FRET between Close-Packed Quasi-Monodispersed PbS QDs in a

Article pubs.acs.org/JPCC

FRET between Close-Packed Quasi-Monodispersed PbS QDs in a Porous Matrix Aleksandr P. Litvin, Elena V. Ushakova, Peter S. Parfenov, Anatoly V. Fedorov, and Alexander V. Baranov* National Research University of Information Technologies, Mechanics, and Optics, 197101 Saint Petersburg, Russia ABSTRACT: Fö rster resonant energy transfer (FRET) between PbS quantum dots (QDs) in assemblies of QDs with a narrow size distribution (quasi-monodispersed), embedded in a porous matrix, is investigated. Analysis of size-selective steady-state and transient photoluminescence (PL) of these assemblies demonstrates the influence of FRET on the QD optical properties. In particular, we found that FRET drastically changes the QD PL lifetime sizedependence. We show that the FRET efficiency increases up to 35% as the QD concentration in the matrix increases. The observed saturation of the energy transfer efficiency is attributed to the formation of ordered, closepacked, QD structures with minimal interdot distance and, therefore, maximal FRET efficiency. Evidence supporting this conclusion is supplied by smallangle X-ray scattering (SAXS) measurements. Thus, we demonstrate that FRET analysis supplies information regarding the formation of a close-packed ordered structure.

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organized assemblies26 and PbS QD cascaded superstructures.27 Although spectral selected time-resolved spectroscopy is often used for analysis of FRET between QDs, the influence of FRET on the PL dynamics of the QD assemblies has not been investigated thoroughly yet. Here we show that energy transfer leads to a fundamental change in the size-dependence of the QD PL lifetime that is important for improving the performance of light detectors and solar energy converters based on PbS QD superstructures.28−30 Our study demonstrates that FRET technique may supply information regarding the formation of QD superstructures.

INTRODUCTION Infrared (IR) quantum dots (QDs) such as PbS1 and PbSe2 are beginning to replace traditional organic dye luminophores in various photonic applications. A high quantum yield of IR photoluminescence, a broad absorption band, and a high extinction coefficient3 make them attractive for the construction of optical amplifiers, absorbers,4 fluorescence imaging,5 and solar cells.6−8 The optical transitions of lead chalcogenide QDs can be tuned over a wide spectral range, and thanks to their large exciton Bohr radii, they will still be influenced by strong quantum confinement.9 Increasing interest in semiconductor quantum dots has led to the discovery of unusual properties in QD assemblies. It has been shown that the optical properties of these assemblies drastically depend on their density and geometry.10 Alteration of the QD concentration in the assembly can also be used for QD PL optimization.11 Förster resonant energy transfer (FRET) is the most common mechanism causing changes in QD optical properties.12,13 Even in quasi-monodisperse QD assemblies with a narrow QD size distribution, FRET may enhance PL yield.14 When QDs are located close to each other, trapped excitons may transfer to another QD and relax radiatively.15 Self-ordered QD superlattices attract special attention. These structures have already been fabricated with semiconductor,16 metallic,17 and magnetic18 nanocrystals on various substrates and in matrices. An investigation of QD superlattices is essential for the development of nanophotonics.19,20 In the present work, we investigate FRET between PbS QDs in assemblies of QDs with a narrow size distribution, embedded in a porous matrix. FRET between close-packed PbS QDs has been recently studied for nominally monodisperse21−23 and bimodal assemblies,24,25 as well as for monomodal self© 2014 American Chemical Society

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EXPERIMENTAL SECTION Colloidal PbS QDs with a mean diameter of 4.6 nm and a size distribution of ∼10% were synthesized using the standard procedure described in detail in ref 31. The QDs obtained are redispersed in tetrachloromethane (TCM). Absorption and PL spectra of PbS QDs in TCM with peaks at ∼1185 and ∼1255 nm, respectively, are shown in Figure 1a. Owing to overlap of the PL and absorption spectra, a photoexcitation energy transfer can occur in this quasi-monodispersed PbS QD ensemble. We prepared samples consisting of assemblies of PbS QDs in a porous matrix by the method developed in ref 32, i.e., by soaking strips of a 388 grade Sartorius filter paper in solutions of PbS QDs at various concentrations. The averaged over volume of the matrix concentration of QDs in the matrix was obtained by the absorption spectroscopy and the Beer law and varied from 1.2 to 2.8 × 1016 cm−3. Received: January 30, 2014 Revised: March 4, 2014 Published: March 4, 2014 6531

dx.doi.org/10.1021/jp501068a | J. Phys. Chem. C 2014, 118, 6531−6535

The Journal of Physical Chemistry C

Article

Figure 1. (a) Normalized absorption (blue dotted line) and PL (red solid line) spectra of 4.6 nm PbS QDs in TCM; (b) increasing red shift of the QD PL peak with concentration of QDs in the matrix.

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RESULTS AND DISCUSSION In Figure 3, representative PL decay curves for the sample with the highest QD concentration of 2.8 × 1016 cm−3 are shown. All

These samples are characterized by a concentration-dependent red shift of the PL spectra from the QDs in the matrix. The dependence of the QD PL peak position on QD concentration is shown in Figure 1b. It should be noted that photobleaching during the measurement in these matrices blue shifts the QD PL spectrum. Thus, we can conclude that the actual redshift is somewhat larger than that shown in Figure 1b. For steady-state and transient PL analysis we use a setup analogous to that described in refs 24, 33, and 34. To conduct size-selective PL kinetics measurements, a custom-built setup based on a YLF:Nd3+ Q-switched laser, operated at 527 nm for excitation, and a custom-built, monochromator-based, spectral filter with a large aperture for wavelength selection are used.35 The laser produces 5 μJ pulses at a 4 kHz repetition rate. The excitation radiation fluence at the sample did not exceed 0.01 MW/cm2, which is 2 orders of magnitude lower than the absorption saturation intensity reported in ref 36. The PL signal is collected by a Femto HCA-S-200M-IN detector based on an InGaAs pin-photodiode. The results of 105 measurements are automatically averaged by purpose-built software. We select ∼40 nm wide spectral bands in the QD luminescence, shown in Figure 2 as band 1−band 5, centered at 1140, 1200, 1260, 1320, and 1380 nm, respectively, corresponding to PL emission from subensembles of QDs of gradually increasing size. PL decay curves are recorded at bands 1, 3, and 5 for all samples, and PL decay curves are recorded at all bands for the samples with the highest, lowest, and a middle QD concentration.

Figure 3. Decay curves of the PL from PbS QDs in the matrix at a concentration of 2.8 × 1016 cm−3 detected at bands 1−5. The inset shows the average PL lifetime at each band.

the decay curves are well fitted using a 3-exponential decay law and the average PL lifetime is calculated as

τav =

∑i Iiτi 2 ∑i Iiτi

(1)

where Ii and τi are the amplitude and the decay time of the ith component, respectively. The calculated average PL lifetimes at each band are shown in the inset of Figure 3. From Figure 3, it is clear that the PL lifetime increases with the detected wavelength or with increasing quantum dot size. The dependence observed here contradicts the previously established reduction of PL lifetimes for PbS QDs, in either a matrix32 or in solution,31,37,38 with an increase in the QD size. In Figure 4a, the measured wavelength dependencies of the PL lifetime are shown for different QD concentrations within the matrix. Clearly, PL lifetime increases with QD size for the matrix with the highest concentration of QDs, while for the matrix with the lowest QD concentration a reduction of the PL lifetime with QD size is observed, as expected. At intermediate QD concentrations (magenta asterisks in Figure 4a) there are no significant differences between the PL lifetimes measured for each spectral band. For the smallest QDs with PL corresponding to band 1, a strong reduction in the PL lifetime

Figure 2. Selection of 40 nm width spectral bands for transient PL analysis. The red line demonstrates the PL spectrum from 4.6 nm PbS QDs in the matrix. 6532



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Figure 4. (a) Measured PL lifetimes for all samples at bands 1−5. The corresponding concentrations of PbS QDs in the samples are listed in the legend. Dashed lines are guides for the eye. (b) FRET scheme between QDs inside the quasi-monodispersed QD assembly.

with an increase in QD concentration is observed. Conversely, for the biggest QDs with PL corresponding to band 5, the average PL lifetime is only weakly dependent on the QD concentration. These features can be easily explained by taking into account the FRET process in a close-packed assembly of quasi-monodispersed QDs, as shown in Figure 4b. The reduction of the PL lifetime at the low-energy side of the inhomogeneously broadened PL band is typical for closepacked QD assemblies, where strong FRET takes place.39,40 Here FRET has the highest efficiency for the smallest QDs contributing PL at the blue side of the luminescence band, which can act as donors of energy only. These QDs transfer energy nonradiatively to the bigger QDs in the assembly leading to a reduction in their PL lifetime. PL contributions from QDs to the middle and red side of the PL band cannot be quenched as efficiently as those contributing to the blue side, and the corresponding QDs can act as both donors and acceptors. In this case, the influence of the FRET on the QD luminescence decreases, so we can expect a smaller difference between PL lifetimes with changes in the QD concentration. Therefore, the FRET process, followed by quenching of the blue side of the PL spectrum, drastically alters the optical properties of PbS QD assemblies. In particular, at low QD concentrations, when the QDs do not interact with each other, FRET does not occur. The PL lifetime decreases as dot size decreases. Conversely, at high QD concentrations, FRET does occur and the PL lifetime increases with decreasing dot size. If we assume that FRET does not occur at the lowest QD concentration in a matrix, we can consider the PL lifetime at band 1 from the corresponding sample (τD) as an intrinsic PL lifetime. For FRET within the quasi-monodispersed QD assembly, where these QDs act as donors, the FRET efficiency can be estimated as E FRET

τ = 1 − DA τD

Figure 5. PL lifetime at band 1 (τDA) and estimated FRET efficiency (EFRET) for all measured samples.

of energy in donor−acceptor QD assemblies, the observed FRET saturation (Figure 5) can be used to improve donor-toacceptor FRET efficiency through further increasing the QDdonor concentration. FRET efficiency saturates at ∼35%. The corresponding average interdot distance RDA can be calculated from the formula:

E FRET =

RF6 6

RF + RDA 6

(3)

where RF is the Förster radii, which can be obtained from the spectral overlap of the absorption and the PL spectra from the QDs (Figure 1a): RF6 =

9000 ln 10k 2Q d 128π 5n 4N

∫ ID(ν)εD(ν)ν−4dν

(4)

2

where k = 2/3 is the orientation factor, QD = 0.2 is the quantum yield of donor QD, n = 1.5 is the refractive index of the media, N is the Avogadro constant, ID(ν) and εD(ν) are the PL and the extinction spectra, respectively. For our system the equation gives an RF value of 5.7 nm, and an interdot distance, RDA, of ∼6.4 nm. The observed saturation of the FRET efficiency can be explained by the formation of close-packed QD assemblies in the matrix. Indeed, it is known that colloidal PbS QDs can form ordered structures in various matrices32 or on substrates.25,41 Coricelli et al.26 showed, for PbS QDs, that as QD concentration increases, so does the extent of ordering too. Self-organizing of PbS QDs into a close-packed ordered

(2)

where τDA is the PL lifetime at band 1 for samples with a higher QD concentration. The PL lifetime at band 1 for all the samples measured and the FRET efficiency obtained as a function of QD concentration are shown in Figure 5. It has been recently shown11 that energy transfer between donors in mixed donor− acceptor QD assemblies, where donors and acceptors are very different in size, can act as a competing process. At high QDdonor concentration, energy transfer between donors dominates, so the efficiency of the donor-to-acceptor energy transfer cannot be increased. If the QDs studied here are used as donors 6533



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structure in a filter paper porous matrix analogous to that used in our work has been recently demonstrated.32 We propose that this self-organization process consists of several stages. Initially, QDs form clusters consisting of several particles. Next, these clusters grow, and their size and number increase with QD concentration. This is followed by a gradual increase in FRET efficiency up to a value corresponding to the formation of closepacked QD assemblies42 in the matrix pores with a mean interdot distance, R, of 6.4 nm. When such organized structure is formed, the optical properties and FRET efficiency of the QD assembly should be independent of further increases in the QD concentration. So, the saturation of FRET efficiency may indicate the formation of QD solids in the matrix pores. The suggestion that formation of ordered QD-solids is occurring is supported by SAXS analysis. The SAXS technique cannot be applied to the samples studied here due to their comparatively low QD concentration since the interference peak, which indicates the formation of an ordered PbS QD structure, is masked by scattered X-ray radiation from the matrix. However, we have obtained the SAXS pattern from a sample with a higher QD concentration of about 1018 cm−3, and this is shown in Figure 6. We observe a decrease in the scattered intensity near

FRET from the smaller to the larger nanocrystals. This energy transfer leads to a fundamental change in the size-dependence of the QD PL lifetime. It is found that the FRET efficiency increases to ∼35% with increasing QD concentration and then saturates. We attribute this saturation to the formation of closepacked ordered assemblies of QDs in the matrix pores, with an average interdot distance of 6.3 nm. Our conclusion, that an ordered QD solid forms within the porous matrix, is supported by SAXS analysis. This clearly indicates the presence of ordered QD structures with interdot distances in excellent agreement with those estimated from FRET saturation.

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AUTHOR INFORMATION

Corresponding Author

*(A.V.B.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the RFBR (Grants 12-02-01263 and 12-02-00938), the Government of Russian Federation (grant 074-U01), and the Ministry of Education and Science of the Russian Federation (grant no. 14.B25.31.0002). The authors would like to thank Dr. M. V. Artemyev of the Institute for Physico-Chemical Problems (Minsk, Belarus) for providing the PbS quantum dots.

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REFERENCES

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Figure 6. SAXS pattern from PbS QDs in matrix (triangles). The SAXS pattern from PbS QDs in TCM solution (dashed line) is shown for reference. Inset: the image of a porous matrix with embedded QDs obtained with a Carl Zeiss LSM 710 confocal microscope in transmission mode shows that fibers act as an adsorbing surface for QD assembling.

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CONCLUSIONS To summarize, steady-state and transient size-selective analysis of photoluminescence from PbS QDs embedded in a porous matrix at different concentrations shows that dispersion of QD sizes in a nominally monodispersed PbS QD assembly exhibits 6534



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FRET between Close-Packed Quasi-Monodispersed PbS QDs in a

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