**4. Conclusions**

In summary, this article presents a detailed study of semi-continuous gold films near the percolation threshold deposited on two types of substrate—SiO2/Si and graphene/SiO2/Si. We demonstrated that the thickness of the deposited gold films measured by AFM and sensor values can vary significantly. The percolation threshold has been determined by two independent experimental methods as a four-probe measurement of the sheet resistance and spectroscopic ellipsometry. These methods show good agreemen<sup>t</sup> with each other for both types of substrate with and without graphene. According to them, the thicknesses of the percolation threshold is between 7 and 8 nm for the films on the SiO2/Si substrate and between 6 and 7 nm on the graphene/SiO2/Si substrate. The maximum SERS signal was obtained for the gold films with thicknesses near the percolation threshold in the case of both types of substrate and amounted to be ~6.0 × 10<sup>4</sup> (graphene/SiO2/Si) and ~1.1 × 10<sup>5</sup> (SiO2/Si), respectively. SERS measurements of the dye Crystal Violet demonstrated the ability of graphene to e ffectively quench luminescence by an average of ~60%. Thus, the substrates with and without graphene show comparable SERS signals. However, the presence of graphene shows the ability to quench luminescence, which provides a grea<sup>t</sup> advantage over other types of SERS substrates. Our results demonstrate that the high intensity of the SERS signal is also observed for the films thicknesses adjacent with the percolation threshold, but only for thicknesses slightly below. Additionally, we show a strong correlation between FOM and intensity of SERS spectra. The maximum EF for both types of substrate corresponds to zero slopes of the FOM curves in the infrared region. We propose to use FOM curves as an additional criterion for finding the percolation threshold and the thicknesses of the films that exhibit the maximum EF. We believe that the reported results will be interesting for SERS applications, especially for bio- and molecular sensing.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2079-4991/10/1/164/s1, Figure S1: Image of the substrate with CVD graphene in white light; Figure S2: SEM images of gold films with thicknesses from 3 to 10 nm deposited on (a)–(h) SiO2/Si and (i)–(p) graphene/SiO2/Si substrates respectively; Table S1: Table with averaged parameters of gold films deposited on graphene/SiO2/Si substrate; Table S2: Table with averaged parameters of gold films deposited on SiO2/Si substrate Figure S3: The schematic representation of the experimental setup used for the resistance measurements; Figure S4: An example of measured (dashed lines) and calculated (solid lines) from the fit ellipsometry parameters Ψ and Δ, used for Figure 4: Figure S5: The dependence of EF on the thicknesses of gold film (plotted with an integrated intensity of 1626 cm<sup>−</sup><sup>1</sup> Raman mode).

**Author Contributions:** S.M.N. supervision; D.E.T., S.M.N., A.A.V., A.V.A. and V.S.V. proposed the concept and designed the experiment; D.E.T., D.I.Y., S.M.N., G.A.E. and Y.V.S. contributed to the measurement results; D.E.T. and S.M.N. wrote the original draft. All authors discussed the results and contributed to manuscript preparation. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Russian Science Foundation, gran<sup>t</sup> number 18-79-10208.

**Acknowledgments:** We thank the Shared Facilities Center of the Moscow Institute of Physics and Technology (grant no. RFMEFI59417 × 0014) for the use of their equipment.

**Conflicts of Interest:** The authors declare no conflict of interest.
