NANO LETTERS
Epitaxially Driven Formation of Intricate Supported Gold Nanostructures on a Lattice-Matched Oxide Substrate
2009 Vol. 9, No. 12 4258-4263
Gabriel A. Devenyi,†,‡,§ Jianfeng Li,⊥,# Robert A. Hughes,‡,¶ An-Chang Shi,‡,# Peter Mascher,†,§ and John S. Preston*,†,‡ Department of Engineering Physics, McMaster UniVersity, Hamilton Ontario, Canada L8S 4L7, Brockhouse Institute for Materials Research, McMaster UniVersity, Hamilton Ontario, Canada L8S 4M1, Center for Emerging DeVice Technologies, McMaster UniVersity, Hamilton, Ontario, Canada L8S 4L8, Department of Macromolecular Science, Fudan UniVersity, Shanghai 200433, China, and Department of Physics and Astronomy, McMaster UniVersity, Hamilton, Ontario, Canada L8S 4M1 Received July 31, 2009; Revised Manuscript Received October 9, 2009
ABSTRACT A new class of gold nanostructures has been fabricated on the (100), (111), and (110) surfaces of lattice-matched MgAl2O4 substrates. The nanostructures were fabricated through a synthesis route where a thin gold film dewets, liquefies, and then slowly self-assembles. The supported nanostructures are intricately shaped, crystalline, and epitaxially aligned. Simulations based on a continuum elastic theory indicate that the self-assembly is driven by strained epitaxy and minimization of the surface free energy.
Nanostructures derived from noble metals catalytically enhance chemical processes,1 exhibit intense localized surface plasmon resonances,2 mediate nanowire growth via the vapor-liquid-solid mechanism,3 and are easily bioconjugated.4 As a result, they are objects of great interest for optical, chemical, and biological applications. Such structures are now routinely fabricated in aqueous solutions using seedmediated chemical growth modes.5,6 Photochemical7 and electrochemical8 methods are also used and follow similar growth pathways, but with photons or electric fields triggering the reaction mechanism. Particle shapes produced by such reactions are widely varying, depending on the functionalization of the noble metal atoms, the concentration and makeup of the components within the solution, and the catalytic method used. A wide variety of shapes including nanospheres,9 rods,10 triangular nanoprisms,7 shells,11 disks,12 stars,13 and cubes14 are now routinely fabricated. Solutionbased plasmonic nanostructures have also received significant attention in terms of potential applications in fields such as biological detection, cancer diagnosis, and photothermal therapy.4 * To whom correspondence should be addressed.
[email protected]. † Department of Engineering Physics, McMaster University. ‡ Brockhouse Institute for Materials Research, McMaster University. § Center for Emerging Device Technologies, McMaster University. ⊥ Fudan University. # Department of Physics and Astronomy, McMaster University. ¶ Present address: Department of Mechanical Engineering, Temple University, 1947 N. 12th St., Philadelphia, PA 19122. 10.1021/nl902491g CCC: $40.75 Published on Web 10/20/2009
2009 American Chemical Society
While solution-based noble metal nanostructures have shown tremendous potential, it should be recognized that it is often highly desirable to have these nanostructures placed on a substrate in a manner which renders them immobile. Such nanostructures have been used to enhance solar cell efficiencies,15 enhance the emission from light-emitting diodes,16 detect biological agents,17 measure biological distances,18 achieve nonlinear optical properties19 and negative indices of refraction20 through the formation of metamaterials, and enhance the Raman signal from surface-adsorbed species.21 Numerous routes exist for fabricating these substratebased nanostructures, including the attachment of functionalized solution-based nanoparticles to the surface,17 growth off of surfaces seeded with linked nanoparticles,22 lithographically patterning continuous thin films,23 and selfassembly.24 Among these various techniques, self-assembly stands out as an attractive means of forming substratesupported nanostructures over large areas because there exists the potential to engineer the shape, size, and crystallographic orientation of the nanostructures through substrate-imposed strains, epitaxy, crystallographic symmetries, substrate surface morphology, interface chemistry, and wettability. Other advantages of these self-assembly methods are that the nanostructures often become well-bonded to the substrate and can show a preferential alignment due to epitaxy, a property which can be exploited to enhance the anisotropic
optical properties associated with arrays of asymmetric plasmonic nanostructures.25,26 Growth of substrate-based metallic nanostructures via selfassembly has resulted in the formation of a myriad of shapes including triangular prisms,27 square and rectangular islands,28,29 faceted spheres,30 rings,31 and horseshoes.32 Oxide substrates, such as mica and SrTiO3, have been particularly effective in the production of supported nanostructures due to their chemical and thermal stability, crystallographic perfection, and the wide variety of accessible surface reconstructions.27-29,33-35 Of considerable relevance to this work is a series of reports by Silly et al.27-29,34-37 detailing the self-assembly of intricate gold, silver, palladium, copper, and iron nanocrystals on surface-reconstructed [001] SrTiO3 substrates at varied substrate temperatures. Scanning tunneling microscopy (STM) measurements indicate a selfassembly process which is strongly influenced by the properties of the underlying substrate. In this report, we present an approach for the epitaxially driven formation of self-assembled gold nanostructures on MgAl2O4 substrates. This substrate allows for excellent gold epitaxy since its lattice constant of a ) 8.083 Å is approximately two times the gold lattice constant of a ) 4.078 Å (compressive mismatch ) 0.89%). The nanostructures, formed on [100]-, [111]-, and [110]-oriented substrates, were intricate, aligned, and have not been previously observed. The structures have been observed via scanning electron microscopy (SEM) over several months and are stable. The shapes of the nanostructures formed were in excellent agreement with those predicted by modeling based on a continuum elastic theory. The gold nanostructures were formed through the deposition of gold films on MgAl2O4 substrates (MTI Corp.) followed by an annealing procedure which facilitated film dewetting and nanostructure formation. The films were sputter-coated at room temperature to a thickness of 5 Å-15 Å with a GATAN PECS Model 682 ion beam coating/ etching system. The samples were then placed in a tube furnace with a 100 sccm flow of argon, heated to 1100 °C in 45 min, and then held at that temperature for 1 h. Following this treatment, the sample was cooled to 1000 °C in 30 min, held at that temperature for an additional hour, and then allowed to cool to room temperature over an interval of approximately 8 h. Holding the temperature at both 1100 and 1000 °C was crucial to the formation of the nanostructures described here. Removal of either step results in the formation of faceted gold spheres sitting directly on the substrate. Scanning electron microscopy (SEM) images of the gold nanostructures formed on the (100), (111), and (110) MgAl2O4 substrates, obtained using a JEOL-7000F SEM in secondary electron mode, are shown in Figure 1. For each substrate orientation, one observes two types of features, (i) spheres supported by a necking region attached to a geometrically shaped base (Figure 1a-c) and (ii) standalone base structures (Figure 1d-f). Convergent beam electron diffraction (CBED) performed using a Phillips CM12 confirmed that the supported spheres are crystalline. For each case, the Nano Lett., Vol. 9, No. 12, 2009
Figure 1. SEM images showing the gold nanostructures formed on MgAl2O4 substrates. The three upper images show spheres supported by a necking region attached to a geometrically shaped base for the (a) [100]-, (b) [111]-, and (c) [110]-oriented substrates. Each of these images was taken at a 70° tilt. The aura seen around nanostructures is an artifact of imaging. The three lower images show the top-down view of both standalone base structures and supported spheres for the (d) [100]-, (e) [111]-, and (f) [110]oriented substrates. The in-plane Miller indices of the substrate are denoted on each of these images. For all cases, the samples were coated with a thin layer of platinum to improve imaging. Imaging without platinum shows the same structures but is of poor quality due to substrate charging effects.
shape of the base structure reflects the underlying symmetry of the substrate which is four-fold, three-fold, and two-fold symmetric for the (100), (111), and (110) surfaces, respectively. X-ray diffraction measurements, using a Bruker 6000 CCD detector on a Bruker three circle D8 goniometer with a Rigaku RU-200 rotating anode Cu KR X-ray generator and parallel-focusing mirror optics, were used to determine the substrate orientation relative to the edges of the base structures and are denoted on the three top-down SEM images (Figure 1d-f). The crystallographic alignment of these nanostructures is a clear indication of epitaxy and is strongly suggestive of {111} gold faceting of the base structures associated with the [100]- and [111]-oriented substrates. For the (110) surface, the standalone base structures are ill-defined and show no obvious faceting, while those formed in combination with a sphere show shapes consistent with mixed faceting, possibly having {111} and {100} facets for the short and long dimension, respectively. The standalone base dimensions are remarkably uniform with side lengths of 40, 65, and 65 nm × 110 nm for the (100), (111), and (110) substrates, respectively. While there are two basic types of nanostructures formed on each substrate orientation, these structures are found in various stages of development. For the most part, the bases are well-developed and show little size variation. The spherical structures, however, vary dramatically both in their size and position relative to the base structures. Figure 2 shows a series of top-down SEM images for the case of the (111) MgAl2O4 substrate showing an evolution of the nanostructures from a standalone triangular base to bases supporting spheres of increasing size. Notable is the fact that the nanostructure, shown in Figure 2b, manifests itself as a small sphere which is offset from the center of the base while 4259
Figure 2. SEM images showing the top-down view of gold nanostructures formed on the (111) surface of MgAl2O4 substrates. The sequence of images is chosen to show progressively larger spheres atop the base structures. Note that only the smallest sphere, shown in (b), is offset from the center of the triangular base and that the base size is slightly larger when supporting larger spheres, as is the case for (e) and (f). The size of each image is 130 × 130 nm2.
for the larger spheres, this asymmetry disappears. Such asymmetries are observed for all three substrate orientations, but only those nanostructures formed on the (111) substrate consistently show a centrally placed sphere for the large sphere sizes. Also noteworthy is a systematic effect whereby the size of the triangular base structure increases for sphere diameters greater than 80 nm (see Figure 2e and f). The base structures formed on each substrate orientation are a clear consequence of the epitaxial relationship formed between gold and the latticed-matched MgAl2O4 substrate. This is apparent from the fact that the geometries of the base structures mimic the underlying symmetry of the substrates. It is also likely that the base sizes are a consequence of the substrate-imposed strains. Arguments based on epitaxy, however, cannot explain the self-assembly of the gold spheres atop the base structures and the associated necking behavior which facilitates their connection to the base. It is our hypothesis that the necking behavior results from an attempt to minimize the surface energy of the structure. Thus, the overall shape of these nanostructures is governed by an interplay between the constraints imposed by epitaxy and a requirement that the surface free energy be minimized. This situation has much in common with formation of soap bubbles affixed to a wire frame.38 This statement is based on the facts that the frame imposes a constraint analogous to that imposed by lattice mismatch and that the shape of the soap bubble is, to a large degree, determined by the surface free energy. This analogy provided the impetus for applying the well-developed models associated with soap bubble formation to the nanostructures described here. Such modeling has also been successfully used to predict the equilibrium shape of biological lipid bilayers (blood cells) when exposed to abnormal pressure, temperature, magnetic, and chemical environments.39-44 The gold nanostructures were modeled as a continuum elastic surface constrained by a footprint. Three different footprint geometries (square, equilateral triangle, and rectangle) were used in order to mimic the four-fold, three-fold, and two-fold symmetries associated with the (100), (111), 4260
and (110) surfaces of MgAl2O4. The size and shape of the footprint were kept constant during the simulated growths in order to match the experimental observation indicating a high degree of base uniformity. For each orientation, the contact angle (i.e., the angle between the footprint plane and the tangent plane of any surface connected to the footprint’s edge) was set to a constant where the value was chosen to be consistent with the observed faceting, as is schematically shown in Figure 3. With these constraints, the shape of an open elastic surface can be fully described by the mean curvature, H, and the Gaussian curvature, K, while its corresponding elastic properties can be characterized by a bending modulus κ and a Gaussian modulus κG. The surface energy (F) can then be formulated as F)
∫ 2κ H dA +∫ κ KdA + λS + PV 2
G
(1)
where λ, V, S, and dA are the particle’s surface tension, volume, total surface area, and surface area element, respectively.45,46 The pressure, P, serves as a Lagrange multiplier which ensures that a constant volume is enclosed between the structure and the footprint plane. The second term gives the integrated Gaussian curvature, which is constant according to the Gauss-Bonnet theorem.47 For a given surface tension and volume, the equilibrium shape will correspond to an energy minimum determined by the shape equation δF ) 0. The structures are more readily solved by first rescaling the free energy of the model to become dimensionless, such that F˜ )
∫ (κ˜ H˜ /2 + 1)dA˜ + P˜V˜ 2
(2)
where A˜ ) A/S0
V˜ ) V/S3/2 H ) HS1/2 0 0 1/2 ˜ κ˜ ) κ/λS0 P ) PS0 /λ F˜ ) F/λS0
(3)
and S0 is the area of the base. Thus, according to this dimensionless free-energy expression, there are two independent controlling parameters, κ˜ and P˜. Helfrich and Ou-Yang45 have analytically solved the shape equation for some symmetrical geometries. For the work presented here, the surface is sectioned into discrete elements using a triangulation mesh, and a simple dissipative model is used to minimize the energy, as in eq 248 δF˜ ∂r ) -M ∂t δr
(4)
where r(t) is the position vector of a point on the particle surface at the time t and M is a kinetic coefficient. These methods, developed by Taniguchi et al.,48 are, however, unable to simulate large deformations. To circumvent this limitation, we employed two techniques, equiangulation and vertex averaging, available through the Surface Evolver Nano Lett., Vol. 9, No. 12, 2009
Figure 3. Proposed faceting of the base structures grown on (a) [100]-, (b) [111]-, and (c) [110]-oriented substrates.
Figure 4. Simulations based on the continuum elastic model showing the shape evolution of structures with a triangular footprint as the total volume is progressively increased. The shape of these modeled structures is remarkably similar to that of the self-assembled gold nanostructures formed on (111) MgAl2O4 substrates (Figures 1b and e and 2). The scale is in arbitrary units.
software developed by K. Brakke.49 Following the procedure of Lim et al.,39,42,43 the curvature was discretized based on the methods of Julicher,50 which exactly describe the curvature in the continuum limit. The variational derivative used in the triangulation scheme was evaluated analytically. For the Surface Evolver technique, variables were solved numerically when analytical variations for discrete curvatures proved difficult. Using the numerical methodology, a progression of structures with increasing volume were calculated using square, triangular, and rectangular footprints having contact angles of 54.7, 70.5, and 35° (long-axis) by 45° (short-axis), respectively. The chosen contact angles are consistent with the inferred faceting, as shown in Figure 3. For each case, the footprint area and surface tension are set to unity, while Nano Lett., Vol. 9, No. 12, 2009
the bending modulus is allowed to vary. Figure 4 shows the calculated progression for the triangular footprint. As the volume is increased, there is an evolution from a nearly flat base, to a base with a bulge, and then finally to a spherical structure supported by a necked region to a triangular base. These simulated structures are remarkably similar to the gold nanostructures formed on the (111) MgAl2O4 substrate (see Figures 1b and c and 2). Similar trends are observed for the square and rectangular footprints. Figure 5 shows the simulated high volume structures for the square and rectangular footprints, which, once again, are consistent with experimental observations. The simulations do not, however, account for any of the observed asymmetries. The shape of the base structures of the self-assembled gold nanostructures is strongly influenced by epitaxy and the 4261
Figure 5. Simulations based on the continuum elastic model showing the expected high volume shape for the (a) square and (b) rectangular (length/width ) 1.42:1) footprints. These structures show a resemblance to the self-assembled gold nanostructures formed on the (100) and (110) MgAl2O4 substrates (Figure 1) but show none of the observed asymmetries. The scale is in arbitrary units.
Figure 6. A comparison of the (a) topographical color map derived from the continuum elastic model and (b) the AFM image of a self-assembled gold nanostructure deposited on the (100) MgAl2O4 substrate. Note that the simulation predicts both the presence of four lobes at the corners and a central depression. The scale of the topographic image is arbitrary, and the scale of the AFM image is 10 nm.
underlying symmetry of the substrate surface. That being said, it is difficult to account for the hollowed-out center observed for the base structure formed on the (100) MgAl2O4 using epitaxy-based arguments. This feature is, however, predicted by the continuum elastic model. Figure 6a shows the topographical color map obtained from the modeling for the low-volume structure. It clearly shows a circular depression in the middle of the structure as well as a lobe near each corner. Motivated by the simulation results, we examined the topography of the self-assembled gold nanostructure using atomic force microscopy (AFM). Figure 6b shows a tapping mode AFM image of the base structure obtained using a Digital Instruments scanning probe microscope (SPM) and a NanoScope IIIa controller. Even though the features of the nanostructure are somewhat washed out due to the fact that the resulting image is a convolution of the nanostructure and the AFM tip geometry, the nanostructure’s four lobes and central depression are clearly visible. Taken together, the experimental observations and the continuum elastic modeling results strongly suggest that epitaxy and a minimization of the surface free energy are the two primary drivers in determining the shape and size of the self-assembled gold nanostructures. The fact that similar structures have not been previously observed is likely a consequence of the synthesis route used. The route 4262
employed here not only involves temperatures well in excess of those typically used when forming substrate-supported nanostructures but also requires an annealing profile which accesses two temperatures. It is possible that the initial 1100 °C anneal is needed to induce surface reconstructions in the MgAl2O4 substrates which are essential to the growth of these nanostructures. Surface reconstructions have been shown to strongly influence the growth of both nanostructures28,34,35 and thin films51 when using (100) SrTiO3 substrates. We, however, consider it more likely that the formation of these nanostructures requires temperatures in excess of the melting point of bulk gold (1064 °C). Significant deviations from the bulk value, due to finite size effects, are considered unlikely since such effects appear to occur only in nanostructures smaller than 5 nm.52 Once molten, the nanostructures are cooled to 1000 °C and held at this temperature, which is just below the melting point. Such a temperature allows for solidification while maintaining high adatom mobility. The fact that this fabrication step is crucial to the formation of the observed intricate nanostructures provides compelling evidence that considerable adatom motion is essential. In this scenario, it is likely that an Ostwald-like ripening process will play a role where larger nanostructures grow at the expense of smaller ones. Substrate surface steps, due to the inherent miscut of the substrate,53 could also influence the process by providing energetically favorable nucleation sites. Nanostructure formation is also heavily reliant on the epitaxial relationship between the nanostructure base and the underlying substrate. This relationship determines the crystallographic alignment of the base structures, while the consistency in size is likely a consequence of the strain imposed by lattice mismatch. Once the 1000 °C anneal ends, the adatom motion will be quickly quenched by the lower temperatures, allowing no further alterations to the shape or size of the nanostructures. The end result is intricately shaped nanostructures whose size and shape are determined by a minimization of the surface free energy while simultaneously being subject to the constraints imposed by epitaxy. In conclusion, we have demonstrated a new synthesis route for the fabrication of self-assembled gold nanostructures. The shape and size of these supported nanostructures are highly dependent upon the crystallographic orientation of the substrate. Continuum elastic modeling shows remarkable success in predicting the shape of the structures with the implication that the self-assembly is driven by strained epitaxy and a minimization of the surface free energy. Acknowledgment. This work is funded by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Ontario Centres for Excellence, and the Canadian Institute for Advanced Research (CIFAR). The authors also acknowledge The Canadian Centre for Electron Microscopy (CCEM) for access to their facilities, Andy Duft for AFM technical support, Yuepeng Zhang for interpretation of CBED results, and Svetlana Neretina (Temple University) for helpful discussions. Simulations were carried out using the McMaster University SHARCNET facilities. Nano Lett., Vol. 9, No. 12, 2009
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