ZnS Quantum

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C: Physical Processes in Nanomaterials and Nanostructures

Inherently Broadband Photoluminescence in Ag-In-S/ZnS Quantum Dots Observed in Ensemble and Single Particle Studies Oleksandr L. Stroyuk, Florian Weigert, Alexandra E Raevskaya, Felix Spranger, Christian Würth, Ute Resch-Genger, Nikolai Gaponik, and Dietrich R. T. Zahn J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11835 • Publication Date (Web): 15 Jan 2019 Downloaded from http://pubs.acs.org on January 17, 2019

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The Journal of Physical Chemistry

Inherently Broadband Photoluminescence in Ag-In-S/ZnS Quantum Dots Observed in Ensemble and Single Particle Studies O. Stroyuk1,2*＃, F. Weigert3＃, A. Raevskaya2,4, F. Spranger4, C. Würth3, U. Resch-Genger3*, N. Gaponik4, D.R.T. Zahn1 1Semiconductor 2L.V.

Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany

Pysarzhevsky Institute of Physical Chemistry, National Academy of Sciences of Ukraine, 03028

Kyiv, Ukraine 3Federal

Institute for Materials Research and Testing (BAM), Division Biophotonics, 12489 Berlin,

Germany 4Physical

Chemistry, Technical University of Dresden, 01062 Dresden, Germany

*Corresponding

＃Both

authors: [email protected] (O. Stroyuk), [email protected] (U. Resch-Genger)

authors contributed equally to this work

Abstract We present a series of results that demonstrate that the broadband photoluminescence (PL) of aqueous glutathione-capped Ag-In-S (AIS) nanocrystals (NCs) is an inherent property of each NC, rather than a collective characteristic of a NC ensemble. By analyzing parameters affecting the PL features like the post-synthesis annealing and the deposition of a passivating ZnS shell, we found no correlation between the spectral width of the PL band of AIS (AIS/ZnS) NCs and the density of the lattice defects. Analysis of the PL spectra of a series of size-selected AIS/ZnS NCs revealed that the PL width of fractionated NCs does not depend on the NC size and size distribution. The PL measurements in a broad temperature window from 320 to 10 K demonstrated that the PL width does not decrease with decreasing temperature as expected for an emission arising from thermally-activated detrapping processes. Also, we show that the model of the self-trapped exciton can be versatilely applied to reconstruct the PL spectra of different AIS NCs and can account for the effects typically attributed to variations in defect state energy. Measurements of the PL properties of single AIS/ZnS NCs highlighted the broadband nature of the emission of individual NCs. The presented results show that the broadband PL of ternary NCs most probably does not originate from lattice defects, but involves the NC lattice as a whole and, therefore, by tailoring the NC structure PL efficiencies as high as those reported for binary cadmium or lead chalcogenide NCs can be potentially reached. 1 ACS Paragon Plus Environment

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Introduction Ternary metal chalcogenide nanocrystals (NCs), such as CuInS2 (CIS) and AgInS2 (AIS), reveal an unrivaled tunability of optical and other physicochemical properties due to the broad variations in NC composition and size as well as tolerance to abundant doping1-7. This variability of application-relevant features combined with relatively high photoluminescence (PL) quantum yields (QYs) reaching 60-70% for NCs synthesized in water raised strong interest in the use of ternary In-based NCs in optoelectronic systems, such as photodetectors and light-emitting devices, in bioimaging and biosensing systems, as well as in photocatalytic systems and solar cells1,3-7. At the same time, the nature of the excited states of CIS and AIS NCs, as well as the mechanisms of light absorption and PL emission remain topics of vivid discussions1,4,8. Ternary CIS and AIS NCs as well as more frequently studied and more stable core/shell CIS/ZnS and AIS/ZnS NCs reveal many special features in absorption and PL spectra. These include broad absorption bands with relatively intense subbandgap (Urbach) tails that can even mask the fundamental absorption band edge CIS and AIS NCs9,10, broad PL bands with spectral widths of 200-400 meV, and an inhomogeneity of the PL lifetimes across the PL band1,4,8,9,11-14. By analogy with well-studied binary II/VI and IV/VI NCs, such as CdS, CdSe, PbS etc., the PL properties of ternary CIS and AIS NCs are often rationalized in terms of a donoracceptor (D-A) PL model1,4,9,12 with contributions from size and chemical inhomogeneities on the single dot basis. According to the D-A model the photogenerated charge carriers are rapidly trapped by lattice defects such as interstitial atoms, cation/anion vacancies as well as surface states, assumed to be abundant in ternary NCs, especially in non-stoichiometric ones, that can introduce local states within the bandgap. The trapped carriers can then recombine radiatively or non-radiatively with free/trapped carriers of opposite charge. Alternatively, they can be detrapped by thermal activation or recombine via a tunnelling mechanism. The radiative recombination of these electron-hole pairs results in the emission of photons with a distribution of energies, broadened by inhomogeneities in NC size and chemical composition as well as the distribution in depths/energy position of the trap states and the distances between trapped electrons and holes within one particle15-17. However, several experimental observations cannot or can only hardly be explained by the D-A model. In particular, the spectral width of the PL bands of CIS and AIS NCs is not influenced by the average NC size and size distribution11,14,18, temperature11,12,18,19 and excitation intensity variations12,18, all factors being expected to affect the distribution of the emissive centers formed upon light absorption. Moreover, recently we reported the aqueous syntheses of non-stoichiometric CIS and AIS NCs with a relatively narrow size distribution (2-4 nm) stabilized by thioglycolic acid (TGA)13,20-22 or glutathione (GSH)14 revealing PL QY values as high as 40-45% (TGA-capped AIS/ZnS NCs) and 65-70% (GSHcapped AIS/ZnS NCs). Such high PL QYs can hardly originate from an emission mediated 2 ACS Paragon Plus Environment

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solely by NC lattice defects. For example, in binary metal-sulfide NCs, the participation of defect states in the non-radiative recombination of the charge carriers leads to a relatively weak broad PL with a PL QY usually below 5 %15-17. An alternative explanation is the model of self-trapped excitons. This model assumes that one of the photogenerated charge carriers (typically hole) is localized at a certain site within the lattice which results in considerable lattice distortions and strong electronphonon interactions1,8,15,23. In this context, the broad PL band is interpreted as a series of phonon replicas of the pure excitonic (zero-phonon) emission line (ZPL) similarly to the molecular fluorescence with a distinct vibrational structure24. Gamelin et al. applied the selftrapped exciton model to the broadband emission of copper- and silver-doped cadmium chalcogenide NCs and argued that the PL features of CIS and AIS NCs can also be described by this model as ultimate cases of Cu and Ag doping8,23. Indeed, Cu- and Ag-doped CdS and CdSe NCs reveal PL properties resembling those of CIS and AIS NCs. We showed recently, that the PL band parameters of doped binary CdS and CdSe/CdS and ternary AIS and AIS/ZnS NCs synthesized using the same or similar ligands can be attributed to the same strong electron-phonon interaction and can be modelled using the general self-trapped exciton model and corresponding vibrational parameters of bulk semiconductors10,12,14. The self-trapped exciton model allows the broadband PL of ternary NCs to be described without assumptions about the exact nature, density, and energies of lattice defects. This model has two important consequences: (i) the broadband PL is assumed to originate from the NC lattice as a whole, not from singular defects and, therefore, by a careful design of the lattice, ternary NCs can be realized with extremely high PL QYs as already reached for binary metal-chalcogenide NCs15-17; (ii) the broadband PL is an inherent property of each and every single ternary NC and can be only very slightly modulated by variations of NC ensemble properties. Currently, reports of experimental evidence supporting the self-trapped exciton model for ternary NCs are, however, quite scattered and need to be extracted from many studies to obtain a single and consistent picture of the PL mechanism. In this view, the aim of the present paper is to provide more experimental proof in favor of this model from systematic studies of the PL properties of a number of aqueous ternary NCs, including TGA-capped CIS NCs21,22, TGA-stabilized AIS NCs13,21, copper-doped AIS NCs20, GSH-capped AIS NCs14, and the corresponding core/shell NCs with ZnS shells. The findings derived from the analysis and modelling of the stationary PL spectra are combined with temperature-dependent measurements of the PL FWHM of AIS/ZnS NCs and PL spectra of single AIS/ZnS NCs.

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Materials and Methods Colloidal AIS NCs stabilized by GSH were synthesized similar to our previous report14 in water in a reaction between GSH complexes of Ag(I) and In(III) with sodium sulfide. A ZnS shell was then deposited on the AIS cores by decomposition of the Zn(II)-GSH complex at 9698 oC. The NCs were precipitated by adding ethanol, separated from the supernatant, and redispersed in deionized water. The size-selection procedure was performed14 using 2propanol as a non-solvent added to the aqueous AIS/ZnS NC solution in 200-μL portions. For the temperature-dependent and single-particle PL measurements AIS/ZnS NCs were dispersed in toluene using a combination of additional ligands, namely oleylamine and oleic acid. The details of the aqueous synthesis of AIS/ZnS NCs and their transfer to toluene are presented in the Electronic Supporting Information (ESI). PL spectra were recorded in a temperature window of 10-320 K using a Fluorolog 3 spectrometer equipped with a helium cryostat. Room-temperature PL spectra of colloidal solutions were recorded in standard 10.0 mm quartz cuvettes excited at 420 nm. Samples for low-temperature measurements were prepared by drop-casting AIS/ZnS NCs dispersed in toluene onto a cleaned glass plate followed by drying at ambient conditions. Single particle measurements were performed using an inverted confocal microscope setup with an oil immersion 100x objective coupled to an atomic force microscope (AFM). Details on the setup used and the experimental conditions of the single-NC measurements can be found in ESI. The samples were prepared by spin coating of GSH-capped AIS/ZnS NCs dispersed in toluene onto a freshly cleaved atomically-flat mica plate followed by drying at ambient conditions. Prior to spin coating, the initially prepared AIS/ZnS colloids were diluted with toluene by a factor of 100. Finally, the sample was overcoated with a thin polymethylmethacrylate (PMMA) layer to increase the photostability of the NCs. The samples were excited at 405 nm and the PL signal was recorded with two different detectors to simultaneously obtain PL spectra and PL time traces, providing the dependence of the PL intensity on time. Emissive NCs were selected for a detailed investigation based upon their blinking behavior indicating the single-NC character of the recorded signal. AFM and optical microscopic images were taken simultaneously to ensure that the vertical position of the dots in the PMMA film selected for the PL measurements did not exceed 3-4 nm.

Results and discussion The absorption and emission spectra of NC ensembles typically produced by colloidal syntheses always reflect the collective properties of the single particles in the studied NC ensemble. In terms of the D-A model of the radiative electron-hole recombination, the distribution of the PL quantum energy EPL can be assessed using equation (1):8,9,12,18 4 ACS Paragon Plus Environment

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EPL = Eg - (EA + ED) + e2×(εR)-1. (1) Here Eg is the optical bandgap, EA and ED are the binding energies of the acceptor and donor states that trap an electron and a hole. e and ε are the electron charge and dielectric constant of the semiconductor, R is the distance between a donor and an acceptor state participating in the generation of PL. Equation (1) implies that several distributions and sources of inhomogeneity can affect the EPL energies of the emitted photons and, thus, the spectral width FWHM of the resulting PL band. In the case of NCs with sizes below the exciton diameter, that exhibit spatial confinement effects, the energy of the interband electron transitions depends on the NC size d, thus introducing a distribution in Eg(d)15. The relative contribution of this factor to the FWHM of the PL band can be evaluated by studying a size-selected series of NCs provided that other factors like the NC chemical composition, ligand shell, temperature, and PL registration conditions are maintained. The photogenerated electrons and holes are trapped by acceptor and donor states introduced by various lattice defects, with the diversity of the possible defects yielding a distribution of the “energy depth” of the electron and hole trap states or EA and ED levels. Under the influence of the thermal lattice energy, the trapped charge carriers can hop between trap states with closely matching energies which also contributes to the FWHM of the PL band15,16,25,26. The relative contribution of this factor to the total PL band broadening can be evaluated by a partial elimination of the defect states either reversibly by decreasing the temperature and freezing out the thermally-activated detrapping of the charge carriers or irreversibly by annealing of the NCs or by modifying the NC surface with a passivating shell. The third distribution to PL broadening arises from the different distance R between the trapped electrons and holes, as follows from the last term of equation (1). The recombination of closer lying charge carrier pairs results in a larger Coulombic contribution to the PL energy. The relative contribution of this factor is the most challenging one to be directly evaluated. This phenomenon is affected by both the NC size variation, with a narrower distribution of R expected for smaller NCs, and by parameters like temperature and excitation energy. Here, low temperatures and low excitation energies should both favor the population of most distant electron-hole pairs. In the following sections, we assess the PL properties of AIS (AIS/ZnS) NCs and their size dependence with a special emphasis of all factors that can affect the EA (ED) distribution, particularly defect annealing and defect “healing” with a ZnS shell and broad temperature variations. In addition, the PL properties of single AIS/ZnS NCs are examined for proofs of inhomogeneous PL broadening. 1. PL properties of size-selected AIS/ZnS QDs. Earlier we showed that aqueous ensembles of AIS and core/shell AIS/ZnS NCs can be resolved into a series of fractions with 5 ACS Paragon Plus Environment


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distinctly different average size and optical properties (absorption/PL spectra and visual coloration)13,14,20 using size-selective precipitation with a non-solvent15. In the case of TGA- and GSH-capped NCs the stability of the colloidal system is believed to originate from the electrostatic repulsion between NCs achieved by the deprotonation of free carboxyl groups of both ligands15. The non-solvent 2-propanol or other moderately polar solvents (ethanol, tetrahydrofuran, etc.) can shift the deprotonation/protonation equilibrium towards the uncharged COOH form resulting in NC agglomeration, which is the stronger the larger the NC size is. As a result, by stepwise addition of the non-solvent followed by centrifugation, size-selected fractions can be separated from the initially prepared NC ensemble, with the average size of the NCs decreasing as the fractionation proceeds and the size distribution being narrowed. We recently showed that the resulting size-selected AIS and AIS/ZnS NCs reveal roughly the same chemical composition of both the core and the ZnS to AIS ratio13,14,20. Analysis of the absorption spectra of size-selected TGA- and GSH-capped AIS/ZnS reveals that almost 70% and more than 90% AIS from the original ensemble can be found in the first three fractions of TGA-capped (ESI, Fig. S1a) and GSH-capped (Fig. S1b) NCs. As the size-selected precipitation results automatically in a stepwise narrowing of the NC size distribution of each fraction, the FWHM of the PL bands of size-selected NCs should be narrower than that of the initial NC ensemble and should even shift in spectral position in case of a considerable size-dependence of the PL features. Additionally, as the size of AIS NCs is decreased, the range of possible distances between donor and acceptor states (see eq. (1)) is expected to narrow, thereby also favoring a narrowing of the PL band with increasing fraction number. The PL spectra of the seventeen size-selected fractions of the AIS/ZnS NCs are shown in Figure 1a and Fig. 1b illustrates the respective emission colors under illumination with UV light. As the fraction number is increased the PL maximum shifts to higher energies indicating an increased exciton confinement in the smaller NCs. Earlier we showed14 that the real Ag:In:Zn ratio in the GSH-capped AIS/ZnS NCs, 1:3:(6-6.5), differs somewhat from the nominal Ag:In:Zn ratio set during the synthesis at 1:4:10 due to the incomplete binding of In-GSH and Zn-GSH complexes with the NC surface. At the same time, the size-selected AIS/ZnS NCs showed almost the same composition in each fraction separated from the original ensemble14 allowing to assign the observed spectral changes exclusively to variations of the average size of AIS/ZnS NCs. Remarkably, the PL maximum energy changes in an almost linear manner with the fraction number (red squares in Fig. 1c) revealing a continuous variation of the size and bandgap of the NCs in the size-selected fractions. The PL FWHM, however, remains almost unchanged varying between 0.38 and 0.40 eV with an average width of 0.39 eV very close to the PL FWHM of the initial NC ensemble (Fig. 1c). This confirms that a possible variation in the NC size distribution in the different NC fractions does not contribute to the spectral width of the PL band of AIS/ZnS NCs. 6 ACS Paragon Plus Environment

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According to the assumptions reported in Ref. 27 for core-shell CIS/ZnS NCs, the hole localization center in these NCs is characterized by a radius of around 0.3 nm, which is considerably smaller than the size of about 12-13 nm of the studied NCs. This can favor a scatter of possible hole positions from the NC center up to the NC surface. In the case of our 2-4 nm sized AIS/ZnS NCs, this distribution should be considerably narrower. For the smallest AIS/ZnS NCs with a size of around 2 nm, the NC core size becomes comparable with the reported hole localization diameter of 0.6 nm. Thus, the distribution of Coulombic energies of the interacting free electron and trapped hole is also expected to be considerably reduced. However, the smallest AIS/ZnS NCs still reveal almost the same FWHM as the largest ones (Fig. 1c), thereby underlining the absence of a FWHM dependence on a possible distribution of electron-hole distances. Similar observations were already made for small CdS NCs in 1986 by Brus et al. and rationalized by the assumption that the minimal D-A distance corresponds to the length of the Cd-S bond or that the NC surface acts as a collective defect state for hole trapping28. Both assumptions imply that the broadband PL is an inherent property of the NCs rather than a collective property of a NC ensemble.

Figure 1. (a, b) PL spectra (a) and photograph (b) of size-fractionated AIS/ZnS QDs (fraction numbers are given in figures). Higher fraction numbers correspond to smaller average NC sizes in the fractions. The photograph was taken under UV illumination (365 nm). (c) Energy of PL maximum (red squares) and spectral width (blue circles) of the PL bands of size-selected AIS/ZnS QDs.

2. PL properties of AIS/ZnS QDs – influence of heating. An essential step for the formation of stable and highly luminescent core AIS NCs independent of the ligand used is heating of the colloidal solution during AIS NC formation close to the water boiling point of 96-98 oC13,14,29,30. Typically, heating of a colloidal NC ensemble results in the increase of the overall PL intensity and a shift of the PL maximum toward lower energies. The former is associated with the elimination of the sites responsible for the non-radiative recombination as a result of the thermally-induced lattice reconstruction15. Simultaneously with the lattice reconstruction, Ostwald ripening of the colloidal NC ensemble occurs, leading to an increase of the average NC size, which is commonly reflected by a red shift of the PL maximum. Both effects are observed for AIS NCs (Fig. 2a). For the conventional D-A model of the broadband 7 ACS Paragon Plus Environment


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PL originating from lattice defects, the heating-induced partial elimination of sub bandgap states associated with lattice defects should result in a considerable narrowing of the PL band.

Figure 2. (a) PL spectra of colloidal GSH-capped AIS QDs produced at different duration of heating during the synthesis, Ag:In:S = 1:4:5; (b) PL intensity (red squares) and PL band FWHM (blue circles) on a different heating phase during the synthesis of GSH-capped AIS QDs.

This expectation contradicts the experimental results presented in Fig. 2b. As the heating of the colloidal NC ensemble proceeds, the integral PL intensity increases by almost an order of magnitude, thereby confirming the suppression of non-radiative recombination pathways (see Fig. 2b, red squares). The FWHM of the PL band is reduced from 0.43 eV to around 0.40 eV in the first ten min of the thermal treatment (Fig. 2b, blue circles), and then remains almost unchanged during the rest of the heating procedure. Apparently more than half of the thermally induced increase in PL intensity between 10 min to 80 min of the heating phase occurs without changes in PL FWHM. As the size variation of the AIS NCs does not affect appreciably the FWHM of the emission band, all variations of the FWHM during heating should be attributed to changes in the defect state population. As no changes in FWHM is observed we can conclude that any possible reduction of the density of defect states responsible for the non-radiative recombination processes is not reflected in the spectral width of the PL band. 3. PL properties of AIS/ZnS QDs – ZnS shell. A universal and very efficient way of increasing the PL intensity of metal chalcogenide NCs is the deposition of a passivation shell on the NC core using a wider-bandgap semiconductor material with a closely related lattice parameter, typically zinc sulfide15. This shell eliminates the defects on the NC core surface, mostly „dangling bonds“, originating from undercoordinated metal atoms forming chalcogenide vacancies11,31-33. Simultaneously, the shell enhances the confinement of the photogenerated charge carriers in NC core inhibiting their interfacial transfer and promoting the radiative recombination11,31,33. As established earlier, the formation of a ZnS shell on AIS or CIS NC cores results in a considerable increase of the PL efficiency, while not affecting the 8 ACS Paragon Plus Environment

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spectral PL parameters in a decisive way13,14,21,22. For the aqueous AIS/ZnS system the effect of the ZnS shell depends on the amount of the Zn(II)-ligand (TGA, GSH) complex which is decomposed during the second heat treatment and transformed into a ZnS layer on the surface of the AIS NCs. A PL increase was also observed for doped AIS NCs like copper-doped AIS (CAIS) NCs as shown in Figure 3a, revealing an increase in PL efficiency by a factor of around four by elevating the molar zinc to silver ratio from 1:1 to (25-30):1. A small shift of the PL maximum to higher energies results from the inclusion of Zn cations into the AIS core lattice leading to an increase of the optical bandgap11,31-33.

Figure 3. (a) PL spectra of colloidal TGA-capped CAIS/ZnS QDs produced at different ZnS content, Cu:Ag:In:S = 0.2:2:7:10; (b) PL intensity (1, red squares) and PL band FWHM (2, blue circles) as functions of the ZnS content.

Similarily as the previously discussed heat treatment, the formation of the ZnS shell affects the PL FWHM only using very small amount of ZnS (blue circles 2 in Fig. 3b). For higher Zn-to-Ag ratios, the FWHM remains almost constant although the integral PL intensity increases monotonously as the Zn/Ag ratio is elevated from 1 to 25-30. This indicates that the ZnS deposition eliminates the lattice defects both on the AIS NC core surface and in the NC volume by filling the anion vacancies and inclusion of the Zn2+ into the lattice cation vacancies, thereby blocking non-radiative decay channels, but obviously these lattice defects do not contribute to the spectral width of the PL band. 4. Temperature (T)-dependent PL properties of AIS/ZnS NCs. The dynamics of the trapping of the charge carriers in subband gap states in semiconductor NCs as well as the probability of detrapping and charge migration/exciton diffusion should be strongly affected by temperature15. At very low T, the migration of charge carriers between the trap states stimulated by the thermal lattice energy can be frozen. This is expected to affect the spectral parameters of the D-A luminescence, such as the energy position of the PL maximum and the PL FWHM19,34-36. Particularly the latter is expected to decrease with decreasing T because the probability of populating deeper defect states increases and the probability of detrapping and population of shallower states is reduced16,25,26,36. 9 ACS Paragon Plus Environment


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This encouraged us to perform T-dependent studies of the PL of AIS and AIS/ZnS NCs to obtain more information on the spectrum of defect states possibly involved in the radiative recombination of charge carriers. Figure 4 shows a set of PL spectra of GSH-capped AIS/ZnS NCs deposited on a glass substrate that were measured at T varied from 320 K to 10 K (Fig. 4a).

Figure 4. (a) PL spectra of GSH-capped AIS/ZnS NCs (unfractioned ensemble) registered at different temperatures varying from 10 to 320 K; (b, c) integral PL intensity (b) and PL band FWHM (c) as functions of T.

The PL intensity increases considerably with decreasing T by almost an order of magnitude in the range of 70-320 K and eventually saturates. At T < 70 K (Fig. 4b), the PL efficiency decreases, underlining the need for thermal activation of the exciton self-trapping in such NCs which becomes inefficient at temperatures lower than 50 K34,35. The shape and spectral width of the PL band remains, however, almost unchanged (Fig. 4a). A similar behavior was also reported for AIS NC12, Zn-Ag-In-S (ZAIS) NCs11, ZAISe NCs19, and Zn-Cu-InS/ZnSe/ZnS NCs37 synthesized in high-boiling-point solvents by conventional heating-up or hot-injection methods. This suggests a general character of the observed trend for silverindium chalcogenide NCs. Subsequently, the PL bands were fitted with single Gaussian curves (Fig. 4c). The resulting very moderate T-dependence of the PL FWHM shows a slight upward shift with decreasing T, changing from around 0.38 eV at 320 K to 0.4 eV at T = 10-100 K. Typically, broadband-emitting NCs demonstrate a slight narrowing of the FWHM when T is decreased to 4-10 K19,34. The slight upward shift of the FWHM observed here can possibly be explained by a thermally-activated rearrangement of ligands overlaying the typical T dependence of the electron-phonon interaction. The lack of a distinct T-dependence of the PL FWHM of AIS/ZnS NCs provides direct evidence that the redistribution of charge carriers among the trap states with different energies does not contribute appreciably to the spectral width of the PL band. Apparently, other explanations for the broadband PL beyond the conventional D-A model are needed. 5. Modelling of broadband PL of AIS NCs. As discussed in the introductory part, the shape of the broad PL band of a series of aqueous metal-chalcogenide NCs can be described 10 ACS Paragon Plus Environment

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by a self-trapped exciton model. This model does not presume a participation of lattice defects in the radiative recombination of the charge carriers and can be applied without fitting parameters. According to the self-trapped exciton model, the PL spectrum consists of a series of emission lines with the energies given by equation (2): En = EZPL - nħω, (2) where, En is the energy of a given line, n is the number of phonons emitted after the PL quantum emission and ħω is the phonon energy. The relative intensity In of each En line is given by equation (3): In ~ Sn×exp(-S)×(n!)-1, (3) where S is the Huang-Rhys factor, representing an average number of phonons emitted after the PL emission. It can be derived from the Stokes shift between EZPL and the PL band maximum EPL: EPL = EZPL - Sħω. (4) Hamanaka et al. applied the self-trapped exciton model to reconstruct the broad PL spectrum of 2.5 nm-sized AIS NCs,12. introducing the three fitting parameters ZPL energy (EZPL), ħω, and S to achieve a good correlation between the experimental and model spectral curves. The fitted phonon energy (33 meV) is close to the known range of the longitudinal optical (LO) phonon of AgInS2, while EZPL corresponds to a weak excitonic feature in the absorption spectrum of the studied AIS NCs12. Earlier we found that the broadband PL of ultra-small (

ZnS Quantum

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