## 4 Results and Discussion
### Performance of the SERS Substrates  
In order to see how the different substrate morphologies affect the SERS signal, we measured SERS spectra of R6G solution using substrates with different sputtering times. Figure 7 shows the results of measured SERS spectra of a \(10^{-6}\) M concentration of R6G solution using substrates with different sputtering times. We can see that before the nanospheres merge, as the sputtering duration becomes longer, the gap between the nanospheres becomes smaller and the SERS signal intensity increases rapidly. After the nanospheres merge, the SERS intensity begins to decline. By plotting the peak intensities of 1503 cm\({}^{-1}\) in the R6G SERS spectra against the corresponding inter-nanosphere gaps, we found that before the nanospheres merge, the intensity of the SERS signal is a logarithmic function of the inter-nanosphere gap, as shown in Figure 8. This result is consistent with the findings of [PERSON] et al. [13]. It also indicates that when the inter-nanosphere gaps are as small as 10 nm or less, we can obtain strong hot spots, so that a good SERS enhancement effect can be obtained. Figure 9 shows the SERS spectra of blank SERS substrate, bulk R6G, and R6G solutions with concentrations of \(1\times 10^{-6}\) M, \(1\times 10^{-7}\) M, \(1\times 10^{-8}\) M, and \(1\times 10^{-9}\) M, respectively, using our SERS substrate with sputtering duration of 200 s. The Raman band assignment of the main peaks for R6G were given in Figure 9. Characteristic peaks of R6G at 607, 765, 1176, 1304, 1355, 1503 and 1640 cm\({}^{-1}\) were clearly observed from these spectra. These spectra demonstrate the good enhancement factor of the SERS substrate we have developed. As can be seen from the figure, the signal from the SERS system itself is very small compared to the SERS signal of the analyte and does not mask the measured  
Figure 8: Intensities of the 1503 cm\({}^{-1}\) SERS signal of R6G recorded as a logarithmic function of the nanosphere gap size. Figure 7: The SERS spectra of the R6G molecules on the developed SERS active substrate with sputtering durations of 50, 100, 150, 200, 250 and 300 s, respectively. analyte signal. One might question that polycarbonate is a Raman-active compound that can interfere with molecular signals for SERS detection. Here we show that proper decoration of the polycarbonate surface with silver metal can suppress the background Raman signal of the polycarbonate substrate and also prevent melting and degradation of the polycarbonate substrate when exposed to the focused laser beam. This result is consistent with the findings of [PERSON] et al. [21]. To estimate the enhancement factor (EF) values of R6G, the following commonly used formula [2] was used:  
\[EF=(I_{SERS}/I_{bulk})/(N_{bulk}/N_{SERS}) \tag{1}\]  
where \(I_{SERS}\) and \(I_{bulk}\) are the vibration intensity of the SERS and the normal Raman spectra of R6G molecules (the vibration band at 1503 cm\({}^{-1}\) was selected in this study), respectively. \(N_{SERS}\) and \(N_{bulk}\) are the number of molecules irradiated by laser spots under SERS and normal Raman of bulk sample condition, respectively. The average surface density of rhodamine 6G (R6G) molecules in densely packed monolayers is reported to be approximately one R6G molecule per 4 nm\({}^{2}\)[22]. Then, the surface coverage of the R6G monolayer on the SERS substrate is \(4.15\times 10^{-11}\) mol/cm\({}^{2}\) (molecular density = 1/(4 \(\times 10^{-14}\))/(6 \(\times 10^{23}\)) mol/cm). For the laser spot of 2 \(\upmu\)m in diameter, the \(N_{SERS}\) has a value of \(1.3\times 10^{-18}\) mol (\(N_{SERS}=4.15\times 10^{-11}\) mol/cm\({}^{2}\times\pi\times 1\)\(\upmu\)m\({}^{2}\)). For bulk samples, the sample volume is the product of the laser spot area (about 2 \(\upmu\)m diameter) and the penetration depth of the focused laser beam (\(\sim\)2 \(\upmu\)m).