Local Field Enhancement of Pillar Nanosurfaces for SERS - The

Oct 1, 2010 - We define an enhancement factor in terms of the local field integrated over the nanoparticle surface and find that this figure of merit ...
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Local Field Enhancement of Pillar Nanosurfaces for SERS Alessia Polemi,†,‡ Sabrina M. Wells,§ Nickolay V. Lavrik,| Michael J. Sepaniak,§ and Kevin L. Shuford*,† Department of Chemistry, Drexel UniVersity, Philadelphia, PennsylVania 19104, Department of Chemistry, UniVersity of Tennessee, KnoxVille, Tennessee 37996, and Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 ReceiVed: July 14, 2010; ReVised Manuscript ReceiVed: September 8, 2010

We present studies on the analysis and characterization of a unique nanosurface used for Surface-Enhanced Raman Spectroscopy. The optical properties of a nanostructure composed of dielectric pillars that support plasmonic nanoparticles have been investigated. A theoretical analysis has been performed to determine the structural properties that localize the electric field around the silver disk. We define an enhancement factor in terms of the local field integrated over the nanoparticle surface and find that this figure of merit varies considerably depending upon the pillar attributes. An analytic model is presented and validated via full wave analysis, which elucidates the optical effects occurring in the nanostructure. Starting from the basic phenomenology associated with a single pillar structure, we show that several different effects combine to create a global resonance. Introduction Surface-Enhanced Raman Spectroscopy (SERS) has attracted renewed interest in the past decade as a useful technique for detection and sensing. One of the most intriguing uses of SERS is the detection of single molecules.1,2 Although two main mechanisms are invoked in the SERS enhancement, the chemical enhancement and the electromagnetic, it has been shown that the latter gives the larger contribution.3–5 This effective enhancement of the Raman scattering can be obtained when the molecule under study is placed near a plasmonic surface. Indeed, the localized surface plasmon resonance (LSPR) enhances the weak Raman spectrum intensity. A surface plasmon resonance in a metal is achieved when, upon illumination with light, a nanostructure sustains collective oscillations of its surface electrons.6 The resonance frequencies are greatly affected by particle material, morphology, and environment.7–10 When the excitation field is resonant with a plasmon, the metal particle will emit coherent electromagnetic radiation. This radiation increases the local field intensity that molecules feel when located near the plasmonic structure. It has been established that the Raman scattering enhancement5 scales approximately as |E|4. Thus, the use of a proper plasmonic nanostructure is essential to maximize the SERS effect. Initially, research was focused on randomly roughened surfaces, but the inherent irreproducibility suggested a shift toward well-defined surface features. In practical applications, it is indispensable to be able to reproduce and tune the SERS enhancement. This can be achieved by choosing the properties of the metals involved, the dielectric environment, the size and shape of the nanoparticles, and their interspacing.11–13 For this purpose, electron beam lithography (EBL) is an extremely * To whom correspondence should be addressed E-mail: shuford@ drexel.edu. † Department of Chemistry, Drexel University, Philadelphia, PA 19104. ‡ Department of Information Engineering, University of Modena, Italy. § Department of Chemistry, University of Tennessee, Knoxville, TN 37996. | Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831.

Figure 1. Nanopillar resulting from a fabrication sequence involving electron beam lithography, anisotropic reactive ion etching of Si, plasma enhanced chemical vapor deposition of SiO2 and physical vapor deposition of Ag. The scale bar is 200 nm.

powerful technique that provides the ability to produce metal nanoparticle structures with controlled dimensions and spacing.14–17 In particular, we have developed a recent fabrication scheme16,17 that can produce pillar nanostructures for SERS measurements (see Figure 1). The surface is obtained through a sequence that involves EBL, anisotropic reactive ion etching (RIE) of Silicon (Si), plasma enhanced chemical vapor deposition (PECVD) of SiO2, and physical vapor deposition (PVD) of Ag. The resulting nanoelement is a Si pillar with an Ag disk on top of it, which resides on a glass disk of roughly the same diameter. The nanoelement is sitting on a Si substrate, covered by a double layer of SiO2 and Ag. The same geometry can also be realized in a well-defined array permitting a periodic plasmonic nanostructure. The fabrication scheme allows control over several structural properties, which prompted a theoretical modeling effort on our part to provide insight with respect to the electromagnetic effects that contribute to the enhanced electric field. Here, we investigate the single pillar nanoelement, where interpillar coupling

10.1021/jp106540q  2010 American Chemical Society Published on Web 10/01/2010

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J. Phys. Chem. C, Vol. 114, No. 42, 2010 18097 power of the local field around the nanoparticle, has a strong variation with the geometric parameters. The purpose of the present study is to understand the electromagnetic response of the structure in order to achieve the best enhancement of the local field. Motivation resides in the very large SERS enhancements experimentally observed for similar nanostructure systems.16,17 Model for the Pillar Nanosurface

Figure 2. Geometry of the single pillar nanostructure. (a) Overall view (b) Detailed view with geometrical parameters.

is absent. These results will be the basis for understanding the periodic arrangements at a later time. This work is organized as follows. Initially, we summarize the geometry of the pillar nanostructure and the materials involved with reference to the fabrication process. Next, we derive an analytic model to predict the local field of the nanoparticle interacting with a dielectric pillar and substrate. Finally, we show how the model can be applied to the real structure to calculate the enhancement factor and compare these results to the full wave simulation. The Pillar Nanosurface The general fabrication process of the nanostructure explored here has been described elsewhere,16,17 so we only briefly outline the salient points. The hybrid nanopillar resonator structures can be realized through a sequence involving EBL, anisotropic RIE of Si, PECVD of SiO2 and PVD of Ag. The process is summarized in Figure 1, where the resulting nanopillar element is also shown on the right. We model this geometry as shown in Figure 2(a), where the detailed view of the single pillar is shown in Figure 2(b) with the relevant geometrical parameters. This structure is numerically analyzed using a full wave method based of the Finite Difference Technique18 implemented by CST Microwave Studio.19 The pillar is modeled as an Si rod with refractive index20 nSi ) 3.875 + j0.018 and diameter dp. The pillar sits on a macroscopic Si slab (assumed infinite). The glass layer (SiO2) covering the Si slab and the top of the pillar is hSiO2 ) 20 nm high, and it has refractive index nSiO2 ) 1.45. The silver layer has a height hAg ) 25 nm, and its dispersion has been incorporated via experimentally determined values of the optical constants.21 The structure has been meshed with hexahedrons, and in particular, the mesh size of disk is 2 nm. In Figure 2(a), a plane wave (PW) is impinging on the structure with an operating frequency corresponding to λ ) 633 nm. The PW is normally incident with a linear polarization along y (this can be easily extended to the case of different polarizations, such as double linear or circular) and has an amplitude of 1 V/m. Notice that the model includes a trough at the base of the pillar, which approximates the surrounding space left by the fabrication process at the pillar bottom (shadow effect). The trough diameter is d. The top edge of the silver disk has been rounded to better approximate the real fabricated pillar. The SERS enhancement factor, which is proportional to the fourth

Despite the simplicity of the geometry, numerous electromagnetic effects contribute when an external source illuminates the nanostructure due to the combination of metal and dielectric environments.22 The silver particle emanates an electromagnetic field that is characteristic of a LSPR for a plasmonic disk-shaped particle.23–26 According to the disk diameter, the leading phenomenon will be absorption or scattering, but in terms of the local field, the particle can be modeled as a dipole radiating a near field, which can be obtained by differentiating the charge potential.25 Furthermore, the presence of a silver mirror acts like a reflecting surface for the wave illuminating the structure giving rise to a modulation of the total field. Thus, the position of the nanoparticle with respect to the surface is crucial to avoid destructive interference. Note that the reflection mechanism also occurs when the Si surface is not covered by silver since the Si refractive index is much greater than free space. Thus, the wave still encounters a large discontinuity. Finally, since the nanoparticle is supported by a pillar, we focus on the effect that this dielectric post has on the global mechanism and show how the pillar functions primarily as a dielectric waveguide supporting propagating modes.27 Even under the assumption of a monomodal propagation, the field distribution at the air-dielectric interface is forced to match the boundary conditions underneath the disk and on top of the mirror surface resulting in further modulation. We will show how the effect significantly alters the local field around the nanoparticle. In this section, we develop and present an approximate analytic model, which is useful when examining the structural characteristics that affect the enhancement. The components of the true nanopillar are introduced sequentially into the model, which allows us to determine how particular interactions alter the optical properties. Numerical results will show how this approximation works and the range of reliability for simplified structures or for the real nanopillar. For the latter case, we will also show how an effective enhancement factor defined by averaging the local field over the surface of the nanoparticle is affected by altering pillar height. Dipole Model for the Nanoparticle. We will assume that the complete set of discs (Ag + SiO2) is the nanoparticle of the system. It is clear that the refractive index of the glass is small, thus it will not affect the overall behavior of the nanoparticle except for a red shift of the extinction cross section. Table 1 shows the extinction cross section Cext of the nanoparticle in Figure 3(a) in terms of its diameter d. When the PW illuminates the silver disk, a LSPR occurs since the electrons in the particle interact with the electromagnetic radiation, which leads to absorption and radiation. The amount of absorption or radiation depends on the disk diameter, and the maximum extinction occurs for a disk with a d ≈ 160 nm diameter. The electric field around the particle is shown in Figure 3(a) for a disk with

TABLE 1: Extinction Cross Section of the Nanoparticle As a Function of Particle Diameter d(nm) 2

Cext(m )

100 1.35 × 10

120 -14

4.97 × 10

140 -14

1.41 × 10

160 -13

1.79 × 10

180 -13

1.53 × 10

200 -13

1.33 × 10-13

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Polemi et al. throughout the visible range by setting the dipole moment |p b| ) 3.8 × 10-16 C m validating the dipole approximation of the disk. Confident about the far field results, we now calculate the local field around the particle. Under the assumption that the dipolar charges are displaced d apart along the y direction, the electric field can be calculated through the potential,

Φ) Figure 3. (a) Total field of the nanoparticle. (b) Far field on the principal planes φ ) 90° (E-plane) and φ ) 0 (H-plane) calculated through the analytic expression in eq 1 and compared with the full wave simulation.

d ) 200 nm (the silver and the glass thicknesses are hAg ) 25 nm and hSiO2 ) 20 nm, respectively). It is evident how the field emanated by the disk resembles that of a dipole with an equivalent moment oriented along the polarization of the electric field (y in our case). In the far field, the dipole field can be written as follows:

(

Q 1 1 4πε0 r+ r-

)

(2)

where Q is the charge, and r( are the distances from ( charges to the observation point. The relation between charges and dipole moment is given by Q ) |p b|/d (nevertheless, even in this case we will use the full wave result to assign the Q value). We tracked the near field on a linear scan along y above the disk at distance l ) 5 nm from the upper surface (see the dashed line in the inset of Figure 4). We assume a PW propagating along negative z and place the reference plane at a distance l from the surface of the disk. The PW will be reflected by the disk, or it will pass through outside the disk area. Thus the total near field can be approximated as follows:

-jkr

e b E ) jkξ

r

rˆ × rˆ × b p

(1)

where ξ is the free space impedance, k ) 2π/λ is the free space wavenumber, r is the distance from the center of the particle to the observation point characterized by the unit vector rˆ. In eq bi is the equivalent dipole, which is dependent on the 1, b p ) RE nanoparticle polarizability R and the incident PW field b E i. The polarizability of a nanoparticle is determined both by the constituent material and by the particle size and shape.28,29 For a known material and geometry, the polarizability may be determined analytically23,30 or by computational methods;31 however, small deviations from the specified shape may introduce significant optical changes.32 Since the calculation of polarizability is outside the scope of the present work, we will fit the value of the dipole moment by using the CST results as a reference. In Figure 3 (b), the amplitude of the copolar component of the field (Eθ) from eq 1 is shown (black curves) on both the principal planes φ ) 90° (E-plane) and φ ) 0 (Hplane). This result is compared with CST Microwave Studio results (red curves), where good agreement has been found

b E ≈ -∇Φ + 1 · yˆ if the observation lies outside the disc (1 + Γupe j2kl) · yˆ if the observation lies inside the disc (3)

{

where Γup is the reflection coefficient calculated at the upper surface of the particle through the standard reflection theory for multilayered structures.33 The result is shown in Figure 4 in terms of the y and z components of the electric field, where Q has been set as 1.8 × 10-25 C. Despite the degree of approximation, the results are in good agreement with CST simulations. It is clear that the field tends to be singular at the edges of the disk (y ) ( 100 nm), as expected. The influence of the mesh size in the full wave simulation affects the singular signature of the field at the rim of the disk. Furthermore, in the CST model, the top disk edge is rounded slightly in order to better resemble the real nanostructure; thus, these discrepancies are reasonable in the framework of the present approximation. Outside the disk, the field tends instead to resort to the external

Figure 4. Amplitude of the y (a) and z (b) components of the near field calculated using eq 3 and compared with the CST simulation. The near field is tracked on a linear scan along y above the disk at a distance l ) 5 nm.

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Figure 5. (a) Nanoparticle in presence of a PEC surface at distance h ) 150 nm. (b) Far field on the principal planes φ ) 90° (E-plane) and φ ) 0 (H-plane) calculated through the analytic expression in eq 1 and compared with the full wave simulation.

Figure 6. Amplitude of the y (a) and z (b) components of the near field calculated through the approximation in eq 4 and compared with the CST simulation. The near field is tracked on a linear scan along y above the disk at a distance l ) 5 nm.

PW field. The PW field is polarized along y, and the z component outside the disk area quickly goes to zero. Effect of the Mirror. An additional factor that affects the local field around the disk is the presence of a silver mirror at the base of the pillar (see Figure 2). For a better understanding of the overall physical phenomena, we consider here a perfect electric conductor (PEC) in place of the silver layer. This assumption will simplify the treatment at this point but without lack of accuracy. We will reintroduce the effect of the silver surface below. The geometry under investigation is depicted in Figure 5(a), where h ) 150 nm. As was done in the previous section, we can approximate the field scattered by the disk as that of an equivalent dipole. The presence of the PEC is solved by applying image theory.34,35 The total field is calculated as in eq 1 plus the field radiated by an image source at a distance 2h from the original one along the negative z -axis with the opposite direction of the moment. For this configuration, the copolar components of the far field on both principal planes are shown in Figure 5(b) and compared with the CST results. Again, we calculate the near field as was done in the previous section but now add the effect of a perfectly reflecting surface, which means that the PW will be bounced back with a reflection coefficient Γ ) -1. Moreover, a further contribution will be given by the image source (i.e., an equivalent dipole with the same amount of charge Q but opposite sign placed at a distance 2h along the negative z-axis). We call this field b Eimage ) -∇Φimage, where Φimage can be calculated as in eq 2 upon substituting the correct distances from the image source to the observation point. Thus, the total near field can be approximated as follows:

b E ≈ -∇Φ + b Eimage +

{

(1 + Γmirrore j2k(l+h)) · yˆ observation outside the disc (1 + Γupe j2kl) · yˆ

observation inside the disc (4)

where Γmirror ) -1 for a PEC reflecting surface; while, in the real structure with a silver surface, it will be replaced by the pertinent reflection coefficient Γmirror calculated on top of the mirror. This calculation can be easily performed through the standard reflection theory for multilayered structures.33 Figure 6 shows the amplitude of the y and z components of the electric field tracked along a linear scan at a distance 5 nm from the upper surface of the disk. The results are again in good agreement with the CST simulations. Effect of the Dielectric Rod. In order to move toward the real nanosurface configuration, we now consider the SiO2 + Ag disk placed on top of a pillar, which is a dielectric Si rod with diameter dp. The geometry is depicted in Figure 7. The reflecting surface is still assumed to be a PEC for simplicity. The presence of the pillar creates a nanocavity between the silver disk and the top of the pillar, thus resulting in redistribution of the local field on top and at the side of the nanoparticle. In addition, the nanoparticle can be seen as the feeder of a cylindrical dielectric waveguide, which supports different modes depending on the refractive index of the medium and on its diameter. In a cylindrical dielectric waveguide, a hybrid HE11 mode is always propagating, since it does not have a cut off frequency. The propagation wavenumber kg can be calculated27 by solving the dispersion equation for the zeroth order Bessel

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Polemi et al. between the PEC wall at one side and the SiO2 + Ag disk (see Figure 7). This results in a further redistribution of local energy, since the electromagnetic field is engaged in a resonant mode, as is clear from Figure 8(a),(b), where the absolute value of the y and z components of the electric field are shown for a pillar height h ) 250 nm. This resonant effect can be approximated as a further modulation of the local field around the disk given by eq 4 as follows:

Figure 7. Configuration of the SiO2 + Ag disk placed on top of the Si pillar over a reflecting PEC surface. A qualitative view of two main effects is sketched. First, the SiO2 substrate between the Ag disk and the Si pillar acts as a nanocavity storing some of the local field. Furthermore, the dielectric rod acts as a waveguide entrapping the field between the reflecting surface and the bottom of the nanoparticle. This resonant effect can be interpreted as a Fabry-Perot cavity mode.

Figure 8. Absolute value of the y and z components of the electric field for a pillar height h ) 250 nm. (a),(b) dp ) 150 nm, d ) 200 nm. (c),(d) dp ) 80 nm, d ) 120 nm.

function J0(u) ) 0, where u ) ktdp/2 and kt ) √kSi2 - kg2 is the transverse wavenumber, in which kSi ) nSik (k is the free space wavenumber). In our case, for a pillar diameter dp ) 150 nm, we obtain kg ≈ (3 - j0.02)k. This field is guided internally and then reflected back from the surface (assumed a PEC for simplicity), thus resulting in a resonant effect established

b Epillar ≈ [Γmirrore jkgh - Γdowne-jkgh]Etˆt + [Γmirrore jkgh + Γdowne-jkgh]Ezzˆ

(5)

where the field b E has been decomposed into a transverse-to- z component and a longitudinal (z) component. If we look at the incident plane (zy) Et ) Ey. In eq 5, Γmirror ) -1 is the reflection coefficient at the PEC side and Γdown is the reflection coefficient at the lower side of the nanoparticle.33 The larger the pillar diameter, the more complicated the field structure is inside the dielectric rod, as more modes can be excited. Then we expect that the approximation in eq 5 works better for rather small dimensions of dp. In fact, when the dielectric rod diameter becomes smaller, then the parameter u ) ktdp/2 becomes smaller too. The solution of the dispersion equation J0(u) ) 0 gives rise to kg f k, and the HE11 field tends to confine more and more at the air-dielectric interface as shown in Figure 8(c),(d). Thus, the internal resonance almost coincides with the external PW bouncing resonance in free space, and the presence of the pillar does not influence substantially the global behavior of the disk nanosurface but does alter the spatial properties of the local field. As a demonstration of applicability of the approximation in eq 5, we calculate the absolute value of the total electric field at the central point of the disk at a distance l ) 5 nm from the top upon varying the pillar height h. In this way, the resonant effect is clearly visible from the periodic replica of maxima and minima. Results are shown in Figure 9 (black lines) compared with the CST full wave simulations (red dashed lines) and also for the same case in the absence of the pillar (blue dotted lines) to demonstrate how the resonant mode affects the result. In Figure 9(a), we show the results relevant to the dimensions dp ) 150 nm and d ) 200 nm, for which we know the internal resonance is strongly excited (see Figure 8(a),(b)). Indeed, the periodicity of maxima and minima in this plot is approximately set by λg/2 ≈ 106 nm, where λg ) 2π/kg. The results in Figure 9(b) are for dimensions dp ) 80 nm and d ) 120 nm, for which we know the internal resonance almost coincides with the free space resonance of the PW bouncing at

Figure 9. Absolute value of the electric field at a point 5 nm from the top of the silver disk (red dot) in terms of the pillar height h. (a) Dimensions dp ) 150 nm and d ) 200 nm. (b) Dimensions dp ) 80 nm and d ) 120 nm. The analytic trace has been normalized to the CST result.

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Figure 10. Esurfavg in terms of the pillar height h. (a) Dimensions dp ) 150 nm and d ) 200 nm. (b) Dimensions dp ) 80 nm and d ) 120 nm.

Figure 11. Absolute value of the electric field: dp ) 150 nm, d ) 200 nm, h ) 250 nm.

Figure 12. Absolute value of the electric field: dp ) 80 nm, d ) 120 nm, h ) 150 nm.

the reflecting surface. In fact, the periodicity is slightly greater than λ/2 ) 316.5 nm. The comparison between the curves shows that the analytic approximation in eq 4 and eq 5 is able to describe the global trend of the local field in the vicinity of the nanoparticle, and, as expected, the discrepancies are bigger when the field distribution inside the pillar becomes more complicated.

away from the nanoparticle region. Also, we expect that Et in eq 5 will not be modulated by the resonant effect. Instead, the z component, which is more confined at the air-dielectric interface of the pillar, is still engaged in a reflection mechanism due to the presence of the mirror outside (under the assumption that the surface void is relatively small). Thus, we slightly modify the model as

Field Enhancement of the Pillar Nanosurface We move now toward the real configuration (Figure 2), and we apply the analytic approximation in eq 4 and eq 5 to model the enhancement factor of the pillar nanostructure. Here, the PEC surface is replaced by the actual multilayer composed by an infinite layer of Si, a layer of SiO2 (hSiO2 ) 20 nm), and a layer of Ag (hAg ) 25 nm); thus, the reflection coefficient Γmirror is calculated accordingly.33 Note that in the real surface, the pillar does not sit on a uniform mirror but on the same Si material through a void in the Ag + SiO2 layers. As a consequence, the transverse-to-z electric field, which is mainly confined at the center of the pillar, propagates almost undisturbed throughout the Si base resulting in a transfer of energy

b Epillar ≈ Etˆt + [Γmirrore jkgh + Γdowne-jkgh]Ezzˆ

(6)

There are different ways to define the SERS enhancement factor G of this structure. We assume that G is proportional to the fourth power of the local field. But since the local field around the nanoparticle shows peaks in the proximity of its edges, we define a figure of merit by averaging the field over the surface area of the disk accessible to molecules. In particular, we define Esurfavg as the sum of the total absolute field integrated along the surfaces S1 (side of the disk) and S2 (top of the disk) as seen in the inset of Figure 10. Thus,

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avg Esurf )

1 πdhAg

∫02π ∫0h

Ag

4 πd2

Polemi et al.

|bE (F ) 2d, φ, z)|dzdφ + pillar

∫02π ∫0d/2 |Ebpillar(F, φ, z ) hAg)|dFdφ

(7)

where b Epillar is defined in eq 6 for the analytic model or taken from CST for the full wave simulation. In this way, we define the enhancement factor as G ∝ (Esurfavg)4. In Figure 10, we show the value of Esurfavg calculated through eq 7 in terms of the pillar height h. The analytic result (black line) is normalized to the CST simulation (red dashed line), for the same cases analyzed previously, i.e. dp ) 150 nm, d ) 200 nm in Figure 10(a) and dp ) 80 nm, d ) 120 nm in Figure 10(b). As expected, the curves are in a better agreement for the small diameter pillar case. Although there is a large degree of approximation in the analytic model, it is a good instrument for fast calculations on the nanostructure and allows one to glean knowledge about the numerous optical effects present in these unique pillar nanostructures. From Figure 10, it is also clear that the dp ) 80 nm, d ) 120 nm configuration provides a stronger field enhancement than the dp ) 150 nm, d ) 200 nm configuration. This was expected, since the smaller pillar diameter prevents a considerable amount of electromagnetic field being lost to the waveguide. Color plots are displayed in Figures 11 and 12 to better show how the field is emanated and where it is confined. The value of h in each case is reported in the caption. This representation is especially useful in the case dp ) 150 nm, d ) 200 nm (Figure 11), where it is evident that the electromagnetic field is strongly engaged by the dielectric rod. On the right of the same figures, the absolute value of the electric field is shown tracked on a linear scan just above the nanoparticle (white dashed line). We want to emphasize that the peak value at the edges of the disk is greater than the corresponding Esurfavg value. For the case dp ) 150 nm, d ) 200 nm, h ) 250 nm the ratio is approximately 1:1.25, and for the case dp ) 120 nm, d ) 80 nm, h ) 150 nm the ratio is ∼1:3. For the latter configuration, this corresponds to a SERS enhancement factor of G ≈ 1785 and Gmax ≈ 1.8 × 105 for the surface averaged and maximum value respectively. However, in the calculations, the field amplitude near the disk surface is strongly related to the mesh size, and G will increase substantially upon decreasing the grid spacing used in the calculations. The goal of this work was not to extract a quantitative value of G but to understand the numerous optical effects occurring in these unique hybrid nanostructures, and the grid spacing utilized for the calculations was sufficient for this purpose. Due to the spatial confinement of the maximum field value, we speculate that the surface-averaged result is likely a more reliable figure of merit. Studies are currently underway to explicitly compare the modeling results to experimental SERS measurements on these nanostructures. Conclusions Results obtained on the analysis and characterization of a unique nanostructure used for SERS have been presented. In particular, the optical properties of a nanostructure composed of pillars supporting plasmonic nanoparticles have been analyzed. The enhancement factor has been defined in terms of a figure of merit based on the local field integrated on the nanoparticle surface and found to vary considerably depending upon pillar structure. We have carried out a theoretical analysis to provide insight regarding how to maximize the nanoparticle local field and determined that the smaller diameter pillars

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