Band-Edge Exciton Fine Structure and Recombination Dynamics in

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Band-Edge Exciton Fine Structure and Recombination Dynamics in InP/ZnS Colloidal Nanocrystals Louis Biadala, Benjamin Siebers, Yasin Beyasit, Mickael D. Tessier, Dorian Dupont, Zeger Hens, Dmitri R. Yakovlev, and Manfred Bayer ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b07065 • Publication Date (Web): 18 Feb 2016 Downloaded from http://pubs.acs.org on February 24, 2016

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Band-Edge Exciton Fine Structure and Recombination Dynamics in InP/ZnS Colloidal Nanocrystals Louis Biadala†,*, Benjamin Siebers†, Yasin Beyazit†, Mickaël. D. Tessier ‡,∩, Dorian Dupont‡,∩, Zeger Hens ‡,∩, Dmitri R. Yakovlev †,ǁ, Manfred Bayer †,ǁ † Experimentelle Physik 2, Technische Universität Dortmund, 44221 Dortmund, Germany ǁ Ioffe Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia ‡ Physics and Chemistry of Nanostructures, Ghent University, Belgium ∩Center for Nano and Biophotonics, Ghent University, Belgium ABSTRACT We report on a temperature-, time-, and spectrally-resolved study of the photoluminescence of type-I InP/ZnS colloidal nanocrystals with varying core size. By studying the exciton recombination dynamics we assess the exciton fine structure in these systems. In addition to the typical bright-dark doublet, the photoluminescence stems from an upper bright state in spite of its large energy splitting (~100 meV). This striking observation results from dramatically lengthened thermalization processes among the fine structure levels and points to optical-phonon bottleneck effects in InP/ZnS nanocrystals. Furthermore, our data show that the radiative recombination of the dark exciton scales linearly with the bright-dark energy splitting for CdSe and InP nanocrystals. This finding strongly suggests a universal dangling bonds-assisted recombination of the dark exciton in colloidal nanostructures.

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KEYORDS Cd-free, fine structure, dark exciton, dangling bonds, phonon bottleneck

Colloidal nanostructures are taking off in many fields of application such as in display,1 spectrometer,2 sensing,3 light-emitting diode,4 or biolabelling.5 Moreover, colloidal quantum dots are promising in various fields from laser technology,6 as low threshold amplification medium, to quantum optics as a source of single photons or polarization-entangled photon pairs.7 Over the past decades the research has been mainly conducted on CdSe-based core/shell nanocrystals (NCs) leading to a deeper understanding of the optical properties as well as their chemical synthesis. It is now possible to grow colloidal nanostructures having all types of quantum confinement: 0D, 1D and 2D systems, commonly referred to as quantum dots,8 quantum rods,9 and nanoplatelets,10 respectively. As fluorescence properties of semiconductor colloidal quantum dots are linked to the band-edge properties, it is essential to have a deep knowledge of their excitonic fine structure. Extensive researches aiming at understanding the excitonic states of Cd-based colloidal NCs have been conducted over the past two decades. One of the main models used to describe of the band-edge exciton in CdSe NCs involves the existence of optically-active states (or bright states) and optically-forbidden states (or dark states) separated by a few meV.11 At room temperature, these states are hard to detect separately as temperature broadening leads to recombination from the states with the higher oscillator strength. However, the bright and dark states can be easily identified by cryogenic-temperature fluorescence lifetime measurements. The forbidden state shows considerably smaller oscillator strength and, consequently, its fluorescence lifetime is much longer than the bright state fluorescence lifetime.11–14 Parameters of the bright and dark exciton states (energy splitting, radiative time, spin-flip rate) can then be deduced from the temperature dependence of the recombination dynamics, when the populations between the


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bright and dark states become redistributed. This is often referred to as a thermal mixing effect, even if a temperature increase does not mix the exciton states but only changes their populations. These models and methods have been extensively used for the analysis of the band-edge exciton fine structure of a variety of colloidal Cd-based NCs.12–16 As Cd-based technological applications interest is limited because of the high toxicity of cadmium, significant efforts are made to develop colloidal synthesis schemes yielding heavy metal-free quantum dots that have optical properties comparable to or better than cadmium-containing ones. Among the potential materials, InP appears to be an ideal candidate since it has bandgap close to CdSe as well as a reduced toxicity.17 However, the lack of knowledge on the fine structure above the dark ground state and on the exciton recombination dynamics limits the understanding of the optical properties of InP NCs as well as their theoretical modeling. Besides the level ordering, the size dependence of the fine structure parameters (radiative recombination dynamics, energy splitting) are highly desirable to refine theoretical calculations. Surprisingly, only little studies have addressed the physics of colloidal InP NCs and more especially their band-edge exciton fine structure and exciton recombination dynamics. Possibly, this is because InP NCs synthesis protocols were more difficult to implement due to the use of an expensive and highly pyrophoric phosphorus precursor.18–20 Recently, new synthesis protocols based on a cheap and easy-to-use phosphorus precursor that leads to high quality InP NCs have been published.21,22 These protocols facilitate the production of InP NCs and should lead to more optical studies by enabling an easier access to high quality materials. In any event, pioneering work on the steady-state photoluminescence properties of fluorhydricacide (HF) etched colloidal InP NCs performed by Micic et al.23 suggested that at cryogenic temperatures the PL stems from a spin-forbidden dark exciton state. More recent work on the temperature dependence of the PL decay of a commercial sample of InP/ZnS NCs with 3.5 nm diameter seems to support this


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assumption, but remains restricted because of the presence of trapping sites at energies comparable to the fine structure energy splitting.24 To the best of our knowledge systematic studies of the exciton fine structure and exciton recombination dynamics are still missing for colloidal InP-based NCs. Here we report on temperature-, time- and spectrally-resolved studies of the band edge exciton recombination on ensemble of type-I InP/ZnS NCs. The InP core size is varied from 2.4 nm to 3.3 nm in diameter, resulting in emission in a spectral range between 2.45 eV to 1.9 eV. We show that at cryogenic temperatures the photoluminescence stems from the thermal mixing between a bright allowed state and a dark spin-forbidden state. The energy separation between these two lowest exciton levels, ∆E, decreases from 16 meV down to 5 meV when the core size is increased from 2.4 nm to 3.3 nm. This size dependence is consistent with theoretical calculations. In addition, we demonstrate that the upper bright level within the exciton fine structure lays between 120 meV and 40 meV above the bright-dark doublet. The systematic study of the radiative recombination of the bright and the dark states reveals that the bright exciton lifetime increases with increasing InP core size, similar to what is found with CdSe and CdTe NCs. It further shows that in InP NCs, the radiative recombination of the dark exciton can be achieved by a mixing with the bright exciton. This effect is evidenced by a clear linear dependence on the bright-dark energy splitting of the dark exciton lifetime, which shortens from 1 µs to 350 ns with increasing NCs size from 2.4 nm to 3.3 nm. This linear dependence is also found in various CdSe-based NCs. The slope is found to strongly depend on the surface/interface properties of the NCs. Interestingly the slope is found to be identical for CdSe/CdS colloidal dot-in-rod NCs and InP/ZnS NCs. This similarity may point towards a universal mechanism in the dark exciton radiative recombination mediated by the NCs surface. Finally our results evidence that in InP/ZnS NCs, the phonon-assisted processes of the spin-flip scattering between the fine structure levels are dramatically lengthened by


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more than one order of magnitude compared to CdSe-based NCs. This feature indicates the possibility to extract high energy exciton prior to their thermalization to the ground exciton state and, therefore, to boost the efficiency of colloidal-made solar cells.25 This striking result also paves the way to achieve a phonon bottleneck within the exciton fine structure in InP/ZnS NCs.

RESULTS AND DISCUSSION InP/ZnS NCs are grown following protocols using aminophosphine-type precursors21,22 (cf. supporting information for more details). We studied six samples with InP core diameter, D, varied from 2.4 nm to 3.3 nm (see Table 1); all have a 2 nm-thick ZnS shell, which reduces surface non-radiative recombination and increases PL efficiency. In InP/ZnS NCs, the band alignment leads to a type-I confinement (Figure 1b), so the electron and the hole are strongly confined in the vicinity of the InP core. In the case of core/shell NCs with 2.9 nm InP core, the ensemble PL spectrum is centered around 2.0 eV with a full width at half maximum (FWHM) of 190 meV (~54 nm) (Figure 1a). This is significantly wider than in CdSe-based NCs where the typical FWHM is around 100 meV, mainly because of a larger size distribution of InP NCs.26 When increasing or decreasing the NCs size, the PL maximum is shifted towards lower or higher energies, respectively, as a result of a the quantum confinement of the charge carriers (Figure 1c). In agreement with a simple particle-in-a-box model, the PL maximum energy depends on the inverse square diameter (D-2) of the core (Figure 1c, inset). In addition, PL spectra display a low energy tail shifted by about 300 meV from the PL maximum (Figure 1d, inset). This emission, which is probably due to deep traps, decreases with increasing NCs size and is decoupled from the band-edge emission (Supporting Information, Figure S1-S3 and discussion). When lowering the temperature, the PL maximum is shifted to higher energy and the deep trap emission increases (Figure 1d


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insets). The former effect is well known and results from the thermal contraction of the material and is described by the Varshni expression.27 The energy of the PL maximum at the temperature T, E(T) is given by: = −

+

(1)

where E0 is the energy at T = 0 K, α and β are constants. The corresponding fit is displayed in Figure 1d (red). For this NC size (2.9 nm core, sample #4) we find E0 = 2.019 eV, α = 5.8x10-4 eV/K and β = 320 K in very good agreement with previous work on InP NCs.28

Table 1: Parameters of the InP/ZnS NCs obtained from the fit of the temperature dependence of the long component of the PL decay. All samples have a ZnS shell thickness of ~2 nm. Sample

#1

#2

#3

#4

#5

#6

Core diameter, D (nm) Bright exciton radiative time, ΓA-1 (ns)

2.4 21

2.6 22.7

2.8 22

2.9 27

3.1 27.7

3.3 38

Dark exciton radiative time, ΓF-1(ns)

990

635

496 431

374

350

Bright-dark splitting, ∆E (meV)

16

10

9.7

7.2

6.4

5.2

Bright-bright splitting, ∆bb (meV)

X

147

100

85

60

40

X indicates that we have not been able to measure the bright-bright splitting.


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Figure 1: a) Photoluminescence spectrum of InP/ZnS NCs (sample #4) at T = 290 K (black) together with absorption spectrum (red). b) Band alignment diagram of InP/ZnS heterostructures. c) Ensemble PL spectra of InP/ZnS NCs having various core sizes. Inset: Energy of the PL spectra maximum as a function of the inverse square diameter of the InP core. Dashed line is a linear fit. d) Temperature dependence of the maximum PL emission (black dots) of InP/ZnS NCs (sample #4). The red line corresponds to a Varshni fit with E0 = 2.019 eV, α = 5.8x10-4 eV/K and β = 320 K. Inset: PL spectra at various temperatures of the same sample. The low energy part of the spectra is zoomed in inset.

In order to probe the band-edge exciton fine structure we performed a temperature dependence analysis of the photoluminescence decay. Pioneering work on the time-resolved optical properties of individual CdSe/ZnS NCs showed that from the temperature dependence of the PL decay, the energy splitting between the lowest exciton states as well as their radiative lifetimes can be determined.12 This method is now routinely used to investigate the exciton fine structure in various NCs.13–16,29 In Figure 2a, we show the time-integrated 7 ACS Paragon Plus Environment

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ensemble PL spectrum of InP/ZnS NCs with a 2.9 nm core diameter measured at T= 4.2 K. In inset we plot the spectrally-integrated PL decay as a function of time (black) that is multiexponential with no clear characteristic time. This non-exponential behavior probably reflects sample heterogeneity to, e.g. size distribution or strain within the ensemble of NCs. To circumvent this, we filtered the PL spectrum with a monochromator around the maximum of the PL spectrum (Figure 2a, dash area) to select a subset in the ensemble. The inset of Figure 2a shows the corresponding filtered PL decay (grey), which can be well reproduced by a biexponential decays (red line) with characteristic times τfast = 1.5 ns and τlong = 430 ns.

Figure 2: a) Time-integrated PL spectrum of the sample #4 with 2.9 nm core. Inset: spectrally-integrated PL decay (black) and spectrally-filtered PL decay (grey) fitted by biexponential decay (red line) with characteristic times τfast = 1.5 ns and τlong = 430 ns. b) Spectrally-filtered PL decay of all studied InP/ZnS samples. Inset: early part of the PL decays showing the size dependence of the fast component. c) PL decay at the PL maximum for 8 ACS Paragon Plus Environment

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different temperatures of the sample #4. The long component dramatically shortens with increasing temperature. Inset: Early part of the PL decay. The amplitude of the short component decreases and eventually vanishes above T = 100 K. d) Three level system used to interpret the data. It is composed of a zero exciton state |G⟩ and two states, denoted |A⟩ and |F⟩ corresponding to the bright and dark excitons.

Figure 2b shows the spectrally-filtered PL decay of the studied InP/ZnS NCs at T = 4.2 K. For all the samples, the PL decay occurs on two markedly different characteristic times: a fast initial decay in the ns-range and a long tail in the 100-ns range. Interestingly, both components exhibit a marked and systematic size dependence. The long component shortens with increasing NCs size, while the short component lengthens. These dependencies will be discussed in the following. In order to unveil the origin of the emission decay and the size dependences, we measured the PL decay as a function of the temperature for all NC sizes. Figure 2c shows the PL decays at various temperatures for the sample #4 with a 2.9 nm diameter core. When increasing the temperature the long component of the PL decay shortens and the amplitude of the short component vanishes (Figure 2c, inset). This behavior is a signature of an emission stemming from the thermal mixing between two levels having very different oscillator strength, thus different spin nature.12,14–16 Importantly, this temperature dependence is representative for all the studied samples (Supporting Information, Figure S4). It is noteworthy that the InP core have a zinc blende crystal structure, so the dark and the bright states should correspond to the band edge states in the case of perfectly spherical NCs.30 However, as it has been demonstrated experimentally31,32 and theoretically30 for CdSe NCs, a slight deviation from spherical symmetry leads to a splitting of the 2 band edge states into 5 fine structure levels.


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The dark and bright states correspond then to the 2 lowest fine structure state. Depending on whether the light-hole or the heavy-hole is the ground hole state, the bright-dark doublet corresponds to {|0>;|±1>} or {|±2>;|±1>}, respectively. The poor contrast on TEM images of bare InP core does not allow studying the core shape asymmetry (Supporting Information, Figure S6) and then assigning unambiguously the nature of the bright and dark states. Further spin-sensitive optical experiments are required to assign the spin nature of the dark and the bright exciton. The PL decay can be well described by a three level system (Figure 2d) composed of a dark ground exciton state |F>, a bright upper exciton state |A> and a zero exciton ground state, |G>. The bright and dark states are separated by the fine structure splitting, ∆E, and have radiative rates ΓA and ΓF, respectively. In this model is the spin-relaxation rate from the bright to the dark exciton state and = is the spin-relaxation rate induced by thermal mixing of bright and dark excitons, where =

∆

is the Bose-Einstein phonon occupation. It

is noteworthy that the bright-dark picture is valid whether the exciton is formed from heavyhole or the light-hole bands. Indeed, theoretical calculations11 and experimental results31 show that the lowest exciton level is always a dark state. The signal intensity I(t) is proportional to the time-dependent populations of both the bright and dark state, reading = η! ρ! Γ! +

η$ ρ$ Γ$ , with ηi the quantum yield, ρi the time-dependent population, and Γi the radiative rate of the state i. With the approximation of a very fast thermalization between the bright and the dark states (γ0 >>ΓA) and assuming that the quantum yield of both the dark and bright excitons is 1,33 we can write I(t):

= &' ( )* + &+ ( ), =

Γ- + Γ. ) ( * + Γ- 12- 0 − 4 ( ), 1 + 2 1 + 2

(2)


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Here, 2- 0 is the population of the bright state after the non-resonant excitation and, ΓL and ΓS are the decay rates for the long and the short component of the PL decay, respectively. They are given as a function of the radiative rates ΓA and ΓF,

Γ' =

Γ- + Γ. Γ- − Γ. Δ − 56ℎ 2 2 29

Γ+ = 1 + 2

(3) (4)

Eqs (3) and (4) demonstrate that the bright and dark radiative rates, as well as the bright-dark splitting, can be obtained from the temperature dependence of the long component of the PL decay. For low temperatures (9 ≪ Δ) both equations are reduce to Γ' = Γ. and Γ+ = . Therefore, the dark exciton radiative rate and the bright-to-dark spin-flip rate can be directly obtained from the two-exponential decay at low temperatures. At high temperatures (9 ≫ Δ ), the long component of the PL decay becomes Γ' = Γ- /2 and the amplitude of the second

term in Eq. 1 vanishes (&+ = 0. It is noteworthy that Δ can also be obtained independently from the radiative rates, namely from the normalized amplitude of the bi-exponential decay since &+ = &' = 0.5 for 9 = Δ. Figure 3 shows temperature dependences of the long decay rate of the PL decay for all studied samples. Below T = 10 K, Γ' remains constant for all samples indicating, according to Eq. 3, that Δ ≫ 9 ~ 1meV. With temperature increase up to 100 K, Γ' strongly increases to values around 0.01 ns-1, while the PL intensity remains constant (Supporting Information, Figure S5). Above 100 K, Γ' decreases to values that strongly depend on the NCs size and the PL intensity drops. This suggests a thermal activation of non-radiative channels. Our model does not account for this effect. Therefore, in the following we fit the experimental data for the temperature range T < 100 K, where the PL intensity remains constant. The fits with Eq. 3 are shown by lines in Figure 3a. ?- , ?. , and Δ are used as fitting parameters (see Table 1) and are assumed to be temperature independent in this temperature range.


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Figure 3: a) Temperature dependences of the long decay rate of the PL decay, Γ' , of InP/ZnS NCs. Lines are fits according to the three level system (see text). b) Temperature dependences of the normalized amplitude of the short component of the PL decay, AS. Lines are simulations without fitting parameters. The bright-dark energy splitting can also be determined from the amplitude of the short component of the PL decay. Indeed, according to Eq. 2, the normalized amplitude of the short component simply writes: &+ = 1 + 2 + Γ. /Γ- , with Γ. /Γ- ≪ 1 . Therefore, the temperature dependence of the amplitude of the short component is directly given by the Bose-Einstein phonon occupation NB, which depends on the bright-dark splitting. Figure 3b shows the temperature dependence of the normalized amplitude of the short component for all samples together with the simulation curves according to the previous expression. The simulation curves are obtained without fitting parameters, we used the values Γ! , Γ$ , and Δ from Table 1. The simulated values are in good agreement with the experimental data. These results reinforce our analysis based on bright and dark exciton and allow us for unambiguously assigning the fast component of the PL decay to the bright-to-dark spin-flip time. It should be noted, that for the largest core size, the normalized amplitude of the short component is significantly smaller than we estimated from the fine structure parameters. We believe that this might be due to additional contributions of charged excitons or biexcitons.


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From Table 1 one clearly sees a strong size dependence of all parameters of the fine structure, notably the bright-dark splitting. Indeed, ∆E strongly decreases from 16 meV to 5.2 meV as the NCs core increases from 2.4 nm to 3.3 nm, in broad agreement with the resonant Stokes shift measured by fluorescence line narrowing on HF etched InP NCs.34 Note that the discrepancy might come from the different scaling law used to estimate the size of the NCs, the surface passivation (HF etched or thick (2 nm) ZnS shell), and the shape anisotropy. Pseudo-potential calculation performed by Franceschetti et al. on the exciton fine structure in spherical InP NCs shows that the energy splitting between the band edge state is compatible with our results.35 At the same time, in the effective mass approximation (EMA) framework, by taking into account an InP core shape asymmetry, the energy splitting between the 2 lowest fine structure states also agree with our experimental values (Supporting information, Figure S7 and text). Therefore further calculations, that go beyond the scope of this work, are needed to clarify the origin of the bright-dark energy splitting in InP/ZnS NCs.

Figure 4 a) Bright exciton radiative rate as a function of the energy transition of InP/ZnS NCs. b) Bright-to-dark spin-flip rate as a function of the inverse square diameter of the InP/ZnS NCs. Lines are linear interpolation.


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Figure 4a shows the radiative rate of the bright exciton as a function of the transition energy. As the core size increases from 2.4 nm to 3.3 nm, the radiative rate of the bright exciton decreases from 47 µs-1 to 26 µs-1. These results are in very good agreement with the Fermi golden rule, that predicts a linear scaling of the radiative rate with the energy transition.36 Therefore, similarly to CdSe and CdTe NCs,37 the radiative rate in InP/ZnS NCs is mostly determined by the size dependence of the emission energies. A marked difference arises when comparing the bright-to-dark spin-flip rate in InP/ZnS and CdSe-based NCs. In Figure 4b we plot the bright-to-dark spin-flip rate, deduced from the fast component of the PL decays at T = 4.2 K, as a function of D-2 for InP/ZnS NCs. The rate decreases from 1 ns-1 to 0.6 ns-1 with increasing the core size from 2.4 nm to 3.1 nm. The spin-flip rates are more than one order of magnitude larger than the bright exciton radiative rates, which confirms our assumption ( ≫ Γ- ) used in the model. Interestingly, the spin-flip rate scales roughly with the inverse square diameter of the InP core, similarly to bare CdSe NCs.38 Although the size dependence is comparable, the spin-flip rates themselves differ by more than one order of magnitude. In bare CdSe NCs, the spin-flip rates are around 50 ns-1 for D ~ 3 nm.38 Instead, our InP/ZnS samples show rates smaller than 1 ns-1 for D ~ 3 nm. This spin-flip process, mediated by acoustic phonon, strongly depends on the bright-dark energy splitting and the confined acoustic phonon energy spectrum. In small CdSe NCs, ∆E is larger than the characteristic acoustic phonon energy such that several phonons modes are available to provide relaxation. When increasing the size, ∆E becomes comparable to the confined phonon energy and the bright-dark spin-flip rate is significantly smaller since a reduced number of accessible phonons.13,15,39 In InP and CdSe NCs the characteristic acoustic phonon energy is comparable.40,41 Therefore the slow thermalization process in InP/ZnS may result from a weaker coupling strength between excitons and acoustic phonons. This is highly desirable in


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quantum optics application since the exciton-phonon interaction participate to the optical dephasing.

Figure 5 Dark exciton radiative time as a function of the bright-dark splitting, ∆E for various core/shell NCs. Red symbols are data for CdSe/CdS dot-in-rod NCs (Ref

15

). Blue symbols

corresponds to data on CdSe/ZnS NCs (Ref 12,13,39,42). Green symbols corresponds to spherical CdSe/CdS NCs (Ref 16,29). Pink symbols correspond to organically capped CdSe NCs (Ref 14) . Dashed line are a linear interpolation with a slope of 57 (red), 112 (blue), 441 (green) and 757 (pink) ns/meV. In addition to the bright radiative rate and bright-to-dark spin-flip rates, these results allow studying the dark exciton radiative rate. In Figure 5, we plot the dark exciton radiative time as a function of the bright dark energy splitting for InP/ZnS and for various CdSe-based core/shell NCs.13–16,29,39 These NCs strongly differ by their synthesis, shell type (ZnS, CdS, organic), core/shell interface (sharp, smooth) and core materials (CdSe, InP). Strikingly, the dark exciton radiative time increases linearly with ∆E for each type of core/shell NCs. This result evidences a universal mechanism in the radiative recombination of the dark exciton through an intrinsic coupling to the bright exciton.14,15,42 The mechanism at the origin of this 15 ACS Paragon Plus Environment

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coupling has remained undisclosed for decades because of a large discrepancy within the results. In fact for CdSe-based NCs, the dark exciton lifetime can vary by more than one order of magnitude for a constant bright-dark splitting of ~2 meV from less than 100 ns for CdSe/CdS dot-in-rod (sharp interface) to more than 1300 ns for organically capped CdSe NCs. From Figure 5 we clearly see that the NCs surface and the core/shell interface play a pivotal role in this coupling. Importantly, the radiative recombination of the dark exciton in InP/ZnS NCs and in CdSe/CdS dot-in-rod follow exactly the same scaling law. This result indicates that the bright-dark coupling, given by the radiative time of the dark exciton, has the same physical origin in InP/ZnS NCs and in CdSe/CdS dot-in-rod NCs in spite of their markedly different physical properties. It is noteworthy that these NCs also strongly differ in their chemistry (ligands, solvent). Therefore, the presence of dangling bonds at the surface and/or at the core/shell interface appears to be the only common feature. These results strongly suggest that the radiative recombination of the dark exciton can be mediated through dangling bond-assisted mechanism. We must stress that this hypothesis supports recent theoretical work on the influence of surface dangling bonds in the optical properties of CdSe NCs at cryogenic temperatures.43 The authors notably show that the dangling bond at the NCs surface or at the core/shell interface can explain the origin of the zero phonon line in PL of bare CdSe NCs. An important result obtained with InP/ZnS NCs is the spectroscopic signature of a bright exciton state at higher energy than the bright-dark doublet. This line is clearly seen at early time in the time-resolved PL spectra (see Methods). Figure 6a shows the time-resolved PL spectra of InP/ZnS NCs with a core diameter of 2.9 nm (sample #4). At t = 0 ns, immediately after the laser pulse, the PL maximum is shifted to higher energy by 85 meV as compared to the time-integrated spectrum and has a sharper FWHM of about 100 meV (~30 nm). In the time range between t = 0 ns and 2 ns, the PL spectra can be nicely reproduced by two


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Gaussian lines having similar linewidth of 100 meV and fixed spectral positions (Figure 6b). A careful analysis of the time-resolved PL spectra shows that the intensity of the peak at higher energy decreases and eventually vanishes 2-3 ns after the laser pulse. Concomitantly, the low energy peak intensity increases (Figure 6b, inset). This behavior that is qualitatively representative for all the studied samples, indicates a population transfer from a high energy level to a lower one. A scheme of the level diagram is represented in Figure 6c. In this model we consider a bright exciton level |U > that is higher in energy than the bright-dark doublet by ∆bb. This upper bright exciton can either relax to the zero-exciton state |G > by photon emission with a rate ΓU or to the bright-dark doublet by a phonon assisted spin-flip mechanism with a rate γbb. This assignment is further confirmed by several experimental results.

Figure 6: a) Time-resolved PL spectra at T = 4.2 K of InP/ZnS NCs with 2.9 nm core (sample #4) at various delays after the laser excitation. For comparison the time-integrated PL spectrum is indicated. The spectra are offset for clarity. b) Time-resolved PL spectrum at a 17 ACS Paragon Plus Environment

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delay t = 512 ps after laser excitation (open circles) fitted with two Gaussians (red and blue lines) with FWHM of 100 meV and centered at 2.098 eV and 2.187 eV, respectively. The fitted spectrum is indicated in green. Note, that we neglected the deep trap emission contribution at the low energy part of the spectrum. Inset: temporal evolution of the high (blue) and low (red) energy peak intensities fitted by a single exponential function with τ = 700 ps (solid lines). c) Four level system used to interpret the data. The bright state |U> is located above the bright-dark doublet by an energy ∆bb. The transition to the zero-exciton ground state |G> and the spin-flip to the bright-dark doublet are achieved with rates ΓU and γbb, respectively. d) Bright-bright energy splitting ∆bb (black dots) and the bright-to-bright spin-flip time, γbb-1(red dots) as a function of the core size. Dashed line indicates the LO phonon energy of 43 meV in InP. The energy splitting between the high and the low energy peak, ∆bb, collected in Table 1, strongly depends on the core size of InP/ZnS NCs (Figure 6d). It decreases from 147 meV down to 40 meV for core size increase from 2.6 nm to 3.3 nm, due to decrease of the quantum confinement. The high energy peak cannot be attributed to the biexciton emission, as the involved energies are much larger than typical biexciton binding energies (~10 meV).31 Moreover, a positive binding energy (biexciton line moved towards higher energies than the exciton line) are characteristic for NCs with a type-II band alignment, where the electron and the hole are spatially separated.44 The temporal evolution of the PL intensities supports our assignment. Indeed the similar value of the time (τ = 700 ps) involved in both increase and decrease of the low and high peak intensities, respectively, indicates a common mechanism (Figure 6b, inset). Namely, the energy relaxation from the upper bright state to the lower one. This behavior is observed for all studied samples. The systematic study of the PL intensity decay of the high energy peak shows that the spin-flip time from the upper to the lower bright exciton level depends strongly 18 ACS Paragon Plus Environment

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on their energy splitting (Figure 6d). Remarkably, the spin-flip time remains constant around 700 ps for ∆bb values well above the LO phonon energy (ELO~ 43 meV). When reaching ∆bb values close to ELO, the spin-flip time increases to 1 ns. It is interesting to note, that in InP/ZnS NCs the spin-flip time for ∆bb < ELO are more than one order of magnitude longer than in CdSe-based NCs.45 This dramatic lengthening of the thermalization processes makes InP/ZnS NCs very appealing notably for quantum optics applications.

CONCLUSION In summary, studying the temperature-, time- and spectrally-resolved photoluminescence properties of InP/ZnS colloidal nanocrystals, we obtain direct evidence that at cryogenic temperatures the emission stems from the radiative recombination of a bright exciton and a dark exciton split by a few meV. We also unveil the emission from a bright exciton state lying few 10-meV above the bright-dark doublet. A careful analysis allowed unveiling the size dependence of all parameters, providing a full description of the exciton fine structure in InP/ZnS NCs. We find that the dark exciton radiative time follows a linear increase with the bright-dark energy splitting. The slope strongly depends on the surface and/or the core/shell interface and does not depends on the materials. This important feature points to a dark exciton radiative time mediated by dangling bonds, in addition to phonon assisted mechanisms, in agreement with recent theoretical calculations. Moreover, we found that thermalization processes in InP/ZnS NCs are slowed down by more than one order of magnitude compared to CdSe-based NCs. This finding opens new perspectives for InP/ZnS NCs in the control of phonon-induced mechanisms (spin dynamics, optical decoherence). We believe that this communication will stimulate further work on the colloidal synthesis of III-V NCs to improve and tailor their optical properties, as well as on the optical characterization to further understand the physical phenomenon involved in these NCs, but also on theoretical


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calculations of the exciton fine structure in InP NCs and on the origin of the dark exciton radiative recombination. METHODS The samples were prepared for ensemble measurements by drop casting the solution with InP/ZnS NCs on a quartz plate. For experiments at low temperatures the sample was mounted in a helium bath cryostat. The InP/ZnS samples were excited non resonantly using a pulsed diode laser (photon energy 3.06 eV, pulse duration 50 ps, repetition rate between 300 kHz and 100 kHz) with a weak average excitation power density (

Band-Edge Exciton Fine Structure and Recombination Dynamics in

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