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Langmuir 2007, 23, 3388-3394
Photoassisted Tuning of Silicon Nanocrystal Photoluminescence Jonghoon Choi,†,‡ Nam Sun Wang,† and Vytas Reipa*,‡ Department of Chemical and Biomolecular Engineering, UniVersity of Maryland, College Park, Maryland 20742, and Biochemical Science DiVision, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 ReceiVed October 3, 2006. In Final Form: December 19, 2006 Silicon is a rather inefficient light emitter due to the indirect band gap electronic structure, requiring a phonon to balance the electron momentum during the interband transition. Fortunately, momentum requirements are relaxed in the 1-5 nm diameter Si crystals as a result of quantum confinement effects, and bright photoluminescence (PL) in the UV-vis range is achieved. Photoluminescent Si nanocrystals along with the C- and SiC-based nanoparticles are considered bioinert and may lead to the development of biocompatible and smaller probes than the well-known metal chalcogenide-based quantum dots. Published Si nanocrystal production procedures typically do not allow for the fine control of the particle size. An accepted way to make the H-terminated Si nanocrystals consists of anodic Si wafer etching with the subsequent breakup of the porous film in an ultrasound bath. Resulting H-termination provides a useful platform for further chemical derivatization and conjugation to biomolecules. However, a rather polydisperse mixture is produced following the ultrasonic treatment, leading to the distributed band gap energies and the extent of surface passivation. From the technological point of view, a homogeneous nanoparticle size mixture is highly desirable. In this study, we offer an efficient way to reduce the H-terminated Si nanocrystal diameter and narrow size distribution through photocatalyzed dissolution in a HF/HNO3 acid mixture. Si particles were produced using the lateral etching of a Si wafer in a HF/EtOH/H2O bath followed by sonication in deaerated methanol. Initial suspensions exhibited broad photoluminescence in the red spectral region. Photoassisted etching was carried out by adding the HF/HNO3 acid mixture to the suspension and exposing it to a 340 nm light. Photoluminescence and absorbance spectra, measured during dissolution, show the gradual particle size decrease as confirmed by the photoluminescence blue shift. The simultaneous narrowing of the photoluminescence spectral bandwidth suggests that the dissolution rate varies with the particle size. We show that the Si nanoparticle dissolution rate depends on the amount of light adsorbed by the particle and accounts for the etching rate variation with the particle size. Significant improvement in the PL quantum yield is observed during the acid treatment, suggesting improvement in the dangling bond passivation.
Introduction Bulk Si is a rather inefficient light emitter due to the indirect band gap electronic structure, requiring a phonon to balance the electron momentum during interband transition. Fortunately, the momentum requirements are relaxed in the 1-5 nm diameter Si crystals as a result of the so-called quantum confinement effects that allow for efficient light emission. Silicon nanocrystals (SNs) are increasingly studied due to their unique physicochemical properties,1 including photoluminescence in the visible part of the electromagnetic spectrum. Significant progress in studying related phenomena in II-VI compound semiconductor quantum dots and successful photonic applications2,3 have re-energized interest in the nanoscale Si, a phenomenon discovered back in the 1950s.4 Notwithstanding their excellent optical characteristics and advanced fabrication technology, application of the II-VI quantum dots as biological probes has been held back by their inherent chemical toxicity5 that necessitates encapsulation in a robust inert material shell and notably increases the probe diameter. Photoluminescent SNs along with the C- and SiCbased nanoparticles are considered bioinert6 and could lead to * To whom correspondence should be addressed. † University of Maryland. ‡ National Institute of Standards and Technology. (1) Cullis, A. G.; Canham, L. T.; Calcott, D. J. J. Appl. Phys. 1997, 82, 909. (2) Trindade, T.; O’Brien, P.; Pickett, N. L. Chem. Mater. 2001, 13, 3843. (3) Michalet, X.; Pinaud, F. F.; Bentolila, L. A.; Tsay, J. M.; Doose, S.; Li, J. J.; Sundaresan, G.; Wu, A. M.; Gambhir, S. S.; Weiss, S. Science 2005, 307, 538. (4) Uhlir, A. Bell Syst. Tech. J. 1956, 35, 333. (5) Clarke, S. J.; Hollmann, C. A.; Zhang, Z. J.; Suffern, D.; Bradforth, S. E.; Dimitrijevic, N. M.; Minarik, W. G.; Nadeau, J. L. Nat. Mater. 2006, 5, 409. (6) Reboredo, F. A.; Galli, G. J. Phys. Chem. B 2005, 109, 1072.
the development of smaller biocompatible probes7,8 that potentially will facilitate their use in the biomedical field. Moreover, SN surfaces are open to various chemical functionalizations thus offering numerous stabilization and bioconjugation options.9 SN preparation methods, in general, are more complicated than the well-established protocols for the II-VI compoundbased nanoparticles. Published procedures, including chemical synthesis,10 silane chemical11 or electrochemical12 reduction, laser assisted pyrolysis,13 and wet Si wafer etching in hydrofluoric acid (HF),14 provide milligram quantities of size-dispersed SNs. A rather straightforward procedure of the electrochemical Si wafer etching7,14 is based on the protocols developed for obtaining nanoporous Si.15 Anodic wafer etching is followed by sonication that partially crumbles the porous Si film, resulting in the nanoparticle suspension.7 Immediately after etching, the particle surface is hydrogen atom passivated and can be oxidized or substituted by a variety of organic groups using postetching functionalization.9 Typically, particles of various sizes and shapes are produced during such procedures, represented by a wide range of physicochemical properties. Narrow particle size (7) Wang, L.; Reipa, V.; Blasic, J. Bioconjugate Chem. 2004, 15, 409. (8) Ding, Z.; Quinn, M. B.; Haram, A. K.; Pell, L. E.; Korgel, B. A.; Bard, A. L. Science 2002, 296, 1293. (9) Buriak, J. M. Chem. ReV. 2002, 102, 1271. (10) Bley, R. A.; Kauzlarich, S. M. J. Am. Chem. Soc. 1996, 118, 12461. (11) Heath, J. R. Science 1992, 258, 1131. (12) Aihara, S.; Ishii, R.; Fukuhara, M.; Kamata, N.; Terunuma, D.; Hirano, Y.; Saito, N.; Aramata, M.; Kashimura, S. J. Non-Cryst. Solids 2001, 296, 135. (13) Hua, F.; Swihart, M. T.; Ruckenstein, E. Langmuir 2005, 21, 6054. (14) Yamani, Z.; Ashhab, S.; Nayfeh, A.; Thompson, W. H.; Nayfeh, M. J. Appl. Phys. 1998, 83, 3929. (15) Jung, K. H.; Shih, S.; Hsieh, T. Y.; Kwong, D. L.; Lin, T. L. Appl. Phys. Lett. 1991, 59, 3264.
10.1021/la062906+ CCC: $37.00 © 2007 American Chemical Society Published on Web 02/13/2007
Si Nanocrystal Dissolution and Photoluminesence
distribution is desirable in most applications due to the strong size dependence of the particle electronic structure when the particle diameter is 50% at room temperature21). However, such low values result from the ensemble averaging of the photoactive and inactive particles and suggest that SNs can potentially achieve QY comparable to the II-VI compound quantum dots, if bright particles can be separated from the optically inactive SNs. Quantum yields up to 90% were recently reported when a single Si nanoparticle photoluminescence was measured.22 Several studies have demonstrated that photoinduced oxidation can produce a PL blue shift in porous Si.14,23-25 Photoinduced oxidation followed by silicon oxide attack by HF leads to the gradual decrease in the average porous Si surface crystallite size, resulting in a blue shift that is consistent with the band gap dependence on the nanoparticle size.16,23 In a similar fashion, we expect that the wet chemical etching can be applicable to control the size of the suspended H-terminated Si nanocrystals. In the current study, we offer an efficient way to reduce the average SN diameter and simultaneously narrow the size distribution through photocatalyzed dissolution. By measuring both the absorbance and the photoluminescence during particle dissolution, we can track the nanoparticle band gap growth with shrinking crystal size. Etching in the HF/HNO3 acid mixture increases the PL quantum yield and the homogeneity of particle preparation by improving their surface passivation. It is wellknown that Si does not dissolve in pure HF, and an oxidizer is necessary to produce silicon dioxide that reacts vigorously with HF. The overall dissolution reaction is written in eq 1.26
3Si + 4HNO3 + 18HF ) 3H2SiF6 + 4NO + 8H2O (1) Li et al. have shown that the dissolution reaction rate is controlled by the Si surface oxidation rate by nitric acid and is catalyzed under UV illumination.20 When etched with the low concentrations of an oxidizer, HNO3, the Si particle surface retains its predominantly H-termination form.13 We show that the SN dissolution in the acid mixture follows the shrinking core model, accounts for the dissolution rate dependence on the particle size, and results in a more homogeneous dispersion. Photocatalyzed acid dissolution may offer a straightforward method to alter the SN photoluminescence wavelength and significantly improve the SN photoluminescence efficiency. (16) Belomoin, G.; Therrien, J.; Smith, A.; Rao, S.; Twesten, R.; Chaieb, S.; Nayfeh, M. H.; Wagner, L.; Mitas, L. Appl. Phys. Lett. 2002, 80, 841. (17) Wilson, W. L.; Szajowski, P. F.; Brus, L. E. Science 1993, 262, 1242. (18) Rogozhina, E. V.; Eckhoff, D. A.; Gratton, E.; Braun, P. V. J. Mater. Chem. 2006, 16, 1421. (19) English, D. S.; Pell, L. E.; Yu, Z.; Barbara, P. F.; Korgel, B. A. Nano Lett. 2002, 2, 681. (20) Li, X.; He, Y.; Talukdar, S. S.; Swihart, M. T. Langmuir 2003, 19, 8490. (21) Bruchez, M.; Moronne, M.; Gin, P.; Weiss, S.; Alivisatos, A. P. Science 1998, 281, 2013. (22) Credo, G. M.; Mason, M. D.; Buratto, S. K. Appl. Phys. Lett. 1999, 74, 1978. (23) Koyama, H.; Koshida, N. J. Appl. Phys. 1993, 74, 6365. (24) Mizuno, H.; Koyama, H.; Koshida, N. Appl. Phys. Lett. 1996, 69, 3779. (25) Seraphin, A. A.; Werwa, E.; Kolenbrander, K. D. J. Mater. Res. 1997, 12, 3386. (26) Steinert, M.; Acker, J.; Henβge, A.; Wetzig, K. J. Electrochem. Soc. 2005, 152, C843. (27) Wilcoxon, J. P.; Samara, G. A.; Provencio, P. N. Phys. ReV. B 1999, 60, 2704.
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Previously, PL profiles have been measured on various sizes of Si nanocrystal preparations (for summary, see ref 27). A major uncertainty in establishing the PL peak dependence on particle size is related to the difficulties of accurately measuring particle sizes in the single nanometer range. Also, transmission electron microscopy (TEM) images frequently do not show particle size polydispersity. Photoluminescence excitation measurements on a series of discretely sized Si nanoparticles in the range from 1 to 2.9 nm resulted in a power law relation between the band gap (Eg) and particle diameter (d),16 Eg ) 3.44/d-0.5, suggesting a significant band gap widening in this size range. Other studies conducted using Si nanoparticles embedded in silicon nitride28 or silicon oxide29 or encapsulated in the organic shells18,19,30 confirmed the inverse dependence of the band gap on the Si particle diameter. Experimental Section Particle Preparation. Silicon wafers (〈111〉 oriented, 0.0010.01 Ω cm, As doped) were purchased from Virginia Semiconductor, Inc. (Fredericksburg VA). (Certain commercial equipment, instruments, materials, or companies are identified in this paper to specify adequately the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are the best available for the purpose.) Wafers were electrochemically etched in the HF/H2O/ethanol (2:1:1, volume ratio) mixture using the lateral etching method.15 Anodic etching was performed in a polycarbonate cell that accommodates a 100 mm diameter Si wafer placed between two Pt wire mesh cathodes. Electric contact was provided to the top edge of the vertically mounted wafer, and the electrolyte was slowly pumped into the cell, hence providing a moving electrolyte boundary. The total etch time typically was about 4 h per 100 mm diameter wafer at a 120 mA constant current supplied by the galvanostat (model 363, EG&G Inc., Princeton, NJ). Following anodic etching, the wafer was washed with copious amounts of deionized water and methanol (HPLC grade, Mallinckrodt Chemicals, Phillipsburg, NJ) and then blow-dried with nitrogen gas. Dried wafers displayed intense orange-red luminescence when excited by a 365 nm UV lamp. Next, the Si wafers were sonicated (Ultrasonik, York, PA) in deaerated methanol for 2 h under vigorous N2 purging. The resulting suspension appeared brownish and exhibited weak broad-band PL under UV excitation. Particle Etching. Hydrofluoric acid (48%) and nitric acid (6970%), both from J.T. Baker (Phillipsburg, PA), were premixed at a 10:1 volume ratio, and 10 µL of the acid mixture was added to a 1 cm fluorimetric quartz cuvette containing 2 mL of the Si particle suspension in methanol. Immediately following mixing, the cuvette was exposed to a 340 nm light in the photoreactor (RMR-600, Southern New England Ultraviolet Company, Branford, CT). The nitrogen atmosphere was maintained throughout the dissolution process. All experiments were performed at t ) 20 °C. Particle Characterization. TEM images were acquired using a JEOL 2100F Field Emission electron microscope (JEOL Inc., Tokyo, Japan). Samples were prepared by placing a drop of the Si nanocrystal suspension in methanol on a carbon grid followed by drying. The SN photoluminescence spectra were recorded using a spectrofluorimeter (model LM800, SLM Inc.). A quartz cuvette containing the SN particle suspension and an acid mixture was removed briefly from the photoreactor at various reaction stages, and the PL spectra were recorded using 360 nm excitation. Absorbance spectra during the Si suspension dissolution after adding 10 µL of the 10:1 HF/HNO3 mixture were recorded with an Ocean Optics Chem2000 fiber optic spectrophotometer (Dunedin, FL). Time-resolved PL measurements were carried out on a Photon (28) Kim, T. W.; Cho, C. H.; Kim, B. H.; Park, S. J. Appl. Phys. Lett. 2006, 88, 123102. (29) Kanemitsu, Y. Phys. ReV. B 1994, 49, 16845. (30) Warner, J. H.; Hoshino, A.; Yamamoto, K.; Tilley, R. D. Angew. Chem., Int. Ed. 2005, 44, 4550.
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Figure 1. TEM images of Si nanocrystals prior to photoassisted dissolution. A high-resolution image shows visible lattice planes in the 8 nm diameter particle. The particle size distribution was obtained from image analysis (lower panel). Technology International spectrometer (Birmingham, NJ) equipped with a GL-3300 nitrogen laser (λ ) 337 nm). The quantum yield (QSi) of the SN PL was measured by comparing it with the fluorescence standard quinine bisulfate (Qst ) 0.55 at λ ) 366 nm). Under conditions of similar excitation intensity, wavelength, and instrumental parameters, the measured PL intensity ratio (fSi/fst) between the two solutions can be expressed through PL quantum yields (QSi and Qst) and optical densities (ODSi and ODst) at the excitation wavelength, fSi/fst ) (QSi/Qst )(ODSi/ODst). SN particle size distribution was analyzed with a dynamic light scattering-based sub-micrometer particle analyzer (model N4MD, Coulter, Inc., Fullerton, CA) and with TEM image analysis.
Results and Discussion TEM images of particles, acquired on a carbon grid by depositing and evaporating a drop of the Si particle suspension in methanol, confirm the presence of a polydisperse mixture of the nanometer-sized crystals (Figure 1). A 3.1 Å lattice spacing, characteristic for the (111) planes in the diamondlike Si lattice, is visible in the high-resolution image of the 8 nm diameter particle (Figure 1). The initial absorbance spectrum of the Si nanoparticle suspension in methanol (upper curves in Figure 2), recorded prior to the acid mixture addition, can be deconvoluted into the
Choi et al.
Figure 2. Si particle suspension in methanol. Upper panel: Absorbance of freshly prepared particles (solid line) decomposed into the scattering (dotted line) and absorbing (dashed line) components. Lower panel: Absorbance evolution after introduction of 10 µL of the 10:1 HF/HNO3 mixture and exposure to UV light. Spectra were recorded sequentially following acid introduction: 1-2, 2-8, 3-12, 4-18, 5-34, 6-72, 7-160, and 8-300 min. Inset: Comparison of the 320 nm absorbance decay rates with and without UV exposure (full and open circles, respectively). T ) 293 K.
sum of the elastic scattering by small particles in the visible region and two Gaussian oscillators centered at 249 and 311 nm (Figure 2, upper panel). Light attenuation due to the elastic scattering was accounted for by fitting the 400 < λ < 650 spectral region data to the 1/λn function (n ∼ 4). A significant scattering component in the initial Si nanoparticle absorbance may be caused by a small subpopulation of the micrometer-sized particles. The strongest absorbance features in the bulk Si were previously assigned to the direct interband transitions at the Γ point of the Brillouin zone;27 however, they are blue shifted by 0.8 and 0.6 eV in our Si crystals as a result of the quantum confinement in the nanometer diameter crystals.31 An absorbance increase with the photon energy below 400 nm is typical for the spectra of bulk Si reflecting the slow onset of the indirect transition Γ f X.27 (31) Brus, L. E.; Szajowski, P. F.; Wilson, W. L.; Harris, T. D.; Schuppler, S.; Citrin, P. H. J. Am. Chem. Soc. 1995, 117, 2915.
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Figure 3. Si particle size distribution estimated from dynamic light scattering measurements. Full bars represent the suspension following Si wafer sonication in methanol. Shaded bars represent the suspension after 30 min of photocatalyzed etching of the Si wafer in the HF/ HNO3 mixture.
Figure 4. Si particle suspension photoluminescence recorded during various stages of photocatalyzed dissolution in the acid mixture. λexc ) 360 nm.
The introduction of the 10 µL 10:1 HF/HNO3 acid mixture to the Si particle suspension together with exposure to 340 nm light results in an exponential absorbance drop (Figure 2, inset in the lower panel), while the spectral shape evolution is consistent with the average particle size reduction. The dissolution reaction is noticeably photocatalyzed as the dissolution rate (estimated from the time required to achieve equivalent absorbance change) increases ∼20 times upon exposure to UV light (see Figure 2 inset). A pronounced reduction of the elastic light scattering constituent is observed in the initial dissolution stage (t < 30 min), indicating the removal of the larger particles. The particle size distribution (after 30 min of etching) acquired from the dynamic light scattering measurements supports the significant reduction of the average particle size with the median diameter in the 5 nm range (Figure 3). Visually, the suspension turns totally transparent in ∼15 min. Gaussian component amplitudes at 311 and 249 nm gradually decrease during the course of the dissolution with both peaks experiencing wavelength shifts. The lower energy feature blue shifts from 311 nm (3.9 eV) prior to the acid addition to ∼290 nm (4.3 eV) after 2 h of photocatalyzed dissolution, while the 249 nm (4.97 eV) band red shifts to 258 nm (4.81 eV) (Figure 2). An intermittent fine structure was also observed in the 250 nm absorbance peak. It is notable that the absorbance reaches a limiting value in about 5 h, indicating the remarkable stability of some of the smallest crystals against further dissolution, even after the introduction of the additional acid mixture. Koshida has described the effect of dissolution phototuning when a nanoporous Si wafer was etched in HF.23,24 Following their interpretation, Si dissolution in HF is significantly retarded in the absence of UV light-induced oxidation. As the particle size shrinks, the band gap expands (as established in our investigation by the absorbance edge shift in Figure 2) and ultimately can exceed the energy of the UV lamp photons (hν ∼ 3.65 eV) thus hindering further light-induced oxidation. Another possible reason for the Si dissolution self-limitation could be the inverse oxidation rate dependence on particle size, as reported by Okada et al.33 However, their study was performed with the larger Si particles (20 nm < d < 500 nm), and it is not obvious whether this dependence can be extrapolated to Si crystals in the single nanometer size range. A specially designed study would be required to evaluate the possible role of these mechanisms in hampering complete Si nanoparticle dissolution.
Figure 5. Multicolor photoluminescence pattern in the stationary Si nanoparticle suspension during UV-catalyzed acid dissolution. The sample cell was illuminated at 340 nm through the bottom cell window.
(32) Holmes, J. D.; Ziegler, K. J.; Doty, R. C.; Pell, L. E.; Johnston, K. P.; Korgel, B. A. J. Am. Chem. Soc. 2001, 123, 3743. (33) Okada, R.; Iijima, S. Appl. Phys. Lett. 1991, 58, 1662.
The PL of Si nanoparticles during photocatalyzed dissolution blue shifts across the wide range of the visible spectrum and is consistent with the gradual average size particle reduction. The extent of the PL shift was limited to the blue-green region in most experiments prior to the intensity drop below the detector sensitivity limit. However, several samples demonstrated the PL shifts up to λmax ) 400 nm. The dissolution reaction is visibly photodriven, as evidenced by the stratified multicolor PL pattern in a sample cell that was illuminated through the bottom cell wall with a 340 nm lamp (Figure 4). Consistent with the Si particle suspension absorbance spectrum (see Figure 2), the 340 nm light from the UV lamp would be gradually attenuated along the vertical dimension, and consequently, it will result in the slower dissolution reaction. Given that PL colors can be directly related to a discrete series of Si particle sizes in the range from 1.67 to 3.7 nm,16 the stratified PL pattern reflects the distribution of particle size as a result of the dissolution rate variation along the cuvette height (Figure 5). Si particle PL (λexc ) 360 nm) was measured during the dissolution process using a scanning spectrofluorimeter (Figure 6). Spectra were recorded by moving the Si particle and acid
3392 Langmuir, Vol. 23, No. 6, 2007
Figure 6. Photoluminescence spectra recorded during photocatalyzed Si nanoparticle dissolution: (1) prior to acid introduction and (2) 30 min, (3) 50 min, (4) 80 min, (5) 110 min, (6) 130 min, (7) 170 min, and (8) 200 min after acid addition.
containing quartz cuvette from the UV reactor to the fluorimeter sample compartment for the duration of the scan (∼30 s). Typically, the PL spectrum prior to acid introduction contains a broad emission peaking at 650 nm (Figure 6). Adding the acid mixture and exposing the suspension to 340 nm light results in a smooth blue shift of the broad PL feature as shown in Figure 6. The PL peak intensity and bandwidth also vary noticeably throughout the course of the particle dissolution. The PL peak intensity rises with the commencement of the reaction, reaches a maximum value at λ ) 560 nm, and gradually declines with a further wavelength shift to the green-blue region. The final PL peak wavelength typically in the 460-510 nm interval before emission is no longer detectable. If decreasing particle size were the only factor responsible for the PL blue shift due to quantum confinement, we would expect a further emission wavelength shift as suggested by the higher band gap values consistent with the absorbance spectra (Figure 2). In a study of oxidized nanoporous Si, Wolkin et al. have shown that exciton recombination proceeds through the defect levels in the band gap if the Si surface is exposed to oxygen.34 The PL experiments, conducted in strict anaerobic conditions, led to the conclusion that the presence of a SidO bond introduces electron and hole trap levels in a Si nanocrystal band gap, thus effectively limiting the emission energy to ∼2.1 eV, even in the smallest particles. In a theoretical study, Zhou et al. have determined that the band gap can be lowered by 1.5-2.4 eV in 1 and 1.4 nm Si nanocrystals when H passivation is replaced with hydroxyl.35 As our experiments were conducted in deoxygenated solutions that contain HF, extensive Si surface oxidation was suppressed. However, exposure to HNO3 and UV light may facilitate the partial passivation by oxygen that competes with the Si-H bond, which is a prevalent surface functionality in the HF environment.36 The sensitivity of the final PL wavelength to the presence of residual oxygen thus illustrates the competition between H and various oxygen species in the Si particle passivating shell. PL decay lifetime data show the different nature of the optical transitions occurring in the blue and yellow-green particle populations. We have measured the average PL decay lifetime to be t ) 6 ns when a blue particle subpopulation (λexc ) 420 nm; λexc ) 360 nm) was selectively excited. Such values are consistent with the dipole-allowed direct interband transitions that are expected for H-terminated nanocrystals.35 In contrast, (34) Wolkin, M. V.; Jorne, J.; Fauchet, P. M.; Allan, G.; Delerue, C. Phys. ReV. Lett. 1999, 82, 197. (35) Zhou, Z. Y.; Brus, L.; Friesner, R. Nano Lett. 2003, 3, 163. (36) Hua, F. J.; Erogbogbo, F.; Swihart, M. T.; Ruckenstein, E. Langmuir 2006, 22, 4363.
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Figure 7. Initial Si nanocrystal size distribution function used in the dissolution model. The inset shows the initial particle size distribution calculated from the absorbance spectrum according to the procedure described in ref 38.
during Si particle suspension, etching induced a PL shift from red to green, and the measured radiative lifetimes were in the range from 5 × 10-5 s to 10-5 s, which is typical for the indirect transitions. It was suggested previously that the oxide passivation creates a dipole-forbidden “indirect gap” that may be up to 2.3 eV smaller than the direct gap in the 1 nm diameter H-passivated species.35 It is notable that PL peak bandwidth is gradually reduced all the way through the photocatalyzed reaction (Figure 6). The full width at half-maximum (fwhm) of the initial red PL band decreases from (1.1 ( 0.1) to (0.4 ( 0.15) eV for particles with blue-green PL (Figure 6). However, the PL spectrum narrowing was much less pronounced when particles were etched in the dark (Figure 9). Given that, at a single Si nanoparticle level, the fwhm is ∼0.2 eV,19 it indicates a considerable narrowing of the emissive particle size dispersion during the dissolution process. The narrowing of the particle size polydispersity is also supported by the absorbance spectra evolution (Figure 2); however, a direct comparison with the PL can hardly be made, as different particle subpopulations are represented in these two measurements. While Si particles of all sizes contribute to the absorbance signal, only the emissive or “bright” nanocrystals are represented in PL. The fraction of “bright” particles controls the overall PL efficiency, since this parameter can exceed 90% at a single Si nanocrystal level.22 The external quantum yield, measured relative to a quinine sulfate standard, in our Si suspensions was up to 60% in samples exhibiting yellow PL. Taken together with the microsecond PL decay rates, high QY values point to a sluggish, nonradiative recombination even in the oxide passivated Si nanocrystals and a relatively defect-free particle structure. The dissolution reaction can be stopped and PL can be stabilized at any stage either by turning off the UV light or by diluting the suspension with methanol. Particle Dissolution Simulation. We have modeled Si particle dissolution using a shrinking core approximation that is frequently utilized in small particle dissolution simulations.37 The initial particle size distribution could be obtained from the absorbance data, following the procedure described in ref 38, and the resulting curve (inset in Figure 7) can be approximated with a log-normal (37) Fogler, H. S. Elements of chemical reaction engineering, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 2005. (38) Soni, R. K.; Fonseca, L. F.; Resto, O.; Buzaianu, M.; Weisz, S. Z. J. Lumin. 1999, 83, 187.
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Figure 8. Simulated distribution function during Si nanoparticle suspension dissolution in the acid mixture: (1) initial distribution and (2) 10 min, (3) 30 min, (4) 60 min, (5) 100 min, (6) 160 min, and (7) 250 min after acid addition.
distribution:
[ ] ( ) ln
exp F(d,0) ) N0
Figure 9. Photoluminescence bandwidth at half-maximum during the photocatalyzed dissolution reaction of the Si nanocrystal suspension in the HF/HNO3 mixture: open circles, dissolution in the dark; full circles, dissolution under 340 nm light.
d dg
2
2(ln σ2)2
d ln σ2x2π
(2)
Here, F(d,0) is the initial fraction of particles with diameter d, N0 is the total particle number, and dg and σ2 are determined from the experimental particle diameter distribution. Using the relationships between the particle’s diameter and the PL emission wavelength, we can relate the 650 nm PL peak (Figure 6) to the largest fraction of Si particles (d ) 5 nm). The log-normal distribution also includes larger particles (>5 nm), which initially do not contribute to the visible PL. Since the dissolution reaction is photocatalyzed, we assumed that the reaction rate (kr) depends on the amount of light absorbed by the particle. The light absorbance would be size-dependent due to the inverse relation between the particle band gap (Eg) and the diameter (d).
kr ) pR
(3)
Here, p is a constant and R ) K(E - Eg)2 is the band gapdependent absorption coefficient for an indirect transition in the region of the band edge27 (K is a constant). The band gap is related to the particle diameter:16
Eg ) 3.44d -0.5
(4)
In our experiment, E ) 3.65 eV (λ ) 340 nm); therefore, kr can be expressed as follows:
kr ) pK(q - sd -0.5)2
(5)
At the steady state, the acid reaction rate at the surface of the nanoparticle is assumed to be equal to the rate of external acid diffusion to the nanoparticle surface.
-racid surface ) krCacid surface ) kc[Cacid 0 - Cacid surface] (6) Solving eq 6 for Cacid
surface
gives
-racid ) krCacid surface )
krkc C kr + kc acid 0
(7)
where Cacid is the acid concentration, racid is the acid consumption rate, kr is the dissolution reaction rate constant, and kc is the mass transfer coefficient of the acid mixture.37 The mass transfer coefficient is obtained from the Frossling correlation:
Sh )
kcd
) 2.0 + 0.6 Re1/2Sc1/3
Dacid-SiNP
(8)
where Sh is the Sherwood number, Dacid-SiNP is the component diffusion coefficient, Re is the Reynolds number, and Sc is the Schmidt number. For small particles, Sh ≈ 2, and the mass transfer constant can be simplified as
Sh ) 2.0 + 0.6
( )() υs d ν
1/2
ν D
1/3
)
kcd
) 2.0 Dacid-SiNP (d is very small) (9)
where υs is the mean fluid velocity, ν is the kinematic fluid viscosity, and D is the mass diffusivity. The reaction rate can be expressed by combining eqs 4-9:
-racid )
pK(q - sd -0.5)2Cacid 0 pK(q - sd -0.5)2d 1+ 2Dacid-SiNP
(10)
To account for the polydisperse sample nature, we selected a small interval ∆d from the particle size distribution function (Figure 7) and derived the balance equation for that interval:37
R(d) F(d,t)|d - R(d) F(d,t)|d+∆d )
∂[F(d,t)∆d] ∂t
(11)
Solving a partial differential equation (eq 12) in terms of reaction time, we arrive at a series of particle number density (F) and particle diameter (d) dependencies as shown in Figure 8:
3394 Langmuir, Vol. 23, No. 6, 2007
∂F ∂t
pK(q - sd -0.5)2Cacid 0
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∂F + -0.5 2 pK(q - sd ) d ∂d 3FSiNP 1 + 2Dacid-SiNP 1 s + Cacid 0 2Dacid-SiNP pK(q - sd -0.5)3d1.5 ) 0 (12) F 2 1 d 3FSiNP + pK(q - sd -0.5)2 2Dacid-SiNP
(
(
(
)
)
)
These distribution profiles were calculated using the Mathematica (version 5.2, Wolfram Research, Champaign, IL) software package. The particle diameter profile evolution can be compared with the PL spectra, acquired during our Si particle suspension dissolution (Figure 6), given that the PL peak wavelength tracks Si particle size. Consequently, the PL intensity profile would result from the additive effect of a certain size of particles and can be directly related to their density within a fixed size interval. Two major characteristics of the PL profiles during the dissolution are simulated by our calculation. First, the median particle size is monotonically reduced, leading to the blue PL shift. Using the size-band gap relation for the H-terminated spherical Si nanocrystals, given in ref 16, we can deduce from the PL peak position (Figure 6) that the median particle diameter is reduced from 5 to 1.5 nm during the course of a 2 h dissolution. Further particle size reduction may not be reflected by the PL wavelength shift due to oxidation-induced band gap narrowing, as suggested by Wolkin et al.34 A second notable characteristic, predicted by our simulation, is a monotonic reduction of the particle size polydispersity during the photocatalyzed dissolution reaction. Initially, we obtained a rather broad nanometer-sized population after wafer etching and sonication (Figure 3). Therefore, a reduction in the polydispersity would be highly desirable for practical nanocrystal applications. Indeed, a significant reduction of both the PL peak width (Figure
9) and the absorbance edge slope (Figure 2) indicate a progressively homogeneous mixture. A significant narrowing of the PL profile was only observed when dissolution was conducted with UV illumination (Figure 9). In summary, H-terminated Si nanoparticle photoluminescence wavelength and intensity can be tuned using photoinduced dissolution in a HF/HNO3 acid mixture. By measuring both the absorbance and the photoluminescence during particle dissolution, we have tracked the Si nanoparticle band gap growth with a shrinking crystal size. Etching of the Si nanoparticle methanol suspension in the HF/HNO3 acid mixture increases the PL QY up to 60%. The microsecond PL decay rates are consistent with the indirect radiative recombination mechanism for particles exhibiting red to green PL. Together with high quantum yield, it implies a slow nonradiative recombination and reflects a relatively defect-free particle structure. The nanosecond decay times were recorded in Si particles exhibiting blue PL, suggesting a direct interband transition and, possibly, a different emission mechanism. Our simple etching procedure can be employed to control the particle size and prepare bright Si nanoparticle suspensions with emissions spanning the visible range, which is required for biological fluorescence tagging. A considerable narrowing of particle size distribution was observed during photoassisted dissolution and was predicted by the dissolution reaction simulation. The reaction rate dependence on particle size, anticipated by our model, was in reasonable agreement with the experimental findings. Both the absorbance and the PL results suggest that the median particle diameter is reduced from 5 to
