Surface-enhanced Raman Scattering (SERS) is studied in sub-wavelength metallic gratings on a substrate using a rigorous electromagnetic approach. In the ultraviolet SERS is limited by the metallic dampening, yet enhancements as large as 105 are predicted. It is shown that these enhancements are directly linked to the spectral position of the plasmonic band edge of the metal/substrate surface plasmon. A simple methodology is presented for selecting the grating pitch to produce optimal enhancement for a given laser frequency.
©2012 Optical Society of America
Since its first observation  and discovery [2,3], surface-enhanced Raman scattering (SERS) has been widely studied both theoretically and experimentally  due to a large variety of potential applications in chemical and biological sensing . SERS is commonly attributed to two mechanisms: a) enhancement in polarizability and b) electromagnetic enhancement. The former are due to chemical effects such as charge-transfer excited states , while the latter are due to the excitation of surface plasmons (SPs) on a periodically patterned metal surface  or localized plasmons over a rough metal surface [8,9].
Because Raman scattering cross sections approximately scale as the fourth power of the laser frequency  ultraviolet SERS spectroscopy should produce much stronger signals than traditional visible or infrared wavelength SERS. These signals may be further enhanced in certain proteins and nucleic acids that exhibit an electronic resonance in the ultraviolet (UV) region [11, 12]. Furthermore, an analyte’s UV SERS spectra generally will not overlap with its fluorescence spectra, thereby enabling better recognition specificity through the simultaneous measurement of both . UV SERS has been experimentally studied for roughened aluminum (Al) surfaces in Refs [14,15]. and numerically studied for an array of nano-holes in Ref .
However, the study of SERS in the UV poses several challenges. First, the most commonly used metals for SERS, silver and gold, do not have a negative real part of the electric permittivity in the frequency range of interest. Second, even for metals like aluminum (Al) which does posses a negative electric permittivity in the UV, the SP will be severely dampened in that frequency range due to the large value of the imaginary part of the electric permittivity. As an example, Fig. 1 presents the propagation length of a SP at an Al/sapphire (Al2O3) interface (left y-axis) and its effective index (right y-axis). Using realistic values of the dispersion taken from Palik , the propagation length and the effective index have been calculated respectively as :Fig. 2 ) to estimate UV SERS performance as a function of grating period and laser wavelength. The calculations have been performed using a rigorous electromagnetic approach based on the Fourier-modal method (FMM) [19,20] which lends itself well for calculation of the transmission (T), reflection (R), absorption (A = 1-R-T), and field localization in periodic structures.
2. Results and discussion
Let us start our analysis by showing in Fig. 3(a-c) the absorption calculated in the plane (ω, kx) using the FMM for three different structures with periods Λ = 160nm, 128nm, and 96nm. In all three cases, the thickness of the Al grating is d = 50nm, and the slit aperture is a = 16nm. Calculating the absorption of the grating provides useful information about its plasmonic band structure. According to the fluctuation-dissipation theorem , the absorption is proportional to the average electric field localization in the metal through the imaginary part of its electric permittivity: A(ω)≈Im(ε)〈|E(ω)|2〉.
Therefore, regions of high absorption are an indication of resonant fields inside the metal. In the figures are also reported the analytical dispersion of the unperturbed Al/Al2O3 SP and the unperturbed Al/air SP. Both have been folded in the (ω, kx) plane using the various reciprocal lattice vectors G = 2π/Λ of the grating according to ω(kx) = Ω(|kSP ± mG|). For completeness, the figures also report the dispersion of the Rayleigh condition in the substrate: ω(kx) = Ω(|kAl2O3 ± mG|). In this case the Rayleigh condition corresponds to having the first diffraction order propagate tangentially to the grating at the grating/substrate interface . The actual, full dispersion ω = ω(kx) of the gratings (thick-dashed line) has also been numerically calculated by finding the zeros of the determinant of the respective scattering matrices |det M(ω, kx)|.
Figures 3(a-c) highlight four relevant features. First of all, note that the periodic texturing of the grating modifies the unperturbed dispersion of the Al/Al2O3 and air/Al SPs, leading to the formation of plasmonic band gaps in the region of intersection of the unperturbed dispersions. In particular, in the propagation region (kx < k0), the plasmonic band gap is formed at the intersection of the unperturbed dispersions of the Al/Al2O3 SP folded along G and –G. The plasmonic band gap is bounded by a low frequency and a high frequency band edge where SP standing waves can be excited [18,22]. This is the classical mechanism that leads to band gap formation, well known in solid-state physics and wave-physics .
Second, the numerically calculated dispersion (thick-dashed line) follows the absorption resonances of the structures remarkably well, as expected based on the above-mentioned considerations. In particular, the maximum of the absorption follows the low frequency plasmonic band edge which is located at ω = 3.82eV (λ~325nm) for Λ = 160nm, at ω = 4.16eV (λ~300nm) for Λ = 128nm, and at ω = 4.4eV (λ~280nm) for Λ = 96nm. Third, the spectral position of the plasmonic band edge can be moved toward high frequencies by simply decreasing the period of the grating. Fourth, the spectral width of the plasmonic band gap enlarges as it is pushed toward higher frequencies. It will be seen later that all these characteristics can be described by using a simple, analytical model.
Raman enhancement increases approximately as the fourth power of the modulus of the electric field [5,9,10]. For a molecule randomly positioned inside the slits of the grating the average Raman enhancement is calculated as :Fig. 3(d-f). The figures show the Raman enhancement in the (ω, kx) with the dispersion superimposed. The figures make clear that the Raman enhancement follows the plasmonic dispersion of the structure extremely well, with the consistent enhancement in the region near the low frequency plasmonic band edge. Note that the plasmonic dispersion has been calculated from the absorption of the metal structure while the Raman enhancement has been calculated as in Eq. (2), so the two quantities are not in general related to each other. The fact that the Raman enhancement follows the plasmonic dispersion is a clear indication of the dominant role played by the plasmon modes in the cases analyzed.
To highlight the resonant characteristics of the process, Fig. 4 summarizes the average Raman enhancement calculated for normal incidence (kx = 0). The enhancement decreases and linewidth broadens as the frequency increases as expected considering the increasing dampening suffered by the Al/Al2O3 SP in these cases (see for comparison Fig. 1). For Λ = 160 nm, the propagation length of the SP is still enough to encompass more than ten elementary cells of the grating, while for Λ = 96 nm only few elementary cells are encompassed. Still, even at the highest frequencies, the enhancement factor remains quite large with an average enhancement in the slit of ~103.
In Fig. 5 is shown the absolute value of the electric field in an elementary cell of the grating. In particular, Fig. 5 (a-c) plots the normal incidence absolute value of the electric field in logarithmic scale at the frequencies corresponding to the maximum Raman enhancement for the three structures. The field intensity at the Al/Al2O3 interface decreases for increasing frequency in agreement with the predicted increase of the damping of the Al/Al2O3 SP. For a better perspective, Fig. 5 (d-f) plots instead the same quantity in a 3-D view. Both panels report the position of the “hot spots” where the maximum Raman enhancement is available.
It is shown that these “hot spots” are located near the edges of the grating at the air/Al interface, and their strength gradually decreases for increasing frequency in agreement with the previous results. In general, it is well known that the greatest electromagnetic field localization occurs near imperfections in the form of a metallic tip or step in an otherwise flat surface . In the present cases the “hot spots” are located near the step of the grating at the air/Al interface and, less intensely, at the Al/Al2O3 interface. Note that the strength of these “hot spots” is still determined by the strength of the Al/Al2O3 SP; in fact, it is found that |E/E0|Max~23 for Λ = 160 nm, |E/E0|Max~19 for Λ = 128 nm, and |E/E0|Max~17 for Λ = 96 nm, corresponding respectively to local Raman enhancements approximately of 234 = 2.7x105, 194 = 1.3x105, and 174 = 8x104. Moreover, the strength of the “hot spots” depends on the thickness of the Al grating d. As d increases, Ohmic losses increase and the electromagnetic field funneled inside the slits is increasingly dissipated. Conversely, as d decreases the electromagnetic field is less effectively funneled through the slits, while a portion of the field continues to be dissipated by Ohmic losses in the metal itself. The result is the same in both cases: a decreased coupling efficiency of the field to the Al/Al2O3 SP and a reduced intensity of the “hot spots.” The optimal thickness for the formation of the “hot spots” comes from a balance of these two effects and must be assessed on a case by case basis.
The position of the plasmonic band edge and the width of the band gap can be recaptured by the following simple analytical dispersion model that uses the Bloch vector Kβ of an ideal 1-D, multilayered structure :Fig. 1. Figure 6 shows the plasmonic band gap position predicted by the Bloch vector approach as in Eq. (3) for the structures with periods Λ = 160 nm and 128 nm, respectively. Comparing Fig. 6 with the plots in Fig. 3 for the first two structures, note how the position and width of the plasmonic band gap are predicted with remarkable accuracy, especially considering that the analytical model does not take into account the finite thickness of the Al grating and neglects the damping of the SP. This simple model confirms the notion of a plasmonic band edge and provides a simple tool for estimating the grating pitch that will produce the greatest Raman enhancements for a given UV laser frequency. In particular, the enlargement of the plasmonic band gap for higher frequencies can be ascribed to the increasing index contrast between the “air layers” and neff of the “plasmonic layers” (see Fig. 1), in complete analogy with the band gap of conventional 1-D multilayered structures .
The kind of structures proposed in this work can be fabricated using current nanofabrication techniques. Aluminum gratings will rapidly oxidize upon exposure to air and will typically be coated by a 2-3nm layer of Al2O3 [13,26,27]. Figure 7(a) reports the average Raman enhancement for molecules inside the slits with the oxide overlayer, and the results should be compared with those reported in Fig. 4 for the bare grating. Notice that the reduction in the Raman enhancement caused by the oxide overlayer becomes more severe as Λ decreases. The effect of the oxide on the average Raman enhancement has also been calculated for two experimentally relevant cases: the molecules occupy a region that includes the slits and some space above the grating (Fig. 7(b)), and the molecules form a self-assembled monolayer 3nm thick (Fig. 7(c)). The figures show how the salient physical characteristics of the Raman enhancement are basically preserved under the various circumstances mentioned above, although the degree of enhancement depends on the spatial separation between the plasmon and the analyte . This is another indication of the dominant role played by the plasmonic band edge associated to each structure.
In conclusion, we have studied UV SERS for an Al grating grown on a sapphire substrate and shown that, despite large ohmic losses, large Raman enhancement factors can be achieved by operating at the plasmonic band edge. An analytic dispersion model accurately reproduces the calculated plasmonic band edge and provides a simple tool for estimating the grating pitch to produce optimal Raman enhancement for a given UV laser. Note that the methodology presented here has a general validity and therefore we should expect similar results for properly designed gratings made of other metals like Ga and In , for example, opening new venues for UV SERS.
N.M., G.D. and M.C.B. acknowledge financial support from DARPA SBIR project “Nonlinear Plasmonic Devices” contract number W31P4Q-11-C-0109.
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