Enhancing Silicon Nanocrystal Photoluminescence through

Article pubs.acs.org/JPCC

Enhancing Silicon Nanocrystal Photoluminescence through Temperature and Microstructure Samuel L. Brown,† Dayton J. Vogel,⊥ Joseph B. Miller,†,§ Talgat M. Inerbaev,∇,# Rebecca J. Anthony,‡,¶ Uwe R. Kortshagen,‡ Dmitri S. Kilin,† and Erik K. Hobbie*,† †

North Dakota State University, Fargo, North Dakota 58108, United States University of South Dakota, Vermillion, South Dakota 57069, United States ∇ Eurasian National University, Astana, 010008 Kazakhstan # National University of Science and Technology MISIS, Moscow, 119049 Russian Federation ‡ University of Minnesota, Minneapolis, Minnesota 55455, United States ⊥

S Supporting Information *

ABSTRACT: Routes to enhancing the photoluminescence (PL) of colloidal silicon nanocrystals (SiNCs) typically focus on changes in surface chemistry and the associated improvements in quantum yield. Here, we report a new more indirect approach that instead exploits the structure of the host matrix. Specifically, we demonstrate that changes in microstructure associated with a thermotropic phase transition in unbound ligand can increase the excitation fluence through scattering, yielding dramatic improvements in PL intensity without any discernible changes in fluorescence lifetime or quantum yield. Using size-purified plasmasynthesized SiNCs prepared as solid and liquid samples, we use experiment and computation to examine both intrinsic size-resolved differences in the temperature-dependent PL and an anomalous contribution linked to matrix microstructure. Beyond revealing a potential new route to improved PL intensity, our results further clarify the role of surface states and the challenges that they present.

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been successfully utilized for bioimaging25−27 and luminescent polymer−nanocomposite applications,28−30 a number of fundamental questions, such as the precise role of surface states,31 higher-order details related to quantum confinement,32 and the importance of internanocrystal interactions,33−36 remain unresolved. An issue of particular importance for any application that seeks to exploit the luminescence from SiNC ensembles is fluorescence quantum yield (QY). Routes to enhancing the QY of colloidal SiNCs typically focus on surface engineering.37−40 For plasma-synthesized SiNCs passivated with short alkyl chains, the QY drops off dramatically with decreasing nanocrystal size,17,21 which limits applications targeting green or blue emission. In terms of controlling the QY externally, a significant amount of recent work has focused on the temperature-dependent PL emitted by SiNCs dispersed in a variety of environments.30,41−47 We recently explored how the band gap and PL lifetime change with size and temperature for monodisperse colloidal SiNCs, both as pure solid films and as polymer nanocomposites.30 In general, the lifetime increases

INTRODUCTION Semiconductor nanocrystals show considerable promise for a variety of potential applications, from color displays and solar cells to fluorescent labels and dyes.1,2 Without question, the reigning nanomaterial in this regard has been CdSe, which can be solution synthesized into highly monodisperse colloidal suspensions.3 Despite this recent success, potential health and environmental concerns surrounding the metal chalcogenides4−6 have generated a significant amount of interest directed at nontoxic, earth-abundant alternatives, and nanocrystalline silicon is receiving considerable attention in this regard. Although bulk silicon currently dominates the microelectronics industry, it has enjoyed limited success in the realm of photonics due in part to relatively poor optical performance. At the nanoscale, however, the emission characteristics of silicon are enhanced by changes in band structure imposed by quantum confinement. Silicon nanocrystals (SiNCs) can be synthesized in a number of different ways.7−17 With the appropriate surface passivation, they can exhibit tunable photoluminescence (PL) across the visible to the near-infrared.16−20 Surface treatment also renders the particles soluble in common organic solvents, which allows for additional purification by size into highly monodisperse colloidal suspensions.21−24 Although the PL from SiNCs has © XXXX American Chemical Society

Received: June 9, 2016 Revised: August 1, 2016

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DOI: 10.1021/acs.jpcc.6b05837 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C significantly with decreasing temperature, reflecting a suppression of nonradiative effects,30,41−47 while the wavelength of peak emission shifts in response to thermally induced changes in the quantum-confined band gap.30,41−47 Here, we revisit the temperature-dependent PL of these materials, utilizing a new set of samples to specifically focus on the interrelated effects of temperature and matrix microstructure, a topic that has received relatively limited consideration. Using size-purified plasma-synthesized SiNCs prepared as solid or liquid samples, we use a combination of experiment and computation to examine intrinsic size-resolved differences in the temperature dependence of the relative PL intensity. Our computational approach employs a mixture of molecular dynamics (MD) simulation and ab initio density functional theory (DFT) to specifically target the importance of surface effects and thermal fluctuations. Both approaches demonstrate a low-temperature rise in PL intensity that increases exponentially with decreasing size, which to the best of our knowledge represents novel insight. It might provide additional clues into the precise origin of intrinsic size limitations in the QY of colloidal SiNCs. In addition, we demonstrate that changes in the microstructure of the host material, in this case associated with the thermotropic crystallization of unbound ligand, act to increase the excitation fluence through scattering, leading to dramatic improvements in PL intensity without discernible changes in fluorescence lifetime or QY. This opens up new routes to optimizing PL emission by simply tuning the microstructure of the host phase.

Figure 1. (a) PL spectra of the parent material (black dashed) and the SiNC fractions used in this study. (b) TEM image of a 3.5 nm diameter SiNC (top, 1 nm scale) and TEM image of the packing arrangement in a dried SiNC film (bottom, 10 nm scale).

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RESULTS AND DISCUSSION The parent material was a suspension of plasma-synthesized SiNCs surface passivated with 1-dodecene through thermal hydrosilylation in a mesitylene/ligand solution.10,11 The nanocrystals had a mean size of 4 nm and a solution-phase QY of 45−50% immediately after passivation.21 Although the materials were stored and handled in a glovebox under a nitrogen atmosphere, the PL exhibited a small blue shift (∼10 nm) over extended time, consistent with a degree of oxidation. Fractions with a polydispersity index less than 1.01 were generated through density-gradient ultracentrifugation (DGU) in chloroform/m-xylene mixtures.21−23 Figure 1a shows PL spectra of the fractions, referenced to the parent, and Figure 1b shows a TEM image of a single SiNC (top) and a TEM image of a SiNC ensemble (bottom). As noted above, the size and temperature dependence of the PL lifetime and band gap of pure SiNCs and their polymer (PDMS) composites are detailed in a previous publication.30 Here, we focus specifically on the inherent size and temperature dependence of the PL intensity and how these trends are impacted by a “matrix” or solvent of excess ligand. Like the QY,17,21,30 the temperature dependence of the PL intensity depends strongly on size (Figures 2 and 3). When normalized by the intensity measured at 93 K, nanocrystals at the large end of the fraction set (Figure 2a) show a much weaker dependence on temperature compared to smaller SiNCs (Figure 2b). PL relaxation in colloidal SiNCs typically exhibits both a “fast” and “slow” decay mode,19,48 and this is the case for the materials used here (Figure 3a). Although the precise temperature and size dependence of the two modes will be reported elsewhere, it suffices to note that a simple area estimate in Figure 3a confirms that the slower mode dominates the integrated PL intensity and hence the QY. The inset to Figure 3a shows a comparison of the slow relaxation time,

Figure 2. Temperature-dependent PL spectra of (a) a large SiNC fraction and (b) a small SiNC fraction.

normalized to the value at 293 K, at the two ends of the size window. As would be anticipated for a simple model in which the QY is proportional to the PL lifetime,30 the temperature trends in the inset to Figure 3a mirror the trends in Figure 2. A complete qualitative picture of PL intensity in the plane of SiNC size and temperature then follows from plots of normalized intensity versus T in Figure 3b coupled with the PL lifetime as a function of SiNC size at ambient (293 K, inset, Figure 3b). Although smaller nanocrystals exhibit relatively weaker PL at room temperature, they show a much stronger increase in PL upon cooling compared to the larger SiNCs. Before delving into the origins of the variation in PL intensity with nanocrystal size and temperature, we consider a novel feature exhibited by the smallest fractions related to the morphology of the samples. The behavior in question appears as a discontinuous PL jump (Figure 3b) near 145 K for the smallest fraction. Smaller fractions pulled from the top of the density gradient typically contain residual amounts of extra ligand.22,23 Although there is relatively little unbound 1dodecene in the parent, the small amount present remains B


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Figure 3. (a) PL decay curves (193 K) of a “large” and “small” fraction, where the inset shows the temperature dependence of the lifetime of the slow mode (normalized by the value at 293 K). (b) Temperature dependence of the PL intensity for some of the fractions on cooling (normalized by the intensity at 293 K). Note the jump in emission near 140 K for the smallest fraction. The inset shows the corresponding slow lifetime at 293 K. (c) Optical micrographs of the sample in Figure 2b at 153 and 133 K (width = 670 μm). (d) AFM image of a cooling-induced crack in a film from a larger fraction (taken at room temperature where the crack persists).

Figure 4. Impact of vacuum annealing on the temperature-dependent PL intensity of a smaller SiNC fraction. The initial behavior (a) differs from that of the same sample annealed under vacuum for 4 days (b), which no longer exhibits a PL jump. (c) Normalized PL intensity versus temperature for varied sample history, demonstrating how the low-temperature PL jump disappears in response to vacuum annealing.

near the top of the gradient being relatively small and less dense and is thus over-represented in the smallest fractions. Here, additional insight follows from the experiment summarized in Figure 4a−c, where progressively longer periods of vacuum exposure reduce and ultimately eliminate the jump, implicating excess ligand. We independently confirmed that pure 1dodecene is easily evaporated in our vacuum system. The pure ligand freezes near 238 K, but our measurements suggest that this temperature is significantly suppressed by high concentrations of SiNCs. Microscopic observation confirms that the microstructural change of interest occurs near 143 K. The two obvious morphological changes induced by cooling are (i) cracking associated with thermal expansion and contraction (Figure 3c,d) and (ii) optical turbidity associated with ligand crystallization and scattering. Thermoreversible cracking was observed in the small fractions, while irreversible cracking was observed in the large fractions. To explain this difference, we again appeal to excess ligand in the smallest fractions, which acts as a “plasticizer” by providing fluidity, giving the sample the ability to flow and “recover” after lowtemperature cracking. Cracking can lead to an effective increase in the local PL intensity because of an implied increase in local surface area, but the effect is too isolated to be the predominant cause of the PL jump. Rather, the jump is predominantly due to the microstructure associated with crystallization of the

unbound ligand, evident in the micrographs of Figure 5. Microscopic observation confirms that a PL jump or sudden increase always correlates with crystallization of the matrix. The observation that the PL is enhanced in the presence of a matrix microstructure is intriguing. To investigate further, we prepared “solution” samples by mixing fractions with excess ligand in a 5:1 ratio of ligand to SiNC. This was done for several short hydrocarbon chains, but we only report results for two, 1-dodecene (the same ligand used to passivate the SiNCs) and decane, which have neat freezing transitions at 238 and 243 K, respectively. Figure 5 compares the temperature-dependent PL for a pure fraction, the same fraction dispersed in 1dodecene, and the same fraction dispersed in decane. There is a 2-fold PL increase at low T for both samples prepared with ligand “solvent”, which can be seen in both gray-scale micrographs normalized to the same absolute intensity at the highest temperature (Figure 5, top) and the measured PL spectra normalized to a common intensity scale (Figure 5, bottom). Note that the mixtures in panels b and c are predominantly comprised of free ligand, and the PL enhancement in each appears close to the freezing point of the pure hydrocarbon phase. As a final characterization step, we measured the spectral extinction of pure decane and 1-dodecene at varied temperatures (Figure 6) to analyze the attenuating effects of scattering C


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extinction curves provides an explanation for the PL enhancement. Qualitatively, the trends are reminiscent of Rayleigh scattering, in that there is stronger scattering at shorter wavelength,49 but the situation is considerably more complex because the structure is not constrained to be both dilute and small compared to the wavelength of light. Both materials scatter strongly near 365 nm (λex, the excitation wavelength) but scatter significantly less at the wavelength of emission (λem, 600−700 nm). Once the matrix crystallizes, incident UV photons are repeatedly scattered, but not absorbed, until they encounter a nanocrystal, at which point they get absorbed and trigger PL in accord with the QY of the fraction. The emitted light then undergoes scattering to a lesser extent, as dictated by the extinction spectra in Figure 6. The overall effect of the thermoresponsive microstructure on the PL is strikingly evident in the Supporting Information movies, which show the concurrent change in microstructure and PL during cooling for the samples in Figure 5a and c. The drop in scattering between λex and λem in Figure 6 is what gives rise to the enhancement; strong scattering at λex ensures that more incident photons get absorbed by SiNCs, while weaker scattering at λem ensures that the subsequently increased number of emitted photons have a better chance of leaving the sample. From Figure 6 at T = 83 K, we estimate the ratio of extinction at λex to λem to be ∼1.5 for both compounds, suggesting a comparable effect for each. On average, our data agree with this; PL enhancements in a 1-dodecene matrix are the same order of magnitude as those observed in decane. It is important to emphasize that there is no enhancement or change in the QY associated with the PL jump, although the PL lifetime and hence the QY increase dramatically (but continuously) as the temperature is lowered. Rather, the jump reflects an increase in absorption enabled by a sudden increase in microstructural scattering. This is further evidenced by the lack of any detectable jump in PL lifetime at the corresponding transition temperature (inset, Figure 3a). Finally, to confirm that there is no associated change in SiNC structure, we performed in situ cryoTEM on SiNCs dispersed in excess hydrocarbon, as detailed In Figure 7. Small SiNC aggregates dispersed in a matrix of 1-dodecene have internal structure that is initially disordered or fluid-like at 293 K (Figure 7a). As the excess 1-dodecene begins to freeze, darker regions of higher hydrocarbon density, representing ordered domains of 1-dodecene, start to form around the SiNCs (Figure 7b). Although these coarsen (Figure 7c), the nanocrystal aggregates retain their initial structure (Figure 7b−d). In light

Figure 5. Temperature-dependent PL of a larger fraction (a) as-cast, (b) suspended in 1-dodecene, and (c) suspended in decane, where the data are all normalized to a common intensity scale. The micrographs at the top are PL images of the associated microstructure at 213 K (width = 230 μm), where the images all correspond to a common gray-scale intensity.

Figure 6. Temperature-dependent spectral extinction due to matrix scattering measured for (a) pure 1-dodecene and (b) pure decane (the same solvents used in Figure 5b,c).

(as opposed to absorption). Both materials are transparent down to the freezing temperature, at which point there is a jump in extinction associated with the appearance of crystalline microstructure. We suggest that the spectral shape of the

Figure 7. TEM images of (a) SiNCs in 1-dodecene at 293 K and (b) the same mixture immediately after cooling to 113 K. Dark regions are rich in the crystalline phase of the ligand. (c) Annealing the mixture at 113 K for 4 h leads to coarsening of the ligand domains and the formation of ice crystals. (d) After returning to 293 K, the structure of SiNC domains is unchanged. The scale in (a) applies to all images. D


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Figure 8. (a) Optimized SiNCs containing 29, 66, and 220 Si atoms (yellow) with H-passivated surface bonds (white). (b) Computed DOS for the three different SiNC sizes, with nanocrystal size increasing from top to bottom. (c) Computed PL spectra at temperatures of 77 (solid) and 300 K (dashed) for SiNCs comprised of 29 (green), 66 (blue), and 220 (red) silicon atoms.

Figure 9. Multiframe composites showing a superposition of atomic coordinates along the MD trajectory at 300 (top) and 77 K (bottom) for (a) 29 and (b) 220 Si atoms. (c) Relative increase in PL upon cooling from both experiments (open, Tlow = 93 K, Tamb = 293 K) and computation (closed, Tlow = 77 K, Tamb = 300 K) fit to the same exponential size trend. (d) Peak PL emission wavelength as a function of nanocrystal diameter from experiment (open) and computation (closed) at the two temperatures. The black curve is the empirical trend reported elsewhere.21

of the results of Figure 4, the fact that the ligand remains on the TEM grid under high vacuum can be attributed to the low temperatures of observation and the subsequent crystallization of the ligand. While our explanation invokes arguments more focused on the phase behavior of SiNC/ligand blends,50 CdSe nanocrystals can, with the appropriate ligands, show changes in photophysics triggered by ligand freezing.51,52 Indeed, it is perhaps somewhat surprising that there is no associated signature of ligandfreezing in the PL lifetime. Although the ligand is covalently bound to the SiNC surface, its structure would likely be perturbed by the phase ordering of an unbound host. If ligandrelated surface states play a significant role in PL relaxation,53

we might expect to see an associated effect. The fact that the QY is unaffected suggests that the surface states associated with the covalent ligand−SiNC bond are stable with respect to structural perturbation. With this in mind, we turn to an explanation of the underlying intrinsic trends with size and temperature. To model the size dependence, we use ab initio PL calculations, where details can be found in the Materials and Methods section. Our somewhat novel approach models radiative recombination in the presence of thermal fluctuations; as the nuclei move, the electronic configuration deviates from the optimized 0 K ground state. Specifically, we follow Kohn− Sham (KS) energy fluctuations along a MD trajectory dictated E


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cooling. Beyond this, the precise origin of the exponential trend is unclear because our treatment includes size variations that reside in the DOS (Figure 8b) as well. Here, the parameter (Ilow/Iamb) − 1 (Figure 9c) provides a measure of surface effects. Fitting this to an exponential of the form exp(−R/R0), we obtain a characteristic length scale (2R0) of 0.38 nm from simulation and 0.42 nm from experiment, in good agreement. The magnitude of R0 is consistent with surface effects. A detailed understanding is critical because the effect ultimately dictates the drop in ambient QY with deceasing SiNC size, which will be the subject of future research specifically focused on a quantitative treatment of phonons.

by temperature. The KS energy levels are relatively dense, and with a high density of states, large fluctuations in energy distort the orbitals. If the optimal radiative transition is from the HOMO to LUMO, the crossing of KS energies decreases the brightness, and the PL intensity would thus be expected to be higher at lower temperatures where fluctuations are suppressed. To describe the motion of a specific Si atom, the relative position of the atom in the nanocrystal is important. Atoms in the core will be coordinated with four other atoms and will thus be less susceptible to positional fluctuations. In contrast, a surface silicon atom coordinated with two Si atoms and two H atoms will undergo large thermal fluctuations, primarily because of the relative influence of the light single-bonded hydrogen. In general, surface atoms with low coordination number will experience larger thermal fluctuations and hence stronger KS energy fluctuations along the MD trajectory, implying that they will be more susceptible to the effects of temperature. Simulation results are presented in Figure 8. Three different SiNC sizes (29, 66, and 220 silicon atoms) with hydrogenpassivated surfaces were optimized at the DFT level (Figure 8a). Variations in the ab initio density of states (DOS) with nanocrystal size qualitatively show the anticipated band gap trends of quantum confinement, as well as significant sizedependent higher-order structure in the DOS (Figure 8b). Low- and high-temperature PL spectra for each of the three sizes are shown in Figure 8c. Qualitatively, the simulations support the experimental observations of (i) stronger PL at lower temperature, (ii) decreased PL with decreasing nanocrystal size at ambient temperature, and (iii) an increase in the low-temperature PL enhancement with decreasing size. A more quantitative comparison of experiment and computation is presented in Figure 9. On the basis of a time superposition of atomic coordinates along the MD trajectory (Figure 9a,b), the amplitude of thermal motion of the passivating (H) groups is clearly more sensitive to temperature than the motion of the core Si atoms. Figure 9c compares the relative increase in PL upon cooling, Ilow/Iamb − 1, as a function of SiNC diameter, while Figure 9d compares the wavelength of peak emission as a function of nanocrystal diameter. Computational constraints require that the range of SiNC sizes be different in experiment and computation. Typically, the two distinct approaches can thus be expected to provide only qualitative agreement. Quantitatively, the simulations do not reproduce the dependence of peak emission wavelength on size (Figure 9d), while the magnitude of the simulated lowtemperature PL enhancement is much weaker than experiment (Figure 9c). Beyond the obvious difference in size, there are a number of possible reasons for the discrepancy between computation and experiment, with the most glaring being the stark difference in surface-capping agent (hydrogen vs 1dodecene). A concise recent review by Shirahata54 on the importance of SiNC surface chemistry provides clarity on this question, but the same constraints that limit our simulations to small SiNC sizes also put limits on the complexity of the capping group. Nonetheless, there is one particularly intriguing quantitative similarity evident in Figure 9c. Both experiment and simulation show a low-T PL enhancement that increases exponentially with decreasing nanocrystal size. Despite the clear difference in amplitude, the functional form of the trend is quite similar. From the simulations, we know that this size dependence relates to the increased importance of surface fluctuation effects in smaller SiNCs and the suppression of such effects upon

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CONCLUSIONS In conclusion, we have used size-purified, plasma-synthesized SiNCs, prepared as both solid films and bulk “fluids” suspended in unbound ligand, to examine intrinsic and extrinsic sizeresolved differences in the temperature dependence of PL. Our findings reveal a new potential route to optimizing PL intensity by exploiting the structure of the host matrix through multiple scattering. Specifically, changes in microstructure associated with the thermotropic crystallization of a matrix comprised of unbound ligand can increase the effective excitation fluence through scattering, yielding dramatic improvements in PL intensity without any discernible changes in fluorescence lifetime or QY. In a variation on this theme, grafting55 a crystallizing polymer onto the surface of the SiNC could potentially yield similar effects. On a more fundamental level, our comparison of experiment and hybrid simulation lends further support to the notion that surface effects lie at the core of the relatively poor ambient luminescent characteristics of smaller SiNCs passivated with simple hydrocarbon ligands. Both experiment and simulation suggest that the detrimental PL effects linked to thermal fluctuations increase exponentially with decreasing nanocrystal size, where a more detailed understanding of this dynamic has the potential to offer critical insight into the design and synthesis of colloidal SiNCs with tunable bright emission at blue to green wavelengths.

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MATERIALS AND METHODS Plasma-synthesized SiNCs were surface-passivated with 1dodecene through a thermal hydrosilylation process34 and separated by size using DGU in chloroform/m-xylene mixtures.21−23 Solid samples cast from organic solvents were prepared on UVO-cleaned glass coverslips annealed in perfluorodecyltriethoxysilane vapor to generate a fluorinated self-assembled monolayer (SAM). Colloidal SiNCs in common organic solvents typically dewet from such substrates as they dry, forcing the SiNCs into a smaller area and boosting the PL signal. Modulated pulsed excitation at 375 nm was delivered through a notch filter with a fiber-coupled pulsed UV laser (Advanced Laser Diode Systems, PiL037, 30 ps pulse width, 140 mW peak power, 1 kHz modulation) coupled through an optical fiber to a photomultiplier tube. Temperature-dependent PL measurements were taken in transmission mode on a customized upright microscope with a 4× long-workingdistance NA 0.13 objective and a Linkham BCS196 CryoBiology stage. All relaxation curves were corrected for instrument artifacts using measured backgrounds. A 365 nm LED was used to measure steady-state spectra. Transmission electron microscopy (TEM) images were taken with a JEOL F


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JEM-2100 analytical TEM operated at 200 kV with a GATAN Orius SC1000 CCD. First-principles MD sampling and time integration were used for computing the emission spectra of the nanocrsytals.56 Excited-state lifetimes were assumed to be short-lived due to cascade thermalization, leading to intense PL peaks. Computed PL for large band gap semiconductors, such as Si nanocrystals, was dominated by radiative transitions across the band gap, as predicted by Kahsa’s rule.57 To accurately describe experimental PL, one must account for emission broadening due to a change in atomic coordinates along a MD trajectory. Geometry optimization, ground-state electronic structure, and adiabatic MD ab initio calculations were completed with DFT within the Vienna ab initio Simulation Package (VASP). The electronic structures were optimized with the Perdew−Burke−Ernzerhof (PBE) functional58 in a plane wave basis set59 utilizing projector augmented wave (PAW) potentials60,61 and periodic boundary conditions. MD visualization with multiframe imaging was performed using Jmol.62,63

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b05837. Movie depicting changes in the microstructure and PL during a linear cooling ramp from ambient down to 90 K for a pure fraction (AVI) Movie depicting changes in the microstructure and PL during a linear cooling ramp from ambient down to 90 K for a pure fraction dispersed in a solvent of pure decane (AVI)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 701-231-6103. Present Addresses §

J.B.M.: Rice University, Houston, TX 77005. R.J.A.: Michigan State University, East Lansing, MI 48824.

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Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS E.K.H. acknowledges support of the National Science Foundation (NSF) through CBET-1133135. R.J.A. and U.R.K. acknowledge primary support through the NSF under MRSEC Grants DMR-0819885 and DMR-1420013. T.I. gratefully acknowledges financial support of the Ministry of Education and Science of the Russian Federation in the framework of the Increase Competitiveness Program of NUST MISIS (K3-2016-021).

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REFERENCES

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