1. Introduction

Since the first observation of single-molecule surface-enhanced Raman scattering (SERS) from aggregates of colloidal particles and deposited metallic nanoparticles [1,2], SERS has become a powerful and sensitive technique for the detection of chemical and biological agents. Two main mechanisms are generally attributed to the strong SERS enhancement – the electromagnetic enhancement and the chemical enhancement. Metallic nanoparticles and roughened electrodes have been used as SERS-active substrates in which the enhancement factor (EF) can be 10⁶ (average value for conventional SERS) and around 10¹² (maximum value for single-molecule SERS) [3]. It is well established that the electromagnetic enhancement arises from optical excitation of surface plasmon resonances at the metal nanoparticles, which leads to a gigantic increase in the electromagnetic field strength at the particle surface. The origin of the chemical enhancement is believed to be the formation of charge-transfer states by molecules adsorbed at certain surface sites [4]. Its contribution was estimated to be up to 10² times on the enhancement factor [5]. Although chemical enhancement can contribute significantly, the majority of the enhancement of Raman scattering intensity is related to the electromagnetic field strength on the surface of the metallic substrate.

For practical applications, it is indispensable to produce SERS-active substrate with reproducible and tunable SERS enhancement. The key to obtain strong and robust SERS enhancement is to excite the localized surface plasmon (LSP) resonance in nanostructured substrate, which is determined by the properties of the metals, the size and shape of the nanostructures, the inter-particle spacing, and the dielectric environment. Most SERS-active substrates consist of disordered metal surface such as metallic nanoparticles, nanorods, nanowires, nanosphere arrays, nanodisks, and nanostrips [1,2,6–10]. Recently, there has considerable attention on the electromagnetic field enhancement in gap surface plasmon polaritons (GSPPs) [11–13], which is excited at the narrow gap of the dielectric layer between two metal surfaces. Furthermore, it has been demonstrated that resonators formed by introducing a narrow gap between metal surfaces can support slow SPP modes in the gap region, resulting in strongly enhanced local fields. Those strong enhancements are attractive for important applications such as optical spectroscopy, molecular sensing and detection, and manipulation of light at the nanoscale.

In 2004, the SERS EFs for particle nanostructures were analyzed by Hao and Schatz [3]. In their calculations, it was found that the SERS EFs vary rapidly with the gap size of the dimer structure, and it is only for gaps on the order of 1 nm to 2 nm that can provide exceptionally large EF values such as |E|⁴ = 10¹¹. For practical applications, however, it is very difficult to control the gap size on the order of 1 nm to 2 nm to reproducibly achieve the predicted results. However, in microelectronic fabrication, it is easy to control the thickness of a deposited film to a high resolution. This makes it straightforward to reproducibly fabricate metal-thin dielectric-metal structures that support GSPPs for SERS applications. In this study, we numerically investigate the optical field enhancement in a silver nanostructure formed on a thin SiO₂ spacer and a thick bottom silver layer.

2. Modeling and simulation methodology

Manipulation of light on the nanometer length scale has been explored in a variety of configurations. In addition to metallic nanoparticle substrate, other configurations used for SERS experimentation can be found in Ref [3,14–16].

Figure 1 illustrates the schematic diagram of our proposed structures, where an isolated structure, including equilateral triangle, square, and cylinder, is formed on a thin dielectric spacer layer (i.e., SiO₂) on a thick silver substrate. The thickness of the isolated silver nanostructure, the SiO₂ spacer layer and the thick silver layer is fixed at 40 nm, 20 nm and 100 nm, respectively. In our simulation, we use the excitation wavelengths of 785 nm and 633 nm, both are commonly used in Raman spectrometers. The dielectric constants at those wavelengths are: ε_Ag = −26.7 + 1.48i for 785 nm and −15.88 + 1.077i for 633 nm, and ε_SiO2 = 2.10 for 785 nm and 2.13 for 633 nm [17]. The light used to excite the GSPPs in the thin spacer region is a circularly polarized wave with normal incidence from the top of the isolated nanostructures. Silver and gold are the most widely used materials for SERS enhancement. It is generally accepted that silver has higher EFs than gold [8]. The field confinement properties of the proposed structures are simulated and analyzed by TEMPEST, a Maxwell equation solver based on 3D finite-difference time-domain (FDTD) method.

 

Fig. 1 A schematic of the proposed nanostructures.

Download Full Size | PDF

3. Calculations of effective refractive index and propagation length

As shown in Fig. 1., we can regard the structure as a metal-insulator-metal (MIM) waveguide in which a thin dielectric layer with a thickness t is sandwiched between two metal layers. It is the SPP modes in the symmetric MIM waveguide that lead to strong field enhancement. The gap surface plasmon (GSP) propagation constant (k_gsp) can be written as [11]:

Figure 2(a) and (b) plot the real part of the effective refractive index and the GSP propagation length as a function of the SiO₂ spacer thickness. Notice that there is a trade-off between the real parts of the effective refractive indices and the GSP propagation lengths. The real parts of the effective refractive indices decrease as the spacer thickness increases, while the GSP propagation lengths increase. It is also observed that the real parts of the effective refractive indices vary rapidly but the GSP propagation lengths change quasi-linearly with the thickness of the SiO₂ spacer. It is noteworthy that even in a very thin SiO₂ spacer, the GSP propagation length can be moderately long. For instance, at λ = 785 nm and t_SiO2 = 20 nm, the real part of the effective refractive index and the GSP propagation length are 2.82 and 1.6 μm, respectively. At λ = 633 nm and t_SiO2 = 20 nm, the real part of the effective refractive index and the GSP propagation length are 3.0 and 0.8 μm, respectively.

 

Fig. 2 Calculated effective refractive index Re(n_eff), n_eff = k_gsp/k₀, and GSP propagation length L_gsp = (2Im(k_gsp))⁻¹, as a function of the SiO₂ spacer thickness. The incident wavelengths are 785 nm in (a) and 633 nm in (b).

Download Full Size | PDF

4. SERS EFs for various nanostructures

The understanding that LSPs play a crucial role in the Raman signal enhancement for molecules at a metal surface has triggered a great amount of research into the design and fabrication of SERS-active substrates with controlled surface nanostructure for field enhancement. In our study, we focus on the field intensity distribution as defined in terms of the square of the local electric field, |E_Loc|². Local field EF can be simply given by |E_Loc|² = |E_max|²/|E₀|². The SERS EF due to electromagnetic mechanism is usually expressed as |E_Loc|⁴. As mentioned previously, the EF in a conventional SERS experiment is around 10⁶ and the EF in a single-molecule SERS experiment is around 10¹². In order to directly compare the SERS EFs, we calculate the |E_Loc|⁴ as the SERS EF in our structures.

Figure 3 shows the distribution of the field intensity on the xy-plane at the bottom and the top region (indicated by the red lines in the inserts in Fig. 3(a) and 3(b)) of the various nanostructures. It shows that stronger field confinement can be obtained for sharper geometries such as the triangular nanostructure. In practical SERS applications, the region where molecules contact directly on the substrate is the top region of the metallic nanostructure. To account for this, we compare the field intensity at the top region and the bottom region of the nanostructures. Because the bottom region of the metallic nanostructure is in contact with SiO₂ layer while the top region is in contact with air, the bottom region has locally higher effective refractive index. It is well known that a light wave tends to localize itself mostly in a medium with higher refractive index and thereby the light prefers to propagate with lower phase velocity [18]. The simulation results are in agreement with this, showing stronger field intensity at the bottom region than that at the top region.

 

Fig. 3 Intensity distribution of the triangular ((a) and (b)), square ((c) and (d)), and circular ((e) and (f)) nanostructures in xy plane. (a), (c) and (e) corresponds to the intensity distribution at the bottom region of the nanostructures (indicated by the red line in (a)) and (b), (d), and (f) corresponds to the intensity distribution at the top region of the nanostructures (indicated by the red line in (b)). The incident wavelength is 785 nm.

Download Full Size | PDF

In general there are two SERS EFs defined for a given SERS-active substrate: the average SERS EF and the maximum SERS EF [19]. The average SERS EF is the one averaged over all possible positions on the surface of the metallic nanostructures. Typically, the SERS EFs for optimized configurations are in the range of 10⁵ to 10⁶, and are easily achievable with standard substrates. The maximum SERS EF typically occurs at specific positions known as hot spots on the substrate and only molecules absorbed there can benefit from it.

To evaluate the effect of the geometrical parameters on SERS EFs, simulations are performed by varying the length of the nanostructures in various shapes. The results are shown in Fig. 4 . In general, the maximum SERS EF at the top region is about an order of magnitude smaller than that at the bottom region. It can be explained by the localization of the light to the spacer region which has a locally higher effective refractive index. For smaller structures, extinction is mainly dominated by absorption, with little scattering. This trend is reversed as the size of the structure increases. For larger structures, they emit radiation so efficiently that it is difficult to induce a large polarization in them [20]. In Fig. 4(a) and (c), it is clear that at the edge of the equilateral triangular nanostructure, the maximum SERS EFs are estimated to be about 7.0 × 10¹¹ at λ = 785 nm and L = 110 nm, and about 2.1 × 10¹¹ at λ = 633 nm and L = 100 nm. In the case of equilateral triangular nanostructure on a pure SiO₂ substrate, the maximum SERS EFs are estimated to be about 3.0 × 10⁸ at λ = 785 nm and L = 110 nm, and about 1.1 × 10⁸ at λ = 633 nm and L = 100 nm. Recently, it is reported that a metal nanostrip can serve as an optical resonator at the ultrathin metal thickness [21]. It is predicted that this nanostrip is capable of a significant field enhancement under resonant excitation when the resonance length is precisely tuned to the resonance scattering peak. In this study, the GSPPs exhibit substantially enhanced effective refractive index and strong field confinement at the spacer region that is much thinner than the wavelength of light. When we compare simulation results at λ = 785 nm and at λ = 633 nm, it is clearly observed that, as the incident wavelength decreases, the size of the nanostructure at the resonance decreases. In other words, if the size of the nanostructure increases, the resonance is red-shifted to longer wavelengths. For SERS applications, in addition to large field enhancement, the resonances must be broad enough to encompass both the exciting laser and the Stokes frequencies. In all simulated nanostructure shapes, the maximum SERS EF and the broadest resonance are both achieved in the equilateral triangular nanostructure. Since the lengths of the nanostructures are on the order of 100 nm, all structures simulated in this work can be easily fabricated by electron-beam lithography (EBL), which has precise control of the nanostructure size and shape as well as their arrangement on the substrate [22]. Some shapes may also be achieved by low-cost nanosphere lithography (NSL), which has been pioneered by Van Duyne’s group to prepare efficient SERS-active substrate [23,24].

 

Fig. 4 Comparison of SERS EFs for different incident wavelengths and nanostructure dimensions. The incident wavelength is 785 nm in (a) and (b), and 633 nm in (c) and (d). (a) and (c) show the EFs at the bottom region of the nanostructures and (b) and (d) show the EFs at the top region of the nanostructures.

Download Full Size | PDF

5. Dependence of SERS EFs on spacer thickness and surrounding medium

Because the maximum SERS EFs are induced from LSP resonance based on GSPPs, simulations are carried out to evaluate the influence of the thickness of the SiO₂ spacer layer. Figure 5(a) and (b) show the maximum SERS EFs and the real part of the effective refractive index in equilateral triangular nanostructures for incident wavelengths of 785 nm and 633 nm, respectively, as a function of the thickness of the SiO₂ spacer. At both wavelengths, the nanostructure exhibits a general trend of decreasing in the maximum SERS EFs when the thickness of the SiO₂ spacer increases. To explain this, we can regard the top equilateral triangular nanostructure as a resonant optical antenna on a substrate. The optical properties of an optical antenna are strongly influenced by the substrate material as well as the geometry of the antenna. When the SiO₂ layer thickness increases, the real part of the n_eff of the substrate decreases as shown in Fig. 5 (a) and (b), and consequently the field enhancement in the equilateral triangular nanostructure decreases. The resonant wavelength of an optical antenna can also be shifted by the refractive index of the substrate. This may explain the faster drop in EFs in Fig. 5(a) at 60 nm thick SiO₂ and in Fig. 5(b) at 40 and 80 nm thick SiO₂ because at those points the incident wavelength is off-resonance with the equilateral triangular nanostructure. Notice that the EFs in the nanostructure with ultrathin spacer layer (i.e., t_SiO2 = 10 nm) is much lower. This is due to stronger damping by the metal and shorter propagation length of the GSPPs supported by an ultrathin SiO₂ spacer.

 

Fig. 5 Comparison of SERS EFs at the bottom and the top region of the nanostructures and the real parts of the n_eff as a function of the spacer thickness. The incident wavelengths are 785 nm in (a) and 633 nm in (b). The simulated structure is the equilateral triangular nanostructure with a resonant length of 110 nm for 785 nm incident wavelength and 100 nm for 633 nm incident wavelength, respectively.

Download Full Size | PDF

In many practical SERS experiments for molecular detection, the SERS-acitve substrates are immerged in a liquid environment. In order to gain insight on how surrounding medium affects the SERS-active substrates, we calculate the SERS EFs for equilateral triangular nanostructures of various sizes in water at both λ = 785 nm and λ = 633 nm (Fig. 6 ). The dielectric constant of water is 1.77. As shown in Fig. 6, similar trends in the maximum SERS EFs are observed as those nanostructures in air (Fig. 4). The maximum SERS EFs in liquid solution are similar to those in air. When compared to the nanostructures in air, the resonant lengths of the nanostructures in water are smaller for both incident wavelengths. Because of the higher refractive index of water, the effective wavelengths in the liquid solution decrease from 785 nm and 633 nm to 590 nm and 476 nm, respectively. Hence, the resonance peaks are shifted from 110 nm (in air at 785 nm) and 100 nm (in air at 633 nm) to 80 nm (in water at 785 nm) and 70 nm (in water at 633 nm), respectively. Furthermore, the maximum SERS EFs of the nanostructures in liquid solution are less sensitive to the length of the nanostructures. This is manifested by the broader peaks in Fig. 6 than those in Fig. 4.

 

Fig. 6 Comparison of SERS EFs of equilateral triangular nanostructures in water as a function of the length (L) of the nanostructures. The incident wavelengths are 785 nm in (a) and 633 nm in (b).

Download Full Size | PDF

6. Conclusion

In conclusion, we have numerically investigated the SERS EFs in MIM structures with various geometrical shapes and sizes. Due to higher effective refractive index for the GSPPs in the SiO₂ spacer region, incident light tends to localize itself mostly in higher index region and thereby the light can be confined with a large optical field enhancement. By utilizing the GSPPs, we attained SERS EFs up to 10¹¹ by the electromagnetic mechanism alone in the proposed nanostructure. Moreover, the nanostructures exhibit drop in SERS EFs when the thickness of the SiO₂ spacer increases. When the nanostructures are immersed in an aqueous solution, the maximum SERS EFs are achieved in smaller structures. In solution, very large (> 10¹¹) EFs can be attained over a broad range of size distribution in the nanostructures. The nanostructures investigated in this work can be easily fabricated by microelectronic fabrication techniques such as EBL, NSL and nanoimprint lithography. By utilizing GSPPs, we can achieve SERS hot spots with very large EFs at pre-determined locations on a substrate. Such nanostructures, with reproducible and low-cost fabrication, and large SERS EFs, are expected to be widely used as SERS-active substrates for optical sensing.