Effect of Thermal Annealing on Structure and Optical Properties of

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Effect of Thermal Annealing on Structure and Optical Properties of Poly(p-xylylene)-PbS Thin Films Alexander A. Nesmelov, Leonid N. Oveshnikov, Sergei A. Ozerin, Sergei A. Zav'yalov, Yan V. Zubavichus, Anton S. Orekhov, Dmitry R. Streltsov, Yu. I. Kiryukhin, and Sergei N Chvalun J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 29 Mar 2019 Downloaded from http://pubs.acs.org on March 29, 2019

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The Journal of Physical Chemistry

Effect of Thermal Annealing on Structure and Optical Properties of Poly(p-xylylene)-PbS Thin Films A.A. Nesmelov,†,‡ L.N. Oveshnikov,∗,†,¶ S.A. Ozerin,† S.A. Zav’yalov,† Ya.V. Zubavichus,†,§ A.S. Orekhov,†,∥ D.R. Streltsov,⊥,†,‡ Yu.I. Kiryukhina,† and S.N. Chvalun†,⊥,‡ †National Research Center "Kurchatov Institute", Moscow, 123182 Russia ‡MIREA - Russian Technological University, Moscow, 119454 Russia ¶P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991 Russia §Boreskov Institute of Catalysis, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia ∥Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, 141701 Russia ⊥Enikolopov Institute of Synthetic Polymeric Materials, Russian Academy of Sciences, Moscow, 117393 Russia E-mail: [email protected] a

Deceased 27 December 2018

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Abstract In this study, wide-angle X-ray diffraction, X-ray absorption spectroscopy and transmission electron microscopy were employed to address the crystalline structure and morphology of poly(p-xylylene)-PbS nanocomposite thin films prepared by vapor deposition polymerization as well as their evolution upon thermal annealing. It was found that as-synthesized samples with different PbS content demonstrate similar diffraction patterns that cannot be fully ascribed to a decrease in crystallite size, indicating distorted crystal structure of PbS nanoparticles compared to the bulk PbS. X-ray absorption spectroscopy reveals wide distribution of Pb–S bond lengths with a minimum value of 2.67 Å, which can be attributed to the presence of molecular (PbS)n clusters in the studied films. It was shown that thermal annealing can be used to control the size of PbS nanoparticles and, as a consequence, optical properties of the composite films. The UV-Vis absorption spectra demonstrate pronounced red-shift of the absorption edge correlated with the growth of PbS nanoparticles upon annealing. Comprehensive analysis of several theoretical models describing the effect of nanoparticles size on optical bandgap of the composite material has been performed and compared with the experimental data.

1. Introduction Thin nanocomposite films, consisting of inorganic (metallic, semiconducting or dielectric) inclusions (nanoparticles, nanowires etc.) embedded into polymer matrix, have gained a great deal of interest in recent years. It is related both to the wide application spectrum of such materials and to the lack of comprehensive insight into fundamental properties of nanostructures. Since the properties of nanoinclusions frequently differ from those of corresponding bulk material or single atoms and molecules, nanocomposite films demonstrate various unusual electric, magnetic, catalytic and other features. 1–3 Another advantage of nanocomposite films is the possibility to control structure of nanopar-

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ticles and their spatial distribution by variation of synthesis conditions or external stimuli. It was shown that nanoparticles are able to self-assemble into highly ordered superstructures, similar to atoms in conventional crystals. 4–6 Usually the material of nanoparticles determines primary functional properties of a composite, e.g. using lead sulfide (PbS) nanoparticles as a filler makes composite film suitable for optical applications. Bulk PbS crystals demonstrate several specific features, noted in early studies. 7 Unlike most semiconductor materials, 8 the energy gap in PbS decreases under hydrostatic pressure. 9 Moreover, it decreases with temperature from 0.41 eV (300 K) to 0.29 eV (4.2 K). 10 Under normal conditions PbS has the rock-salt crystal lattice with a unit cell parameter of 5.936 Å. 11 It is a direct narrow-gap semiconductor with main extrema in the L points of Brillouin zone. 12 The band diagram of PbS and its response to the external factors (such as pressure) was studied in numerous theoretical works. 13 Due to low effective masses of charge carriers and high dielectric constant, PbS has large Bohr exciton radius (≈ 20 nm 14 ) which suggests that strong quantum confinement limit can be reached even for relatively large nanoparticles. Pronounced quantum confinement effects in PbS nanocrystals motivated numerous experimental studies. Recently, they have gained additional interest due to theoretical predictions of the strain-induced phase transition to crystalline topological insulator state under hydrostatic pressure 12 or because of the lattice mismatch with the substrate for thin films. 15,16 Now, PbS is widely used in industry for fabrication of photoresistors, IR-detectors, lasers and light-emitting diodes, thermoelectric and thermophotovoltaic transducers. 17 In addition, PbS is considered as a very promising material for non-linear optics and multi-exciton generation. 14 PbS nanoparticles within some functional matrix should preserve their interesting properties, although, the actual composite structure can result in the appearance of new phenomena. The properties of PbS-polymer nanocomposites can be effectively adjusted by varying the size of nanoparticles, 18 which can be realized in films with different filler (PbS) content. 19,20 It is important to note, that overall properties of nanoparticles are greatly affected

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by the synthesis method. For example, PbS thin films can be synthesized via chemical deposition from water solution of lead acetate and thiourea, 21 sol-gel methods or chemical reactions in solutions and electrolytes. 6 As for PbS nanoparticles, they can be obtained in low-temperature colloid solutions 22 and via reduction of Pb(CH3 COO)2 within ethylene-15% methacrylic acid copolymer matrix. 18 The actual properties of PbS nanoparticles may vary for different synthesis routes and depend on the surroundings (i.e. matrix or solution). In present work, thin nanocomposite films with PbS nanocrystallites stabilized in polymer matrix were synthesized via vapor deposition polymerization (VDP) technique. 2 This method is based on co-condensation of monomer (p-xylylene) and filler (PbS) vapors in high vacuum, followed by polymerization of the monomer and formation of PbS nanoparticles stabilized within the poly(p-xylylene) (PPX) matrix. It is worth mentioning, that PPX is widely used for various applications because of its high dielectric and barrier characteristics. Unlike solution-based deposition techniques, VDP synthesis route does not involve any solvent or catalyst, which prevents byproducts appearance and ensures high purity of the films. By varying intensities of the corresponding flows, it is possible to control the thickness of the films, as well as monomer and filler concentrations. In general, VDP technique allows to use not only semiconducting (e.g. binary CdS and ZnS compounds or elemental Ge 23 ), but also metallic fillers. The structure and properties of PPX-based composites with metallic filler have been studied for silver, 24 titanium, 25 nickel, 26 palladium, tin and aluminum 27 nanoparticles. It is noteworthy, that the formation of nanoparticles in VDP process starts from small filler clusters (down to several atoms) at liquid nitrogen temperature. Analogously to other cryo-synthesis methods it may result in the unconventional crystal structure of nanocrystallites. 28 Previously we have studied the structure of thick PPX-PbS films by wide- and smallangle X-ray diffraction. 19,20 It was found that PbS nanoparticles affect crystalline structure of the PPX matrix, e.g. intensity of X-ray reflections corresponding to the low-temperature β-modification of PPX diminishes with the increase of PbS content, while new peaks corre-

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sponding to the α-modification of PPX appear. In addition, the size distribution functions of nanoparticles were calculated. It was shown that the corresponding function is lognormal at low filler content and becomes bimodal at higher PbS content (above 10 vol.%). Optical studies of systems containing PbS nanocrystallites are widely presented in literature. However, the quantitative results seem to be rather scarce, especially when optical absorption data are used for evaluation of nanoparticle size. The simplest model of sizedependent shift of the absorption edge, developed by Brus, 29 describes the properties of large PbS nanoparticles quite well. 21,30 However, for small PbS nanocrystallites one needs to take into account additional effects. Thus, in this paper we discuss various details relevant for proper optical data processing and compare different models used for nanoparticle size determination. Previous study of PPX-PbS composites absorption spectra revealed that a decrease of PbS content results in considerable blue-shift of absorption edge, related to a decrease of mean particle size. 31 However, the variation of filler content not only changes the parameters of nanoparticles, but may also affect the structure of the matrix, making prediction of the optical properties of such film difficult. Respectively, to establish an adequate model for its description further studies are required. In this work we investigate the effect of thermal annealing on structure and optical properties of PPX-PbS composite films. Previously, it was shown that for PPX-Ag composites the annealing procedure can substantially increase the size of nanoparticles and change their spatial distribution. 32 Thus, one can expect that thermal treatment of PPX-PbS films will have analogous effect, which can be used for optical properties engineering.

2. Methods The poly(p-xylylene) - lead sulfide (PPX-PbS) nanocomposites were synthesized via lowtemperature vapor deposition polymerization (VDP) technique within a high vacuum (10−5 −

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−10−6 Torr) chamber. The details of process and scheme of the chamber were described elsewhere. 2 As a precursor, [2.2]p-cyclophane (Daisan Kasei, Japan) was used. Sublimation temperature was 100 - 120 ◦ C. In the pyrolysis zone (Tpyr = 650 ◦ C), strained p-cyclophane molecule decays with formation of two reactive p-xylylene monomers. Simultaneously, lead sulfide (99.9%, Sigma-Aldrich) was evaporated from a tantalum boat heated up to 600– 650 ◦ C. By changing temperatures of the heaters, we adjusted the PbS/monomer flow ratio, and consequently PbS content in the nanocomposite films. The vapors of monomer and inorganic filler were deposited on a substrate, cooled by liquid nitrogen (T = −196 ◦ C). During slow heating of the co-condensate up to room temperature, the polymerization of p-xylylene into PPX and formation of nanoparticles occur. The resultant composite films consist of PbS nanocrystallites stabilized in the polymer matrix. We used different substrates for different measurements: polyethylene terephthalate (PET) films for X-ray diffraction and absorption spectroscopy studies, standard copper meshes (300 mesh) covered with amorphous SiO2 for electron microscopy, polished quartz substrates for optical studies. Thickness of the films for X-ray and optical studies was around 1 µm. Structure of the PPX-PbS nanocomposites was investigated by synchrotron radiationbased powder X-ray diffraction and X-ray absorption spectroscopy (XANES/EXAFS) techniques. The experimental data were acquired at the Structural Materials Science Beamline of the Kurchatov Synchrotron Radiation Source (NRC "Kurchatov Institute", Moscow). 33 The diffraction measurements were performed in the transmission mode for the as-prepared PbS-PPX composite films on PET substrates as well as on the films subjected to postsynthesis thermal treatment at different temperatures. Diffraction patterns were obtained using Imaging Plate (FujiFilm, Japan) 2D detector at λ = 0.69654Å. The X-ray beam size was approximately 300×300 µm, the sample-to-detector distance – 120 mm, and exposure time – 15 min. Polycrystalline powder of Si was used as a reference for the calibration of geometrical parameters of the experiment. The mean size of PbS nanocrystallites was

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estimated from integral widths of diffraction peaks using the Scherrer equation taking into account instrumental broadening. 34 Pb L3 -edge XAS spectra for the composite films were measured in the fluorescence yield mode using an Si avalanche photodiode as the fluorescence detector. For the sake of comparison XAS spectra of PbS powder (the target material used for the film preparation denoted as block PbS) were measured in the transmission mode using two ionization chambers filled with nitrogen and argon mixture. The processing of raw experimental data and non-linear curve fitting were performed using the IFEFFIT software package with FEFF ab initio photoelectron phase and amplitude functions. 35 Transmission electron microscopy (TEM) studies were performed on Titan 80-300 (FEI, USA) microscope with accelerating voltage of 300 kV. Images were processed using Digital Micrograph (Gatan, USA) software. Optical absorption spectra of the PPX-PbS nanocomposite thin films were obtained with Shimadzu UV-3600 spectrometer in the wavelength range from 190 to 3300 nm.

3. Results and discussion 3.1. Structural properties The X-ray studies of as-prepared PPX-PbS composite films with various PbS content (denoted as C) revealed similar features without substantial qualitative changes of the corresponding patterns (see Supporting Information (SI), Sec. I). Nevertheless, with the increase of PbS content the color of the films changed from light yellow to dark brown (see Fig. S1, SI, Sec. I). Experimental X-ray diffraction patterns for a representative sample (C = 30 vol.%) are shown in Fig. 1. The composite films had two distinct areas, viz. central and peripheral. The latter ones were always darker in color than the former ones (see inset in Fig. 1). The central part was formed under well controlled conditions (due to good thermal contact with the cryogenic head that hold the substrate temperature around -196 ◦ C), the 7



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Block PbS

Intensity (arb. units)

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(HT) C = 30 vol.%

(LT) C = 30 vol.%

PET \ PPX 0 5

10

15

20

25

30

35

40

45

2θ (deg)

Figure 1: Experimental X-ray diffraction patterns of the as-prepared PbS-PPX composite film with C = 30 vol.% (λ = 0.69654 Å). Diffraction patterns for block PbS crystal and pure PPX film on a PET substrate are shown as a reference. Inset illustrates HT and LT regions of the sample. respective curve is denoted in Fig. 1 as (LT). On the contrary, the peripheral part of the film beyond the cold head area was formed under poorly controlled conditions (due to bad thermal contact). Apparently, in that case the film deposition process proceeded at a significantly higher substrate temperature affecting sticking coefficient of the p-xylylene monomer. 36 The diffraction pattern of that peripheral part of the composite film (denoted as (HT) in Fig. 1) reveals a well pronounced peak structure typical of nanocrystalline PbS (characteristic size of crystallites estimated using the Sherrer equation is around 6 nm), showing that there were no PbS decomposition during the sublimation process. But the central LT-region of the film is characterized by ultimately broad peaks that cannot be unambiguously indexed within the cubic face-centred lattice of PbS. Note that the relatively narrow diffraction peaks at 2θ = 7.2◦ and 2θ = 18.8◦ are due to the semicrystalline PET substrate. The fact that the chemical nature of inorganic component of the composite films is indeed PbS can be confirmed by changes observed in X-ray diffraction patterns upon post-growth consecutive annealing at Tann up to 190 ◦ C for 1 hour (see Fig. 2). Note here that for

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(HT)

C

= 30 vol.% |

Tann

= 20

C

Model 3

(arb. units)

Model 2

Intensity

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(LT)

C

Tann

= 190

C

Tann

= 180

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Tann

= 160

C

Tann

= 140

C

Tann

= 100

C

= 30 vol.% |

Tann

= 20

C

Model 1

2

(deg)

Figure 2: The evolution of X-ray diffraction pattern of the PbS-PPX composite film (C = 30 vol.%) upon annealing. Data for HT region of the sample and three simulated patterns (Model 1 - disc; Model 2 - cube; Model 3 - whisker) are shown for the reference. For comparison, we also added normalized pattern for pure PPX film on a PET substrate to the simulated curves (see text). The result is shown by dashed lines. simplicity we ascribe to the initial non-annealed film Tann = 20 ◦ C, i.e. room temperature. X-ray diffraction patterns of the composite films annealed above 160 ◦ C evolve so that the peaks of PbS crystal structure become distinct. Annealing at even higher temperature gives rise to the growth of PbS crystallites, which is manifested itself as a decrease in the peak half-widths. The nominal size of crystallites in the sample annealed at 190 ◦ C becomes about 3.5 nm. It is also worth noting that the lattice parameter of PbS nanoparticles in the annealed composite films is larger than that in the crystalline reference, i.e. 5.96– 5.98 Å instead of 5.94 Å. To estimate possible variations of diffraction patterns related to the morphology of nanoparticles, we have conducted a simulation based on the Debye formula. 37 9



As an illustration we provide patterns for three models with different amount of molecular PbS units (see Fig. 2). Model 1 corresponds to a (PbS)125 disc with the developed face parallel to (111) plane of PbS lattice. The diameter of such nanoparticle is about 2 nm, and its height is about 0.35 nm. Model 2 corresponds to a (PbS)1100 cube with an edge of about 3.5 nm. Model 3 corresponds to a (PbS)4150 whisker with a diameter of 3.5 nm and height of 14 nm parallel to (100). To account for the composite nature of studied sample, we added pattern for pure PPX film on a PET substrate to the simulated curves. Prior to the summation, the reference PPX pattern was normalized to fit the peak height at 2θ ≈ 7.2◦ of the experimental patterns for Tann = 20 ◦ C and Tann = 190 ◦ C (for model 1 and model 2 / model 3, correspondingly). As one can see in Fig. 2 the pattern for model 1 is somewhat similar to the pattern for as-prepared sample (Tann = 20 ◦ C), while the pattern for model 2 is comparatively close to that for the annealed film (Tann = 190 ◦ C). It is worth mentioning that the evolution of relative intensities of peaks at 2θ ≈ 11.5◦ and 2θ ≈ 13.4◦ upon annealing indicates that further increase of Tann values may eventually transform corresponding pattern into something close to that for model 3 (which is also similar to the pattern for HT region of the sample, see Fig. 2). These results suggest possible evolution of the nanoparticle shape upon annealing (along with the size increase) from disc-like to cubic-like, or even whiskerlike. However, simulated patterns show only moderate agreement with the experimental data, thus, it cannot be used for unambiguous determination of nanoparticle morphology, implying possible role of other effects. The exact chemical speciation of PbS component in the as-prepared composite films can be established using Pb L3 -edge XAS as shown in Fig. 3. Analogous to X-ray diffraction data, the studied samples revealed similar character of XAS spectra in the wide range of PbS content. Thus, here we present the processed data with increased signal-to-noise ratio (for details see SI, Sec. I). The fine structure near the absorption threshold (XANES) of the (LT) PPX-PbS samples is strongly smeared as compared to both (HT) PPX-PbS and block PbS crystal reference samples (Fig. 3a). This implies that the composite sample

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Block PbS

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(HT) PPX-PbS

(arb. units)

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(HT) PPX-PbS

(LT) PPX-PbS

(a)

13050

13100

E (eV)

0

1

2

R (Å)

3

4

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Figure 3: (a) Pb L3 -edge XANES spectra. (b) Fourier transforms of Pb L3 -edge EXAFS spectra. Experimental data are shown as solid lines and best-fit theoretical simulation as open circles. Structural parameters of refined models are listed in Table 1. prepared at low temperature is characterized by a very irregular local structure with a broad distribution of Pb–S bond lengths. Moreover, the Fourier transform of EXAFS part for this sample reveals a very strong shift in the position of the first-coordination-shell peak to shorter distances with respect to block PbS (Fig. 3b). A quantitative analysis of EXAFS (Table 1) indicates that the shortest Pb–S bond length is about ∼2.67 Å instead of 2.96 Å as in the known crystal structure of bulk PbS. This result together with the aforementioned diffraction data clearly suggest that PbS species evaporated at liquid nitrogen temperature and stabilized by PPX matrix cannot be described simply as PbS nanoparticles. As a possible structural prototype for such unusual species we suggest low-nuclearity molecular clusters (PbS)n , which, according to some earlier computational studies, 38–40 are reasonably stable and have characteristic structure parameters similar to those observed in the present work. It is important to note, that isolated (PbS)n clusters approach bulk PbS structure already for n = 15 (approximately 1 nm cluster). It suggests that the studied as-prepared

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Table 1: Local-structure parameters around Pb atoms in the samples according to Pb L3 -edge EXAFS. Coordination Coordination Interatomic Discrepancy sphere number, N distance, R [Å] factor, Rf 4.0 2.93 Block PbS Pb–S 0.016 2.0 3.17 0.2 2.66 (HT) PPX-PbS Pb–S 3.0 2.92 0.039 1.6 3.17 1.0 2.67 (LT) PPX-PbS Pb–S 1.0 2.86 0.006 0.4 3.10 −1 Fitting ranges: k = 2.0 − 12.0 Å ; R = 1.6 − 3.0 Å; weighting scheme k n , n = 3. Sample

∗

films should have a dominant portion of sub - 1 nm clusters. Thus, by varying the details of VDP synthesis procedure and post-growth treatment one can, in principle, obtain films with desired portion of (PbS)n clusters. Given the fact that the properties of such clusters can be strikingly different from those of larger nanoparticles, PPX-PbS films seems to be a suitable platform for their investigation. To the best of our knowledge, experimental studies of (PbS)n clusters are extremely limited, e.g. their optical properties were investigated only in the gas-phase. 41 Considering vast amount of related theoretical works and predictions, the realization of stable (PbS)n clusters (e.g. in polymer matrix) is highly desired. It is worth mentioning that shorter Pb–S bond lengths may also appear due to sizedependent nanoparticle surface strain. There are several models that explain such deformations in terms of coordination number imperfections of surface atoms, 42–45 interaction with surrounding ligands 46 or considering simple surface stress. 47 All these models imply that surface strain will also affect the bulk of nanoparticle. In our case, observed Pb–S bond contraction suggests substantial bulk strain, which cannot be resolved from our diffraction data for the as-prepared films. However, the sign of surface strain is usually opposite to that of the bulk, implying the appearance of longer Pb–S bond lengths, which was not observed in our XAS data. The latter favors the assumption of (PbS)n clusters formation. It is worth

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mentioning that surface strain can affect the structure of formed nanoparticles, i.e. it can induce small deviation of lattice parameter observed for annealed sample. We will discuss possible strain-related effects later in the text. The structure of samples deposited on copper meshes with amorphous SiO2 coating was studied using transmission electron microscopy (TEM). Representative TEM image for the sample with C = 15 vol.% is shown in Fig. 4a, from which one can easily distinguish a textured pattern of polymer matrix (lighter regions) and PbS nanoparticles (darker regions). Closer inspection reveals the occasional presence of large nanoparticles (Fig. 4b) with ordered crystalline structure. Corresponding FFT pattern reveals four symmetric intensive peaks (Fig. 4c) corresponding to the interplanar distance of about 0.297 nm. Thus, in terms of PbS lattice these peaks can be identified as (200) reflection series, meaning that the image is obtained with B = [001] zone axis as illustrated in Fig. 4d. Despite the low contrast of initial image (Fig. 4a), we were able to estimate the size distribution of nanoparticles. The diameter of nanoparticles follows lognormal distribution with mode of about 1.5 nm, mean value of 1.75 nm and σ ≈ 0.38 nm (see inset in Fig. 4a). It is important to note, that electron beam can affect the initial structure of the film by evaporating polymer and inducing additional PbS aggregation. 41 Aside from that, lognormal size distribution usually indicates the coalescence-type growth regime of nanoparticles. 48 Previously we have obtained analogous distribution curves from the X-ray data for thick PPX-PbS films, thus, this result seems to be rather consistent. 19,20

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(a)

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Figure 4: (a) TEM - image of the PPX-PbS nanocomposite sample with C = 15 vol.%. Inset shows the size distribution function of PbS nanoparticles in the studied film. (b) Magnified image of occasional large dark region confirming the presence of crystalline nanoparticles. (c) FFT pattern of nanoparticle region shown in (b). The most intensive peaks, indicated by red circles, correspond to the interplanar distance of about 0.297 nm. (d) Schematic image of PbS lattice projection corresponding to B = [001] zone axis.

The comparison of results obtained via various methods suggests that the as-prepared PPX-PbS composite films contain (PbS)n clusters and PbS nanoparticles embedded into polymer matrix. Post-growth annealing results in the appearance of well defined diffraction peaks, which can be related to the increase of number and size of nanoparticles. It implies the aggregation of (PbS)n clusters, meaning that the annealed sample consist mostly of PbS nanoparticles.

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3.2. Optical properties Optical properties of the PPX-PbS films with C = 10 and 30 vol.% deposited on polished quartz substrates were investigated by UV-Vis spectroscopy. Previous optical studies of thick PPX-PbS films revealed a substantial composition-dependent blue-shift of the absorption edge compared to the bulk PbS. 31 Generally, the possibility of tuning the optical properties of a film by changing synthesis conditions (e.g. by changing the PbS content) paves a way for the production of materials with predetermined parameters, which is required for various applications. Here we investigate the effect of post-growth annealing on optical properties of PPX-PbS films and estimate relative changes of PbS nanoparticle size. As we will show below, such thermal treatment procedure can be used as an effective instrument for fine tuning the optical parameters of PPX-PbS films. For the proper characterization of associated effects, we compare extinction spectra of the films that were consequently annealed in vacuum for two hours at temperatures, Tann , in the range from 160 to 300 ◦ C. Although, we measured the extinction spectra, due to the weak reflectance of small PbS nanoparticles even at high densities, 49 we ascribe all observed spectral features solely to the absorption (thus, we denote measured data as absorption, α, spectra below). Obtained spectra for both samples after each annealing step are given in Fig. 5. As one can see, the increase of annealing temperature Tann results in a red-shift of the absorption edge. Also, the color of films becomes darker upon annealing, thus, the region of substantial absorption shifts over almost the whole visible light range. It is worth mentioning, that in the long-wavelength region (especially for the sample with C = 30 vol.%) one can distinguish pronounced oscillations related to the interference effects within a film. The presence of interference bands in obtained absorption spectra suggests high homogeneity of composition and thickness of the films under study. 50,51 The red-shift of absorption can be ascribed to the increase of nanoparticle size, but to estimate corresponding changes one needs to determine characteristic absorption energies properly. In general case, the absorption spectra of nanoparticles strongly depend on their size dis15



C = 10 vol.% 1.0

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α (arb. units)

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0.8

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Figure 5: Absorption spectra and images of the PPX-PbS nanocomposite films with C = (a) 10 and (b) 30 vol.% annealed at temperatures Tann from 160 to 300 ◦ C. tribution. Thus, absorption spectra of highly monodisperse nanoparticles should have single absorption band of finite width, with peak position corresponding to the mean nanoparticle size. 52 Depending on the surroundings of nanoparticles, one can also observe a narrow absorption peak corresponding to the exciton formation (e.g. observed for colloidal PbS quantum dots 53 ). However, in the most cases of nanoparticles with finite polydispersity (especially in composites), the absorption changes in rather wide range of energies without pronounced peak feature, which is also characteristic for the films under study (see Fig. 6a). To determine relevant energies in this case, the Tauc-plot method is usually applied. It

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implies the replotting of initial spectrum in accordance with following relation: 54

(αhν)1/n = A(hν − En ),

(1)

where α is absorption coefficient, hν is photon energy, A is constant, En is corresponding optical bandgap. The exponent n depends on the nature of corresponding optical transition (i.e. n = 1/2 for allowed direct transition, n = 2 for allowed indirect transition, n = 3/2 for forbidden direct transition, n = 3 for forbidden indirect transition). 55 In general, the replotting of absorption spectrum according to relation (1) allows one to extrapolate linear region (for a given n) to hν-axis and determine En for the corresponding transition. Thus, it simply gives a representation in rectifying coordinates, which is commonly used for amorphous semiconductors due to the presence of exponential region in the spectrum (related to the Urbach energy) that hinders the determination of absorption edge energy from the initial data. While Tauc-plot method played a crucial role in optical studies of amorphous systems, 56 it has two severe drawbacks when applied to ensembles of nanoparticles in simple straightforward manner. First, Tauc-plot method substantially changes the shape of absorption curve when applied to spectrum within wide energy range, thus, the choice of linear region for extrapolation becomes ambiguous. 57 Second, for the ensemble of nanoparticles Tauc-plot method frequently gives En values for n = 2 smaller than those for n = 1/2. It is often interpreted as that the absorption edge corresponds to the indirect transition, 58 which is very questionable for direct gap semiconductors such as PbS. The latter is most probably related to the fact that the aforementioned correspondence between transition type and n values were derived for three-dimensional systems. For example, n = 1/2 for direct transition arises from the character of density of states dependence on energy (which has square root functional form for simple 3D system). 59 However, the energy spectrum of nanoparticles in strong quantum confinement limit is represented by the series of discrete levels with extremely narrow density of states peaks (delta-functions). When we

17



ln(

(arb. units)

)

(a)

E

1

2

3

h

(eV)

4 d E

1/n

(arb. units)

E

h )

H

d(h

)

n = 1/2

n = 2

(b)

n = 2

C = 30 vol.% T

ann

= 20

C n = 1/2

(

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 38

1

2 h

3

4

(eV)

Figure 6: (a) Absorption spectrum and its first derivative for the non-annealed PPXPbS nanocomposite film with C = 30 vol.%. Dots correspond to several characteristic energies. Inset shows logarithmic dependence of absorption coefficient on photon energy. (b) Corresponding Tauc-plots for n = 1/2 and 2. consider interacting nanoparticles of various sizes, the resultant energy spectrum (as well as the density of states function) can be transformed into series of electron bands with finite width depending on size distribution and distances between particles. Therefore, the n values corresponding to different transition types for ensemble of nanoparticles depend on various details of the studied system. Thus, in present work we will use relation (1) only as a rectifying coordinates representation assuming that the observed absorption is related to direct transitions (indirect band gap in bulk PbS appears only under strong uniaxial strain 15 ). The absorption spectra of studied films can be characterized via several representative energies (Fig. 6a). The shape of the first derivative of obtained spectra (Fig. 6a) suggests the absence of any pronounced features related to the fine structure of optical transitions, which can be revealed via negative second derivative analysis. 60,61 The inset in Fig. 6a shows the logarithmic dependence of absorption coefficient on photon energy. The absence of

18


C = 10 vol.%

(b)

3.5

E (eV)

E

(a) T

n = 1/2

3.0

C = 10 vol.% 2.5

E

ann

n = 2

2.0 1

2

3

h

4

(eV) 2.5

C = 30 vol.%

E (eV)

(arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(arb. units)

Page 19 of 38

(c)

n = 1/2

2.0

C = 30 vol.%

1.5

T

2

h

E

n = 2

ann

1.0 1

E

3

4

0

(d) 100

T

(eV)

ann

200

300

( C)

Figure 7: Absorption spectra of the PPX-PbS nanocomposite films with C = (a) 10 and (c) 30 vol.% annealed at various temperatures Tann . Black arrows indicate the increase of Tann . Dependencies of characteristic energies En=1/2 and En=2 on annealing temperature for samples with C = (b) 10 and (d) 30 vol.%. pronounced linear regions suggests that exponential tails, usually observed for amorphous semiconductors, make only small contribution to the overall absorption in the studied films. The latter justifies the use of (1) for the spectrum analysis. Fig. 6b shows Tauc-plots for n = 1/2 and 2. Extrapolating these curves we obtain En=1/2 and En=2 , correspondingly. As it is illustrated in Fig. 6a, En=2 basically defines the absorption edge, while En=1/2 is close to the half of maximum absorption. At higher energies absorption saturates for both samples, in presented notation saturation appears above EH . The evolution of absorption spectra upon annealing and corresponding dependencies of characteristic energies are shown in Fig. 7. As it can be seen, the most substantial changes appear after the first annealing step (Tann = 160 ◦ C) resulting in a red-shift of the whole spectrum, while following annealing steps have less pronounced effect. Although, obtained dependencies of characteristic energies on Tann can be roughly treated as linear, we observe stronger relative change for En=2 , which appears to be even stronger for the sample with C = 30 vol.%. The evaluated En values can be used to estimate corresponding nanoparticle sizes dn .

19



Page 20 of 38

However, this commonly used procedure requires additional comment on various theoretical models provided in literature. It is worth mentioning, that (PbS)n molecular clusters, which, we assume, are present in the studied films, should demonstrate oscillating dependence of absorption energy (corresponding to HOMO-LUMO transition) on cluster size. 38–40 Wu et al. reported that typical absorption energies of (PbS)n clusters are above 4.5 eV, 41 which is considerably higher than En values in our case. Thus, we are tempted to relate all observed features of absorption spectra solely to the PbS nanoparticles and use general theories that suggest different size dependencies of energy gap Eg (between ground states of electrons and holes) in nanocrystallites. In what follows, we will restrict ourselves only to analytical models and consider Eg (d) dependencies only for d ≥ 1 nm (because it appears to be rather ambiguous if nanoparticles below 1 nm should be described by the presented models or by the results of ab initio calculations for molecular clusters). The most widely used expression was obtained using a simple quantum confinement model in the effective mass approximation, considering nanoparticles as 3D potential boxes with infinite walls (we denote this model as IW-QC) containing carriers with parabolic dispersion. 29 Generally, this expression consists of four terms. Introducing reduced carrier effective mass µ = m∗e m∗h /(m∗e + m∗h ), where m∗e and m∗h are the effective masses for electron and hole, it can be written in SI units as: 62 EgIW −QC = Eb + EQL + EC + ER = Eb +

e2 µe4 2π 2 h ¯2 − 0.893 − 0.00775 , µd2 πε0 εd πε20 ε2 h ¯2

(2)

where Eb is the energy gap in bulk material, h ¯ is the Planck constant, e is the electron charge, ε is a dielectric constant of bulk material, ε0 is the vacuum permittivity. While the first term in (2), Eb , sets a minimum band gap value when nanoparticles become sufficiently large, other terms describe different corrections that play significant role mostly for small particles. In particular, EQL represents the quantum localization energy, EC is the energy of electron-hole Coulomb attraction, and ER is the correlation energy. In the following, we assume Eb = 0.41 eV, and m∗e = m∗h = m∗ = 0.085me , where me is the free electron mass,

20


Page 21 of 38

5

Models

4

IW-QC HB

Eg (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3

FW-QC ER-CQD

2 1 1

2

3

4

d

5

6

7

8

9

10

(nm)

Figure 8: Comparison of various theoretical models. yielding µ = m∗ /2 = 0.0425me . 18 Although there is some controversy concerning the value to use for the dielectric constant, i.e. static ε(0) or optical ε(∞) 4 (for PbS ε(0) = 161 and ε(∞) = 17.2 63 ), for IW-QC model we use ε(∞) value (Fig. 8). It should be noted that due to high ε values in PbS, usually EC and ER terms are negligibly small, but, in general, they can play significant role. 63 Thus, we will keep them in further estimations. Soon after the IW-QC model was established, it became evident that this model fails to explain experimental Eg (d) dependencies for d < 10 nm, which was attributed to the effective mass approximation breakdown at this scale. 18 It is important to note, that the IWQC model is still sufficient to describe size-dependent optical properties for large particles. 30 The next step in the consideration of PbS nanoparticles is to account for nonparabolic effects by assuming hyperbolic mirror-like (m∗e = m∗h ) bands that approach parabolic form only close to L point of Brillouin zone. To employ the hyperbolic band (HB) model, one needs simply to replace the first two terms in (2) in the following way: 18 √

EgHB =

Eb2 +

8π 2 h ¯2 Eb + EC + ER . m∗ d 2

(3)

The HB model agrees with experimental data for PbS nanoparticles with sizes down to d ≈ 2.5 nm and with ab initio calculations. 18 Although, usually the ε values are assumed to be independent of nanoparticle size (which we implied for the IW-QC model), there is more

21



Page 22 of 38

general approach that makes ε size-dependent. We use the Hanken expression, 4,63 which can be simplified for mirror-like bands (m∗e = m∗h ) and written as: [

]

( ∆r ) 1 1 1 1 = − − · 1 − e− ρ . ε(∆r) ε(∞) ε(∞) ε(0)

(4)

Here ∆r is the distance between the electron and hole, for which an average value of 0.34966d should be used, 63 and √

ρ=

h ¯ 2m∗ ω

(5)

, LO

where ωLO = 210 cm−1 is the longitudinal-optical phonon frequency for PbS. 63 Thus, applying equations (4) and (5) we get ε(d) dependence, which was used for EC and ER terms calculation in the HB model. Resulting theoretical Eg (d) dependencies are presented in Fig. 8. As one can see, the curves corresponding to the IW-QC and HB models start to deviate from one another as the size of nanoparticle decreases. Probably the most controversial feature of the IW-QC and HB models application to real systems is that they describe properties of nanocrystallites basing solely on parameters of the corresponding bulk material without considering an impact of the matrix, in which they are embedded to. To illustrate the impact of matrix we will reproduce the empirical relation for E(d) dependence of exciton peak position in highly-monodisperse colloidal PbS quantum dots (ER-CQD) derived by Moreels: 53

E ER−CQD = Eb +

1 , + 0.282d

0.0252d2

(6)

where Eb is in eV and d in nm (Fig. 8). Although ER-CQD does not have any particular underlying physical model, it is surprisingly close to the results of tight-binding calculations for small spherical PbS nanoparticles (d ≤ 3.5 nm) with spin-orbit interaction taken into account performed by Kane, 64 which also suggested the E ∝ 1/d leading dependence for

22


Page 23 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the smallest particles. Considering that the HB model described optical properties of PbS nanoparticles in ethylene-15% methacrylic acid copolymer matrix quite well, while d values were defined from non-optical data, 18,53 large discrepancies between (3) and (6) results can be attributed only to different matrix impacts (there are many other examples of such discrepancies 63,65 ). To account for matrix-related effects it was proposed to consider a model similar to the IW-QC, but with finite potential walls (FW-QC). 63,65 In this case, the amplitude of barrier U ("height" of potential walls) is defined by parameters of the matrix and can be different for the electrons and holes. However, it was shown for PbS nanoparticles that the use of equal U = (Egmatrix − Eb )/2 values for both types of carriers gives sufficient accuracy in this approach (approximately 10% of difference in EgF W −QC for d = 1 nm). 63 Thus, for the band gap in PPX EgP P X = 4.5 eV, 66 we obtain U ≈ 2.05 eV. Yet again, assuming m∗e = m∗h , one can rewrite original expressions in a simple form: 65 EgF W −QC = Eb +

2π 2 h ¯2 2 · η + EC + ER , µd2

(7)

where dimensionless parameter η = βd/2π should be obtained by solving the following equation: v u

u m∗ βd βd m∗ cot =1− ∗ −t ∗ 2 2 mM mM

(

)

U β 2 d2 − , ∆ 4

(8)

where m∗M is the effective mass of charge carrier in matrix, and ∆ = 2¯h2 /(m∗ d2 ). It is worth mentioning, that this equation rises from the approximate solution for initial Hamiltonian, but to increase the accuracy of this model one needs to apply much more complex theoretical methods. Usually (8) should be solved numerically to obtain η(d) dependence. 65 Nevertheless, one can easily see that βd/2 = ξ can be treated as an independent variable, while d is

23



Page 24 of 38

included only in ∆, thus, we can analytically calculate the inverse relation v u( u u 1− u d=u t

m∗ m∗M

− ξ cot ξ

m∗ m∗M

·

U m∗ 2¯ h2

)2

+ ξ2

2¯h2 . U m∗

(9)

Assuming m∗M = me 65 and considering size-dependent ε (as we did for the HB model) we have obtained the resulting FW-QC curve presented in Fig. 8. As one can see from the Fig. 8, the obtained curve for the FW-QC model corresponds to the lowest energies. Although, such values agree well with the experimental data for an analogous system with close U value, 63 in our case it basically means that for the sample with C = 10 vol.% the most part of absorption spectra corresponds to sizes below 1 nm, for which the applicability of this theory remains questionable. Thus, we believe that the chosen U value is rather low, which can be attributed to the mutual impact of the PbS nanoparticles and the PPX matrix. It was already shown that nanoparticles have a pronounced effect on the structure of the polymer, 20 thus, it is quite possible that local surrounding of a nanoparticle also exhibits higher barrier value than pure PPX. We should also point out, that the barrier height for a real particle can be also affected by the details of its surface structure. Nevertheless, it is useful to compare results for all three models in order to analyse their basic trends. The obtained values of particle sizes dn=1/2 and dn=2 for the non-annealed samples determined via different models are presented in Table 2 (other numerical values Table 2: Corresponding sizes dn=2 and dn=1/2 determined via different models for the non-annealed samples. C dn=2 10 vol.% dn=1/2 dn=2 30 vol.% dn=1/2

IW-QC 4.27 nm 3.26 nm 4.9 nm 3.91 nm

24

Models HB 2.28 nm 1.41 nm 2.87 nm 1.95 nm


FW-QC 1.35 nm 0.65 nm 1.8 nm 1.1 nm

Page 25 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


are listed in Table S1, SI, Sec. II). Expectedly, the IW-QC model yields largest size values, while the FW-QC gives the smallest. Correspondingly, the relative change of dn=1/2 and dn=2 values upon annealing have inverse magnitudes for different models (see Fig. 9a and 9b). While it is pretty obvious that a red-shift of absorption spectra implies the increase of corresponding nanoparticle sizes, the actual relation between size distribution function and absorption in our case remains vague. As a mere indicator of such correlation one can propose a difference between d values corresponding to the various characteristic energies, which were used to obtain polydispersity index for nanoparticles with finite absorption band. 52 In our case, the difference between sizes corresponding to En=2 and En=1/2 can be considered as a roughly approximated value of size distribution width. While the quantitative change of (dn=2 − dn=1/2 ) substantially depends on the chosen model (here we show the result for the HB model which yields medium values), it can be clearly seen that this difference also increases upon annealing (Fig. 9c), and relative change is larger for C = 30 vol.% sample. Thus, we can presume that annealing not only increases nanoparticle size, but also increases the width of the corresponding size distribution function, which agrees well with the results for thermal treatment of PPX nanocomposites with silver nanoparticles. 32 We should mention that the increase of dn=2 upon annealing is much more pronounced, than that of dn=1/2 . The nominal size of nanoparticles (evaluated from the X-ray data) in the PPX-PbS film (C = 30 vol.%) annealed at 190 ◦ C is dX−ray ≈ 3.5 nm. It is natural to expect that dX−ray should be smaller than dn=2 , which implies that in our case the HB model gives the best quantitative agreement (see SI, Sec. II). As it was mentioned earlier, X-ray diffraction reveals small deviation of the lattice parameter in the studied PbS nanoparticles from its bulk value. The latter corresponds to the presence of a tensile strain of about 0.6%. Although it can be considered as small, for narrow bandgap semiconductors, such as PbS, even small strain can result in substantial quantitative changes. It is important to note that aside from simple bulk strain (which can have a core-shell profile), there are several

25



d

n=2

(%)

50 30

100

150

C

IW-QC

200

250

300

= 10 vol.%

HB

20

FW-QC

10 (a)

n=2

-d

n=1/2

) (%)

d

n=2

(%)

0 120

C

IW-QC

= 30 vol.%

HB

80

FW-QC

40 (b) 0 300

HB model

C

200

= 30 vol.%

100 (c)

C

(d

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 38

= 10 vol.%

0 50

100

150

Tann

200

250

300

( C)

Figure 9: Relative change of dn=2 value obtained from the absorption spectra upon annealing for the samples with C = (a) 10 and (b) 30 vol.%. Different colors correspond to different theoretical models used for dn=2 determination. (c) Relative change of difference between dn=2 and dn=1/2 determined via HB model upon annealing. indications of uniaxial 46 and tetragonal 62,67 deformations in small PbS nanoparticles. To estimate strain-related corrections to the obtained size values, we performed simple simulation based on various analytical models of Eg (d) dependence for constant strain values δ (for more details see SI, Sec. III). We considered strain as a source of linear change of parameter values used for Eg (d) calculation. As a reference, we used calculation results suggesting gap closing in PbS crystal for critical bulk strain of δB = −2.1% (compression). 12 We used different strain profiles (bulk, uniaxial, tetragonal) with corresponding values −1.5% ≤ δ ≤ +1.5% and assumed that the variations of effective mass, m∗ , and of the bulk band gap, Eb , are strictly proportional to each other (relying on the fact that both Eb and m∗ turn zero for the critical strain value), thus, the ratio Eb /m∗ remains constant. In the framework of chosen assumptions, the variation of δ shows only weak effect on Eg (d) dependencies (corresponding to the HB and FW-QC models) for small d values (see SI, Sec. III). Although, the IW-QC model shows strikingly different behavior, due to the numerous

26


Page 27 of 38

2.35

30 HB model

2.30

n=2

d

n=2

(%)

T

20

d

2.25 -1

0

10

1

(%)

=

(a) 0 HB model

+1%

T

=

+1%

=

-1%

B

=

+1.5%

(nm)

T

-1

2.9

0

1

2.8

(%)

50

C = 30 vol.%

(b) 0

B

d

(%)

=

3.0

B

E = 1.82 eV

100

0%

B

n=2

150

n=2

C = 10 vol.%

(nm)

B

E = 2.28 eV

d

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50

100

150

Tann (

200

250

300

C)

Figure 10: Relative change of dn=2 value determined via HB model upon annealing for the samples with C = (a) 10 and (b) 30 vol.%. Different colors correspond to different bulk δB and tetragonal δT values. Insets show the dependence of dn=2 value for the non-annealed samples on different types of strain. indications of inapplicability of this model, we will omit it in the further discussion. Using simulation results, we estimated the variation of dn=2 (Tann ) dependencies for the investigated samples (Fig. 10). The insets in Fig. 10 show dependencies of dn=2 values for the non-annealed samples on bulk (δB ) and tetragonal (δT ) strain. As it can be seen, the uncertainty of corresponding dn=2 value determination is larger for C = 30 vol.% sample, but still it is below 3% and can be neglected. For C = 10 vol.% sample the dn=2 (Tann ) dependence does not change significantly for all tested strain values (Fig. 10a), while for C = 30 vol.% sample the variation is significant and reach maximum of dn=2 (δB = +1.5%)/dn=2 (δ = 0) ≈ 1.3 at Tann = 300 ◦ C (Fig. 10b). Nevertheless, these variations are insufficient to substantially affect the obtained results. It is important to mention, that here we assumed strain values to be constant (i.e. sizeindependent). However, there are many experimental findings that the amplitude of strain is greater for small nanoparticles. 58 Theories of size-dependent strain (e.g. due to surface

27



atoms coordination number imperfection 42–45 ) suggest that the strain value δ should be roughly proportional to the inverse particle size (i.e. δ ∝ 1/d). Various theories suggest different strain values for the smallest nanoparticles, but in all of them the corresponding effect vanishes for larger nanoparticles (e.g. for d = 40 nm). Thus, high strain amplitudes are expected only for the smallest particles, for which Eg (d) dependencies for the HB and FW-QC models do not change with δ. Therefore, if we include size-dependent strain in our simulation procedure we will get almost the same results (see SI, Sec. III). We should note that PbS nanoparticles in the studied films are in strong quantum confinement regime (En /Eb > 2). Thus, the absence of any pronounced peak feature (related to the size distribution function) in the absorption spectra suggests that these nanoparticles form an effective 3D media with complex density of states, rather than being isolated. From the one hand, it suggests that we should take into account an additional interaction term when we convert absorption energies into nanoparticle size. From the other hand, the resultant density of states function depends not only on particle sizes, but also on the distances between them. Therefore, the function form of absorption spectra can be severely different from the conventional picture on which the Tauc-plot method is based. Although, the obtained dn values seem to describe the effect of annealing on size of PbS nanoparticles properly, we believe that further studies are required to establish appropriate Eg (d) relations for this type of interacting systems. We should also note that the absence of absorption features related to (PbS)n clusters in our case can be related to various reasons. For example, some experimental studies suggest that extinction coefficient of a nanoparticle is proportional to its size. 61 Therefore, the overall optical response related to the smallest particles, such as (PbS)n clusters, can be rather small. Thus, additional assumptions should be made to extract corresponding contribution. In our case, the latter implies matrix-related effects on the optical properties of (PbS)n clusters, which have not been considered yet.

28


Page 28 of 38

Page 29 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4. Conclusions We have studied structure and optical properties of thin PPX–PbS nanocomposite films as well as their evolution upon stepwise annealing. Wide-angle X-ray diffraction shows that the as-prepared films are characterized by ultimately broad diffraction pattern, which cannot be unambiguously indexed within the cubic face-centered lattice of bulk PbS. X-ray absorption spectroscopy (EXAFS and XANES) reveals broad distribution of Pb–S bond lengths, which corresponds to substantially shorter bonds, as compared to the bulk PbS. This observation can be explained by the presence of a notable portion of molecular (PbS)n clusters. However, transmission electron microscopy reveals that some PbS nanoparticles with crystalline lattice of bulk PbS are present even in the as-prepared films. It was found that annealing promotes aggregation and recrystallization of PbS nanoparticles and, as a consequence, results in a considerable red-shift of the UV-Vis optical absorption spectra. Several theoretical models establishing a relationship between nanoparticle size and optical bandgap of the composite materials were analyzed and compared with the experimental data. It was shown that the hyperbolic band model is the most appropriate for description of optical properties of the studied composite films, whereas the lattice strain of PbS nanocrystallites should not affect the bandgap substantially. The absence of pronounced peak features in the absorption spectra indicates strong interaction between adjacent PbS nanoparticles, which agrees with the large exciton radius of PbS. Although further studies are required to estimate the relevant interaction term and elucidate the optical properties of (PbS)n clusters, the obtained results illustrate that thermal treatment can be effectively used for fine-tuning the properties of PPX–PbS thin composite films.

Supporting Information Available Additional structural data - X-Ray diffraction patterns and EXAFS spectra for all studied samples. Pictures of the composite films with various PbS content. The table with numerical 29



values of energy parameters and corresponding sizes of nanoparticles for various annealing temperatures, estimated using different models. The description of strain-related corrections estimation procedure and obtained data, both for constant and size-dependent strain cases. Reference values used for estimation are also listed. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgement This work was supported by the Ministry of Science and Higher Education of the Russian Federation, grant No. 14.577.21.0273 (unique identifier – RFMEFI57717X0273). Measurement results presented here were obtained using the equipment of resource centers of NRC "Kurchatov Institute".

References (1) Hopf, H.; Gerasimov, G. N.; Chvalun, S. N.; Rozenberg, V. I.; Popova, E. L.; Nikolaeva, E. V.; Grogoriev, E. I.; Zavjalov, S. A.; Trakhtenberg, L. I. Metal-containing poly(p-xylylene) films by CVD: Poly(p-xylylene) with germanium crystals. Chem. Vap. Deposition 2004, 3, 197–200. (2) Grigor’ev, E. I.; Zav’yalov, S. A.; Chvalun, S. N. VDP synthesis of poly-p-xylylene - metal (semiconductor) nanocomposite materials for chemical sensors. Nanotechnol. Russ. 2006, 1, 58–70. (3) Trakhtenberg, L. I.; Gerasimov, G. N.; Grigor’ev, E. I. Nanoclusters of metals and semiconductors in polymeric matrices: Synthesis, structure, and physicochemical properties. Russ. J. Phys. Chem. A 1999, 73, 209–220. (4) Yoffe, A. D. Low-dimensional systems: Quantum size effects and electronic proper-

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OPT

XRD

annealed

Absorption

G

Bulk PbS

(eV)

Graphical TOC Entry

1.8 0

TANN

PPX-PbS

100

20

2

30

T

200

EXAFS

R

40

1

38

2

300

( C)

ANN

Bulk PbS

as-grown 10

2.2 2.0

PPX-PbS

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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R

as-grown

(Å)


3

4

Effect of Thermal Annealing on Structure and Optical Properties of

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