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Coherent Acoustic Phonons in Colloidal Semiconductor Nanocrystal Superlattices Caroline Poyser, Thomas Czerniuk, Andrey Akimov, Benjamin T. Diroll, E. Ashley Gaulding, Alexey S. Salasyuk, Anthony Kent, Dmitri Yakovlev, Manfred Bayer, and Christopher B. Murray ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b06465 • Publication Date (Web): 22 Dec 2015 Downloaded from http://pubs.acs.org on December 26, 2015

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Coherent Acoustic Phonons in Colloidal Semiconductor Nanocrystal Superlattices Caroline Poyser,1 Thomas Czerniuk,2 Andrey Akimov,1 Benjamin T. Diroll,3† E. Ashley Gaulding,4 Alexey S. Salasyuk,5 Anthony Kent,1 Dmitrii Yakovlev,2,5 Manfred Bayer,2,5 and Christopher B. Murray3,4 1

School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK Experimentelle Physik 2, TU Dortmund, Dortmund 44227, Germany 3 Department of Chemistry, University of Pennsylvania, USA 4 Department of Materials Science and Engineering, University of Pennsylvania, USA 5 A. F. Ioffe Physical-Technical Institute, Russian Academy of Sciences, St Petersburg 194021, Russia 2

KEYWORDS Nanocrystal Superlattice, Colloidal Nanoparticles, Thin Film, Acoustic Phonons, Speed of Sound

ABSTRACT

The phonon properties of films fabricated from colloidal semiconductor nanocrystals play a major role in thermal conductance and electron scattering, which govern the principles for building colloidal based electronics and optics including thermoelectric devices with high ZTfactor. The key point in understanding the phonon properties is to obtain the strength of the elastic bonds formed by organic ligands connecting the individual nanocrystallites. In the case of very weak bonding the ligands become the bottleneck for phonon transport between infinitively rigid nanocrystals. In the opposite case of strong bonding the colloids cannot be considered as

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infinitively rigid beads and the distortion of the superlattice caused by phonons includes the distortion of the colloids themselves. We use the picosecond acoustics technique to study the acoustic coherent phonons in superlattices of nanometer crystalline CdSe colloids. We observe the quantization of phonons with frequencies up to 30 GHz. The frequencies of quantized phonons depend on the thickness of the colloidal films and possess linear phonon dispersion. The measured speed of sound and corresponding wave modulus in the colloidal films point on the strong elastic coupling provided by organic ligands between colloidal nanocrystals.

Colloidal semiconductor nanocrystals (CSNCs) have attracted a lot of interest after the discovery in them of quantum sized effects in the early 1980s.1-6 This interest is due to their numerous applications in electronics, optics, and medicine.7,8 Among novel prospective applications of CSNCs are: the improvement of lighting efficiency by using nanocrystal quantum dots with controlled interfaces,9-11 building CSNC based electronics,12,13 using CSNCs as thermoelectric devices,14 solar cells,15 photodectors,16 and solid-state memories.17 The detailed information about these applications and related references may be found in the review by Talapin et al..7 Most of the studies with CSNCs have been aimed on the electron properties that govern optical and electronic phenomena. At the same time for realization of practical devices, understanding the phononic properties of CSNCs is equally important. Phonons govern the thermal conductivity and electron scattering in the complex structures fabricated from CSNCs and knowledge of the phonon spectrum allows us to define the symmetry of nanoobjects with CSNCs and the strength of the elastic bonds between the interacting individual CSNCs. Particularly, the strength of the elastic bonds between the CSNCs plays the crucial role in the


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heat conductivity18 and thus defines the efficiency of thermoelectric devices through their ZTfactor.19 Comprehensive information about phonon properties in colloidal nanostructures can be obtained experimentally using picosecond acoustics techniques, in which coherent phonons are generated by an optical pump pulse from a femtosecond laser and detected with femtosecond temporal resolution by the probe pulse originating from the same laser.20 This technique was successfully used to study coherent phonons in various colloidal samples.21-32 Most of these works were aimed to detect the Lamb modes33—phonon modes of individual metallic,22-24 dielectric,26,27,29 or semiconductor21,25 nanoparticles. The frequencies, fL , of these modes are defined by the elastic parameters of an individual colloid and cover the range from several gigahertz (GHz) to several terahertz (THz) for micro- and nanoparticles with typical size between 10-6 and 10-9 m respectively. For example, in a sample with 3 nm PbS CSNs, fL=2.1 THz [21]. Fewer experimental studies have been performed on the properties of coherent phonons originating from the ligands that are responsible for the elastic bonds between the colloidal nanoparticles.30-32 The challenge of these studies is due to the fabrication of the samples where the colloidal nanoparticles form a periodic lattice with controlled symmetry and strength of elastic bonds. Such periodic nanostructures are often called as colloidal superlattices34 or supracrystals,35 and have been recently fabricated for several types of metallic dielectric and CSNCbased superlattices.31,32,34-42 Coherent phonon properties of the superlattices have been studied earlier in Reference 31 for cobalt colloids, but no experiments on CSNC samples have been reported. Theoretical considerations of the phonon spectrum in superlattices suffer from uncertainty due to the unknown strength of the ligand’s elastic bonds which define the average sound velocity s and possible phononic band gaps in the periodic colloidal array.43,44 These


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challenges and the importance of phonons in practical CSNC devices for prospective applications have motivated our present experimental work. In the present paper we report picosecond acoustics experiments performed on superlattices fabricated from CdSe CSNCs. Our measurements show the quantization of coherent phonons defined by the thickness of the supra-crystalline films and, in films with the maximum thickness d=340 nm, the high-order phonon resonances are detected up to the 7th harmonic. Using the model of closed organ-pipe modes we estimate the longitudinal sound velocity in the studied samples s between 2100 and 2900 m/s depending on the thickness of the superlattice film. This value is only a factor of ~1.5 lower than in bulk crystalline CdSe. The “amorphous” spin-coated film containing the same CSNCs show the velocity in the same range as the superlattices. No optical-like phonon modes were observed related to the vibrations of CSNC in the elementary cell of the superlattice. The experimental results and comparison with recent theoretical works43,44 lead us to conclusions about the strength of the elastic bonding between the individual SCs in the studied CSNC superlattices. The estimated wave modulus has a value between 10 and 30 GPa which does not differ strongly from the values obtained for bulk and Young moduli in the static experiments45 and predicted theoretically46 for CSNC films. RESULTS The CSNCs studied in this work were wurtzite (hexagonal) CdSe synthesized by standard colloidal methods following literature procedures.47 To enhance the uniformity of the CSNCs, size-selective precipitation was performed.48 The monodisperse, prolate CdSe nanocrystals are shown in the transmission electron microscope (TEM) micrograph in Figure 1a with a highresolution TEM image showing the highly-crystalline structure inset. The prolate ellipsoidal


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nanocrystals have an average size of 10.0 nm × 6.6 nm as determined by TEM with a size dispersion of ~8%. The surface of the nanocrystals is terminated with tetradecylphosphonic acid (see Figure S1 in Supporting Information), which facilitates solubility in non-polar organic solvents and provides a soft spacer between particles in the solid state. The films studied in this work were prepared by two distinct methods which produce films with differing degrees of interparticle ordering. To prepare films characterized by longrange order, liquid interfacial self-assembly was performed.42 Three samples prepared in this manner (Samples A, B, and C) were made by drop-casting toluene dispersions of CdSe nanocrystals (20 mg/mL) onto diethylene glycol surfaces in Teflon wells, followed by covering the evaporating dispersion within a small headspace and allowing the toluene to evaporate. The average thickness of the films was controlled by changing the amount of toluene dispersion that was drop-cast. After drying, the floating superlattice film was scooped up onto Si substrates. To prepare an “amorphous” film without long-range order (Sample D), a concentrated toluene dispersion (35 mg/mL) of nanocrystals was spin-coated onto Si substrates at a spin rate of 800 rpm.


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Figure 1. (a) The TEM image of the CdSe nanocrystals used in our work. Inset shows a high resolution TEM image of one particle. (b) Optical micrograph of Sample A CSNC superlattice film. (c-e) SEM micrographs of superlattice films at increasing magnification with insets showing the geometry of the superlattice in side-on (d) and top-down (e) views. (f) TEM micrograph of a superlattice film with an inset showing a small-angle selected-area electron diffraction pattern.

Several measurements were performed to confirm long-range periodicity of the CdSe nanocrystals in the superlattice films in Samples A, B, and C. A photograph of the sample A with thickness d=340±40 nm film is shown in Figure 1b with color variation reflecting variation in the thickness of the film. Although superlattice films are more heterogeneous in thickness than a spin-coated film, which typically has a mean roughness on the order of one nanocrystal, the optical micrograph (Figure 1b) and low-magnification scanning electron microscopy (SEM)


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image in Figure 1c show that the films are homogeneous on ~100 µm length scale. AFM measurements of thickness (see Table 1) were performed at several spots on ordered films to obtain the average film thicknesses. Higher resolution imaging in the SEM images of Sample A in Figures 1d and 1e show that the homogeneous regions apparent in optical microscopy and low-resolution SEM contain the close-packed hexagonal microstructure of the CSNC superlattice. Additional SEM survey images demonstrating long-range order, with coherent lattices over several hundred nanometers to microns, and GISAXS demonstrating self-assembly over the substrate are shown in Supporting Information in Figures S2 and S3. A TEM micrograph of a typical film is shown in Figure 1f with the periodic hexagonal packing observed and demonstrated by small-angle selected area electron diffraction (inset Figure 1f). The periodicity of the spacing in plane determined from TEM images is 8.3 nm, which indicates that the prolate nanocrystals stand primarily with the unique long-axis aligned perpendicular to the substrate separated by wall to wall distance ~1.7 nm, packing into an hcp structure apparent from the systematic transmissive regions in the TEM image. This result is the same as obtained earlier in the similar CSNC superlattice.34 The scheme of picosecond acoustics experiments is shown in the inset of Figure 2a. An Al film with the thickness of 100 nm played a role of thermoelastic transducer.20 This was deposited on the side of the 0.4 mm-thick Si substrate opposite to the SC film. The Al film was excited by 800 nm-wavelength optical pulses from a 150 fs pulsed laser with repetition rate 80 MHz. The pump beam was focused to the spot with 100 µm diameter and the excitation density in the excitation pulse did not exceed 10 µJ/cm2. Optical excitation of the Al films resulted in the generation of a picosecond strain pulse,20 which was injected into the Si substrate and propagates towards the SC film with the velocity of longitudinal sound sSi=8490 m/s at the low temperatures


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the experiments were carried out at. After the propagation time of 47 ns, the strain pulse was injected into the CSNC film exciting their coherent phonons, which were detected by measuring the intensity of the probe 400 nm optical pulse, originating from the same femtosecond laser and reflected from the CSNC film. The probe beam was focused to a spot with the diameter less than 20 µm. Measuring the changes of the reflectivity ∆R(t) as a function of the delay t between pump and probe pulses it is possible to obtain the information about the spectrum of coherent phonons excited in the CSNC film by the picosecond strain pulses. At the low temperatures of the experiments, T=10 K, the attenuation of high-frequency (up to 1 THz) phonons propagating in the Si substrates may be neglected.

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Figure 2. (a) Temporal evolution of the reflectivity changes and (b) spectral density obtained as FFT of the curve in (a) for Sample A. Inset in (a) is the scheme of the experiment. Vertical bars point on the spectral position of the maxima in the spectrum and corresponding number indicates the harmonic number of the phonon modes. The inset in (b) shows the measured dependence of resonance frequency fi on the harmonic number i; dashed line is a fit of equation 1 to the experimental data.


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Figures 2a and 2b show the example of the measured ∆R(t) and its spectrum obtained by Fourier transform, respectively, for the thickest superlattice Sample A with d=340 nm. The signal ∆R(t) has oscillatory behavior and its FFT shows with confidence 6 spectral lines marked by vertical bars on Figure 2b. The spectral line with the lowest frequency peaks at 5.5 GHz and a mean equidistant spacing ∆f=4.13 GHz between the spectral lines is observed. Such a spectrum is the result of quantized phonon modes excited in the film by the picosecond strain pulse. This quantization is governed by the mismatch of the acoustic impedances between CSNC film and Si substrate. The corresponding phonon spectrum is classified in this case as closed-pipe organ like mode effect basing on the analogy with the harmonics in the sound of a pipe organ.49-52 The frequency of the phonon modes are described by the well-known equation:53

fi =

(2i − 1)s 4d

(1)

where i=1, 2, 3… , s is the sound velocity in the direction of the film growth and d is the film thickness. The spectral positions fi of the maxima in the spectrum are plotted in the inset of Figure 2b as function of i. The solid line in the inset of Figure 2b shows the linear fit predicted by Eq.(1) and it is seen that the model of closed-pipe organ like modes ideally fits the experimental result if we assign i=2 to the spectral line which has the lowest energy. Actually, the expected line corresponding to i=1 cannot be measured precisely due to the limited 1 ns temporal interval of the measurements. The gradient of the linear fit of Eq.(1) to the experimental results presented in Figure 2 gives the sound velocity s=2810 m/s. To justify the closed-pipe organ-like mode quantization in CSNC films, and to measure s in various films we have studied 3 superlattice samples (Samples A,B,C) with various thicknesses d. We also studied the amorphous Sample D with d=64 nm which was prepared by


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spin-coating and does not possess long scale ordering of CSNCs. In the experiments, the homogeneity of the film thickness becomes crucial for using Eq.(1) and we performed measurements in various points on the sample surface. The results of the measurements are shown in Figure 3 and the values of s calculated using Eq. (1) are presented in Table 1. It is clearly seen that the spacing ∆f between the spectral lines increases with the decrease of d. This fact confirms the closed-pipe organ model for the interpretation of the experimental results and excludes the explanation of resonances being due to the optical phonon-like modes like observed in the films with Co nanoparticles.30 No harmonics with f>30 GHz are observed in any of the studied films.


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Sample A 340 nm

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Figure 3. Phonon spectra obtained from the temporal evolution of the reflectivity in four samples with various thicknesses of the superlattice (samples A, B, and C) and amorphous (Sample D) CSNC films. Different curves in each panel correspond to different points at the surface of the sample. Table 1. The measured sound velocities s and obtained wave moduli M for various CSNC films. Sample A, B, and C are superlattice films and Sample D is spin-coated “amorphous” film with CdSe CSNCs. The values of deviations for s were calculated based on the variations of the film thickness and frequencies of the phonon resonances measured in different points of the film. Sample

Film Sound Wave thickness, velocity , modulus, d, (nm) s, (m/s) M, (GPa)

Superlattice A

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Figure 3 also presents the data for “amorphous” Sample D. It is seen that the spectrum is similar to the superlattice Sample C. These two samples have close thicknesses d and we get the sound velocities to have the same values in the range of experimental uncertainty. Summarizing the full set of the obtained data we may conclude that the sound velocity in the CSNC films varies from 2000 to 3000 m/s depending on the sample and film thickness. These values and its variation are typical for various polymer films studied by ultrafast acoustic techniques49 , but also CdSe ~ 4000 m/s54 for bulk CdSe - the material from which the CSNCs are not much less than s LA

synthesized. There is a similarity in the maximum detected frequency of the closed-pipe organ modes. Indeed the experiments with picosecond acoustic pulses in polymer films showed a cutoff in the spectrum of coherent phonons between 20 and 30 GHz.49 DISCUSSION The phonon properties of colloidal films may be considered on the basis of two opposite approaches corresponding to the cases of weak and strong elastic coupling. In the first case (i.e. weak coupling) the phonon properties may be considered as for a lattice with absolutely rigid colloids which are analogous to nuclei in the crystalline lattice. The phonon spectrum for such weakly coupled system will be similar to the bulk crystal of the same symmetry, but strongly reduced in energy according with the masses of colloids and rigidity constants of the “bonds” between them. The elastic moduli in this case are orders of magnitude lower than for bulk material from which the colloids are synthesized. The moduli values lie in the MPa range and the


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sound velocity drops strongly below 1000 m/s. This case of weak coupling was observed experimentally in superlattices with Co colloids, where the GHz spectral lines in the phonon spectrum are interpreted as the phonon modes in the elementary superlattice cell.30 In the opposite case of strong coupling, the colloids cannot be considered as infinitively rigid beads. The distortion of the superlattice caused by the elastic wave includes the distortion of the colloids themselves. In the extreme case such composite material can be considered as a solid solution of CSNCs and polymer forming ligands. The elastic properties (e.g. elastic moduli) of the colloids are usually well known, but the properties of ligands may be different from the elastic properties of the bulk polymer forming these ligands and have remained unknown. The detailed calculations of the phonon spectrum in the case of strong elastic coupling is quite complex, but for the linear dispersion part for acoustic phonons with the wavelength much longer than the superlattice period one may use the approach based on elastic moduli and estimate the sound velocity using the well-known equations. For instance, in the isotropic approximation, the sound velocity s =

M

ρ

, where M - is a wave modulus and ρ is the density of

the SC film. The value of M may be determined using the bulk and Young’s moduli measured in static experiments, K and E respectively: M =

3K (3K + E ) . 9K − E

The values of M obtained from the measured sound velocity for the studied samples are presented in the Table 1. These values vary between 15 and 26 GPa which are not much less than for bulk CdSe, MCdSe=75 GPa. Based on this comparison with the bulk CdSe we attribute the CSNCs films studied in the present work to be closer to the case of strong elastic coupling.


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In the studied films the quantization of phonon resonances is described well by Equation 1, which shows that the phonon spectrum has a linear dispersion in the range of frequencies studied, where the measured values of fi are small relative to the frequency range close to the first phononic band gap. This is in agreement with the recent theoretical work on the calculation of dispersion curves in CSNCs superlattices where linear dispersion goes up to f~50 GHz [44], which is beyond the highest frequency measured in our work. The spectral width ∆fi of the quantized resonance fit well the estimations of reflection r for acoustic phonons at the interface between CSNC film and Si substrate. Taking s=2500 m/s and ρ≈3.4 g/cm3 for the CSNC film together with well known elastic parameters for Si we get r=0.4 which results in the finesse Q~3 for the n=1 resonance. It is interesting to compare our results with earlier static experiments where mechanical properties and corresponding elastic moduli of CSNC superlattices were studied.45 If we take the values of K and E in our films with 6 nm CdSe SCs from earlier measurements,46 and more recent theoretical analysis, as K=4 GPa and E=6 GPa we get M=7.2 GPa and taking ρ=3.4 g/cm3 we get s=1460 m/s. The values of M and s measured in the present work (see Table 1) are higher than obtained in static experiments, which is most probably due to the use of cryogenic temperatures in our experiments, which increases the elastic moduli.55 However the difference is not so large to suggest that cooling down the sample would change its elastic properties from weak to strong coupling. The reason for the increase of the sound velocity with the thickness d of the films is possibly due to longer fabrication procedure resulting (drying time) in stronger collective ligand interactions in the thicker films. Another reason could be due to better ordering along the growth direction and resulting in anisotropy of the sound velocity.


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The coherent phonon signals last no longer than 1 ns, and the spectrum does not show spectral lines higher than fc≈30 GHz. The decay time and the cutoff frequency, fc, are governed by the frequency dependent scattering of phonons in the bulk, and by the leakage of phonons into the Si substrate. The values of the time decay and fc measured in the present work are similar to values obtained for polymer films with d>100 nm prepared on Si substrates.49 However, for thin (d=45 nm) homogeneous polymer films in the experiments of Reference 49, the detected phonon spectrum spreads up to 50 GHz. The lower cutoff frequency in CSNC films is suggestive of a higher number of defects, which scatter phonons. These defects may be voids of CSNC in the superlattice and inhomogeneity of ligand numbers connecting the CSNCs. These lead to the strong scattering of the coherent phonons injected from the Si and, as a result, high-frequency components including optical phonon-like modes with frequencies higher than 50 GHz43,44 are not excited coherently in the whole CSNC film. In this respect the situation could change if the film was excited directly by the pump laser pulses. However, instability of the samples to the high-intense pump optical excitation did not allow us to do this. CONCLUSIONS We have excited coherent phonons in thin films of superlattices comprised of colloidal semiconductor nanocrystals. We have observed the quantization of phonons related to the vibrational modes of the film supported on the elastically rigid substrate. The results have allowed us to derive sound velocities in the studied films, and reach conclusions about the strength of the elastic coupling between the semiconductor nanocrystals, that points on strong interactions between ligands connecting the individual semiconductor nanocrystallites. The experimental method used in the present work and obtained results provide pathways for exploiting coherent phonons for high-frequency modulation of CSNC-based light sources similarly to the nanomechanical modulation of semiconductor vertical lasers56. The information about the spectrum of coherent phonons, its high-frequency cutoff and mismatch with Si


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substrate is crucial for understanding the thermal transport properties of the CSNC-based devices18. The conclusion about strong elastic coupling between the nanoparticles seems to be disappointing for applications of the CSNCs superlattices in thermoelectricity. However, we hope that our experiments will initiate the search for new chemical and technological solutions which will provide weaker elastic bonds without effecting electrical conductivity in the arrays of CSNCs and finally this may lead to the fabrication of thermoelectric devices with high ZT. The present work demonstrates the efficiency of the experimental technique for studying the strength of elastic bonds in CSNC superlattices, which will contribute to the synthesis of optimized structures for the functions mentioned above.

METHODS Materials. Trioctylphosphine oxide (TOPO, 99%, Strem), trioctylphosphine (TOP, 90%, Aldrich), tetradecylphosphonic acid (TDPA, PCI Synthesis), cadmium oxide (CdO, 99.99%, Strem), and diethylene glycol (Fisher) were purchased from commercial suppliers and used as received. Solvents were ACS grade or higher. CdSe Synthesis. 18.0 g TOPO, 1.40 g TDPA, and 360 mg CdO were combined in a 125 mL 3neck flask and heated under vacuum (~1 torr) to 120 °C, then heated under nitrogen to 300 °C to dissolve the CdO and turn clear. After turning clear, the reaction was cooled to 140 °C and held under vacuum for 1 hour. Then, the reaction was heated to 360 °C under nitrogen pressure, injecting 11.7 mL of TOP during the ramping process. Separately, in a nitrogen-filled glovebox, an injection solution of 348 mg of selenium powder was dissolved in 2.7 mL of TOP by stirring at 50 °C overnight. This solution was injected into the reaction at 360 °C and the reaction was held for 5 minutes at 355 °C, then cooled to ~100 °C and diluted 1:1 by volume with toluene. The contents of the reaction were precipitated with methanol, centrifuged at 8000 rpm for 5


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minutes into a pellet, and redispersed in toluene. This process was repeated with methanol, then ethanol, then isopropanol, dispersing the particles into toluene prior to each precipitation. Sizeselective precipitation was performed to fractionate the sample into more monodisperse subsets. To perform size-selective precipitation, small amounts of isopropanol were added to a solution of nanocrystals in toluene to induce flocculation, stirred vigorously, then centrifuged to produce a pellet and colored supernatant. This process was repeated on the supernatant to isolate nanocrystals of decreasing size. Self-Assembly. 15-45 µL of 20 mg/mL toluene dispersion of colloidal CdSe nanocrystals were drop-cast on to 1.7 mL of diethylene glycol contained in a Teflon well with dimensions 1.5 cm × 1.5 cm × 1.0 cm in depth. The well was immediately covered with a glass slide and then the solution was allowed to evaporate over ~1 hr. Films were carefully scooped up on to the desired substrate, either Si chips used for measurements of the speed of sound or TEM grids (Electron Microscopy Sciences). Thermal Analysis. Thermogravimetric analysis of the CdSe sample was performed using a TA Instruments Q600 instrument. Measurements were performed under air flow (100 mL/min) from room temperature to 550 °C at a rate of 20 °C/min. The analysis shows that the weight percentage of CdSe is 88% which means that the volume of organic mass fraction is in the range of 50-56%, depending on the density of the organic material (0.8-1.0 g/cm3) assuming no void space. Based on these results and taking into account the bulk density of CdSe 5.82 g/cm3 we estimate the density of the CSNC films ρ≈3.4 g/cm3. Electron Microscopy. Routine TEM imaging was performed using a JEOL 1400 microscope operated at 120 keV. High resolution TEM imaging was performed using a JEOL 2100


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microscope operated at 200 keV. SEM imaging of thin films was performed using a JEOL 7500 microscope operated at 5 keV. Atomic Force Microscopy. AFM measurements of film thickness were performed using an Asylum research MFP-Bio-3D AFM in tapping mode. To measure thickness, the films were scratched to the silicon surface using a clean fine-tipped tweezer. For supra-crystal films, the inhomogeneity of the sample apparent from the color variation of the films was analyzed by performing thickness measurements at least five positions for each film. Thickness measurements are reported in Table 1. X-Ray Scattering. Grazing-incidence X-ray diffraction was performed at the 8-ID-E beamline at Argonne National Lab’s Advanced Photon Source. ASSOCIATED CONTENT Additional characterization can be found in the Supporting Information File. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *[email protected] Present Addresses †

Center for Nanoscale Materials, Argonne National Laboratory

ACKNOWLEDGMENT


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The authors acknowledge Al. Efros, A. S. Scherbakov and B.A. Glavin for useful discussions. The work was partially supported by the Department of Energy, Office of Basic Sciences, Division of Materials Science, Award No. DE-SC0002158, Deutsche Forschungsgemeinschaft (BA 1549/14-1) and German Ministry of Education and Research (BMBF) (FKZ: 05K13PE1). ASS thanks the support of the Government of Russia through the Program P220 (Grant 14.B25.31.0025) REFERENCES 1. Ekimov, A. I.; Onushchenko, A. A. Quantum Size Effects in 3-Dimensional Microscopic Semiconductor Crystals. JETP Lett. 1981, 34, 345–349. 2. Efros, A. L. Interband Absorption of Light in a Semiconductor Sphere. Sov. Phys. Semicond. 1982, 16, 772–775. 3. Itoh, T.; Kirihara, T. Excitons in Cucl Microcrystals Embedded in NaCl. J. Lumin. 1984, 31/32, 120–122.

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