Rapid Trapping as the Origin of Nonradiative Recombination in

This allowed us to find analytical formulas and to extract characteristic trapping/detrapping rates, and quantum efficiency as a function of temperatu...
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Letter Cite This: ACS Photonics 2018, 5, 2990−2996

Rapid Trapping as the Origin of Nonradiative Recombination in Semiconductor Nanocrystals Federico Pevere, Fatemeh Sangghaleh, Benjamin Bruhn, Ilya Sychugov,* and Jan Linnros Department of Applied Physics, KTH − Royal Institute of Technology, Isafjordsgatan 22, 16440 Kista, Sweden

ACS Photonics 2018.5:2990-2996. Downloaded from pubs.acs.org by TU MUENCHEN on 08/22/18. For personal use only.

S Supporting Information *

ABSTRACT: We demonstrate that nonradiative recombination in semiconductor nanocrystals can be described by a rapid luminescence intermittency, based on carrier tunneling to resonant traps. Such process, we call it “rapid trapping (blinking)”, leads to delayed luminescence and promotes Auger recombination, thus lowering the quantum efficiency. To prove our model, we probed oxide- (containing static traps) and ligand- (trap-free) passivated silicon nanocrystals emitting at similar energies and featuring monoexponential blinking statistics. This allowed us to find analytical formulas and to extract characteristic trapping/detrapping rates, and quantum efficiency as a function of temperature and excitation power. Experimental single-dot temperature-dependent decays, supporting the presence of one or few resonant static traps, and ensemble saturation curves were found to be very well described by this effect. The model can be generalized to other semiconductor nanocrystals, although the exact interplay of trapping/detrapping, radiative, and Auger processes may be different, considering the typical times of the processes involved. KEYWORDS: quantum dots, photoluminescence, blinking, efficiency, Auger recombination

T

he mechanism of nonradiative recombination in semiconductors was first explained by Shockley, Read, and Hall (SRH) in 1952 as the trapping and subsequent recombination of electrons and holes by a defect or an impurity in the crystal.1,2 While the process involves a diffusive step (long for high-quality bulk crystals), the actual recombination should occur on a very short time scale (∼fs), suggestively through multiphonon emission. As a consequence, for nanoscale systems like semiconductor nanocrystals (NCs) or quantum dots (QDs), where diffusion distances are negligible, such nonradiative process would be very fast and therefore dominant. Thus, in a photoluminescence (PL) experiment NCs with such defects would appear “dark” (cf. silicon NCs with dangling bonds3), while defect-free particles would appear “bright”, their statistical proportion setting the quantum efficiency (QE) for the ensemble. The corresponding QD exciton-recombination models are depicted in Figure 1a,b. While impurities and defects have been vastly studied in bulk semiconductors, the detailed mechanism of nonradiative recombination in nanocrystals remains unclear. For instance, using single-dot spectroscopy on oxide-passivated silicon nanocrystals (Si-NCs) we found that the PL decay time varies largely for different NCs even emitting at the same wavelength (same bandgap energy).4 Thus, there are not only “bright/ dark” but also “grey” nanocrystals and some nonradiative process must be invoked competing with radiative recombination on a similar time scale, that is, ∼μs, usually assigned to unknown defects at the Si/SiO2 interface.5,6 Indeed, less intensive, “grey” nanocrystals have also been observed for direct bandgap QDs phenomenologically associated with ∼ns nonradiative processes. These systems can also exhibit PL decay time fluctuations,7,8 in which case the ∼ns nonradiative © 2018 American Chemical Society

Figure 1. Exciton-recombination models in a semiconductor QD. (a) Bright QDs: only radiative recombination, rate Γr. (b) Dark QDs: ultrafast nonradiative recombination through a midgap state located at the core or at the nanocrystal interface, rate Γnr. (c) Gray NCs: (left) complex scenario where an electron (hole) is trapped at interface states and then recombines with the core hole (electron) via unknown nonradiative mechanism; (right) rapid trapping (blinking) model based on trapping/detrapping of an electron (hole) at interface states and ultrafast nonradiative Auger recombination occurring upon next exciton generation.

processes cannot be assigned to very fast charge trapping at surface states,9−11 usually relevant in hot carrier relaxation. A complex scenario is typically used, as shown in Figure 1c, to explain “grey” NCs: an excited electron (or hole) can be trapped in the shell and then recombines with the other particle via an unknown nonradiative path.12 Obviously, since electron−hole recombination is a resonant process, trap sites for both electrons and holes should exist in the shell, as well as midgap states to facilitate this scenario. So a natural question arises if a simpler physical explanation can be more relevant instead of such a complex artificial construction. Received: May 4, 2018 Published: July 13, 2018 2990

DOI: 10.1021/acsphotonics.8b00581 ACS Photonics 2018, 5, 2990−2996

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to find analytical formulas and extract switching rates and resulting QE as a function of experimental parameters, important for applications. Two different experiments validating the model were designed: (i) in pulsed excitation the PL decay would reveal a fast, temperature-dependent component indicative of the rate of resonant transfer to trap states, but also a slow tail due to delayed luminescence as carriers return from traps; (ii) under continuous excitation in such nanocrystals, a decreased PL efficiency would be observed well before the onset of normal Auger recombination, that is, before the excitation level of one exciton per NC. Here we prove the presence of this nonradiative process, and it is shown to dominate carrier dynamics in oxide-passivated Si NCs. Its exact manifestation in other semiconductor NCs will depend on the characteristic times of trapping/detrapping, radiative and Auger processes involved. Experimental details are mainly outlined in the Supporting Information. In brief, for single-dot measurements, Si-NCs embedded in oxide were fabricated from a low-doped Si wafer via electron-beam lithography, reactive ion etching, and selflimiting oxidation,32 resulting in well-separated (∼2 μm, i.e., resolvable in far-field PL) nanocrystals embedded in oxide walls (Figure S1). For ensemble studies, we compared two samples of Si-NCs with different passivation. In the first, oxidepassivated NCs were formed in a Si-implanted SiO2 layer after thermal annealing.33 In the second, dodecene-passivated NCs were encapsulated into a poly(methyl methacrylate) (PMMA) matrix via heat-promoted polymerization.34 These two samples have identical emission spectra (Figure S2) centered at ∼1.7 eV with a fwhm of ∼300 meV. The microphotoluminescence (μPL) system consisted of an inverted microscope, a spectrometer with a cooled EMCCD camera, an avalanche photodiode for decay acquisitions and a liquid-He cryostat for low-temperature studies. The excitation source was a 405 nm diode laser which could be modulated from cw up to the MHz range for time-resolved measurements. In total, the PL decay and spectrum of 17 QDs were measured at 2, 10, 20, 40, 70, 140, 220, and 300 K. Since their emission range was 1.6−1.9 eV with fwhm of ∼150 meV, we can state that all the nanocrystals probed in this work experience a similar quantum confinement effect and can differ only in the passivation type (oxide or ligands). Figure 2a shows the PL spectra of a single oxide-passivated Si-QD measured at different temperatures, from 2 to 300 K. By

Studies of single QDs (both Si13,14 and from direct bandgap QDs15−18) have also revealed an ON/OFF intermittency (or blinking) under continuous-wave excitation at long time-scales (∼ms−s), from recording of the PL intensity time trace. Indications of the blinking extension to shorter time scales were also obtained via time-correlated measurements.17,18 Furthermore, the recent puzzling observation of delayed luminescence, reported for several direct-bandgap nanocrystals such as CdSe, Cu+-doped CdSe, and CuInS2 NCs, has also suggested the presence of a very fast blinking, with a detrimental effect on the QE.19−22 Note that, during a long accumulation, the blinking obviously would result in a “grey” PL intensity, although the exact effect on observed efficiencies has not been deciphered. In addition, many blinking QDs (e.g., CdSe-QDs) exhibit power-law ON- and OFF-time distributions with heavy tails, making impossible to evaluate average times without introducing artificial truncations.16,23 These kinetically broad distributions seem to hold even when blinking is very fast (∼ns−μs), as shown by the delayed luminescence,19−22 thus, hindering a clear understanding of the underlying physical process as well as its analytical formulation at different time scales. In contrast to non-normalized laws lacking an average ONand OFF-time (and therefore also average PL intensity), monoexponential blinking statistics have been reported for oxide-passivated Si-NCs exhibiting clear ON-OFF intensity levels.13,14 On the other hand, functionalization of the surface with organic ligands has recently allowed to obtain Si-NCs featuring high quantum yields (∼70%) both in colloidal solutions24 and in polymer solids.25 Those reportedly show no blinking26 and feature near-unity internal quantum efficiency (IQE),27 an ideal reference sample without “grey” particles. In this Letter, we demonstrate that nonradiative recombination in semiconductor nanocrystals with strong Auger recombination can be consistently explained as a very fast carrier-trapping phenomenon leading to rapid luminescence intermittency. We call it “rapid trapping” or equivalently “rapid blinking” and it is based on carrier tunneling to and from resonant trap states present in the shell of the NC. In our model, there is no need to assume any slow (∼μs−ns) unknown nonradiative process involving complex scenarios,5,6,12 while the true loss mechanism can be just ultrafast Auger recombination set up by rapid carrier trapping, as depicted in Figure 1c (right schematic). For the case considered here, Si/SiO2-NCs, the static nature of the traps is confirmed by this work, previous blinking data13,14 as well as numerous microelectronics studies of the “random telegraphic noise” effect.28−31 Characteristic nonradiative times seen in the experiment can then vary broadly, defined only by the coretrap separation, naturally bridging over to normal blinking, observed at longer time scales and eventually to dark nanocrystals for very long trapping times (typically observed at low temperatures). Furthermore, our model may explain the increase of nonradiative recombination toward room temperature simply as an effect of phonon-induced broadening of the emission peak giving access to more trap states by resonant tunneling. In order to validate such a rapid blinking scenario, we used Si-NCs featuring monoexponential blinking statistics and similar emission energies (i.e., experiencing similar quantum confinement effects), which allowed (i) to study the physical effect in its purity, unmasked by broad kinetics and to adequately model it by means of a static three-state system; (ii)

Figure 2. (a) Normalized PL spectra and (b) decays of an oxidepassivated Si-QD (dot306) taken at different temperatures under cw and modulated excitation, respectively. Each spectrum has an arbitrary intensity offset and decays show binned data (circles) and mono/ biexponential fittings (dashed lines) in a semilog scale. The decay at 300 K is rescaled in the inset for clarity. 2991

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Figure 3. (a) Electron energy diagram and schematic PL spectra for a rapid blinking Si/SiO2−NC. Energy shift of conduction (ΔECB) and valence (not shown) band and bandgap energy (Eg) as found by Seguini et al.45 The light blue bell is a qualitative sketch of the electron wave function and dashed lines indicate energy-level thermal broadening. N trap states are present in the SiO2 shell. (b) Corresponding state-transition diagram. States: ⟨0⟩ unexcited, ⟨ON⟩ exciton, ⟨OFFi⟩ electron trapped at ith trap, ⟨XX⟩ biexciton, and ⟨X+⟩ positively charged exciton. Rates: ΓG generation, Γr radiative, ΓA Auger, ΓON−OFFi (ΓOFFi−ON) trapping (detrapping) rate to (from) ith trap.

discard the possibility to have delayed emitted photons at much longer times also in our material system, given the limited time scale (∼μs−ms) that can be probed experimentally for single Si-QDs. However, our results are indeed consistent with a link between delayed PL and “rapid blinking”, since our oxide-passivated Si-NCs feature monoexponential blinking statistics instead of power-laws.13,14 In addition, the delayed PL here reported at the single-dot level could also contribute to the long (>100 μs) tail observed in spectrally resolved PL decay of Si-NCs ensembles,44 which cannot be explained by variations in nonradiative rates (SRH recombination is a much faster process). The rapid blinking model we propose here is based on the energy diagram of Figure 3a drawn for a Si-NC emitting at 1.75 eV (as dot306) and on the corresponding state-transition diagram of Figure 3b. Once an exciton is generated (state ⟨ON⟩), the electron in the Si core can tunnel to one of the N static resonant traps present in the neighboring oxide, leaving the NC charged (state ⟨OFFi⟩). In that case, fast nonradiative Auger recombination becomes dominant upon further photon absorption (state ⟨X+⟩).43 The same nonradiative process happens when a biexciton is present in the nanocrystal (state ⟨XX⟩). The finite number of available (resonant) trap states depends on the energy-level broadening which grows linearly with temperature (see Figure S4).37 The nature of these trap states is not clear but their static character is confirmed by this work, previous blinking data,13,14 and microelectronics studies of this material system.28−31 In those works, monoexponential charge switching statistics corresponding to single oxide traps have been reported for small area MOSFETs. The location of a trap was determined by analyzing the dependence of trapping and detrapping rates with carrier concentration: while a weak dependence was found for a Si trap, an increase of trapping rate with carrier concentration characterizes a trap in the gate oxide.30,31 An analogous behavior of the ON-OFF blinking rate with excitation power (i.e., carrier concentration) was found for Si/SiO2−NCs as well.14 For the system considered here (Si-NCs), Auger recombination is strong (ΓA ≫ ΓON−OFFi and ΓA ≫ ΓOFFi−ON) and the NCs relax very fast from states ⟨XX⟩ and ⟨X+⟩. By neglecting high excitations (those affect only amplitudes A1,2, but not eigenvalues Γ1,2), the decay constants of ON-state population can be found either by solving Kolmogorov equations or by using a probability density (PD) approach (more details in Supporting Information). Both methods confirm that the PL decay for a single static trap has a biexponential form, as in eq

decreasing the temperature, the no-phonon (NP) PL line width becomes narrower, revealing characteristic silicon TA (∼15 meV) and TO (∼60 meV) phonon replicas, and the emission energy is blue-shifted. This blue-shift naturally follows from the widening of the Si bandgap (see also Figure S3).5,35,36 For the same dot, the low-temperature PL decays are presented in Figure 2b. Although at 300 K the decay can be well-fitted by a monoexponential function, at low temperatures a biexponential decay becomes apparent. The temperature dependence of the NP-line width37 and its peak position, as well as the clear presence of material-specific phonon replicas38 strongly indicate emission from quantum-confined excitons in silicon: only the measured particles satisfying these stringent requirements were considered as single Si-NCs in our study. Indeed, if we exclude the unlikely event of two distinct and adjacent Si-NCs emitting at the same energy, the temperature evolution of the PL spectrum should reveal two narrow NP emission lines at low temperatures when two different adjacent emitters are measured. The lack of clear singlet−triplet emission line splitting36,39−41 can be attributed to the mixing of dark and bright excitons in the presence of trap states.42 As in Figure 2b for dot306, our decay measurements on many individual objects (see, for example, Figure S5 for better signal-to-noise ratio data) reveal that the PL intensity decay can be generally described as IPL = A1e−Γ1t + A 2 e−Γ2 t

(1)

where Γ1 and Γ2 are respectively the fast and slow rates (Γ1 > Γ2), both in the kHz range. Thus, usually the decay is not governed by a single rate, as we would expect from a fully radiative recombination process,25,27 but other processes rather than the radiative must be involved. Obviously, Γ1 cannot be directly associated with Auger recombination (ΓA > 1 GHz)43 and both Γ1 and Γ2 vary with temperature, as shown later. The existence of a second recombination path in a single Si nanocrystal (Γ2), with a lifetime exceeding the radiative lifetime, suggests the presence of delayed luminescence, which was already observed in other types of NCs featuring powerlaw blinking statistics.19−22 In those works, given the claimed link between blinking and delayed PL, the latter was extending on time scales orders of magnitude longer than the radiative lifetime. Conversely, here the first-reported delayed contribution from single Si-NCs does not show broadly distributed kinetics, but decays monoexponentially with the temperaturedependent rate Γ2. It is important to note that we cannot 2992

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ACS Photonics 1 with Γ2 < Γr < Γ1. In general, with N distinct resonant traps the PL decay can be shown to be the sum of (N + 1) decaying exponential functions, arising from the electron trapping/ detrapping processes. Furthermore, the PD approach can be used to find also the PL decay of a NC with monoexponential ON−OFF and power-law OFF−ON distributions, which could correspond to traps fluctuating in energy or real space over time. Hence, 2

IPL(t ) = Γre tb erfc(t 1/2b), if τ ≪ Γ−r 1 (2a) ÄÅ É 2 Ñ Å ij t 1/2 Γr yzÑÑÑ Γ ÅÅ 1 Γr t jijjj Γbr zyzzz zzÑÑÑ, if τ ≫ Γ−1 j − k { erfcj IPL(t ) = r ÅÅÅÅ e jj zzÑÑ r b ÅÅÅ (πt )1/2 b k b {ÑÑÖ Ç (2b) 1/2

where b = ΓON−OFFθ , erfc is the complementary error function, and θ is the truncation time (more details in Supporting Information). The result is similar to what was found experimentally for example in CuInS2−NCs.22 Due to the need of artificial truncation of the power-law OFF−ON distribution, it is not possible to extract switching rates from such a PL decay curve, neither we can have information regarding the quantum efficiency. On the other hand, unmasked by broad kinetics, Si-NCs allow to extract such useful parameters from detailed analytical analysis based on eigenvalues of the observed decay constants Γ1,2 here. Correct amplitudes A1,2 of eq 1 can be found by simulating the decays using a full Monte Carlo approach, taking into account both high excitations and the experimental square-wave pulse shape used here (Figure S5 and related text). In order to estimate the radiative rate Γr, we first consider that it is passivationindependent for Si-NCs (i.e., core-related emission)25,27,46 and our single-dot sample have a similar photonic embedding as the one used by Miura et al.46 which was also oxidized. Thus, given the emission energies of our Si-NCs (1.6−1.9 eV), the radiative rate can be estimated to be in the range of 10−20 kHz. In addition, Γr can be considered to decrease by a factor of ∼3−5 only from 300 to 2 K, as indicated by recent temperature-dependent decay measurements on ensembles of ligand-passivated Si-NCs47,48 and from the absence of clear triplet-state emission in our sample. Indeed, the transition from singlet to triplet state would be accompanied by a ∼1−2 orders of magnitude decrease of Γr.36,39−41 Measured biexponential decays allow the extraction of trapping/detrapping rates (or rapid blinking switching rates). Given the three decay rates (Γ1, Γ2, Γr), the rapid blinking switching rates and the ON-state duty cycle δON (luminescence efficiency) can be found as (from eq S14) ΓON−OFF = (Γ1 − Γr)(Γr − Γ2)/Γr

(3a)

ΓOFF−ON = ΓΓ 1 2 / Γr

(3b)

δON =

ΓΓ 1 2 Γr(Γ1 + Γ2 − Γr)

Figure 4. Temperature-dependent data of different Si/SiO2−NCs. (a) Fast (blue dots) and slow (red dots) rates from biexponential fitting of measured PL decays. Rates from monoexponential fitting (green dots), calculated slow rates (stars) and assumed radiative rate range (gray area). (b) Rapid blinking ON−OFF rates (purple triangles) and ON-state duty cycles (orange dots) extracted from eq 3a and 3c, respectively. In both plots error bars are uncertainty on data and thick lines are trends.

intrinsically low emission rate (∼10 kHz), it was not possible to measure each dot through all the temperatures. For T > 150 K only Γ1 can be measured since Γ2 becomes much smaller than Γ1, reducing the signal below the noise level. In that range, Γ2 was evaluated from eq 3c, using known values of efficiency δON (10% and 30%, respectively, at 300 and 220 K).49 As the temperature decreases below 150 K, ΓON−OFF drops and δON increases due to less resonant traps available (cf. Figure 3). Consequently, both fast and slow rates can be clearly resolved for several nanocrystals. However, some dots show monoexponential decays also at low temperatures, which are characterized by one rate lying in between fast and slow rates (green circles). This result can be explained if the dots exhibit suppressed rapid trapping, for example, for nanocrystals with fewer or totally absent resonant traps. The OFF−ON rates seem to exhibit a more complex temperature behavior (Figure S7). The difference between ON−OFF and OFF−ON rates could be due to the significant exciton binding energy of SiNCs, ∼200 meV for our emission energies.50 Finally, the contribution of delayed luminescence in the total signal is substantial (>75%) over the whole temperature range (Figure S7), highlighting the importance of this process in nanocrystal luminescence. Regarding other types of QDs the temperature dependence of the trapping/detrapping dynamics as well as the related absolute value of rates can vary due to different radiative recombination rate, Auger process, phonon coupling, singlet−triplet splitting and state intermixing w.r.t. to Si-QDs. For example, in CdSe-QDs the trapping can be faster (∼ns) and the temperature-dependence of the dynamics is shown to be not strong at least from 20 K to room temperature.22 Since the properties of the trapping/detrapping effect are now established, we are in a position to evaluate its manifestation in a continuous-wave excitation experiment. By solving the rate equations in steady-state conditions (see

(3c)

Figure 4a shows measured decay rates Γ1 and Γ2 of different oxide-passivated single Si-NCs as a function of temperature. The extracted rapid blinking ON−OFF rates and ON-state duty cycles from eqs 3a and 3c are illustrated in Figure 4b. As a support of our analytical expressions, Monte Carlo simulations confirmed that the as-extracted parameters are within the simulation statistical uncertainty range (see Figure S5 and related text). It is important to note that, due to the 2993

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considering the presence of rapid blinking only for the oxideembedded sample. Additionally, the inset of Figure 5 shows the normalized IQE (IQE = 1 refers to the unitary slope, not to the absolute quantum yield). There is a significant decrease in quantum efficiency for the oxide-passivated sample with respect to the ligand-passivated one already at moderate excitations. This is a natural outcome of our model, where the strong Auger process appears at lower pumping due to random charging in the oxide-embedded particles. Within this picture no mysterious “slow” nonradiative process is needed to account for the existence of “grey” nanocrystals, that is, with 0 < IQE < 1. For an ensemble of nanocrystals one must also consider dark nanocrystals (with a defect such as a dangling bond) which may decrease the external QE further and the presence of nanocrystals with imperfect ligand passivation,52 whose behavior would be interesting to study in a future work. Finally, for other material systems it is important to note that the combination of radiative, trapping/detrapping and Auger processes can differ in terms of characteristic times. In conclusion, we have demonstrated that nonradiative recombination in semiconductor nanocrystals featuring strong Auger recombination can be consistently described without assuming any slow unknown nonradiative process, but considering instead a very fast carrier-trapping/detrapping process, characterized by rapid luminescence intermittency. We call it “rapid trapping” or “rapid blinking”: it is based on resonant tunneling to trap states resulting in delayed luminescence and leading to ultrafast Auger processes decreasing the efficiency. To prove the model, we have overcome the inherent limitations of nanocrystals with heavytailed blinking distributions lacking average values: oxidepassivated Si-NCs exhibiting monoexponential blinking statistics and very fast Auger processes have allowed to extract characteristic rapid blinking rates and QE as well as their analytical formulas. Analyzing single Si-NCs we have for the first time observed monoexponential delayed luminescence at low temperatures suggesting the existence of a single oxiderelated resonant trap. Our model has allowed to extract switching rates > 10 kHz comparable with the radiative rate of the nanocrystal and generally increasing with temperature. As predicted by our rapid trapping scenario, there is a significant reduction of quantum efficiency under continuous wave excitation for oxide-covered Si-NCs with respect to trap-free, ligand-passivated ones. Ligand-passivated Si-NCs featuring near-unity IQEs25,27 seem to lack this nonradiative mechanism. Thus, the oxide matrix imposes inherent limitations on the luminescence efficiency of silicon nanocrystals due to its intrinsic trap sites. Apparently, the quality of the shell, and not only the interface, needs to be considered for the fabrication of highly efficient luminescent semiconductor nanoparticles. Although the combination of trapping/detrapping, radiative and Auger processes is specific for a certain material system, our rapid blinking model is intended also for other semiconductor NCs. In direct bandgap QDs such as for instance CdSe QDs, these processes may be observed at significantly shorter time scales while decays due to a complex scenario of inter-related trap states, characterized by power-law blinking statistics, become largely nonlinear. Since radiative recombination for these systems is on par with the Auger recombination rate it may be less dramatic than for the SiNC system. Yet, we believe that similar fundamental trapping mechanisms are at play explaining nonradiative recombination.

Supporting Information), the PL integrated intensity of a rapid blinking NC can be found as IPL =

σ Φex 1+

σ Φex Γr δON

+

(σ Φex )2 Γr δON ΓA

≈

σ Φex 1+

σ Φex Γr δON

(4)

where the approximation is valid if Auger recombination is very strong, ΓA ≫ σΦex with σ as the absorption cross-section and Φex as the excitation photon flux. The internal quantum efficiency is then IQE =

ΓrδON ΓrδON + σ Φex

(5)

reaching 100% at low excitations Φex → 0, as would be expected when the only nonradiative process is Auger recombination. eq 4 differs from the usual formula51 by the presence of the equivalent rate ΓrδON which results from the competition between radiative recombination and trapping/ detrapping processes. It is important to note that eqs 4 and 5 can be used for a trap-free NC by considering ΓON−OFF = 0 (i.e., δON = 100%). In addition, when other fast nonradiative processes are present, the equations can be easily modified to include those also. According to eq 4, by comparing a sample of oxide-passivated rapid blinking Si-NCs with a reference one of trap-free Si-NCs, for example, ligand-passivated, where blinking can be suppressed,26 one should notice a different power-dependence behavior. Figure 5 shows the measured PL integrated intensity in arbitrary units at 300 K as a function of excitation flux for two

Figure 5. PL integrated intensity in arbitrary units versus excitation flux (cw mode) for ensembles of Si-NCs: trap-free dodecenepassivated (red) and oxide-passivated (green) solids. Measured data (dots) and theoretical data from eq 4 (dashed lines) with σ = 10−16 cm−2, Γr = 20 kHz, and ΓA = 10 GHz. Black dotted line refers to a unitary slope with normalized IQE of 1. Inset shows normalized IQE for both ensembles. Pale blue area indicates efficiency loss due to rapid blinking.

ensembles of Si-NCs, oxide-passivated and dodecene-passivated in PMMA. Although the samples have similar emission spectrum (Figure S2), that is, they feature similar Γr,46 their power-dependence behavior is remarkably different. In fact, the PL of oxide-embedded Si-NCs shows a saturation-like effect at lower excitation fluxes compared to ligand-passivated ones. An analogous qualitative result was found in CuInS2−NCs, where the intensity of the delayed part of the luminescence reaches a plateau under lower pumping compared to the nondelayed part.21 As shown by the dashed lines in Figure 5, the relative PL intensities can be described well by our model with eq 4 by 2994

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.8b00581. Experimental details, additional data, discussion, and theory (PDF).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Federico Pevere: 0000-0001-5304-913X Ilya Sychugov: 0000-0003-2562-0540 Author Contributions

F.P. and F.S. carried out measurements and analyzed the data. B.B. fabricated the samples. F.P. and I.S. built the theoretical model. F.P. and F.S. wrote the first manuscript draft and I.S. and J.L. contributed to the final version. I.S. and J.L. supervised the overall work. Funding

Swedish Research Council (VR) through an individual contract and through a Linné grant (ADOPT), SPIE through an individual scholarship. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank A. Marinins and T. Chulapakorn for the help with sample preparation. Financial support from the Swedish Research Council (VR) through an individual contract and through a Linné grant (ADOPT) is gratefully acknowledged. F.P. thanks SPIE for an individual scholarship.

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ABBREVIATIONS NC, nanocrystal; QD, quantum dot; PL, photoluminescence; CW, continuous-wave; QE, quantum efficiency; IQE, internal quantum efficiency.

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REFERENCES

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