Substrates for Direct Imaging of Chemically Functionalized SiO2

Nov 22, 2005 - ... °C for 10 min: Wolf, S.; Tauber, R. N. Process Technology: Silicon Processing for the VLSI Era; Lattice Press: Sunset Beach, CA, 2...
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Anal. Chem. 2006, 78, 298-303

Substrates for Direct Imaging of Chemically Functionalized SiO2 Surfaces by Transmission Electron Microscopy Gregory J. Kearns, Evan W. Foster, and James E. Hutchison*

Department of Chemistry and Materials Science Institute, University of Oregon, Eugene, Oregon 97403

A significant challenge in materials characterization is the determination of the structure of nanoparticle assemblies that have been deposited on solid substrates, such as SiO2. The best method for obtaining quantitative information about structure, size, and spacing on the nanometerlength scale is TEM; however, commercially available TEM grids offer a limited range of substrate materials. In addition, the compositions of these grids do not permit much chemical processing. Here we describe siliconbased grids with electron-transparent SiO2 windows suitable for use as substrates for high-resolution TEM that can be easily fabricated using standard silicon microfabrication techniques. These grids are physically and chemically robust and exhibit the same surface chemistry and chemical stability as an oxide grown on a silicon wafer. Thus, the grids make possible the concurrent investigation of chemical and structural information on the same sample. Convenient modification of the surfaces of the grids provides access to a wide range of new substrates for the direct imaging of chemically modified surfaces by TEM. We demonstrate the utility of these grids by aligning DNA on the chemically modified SiO2 surface in order to direct the assembly of linear arrays of nanoparticles. Using these grids, we are able to quantify the effects of assembly conditions on nanoparticle size, spacing, and dispersity in the arrays. An important challenge in nanoscience is the characterization and analysis of nanostructures that are assembled on technologically relevant substrates. A number of scanning probe and electron beam-based microscopies have been employed, each possessing unique advantages, complexities, and substrate requirements.1 Imaging performance is typically enhanced through the use of specialized substrates; however, such substrates are often chemically dissimilar to the substrates used in devices or during assembly reactions, e.g., a carbon-coated transmission electron microscopy (TEM) grid has different surface chemistry than a semiconductor wafer. Here we describe the fabrication of a silicon TEM grid possessing electron-transparent SiO2 windows. We demonstrate the utility of these grids for the concurrent investiga* To whom correspondence should be addressed. E-mail: [email protected]. (1) Surface Analysis Methods in Materials Science, 2nd ed.; O’Connor, D. J., Sexton, B. A., Smart, R. St. C., Eds.; Surface Sciences 23; Springer: New York, 2003.

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tion of the surface chemical interactions and high-resolution imaging of nanoparticles assembled on SiO2. The most commonly used methods for analyzing nanostructures (e.g., nanoparticles) on chemically functionalized surfaces are atomic force microscopy (AFM) and scanning electron microscopy (SEM) because these techniques are compatible with a wide range of substrates including SiO2. In a direct comparison of AFM, SEM, scanning near-field optical microscopy, and TEM, Grabar et al. demonstrated that TEM is the best method for quantifying the size, shape, and spacing of nanoparticles in nanoparticle arrays due to high lateral resolution and straightforward data analysis.2 The primary limitation of using TEM to analyze nanostructures is that the relevant substrate material may not be available as a support film on commercially available grids.3 To obtain images of samples on relevant substrates, time-intensive and destructive sample preparation techniques such as mechanical polishing4 or ion milling must be employed in order to obtain electron transparency.5 Commercially available silicon monoxide (SiOx) TEM grids are often used as approximations for SiO2 surfaces; however, these substrates are not rigid, the surfaces are rough, and SiOx has an ambiguous chemical structure that is a mixture of SiO and SiO2.6 Therefore, the surface does not have the same chemical reactivity as native or thermally grown SiO2 on silicon. Due to the reactivity of the polymer-coated metal grid that typically supports the SiOx film, these grids cannot withstand even the mildest environments that are used for cleaning and processing SiO2/Si. UV/ozone cleaning, RCA SC-1 solution,7 piranha solution,7 and oxygen plasma destroy the polymer support, while RCA SC-2 solution7 or any other acidic environment dissolves most metal substrates. In addition, the chemical environments used to functionalize SiO2, such as self-assembled monolayer chemistry, often involve acidic (2) Grabar, K. C.; Brown, K. R.; Keating, C. D.; Stranick, S. J.; Tang, S.-L.; Natan, M. J. Anal. Chem. 1997, 69, 471-477. (3) Shipway, A. N.; Katz, E.; Willner, I. ChemPhysChem 2000, 1, 18-52. (4) Foster, E. W.; Kearns, G. J.; Goto, S.; Hutchison, J. E. Adv. Mater. 2005, 17, 1542-1545. (5) Perrey, C. R.; Carter, C. B.; Michael, J. R.; Kotula, P. G.; Stach, E. A.; Radmilovic, V. R. J. Microsc.-Oxford 2004, 214, 222-236. (6) http://www.2spi.com/catalog/grids/cusctgrd.html. (7) RCA SC-1 cleaning removes organic contaminants and group I and II metals using a 5:1:1 mixture of H2O/H2O2/NH4OH at 70 °C for 10 min. Piranha solution is an aggressive organic cleaning solution consisting of a 7:3 mixture of H2SO4/H2O2; RCA SC-2 cleaning removes inorganic ions, alkali ions, and heavy metals using a 6:1:1 mixture of H2O/H2O2/HCl at 70 °C for 10 min: Wolf, S.; Tauber, R. N. Process Technology: Silicon Processing for the VLSI Era; Lattice Press: Sunset Beach, CA, 2000; Vol. 1, p 129. 10.1021/ac051459k CCC: $33.50

© 2006 American Chemical Society Published on Web 11/22/2005

environments and organic solvents. The ideal TEM grid for imaging SiO2 surfaces must be electron transparent, smooth, rigid, and robust to chemical processing. Recently, it has been shown that the surfaces of silicon nitride TEM grids can be oxidized through O2 plasma treatment,8 but the chemical nature and reactivity of the surface has not been determined. Elsewhere in the literature9 it has been shown that the chemical composition of oxidized silicon nitride surfaces depends strongly on the method of oxidation, ranging from an oxynitride composition at lower levels of oxidation toward a “silicon oxide-rich” layer after more extensive oxidation. The reactivity of the “native oxide” on silicon nitride has been shown to depend on the method of sample preparation.10 Given the marked dependence of the surface reactivity of silicon dioxide and oxidized silicon nitride on the method of preparation (e.g., native oxide and thermal oxide exhibit different reactivity due, in part, to the differences in surface hydroxyl concentration),11 it remains to be seen whether oxidized silicon nitride surfaces will serve as suitable approximations for a thermal silicon dioxide surface. In any case, the best approach to reliably image nanostructures on chemically modified surfaces is to use a surface that is prepared in the same manner as will be used for bulk measurements. Our previous work on the assembly of 1-D arrays of gold nanoparticles showed that, in solution, DNA can be used as a scaffold to organize close-packed arrays of gold nanoparticles,12 and the spacing between nanoparticles can be controlled by the choice of organic ligand shell on the nanoparticles.13 To make useful devices from these arrays, we aimed to carry out the assembly process directly on surfaces. We first needed to position the DNA scaffold on a chemically modified surface and, second, assemble close-packed arrays of nanoparticles on the surfacebound scaffolds. While a two-step process of aligning DNA followed by coating with positively charged nanoparticles has been reported,14 the arrays were characterized by AFM, so individual nanoparticles could not be resolved; therefore, the nanoparticle size distribution, interparticle spacing, and overall coverage could not be determined. TEM analysis of structures resulting from a two-step assembly process is needed to assess the utility of this patterning strategy. In order to follow the chemical assembly of nanoparticles by TEM, the ideal substrate should consist of technologically relevant materials that withstand chemical treatment and mimic the surface of interest as closely as possible. Furthermore, they should be easy to make in large batches and give good contrast with low background noise. Here we describe a new substrate for TEM that consists of a silicon grid with electron-transparent SiO2 windows with dimensions similar to traditional TEM grids (3-mm-diameter substrate (8) Grant, A. W.; Hu, Q.-H.; Kasemo, B. Nanotechnology 2004, 15, 1175-1181. (9) Kennedy, G. P.; Buiu, O.; Taylor, S. J. Appl. Phys. 1999, 85, 3319-3326. (10) Ito, T.; Namba, M.; Buhlmann, P.; Umezawa, Y. Langmuir 1997, 13, 43234332. (11) Iler, R. K. The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry; John Wiley & Sons: New York, 1979; pp 637-645. (12) Warner, M. G.; Hutchison, J. E. Nat. Mater. 2003, 2, 272-277. (13) Woerle, G. H.; Warner, M. G.; Hutchison, J. E. Langmuir 2004, 20, 59825988. (14) Hidenobu, N.; Shiigi, H.; Yamamoto, Y.; Tokonami, S.; Nagaoka, T.; Sugiyama, S.; Ohtani, T. Nano Lett. 2003, 3, 1391-1394.

Scheme 1. TEM Grid Fabrication

A 500-Å oxide is grown on a 100-µm-thick silicon chip, and the TEM grid is defined by photolithography. The patterned wafers are soaked in buffered oxide etchant to etch through the exposed oxide and the photoresist is removed. The windows are revealed by etching through the silicon with tetramethylammonium hydroxide.

with 30-µm-square windows). Because the substrates are etched from silicon and are composed only of silicon and its thermal oxide, they can be chemically treated in the same manner that thermal oxides on silicon are treated and imaged directly without any further sample preparation. The grids withstand a variety of harsh treatments including UV/ozone, piranha solution, RCA SC-1 and SC-2 solutions,7 and oxygen plasma without any physical damage. The SiO2 windows appear to have better contrast and lower background noise compared to SiOx monoxide films on commercially available TEM grids. Chemical reactions on the SiO2 windows of the grids can be assessed or monitored by surface analytical methods such as X-ray photoelectron spectroscopy or AFM in addition to TEM analysis. We demonstrate the utility of these grids by assembling aligned close-packed, linear nanoparticle (dcore ∼ 1.5 nm) arrays on the grids using a three-step assembly process, including the following: (i) surface silanization, (ii) DNA molecular combing, and (iii) nanoparticle assembly. Our use of TEM with these new SiO2 grids permits the careful investigation of the nanoparticle size, spacing, and coverage on the same substrate used for the assembly reaction. We show that nanoparticle purity has a significant impact on the resulting structures, a finding that could not be determined using previously available grids or other analytical methods such as AFM or SEM. EXPERIMENTAL SECTION TEM Grid Fabrication. An overview of the process used for grid fabrication is shown in Scheme 1. A 500-Å thermal oxide was grown at 1100 °C under flowing O2 on an RCA SC-115 cleaned Ultrathin silicon chip (100-µm-thick wafers, polished on both sides, purchased from Virginia Semiconductor). The chips were coated with positive photoresist on both sides, and the grids were defined by photolithography on one side using a contact mask. The exposed SiO2 was etched in 20:1 buffered oxide etchant,16 and the photoresist was removed. The exposed silicon was etched with (15) Here we use a dilute (200:4:1) solution of H2O/H2O2/NH4OH. This ratio is as effective as the standard SC-1 solution and has been shown to reduce the surface roughness of the silicon substrate; Wolf, S.; Tauber, R. N. Process Technology: Silicon Processing for the VLSI Era; Lattice Press: Sunset Beach, CA, 2000; Vol. 1, p 130. (16) Buffered oxide etchant, 20:1 refers to a solution consisting of 20 parts ammonium fluoride (40%) to 1 part HF (49%).

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Figure 1. SEM images of Si/SiO2 TEM grids. Top views of the TEM grid show (a) the array of windows and (b) a single window with a dust particle (upper 1/4 of the window) indicating the presence of a SiO2 film. Back views of the TEM grid show (c) the array of windows and Si(111) etch planes within the windows and (d) the Si(111) etch planes and residual SiO2 flakes around the larger portion of the window.

10 wt % tetramethylammonium hydroxide (TMAH) solution initiated at 90 °C. Once it was clear that the etch was underway, the solution was cooled to room temperature and allowed to etch through the silicon overnight. The chips were placed in the solution “patterned side up” to prevent trapping gas bubbles in the etching area. The etch was considered complete when the grids (16/1.5-cm square chip) separated from each other. This resulted in TEM grid-shaped silicon disks with 500-Å-thick electron-transparent windows of SiO2 on one side (Figure 1). TEM Grid Functionalization and DNA Assembly. Silanization of the grids and DNA alignment were performed as described by the Bensimon group.17 The grids were cleaned by a 15-min UV/ozone treatment followed by rinsing with ethanol and ultrapure water, dried at 60 °C for 1 h, then put in a desiccator along with a beaker containing 300 µL of n-octyltrichlorosilane for 18 h. This vapor-phase silanization was performed at room temperature and pressure. The silanized grids were rinsed with ultrapure water to hydrolyze any remaining Si-Cl bonds. The grids were incubated in a solution (5 µg/mL) of genomic λ-DNA (purchased from New England Biolabs) in MES18 buffer (0.05 M, pH 5.5) for 5 min at room temperature and then pulled from solution at 300 µm/s.19 The DNA arrays were rinsed thoroughly with ultrapure water and then soaked in a solution of positively charged nanoparticles (1 mg/mL) for 20 min. (17) Bensimon, A.; Simon, A.; Chiffaudel, A.; Croquette, V.; Heslot, F.; Bensimon, D. Science 1994, 265, 2096-2098. (18) MES buffer [2-(N-morpholino)ethanesulfonic acid] is a zwitterionic biological buffer with a useful pH range of 5.5-6.7. (19) Michalet, X.; Ekong, R.; Fougerousse, F.; Rousseaux, S.; Schurra, C.; Hornigold, N.; Slegtenhorst, M. van; Wolfe, J.; Povey, S.; Beckmann, J. S.; Bensimon, A. Science 1997, 277, 1518-1523.

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Nanoparticle Synthesis. The nanoparticles were synthesized as described previously.20,21 Briefly, HAuCl4 in H2O reacts with triphenylphosphine (PPh3) in toluene in the presence of the phasetransfer catalyst tetraoctylammonium bromide. Reduction with NaBH4 yields ∼1.5-nm PPh3-stabilized nanoparticles. Thiocholine [(2-mercaptoethyl)trimethylammonium iodide] was synthesized as described previously.12 A biphasic ligand exchange between thiocholine in H2O and the PPh3-stabilized nanoparticles in CH2Cl2 yielded positively charged, water-soluble Au-thiocholine nanoparticles.22 The thiocholine stabilized nanoparticles were purified by two rounds of ultracentrifugation at 360 000g. A subset of these Au-thiocholine nanoparticles was further purified by diafiltration23 (10 volumes, 10 kDa) to achieve “ultrapure” Au-thiocholine nanoparticles. Nanoparticle Assembly. To observe DNA on only one side of the TEM grid, the nanoparticle soak was performed by placing a 10-µL drop of nanoparticle solution on the top side of the grid. The hydrophobic silanized surface prevents the drop from spreading beyond the edge of the grid. Upon completion of the assembly process, the grids were rinsed thoroughly with ultrapure water to remove any nonspecifically bound nanoparticles. Safety Considerations. Buffered oxide etchant contains a mixture of hydrofluoric acid and ammonium fluoride, which can cause serious damage to tissue and bone. RESULTS AND DISCUSSION TEM Grid Fabrication. A typical process yields 80 TEM grids from 5 silicon chips having 16 grids/chip. Because the oxide film is grown at 1100 °C, viscous flow of the oxide relieves the compressive stress introduced into the oxide during growth.24 Therefore, the windows do not buckle or break when the supporting silicon is etched away, and the windows do not appear to be bowed, as there is no evidence of a change in focal plane over the window area. Using the silicon etching conditions described above, grids have most or all oxide windows intact. More aggressive silicon etch conditions, such as maintaining a 90 °C TMAH solution throughout the process, etch faster (∼2-3 h) but can result in a lower yield of intact windows (1-4) per grid due to turbulence from the rapid production of gas bubbles as the silicon is etched. The grids are durable and easy to handle with tweezers. The windows are robust to harsh processing conditions such as oxygen plasma or swirling in silicon cleaning solutions such as RCA or piranha solutions. SEM images of the grids (Figure 1) show the octagonal shape of the Si grid with 16 windows. The octagonal shape is due to anisotropy of the TMAH etch. Although it is not clear from the SEM images that there is a SiO2 film over the windows, we show an image that displays a dust particle near the upper edge of the window (Figure 1b) in order to illustrate the presence of a film. Images of the backside of the grid also show the Si(111) etch planes in the window (Figure 1c,d) and some residual oxide flakes around the edges (Figure 1d). (20) Weare, W. W.; Reed, S. M.; Warner, M. G.; Hutchison, J. E. J. Am. Chem. Soc. 2000, 122, 12890-12891. (21) Hutchison, J. E.; Foster, E. W.; Warner, M. G.; Reed, S. M.; Weare, W. W.; Buhro, W.; Yu, H. Inorg. Synth. 2004, 34, 228-232. (22) Warner, M. G.; Reed, S. M.; Hutchison, J. E. Chem. Mater. 2000, 12, 3316. (23) Sweeney, S.; Woehrle, G. H.; Hutchison, J. E. J. Am. Chem. Soc., submitted. (24) Wolf, S.; Tauber, R. N. Process Technology: Silicon Processing for the VLSI Era; Lattice Press: Sunset Beach, CA, 2000; Vol. 1, p 296.

Figure 2. TEM images of DNA templated nanoparticle arrays. DNA was aligned on a silanized SiO2 TEM grid and subsequently coated with positively charged nanoparticles. TEM images show that (a) arrays are linear over the entire surface of the substrate and (b) nanoparticles are close-packed along the DNA backbone.

Figure 3. Interparticle spacing of DNA-nanoparticle arrays. Interparticle spacing distributions from TEM images show that (a) assemblies formed from normally prepared Au-thiocholine particles have a spacing of 1.5 ( 0.8 nm (n ) 353) and (b) assemblies formed from ultrapure particles have a spacing of 1.4 ( 0.5 nm (n ) 398).

TEM Analysis of Nanoparticle Arrays. Chemical functionalization of the SiO2 surface with n-octyltrichlorosilane is the key requirement for this assembly process as the silanized surface promotes molecular combing of DNA17 and limits nonspecific adsorption of the positively charged nanoparticles. Low-magnification TEM images show that the nanoparticles form linear, parallel arrays over the entire surface of the substrate (Figure 2a). Higher magnification images show that the nanoparticles are close-packed over the entire DNA molecule (Figure 2b) with an average interparticle spacing of 1.5 ( 0.8 nm (n ) 353) for the Authiocholine particles (Figure 3a) and 1.4 ( 0.5 nm (n ) 398) for the ultrapure Au-thiocholine particles (Figure 3b). An average spacing of 1.4 nm is expected, assuming that the particles are close-packed and that the Au-core spacing is dependent on the thickness of the thiocholine ligand shell.13,25,26 Prior to deposition on DNA, the nanoparticle size distributions were 1.7 ( 0.7 nm (n ) 792) for the Au-thiocholine particles (Figure 4a) and 1.7 ( 0.6 nm (n ) 1476) for the ultrapure Authiocholine particles (Figure 4b). Interestingly, after deposition on DNA, the Au-thiocholine particles grew to 2.7 ( 0.9 nm (n ) 321) (Figure 4c) while the ultrapure Au-thiocholine particles

apparently decreased in size to 1.4 ( 0.5 nm (n ) 706) (Figure 4d).25,27 The decrease in average diameter and increase in monodispersity of the ultrapure particles on DNA may be a result of size selection toward smaller particles that presumably have a higher charge density than larger particles due to their higher surface-to-volume ratio. The difference in the assemblies formed from the normally prepared nanoparticles and ultrapure nanoparticles is surprising. The notable difference between the samples is that the normally prepared Au-thiocholine samples contain traces of free thiocholine ligand associated with the nanoparticles that can be seen as small differences in the NMR spectra. High concentrations of free ligand have been known to destabilize nanoparticles during ligand exchange reactions.28 The increased size of the Au-thiocholine particles may be due to the concentration of free ligand near the DNA, resulting in nanoparticle growth on the DNA backbone. The structures of the normally prepared Au-thiocholine assemblies and the ultrapure Au-thiocholine assemblies are also qualitatively different. The Au-thiocholine particles form linear arrays 1-2 nanoparticles wide (Figure 5a) while the ultrapure

(25) Particle size distributions and interparticle spacing were analyzed using NIH ImageJ for MacIntosh. ImageJ is available free of charge at http:// rsb.info.nih.gov/ij/. (26) Interparticle spacing was calculated by measuring the edge-to-edge distance between all nearest neighbors.

(27) Particle size was measured as the average of the major and minor axes; Woehrle, G. H.; Ozkar, S.; Hutchison, J. E.; Finke, R. G. J. Turk. Chem. submitted. (28) Woehrle, G. H.; Brown, L. O.; Hutchison, J. E. J. Am. Chem. Soc. 2005, 127, 2172-2183.

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Figure 4. Nanoparticle size analysis. Nanoparticle size distributions from TEM images show that (a) normally prepared nanoparticles and (b) ultrapure nanoparticles have similar diameters of 1.7 ( 0.7 (n ) 792) and 1.7 ( 0.6 nm (n ) 1476), respectively. Both appear to have a bimodal distribution that is more pronounced for the normally prepared particles. After assembly on DNA, (c) normally prepared particles grow to 2.7 ( 0.9 nm (n ) 321), while (d) ultrapure particles become more monodisperse via size selection, having a diameter of 1.4 ( 0.5 nm (n ) 706).

Figure 5. Qualitative structural differences between assemblies formed from normally prepared nanoparticles and ultrapure nanoparticles. TEM images show that (a) normally prepared particles form linear arrays 1-2 nanoparticles wide while (b) ultrapure particles form ribbons 4-5 nanoparticles wide.

particles form “ribbons” 4-5 nanoparticles wide (Figure 5b). We have seen examples of ribbons from solution-phase assemblies that are due to the multivalent character of the positively charged nanoparticles cross-linking several DNA strands,12 but this should not be the case for our ribbons, as the DNA scaffolds are aligned prior to the addition of nanoparticles. Another possibility is that higher order DNA structures such as DNA bundles were aligned on the grids used for the ultrapure particle assemblies.29 However, all of the DNA assemblies were prepared from the same DNA solution and the same silanization conditions. These differences (29) Zhang, J. M.; Ma, Y. F.; Stachura, S.; He, H. X. Langmuir 2005, 21, 41804184.

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were reproducible on four grids for each of the two types of nanoparticles, which suggests that the structural differences are not due to differences in the DNA scaffolds. The most plausible explanation is that the normally prepared Au-thiocholine particles also form the ribbon structures, but the particles grow together to form the linear arrays of larger particles. This accounts for both the increase in particle size and decrease in array width of the normally prepared particles. The grids reported here make possible the simultaneous investigation of chemical and structural composition of nanoscale materials on SiO2 and provide the basis for a wide range of new substrates for the direct imaging of chemically modified surfaces by TEM. TEM grids with SiO2 windows will be useful for imaging chemically functionalized SiO2 surfaces ranging from nanoelectronics and photonics to MEMS. The work reported here is just one demonstration of the utility of these grids, and they show promise for many other systems. Because they are fabricated from thermal oxides, they can be used to understand chemistry and assembly on SiO2 without time-consuming and destructive sample preparation methods. The images are high resolution, there is no ambiguity as to how closely the substrate approximates SiO2, and there is no sample preparation that could destroy the structures or take hours per sample. We are currently using these substrates to further understand the factorsssuch as surface chemistry, nanoparticle chemistry, and alignment methodsthat affect linear arrays of DNA/nanoparticle structures on thermal oxides in order to understand these effects when developing electronic test structures. We are also working to understand the factors affecting 2-D arrays of nanoparticles chemically bound to the SiO2 surface.4

Further functionalization of the grid windows will provide opportunities to obtain high-resolution imaging on other new surfaces whereas the development of micro- or nanoscale electrodes on the grids will permit direct imaging and electronic measurements on the same nanostructures. Just as silanization of these grids opens up a wide range of surface modifications using organic species, it may also be possible to functionalize the SiO2 surfaces with inorganic species by atomic layer deposition30 in order to develop a wider range of substrates available for TEM. In conclusion, we have developed a new substrate for TEM consisting of a SiO2 film supported on a Si grid. They have been shown to enhance the understanding of surface reactions on SiO2

and give access to information about nanostructures that could not have been achieved by any method other than TEM. The substrates are easy to make in large batches and, once prepared, provide a simple means to image nanostructures on chemically functionalized SiO2.

(30) Leskela, M.; Ritala, M. Angew. Chem., Int. Ed. 2003, 42, 5548-5554.

AC051459K

ACKNOWLEDGMENT The authors thank Steve Leith for his contributions to this work. Funding was provided by the NSF (DGE-0114419). Received for review August 12, 2005. Accepted October 3, 2005.

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