## 3 Results and Discussion
### Studies of the Effect of Morphology on the Amplitude of the Raman Scattering Signal of Myoglobin  
We demonstrated that Raman signal amplification depends dramatically on the silver SERS-active substrates surface morphology. In order to adequately link the film surface distinctive features and the signal amplification, it is necessary to choose the most significant film surface parameters. We used the Gwyddion software and masking mode to perform film surface feature parameters analysis based on AFM images. An important averaged parameter characterizing the surface is a root-mean-square roughness (Rq) of the films, which reflects the degree of surface coverage with defects (or pores) and describes the surface perfection at macro level. Figure 4 shows detailed image of the microstructure of pore-like structures for the sample type V, which corresponds to one of the largest Raman spectra amplification. Despite the general macroscopic smoothness of the film, one can notice, that locally the size of frequently encountered pores of complex shapes reaches up to 30 nm in depth. The analysis showed that the effective size of the pores (microstructure defects) is 127 nm, the average surface area occupied by these defects equal to 12.5%. The average number of defects in a 10 \(\times\) 10 \(\upmu\)m area is around 250. Calculations showed that the root-mean-square roughness of films of this type is about 5 nm. The kurtosis parameter (Rku), which describes the degree of defects sharpness, is equal to 16.5 for \begin{table}
\begin{tabular}{c c c} \hline
**Type of SERS** & **The Average Intensity of Myoglobin Spectrum for Concentration** & **EF** \\
**Structure** & **10 \(\upmu\)g/mL, CCD cts** & **10 \(\upmu\)g/mL, CCD cts** & **10 \(\upmu\)g/mL** \\ \hline I & 3100 \(\pm\) 700 & \(\sim\)10\({}^{3}\) \\ II & 3100 \(\pm\) 600 & \(\sim\)10\({}^{3}\) \\ III & 4000 \(\pm\) 1350 & \(\sim\)10\({}^{3}\) \\ IV & 35,100 \(\pm\) 10,700 & \(\sim\)10\({}^{4}\) \\ V & 159,000 \(\pm\) 35,000 & \(\sim\)10\({}^{5}\) \\ VI & 4300 \(\pm\) 900 & \(\sim\)10\({}^{3}\) \\ VII & No signal & no \\ Control & 10 \(\pm\) 8 & no \\ \hline \end{tabular}
\end{table} 
Table 1: The characteristic intensities of the myoglobin Raman scattering bands. Figure 4: Type V sample: (**a**) atomic force microscopy (AFM) image of the film surface; (**b**) local defect cross section. the presented film, in contrast to smooth regular films where it is less than 3. The degree of local heterogeneity of the film is estimated by R3z parameter, which is the vertical mean from the third highest peak to the third lowest valley in a sample length over the evaluation length, equals to 13.2 nm. The average maximum profile height Rz was 9.7 nm. Another two parameters describe the profile of the film cross-section at the macro level: mean square waviness (Wq) equal to 57.5 nm that shows the amplitude of the harmonic envelope and the profile of the curve. And the root-mean-square wavelength of the profile (\(\lambda\)a) equals to 590 nm, that shows the envelope wavelength. We have chosen this set of parameters in combination with the measured Raman spectra to determine the optimal surface morphology for high-quality SERS-active substrate nanoengineering. Structures of alike morphology with the sample type V (see its cross section on Figure 5a), but with slightly modified surface pore-like structures parameters (Figure 5b shows cross section of the sample type VI), demonstrate a decrease in the Raman signal amplification. With such a huge number of surface quality parameters, it is naturally difficult to recover the link function between surface parameters, deposition recipe and Raman signal amplification. That is why in the next sections we used machine learning techniques for data treatment to engineer high-effective SERS-active substrates. The sample type VI parameters are: the mean square roughness (Rq) is 7.4 nm, the R3z is 29.0 nm, the kurtosis (Rku) is 3.9, the mean square waviness (Wq) 81.7 nm, the average wavelength of the profile (\(\lambda\)a) is 680 nm.