## 3 Results
### Raman Measurements  
The Raman spectra (Figure 2) of Rhodamine B show a general decrease in intensity with decreasing concentrations, though this decrease is not a simple linear one, nor is it fully monotonous. One can note, in particular, that, almost consistently, the \(10^{-3}\) M spectra are less intense than the spectra for lower concentrations. This is most probably due to the fact that the highly concentrated solution creates a thicker layer of Rhodamine B upon the substrate; however, since the SERS effect is a surface phenomenon, the additional molecules further away from the surface have little to no effect to the increase in the Raman signal. In fact, they seemingly have the opposite effect--blocking light from hitting the active surface and imparting a large luminescence signal on top of the Raman signal; therefore, a larger concentration of the analyte may not be preferable and may not lead to a larger Raman signal intensity when conducting SERS-based spectroscopy. Regarding the various substrates, with the 532 nm incident laser, all substrates show a distinguishable Raman signal down to the \(10^{-9}\) M Rhodamine B solution. Substrates A and B show stronger Raman signals than C, although substrate C takes over in signal intensity compared to substrate B from around \(10^{-7}\) M. However, the strong EF leads to the spectrum of amorphous carbon being more enhanced and overwhelming the signal from Rhodamine B. This amorphous carbon spectral contamination is a known problem with the SERS method [19]. The analytical enhancement factors for each substrate at the 1358 cm\({}^{-1}\) peak are 3.0\(\cdot\)10\({}^{7}\), 4.5\(\cdot\)10\({}^{6}\), and 3.6\(\cdot\)10\({}^{6}\) for substrates A, B, and C, respectively. The EFs have been calculated for concentration \(10^{-6}\) M; a somewhat high analyte concentration is chosen since it allows for more analyte molecules to be evenly distributed on the surfaces,  
Figure 2: Rhodamine B SERS spectra at concentrations \(10^{-3}\)...\(10^{-12}\) M on the substrates: (**a**) substrate A; (**b**) substrate B; (**c**) substrate C. The incident laser wavelength is 532 nm @ 2.55 mW, 1 s exposure. minimising the random error due to large fluctuations in enhancement caused by a lower number of molecules. It must be said that the EF by itself is not the only metric by which to determine the quality of a SERS substrate. Some substrates may show less background fluorescence relative to the Raman spectrum which, in turn, makes the Raman maxima easier to distinguish, even if the AEF of the Raman lines may be smaller. This is apparent with substrate B, especially where the resolution of the Raman spectra is still adequately distinguishable down to \(10^{-12}\) M, although the EF and the general signal intensity for substrate B is at times smaller than those for substrates A and C (Figure 3). The way the analytical enhancement factor is conventionally defined (proportional to the analyte concentration) does not accurately describe the way molecules adsorb on the substrate surface and contribute to the enhanced Raman spectra. This is particularly evident when considering single-layered substrates (such as substrate C), where any additional molecules are quickly pushed further and further away from the active surface, in turn barely contributing to the spectrum at all. More accurate EF definitions use an evaluation of the number of molecules within the analyte volume being excited. An even more accurate EF would be defined by taking into consideration the three-dimensionality and multi-layered structure of the substrate, as well as the ways in which the adsorbed analyte molecules contribute to the Raman spectrum. One such definition is the following  
\[SSE=\frac{I_{ SERS}}{I_{Raman}}\frac{C_{Raman}H_{eff}}{\mu_{MS}A_{M}}[2] \tag{2}\]  
which includes the analyte concentration \(C_{Raman}\), the effective sampling height \(H_{eff}\), the surface density \(\mu_{M}\) and surface area \(A_{M}\) of the metallic nanostructures, and the surface density of the analyte molecules \(\mu_{S}\).