Raman Spectroscopy of Oxide-Embedded and Ligand-Stabilized

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Raman Spectroscopy of Oxide-Embedded and Ligand-Stabilized Silicon Nanocrystals Colin M. Hessel,† Junwei Wei,‡ Dariya Reid,† Hiromasa Fujii,§ Michael C. Downer,‡ and Brian A. Korgel*,† †

Department of Chemical Engineering, Texas Materials Institute, and Center for Nano- and Molecular Science and Technology and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, United States § Department of Electrical Engineering and Information Systems, School of Engineering, The University of Tokyo, Tokyo, Japan ‡

S Supporting Information *

ABSTRACT: Oxide-embedded and oxide-free alkyl-terminated silicon (Si) nanocrystals with diameters ranging from 3 nm to greater than 10 nm were studied by Raman spectroscopy. For ligand-passivated nanocrystals, the zone center Raman-active mode of diamond cubic Si shifted to lower frequency with decreasing size, accompanied by asymmetric peak broadening, as extensively reported in the literature. The size dependence of the Raman peak shifts, however, was significantly more pronounced than previously reported or predicted by the RWL (Richter, Wang, and Ley) and bond polarizability models. In contrast, Raman peak shifts for oxide-embedded nanocrystals were significantly less pronounced as a result of the stress induced by the matrix.

SECTION: Physical Processes in Nanomaterials and Nanostructures

S

Raman signal decoupled from environmental factors like surface-oxide-related strain. The average size of these nanocrystals can also be accurately determined by electron microscopy or X-ray scattering. Here, Raman spectra are reported for a wide size range (3 to >10 nm diameter) of Si nanocrystals that are either embedded in SiO2 or stabilized with organic ligands for direct comparison. The Raman peak positions of oxide-embedded and freestanding ligand-stabilized Si nanocrystals are markedly different. For nanocrystals of equivalent size, the Raman peaks of oxideembedded samples are significantly blue-shifted in comparison to those of the freestanding nanocrystals due to compressive stress induced by the host oxide. The ligand-stabilized nanocrystals are free of such surface-oxide-induced strain. The widely used models of phonon confinementthe RWL and bond polarization (BP) modelssignificantly underpredict the size-dependent peak shifts of the ligand-stabilized Si nanocrystals. Raman spectroscopy was performed on Si nanocrystals obtained from hydrogen silsesquioxane (HSQ, H8Si8O12) heated under forming gas at temperatures ranging between 1100 and 1400 °C. HSQ decomposes into silica embedded with Si nanocrystals of average diameter ranging from 3 to 100 nm depending on the reaction temperature.11,24,25 Etching the

ilicon (Si) nanocrystals exhibit dramatically different optical properties than bulk Si, including visible photoluminescence,1,2 and have been studied for a variety of applications including light-emitting diodes,3,4 high-efficiency photovoltaic devices,5 and fluorescent contrast agents for the in vivo detection of disease.6,7 The optical properties of Si nanocrystals are sensitive to size. Nanocrystal size is typically determined using electron microscopy and X-ray scattering. Raman spectroscopy could also provide a rapid and nondestructive measure of nanocrystal size, especially when located at buried interfaces, but Raman spectra are also very sensitive to subtle differences in crystal structure, defects, composition, and local environmental conditions.8 Use of Raman spectroscopy to provide an accurate measure of Si nanocrystal size requires more accurate experimental data correlating Raman spectra with size. Most reports of size-dependent Raman spectra involve nanocrystals embedded in a host matrix of SiO2,9−13 Si3N4,14 or sapphire,15 which creates enough stress to shift the Raman signal from its size-related peak position by a few wavenumbers and is difficult to quantify.9,10,15,16 The size of nanocrystals embedded in host matrixes is also challenging to measure and often not accurately known.17−21 Recently, methods have been developed to produce crystalline, monodisperse, organic ligandstabilized Si nanocrystals with a wide range of sizes and no surface oxide.22−24 This class of Si nanocrystals has not yet been studied by Raman spectroscopy yet should provide ideal model materials for observing the true size dependence of the © 2012 American Chemical Society

Received: March 14, 2012 Accepted: April 9, 2012 Published: April 9, 2012 1089

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nanocrystals studied by Raman spectroscopy were exhaustively characterized by TEM, XRD, and SAXS in ref 25. Raman spectra were collected from Si nanocrystals using a ReniShaw inVia micrsoscope with backscattering geometry and a 514.5 nm argon laser focused to a circular spot with 5 μm diameter using a 50× microscope objective and a laser power density of 0.018 mW/μm2. This power density is 2 orders of magnitude lower than the threshold (1 mW/μm2) for Fano broadening and peak shifts due to laser-induced heating.19,20 All spectra were collected for 30 s, and multiple measurements were taken at different regions on samples to ensure reproducibility. Figure 2 shows Raman spectra of freestanding ligandpassivated Si nanocrystals. The Si-related Raman peak shifts

oxide in the dark using a 6:1 volumetric ratio of 49% HF/28% HCl liberates the Si nanocrystals without a decrease in size, yielding H-terminated oxide-free nanocrystals.25 These nanocrystals were then passivated with organic ligands by thermal hydrosilylation at 190 °C in a 4:1 volumetric ratio mixture of dodecene/octadecene.25 Figure 1 shows transmission electron

Figure 2. Raman spectra (black open squares) of freestanding alkylpassivated Si nanocrystals. The average diameters d were determined by SAXS, and the HSQ decomposition temperatures T of each sample are also provided. The spectra were fit to the RWL model (blue curve, eq 1) using an arbitrary shift in peak position as explained in the text. The red curve corresponds to a symmetric Lorentzian with arbitrary peak position added to provide the best fit to the data (black curve). A Raman spectrum of a bulk Si wafer (olive dashed curve) is provide for reference.

to lower frequency and broadens asymmetrically with decreasing nanocrystal size. Richter, Wang, and Ley (RWL) first explained this behavior in 1981.26−28 The Raman-active mode in bulk Si occurs at the center of the Brillouin zone (q = 0), leading to a sharp Raman scattering peak at 521 cm−1. Crystal momentum is no longer conserved in Si nanocrystals, and phonon modes become allowed away from the Brillouin zone center (q ≠ q0), which leads to the shift and widening of the Raman peak toward lower frequencies with decreasing nanocrystals size. RWL developed a quantitative model for this, sometimes referred to as the phonon confinement model16,21,28

Figure 1. TEM images of Si nanocrystals passivated with dodecene and octadecene. The HSQ decomposition temperature for each sample is indicated. The high-resolution TEM image in (h) shows the typical crystallinity and shape of the nanocrystals used in the Raman spectroscopy study.

Ic(ω) = Bc

∫0

1

exp(−q2L2 /4)4πq2 dq [ω − ω(q)]2 + (Γc/2)2

(1)

Bc is an arbitrary constant, L is the particle size in units of a0 and is defined as L = d/a0 where d is the particle diameter and a0 is the lattice constant (0.543 nm for Si). Γc is the Raman peak natural line width for bulk Si at room temperature (4.6 cm−1), q is the phonon wave vector in units of 2π/a0, and ω(q)

microscopy (TEM) images of the alkyl-passivated Si nanocrystals used in this study. The particles are highly crystalline with well-defined surfaces and no observable amorphous shell layers of oxide or amorphous Si. Figure 1h shows an example of a high-resolution TEM image of a Si nanocrystal. The 1090

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is the dispersion relation for optical phonons. The dispersion relation, ω(q) = ω(c)(1 − 0.23q2) was used for the calculations; ω(c) is the Raman peak position of bulk Si at room temperature (521 cm−1).29,30 (See the Supporting Information for further discussion about the dispersion relation and the inclusion of the size distribution into the model fits of the data). The RWL model was found to significantly underpredict the Raman shift, as shown in Figure 3.

Table 1. Comparison of Particle Sizes for Freestanding Ligand-Passivated and Oxide-Embedded Si Nanocrystals Determined Using SAXS and Predicted with the RWL Model Based on the Shape of the Curves with an Arbitrary Shift in Raman Peak Position to Match the Data HSQ decomposition temperature (°C) 1100 1150 1200 1250 1300 1350 1400 a

particle sizea (nm)

freestanding nanocrystal size from RWL (nm)

oxideembedded nanocrystal size from RWL (nm)

peak shift difference in RWL predictions (cm−1)

2.7 2.9 5.0 6.0 8.8 11.8 polydisperse

2.88 3.8 4.07 4.89 6.24 8.69 10.86

3.26 4.62 5.43 5.70 7.06 8.15 10.32

+3.8 +3.6 +2.0 0.0 +1.0 −1.0 −1.5

Particle size determined by SAXS of the ligand-capped nanocrystals.

dependence.33 Furthermore, high-resolution TEM of nanocrystal surfaces and XRD of the samples have shown no evidence of amorphous material.25 Others have attributed the position and evolution of this low-frequency contribution to small changes in the crystallinity of nanocrystals with a high surface-area-to-volume ratio.32,34 Nanocrystals with a large fraction of undercoordinated surface atoms are expected to have shortened bond lengths, inducing Raman scattering at lower frequencies.32 The observed shift of this feature to higher frequency with increased particle size is consistent with the idea that this feature is associated with the nanocrystal surface. The oxide-embedded Si nanocrystals had significantly different size dependence than the ligand-stabilized nanocrystals. Figure 4 shows the Raman spectra of the oxide-embedded nanocrystals, and the Raman peak positions are plotted in Figure 3. The Raman peaks are red-shifted from the bulk value

Figure 3. Raman peak position as a function of the nanocrystal diameter for freestanding ligand-passivated (black diamonds) and oxide-embedded (red circles) nanocrystals. The black line is a leastsquares analysis fit of eq 2 to the Raman peak positions of the ligandpassivated freestanding nanocrystals; the blue and magenta curves are the predicted Raman peak positions versus size from the RWL and BP models, respectively. The green dotted curve shows recent model predictions by Faraci et al.17 The error bars represent the particle size polydispersity determined from SAXS.

Since RWL, a variety of other theories have appeared, including the bond polarization (BP) model of Zi and coworkers.29,31 The RWL and BP models yield qualitatively similar results, shown in Figure 3.18,19,28 Ab initio calculations32 have been performed, but due to computational constraints, only nanocrystals smaller than 3 nm with “bare” surfaces or hydride passivation have been examined.29,31,32 Therefore, the RWL model provides a convenient analytical tool for analyzing Raman data. The model by Faraci et al.17 showed better agreement with the data in the smaller size range. We found that although the RWL model was a poor quantitative predictor of nanocrystal size, it provided very good qualitative agreement with the size-dependent spectral line shape. With the addition of an arbitrary peak shift, the shape of the Raman peaks matched the RWL model quite well, as shown in Figure 2. Table 1 lists the size predicted by the RWL model based on the shape of the spectral curve. For the smaller nanocrystals, the RWL model failed to capture the proper line shape of a low-frequency tail of the Raman peaks, and an additional Lorentzian feature was needed in addition to the RWL model curve to adequately match the observed peak shape. This additional low-frequency vibrational mode was more significant for the smaller nanocrystals. A similar feature has been observed previously in Raman spectra of Si nanocrystals. Some have proposed that it comes from an amorphous interfacial region, or an amorphous shell coating the nanocrystals, because it occurs at approximately the same peak location as amorphous Si (480 cm−1).10 In the data in Figure 2, however, this spectral feature shifts significantly with changes in size, appearing at about 479 cm−1 for 3 nm Si and increasing in frequency with size to 497 cm−1 for 6 nm nanocrystals; the Raman spectra of the amorphous Si particle exhibit no such size

Figure 4. Raman spectra (black open squares) of oxide-embedded Si nanocrystals. The HSQ decomposition temperatures (T) are provided for each sample. The spectra were fit to the RWL model (blue curve, eq 1) using an arbitrary shift in peak position as explained in the text. The red curve corresponds to a symmetric Lorentzian with arbitrary peak position added to provide the best fit to the data (black curve). A Raman spectrum of a bulk Si wafer (olive dashed curve) is provide for reference. 1091

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of 521 cm−1, but with a much smaller shift in frequency than the ligand-stabilized nanocrystals. Compressive stress from the oxide matrix is responsible for the differences, shifting the Raman peak to higher frequency and opposing the frequency shift due to phonon confinement.9,10,15,16 The RWL model again does not provide quantitative agreement between the Raman peak positions and the nanocrystal size, as shown in Figure 3, but does provide good qualitative agreement with the Raman line shapes, and the data can be modeled quite well by adding an arbitrary shift in frequency to eq 1 to fit the data. Similar to the ligand-stabilized nanocrystals, the Raman spectra of the smaller oxide-embedded nanocrystals show an additional low-frequency feature. The additional peak is centered at about 460 cm−1 for the nanocrystals processed below 1300 °C. This feature shifts to higher frequency while decreasing in intensity as the temperature increases. In the case of the oxide-embedded nanocrystals, this Raman spectral feature might be attributed to molecular-size clusters of zerovalent Si in the SiO2 matrix.9,34 HSQ disproportionates to Si and SiO2 upon heating, producing clusters of Si in a SiO2 matrix that aggregate and coalesce into nanocrystals.11 Some clusters might not agglomerate and remain dispersed in the oxide matrix along with the larger nanocrystals.35 However, there may be other explanations and it requires further study, especially considering that an additional low frequency contribution to the Raman signal was also observed for the ligand-stabilized nanocrystals. It is highly unlikely that molecular-size Si clusters are present in these samples considering the HF etching, ligand passivation and purification steps involved in their preparation. The Raman peak positions of the oxide-embedded Si nanocrystals are plotted in Figure 3 in comparison to the ligand-stabilized nanocrystals and the RWL and BP model predictions. The RWL and BP models show better size agreement with the oxide-embedded nanocrystals than the ligand-stabilized nanocrystals, but the agreement is simply coincidence. The Raman peak positions of the oxide-embedded nanocrystals shift fairly unpredictably due to variations in matrix-related stress in the samples. Methods have been developed to estimate stress-induced Raman shifts to decouple this effect from the observed peak shift and reveal the peak shift attributed to phonon confinement effects.10,16 This data treatment assumes homogeneous strain throughout the sample, which may not be the case. The ligand-stabilized nanocrystals do not experience such surface stress from their surroundings, and the Raman peaks shift to lower wavelength systematically with decreasing size. More theoretical work is needed to provide a quantitatively accurate model of the size dependence of the Raman spectra of Si nanocrystals. However, a convenient scaling relationship between the Raman peak position and nanocrystal size might be used28,29,31 ⎛a⎞ ω(D) = ω0 − A⎜ ⎟ γ ⎝D⎠

more pronounced shift in the Raman spectra highlights the need for more theoretical work. Nonetheless, the empirical relationship between the Raman shift, peak shape, and size reported here for the ligand-stabilized Si nanocrystals can provide a good baseline for using Raman spectroscopy as a tool to measure size. Raman spectroscopy is extremely sensitive to subtle changes in crystal structure and composition, and some crystal defects that are not perceptible by XRD, or even TEM, are clearly visible in Raman spectra.8 Raman spectroscopy can also provide a rapid and nondestructive measure of the nanocrystal size. A systematic trend of decreasing Raman peak frequency with decreasing nanocrystal size was observed for the alkylpassivated Si nanocrystals. In contrast, Raman peaks observed from oxide-embedded nanocrystals occurred at a significantly higher frequency than those isolated from the oxide matrix and capping with hydrocarbon ligands. Si nanocrystals embedded in an oxide matrix show significant variation in Raman peak shifts, likely due to variable matrix-induced stress. The widely used RWL and BP models for phonon confinement were compared to the data and found to provide poor quantitative agreement; however, the RWL model did provide a good approximation to the observed Raman line shape, requiring only an arbitrary shift in peak position. The data presented here clearly show that more accurate theoretical models for size-dependent Raman spectra of Si nanocrystals are needed.

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ASSOCIATED CONTENT

S Supporting Information *

SAXS data and experimental description, Lorentzian fitting of Raman data for freestanding ligand-passivated and oxideembedded Si nanocrystals, summary of Lorentzian fits, and XRD data for freestanding ligand-passivated Si nanocrystals. Discussion about the choice of the phonon dispersion relation and influence of the size distribution on fitting the Raman spectra. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +1-512-471-5633. Fax: +1-512-471-7060. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge financial support of this work from the National Science Foundation (Grant No. DMR-0706227), the Robert A. Welch Foundation (Grant No. F-1464 and F-1038), and the Natural Science and Engineering Research Council of Canada. H.F. acknowledges support through the Nanotechnology Network Program of MEXT under Project No. 3 NIM-08F-001. We also thank Naoki Fukata, Justin Harris, and José Luís Hueso for informative discussions, and Kjell Schroder for his assistance with Raman measurements.

(2)

ω(D) is the diameter-dependent peak Raman frequency, ω0 is the bulk Raman peak position of bulk crystalline Si (521 cm−1 for crystalline Si), a is the lattice constant (0.543 nm for Si), and D is the particle diameter. A and γ are fitting parameters generated by the models and least-squares analysis. Values of A and γ from the least-squares analysis were −56.63 and 1.00 and −52.3 and 1.586 from the RWL model26,28 and −47.41 and 1.44 from the BP model.31 The data in Figure 3 lie well below the RWL and BP predictions. The observation of the much

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REFERENCES

(1) Canham, L. T. Silicon Quantum Wire Array Fabrication by Electrochemical and Chemical Dissolution of Wafers. Appl. Phys. Lett. 1990, 57, 1046−1048. (2) English, D. S.; Pell, L. E.; Yu, Z. H.; Barbara, P. F.; Korgel, B. A. Size Tunable Visible Luminescence from Individual Organic

1092

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Monolayer Stabilized Silicon Nanocrystal Quantum Dots. Nano Lett. 2002, 2, 681−685. (3) Puzzo, D. P.; Henderson, E. J.; Helander, M. G.; Wang, Z. B.; Ozin, G. A.; Lu, Z. H. Visible Colloidal Nanocrystal Silicon LightEmitting Diode. Nano Lett. 2011, 11, 1585−1590. (4) Cheng, K. Y.; Anthony, R.; Kortshagen, U. R.; Holmes, R. J. High-Efficiency Silicon Nanocrystal Light-Emitting Devices. Nano Lett. 2011, 11, 1952−1956. (5) Liu, C. Y.; Holman, Z. C.; Kortshagen, U. R. Hybrid Solar Cells from P3HT and Silicon Nanocrystals. Nano Lett. 2009, 9, 449−452. (6) Hessel, C. M.; Rasch, M. R.; Hueso, J. L.; Goodfellow, B. W.; Akhavan, V. A.; Puvanakrishnan, P.; Tunnel, J. W.; Korgel, B. A. Alkyl Passivation and Amphiphilic Polymer Coating of Silicon Nanocrystals for Diagnostic Imaging. Small 2010, 6, 2026−2034. (7) Erogbogbo, F.; Yong, K. T.; Roy, I.; Hu, R.; Law, W. C.; Zhao, W. W.; Ding, H.; Wu, F.; Kumar, R.; Swihart, M. T.; Prasad, P. N. In Vivo Targeted Cancer Imaging, Sentinel Lymph Node Mapping and MultiChannel Imaging with Biocompatible Silicon Nanocrystals. ACS Nano 2011, 5, 413−423. (8) Gouadec, G.; Colomban, P. Raman Spectroscopy of Nanomaterials: How Spectra Relate to Disorder, Particle Size and Mechanical Properties. Prog. Cryst. Growth Charact. Mater. 2007, 53, 1−56. (9) Arguirov, T.; McHedlidze, T.; Kittler, M.; Rolver, R.; Berghoff, B.; Forst, M.; Spangenberg, B. Residual Stress in Si Nanocrystals Embedded in a SiO2 Matrix. Appl. Phys. Lett. 2006, 89, 053111. (10) Hernandez, S.; Martinez, A.; Pellegrino, P.; Lebour, Y.; Garrido, B.; Jordana, E.; Fedeli, J. M. Silicon Nanocluster Crystallization in SiOx Films Studied by Raman Scattering. J. Appl. Phys. 2008, 104, 044304. (11) Hessel, C. M.; Henderson, E. J.; Veinot, J. G. C. An Investigation of the Formation and Growth of Oxide-Embedded Silicon Nanocrystals in Hydrogen Silsesquioxane-Derived Nanocomposites. J. Phys. Chem. C 2007, 111, 6956−6961. (12) Khriachtchev, L.; Rasanen, M.; Novikov, S.; Pavesi, L. Systematic Correlation Between Raman Spectra, Photoluminescence Intensity, and Absorption Coefficient of Silica Layers Containing Si Nanocrystals. Appl. Phys. Lett. 2004, 85, 1511−1513. (13) Maslova, N. E.; Antonovsky, A. A.; Zhigunov, D. M.; Timoshenko, V. Y.; Glebov, V. N.; Seminogov, V. N. Raman Studies of Silicon Nanocrystals Embedded in Silicon Suboxide Layers. Semiconductors 2010, 44, 1040−1043. (14) Mercaldo, L. V.; Esposito, E. M.; Veneri, P. D.; Fameli, G.; Mirabella, S.; Nicotra, G. First and Second-Order Raman Scattering in Si Nanostructures Within Silicon Nitride. Appl. Phys. Lett. 2010, 97, 153112. (15) Yerci, S.; Serincan, U.; Dogan, I.; Tokay, S.; Genisel, M.; Aydinli, A.; Turan, R. Formation of Silicon Nanocrystals in Sapphire by Ion Implantation and the Origin of Visible Photoluminescence. J. Appl. Phys. 2006, 100, 074301. (16) Crowe, I. F.; Halsall, M. P.; Hulko, O.; Knights, A. P.; Gwilliam, R. M.; Wojdak, M.; Kenyon, A. J. Probing the Phonon Confinement in Ultrasmall Silicon Nanocrystals Reveals a Size-Dependent Surface Energy. J. Appl. Phys. 2011, 109, 083534. (17) Faraci, G.; Gibilisco, S.; Pennisi, A. R.; Faraci, C. Quantum Size Effects in Raman Spectra of Si Nanocrystal. J. Appl. Phys. 2011, 109, 074311. (18) Gupta, S. K.; Jha, P. K. Modified Phonon Confinement Model for Size Dependent Raman Shift and Linewidth of Silicon Nanocrystals. Solid State Commun. 2009, 149, 1989−1992. (19) Faraci, G.; Gibilisco, S.; Pennisi, A. R. Quantum Size Effects in Raman Spectra of Si Nanocrystals. Phys. Rev. B 2009, 80, 425−429. (20) Gupta, R.; Xiong, Q.; Adu, C. K.; Kim, U. J.; Eklund, P. C. Laser-Induced Fano Resonance Scattering in Silicon Nanowires. Nano Lett. 2003, 3, 627−631. (21) Ossadnik, C.; Veprek, S.; Gregora, I. Applicability of Raman Scattering for the Characterization of Nanocrystalline Silicon. Thin Solid Films 1999, 337, 148−151. (22) Pi, X. D.; Liptak, R. W.; Deneen Nowak, J.; Wells, N. P.; Carter, C. B.; Campbell, S. A.; Kortshagen, U. Air-Stable Full-Visible-

Spectrum Emission from Silicon Nanocrystals Synthesized by an AllGas-Phase Plasma Approach. Nanotechnology 2008, 19, 245603. (23) Gupta, A.; Swihart, M. T.; Wiggers, H. Luminescent Colloidal Dispersion of Silicon Quantum Dots from Microwave Plasma Synthesis: Exploring the Photoluminescence Behavior Across the Visible Spectrum. Adv. Funct. Mater. 2009, 19, 696−703. (24) Hessel, C. M.; Henderson, E. J.; Veinot, J. G. C. Hydrogen Silsesquioxane: A Molecular Precursor for Nanocrystalline Si−SiO2 Composites and Freestanding Hydride-Surface-Terminated Silicon Nanoparticles. Chem. Mater. 2006, 18, 6139−6146. (25) Hessel, C. M.; Reid, D.; Panthani, M. G.; Rasch, M. R.; Goodfellow, B. W.; Wei, J.; Fujii, H.; Akhavan, V.; Korgel, B. A. Synthesis of Ligand-Stabilized Silicon Nanocrystals with Size-Dependent Photoluminescence Spanning Visible to Near-Infrared Wavelengths. Chem. Mater. 2012, 24, 393−401. (26) Richter, H.; Wang, Z. P.; Ley, L. The One Phonon Raman Spectrum in Microcrystalline Silicon. Solid State Commun. 1981, 39, 625−629. (27) Campbell, I. H.; Fauchet, P. M. The Effects of Microcrystal Size and Shape on the Raman-Spectra of Crystalline Semiconductors. Solid State Commun. 1986, 58, 739−741. (28) Paillard, V.; Puech, P.; Laguna, M. A.; Carles, R.; Kohn, B.; Huisken, F. Improved One-Phonon Confinement Model for an Accurate Size Determination of Silicon Nanocrystals. J. Appl. Phys. 1999, 86, 1921−1924. (29) Zi, J.; Zhang, K. M.; Xie, X. D. Comparison of Models for Raman Spectra of Si Nanocrystals. Phys. Rev. B 1997, 55, 9263−9266. (30) Sui, Z. F.; Leong, P. P.; Herman, I. P.; Higashi, G. S.; Temkin, H. Raman Analysis of Light-Emitting Porous Silicon. Appl. Phys. Lett. 1992, 60, 2086−2088. (31) Zi, J.; Buscher, H.; Falter, C.; Ludwig, W.; Zhang, K. M.; Xie, X. D. Raman Shifts in Si Nanocrystals. Appl. Phys. Lett. 1996, 69, 200− 202. (32) Khoo, K. H.; Zayak, A. T.; Kwak, H.; Chelikowsky, J. R. FirstPrinciples Study of Confinement Effects on the Raman Spectra of Si Nanocrystals. Phys. Rev. Lett. 2010, 105, 115504. (33) Harris, J. T.; Hueso, J. L.; Korgel, B. A. Hydrogenated Amorphous Silicon (a-Si:H) Colloids. Chem. Mater. 2010, 22, 6378− 6383. (34) Xia, H.; He, Y. L.; Wang, L. C.; Zhang, W.; Liu, X. N.; Zhang, X. K.; Feng, D.; Jackson, H. E. Phonon Mode Study of Si Nanocrystals Using Micro-Raman Spectroscopy. J. Appl. Phys. 1995, 78, 6705− 6708. (35) Bonafos, C.; Mathiot, D.; Claverie, A. Ostwald Ripening of Endof-Range Defects in Silicon. J. Appl. Phys. 1998, 83, 3008−3017.

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