Size and Temperature Dependencies of the Low-Energy Electronic

Article pubs.acs.org/JPCC

Size and Temperature Dependencies of the Low-Energy Electronic Structure of PbS Quantum Dots Aleksandr P. Litvin, Peter S. Parfenov, Elena V. Ushakova, Ana L. Simões Gamboa, Anatoly V. Fedorov, and Alexander V. Baranov* ITMO University, 49 Kronverkskiy prospekt, Saint Petersburg, 197101 Russia ABSTRACT: The analysis of the steady-state and transient photoluminescence (PL) of PbS quantum dots (QDs) of diameter in the 3.2− 6.9 nm range in porous matrixes at temperatures 77−300 K shows that QDs of different sizes possess entirely different temperature dependencies of their PL properties. The data indicates the presence of two emissive “in-gap” states in the low-energy electronic structure of the QDs with characteristic dependencies on QD size and temperature. The lowest energy state is associated with surface defect states while the higher energy state is “intrinsic” and arises due to size-dependent splitting of the lowest excitons.

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∼4−5 nm QDs, reported values for the temperature coefficients vary from 6022 to 530 μeV/K,23 concentrating mainly at ∼300 μeV/K.15,19,24,25 It seems worth noting that different temperature coefficients have been obtained for absorption and PL spectra peak positions,15,26 indicating that the low-energy electronic structure of PbS QDs possesses some peculiarities that are unusual for other types of QDs. It has been proposed that an electron state of energy smaller than the energy of the band gap, e.g. a surface trap state27 or a dark exciton state,19,26 may be responsible for the temperature dependencies of QD PL peak position and their sizedependence. The existence of an unconventional in-gap state (GS) of size-dependent energy, responsible for the unusual size-dependence of QD PL properties, has been reported in numerous papers.12,14,15,28 For example, a decrease of the PL Stokes shift from 300 to 5 meV and a reduction of the PL decay time from ∼2.5 μs to 250 ns with increasing QD size from 2.5 to 8.8 nm was found for PbS QDs in diluted solutions at room temperature.28 The observed strong size-dependence of the PL decay time was interpreted in terms of a temperature-controlled phonon-induced transition from a long-lived GS to the ground state of the QDs.28,29 The appearance of additional bands with specific temperature dependencies of PL spectra of PbS QDs have been reported in several works. Szendrei et al.21 observed the appearance of a second PL component in the PL spectra of PbS thin films after benzenedithiol treatment. Both PL components exhibit qualitatively similar temperature dependencies, namely, the peaks exhibit a red shift with temperature decrease. Electron or

INTRODUCTION Quantum dots (QDs) of narrow-gap semiconductors (PbS, PbSe) have become promising materials for near-infrared nanophotonics,1 medicine and biology,2,3 and solar energy4−6 applications. Exceptional properties such as high extinction coefficient7,8 and highly efficient multiple exciton generation9,10 make PbS QDs stimulating objects of research. In particular, since the discovery that PbS (as well as PbSe) QDs possess extremely long photoluminescence (PL) lifetimes8,11 and large, size-dependent Stokes shift,12−15 their low-energy electronic structure has been extensively investigated theoretically and experimentally. In contrast to the groups II−VI and II−V QDs, the temperature-induced variation of the electron−hole transition energies and rates of PbS QDs is strongly dependent on QD size. Information about the temperature dependence of PL characteristics of PbS QDs is of great importance for designing PbS QD-based devices operating at reduced temperatures, e.g., infrared photodetectors. A detailed analysis of the temperature dependence of the PbS QD energy gap was first reported by Olkhovets et al.16 It was shown, for strongly confined QDs in glass and polymer matrixes, that the temperature coefficient α = dEG/dT, where EG is the QD band gap energy determined as the energy of the lowest absorption peak, depends on QD size. In particular, when the QD diameter varies from 3 to 15.5 nm, the coefficient changes sign, varying from slightly negative values to a value approaching that of the bulk PbS, ∼500 μeV/K.17 Posterior reported values of dEG/dT for PbS colloidal QDs and QDs embedded in glass matrixes agree well with the data obtained by Olkhovets et al.15,18−21 Meanwhile, the temperature dependencies of QD PL peak positions (dEPL/dT) reported in the literature differ very much from each other, even for QDs of similar sizes. For instance, for © 2014 American Chemical Society

Received: July 18, 2014 Revised: August 18, 2014 Published: August 19, 2014 20721

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RESULTS AND DISCUSSION Typical absorption and PL spectra of PbS QDs of three different sizes in liquid solutions at room temperature are shown in Figure 1. The lowest energy peak observed in the

hole trap states, caused by defects of passivation, have been suggested as the origin of the second PL component. Similar features were observed by Kim et al.,20 who identified three PL components, two of them being attributed to defect-related energy states. Pendyala et al.30 has found similar temperature dependencies of the peak positions for two PL components, where the high-energy component was attributed to the existence of Pb dangling bonds forming shallow donor states. On the other hand, S dangling bonds may create additional shallow acceptor states that would be responsible for the lowenergy PL component. The fact that the energy structure and the mechanisms of energy relaxation in PbS QDs have not been completely understood yet renders difficult the analysis of PL temperature dependencies. Meanwhile, the analysis of temperature dependence of PL energy spectra and kinetics and, in particular, their size-dependence, allows insight into the lowenergy structure of PbS QDs. In the present work, the steady-state and transient PL of PbS QDs of diameter in the 3.2−6.9 nm range in porous matrixes at 77−300 K was analyzed. It has been found that QDs of different sizes possess entirely different temperature dependencies of their PL characteristics. These results suggest a model of QD low-energy electronic structure in which two “in-gap” states of QD size-dependent energies are responsible for the radiative electron−hole annihilation. The energies of these states follow qualitatively similar temperature dependencies, while the origin of the states is speculated to be different. The lowest energy emissive state is associated with a defect-induced surface-trap electron or hole state, while the higher energy emissive state is “intrinsic” and arises, most likely, from sizedependent splitting of the lowest excitons.

Figure 1. Room temperature absorption (solid curves) and photoluminescence (dotted curves) spectra of PbS QDs of three different sizes (d = 3.2, 4.4, and 6.9 nm) in carbon tetrachloride. (Inset) Sizedependent Stokes shift of the PL band.

absorption spectra can be well fitted by one Gaussian for both QD colloidal solutions and QDs in the matrix. This peak has a minor red shift (∼5 meV) and slight widening (∼5 meV) after embedding the QDs into the matrix. The inset to Figure 1 shows that the PL band exhibits size-dependent Stokes shifts (calculated here as the difference between the positions of the first absorption peak and the center gravity of the PL band). This feature arises due to the presence of a GS of sizedependent energy that contributes to the QD PL.12,14,15,28 Decreasing the temperature resulted in an increase of the PL intensity, reduction of the fwhm, and red-shift of the PL peak position for all the samples studied. These dependencies are illustrated in Figure 2 for the 4.6 nm QDs as example. The PL intensity and the fwhm are estimated here using one Gaussian. Obtained dependencies agree well with the literature data.15,19,21

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EXPERIMENTAL SECTION PbS QDs of diameters d in the 3.2−6.9 nm range and band gap energy of 1.46−0.77 eV, respectively, stabilized by oleic acid, were synthesized via the procedure described in ref 28. The QDs were dissolved in carbon tetrachloride and embedded into the porous matrix, as described in ref 31. In order to exclude the influence of nonradiative energy transfer between QDs, their concentration in colloidal solutions was kept as low as ∼5 × 10−6 M.32 For the PL measurements, the samples of porous matrix with embedded QDs were placed into a Linkam THMS600 Microscope Stage cryostat connected to a Linkam LNP94 cooling pump and controlled by a Linkam TMS94 temperature controller, which allowed tuning the sample temperature in the 77−300 K range. Steady-state and transient PL analysis was conducted using a purpose-built experimental setup described in refs 33 and 34. Continuous wave radiation at 633 nm from a 15 mW He−Ne laser or 10 ns pulse 527 nm radiation from a 8 mW YLF:Nd3+ laser with 4 kHz repetition rate was focused onto the sample into a 0.1 mm spot. Under these conditions, the average laser fluence did not exceed 15 kW/cm2. PL spectra of 6 nm spectral resolution were measured using an Acton 2552 spectrometer equipped with a InAsGa photodiode cooled down to −20 °C. In the transient experiments the QD PL was detected by a fast InGaAs photodiode with time response as fast as 5 ns. The PL decay curves were averaged over 105 measurements by means of purpose-built software.35 Four independent measurements of the PL spectra and PL decays were made for random areas of the samples at each temperature.

Figure 2. Typical shift of PL band with temperature change in the 77− 300 K range. (Inset) Typical temperature dependencies of PL intensity and fwhm.

It has been shown that the spectral and kinetic characteristics of QD PL at particular temperatures are governed, respectively, by the gap ΔE between the GS and the lowest energy-confined electron−hole 1s1s state and by the diameter of the QDs.28 Conversely, for a given QD size the QD PL characteristics are controlled by temperature.19 Hence, different temperature 20722

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dependencies of the PL parameters for QDs of different sizes may be anticipated. According to the energy gap (ΔE), three size categories of the QDs studied in this work can be considered: (a) the largest PbS QDs (d = 6.9 nm), where the GS does not influence the QD PL and the PL relates mostly to the transition from the 1s1s state to the ground state; (b) the smallest PbS QDs (d = 3.2, 3.6 nm), where the GS dominates the QD PL (due to the very large energy gap and low probability of nonradiative transitions from the GS to the 1s1s state) and the PL relates mostly to the GS; and (c) the intermediate-sized PbS QDs (d = 4.4, 4.6, and 6.0 nm), where the QD PL is governed by radiative recombination via both the 1s1s state and the GS (PL1 and PL2), since direct and inverse nonradiative transitions between these states take place. The low-energy electronic structure of the PbS QDs for the proposed scenario is illustrated in Figure 3.

Figure 4. Temperature dependencies of the PL peak position for PbS QDs with d = 6.9 nm in a porous matrix. The solid line shows the Varshni fit of the experimental data with the parameters listed in the legend.

depend on the temperature, and no additional effects should be considered in the case of the largest QDs studied. b. Smallest PbS QDs. For the smallest QDs studied (d = 3.2, 3.6 nm), the effect of the GS on the PL should play a crucial role because of the large energy gap ΔE between the 1s1s state and the GS (cf Figure 3), which causes a large Stokes shift of ∼230 meV. The nonradiative transition rate from the 1s1s state to the GS may be comparable to or even higher than the recombination rate from the 1s1s state. Meanwhile, reverse transitions from the GS to the 1s1s state are negligible because of the large ΔE. Thus, the PL component related to the GS will dominate the total PL spectrum. Indeed, the PL spectra of d = 3.2 and 3.6 nm QDs may be well fitted by one Gaussian for all the temperatures studied. The temperature dependence of the PL peak positions is due to the GS and can be also well-fitted using the Varshni equation with coefficients α = 110 ± 10 and 120 ± 25 μeV/K for PbS QDs of diameter d = 3.2 and 3.6 nm, respectively. c. Intermediate-Sized PbS QDs. For QDs of intermediate sizes, both direct and reverse nonradiative transitions between 1s1s and GS states can be effective at temperatures T, when ΔE becomes comparable with kBT, where kB is the Boltzmann constant. Then, the QD PL spectrum is expected to be composed of two PL components, PL1 and PL2, related to the transitions from the 1s1s state and from the GS to the ground state, respectively.28 The lower the temperature, the smaller the efficiency of the reverse nonradiative transition, leading to a weakening of the PL1 component in the total PL signal. Indeed, the observed PL spectra for d = 4.4, 4.6, and 6.0 nm QDs are broadened and asymmetrical. They can be well-fitted by two Gaussians in the whole range of temperatures studied. This is illustrated in Figure 5 for the d = 6.0 nm QDs as an example. As expected, the contribution of the high-energy component to the PL signal decreases with temperature. An analogous fitting for the PL spectra of d = 4.4 and 4.6 nm QDs also showed two PL bands. In contrast to PbS QDs in liquid solution,28 it was found that the high-energy PL component, usually ascribed to the transition from the 1s1s state to the ground state, has a size-dependent Stokes shift (Δ1) increasing from 5 ± 3 to 53 ± 5 meV with reduction of the QD size from d = 6.9 to 4.4 nm. This indicates that, besides a conventional GS, PbS QDs embedded in the porous filter paper matrix have an additional luminescent in-gap electronic state, GS1, that gives rise to the PL1 bands. The probable origin of this state will be discussed below and it will be tentatively ascribed to the low-energy component of the split 1s1s exciton

Figure 3. Low-energy electronic structure of PbS QDs of different sizes (largest QDs, d = 6.9 nm; intermediate size QDs, d = 4.4, 4.6, and 6 nm; smallest QDs, d = 3.2, 3.6 nm). Δ1 and Δ2 indicate the Stokes shifts for the PL1 and PL2 luminescence bands, respectively, and ΔE shows the energy gap between the states responsible for the PL1 and PL2 bands.

a. Largest PbS QDs. For the largest QDs studied in the present work (d = 6.9 nm), the PL band can be well fitted by one Gaussian in the whole temperature range. The Stokes shift is only Δ1 = 5 meV at 300 K while the widths of the PL and absorption bands are equal. This suggests that the PL relates to the 1s1s state only and that the effect of the GS is not manifested for QDs of this size. The analysis of the PL kinetics supports this conclusion, since the PL decay can be well fitted by one exponential with decay time increasing from ∼80 to ∼100 ns and temperature decreasing from 300 to 77 K. The temperature shift of the PL peak position may be described using the Varshni equation36 EG(T ) = EG(0) + α

T2 T + θD

where EG(0) is the band gap energy at 0 K, α is the coefficient of the band gap shift dEG/dT, T is the temperature, and ΘD is a constant which is generally close to the Debye temperature.37,38 When this equation is used for the analysis of QDs PL, EG usually means the energy of the lowest 1s1s excitons state.19 Since the equation is used here to describe the PL both from the 1s1s state and GS, the notations E1s1s and EGS are used for clarity. The constant ΘD was kept at 145 K (which corresponds to the bulk PbS value) for all fits. Fitting the temperature dependence of the PL peak position for d = 6.9 nm QDs using the Varshni equation (Figure 4) gives α = 150 ± 5 μeV/K. This value is in good agreement with that obtained from the temperature dependence of the PbS QD energy gap (EG) by Olkhovets et al.16 for QDs of the same size. This evidences that the PL relates to the 1s1s state only. The Stokes shift does not 20723

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Figure 5. Two-Gaussian fit of PL spectra of PbS QDs with d = 6.0 nm at different temperatures. PL1 and PL2 are the luminescence bands related to the 1s1s and GS states, respectively.

trap states of PbS QDs. However, in the present study, they have different α values. The high-energy PL1 component is characterized by α = 155 ± 20 μeV/K. This value is close to that obtained for the largest QDs (d = 6.9 nm), for which only the PL1 component was detected. The low-energy PL2 component has α = 120 ± 15 μeV/K, which is close to the value α obtained for the smallest d = 3.2 and 3.6 nm QDs, where PL2 dominates the QD luminescence. It can be seen that the temperature coefficients α for the PL2 components are very close for QDs of different sizes and lie in the range 110−140 μeV/K; i.e., α for PL2 is independent of the QD size within the estimation error. This constitutes additional evidence for the surface-trap electron or hole state as the origin of this PL component.12,15,20,28 On the other hand, α values for PL1 are very different for d = 4.4, 4.6 and 6.0, 6.9 nm QDs, with α being considerably larger for smaller QDs. This result cardinally differs from the α size dependence for absorption spectra obtained by Olkhovets et al.,16 where α increases monotonically from ca. −50 μeV/K for 3 nm QDs to ca. 400 μeV/K for 15.5 nm QDs. The authors16 showed that different mechanisms, such as thermal expansion of the lattice and the wave function envelope, mechanical strain, and electron−phonon coupling, contribute to the temperature dependence of the quantum-dot energy gap and dEG/dT variation with QD size. These differences indicate that the PL1 component in luminescence spectra of the d = 4.4, 4.6 nm QDs originates from an additional in-gap electronic state GS1. Different temperature dependencies for PL and absorption peaks of PbS QDs have been reported by Lewis et al.,15 who pointed out the existence of a peculiar emissive in-gap state. In particular, for d = 4.2 nm QDs at 300 K, they found that the Stokes shift is ∼80 meV and dE/dT is about 300 μeV/K for the PL band. Those values are close to the data obtained in the present work for QDs of intermediate sizes if a one-Gaussian fit of the PL spectra is used as in ref 15. Gaponenko et al.26 have also reported a difference between temperature dependencies of PL and absorption bands for d = 4.8 nm PbS QDs in a glass matrix. In this case, however, the authors claimed that the difference was caused by a temperature-dependent splitting of the 1s1s state and that different intrinsic exciton states were responsible for the absorption and PL processes. It should be noted that the reported Stokes shift of 55 meV at 300 K is close to that of PL1 (Δ1) but not to that of PL2 observed in the present work for QDs of similar size. A ca. 100 meV splitting of the lowest excitons was also supposed to be responsible for the appearance of several bands in the PL spectrum of d = 6.7 nm PbS QDs in borosilicate glass matrixes.41

state, where size-dependent intervalley splitting or electron− hole exchange interaction39,40 is responsible for the 1s1s state splitting. The Δ1 values (cf. Figure 3) for QDs of different sizes are listed in Table 1 together with the Stokes shift (Δ2) of the GS related to PL2. Table 1. Stokes Shifts, Δ, and Temperature Coefficients, α, for PL1 and PL2 of PbS QDs of Different Diameters, d QD d, nm

abs peak (300 K), eV

Δ1 (300 K), meV

± ± ± ± ± ±

0.773 0.849 1.051 1.107 1.298 1.459

5 12 40 53

6.9 6.0 4.6 4.4 3.6 3.2

0.3 0.3 0.2 0.2 0.1 0.1

Δ2 (300 K), meV 46 94 104 138 228

α (PL1), μeV/K 150 155 250 250

± ± ± ±

5 20 30 15

α (PL2), μeV/K 120 135 140 120 110

± ± ± ± ±

15 25 25 25 10

The PL decay curves can be well-fitted by a two-exponential function. The decay time of the short exponent at 300 K is about 80 ns for the QDs of intermediate sizes and the decay time of the long exponent at 300 K lies in the range 280−320 ns. The decay times of both components increase with decreasing temperature. The appearance of the long decay component is caused by the existence of the long-lived GS.28,31 For the smallest QDs (d = 3.2 nm), for instance, the decay time of the slow component reaches 1.5 μs at 300 K. The temperature dependencies of the peak position of PL1 and PL2 for the d = 6.0 nm QDs are shown in Figure 6. They are qualitatively similar to each other, as reported by Szendrei et al.21 for two PL bands attributed to the ground and in-gap

Figure 6. Temperature dependencies of the peak position of PL1 (upper line) and PL2 (lower line) for PbS QDs with d = 6.0 nm fitted with the Varshni equation. The obtained fitting parameters are listed in the legend. 20724

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Ministry of Education and Science of the Russian Federation for support through the scholarships of the President of the Russian Federation for Young Scientists and Graduate Students (2013−2015).

Therefore, it is reasonable to assume that in the present case, when QDs are embedded in a porous matrix, the splitting of the 1s1s state and the existence of an in-gap state take place together. The lowest energy emissive state GS is then associated with defect-induced surface-trap electron or hole state,28,42 while the higher energy emissive state is most likely intrinsic and arises from size-dependent splitting of the lowest excitons,19,26,40,41 which, in turn, is probably caused by intervalley splitting or electron−hole exchange interaction39,43 modified by the presence of a strong internal electric field induced by surface-localized electrical charges.44,45 It is therefore not surprising that different bands in the luminescence spectra of PbS QDs exhibit different temperature dependences of their position and intensity. It should be noted that additional energy states active in emission have been observed, as a rule, in PbS QDs embedded in glass and polymer matrixes20,21,26,30,41 and QD layers.15,44 They may be associated, for example, with a network of surface defects,44 intervalley splitting enhanced by the host, 41 electron−hole exchange interaction,40,43 and traps of sole electrons or holes. The origin of these energy states may be different, but in any cases they are an effect of the host matrices that overlaps with the quantum confinement effect, leading to a variation of the PL band energies with QD size. These facts should be taken into account, for example, for the optimization or discrimination of nonradiative resonant energy transfer in systems of densely packed PbS QDs developed for different applications. Further experiments and theoretical calculations, including bulk and surface QD defects, surface local charges, and the influence of host matrixes, are required in order to fully understand the nature of the optically active states in PbS QDs and their size and temperature dependencies.

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(1) Rogach, A. L.; Eychmüller, A.; Hickey, S. G.; Kershaw, S. V. Infrared-Emitting Colloidal Nanocrystals: Synthesis, Assembly, Spectroscopy, and Applications. Small 2007, 3, 536−557. (2) Mozafari, M.; Moztarzadeh, F.; Seifalian, A. M.; Tayebi, L. SelfAssembly of PbS Hollow Sphere Quantum Dots via Gas-Bubble Technique for Early Cancer Diagnosis. J. Lumin. 2013, 133, 188−193. (3) Cinteza, L. O. Quantum Dots in Biomedical Applications: Advances and Challenges. J. Nanophotonics 2010, 4, 042503. (4) Bhandari, K. P.; Roland, P. J.; Mahabaduge, H.; Haugen, N. O.; Grice, C. R.; Jeong, S.; Dykstra, T.; Gao, J.; Ellingson, R. J. Thin Film Solar Cells Based on the Heterojunction of Colloidal PbS Quantum Dots with CdS. Sol. Energy Mater. Sol. Cells 2013, 117, 476−482. (5) Emin, S.; Singh, S. P.; Han, L.; Satoh, N.; Islam, A. Colloidal Quantum Dot Solar Cells. Sol. Energy 2011, 85, 1264−1282. (6) Jumabekov, A. N.; Deschler, F.; Bo, D.; Peter, L. M.; Feldmann, J.; Bein, T. Quantum-Dot-Sensitized Solar Cells with Water-Soluble and Air-Stable PbS Quantum Dots. J. Phys. Chem. C 2014, 118, 5142− 5149. (7) Cademartiri, L.; Montanari, E.; Calestani, G.; Migliori, A.; Guagliardi, A.; Ozin, G. A. Size-Dependent Extinction Coefficients of PbS Quantum Dots. J. Am. Chem. Soc. 2006, 128, 10337−10346. (8) Moreels, I.; Lambert, K.; Smeets, D.; De Muynck, D.; Nollet, T.; Martins, J. C.; Vanhaecke, F.; Vantomme, A.; Delerue, C.; Allan, G.; et al. Size-Dependent Optical Properties of Colloidal PbS Quantum Dots. ACS Nano 2009, 3, 3023−3030. (9) Midgett, A. G.; Luther, J. M.; Stewart, J. T.; Smith, D. K.; Padilha, L. A.; Klimov, V. I.; Nozik, A. J.; Beard, M. C. Size and Composition Dependent Multiple Exciton Generation Efficiency in PbS, PbSe, and PbSxSe1-X Alloyed Quantum Dots. Nano Lett. 2013, 13, 3078−3085. (10) Nozik, A. J. Nanoscience and Nanostructures for Photovoltaics and Solar Fuels. Nano Lett. 2010, 10, 2735−2741. (11) Clark, S. W.; Harbold, J. M.; Wise, F. W. Resonant Energy Transfer in PbS Quantum Dots. J. Phys. Chem. C 2007, 111, 7302− 7305. (12) Fernée, M. J.; Thomsen, E.; Jensen, P.; Rubinsztein-Dunlop, H. Highly Efficient Luminescence from a Hybrid State Found in Strongly Quantum Confined PbS Nanocrystals. Nanotechnology 2006, 17, 956− 962. (13) Warner, J. H.; Thomsen, E.; Watt, A. R.; Heckenberg, N. R.; Rubinsztein-Dunlop, H. Time-Resolved Photoluminescence Spectroscopy of Ligand-Capped PbS Nanocrystals. Nanotechnology 2005, 16, 175−179. (14) Zhang, J.; Jiang, X. Confinement-Dependent below-Gap State in PbS Quantum Dot Films Probed by Continuous-Wave Photoinduced Absorption. J. Phys. Chem. B 2008, 112, 9557−9560. (15) Lewis, J. E.; Wu, S.; Jiang, X. J. Unconventional Gap State of Trapped Exciton in Lead Sulfide Quantum Dots. Nanotechnology 2010, 21, 455402. (16) Olkhovets, A.; Hsu, R.-C.; Lipovskii, A.; Wise, F. SizeDependent Temperature Variation of the Energy Gap in Lead-Salt Quantum Dots. Phys. Rev. Lett. 1998, 81, 3539−3542. (17) Semiconductors Data Handbook; Madelung, O., Ed.; Springer: London, 2003; p 586. (18) Dey, P.; Paul, J.; Bylsma, J.; Karaiskaj, D.; Luther, J. M.; Beard, M. C.; Romero, A. H. Origin of the Temperature Dependence of the Band Gap of PbS and PbSe Quantum Dots. Solid State Commun. 2013, 165, 49−54. (19) Gaponenko, M. S.; Lutich, A. A.; Tolstik, N. A.; Onushchenko, A. A.; Malyarevich, A. M.; Petrov, E. P.; Yumashev, K. V. TemperatureDependent Photoluminescence of PbS Quantum Dots in Glass: Evidence of Exciton State Splitting and Carrier Trapping. Phys. Rev. B 2010, 82, 125320.

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CONCLUSIONS The steady-state and transient PL characteristics of PbS QDs of diameter in the 3.2−6.9 nm range in porous matrixes at temperatures 77−300 K have been analyzed. It has been found that QDs of different sizes exhibit entirely different temperature dependencies of their PL properties. The data obtained has been interpreted using the model of a QD low-energy electronic structure with two emissive “in-gap” states with particular QD size and temperature dependencies. The lowest energy emissive state is associated with a defect-induced surface trap electron or hole state, while the higher energy emissive state is “intrinsic” and arises, most likely, due to the sizedependent splitting of the lowest excitons, which are attributed to the influence of the matrix.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. All authors contributed equally. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was performed in the framework of the government assignment No. 3.109.2014/K of the Ministry of Education and Science of the Russian Federation. A.P.L and E.V.U. thank the 20725

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dx.doi.org/10.1021/jp507181k | J. Phys. Chem. C 2014, 118, 20721−20726