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A substrate with ease for fabrication is proposed for surface enhanced Raman spectroscopy (SERS). A two-dimensional dielectric grating covered by a thin silver film enables the excitation of both localized surface plasmons (LSPs) and surface plasmon polaritons (SPPs). The finite-difference time-domain simulation results show that the coupling between LSPs and SPPs is able to highly improve the Raman enhancement (2 × 109 as obtained by simulation). In addition, the near-field distribution at the top of cubic bumps along the transverse plane presents a highly regular hotspots pattern, which is required for an ideal SERS substrate.
©2010 Optical Society of America
1. Introduction
Surface enhanced Raman spectroscopy (SERS) is a powerful analytical tool for chemical and biological sensing application which provides detailed material information at molecular level, e.g. at single-molecule sensitivity [1], for which a Raman enhancement factor at an order of 1014 is required. As a basic requirement for sensitive SERS, an ideal substrate must guarantee a high enhancement effect for SERS and a reproducible uniform response, and thus needs a large area with regular hotspots, whereas easiness for fabrication is desired [2]. Since the discovery of SERS in 1970s, researchers have made great effort theoretically and experimentally to develop robust substrates for SERS, including single nanoparticles [1, 3–5], nanoparticle dimers [6], clusters [7], nanorods [8] and nanowire arrays [9]. For the dimer configuration with extremely small gap, which provides a high Raman enhancement factor to perform the single molecule SERS, the reported electromagnetic enhancement is at an order of 1011 [10]. This electromagnetic enhancement effect mainly comes from the excitation of localized surface plasmons (LSPs) with strong interaction among them. Metallic periodic structures are another type of configuration which plays a significant role as SERS substrate in biosensing. Many works, either theoretically or experimentally, have been conducted in recent years [11–15]. The Raman enhancement reported is mainly among 105 – 108, and is only considering the effect of LSPs, or surface plasmon polaritons (SPPs) separately. A recent theoretical work shows that structures comprising metal nanoparticles within periodic arrays can produce highly regular hotspots owing to the excitation of LSPs and SPPs [16]. The coupling between them leads to a high electric field enhancement.
In this article, we propose a structure consisting of a two-dimensional dielectric grating covered by a silver film with a thickness of tens of nanometers for a SERS substrate. Our structure is easy for fabrication and able to provide highly regular hotspots with much high electric field enhancement.
2. Plasmonic Response
Figure 1 shows the proposed structure for SERS in this study. A two-dimensional array of SiO2 cuboids with fixed size of 50 × 50 × 100 nm3 is patterned on the Si substrate, and a layer of 40-nm-thick silver film is covered on the surface. An array of cubic bumps is formed as viewed from the top. Obviously, such a structure can be easily fabricated using the conventional silicon process technology. To obtain the plasmonic response of such a structure, the DiffractMod package based on rigorous coupled wave analysis (RCWA) in the commercial software R-Soft was applied. For water (as the environment), Si, and SiO2, the refractive indices are set to be 1.3364, 3.99, and 1.5458, respectively; while for silver, which is a lossy material possessing wavelength-dependent dielectric constant, the refractive index is obtained from Ref [17]. in the visible range (400 nm-800 nm).Figure 2 shows the absorption characteristics based on various configurations. Using the semi-infinite water-silver flat interface model (dashed line), the reflectance at the interface for normal incidence is: R = ((n0 – nr)2 + k 2) / ((n0 + nr)2 + k 2). Where n0 is the refractive index of environment, nr is the real part of the refractive index of silver and k is the imaginary part which gives rise to the absorption in the silver. For a 40-nm-thick silver film sandwiched between semi-infinite water and Si (dotted line), the absorption will decrease slightly and transmission appears due to the finite thickness of the silver film. Further, if we produce the two-dimensional infinite dielectric grating and cover the whole surface conformally by a 40-nm-thick silver film, multiple absorption peaks will present in the absorption spectra due to the excitation of LSPs and SPPs (solid line). The broad ones denoted as peaks 2 and 3 in Fig. 2 correspond to the first-order LSPs and high order LSPs, respectively, whereas the sharp one denoted as peak 1 corresponds to the SPPs.
Fig. 2 Absorption spectra based on: semi-infinite water-silver flat interface configuration (dashed line), 40-nm-thick silver film sandwiched between water and Si configuration (dotted line), and dielectric grating covered by 40-nm-thick silver film configuration (solid line).
At normal incidence, the SPPs can be excited in a periodic structure satisfying
where Λ is the structural period, k 0 is the wavenumber of light in vacuum, and εm and εe are the permittivity of metal and environment, respectively. The term on the right hand side of Eq. (1) represents the wavenumber of the SPPs propagating along the single interface. Equation (1) predicts an SPP excitation wavelength of 670 nm for Λ = 475 nm, which is slightly longer than the numerical simulation result (637 nm). The difference is due to the modification of Eq [1]. for periodic bump structures. Figure 3 gives the near-field distributions at different resonance conditions in the solid-line curve in Fig. 2, which is obtained by applying the FullWave Package based on the finite-difference time-domain (FDTD) method in R-Soft. In the simulation, the grid size is set to be 2 or 1 nm and the periodic boundary conditions are set for X and Y directions and the perfectly matched layer for Z direction.Fig. 3 |E| distributions at the top of cubic bumps along XY plane at various resonance conditions, i.e., the incident wavelength of (a) 450 nm corresponding to the high order LSPs, (b) 637 nm corresponding to the SPPs, and (c) 670 nm corresponding to the first-order LSPs. The colorbar scale is set as ln(|E|).
If we define Eout(λ) as the local electric field at a wavelength λ, the enhancement factor for SERS is: EFSERS(λs) = |Eout(λ)2 ||Eout(λs)2| / |E0|4, where λs is the Stokes-shifted wavelength [18]. The wavelength difference, Δλ = λs - λ, between the incoming and scattered photons in general is much smaller than the linewidth of a surface plasmon mode, and thus Eout(λ) is approximately equal to Eout(λs), resulting in the commonly used expression for the enhancement of the stocks beam: EFSERS(λs) = |Eout(λ)4| / |E0|4. Since EFSERS(λs) = EFSERS(λs, x, y, z) is spatially varying over the particle surface, we focus on the largest value of EFSERS in this article, like what was done in many previous literatures,. For the case of LSPs and SPPs in Fig. 3, the Raman enhancements are 3 × 107, 4 × 108 and 3 × 108 for the high order LSPs, the first-order LSPs and the SPPs, respectively. Apart from the high Raman enhancement, the highly regular hotspots are obviously produced. In the following section, we take the structural period, the film thickness and the environment refractive index (RI) as variables and investigate their effects on the Raman enhancement.
3. Influence of period, bump size and environment RI on Raman enhancement
Figure 4(a) shows a set of absorption spectra for the period ranging from 402 nm to 546 nm with a step of 24 nm. The peak absorption wavelengths are denoted as λmax and their plots against the structural period for both the LSPs and SPPs are shown in Fig. 4(b). The red-shift trend of the resonance wavelength for SPPs for increasing period can be predicted from the excitation condition [Eq. (1)]. As the structural period increases, the right hand side value in Eq. (1) should be lower accordingly to satisfy the condition. Because of the dispersion property of silver refractive index in visible range, a red shift of excitation wavelength is required from calculation. For the LSPs, the resonance wavelength is affected by the distance between bumps. For large structural period, meaning that bumps are separated far away, the plasmon resonance wavelength shift results from long-range interactions. From Fig. 4(b), LSPs resonance wavelength shows slightly blue shift as bumps distance decreases, which is in consistence with previous works [19, 20].
Fig. 4 (a) Absorption spectra for various periods from 426 nm to 546 nm with a 24 nm increment; (b) absorption peak positions versus different periods for LSPs (circles) and SPPs (squares), with corresponding maximum local |E| at resonance wavelength of SPPs (triangles). The silver film thickness is 40 nm, the bump height is 100 nm and the environment is water.
The Raman enhancement shows a great dependence on the structural period because of the interaction between the LSPs and SPPs. In Fig. 4(b), two peaks can be found from the |Emax(λ)| plot for the resonance wavelength of SPPs at each period (green curve with triangles). The red (with circles) and black (with squares) curves clearly show that there is an intersection between them, implying the occurrence of LSPs and SPPs at the same wavelength. In this case, strong coupling between the SPPs and LSPs will occur, leading to considerable enhancement of the local electric field responsible for the right peak in the |Emax(λ)| curve. As for the left peak at smaller wavelength, the analysis of the |E(λ)| distribution shows that it is from the coupling between the SPPs and the second-order LSPs.
Next, we consider the influence of the silver film thickness to the resonance wavelength and Raman enhancement. For a fixed structural period, the resonance wavelength of SPPs remains constant approximately. For the LSPs, as the film thickness increases, three aspects should be considered for contribution to the wavelength shift. Firstly, the distance between the bumps decreases for increasing film thickness. As stated above, this causes slightly blue shifts of the resonance wavelength. Secondly, since the nanoparticle (bump here) is not pure metal, as the film thickness increases, the effective refractive index of nanoparticles will change accordingly, which induces slightly blue shifts as well. Thirdly, the size and shape of the nanoparticle play an important role in determining the plasmon resonance wavelength. As the film thickness increases, the nanoparticle size is largen and the shape becomes more oblate, both effects contribute to red shift of plasmon resonance wavelength [5]. The tradeoff between these three factors results in the LSPs resonance wavelength shift in a whole. Figure 5 presents the influence of the silver film thickness to the absorption peak positions. The factor of size and shape of the bumps seems to be dominant in our case because of the red shift of resonance wavelength with the film thickness. As suggested in Fig. 5, the resonance wavelengths of the LSPs and SPPs meet at silver film thickness of ~25 nm, leading to a significantly high electric field enhancement due to strong coupling between them. As the film thickness increases, the two resonance wavelengths deviate from each other, implying weaker interaction between the two modes and thus the decreasing Raman enhancement. The maximum field enhancement occurs at silver film thickness of ~29 nm, as shown in Fig. 5. The slight shift with the 25 nm may be due to difference between the RCWA and FDTD methods.
Fig. 5 Absorption peak positions at various silver film thicknesses for LSPs (circles) and SPPs (squares), with corresponding maximum local |E| at resonance wavelengths of SPPs (triangles). The structural period is fixed at 475 nm, the bump height is 100 nm and the environment is water.
Figure 6 shows the electric field distributions under LSPs and SPPs coupling conditions in Fig. 4(b) and Fig. 5. The co-existence of the LSPs and SPPs is clearly seen in both figures. Moreover, the electric field enhancement is greatly maximized under such a circumstance. The Raman enhancements for these two cases are 1 × 109 and 2 × 109, respectively, with improvement of 1 orders of magnitude compared to those in Fig. 3 and 3 orders compared to those without any modes. Such high Raman enhancement ensures this structure as a potential substrate for high sensitive molecule detection experiment.
Fig. 6 |E| distributions under LSPs and SPPs coupling conditions in Fig. 4(b) (left), and in Fig. 5 (right). The colorbar scale in both figures is set as ln(|E|). 1 nm cell size is used in this calculation.
Finally, the influence of environment, i.e. its RI, is considered. For the SPPs, from the right hand side of Eq. (1), the change of the environment RI requires the adjusted permittivity of silver to satisfy the excitation condition for a fixed structural period. According to the dispersion of the silver’s permittivity, there will be a considerable red shift of the resonance wavelength for increasing environment RI (black curve with squares). For the LSPs, using the Drude model of the metal, we can obtain the following equation [5]
for the first-order LSPs, where λb is the bulk plasmon wavelength of silver and ne the environment RI. Figure 7 presents linear relations of SPPs and LSPs absorption peak wavelength with the environment RI. This shows that although Eq. (2) is derived from the spherical model, a similar proportionality exists for nonspherical shapes as well. This linear relationship between the resonance wavelengths and the environment RI allows such a structure to be applicable for biosensing application. In addition, the relationship between the local |E(λ)|max values at the resonance wavelengths of the SPPs and the environment RI (green curve with triangles) shows that increasing the environment RI could lead to higher Raman enhancement.Fig. 7 Absorption peak positions at various environment refractive indices for LSPs (circles), SPPs (squares), and corresponding maximum local |E| at resonance wavelengths of SPPs (triangles). The structural period is fixed at 475 nm, the film thickness is 40 nm and the bump height is 100 nm.
4. Conclusion
We have investigated the plasmonic properties of a potential SERS substrate, on which both the LSPs and SPPs can be excited. The FDTD simulation shows that the resonance wavelengths of LSPs and SPPs can be effectively tuned via changing the structural period and the silver film thickness. LSPs and SPPs can co-exist at specific wavelengths such that the coupling between them can contribute to a considerable boost of Raman enhancement. A Raman enhancement of ~2 × 109 is achieved in the proposed structure. In addition, the good proportionality between the resonance wavelength of LSPs and the environment RI could lead to a potential application for biosensing. This work illustrates a structure with large area, regular hotspots, as well as extremely high Raman enhancement. It is a good candidate for SERS substrates as it can be easily fabricated using conventional silicon process technology.
Acknowledgment
This work was financially supported by the Singapore National Research Foundation (CRP Award No. NRF-G-CRP 2007-01). X. J. Zhang acknowledges the support from the National Natural Science Foundation of China under Grant No. 10804003. X.C. Yuan acknowledges the support from the Ministry of Science and Technology of China under Grant No. 2009DFA52300 for China-Singapore collaborations.
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