Generalization of Self‐Assembly Toward Differently Shaped Colloidal Nanoparticles for Plasmonic Superlattices

Periodic superlattices of noble metal nanoparticles have demonstrated superior plasmonic properties compared to randomly distributed plasmonic arrangements due to near‐field coupling and constructive far‐field interference. Here, a chemically driven, templated self‐assembly process of colloidal gold nanoparticles is investigated and optimized, and the technology is extended toward a generalized assembly process for variously shaped particles, such as spheres, rods, and triangles. The process yields periodic superlattices of homogenous nanoparticle clusters on a centimeter scale. Electromagnetically simulated absorption spectra and corresponding experimental extinction measurements demonstrate excellent agreement in the far‐field for all particle types and different lattice periods. The electromagnetic simulations reveal the specific nano‐cluster near‐field behavior, predicting the experimental findings provided by surface‐enhanced Raman scattering measurements. It turns out that periodic arrays of spherical nanoparticles produce higher surface‐enhanced Raman scattering enhancement factors than particles with less symmetry as a result of very well‐defined strong hotspots.


Introduction
Noble metal nanoparticles (NPs) are known for their ability to confine visible light at the nanoscale. The wavelength of the light that causes corresponding plasmonic resonances can be tuned by changing the shape, dimensions, material, or the environment of the nanostructure. [1,2] To extend the features of plasmonic resonances, NPs can be arranged into periodically organized clusters, also called superlattices. The NPs can then interact with each other through far-field coupling, [3] giving rise to plasmonic surface lattice resonances with interesting properties, as high Q factors, [4] near-field enhancement [5,6] or tunability by period, [7] incident angle, [8] and polarization. Moreover, the inner structure of a unit cell of the periodic arrangement strongly influences the plasmonic response. Fabrication of periodic metallic nanostructures is generally done by electron-beam lithography (EBL), which allows for precise placement and control of the NP shape. [9] Corresponding nanostructures that support plasmonic surface lattice resonances have shown interesting applications in metamaterials, nanolasing, long-range energy transport, or structural plasmonic color generation. [10] Unfortunately, EBL is an expensive and slow technology, and the fabrication of sub-wavelength gratings of 1 cm 2 can even take several days. Moreover, the spatial resolution of EBL is too low for fully taking advantage of strong plasmonic coupling between NPs. [11][12][13] Lately, several chemical growth techniques, such as vaporor liquid-phase assembly, have been applied to synthesise single NPs of various shapes, such as circular, [14] triangular, [15,16] hexagonal, [17] spiral [18,19] and star-shaped [20] geometries. In a recent publication, Neal et al. demonstrate the synthesis of regular large-area, single triangular particle arrays, formed by EBLassisted liquid-phase growth. [21] Self-assembly of colloidal NP, on the other hand, is a lowcost and fast alternative for producing plasmonic superlattices. [22] Progress in the synthesis of monodisperse colloidal NPs makes the production of useful building blocks with close-packed clusters of NPs possible. [23,24] Self-assembly is based on van der Waals forces and allows for close packing of NPs with interparticle distances even below 1 nm, realized by controlled functionalization of the surfaces. The range below 2 nm is highly interesting for strong plasmonic coupling [25] because of strong electric field enhancement at the junctions. [26] Such so-called hotspots can be exploited for sensing, as for example surfaceenhanced Raman spectroscopy (SERS) [27,28] or surface-enhanced infrared absorption. [29] Self-assembly using nanostructured templates provides a versatile technology platform for producing plasmonic substrates with periodically arranged NP clusters. For trapping the NPs in the wells of the template, different forces can be utilized, as for example Coulomb attraction, [30] chemical bonding [31] or capillary forces. [5,32] Periodic arrays of single NPs do not produce high near-field enhancement compared to close-packed clusters of NPs, thus limiting their application in SERS. The fabrication of close-packed NPs by a template-assisted self-assembly process with micrometer wells was demonstrated by the authors before. [32] By decreasing the lattice period to sub-wavelength regions using superlattices of nanospheres, near-field enhancement due to lattice effects was observed for SERS. [5] Assembling a controlled number of NPs into clusters on largescale has still remained a challenge, [33] mainly because of the coffee ring effect. [34] However, homogeneity on a large scale supplies homogeneous near-field enhancement and allows for quantitative mapping of analytes by SERS. [35] At the same time, a good control of the number of NPs in a cluster gives rise to controlled optical properties. [36][37][38] By using single anisotropic NPs instead of spheres, higher extinction cross sections, and hence, higher near-fields can be achieved. So far, few studies have shown the assembly of anisotropic NPs into clusters, [39] and a comparative study of the optical properties of superlattices comprising different NP shapes is still lacking by today. The understanding of the optical response of such systems would help optimize the designs of plasmonic substrates for surface-enhanced spectroscopies.
At specific matching between lattice period and excitation wavelength, NP clusters can coherently interact with each other due to in-plane diffracted waves, yielding similar phenomena as Rayleigh or Wood anomalies. [40] Especially in case of homogeneous superlattices, stronger extinction and increased near-field enhancement result. The sharpness of plasmonic resonances also correlates with the uniformity in size of the NPs, as demonstrated for EBL-produced nanostructures. [41] This property is a crucial parameter for nanolasing applications, where high Q factors play an important role. [4] Motivated by these findings and based on the developments of a template-assisted assembly technique for Au nanospheres, [5] we extended the templated self-assembly process driven by capillary forces to assemble a controlled number of nanospheres, nanorods, and nanotriangles into superlattices on centimeter scale. During assembly, a nanostructured mold confines the NPs in periodically arranged wells. We first show how the chemical composition of the NP dispersion influences homogeneity. The impact of homogeneity is studied with respect to extinction properties and near-field enhancement. Second, we demonstrate the generalization of our process regarding different NP shapes. The fabrication of superlattices with a defined number of NPs in each cluster allows us to compare their extinction properties and the formation of hybrid plasmonic modes originating from the coupling of cluster and lattice modes. Both experimentally deter-mined extinction properties as well as near-field enhancement measured by SERS are complemented by electromagnetic simulations.

Development of Self-Assembly
The systematic investigation of the fabrication technology is inspired by developments of a self-assembly process for nanorods coated with MUHEG (11-mercaptoundecyl)hexa(ethylene glycol) and stabilized with cetyltrimethylammonium bromide (CTAB). [34] The technology builds upon a template-assisted selfassembly process, which constitutes a versatile and easily scalable technique for creating nanostructures. Figure 1 illustrates the fundamental steps for assembling Au NPs. A droplet of a Au NP dispersion-in our case functionalized with polyethylene glycol (PEG) and stabilized with cetyltrimethylammonium chloride (CTAC)-is cast onto the center of a nanostructured mold made of polydimethylsiloxane (PDMS). Actually, PEG is stabilizing the NPs, however, it was figured out previously that without CTAC the NPs start to aggregate. [24] After a waiting time of typically a few tens of seconds, a glass substrate is put on top of the droplet yielding a thin film of the NP solution between the glass and the PDMS template. During the drying process of this liquid film, the NPs get trapped in the wells of the template through capillary forces, and after complete drying, the substrate is removed featuring a patterned NP superlattice. Unlike capillary-assisted self-assembly, which uses a motorized blade to drag the meniscus over the nanostructured mold, templated self-assembly takes advantage of the meniscus movement due to drying of the liquid film, and particles get trapped at the meniscus through capillary forces. A technological challenge is to control the drying front of the meniscus for firstly getting a precise number of NPs into one well, and secondly for achieving homogeneity over the entire macroscopic sample. The homogeneity of the superlattice is strongly affected by the coffee ring effect, which is an accumulation of NPs at the liquid-substrate contact line due to convection flows. A previous study showed that ethanol as a co-solvent supports the fabrication of homogeneous samples on a large scale. In the presented work, we extend the studies regarding the impact of waiting time, the influence of systematic changes of ethanol concentrations as co-solvent, and the effect of surfactant concentration in the solution of dispersed NPs on self-assembly homogeneity [34] towards a generalization to further particle geometries, as spheres, rods, and triangles. All these parameters allow us to control the Marangoni flows, and hence, to optimize the self-assembly conditions.
The repartition of NPs in the droplet is changing over time as a result of different flows in the droplet. [42] . The second row in Figure 1 shows the evolution of the droplet at different waiting times. After 45 s, a golden film starts to appear at the rim of the droplet, indicating a high accumulation of NPs between the fluidair interface in the form of a close-packed layer. After 120 s, the droplet appears totally golden. Putting the substrate at different stages of waiting time onto the droplet, results in different assembly patterns, as depicted in the third row of Figure 1   A golden layer appears at specific waiting times due to accumulation of NPs at the interface; 3rd row: scheme of Marangoni flows in the droplet at different waiting times, where the black arrows indicate the general resulting movement of Au particles; 4th row: visual inspection and SEM images at the three flow regimes. The red frames in the blue insets of visual inspection define the area of SEM images (outer image with red frame); the yellow frame defines the SEM images in the 5th row: magnified SEM images for different waiting times that correspond to the different regimes of Marangoni flow. The colored frame refers to the zone of SEM images in the 4th row. tension gradients. As reported by Christy and Kim, [43,44] in a droplet composed of water, ethanol and surfactant, different Marangoni flows can develop: In the first regime, the solutal Marangoni flow dominates, as illustrated in the third row of Figure 1; it emerges from the differences in ethanol concentration along the contact line of the droplet due to a non-uniform evaporation rate along the contact line and creates a circular flow, impeding the NP accumulation at the droplet rim. When ethanol evaporates, the solutal Marangoni flow becomes weaker and the surfactant-driven Marangoni flow takes over; this second regime is known as flow reversal and is extensively studied theoretically by various research groups. [45,46] The surfactant-driven Marangoni flow arises from a surface tension gradient caused by the gradient of concentration of surfactant molecules at the www.advancedsciencenews.com www.small-methods.com contact line of the droplet. Changes in surfactant concentration will cause changes in the intensity of this type of flow. During this phase, the NPs accumulate at the edge, which is seen by the formation of a golden film at the rim of the droplet. [42] Finally, in the third regime, a close-packed layer is formed on the droplet, and the presence of the NPs reduces the shear stress evolved through the gradient of the surfactant. In this last stage, we go back to a coffee ring-like scenario with outward flow caused by convection.
Visual inspection of the samples at different time stamps shows a ring that indicates the margins of the droplet, which can be seen in the insets of the scanning electron microscopy (SEM) images in the 4th row of Figure 1. The lighter blue indicates a higher NP accumulation, as confirmed by the SEM images. Before 45s of waiting time, the ring is depleted of NPs; after 45s, the ring presents an accumulation of NPs; and after 120s, the whole droplet area is filled with Au NPs. The development of the selfassembly in relation with the different flow regimes is demonstrated bySEM images of superlattice samples at different time stamps in the last row of Figure 1. It turns out that the regularity of self-assembled clusters is best between around 60 and 90 s.
To find the optimum parameters for self-assembly, the surfactant and ethanol concentrations were systematically changed, and assemblies for different waiting times were processed. A detailed kinetic study can be found in Figure S1, Supporting Information. An increase in the concentration of the surfactant and a decrease of the concentration of ethanol in the solution show comparable effects, namely the accumulation of NPs in the center of the substrate at low waiting times. Increasing the surfactant's concentration favors the surfactant-driven Marangoni flow; accordingly, the flow reversal happens at shorter waiting times. Likewise, by reducing the ethanol concentration, the solutal Marangoni flow gets less important, resulting in a flow reversal at shorter waiting times. The best parameters for homogeneous self-assembly were found to be 200 μ M CTAC as surfactant, 66% concentration of ethanol, and waiting times around 60 s. Figure 2 shows SEM images of plasmonic superlattices from 65 nm Au nanospheres fabricated with different ethanol ratios, while keeping the other parameters fixed (200 μm CTAC and 60 s waiting time). Whereas at low ethanol ratios of 0% and 33% the NP clusters exhibit poor homogeneity, the periodical organization becomes more homogeneous at higher ethanol ratios. The regularity of the clusters strongly influences the optical properties, as shown in Figure 3a. For 50% and 66% of ethanol, a strong and sharp extinction peak appears around 695 nm; at lower concentrations of 0% and 33%, only a little peak develops at that wavelength. Best performance is achieved at around 66% of ethanol. The extinction results very nicely reflect the quality of the self-assembly reflected in the SEM images.
As a figure of merit for homogeneity, the full width at half maximum (FWHM) of the plasmonic lattice resonance at 695 nm is plotted in Figure 3b. By increasing the ethanol concentration from 0 to 66%, the FWHM decreases from 400 nm to 50 nm; further increase in ethanol concentration again broadens the peak. At concentrations of 50-66%, well-organized clusters with mostly 6-7 NPs per cluster are formed. A further increase to 75% results in a lower transfer of NPs to the substrate due to a lower concentration of NPs in the accumulation zone caused by Marangoni flow reversal at longer times.
Homogeneity in terms of regular superlattices leads to stronger far-field coupling and has a strong effect on the sharpness of lattice resonances in corresponding extinction spectra. Near-field enhancement depends on the size of the NPs, the interparticle distance, the surrounding dielectric medium, the number of NPs per cluster, and their arrangement in the cluster. Considering this complexity, a controlled number and arrangement of NPs in each cluster on a large scale is essential for triggering the near-field, and hence, for improving far-field coupling.
To study the effect of homogeneity on near-field enhancement, SERS spectra from 4-mercaptobenzoic acid (4-MBA) as target were measured. Due to its thiolated groups, 4-MBA binds covalently to the gold NPs and constitutes an excellent agent for SERS measurements. Spectra were taken at 100 random points over the plasmonic substrates to probe the homogeneity of the near-field enhancement. For each ethanol concentration, 100 SERS spectra were averaged and are plotted in Figure 3c. The highest signal intensities are found for the 12 ring stretching vibration at 1079 cm −1 and for the 8a ring stretching vibration at 1591 cm −1 , associated with the phenyl ring of 4-MBA. Figure 3d shows the performance in terms of the SERS enhancement factor for the characteristic Raman peak at 1079 cm −1 and the standard deviation calculated from the statistics of the 100 randomly taken SERS spectra, which represents the deviation from the averaged peak intensity in percentage. Both figures of merit from this graph reaffirm highest performance for the sample made with 66% ethanol. Using our co-solvent assisted process, we could reduce the SERS standard deviation from 120% to 15% on a sample with the remarkable size of 8 ×8 mm 2 , which again reflects best sample homogeneity for processing with 66% ethanol.

Results and Discussion
Shape, size and arrangement of NPs have a great impact on SERS enhancement, [47] and it is well-known that anisotropic NPs can strongly amplify the electric field, especially at tips and sharp edges. Due to the complexity of fabricating welldefined lattice structures of clusters from differently shaped NPs, there are only few comparative studies available that investigate corresponding SERS effects. [48] This motivated us to extend the fabrication of well-ordered plasmonic superlattices to other shapes than spheres and study their optical properties. SEM images in Figure 4a-c demonstrate that the process can be transferred to and generalized for other NP shapes. Particularly, the differently shaped NPs were assembled into regular superlat-tices using the same optimized parameters developed for gold nanospheres. Nanorods of 110 nm× 30 nm were assembled in wells of PDMS molds with periods of 400 and 500 nm, yielding primarily superlattices of nanorod trimers assembled at their long sides, tetramers with side by side arrangement and pishaped arrangements with 3 nanorods side by side and the fourth www.advancedsciencenews.com www.small-methods.com adjacent at the tips. In the same way, nanotriangles of 40 nm edge length were assembled, yielding clusters of side-by-side assemblies with various morphologies.
For a proper understanding of the UV/Vis/NIR spectra of superlattices, we first analyzed the extinction properties of dispersed gold NPs displayed in black in Figure 4d-i. For instance, the nanosphere dispersion displays an extinction peak at 535 nm due to the dipolar resonance of plasmonic NPs, while the nanorods dispersion displays two extinction peaks, one at 520 nm, corresponding to the transversal plasmon mode, and the other around 860 nm corresponding to the longitudinal plasmon mode. The nanotriangles dispersion displays a strong and narrow extinction peak around 650 nm, corresponding to a longitudinal in-plane mode, and a weak shoulder at 530 nm, corresponding to a transversal out-of-plane mode. [49] Based on measured data from dispersed NPs, the simulation parameters, as for example the complex dielectric properties, the dimensions of NPs, and the refractive index and functionalized PEG layer thickness, were optimized as starting point for the simulations of absorption spectra of superlattices.
The coupling between plasmonic lattice modes and clusterspecific plasmons was studied by UV/Vis/NIR spectroscopy for superlattices of these three particle types. By finite-element method (FEM) simulations, the experimental data were analyzed regarding the occurrence of cluster and lattice-specific resonances. For better visual comparison of the peaks of NP extinction curves in dispersion with the NPs in supperlattice, the curves are normalized at the wavelength of 300 nm (only the superlattice with 400 nm period) in Figures 4d-g and 4i. Since the superlattices include sub-units with different numbers, orientation and morphologies of particles, the simulations were carried out with different arrangements that best reflected the statistical occurrence of experimental assemblies (see Figure S2, Supporting Information). Experimental extinction spectra were taken with unpolarized light, and hence, simulation data were averaged as first order approximation from two perpendicular linear polarization states. Moreover, for each particle type, two morphologies were taken into account: hexamers and heptamers for spheres, trimers with parallel rods and tetramers with one rod along the tips of the three other parallel ones, circular hexamers and a linear hexamer arrangement of triangles.
It turned out that the simulated absorption spectra of heptamers from spheres are invariant to the rotation of the polarization plane of the incoming light. This finding was also experimentally confirmed. The same is true for nanotriangles in circular hexamers where the absorption spectra is identical for the two polarization states. The anisotropy of the nanorods leads to different absorption characteristics for the polarization states along the longitudinal and transversal axis. More details of the simulation data are included in the Supporting Information.
As a result of plasmonic hybridization, the plasmonic modes in the extinction spectra of superlattices differ from those of dispersed NPs. Basically, one has to distinguish between localized surface plasmon resonances (LSPR), cluster-specific plasmons and plasmonic lattice effects that arise from in-plane diffracted waves. The latter ones are the analog to Rayleigh or Wood anomalies in metal gratings, where in-plane diffracted orders couple to the periodic structure of the superlattice and produce increased extinction at a specific wavelength depending on lattice period and refractive index of substrate and superstrate. [50] Generally, LSPRs from single NPs do also appear in the extinction spectra of plasmonic superlattices, [51,52] however with spectral shifts due to intra-cluster coupling and different refractive index in the environment; the optical properties of superlattices were measured in air. The shifted modes can be explained by anti-bonding coupling modes between the assembled NPs, generally leading to a small blueshift of the LSPR of single NPs. [53] Detailed explanations of the extinction and absorption spectra are given subsequently for each particle type individually.
In the case of nanosphere simulations, an extinction shoulder appears at around 520 nm due to dipolar resonance, which corresponds to the LSPR of dispersed NPs. Nanosphere superlattices show a strong plasmonic mode shifting with the lattice period, as in Figure 4d. Since simulation plots combine only two major cluster morphologies and two identical polarization states for both morphologies with equal weight, two peaks appear that shift with the lattice period. For the 400 nm superlattice, the first peak is at 660 nm and arises from the coupling mode visible in the heptamer model (see Figure S3a, Supporting Information). The second coupling mode arises from hexamers for the same lattice period at 720 nm (see Figure S3b, Supporting Information); the corresponding coupling modes for the 500 nm superlattice appear at 685 nm and 750 nm. At 780 nm appears another coupling mode originating from the heptamer clusters, which does not shift with the lattice period, and as a result, it appears in both superlattices. Further coupling mode is observed in the simulated absorption spectra of both hexamers and heptamers around 550-560 nm (see Figure S3a,b, Supporting Information). A Similar coupling mode is experimentally visible at a higher wavelength of 600 nm, for both lattice periods. Various studies attributed such modes to higher-order longitudinal bonding coupling modes that generally appear at a slightly higher wavelength than the LSPR of single nanospheres. [53,54] As expected, colloidal nanorods show two main plasmonic resonances, the fundamental and dominant longitudinal mode at 930 nm, depicted in Figure 4h, and the weaker transversal mode at 420 nm. The corresponding experimental results show slightly blue-shifted and broadened resonances compared to simulations. We address this discrepancy to the synthesis-induced variations in the rods' tip radii, influencing the experimental extinction profiles. The simulations in Figure 4h are a result of the superimposition of two polarization states and two dominant cluster morphologies. The superimposition approximates multiple orientations and varying numbers of NPs in the clusters, as can be seen in the SEM image. In practice, the measured extinction profile provides a much smoother curve than the simulations due to this strong variety of cluster configurations. The simulation plot shows that four distinct main peaks contribute to the optical response of each superlattice parameter. The first peak is visible at around 625 nm, which does not change with the lattice parameter. This peak corresponds to the transverse polarization of three NPs per cluster. The second peak, also for three NPs per cluster, is the longitudinal polarization, visible at 695 nm for 400 nm superlattice and shifts to 730 nm for 500 nm superlattice (see Figure S4, Supporting Information). The four-NP configuration shows a slight shift in transverse polarization with the lattice period, from 640 nm to 650 nm due to one transversally aligned NP. In longitudinal polarization of four nanorods, the www.advancedsciencenews.com www.small-methods.com plasmonic resonance shifts from 750 nm to 790 nm for 400 nm and 500 nm lattice period (see Figure S5, Supporting Information), respectively. The superimposition takes all configurations with equal weights. Interestingly, the longitudinal polarization of four nanorods agrees very well with experimental results with plasmonic resonances at 750 nm and 772 nm for the two superlattice parameters. The result implies that the dominant contribution originates from the four-nanorod configuration in longitudinal polarization over other configurations visible in the SEM image.
The simulation results for dispersed nanotriangles match very well experimental data for the main peak at 655 nm, which is caused by plasmonic resonances along the edges between two adjacent nanotriangle vertices. There are two smaller peaks at 530 nm and 580 nm due to resonances between vertices and their opposite edges. The nanotriangle plasmonic resonances consequently depend strongly on their edge length and thickness. Similar to simulations for nanospheres and nanorods, we superimposed four major models consisting of two polarization states and two cluster morphologies. For six circularly arranged nanotriangle clusters, the polarization is invariant with the rotational angle, like in the case of heptamers. The plasmonic resonance at 660 nm shifts to 680 nm when the superlattice parameters change from 400 nm to 500 nm for both polarizations (see Figure S6, Supporting Information). The other statistically significant morphology is a row of four nanotriangles, where similar results occur as with three nanorods in transverse polarization. The plasmonic resonance at 590 nm is invariant with the lattice parameter, and hence, a cluster-specific feature. For the longitudinal direction, the plasmonic resonance at 775 nm shifts to 800 nm when the lattice parameters change from 400 nm to 500 nm. The simulation results for the 400 nm superlattice with circular symmetric clusters of nanotriangles shows better agreement with the experiment, implying that the dominant morphology is the cluster of such symmetrically arranged nanotriangles. By changing the lattice period to 500 nm, other coupling mechanisms become dominant, and a broad peak around 700 nm appears in the experiment, implying the influence of other morphologies over the symmetrical nanotriangle clusters.
For a deeper understanding of the complex structure of the absorption spectra, more details are included in the Supporting Information. Plasmonic resonances have different origin, as the individual particle, various intra-cluster couplings, and intercluster couplings across the lattice. In Figure S7, Supporting Information, the extinction properties of single hexamer and heptamer clusters of nanospheres are explained by simulations and compared to the two lattice configurations of 400 nm and 500 nm. Figure S8, Supporting Information explains the nature of the individual absorption peaks in detail by corresponding nearfield plots.
To enhance Raman lines in SERS spectra, the excitation wavelength should ideally match the plasmonic response of the measured extinction spectra. [49,55,56] Changing the periods of plasmonic superlattices, as shown above, helps adapt the near-field response to typical laser light sources. In our case, superlattices with 500 nm period show stronger absorption/extinction for 785 nm excitation wavelength, whereas the 400 nm lattice is much better adapted to 633 nm excitation for higher SERS enhancement. Figure 5a,b show the influence of laser wavelength in com-bination with two different lattice periods for all three particle types. The figure shows SERS spectra, averaged from 100 random points over the sample, of 4-MBA as target molecule and demonstrate that the lattice period can be easily adapted to enhance SERS signals for specific laser excitation wavelengths. The standard deviations of the intensity of the peak at around 1080 cm −1 , calculated from 100 spectra across the sample, are in the order of 20%, which reflects quite homogeneous self-assembly properties over the substrates. More details of measured SERS spectra with different configurations can be found in Figure S9, Supporting Information.
The near-field enhancement factor EF(⃗ r, ) as a function of frequency and position of the NP surface was approximated using E 4 in the simulations (see Comutational Methods). The approximation assumes negligible difference between Raman emission and plasmonic excitation frequencies. The simulations show the same qualitative behavior as the experimental findings, as outlined in Figure 5c. Corresponding analytical SERS enhancement factors (AEF) were calculated for the peak at 1600 cm −1 , using  Figure S10, Supporting Information and exhibit several ethanol peaks, at 885, 1053, 1099, 1278 and 1458 cm −1 , as well as a peak due to the 8a phenyl ring stretching of 4-MBA at 1600 cm −1 . In comparison, SERS spectra show several peaks originating from 4-MBA with two dominant ones at around 1080 and 1600 cm −1 . Since the Raman spectra show only the peak at 1600 cm −1 , this peak was used to calculate the AEFs of the different superlattices and configurations. Our AEF values vary between 6.8 · 10 4 and 3.06 · 10 6 for plasmonic superlattices of different NP shapes, which lies within the highest AEFs reported in the literature for assembled colloidal NPs. [57,58] Interestingly, the gold nanosphere superlattices yield the highest AEFs, which contradicts our first hypothesis that anisotropic gold NPs would result in better SERS performance. To confirm this result, the AEFs were re-calculated by integrating the simulated electric field over the NP surface of the different superlattices (simulated EF). Examples of electric field distributions for 633 nm and 785 nm excitation wavelengths for superlattices of differently shaped NPs can be seen in Figure 5. Taking into account the different morphologies of clusters, the simulated EFs were averaged in the same way as described above for the absorption spectra. The average simulated EF for nanorod superlattices at 633 nm excitation predicts two times higher SERS signals compared to nanosphere superlattices, contrary to measurements. However, in Figure S11, Supporting Information, the simulated EF calculations for hexamers with spheres, four nanorods, and circularly arranged nanotriangles with transversely polarized light are in close agreement with the measured AEF; discrepancies are a result of typical sample inhomogeneities. Even though the self-assembly process delivers reasonably well-ordered samples, the experiment with real Figure 5. a) SERS spectra of 4-MBA using nanosphere, nanorod, and nanotriangle superlattices at 633 nm excitation for a 400 nm lattice. b) SERS spectra of 4-MBA using nanosphere, nanorod, and nanotriangle superlattices at 785 nm excitation for a 500 nm lattice. c) Experimental SERS enhancement factor and simulated E 4 approximation averaging two polarization states and two cluster morphologies as in Figure 4. d) Near-field plots of 400 nm superlattices at 633 nm excitation wavelength with longitudinal polarization. e) Near-field plots of 500 nm superlattices at 785 nm excitation wavelength with longitudinal polarization. samples exhibits uncertainties, and the simulations consider only two different polarization states and one single orientation of perfect clusters in the lattice. As a final result, we can deduce that clusters of anisotropic NPs do not necessarily yield higher SERSenhancement.

Conclusion
We optimized the templated self-assembly process for periodically arranged gold NP clusters by varying several parameters that influence the Maragoni effect, which occurs as a result of surface tension gradients at the interface between two phasesin our case the liquid-gas interface. Best results in terms of homogeneous superlattices on a large scale were achieved for 200 μm CTAC as a surfactant in the NP dispersion, 66% ethanol concentration, and a waiting time of 60 s before confining the fluid in the nano-wells of the template. The homogeneity of periodic clusters over the whole substrate, as a result of the optimization process, produces sharper resonances in the extinction spectra and stronger near-field enhancement, which was demonstrated by SERS measurements. The self-assembly process was successfully transfered from spherical NPs to rods and triangles. Thanks to a good control of the self-assembly process, the SERS signals displayed a good homogeneity over the whole sample for nanorods and nanospheres, and a moderate homogeneity for nanotriangles. Changing the period of the lattice allows us to modify the plasmonic surface lattice resonances, and hence, to vary the extinction properties. Simulated absorption spectra www.advancedsciencenews.com www.small-methods.com for different lattice periods and particle types confirmed the experimental findings and help us understand the nature of the plasmonic resonances. As a result of the lattice effect, the nearfields can be increased for a proper combination of lattice period and Raman excitation wavelength. In our case, the superlattices with 500 nm period exhibit higher SERS enhancement using the 785 nm excitation wavelength, whereas the superlattices with 400 nm period show enhanced SERS signal for 633 nm excitation wavelength. As an interesting result, we measured-and validated by simulations-that superlattices from nanospheres provide higher SERS enhancement than their counterparts from rods or triangles, even though anisotropic particles generally produce very high electric fields. We attribute this finding to destructive interference by integration over the clusters and period and to well-defined strong hotspots in the clusters of nanospheres.

Experimental Section
Nanoparticle Synthesis and Functionalization: Synthesis of the various types of NPs followed different reported recipes from literature (nanosphere, [24] nanorods, [59] nanotriangles [23] ). For functionalization with PEG, the NPs were concentrated by centrifugation and redispersed in 1 mm cetyltrimethylammonium chloride (CTAC) to have a final concentration of gold between 2 and 10 mm (as measured by the absorption at 400 nm). Then, 10 mg mL −1 of PEG-6K was added to the solution which was left undisturbed overnight. The NPs were then washed by repeating centrifugation and redispersion in 500 μm CTAC at least 4 times. By repeating this operation several times, the PEG molecules that did not bind to the NPs are completely removed. The functionalization step is repeated by concentrating the NPs to 10 mm in 500 μm CTAC and adding 10 mg mL −1 of PEG-6K. Again the NPs are washed by repeating centrifugation and redispersion in 500 μm CTAC. Finally, the NPs are concentrated to 200 mm in 500 μm CTAC, and the final solutions are stored in the refrigerator at 8°C.
Electron Microscopy: SEM was performed using an environmental SEM (FEI Quanta 250) at an acceleration voltage of 30 kV.
UV/Vis/NIR Spectroscopy: Extinction spectra of colloidal NP dispersions were recorded with an Agilent 8453 UV/Vis/NIR spectrophotometer, using polystyrene cuvettes. Extinction spectra of dry samples were collected using a Carry 5000 UV/Vis/NIR spectrometer (Agilent). The whole sample was illuminated, which is 1 cm×1 cm; for a 400 nm lattice, 6.25×10 8 clusters are involved.
SERS Measurements: For SERS experiments, the samples were cleaned by an oxygen plasma (Diener pico) for 10 s at 100 W and 0.4 mbar, followed by a UV-ozone (bionanoforce) treatment for 5 min. The SERS substrates were incubated in a 100 μm solution of 4-MBA (4-mercaptobenzoic acid) for 2 h, freshly prepared from a stock solution in 10 mm EtOH. After incubation, the substrates were thoroughly rinsed with milliQ water to remove non-covalently bound excess molecules, followed by drying with N 2 flow. SERS spectra were obtained using a Renishaw inVia reflex Raman system equipped with a stigmatic single-pass spectrometer, a Peltier-cooled CCD detector (1024 × 512 px 2 ), a grating with 1800 grooves per mm, a continuous wave HeNe laser as excitation light source for 633 nm operated at 0.55 mW, a continuous wave diode-pumped solid state laser with wavelength locking (frequency stabilized) for 785 nm operated at 4.3 mW, and a 50× lens (LWD, NA 0.5) yielding a spot size of around 20 × 20 μ m 2 . For each sample, more than 100 spectra were taken at random positions.
Computational Methods-Finite-Element Simulations: To verify the experimental results, we performed finite-element method (FEM) simulations, using the commercially available software COMSOL Multiphysics. The simulation cell consists of the different particle arrangements in air, on top of a substrate layer, sandwiched between two 100 nm thick perfectly matched layers (PMLs) on the top and the bottom. According to the experiments, we model the infinite superlattice structure by setting the lateral cell dimensions to the lattice period and by laterally assigning periodic (Bloch) boundary conditions. We excite the structure by a linearly polar-ized plane wave of normal incidence, impinging from the top (air region). Two ports at the PML-air and PML-substrate interfaces register the system reflectance and transmittance response, respectively. For the investigation of plasmonic modes, we subsequently calculate the bulk absorbance by 1reflectance-transmittance.
Determination of Morphological and Material Parameters: Since the material and dimensional parameters and the number of particles per unit cell strongly affect the modal cluster behavior, it is crucial to fit these parameters to the fundamental experimental settings. To this end, we first optimize a model for the extinction curve of a single spherical core-shell NP in dispersion, using Mie theory calculations, [60] considering the experimental result (Figure 4d, black curve). This way, we obtain the experimentspecific gold material parameters, the NP radius, and the polymer shell thickness and refractive index. We subsequently transfer these material parameters to our gold NP cluster model. Here, the potentially porous polymer shell requires specific attention. To mitigate the surrounding medium change from water to air, we assume an effective refractive index via linear approximation, taking into account the pure polymer and water (or air) volume fraction. We found the best match with gold dispersion data reported by Olmon et al., [61] together with a radius of 34 nm for the Au spheres, 1.2 nm shell thickness, and an effective refractive index of 1.425 for the polymer shell.
Sphere Cluster Calculations: To determine the number of particles per unit cell, we performed an image processing-based statistical analysis on the SEM images. The analysis reveals that most clusters comprise 7 particles, as expected for perfect heptamers, but the median actually reads six particles per unit cell ( Figure S2, Supporting Information). Apart from that, also 5-particle clusters are statistically relevant, but much less pronounced than the 6 or 7-particle clusters. The irregularity in the number of spheres and orientations, particularly for hexamers, affects the exact matching of the plasmonic modes in simulation versus the extinction measurement.
Rod Cluster Calculations: A cluster of rods was simulated using the same material and shell settings as derived for the spheres above. To attain the optimum rod geometry, we simulated the dispersion profiles of single rods in solution, using finite-element methods. We assumed cylindrical shapes, together with rounded edges (fillets). The optimization to the experimental results for the extinction curve of a single nanorod (Figure 4e, black curve) leads to a rod length of 114.4 nm, with 16.45 nm cylinder radius and 2.5 nm fillet radius. Due to the inhomogeneity, which can affect the exact model periodicity, a perfect match to the experimental results cannot be expected. Nevertheless, both results demonstrate the strong lattice effect for a cluster of rods, again complementing the experimental findings.
Triangle Cluster Calculations: A similar procedure was followed with the nanotriangles for material and shell settings. Optimization of dispersed nanotriangle parameters based on experimental dispersion curves, yields a side length of 68 nm and a thickness of 25 nm, (Figure 4i, black curve). It turns out that the fillet radius and the polarization have crucial impact on the simulation results. We used 2 nm as the fillet radius derived from the dispersion results for cluster simulations. The SEM image shows various inhomogeneities and various orientations of the clusters. To accommodate the orientations we used two polarization states and two different cluster morphologies.
SERS Enhancement Factor Calculations: The electric field enhancement EF consists of three factors, incorporating the local electric enhancement M loc due to the material-induced plasmonic effect and the enhancement M em related to the Raman emission [62] EF = M loc ( 0 )M em ( r ), where is is a constant in the order of ≈1, depending on the Raman tensor and the scattering configuration. The enhancement factors M loc and M em depend on the the incident laser excitation frequency 0 and the Raman frequency r , respectively, and can be calculated via: www.advancedsciencenews.com www.small-methods.com where E is local electric field and E 0 is the incident electric field. For small Raman shifts compared to the considered frequency range one can assume 0 = r , which leads to the simplified EF equation: In our EF calculation we used the approximation shown in Equation 5. We implemented a two-stage integral computation, including the substrate, with and without scatterers, to obtain the locally enhanced electric field integrals and the incident electric field integrals respectively.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.