PA transition is strong or not. Those observations indicate that the PL does not originate from a transition between the bottom of the conduction band and the top of the valence band, i.e., from the formally parity forbidden first 2PA peak. This reinforces the proposed model that, one of the carriers is trapped on a localized defect state. This is in accordance with several recent works in the literature that suggest the role of a hole trap site on the PL decay.13, 21, 23, 25 Nevertheless, from our data alone, this conclusion is highly speculative. Multiexction dynamics. To gain further insight on the type of trap states, electron or hole trap, and to verify the influence of trap states on the recombination process in CIS QDs, we have studied the band-edge population dynamics, in particular the biexciton Auger recombination and its dependence on the QD size. For these measurements, we have performed transient absorption experiments in which the QDs were excited at 400 nm and probed at the absorption band edge. To make sure the fast decay observed in the transient absorption experiment is due to biexcitons, we have fitted the decay magnitude as a function of the excitation fluence, following a Poisson statistic as described in details in Ref. 41. Figure 4a shows one example of the pump dependent transient absorption signal for CIS QDs. In the inset of Fig. 4a, the Poisson statistics fitting to the magnitude of the fast decay signal 10 ACS Paragon Plus Environment

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follows the expected fluence dependence of biexciton population, indicating that the lifetime measured is due to biexciton Auger recombination and ruling out possible influence of trions or other surface trap states. For semiconductor nanocrystals, in the strong confinement regime, the biexciton Auger rate measured experimentally can be described by a linear dependence with the nanocrystal volume,41-44 and, for most of those, this rate is almost independent of the material, been exclusively a function of the QD volume.42 Assuming that this trend should be true also for CIS QDs, we expect that measuring the dependence of the biexciton Auger lifetime on the QD size and comparing this dependence to other nanomaterials may help to elucidate the role of the trap states in CIS QDs. However, measuring the size for these nanomaterials is a difficult task due to a number of uncertainties. First, the nanomaterial is type-I core/shell and, for Auger recombination in the band edge, the core volume should be taken into account. Unfortunately, we could not obtain TEM with resolution good enough to allow for a systematic size determination, isolating the core and shell dimensions, for all nanomaterials. In addition, our samples show variation of nanocrystal shape from sample to sample that introduces further complexity to that analysis. In order to overcome these difficulties, we choose to study biexciton Auger lifetime as a function of the linear absorption cross section measured at 3.1 eV, 𝜎3.1 𝑒𝑉 (for information about the linear absorption cross section measured at 3.1 eV, see the Supporting Information), a region where there is a quasi-continuum of states. It has been shown that the linear absorption cross section in the high energy region is nearly proportional to the nanocrystal core volume (considering pure ZnS shell, for which the bandgap is above 3.1 eV). Indeed, considering the dependence of the bandgap with the size for CuInS2 reported in 11 ACS Paragon Plus Environment

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45

ref.

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, we can estimate the core size of our nanoparticles and we observe a nearly linear

dependence between 𝜎3.1 𝑒𝑉

and volume (See Supporting Information for details).

Consequently, as described in ref. 41, the dependence of Auger rate on the QD cross-section, 𝜎3.1 𝑒𝑉 , is proportional to its dependence on the QD volume. The dependence of the biexciton Auger recombination on 𝜎3.1 𝑒𝑉 in CIS is presented in Fig. 4b. Figure 4b also shows the 𝜎3.1 𝑒𝑉 dependence of biexciton lifetime measured in other visible emitting QDs (CdSe46 and CsPbBr3 and CsPbI341) in the strong quantum confinement regime. As we can see, similar to all other nanomaterials, the biexciton lifetime for CIS QDs follow a nearly linear dependence on 𝜎3.1 𝑒𝑉 . However, for the same 𝜎3.1 𝑒𝑉 , CIS QDs exhibits a much longer biexciton decay times. Estimating the core size by the model proposed by Omata et.al.,45 (for the spherical samples) and by Booth et.al.27 (for the pyramidal samples), we can compare the biexciton Auger lifetime for CIS to the one for CdSe in terms of the nanocrystal volume (See Supporting Information), and the results show that the slower biexciton decay for CIS QDs is also evident. Note also that the biexciton lifetime in CIS does not depend on the nanomaterial shape, following the same volume scaling for spherical and pyramidal quantum dots. The long biexciton lifetime observed for CIS is more consistent with the long decay time of negative trions observed in CdSe QDs, which is about 4-8 times longer than the biexciton lifetime than with decay time of the biexciton.47 In general, the positive (𝜏𝑋+ ) and negative (𝜏𝑋− ) trions lifetimes are related to the biexction (𝜏𝑋𝑋 ) lifetime by 2 (𝜏

1

𝑋−

1 𝜏𝑋𝑋

=

1

+ 𝜏 ). Considering symmetric conduction and valence band state distributions, 𝑋+

positive and negative trions would have similar lifetimes and they would be about 4 times 12 ACS Paragon Plus Environment

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longer than the biexciton Auger lifetime. However, asymmetries on the electron and hole wavefuncions can make 𝜏𝑋+ and 𝜏𝑋− very different.48 Indeed, it was shown theoretically that biexiton Auger recombination in CdSe nanocrystals is mainly controlled by its recombination via positive trion decay channel, which is practically one order of magnitude more efficient that for the negative trion recombination channel.49 This is a result of the lower density of available excited electron states where an electron can be transferred after the non-radiative Auger recombination. Similar low density of excited electron states is seen in the energy band structure of CIS calculated using density function theory.24 In Fig. 4b we also plot the negative trion lifetime measured in photocharged CdSe/ZnS QDs,50 showing good agreement with the data for CIS QDs biexciton lifetime. According to ref. 50, the negative trion lifetime should depend superlinearly on the QD volume, 𝜏𝑋− ∝ 𝑉 1.4 . Indeed, a free power dependence fitting to the biexciton lifetime for CIS QDs results in a slightly superlinear behavior, 𝜏𝑋𝑋 ∝ (𝜎3.1𝑒𝑉 )(1.25±0.05) , in direct agreement with the findings from ref.

50

for negative trion

behavior. Based on these findings, here we propose that the biexciton recombination in CIS QDs is governed by a negative trion decay with a second hole strongly localized on the deep trap as shown in Fig. 5. After the initial biexciton creation (Fig. 5a), one of the charges is rapidly trapped in a localized state. Due to the negligible overlap of this state with the wavefunctions of the other charges, the influence of the trapped charge on recombination is negligible, and one can consider that it dependents on only three remaining charges spread over the entire nanocrystal (Fig. 5b). Finally, the single exciton decay would occur as a radiative decay from one charge in the quantum confined state and the trapped charge (Fig. 5c).


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In the case of bare core CIS QDs, it is expected electron and holes trap sites to play roles in the recombination dynamics, where the electrons trap are nonradiative paths and the hole trap plays a role on the radiative channel.25, 51 However, in CIS/ZnS structures, as the one investigated here, the electron traps sites should be eliminated and only Cux sites should be available as hole trap.51 Discussions Investigating the two-photon absorption spectroscopy, we have experimentally revealed that the unique band alignment in CIS QDs results in an inversion of parity symmetry on the top of the valence band, as predicted in Ref. 24, and consequently in a belowbandgap 2PA transition. This feature, not yet observed in other organic or inorganic nanostructure, indicates that any band edge emission should result from a formally forbidden one-photon transition, and formally allowed two-photon transition. In a recent paper by Cichy et.al.,52 2PA spectrum has been measured for CIS QDs showing signal below the bandgap. However, the authors attribute that signal to a combination of effects such as impurity absorption, Coulomb screening or higher non-linear process such as three-photon absorption.52 For the first time, in this work, we show unequivocally that the below-bandgap signal observed in the spherical CIS quantum dots samples originates from pure 2PA. Despite the fact that, as indicated by our data, the photoluminescence does not originate from the parity forbidden transition in CIS nanostructures, these findings indicate that, in the absence of defect trapping levels, in nanostructures with similar band alignment it is possible to obtain large Stokes shift and long emission lifetimes involving only quantum confined states from the nanostructure. In this case, due to the parity selection rules, decay


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via two-photon emission would have the probability enhanced compared to other materials, which could lead to the observation of interesting phenomena such as two-photon gain. Twophoton emission has been already demonstrated in GaInP/AlGaInP quantum wells waveguide,53 and recently Reichert et.al. have reported for the first time the experimental observation of two-photon gain in bulk GaAs.54 Nevertheless, no net two-photon gain have been observed, in part due to the competition of the most probable one-photon emission. In an ideal system, such as nanocrystals with inverted parity on the top of the valence band, the one photon emission rate would be drastically reduced and two-photon net gain could be then experimentally demonstrated. Monitoring the size dependent biexciton dynamics in CIS QDs, we have observed that the Auger lifetime corresponding to biexciton recombination is typically slower than for other nanomaterials, with the same absorption cross section, approaching the values observed for trion Auger decay. This result is in line with the findings from the 2PA spectroscopy, and suggests that the recombination path in CIS QDs follows the schematic in Fig. 5, in which one of the charges present in the biexciton is trapped in a localized state, resulting in negligible wavefunction overlap with the others. Doing a further analysis of the multi-exciton dynamics, we find that the trion involved in the multi-exciton decay is a negative trion, indicating that the trapped species is a hole, as we show in Fig. 5. Our method does not allow us to identify what is the nature of this hole trap state, however, the prediction that it is a hole trap, not an electron trap is consistent with recent electroluminescence25 and transient absorption and PL51 studies. Furthermore, in those studies they have indicated that this is a Cux state.


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ASSOCIATED CONTENT Supporting Information: Details about the two-photon absorption spectroscopy, the linear absorption cross section measurements and the estimated size dependence of two-photon cross section and Auger lifetime are included on the online Supporting Information.

AUTHOR INFORMATION Corresponding Author *[email protected] ACKNOWLEDGMENT The authors would like to thank Dr. Emre Yassittepe and LNnano - CNPEM facility (TEM21389) and FAPESP fellowship (2013-05798/0) for TEM measurements. Funding Sources G.N., C.H.B.C., and L.A.P. acknowledge the financial support from FAPESP (2013/169112). Al.L.E. acknowledges the ﬁnancial support of the Oﬃce of Naval Research (ONR) through the Naval Research Laboratory Basic Research Program.

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Figure 1: Linear absorption (full lines) and photoluminescence (dashed line) spectra for the investigated CIS quantum dots.


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Figure 3. Comparison of the 2PA energy transition measured with the 2PA peak positions (dotted blue lines) calculated in ref. 24. The full line corresponds to the linear absorption band edge. The circles correspond to the spherical samples, the triangles correspond to the pyramidal ones, and the diamonds represent the samples for which we could not obtain conclusive TEM. The pink squares indicate the PL energy for each sample.


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Amplitude (a.u.)

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Figure 4. a) Transient absorption for a CIS quantum dot sample. The decay shows the appearance of biexcitons when the pump fluence is increased. The inset shows the amplitude of the fast and slow components fitted considering the Poisson distribution. b) Comparison of the biexciton lifetime, 𝜏𝑋𝑋 , for CIS quantum dots to literature values for CdSe and PQDs. The data is also compared to the negative trion, 𝜏𝑋− , Auger lifetime for CdSe QDs, indicating that, in CIS QDs, biexcitons decays as a negative trion. The dotted line is a linear dependence fit and the full line is the best power dependence fit, 𝜏𝑋𝑋 ∝ (𝜎3.1𝑒𝑉 )(1.25±0.05) . 23 ACS Paragon Plus Environment

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Figure 5. Description of the multi-exciton dynamics in CIS QDs. a) biexciton is generated from a transition from the second highest state in the valence band to the lowest state in the conduction band. b) One hole is trapped rapidly in the Cu impurity, while the second one decays to the band edge and the three band-edge carriers (two electrons and one hole) undergoes a negative trion Auger recombination. c) Finally, PL occurs from the recombination between the electron in the bottom of the conduction band and the trapped hole


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ToC: Transition Energy (eV)

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Evidence of Band-Edge Hole Levels Inversion in Spherical CuInS2

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