Luminescence studies for energy transfer of lead sulfide QD films

Abstract

Lead sulfide (PbS) quantum dots (QDs) of different sizes are deposited with supercritical fluid CO₂ (sc-CO₂) to form laterally uniform PbS quantum dot films on glass substrates as compared to other deposition methods. Fluorescence and photoluminescence (PL) spectra of PbS QDs obtained from these closely packed films prepared by the sc-CO₂ method reveal effective Förster resonance energy transfer (FRET) between PbS QDs of two different sizes, while the films composed of three different sizes of PbS QDs show an even more effective FRET from the smallest to the largest particles. The FRET measured by PL is consistent with that measured by fluorescence spectroscopy at room temperature. From the PL studies of PbS QD films containing two different QD sizes, we demonstrate that the occurrence of FRET under cryogenic conditions is more efficient.

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1. Introduction

The optical properties of semiconductor nanocrystals or quantum dots (QDs) have been extensively investigated over the past decade and still attract growing interest in pursuing both fundamental and applied perspectives.^1–3 Appealing and promising application features such as electronic devices,^4,5 optical materials,^6,7 sensors,^8,9 molecular catalysts,^10,11 and others,^10,12 have substantially increased their popularity. Additionally, nanoparticle colloidal solutions of quantum confined IIB, IIIA–VA semiconductor materials have gained attraction due to the size-tunability of their optical properties arising from the effect of quantum confinement.^13–16 Focusing on optoelectronics, the QD size tunability enables control over the spectral range of absorption, photoluminescence (PL), stimulated emission, and electroluminescence spectra,^17–19 whereas quantum confinement of charge carriers in QDs whose size is comparable to their excitonic Bohr radius lends the ability to fine tune the emission energy with fairly small QD diameter alterations.

Förster resonance energy transfer (FRET) has been studied extensively at room temperature or at cryogenic conditions in CdSe,^20–22 CdSe/CdS,²³ and PbS²⁴ QDs at wavelengths below 1100 nm. In all of these cases the QDs are in close proximity (<6 nm) to each other and Förster processes can occur. FRET can occur between QDs of slightly different sizes in “monodisperse” or in mixed QD assemblies when the dots are in closely packed arrangements so that there is sufficient overlap between the donor emission and the acceptor absorption spectra. FRET involving PbS QDs is of special interest because the emission wavelength of nanometer-sized PbS particles typically occurs in the near infrared region and is sensitive to nanometer-scale changes in the donor–acceptor separation distance. The ability to transfer energy between QDs via non-radiative mechanisms is scientifically interesting, which inspires us to explore FRET in lead salt QDs. The exploration of resonance energy transfer may lead to enhanced understanding of the electronic structure of the lead salt QDs and would provide insight about interaction of lead salt QDs.

Wise's research group²⁴ studied resonant non-radiative energy transfer between closely packed PbS QDs using time-resolved fluorescence spectroscopy. Transient lifetime measurements showed the evidence of fast quenching of small dots and enhanced emission from large dots. Clapp et al.²⁰ in a review article, discussed some basic aspects of FRET applied to QDs as both donors and acceptors, and emphasized the advantages of QDs as energy donors and acceptors compared to conventional dyes. Kagan and Bawendi^21,22 demonstrated that electronic energy transfer in closely packed CdSe QD solids arises from dipole–dipole inter-dot interactions between proximal dots. The authors used continuous wave and time-resolved photoluminescence to study energy transfer in optically thin and closely packed QD solids prepared from CdSe QDs. In mixed two sized QDs, they measured the quenching of luminescence of small dots accompanied by enhanced luminescence of large dots which was consistent with electronic energy transfer from the small to large dots. Bose et al.²⁵ measured the PL spectra with a broad inhomogeneous bandwidth of PbS QDs (∼400 nm) which allow for FRET occurrence in monodisperse assemblies. At 1450 nm wavelength, the energy transfer efficiency increases from 52% at 295 K to 94% at 160 K. At cryogenic conditions, FRET appears more effective.²⁵

Techniques of making uniform films from metal sulfide QDs with controllable inter-particle distances are required for FRET studies. However, it is still a challenge to develop efficient methods of depositing PbS QDs in nanostructures or making uniform films in order to study their optical properties.

Supercritical fluid CO₂ (sc-CO₂) is known to have near zero surface tension and provides an ideal medium for depositing nanoparticles in small structures to form ordered arrays, which cannot be achieved by traditional solvent deposition methods (SDM).^1–3 Its inertness, moderate critical parameters, low cost, and non-toxicity make sc-CO₂ appealing and an environmentally friendly technique for synthesis, extraction, deposition, and dissolution processes. For example, when using sc-CO₂ as a transport medium, gold and platinum nanoparticles can be uniformly distributed in nanometer-sized trenches on silicon wafers forming ordered arrays,² and Ag₂S, CdS and PbS nanoparticles have been deposited in nanostructures of semiconductor substrates.^1,3 Previously, we have made PbS QD films in sc-CO₂ for studying FRET phenomenon at room temperature using fluorescence spectroscopy.³ In this study, thin PbS films were fabricated on glass substrate by employing a specifically designed laboratory made sc-CO₂ deposition apparatus.³ In addition, a benchtop solution deposition method was also employed to compare the optical properties of the films made by sc-CO₂ method. All samples were investigated by spectroscopic studies such as UV-Vis-NIR absorption, fluorescence, and PL at ambient and cryogenic temperatures. The FRET was studied utilizing two and three different sizes of PbS QDs in thin films on glass. The sc-CO₂ deposition technique is capable of producing uniform and thin nanoparticle films which cannot be easily prepared by conventional solvent deposition methods and is enable accurate measurements of FRET phenomenon compared with solvent deposition method. More efficient FRET energy transfer is observed at cryogenic temperature. The technique provides a new means of fabricating good quality nanoparticles films for studying their quantum confinement properties as illustrated by the FRET phenomenon of PbS QDs described in this paper.

2. Experimental section

2.1 Chemicals

Hexane (99.8%), toluene (99.9%), octadecene (ODE) (≥95.0%), bis(trimethylsilyl)sulfide (TMS) (synthesis grade), oleic acid (OA) (reagent grade, ∼99%), ethanol (200 proof), and methanol (99.9%) were purchased from Sigma-Aldrich and used as received.

2.2 Synthesis of the QDs

Oleic acid-capped PbS nanoparticles were prepared in a similar manner to the recipe of Hines et al.²⁶ but with some modifications.

PbO (0.09 g, 0.4 × 10⁻³ mol), ODE (3.9 mL) and OA (0.25 mL, 0.8 × 10⁻³ mol) were added in a 3 neck-reaction flask stirring vigorously, under a flow of continuous argon (Ar) gas at 150 °C for 1 h. After 1 h, TMS (42 μL, 0.2 × 10⁻³ mol) dissolved in 2 mL of ODE were quickly injected at 150 °C into the reaction flask. The solution color was changed from colorless to dark brown immediately. The molar ratio of OA : PbO : TMS was 4 : 2 : 1. The solution temperature was reduced to 100–120 °C, while stirring under continuous Ar gas flow for an additional hour.

Synthesis of large size (∼5 nm) PbS QDs was carried out by mixing 0.09 g PbS with 4 mL oleic acid without adding ODE, while the flask was heated to 150 °C under continuous Ar gas flow for one hour. After that 42 μL TMS dissolved in 2 mL of ODE were quickly injected into the reaction flask. This injection temperature was controlled at 150 °C. Under these conditions particle growth was allowed to proceed for one hour. Afterwards, the stirring was stopped and the reaction flask was removed from the heating source and cooled to room temperature. Finally, the sample was washed 3–4 times and once with absolute 200 proof ethanol and methanol, respectively, using a 8 mL glass vial until the dark brown lower organic phase disappeared, and black PbS QDs were completely precipitated. The nanoparticles were dried in a stream of N₂ and then dissolved in toluene. The size distribution for single sized QDs synthesized in our laboratory is usually around 9–10%.

PbS has an exciton Bohr radius of around 20 nm. The work of Moreels et al.²⁷ for PbS QDs (Fig. 2 in ref. 27) revealed that beyond a diameter of 6–8 nm, the dependence of the band gap on the variation with respect to QD size diminishes. Therefore, PbS QDs less than 6 nm were chosen. In addition, the factor that sufficient overlap of the absorption (excitation) spectrum of the acceptor (large dots) with emission spectrum of the donor (small dots) must be considered. This indicates that the QD size difference cannot be too large. However, the size difference cannot be too close due to the spectral resolution requirement. Therefore, QD sizes at 2.7 nm, 3.1 nm and 4.8 nm were chosen in this study.

2.3 Deposition of PbS QDs in sc-CO₂

The sc-CO₂ deposition process was carried out using a 35.3 mL high-pressure stainless steel chamber. For fabricating a PbS film on a glass substrate, a home-made apparatus was used.³ The PbS sample prepared in the apparatus was inserted into the high pressure chamber, which was then charged with liquid CO₂ (60 atm) at room temperature over a period of 10 min and then the pressure was raised to 80 atm. The system was then heated to 40 °C to convert the liquid CO₂ to the supercritical fluid phase. At this time the pressure inside the chamber was about 145 atm. The Teledyne ISCO pump then slowly raised the pressure up to 180 atm. The high pressure apparatus remained at this condition (40 °C and 180 atm) for 30 min to reach an equilibrium state. The reason for increasing the pressure from 145 atm to 180 atm is to ensure the system pressure is consistent and reproducible. The PbS QDs precipitate evenly and self-assemble a uniform array on the substrates during the sc-CO₂ deposition. The particles are probably deposited by a gas-antisolvent (GAS) mechanism described previously in the literature,^1,2,28 where an increasing amount of CO₂ alters the polarity of the toluene solvent and becomes unfavorable for particle stabilization in the colloid, thus resulting in the particles precipitation from solution.

The oleic acid protected PbS QDs can also form arrays on the substrates immersed in the toluene solution under atmospheric pressure, in which it was termed as solvent deposition method. However, the benchtop solvent evaporation process, due to high surface tension at the liquid/vapor interface, can lead to imperfect nanoparticle ordering forming isolated islands, percolating domains, locally high particle populations, and uneven surface coverage.^29,30

2.4 Instruments and characterizations

Carbon coated copper grids purchased from Ted Pella were used to prepare samples for particle size determination employing transmission electron microscopy (TEM). In order to produce TEM and high resolution TEM (HRTEM) images, a 4 μL droplet of diluted PbS toluene solution was dripped onto a carbon coated copper grid, and then dried at room temperature. A JEM 2100 LaB₆ (Phillips CM 200 FEG TEM) operating at 200 kV was used for both low and high resolution imaging. The average size of the PbS nanoparticles was obtained from the TEM images by counting at least 300 particles using a ImageJ software. Spectra covering the ultraviolet, visible and near infrared (UV-Vis-NIR) wavelength range were obtained with a Cary 5000 Varian UV-Vis-NIR spectrophotometer scanning from 400 to 1600 nm. The fluorescence spectra of the samples were measured with a Horiba Jobin Yvon Nanolog 916B spectrometer equipped with an IGA 512 InGaAs near-IR detector. The photoluminescence (PL) of the samples has been recorded by Fourier transform infrared spectroscopy (FTIR) using a BOMEM spectrometer in conjunction with a liquid nitrogen cooled InSb detector. The PL signal was stimulated with irradiation of 30–85 W cm⁻² at 532 nm provided by the continuous wave (cw) emission of a solid-state laser. To excite the 2.1 nm QDs, a laser source with a proper wavelength is necessary to select. The absorbance peak of 2.1 nm QDs is 857 nm. Therefore, we need to choose a wavelength higher in energy (or shorter wavelength) than that of the 2.1 nm QDs excited state transition. In order to measure the PL at cryogenic temperatures up to ambient conditions, i.e., 5–300 K, the sample was mounted in a closed cycle optical helium gas cryostat. An Axiotron optical microscope (brand: Zeiss) instrument was used to study the low magnification of surface morphology of the PbS QD films produced by sc-CO₂ deposition and open air SDM.

Time-resolved photoluminescence (PL) is done using a Coherent Chameleon laser system tuned to 950 nm. The 80 MHz repetition rate of the laser is downconverted to 1 kHz using an Atseva Pulse Picker before being focused onto the sample. The sample PL is then collected and sent to a Princeton Instrument Acton SpectraPro SP-2750 spectrometer outfitted with two switchable exit ports. One exit port is fitted with a Princeton Instruments PyLoN-IR CCD and is used to collect spectral data to determine where the emission peaks are. The other exit port is fiber coupled to a Single Quantum Eos 410 CS superconducting single photon detector for time-resolved PL. The timing for collection events from the single photon detector is handled by a HydraHarp 400 event timer. The experimental method used to measure the lifetimes is called Time Correlated Single Photon Counting (TCSPT).

3. Results and discussion

The optical properties of the condensed metal sulfide nanoparticle arrays are largely unknown. In particular, PbS QDs assemblies are of interest because they may lead to new optical materials for sensor applications in the infrared region. We have demonstrated previously that sc-CO₂ deposition is capable of making uniform arrays of PbS QDs on flat substrate surfaces using a specially designed apparatus.³ Fluorescence studies on these closely packed samples revealed FRET because sufficient amount of electrons are excited owing to the dense and homogeneous arrangements of QD films made in the sc-CO₂ fluid, leading to an emission intensity increase with respect to the inhomogeneous SDM samples. In order to study this phenomenon in more detail, different sized mixed solutions were prepared, which include PbS QD pairs of 2.7 nm/4.8 nm, and 3.1 nm/4.8 nm in toluene. Using these QD blends, optically transparent films were prepared on glass at 40 °C and 180 atm using the specially designed sample making apparatus reported previously³ in sc-CO₂. The occurrence of FRET, which was observed in fluorescence and PL spectra measured at 4 K, indicates the energy transfer is more effective at cryogenic conditions.

3.1 Optical microscopic and TEM studies, matrix effect and morphology of PbS

An Axiotron optical microscope was used to study the surface morphology of the sc-CO₂ PbS QD films in comparison to samples formed with SDM. The SDM films show a more irregular and coffee ring-shaped coverage (Fig. 1a), which was discussed previously.³ The PbS QD film deposited on glass by sc-CO₂ exhibits uniform coverage of the glass substrate with a known amount of dots in a fixed area for thick or for very thin films (Fig. 1b). The difference is caused by the dependence of the SDM process on surface tension effects at the interface of solvent and vapor, whereas the supercritical state of the sc-CO₂ deposition widely eliminates surface tension at the liquid/vapor interface due to surface-wetting instabilities that have detrimental influences on the assembly of low-defect PbS QDs films.^1–3,28

Fig. 1 Bright field images of PbS QDs deposited on glass using (a) SDM and (b) sc-CO₂ deposition methods with the same concentrations. Film lateral density of (b) is ∼0.95 mg cm⁻².

Fig. 2 shows the comparison of TEM images of the 4.7 nm QD films formed by (a) SDM and by (b) sc-CO₂ deposition. The former can lead to flawed QD ordering, such as isolated islands, percolating domains, locally high particle population, and uneven surface coverage.^29,30 On the other hand, sc-CO₂ films show a long-range order, well organized and regular lateral dispersion.

Fig. 2 TEM images of 4.7 nm QD arrays formed by (a) SDM and (b) sc-CO₂ deposition.

The SEM images of the SDM deposited samples show both closely packed areas and areas with only a few, widely separated PbS QDs (Fig. 1a and 2a). Since the PL excitation spot size has a 1.1 mm diameter, both isolated and close-packed QD emission are involved. The emission spectra will include some shorter wavelength emission from the loosely packed or isolated QDs as well as emission of longer wavelengths from the QDs in the close-packed sites. This combination still produces a red-shift with respect to the emission of the QDs in a toluene solution. In the more uniformly close-packed films deposited by the sc-CO₂ process (Fig. 1b and 2b), due to the homogeneity of the films, energy transfer process would be more efficient. This would shift the overall peak position even more towards the red. In general, PbS QDs with some size distributions, in our case 4.7 ± 0.5 nm (from 4.2 nm to 5.2 nm), lead to an enhanced spectral red-shift, which could be considered as another way for energy transfer to occur among slightly different sized PbS QDs.^21,24 We have also found that the thickness of the QD solid films is a factor to influence the emission wavelength, with thicker films slightly shifting towards longer wavelengths. The film thickness in the SDM samples varies quite differently across the deposition area. Another factor could be slight differences in the composition of the residual matrix surrounding the QDs. The sc-CO₂ process is much more efficient at removing solvent residuals; therefore, these films should only have the oleic acid ligands as the matrix. Matrix effects on PbS QD emission has been reported.^31,32 As reported by Bose et al.²⁵ excellent photostability of PbS QDs enables one to do experiments in an ambient environment at room temperature and the QDs remain remarkably stable over the temperature cycling of PL in the cryostat. The observed red-shift in QD emission in the films is due to the close interparticle distance of the dots and can be directly attributed to the FRET processes.²⁵

For a mixed PbS QD film prepared by SDM under ambient pressure (Fig. 1a), locally particle arrangements can be agglomerated, or loose. Changes in the relative fluorescence intensity were also observed, but the values fluctuated depending on the location of the excitation spot on the film. As such FRET transfer can become less efficient.³³ The uniformity of the PbS QD film prepared in the sc-CO₂ provided a better alternative for studying FRET properties of PbS QD films.

Fig. 3 shows the HRTEM images of the PbS QD mixture consisting of 2.7 nm and 4.8 nm that are concisely packed in a monolayer. The occurrence of FRET depends strongly on the donor (small dots)–acceptor (large dots) distance and the spectral overlap between the donor emission and the acceptor absorption. Zhao and co-workers³⁴ reported that the donor–acceptor interaction distances range from 2 to 9 nm and Wise²⁴ reported a calculated Förster radius of ∼8 nm. When the life time of the small dots (donor) was 2.5 μs, the equation used deduces an estimated separation distance of ∼5 to 6 nm among their donor–acceptor of PbS QDs capped by oleic acids in the close-packed film.²⁴ This suggests that energy transfer can occur effectively in closely packed and uniform PbS QD solid films. Hence, in comparison to solution or SDM films, samples fabricated by sc-CO₂ deposition have more possibilities for energy to be transferred.

Fig. 3 HRTEM images of PbS QDs of 2.7 nm and 4.8 nm.

X-ray diffraction (XRD) pattern of the oleic acid capped PbS nanoparticles is given in ESI Fig. S1.† All diffraction peaks can be indexed to face-centered-cubic (fcc) PbS nanoparticles. The sharp peaks indicate the product is highly crystalline. The following peaks were observed in every XRD pattern of the synthesized PbS nanoparticles: 2θ = 25.96, 30.06, 43.06, 50.98, 53.4, 62.54, 68.88, 70.96, and 78.92° which correspond to the {111}, {200}, {220}, {311}, {222}, {400}, {311}, {420}, and {422} planes of face-centered cubic structure of bulk PbS, respectively. The XRD patterns agree with standard reference data [Joint Committee on Powder Diffusion Standards (JCPDS)] for PbS galena.

3.2 Spectroscopic studies of PbS QD films deposited via sc-CO₂

3.2.1 Fluorescence studies of two differently blended sizes of PbS QDs. Two pairs of different sized PbS QDs (2.7 nm/4.8 nm and 3.1 nm/4.8 nm) were investigated. The film emission at short wavelengths was quenched, whereas the emission at long wavelengths was significantly enhanced, with respect to the mixed PbS solution. A red shifted emission was observed in the close-packed films, one of the FRET features.²⁴ The absorption transition both in solutions and films at the maximum wavelength remains constant.^3,33
A. PbS QD blend: 2.7 nm and 4.8 nm. Fluorescence spectra of mixed PbS QDs solutions and films were measured using the Nanolog 916B spectrometer. The relative fluorescence emission intensity ratio of the peaks of the 2 different sized PbS QDs (2.7 nm and 4.8 nm) was about 1 : 1 in solution (Fig. 4a). Using the same PbS solution, a film was fabricated via sc-CO₂ method. The red-shift of the fluorescence wavelengths of the films was observed for each peak with respect to the fluorescence spectra of the solution. The fluorescence spectrum of the PbS mixed solution (Fig. 4a) has emission features at 1100 nm (2.7 nm) and 1364 nm (4.8 nm), respectively, while the corresponding peaks of the QD film (Fig. 4b) were red-shifted to 1124 nm and 1400 nm. The significant observation here is that the ratio of the two peaks changed drastically from about 1 : 1 in the solution (Fig. 4a) to approximately 0.25 : 1 for the film (Fig. 4b). Notably the ratio change is reversible, i.e., when the film is re-dissolved in toluene, the emission spectrum is reversed from Fig. 4b to a.

Fig. 4 Fluorescence spectra of (a) the solution and (b) the film of 2.7 nm and 4.8 nm PbS QDs deposited by sc-CO₂.

B. PbS QD blend: 3.1 nm and 4.8 nm. Fig. 5b shows that the fluorescence spectrum of the close packed film has a slight red shift in comparison with that of the solution (Fig. 5a), i.e., the emission of the 3.1 nm and 4.8 nm QDs is red shifted from 1148 nm and 1392 nm in the solution to 1178 nm and 1403 nm in the film, respectively. A significant change of the peak intensity ratios of the solution and film was observed, i.e., 2 : 3 (Fig. 5a) to the ratio of 1 : 9 (Fig. 5b).

Fig. 5 Fluorescence spectrum of (a) the PbS solution and (b) the film of 3.1 nm and 4.8 nm PbS QDs deposited by sc-CO₂.

It was previously reported^3,33 that the absorption spectra of a mixture of the two PbS QD solutions and the films prepared from the mixed solution using the sc-CO₂ deposition method have no obvious changes in either the maximum wavelengths or the relative absorbance intensity ratio of the two PbS absorption peaks.

The same phenomenon was observed when the film was redissolved in toluene. As mentioned early, the fluorescence spectrum turned out to be similar to the one in Fig. 4a (a mixed solution of 2.7 nm and 4.8 nm sized PbS QDs), and after redissolving the film of 3.1 nm and 4.8 QDs, the fluorescence spectrum in Fig. 5b was reversed to the emission spectrum of the original solution (Fig. 5a). This reveals that the Förster radius plays an important role in FRET process.

The size difference between the two types of PbS QDs is 2.1 nm for the film fabricated from 2.7 nm and 4.8 nm sized QDs (Fig. 4), while the PbS QD size difference of the film made from 3.1 nm and 4.8 nm sized QDs is 1.7 nm (Fig. 5). It seems there is not much obvious difference in the red-shift between the QDs in both cases, but it was observed that the energy transferred is more efficient in the latter, i.e., the fluorescence peak of 3.1 nm QDs is extremely weak (Fig. 5b), and more energy transferred from FRET donors to FRET acceptors, suggesting FRET is favorable in a closely superimposed condition between an emission spectrum of the donors and an absorption spectrum of the acceptors.

The energy transfer phenomena between different sizes of PbS and CdSe have been previously reported.^{3,20–22,24,33} The kinetic rate of electronic energy transfer offers an alternative pathway for the de-excitation of smaller QDs (higher bandgap energy, energy donor) and excitation of larger QDs (lower bandgap energy, energy acceptor).²¹ For mixed PbS QD films prepared by SDM in this study, under ambient pressure, changes in the relative fluorescence intensity were observed, and signal fluctuations that occurred depended on the film location investigated. The uniformity of the PbS QD film prepared in sc-CO₂ is apparently important for studying optical properties of PbS QD films.

3.2.2 Absorbance and fluorescence studies of three differently sized PbS QDs.
A. PbS QDs blends: 2.1, 3.1 and 4.7 nm. The PbS solution and film mixed with 3 different sizes of 2.1 nm, 3.1 nm and 4.7 nm have strong absorbance around 857 nm, 1100 nm and 1310 nm, respectively. The absorption features at maximum wavelengths and the peak ratios, which are 4 : 2 : 1 for 2.1, 3.1, and 4.7 nm QDs, respectively, both in solutions and in films, remain almost unchanged (Fig. 6).

Fig. 6 Absorbance spectra of (a) a mixture of PbS QDs in solution with sizes of 2.1, 3.1 and 4.7 nm and (b) the film using the same solution fabricated by sc-CO₂.

In order to prove the peak positions of the QDs involved, individual films with different QD sizes of 2.1 nm, 3.1 nm and 4.7 nm have been formed. Fluorescence spectra of the individual and mixed closely packed films have emission wavelengths around 1016, 1125, and 1340 nm, and 1020, 1147 and 1350 nm for 2.1, 3.1, and 4.7 nm QDs, respectively. The corresponding peak ratio changes in the individual QD films and a closely packed film fabricated by mixing the solutions of these three different sized QDs using sc-CO₂ deposition method are from about 4 : 2 : 1 (Fig. 7a) to 0.08 : 0.25 : 1 (Fig. 7b), respectively. The film made by a mixture of three different sized QDs resulted in the emission converging into one broad band, by quenching the emission of small sized QDs. The emission of 4.7 nm QDs is significantly enhanced, the emission peak of 3.1 nm QDs becomes a small shoulder, and the emission of 2.1 nm QDs is almost vanished. The observed phenomenon in QD emission in the dense solid film can be directly attributed to an effective FRET process involving 3 different sized PbS QDs. Grams32 software was used here to smooth and fit the fluorescence spectrum in Fig. 7b.

Fig. 7 (a) Fluorescence spectra of 3 individual films PbS with different QD sizes of 2.1 nm, 3.1 nm, and 4.7 nm and (b) a film prepared with the same amount of PbS solutions fabricated by sc-CO₂. Curve-fit of the spectra and peak positions have been processed by Gram32 software.

3.2.3 Fluorescence studies of PbS films of differing densities. Fig. 8 shows two films with different densities fabricated from mixtures of 2.0 nm and 4.7 nm QDs by the sc-CO₂ method. The densities of the films in Fig. 8a and b are 0.27 mg cm⁻² and 0.11 mg cm⁻², respectively, i.e., the density of the latter is 2.5 times lower than the former, when keeping the same relative amount of QD ratio. The concentration variation did not largely influence the relative fluorescence emission peak ratios and positions. Density of the films is not a factor to influence FRET, as long as the Förster radius of the PbS QD films is less than 8 nm.²⁴

Fig. 8 PbS QD films on glass fabricated by sc-CO₂ with sizes of 2.0 nm and 4.7 nm. The film density in sample (b) is about 2.5 times lower than that in sample (a).

3.2.4 Photoluminescence and fluorescence measurements. Fig. 9a shows the normalized fluorescence and PL spectra of the PbS film at 300 K fabricated by a mixture of 2.1 nm and 4.7 nm PbS solution deposited in sc-CO₂. The results reveal a notable fact: while the peak in PL for the 2.1 nm QDs almost vanished, the peak in fluorescence showed emission from the 2.1 nm QDs at around 1030 nm. Fluorescence and PL results for the 4.7 nm QDs, on the other hand, with peaks at 1380 nm and 1400 nm, respectively, show acceptable agreement. We emphasize here the difference between the fluorescence and the PL experiments, which might contribute to the alteration of the spectral responses. More electrons transfer during the laser excited PL takes place from smaller QDs to the larger QDs in comparison to the fluorescence because the latter were measured with a Horiba Jobin Yvon Nanolog 916B spectrometer equipped with 450 W intense broadband xenon lamp. Consequently, the excitation stage of the samples in both experiments is considerably different. It reveals that at room temperature, the intensity ratio of 4.7 nm QDs/2.1 nm QDs of PL spectrum is about 10, while the intensity ratio of 4.7 nm QDs/2.1 nm QDs of fluorescence spectrum is about 5 (Fig. 9a). More electron transfer from the laser excited small QDs to the larger dots, keeping the PL peak of the 2.1 nm QDs extremely weak. In addition, in the PL experiment the excitation laser spot is 1.1 mm, whereas for the fluorescence, the sampling spot is much larger (∼3 mm). Therefore, locations and sample areas measured are different and that is also why the FWHM varies and maximum wavelength for both fluorescence and PL are slightly different.

Fig. 9 PL and fluorescence spectra of mixed PbS film of 2.1 nm QDs and 4.7 nm QDs fabricated by sc-CO₂. (a) Normalized PL and fluorescence spectra of PbS QDs measured at 300 K, (b) PL spectra of PbS QDs measured at 4 K and 300 K at 30 W cm⁻², (c) PL spectra of PbS QD film measured at different temperatures at 4 K, 10 K, 20 K, 40 K, 80 K, 140 K, and 300 K at 30 W cm⁻².

The measurements in Fig. 9b were taken at 4 K and 300 K with an impinging laser intensity of 30 W cm⁻². The PL emissions at 1120 nm (2.1 nm) and 1460 nm (4.7 nm) were clearly observed at 4 K, while the emission peaks from the 2.1 nm QDs at 4 K and 300 K remain almost at the same wavelength (1120 nm). On the other hand, the emission peaks of the 4.7 nm QDs are located at around 1400 nm at 300 K and 1460 nm at 4 K, respectively. Hence, the PL of the larger QDs revealed a significant wavelength red-shift with approximately 4 fold intensity gain at cryogenic temperatures (Fig. 9b). We attribute the emission intensity gained at 4 K to the high uniformity and high density films produced by sc-CO₂ method. The intensity ratios of 4.7 nm QDs/2.1 nm QDs at 4 K and 300 K are both about 10 (Fig. 9b, PL in Fig. 9a). Energy transfer phenomenon is more effective at cryogenic temperatures. Similar observations have been reported previously.^33,35

We believe the reason of the low PL peak clearly observed at 4 K from the 2.1 nm QDs in Fig. 9b is due to the fact of the absence of effective thermal activation at cryogenic temperatures, which is consistent with the studies reported in the literature.^20,21 For sake of completeness and to show the nearly constant PL peak location of the 2.1 nm QDs, Fig. 9c shows emission spectra for various temperatures from 4 K up to 300 K. At low temperatures, both intensity and peak position changes are more sensitive comparing with these at higher temperatures.

The more closely packed the QD arrangement is, the lower the ground state of the QD ensemble is due to electronic interaction between the dots and, additionally, electrons are easily transferred from higher energy levels to lower levels. Sufficient overlap of the absorption (excitation) spectrum of the acceptor (large dots) with fluorescence emission spectrum of the donor (small dots) is one signature in the FRET process.²⁴ Closely packed uniform PbS QD films deposited by sc-CO₂ (Fig. 1b) provide appropriate FRET transfer sites within Förster radius to satisfy energy transfer requirements.^24,33

However, SDM samples possess more separated QD distance enlarging the energy levels between the ground and excited states, and as a consequence, the energy transfer can become less efficient.³³ Förster energy transfer phenomenon will occur when the interdot distances between closely packed QDs are roughly less than or equal to 5 to 6 nm according to the equation²⁴ of τ = τ_d(R/R_o)⁶. In this equation, τ_d is the lifetime of donors, R_o is Förster radius and R is the separation distance between the dots. Although the estimate is rough, it gives a distance that is quite reasonable for a close-packed film of the QDs stabilized by oleic acid.²⁴ The interparticle distance between two adjacent PbS QDs stabilized by oleic acid was calculated in our study. For instance, for 4.7 nm QDs, the interparticle distance is measured to be 3.1 nm from TEM images using the ImageJ software.

Fluorescence spectrum of mixed 2.7 nm and 4.8 nm sized QD solution was measured (Fig. 10a). Due to dynamic movements and weak interactions of loose distance between the particles in the solution, the intensity ratio from two fluorescence peaks of 4.8 nm and 2.7 nm QD was around 1 : 1. After fabricating this solution into a film via sc-CO₂ method, the fluorescence measured revealed the ratio of the peaks of 4.8 nm/2.7 nm was around 4, while the PL spectral intensity ratio is around 10, indicating more energy transfer from the laser excited small QDs to the larger QDs occurred in PL process (Fig. 10b).

Fig. 10 (a) Fluorescence spectrum of PbS solution in a mixed solution of 2.7 nm and 4.8 nm QDs, and (b) fluorescence and PL spectra of a film of 2.7 nm and 4.8 nm QDs made by the sc-CO₂ method. Fluorescence and PL spectra are overlaid and normalized.

3.2.5 Transient lifetime measurements. Energy transfer can be observed more directly by spectrally resolving the luminescence decays of mixed PbS QD samples. A mixed PbS film with 3.1 nm and 4.8 nm QDs were studied by time correlated single photon counting, for transient lifetime measurements (ESI†). The PL is quenched at the short wavelength (1150 nm), as evidenced by a decay time that is faster than that recorded for the radiative emission decay of the long wavelength peak (1350 nm). The lifetime (decay constant)⁻¹ for the shorter wavelength (1150 nm) is best fitted using a bi-exponential equation with a t₁ value of 56 ns and a t₂ value of 182 ns (Fig. S2 in the ESI†). The bi-exponential fit suggests the decay probably involves two modes, a faster FRET and a normal radiative emission. The long wavelength (1350 nm) decay is best fitted by a mono-exponential equation with a decay lifetime of 199 ns as shown in Fig. S3 in the ESI.† Fig. S4† shows the temporally resolved PL of the mixed QD film at wavelengths of 1150 nm and 1350 nm between 0 and 3 μs (Fig. S4a†) and between 0 and 0.8 μs (Fig. S4b†).

The decay time observations are qualitatively consistent with resonant energy transfer from smaller PbS QDs to larger PbS QDs according to the literature.²⁵ Our observations are consistent with the work undertaken by Bose et al.²⁵ In their work, they demonstrated the measured decay time for the smaller PbS QD at 1400 nm is shorter than that of the larger PbS QD at 1550 nm in the film made of one sample of dots with a broad inhomogeneous bandwidth (∼400 nm), which allows for FRET occurrence. For instance, Förster transfer rate at 1400 nm is (60 ns)⁻¹ and at 1550 nm is (308 ns)⁻¹.²⁵ More theoretical and experimental work is required for a thorough understanding of the radiative lifetimes of PbS QDs in mixed QD systems.

4. Conclusions

PbS QDs of different sizes were synthesized and deposited by SDM and sc-CO₂ methods as thin films on glass. An apparatus for depositing PbS QDs on flat substrates employing sc-CO₂ deposition method was designed for this study. Optical experiments and TEM indicate that the sc-CO₂ method is capable of forming PbS QD arrays with improved uniformity with respect to SDM samples.

The PbS sc-CO₂ samples deposited on glass show clearly resolved absorbance features in the Vis-NIR region, and intense emission in fluorescence and PL, which is attributed to the narrow particle size distribution and homogeneous particle arrangement. Closely packed uniform PbS QD films deposited by sc-CO₂ provide appropriate FRET transfer sites within Förster radius to satisfy for energy transfer. For the film with mixed PbS QDs, emission at short wavelengths is quenched whereas the emission at long wavelengths is enhanced, with respect to the mixed PbS solution. FRET energy transfer between small and large QDs in differently sized pairs occurs in closely packed PbS QD films in fluorescence and PL, especially at cryogenic temperatures. The process of energy transfer from the smallest QDs to the largest QDs is relatively more effective in the PbS QD film containing three QD sizes. Cryogenic measurements of PL of mixed PbS QD film indicate FRET occurs effectively at temperatures as low as 4 K. The observations herein should enhance our understanding of the electronic structures of lead-VIA group QDs and provide insight about the electronic interactions governing their emission features.

Acknowledgements

The fluorescence work was conducted at the University of Idaho. The work at the Air Force Research Laboratory (AFRL/RXAN) was supported by Dr Kitt Reinhardt of AFOSR/RSE. Dr Bruno Ullrich's present address: Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Morelos 62210, Mexico.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra03632e

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