## 4 Discussion  
The graphene layer increased the Young's modulus and hardness of the samples with the indentation depth (Figure 4). As similar trend has been measured before by [PERSON] et al. for the graphene-SiO\({}_{2}\)-Si system with nanoindentation [13]. As the deformation area expanded under the tip with higher loads, the number of C-C bonds participating in the deformation was multiplied, which probably increased the resistance to the tip. The indents on graphene covered substrate were shallower compared to the uncovered areas, yet the lateral sizes of the indents were similar. It is possible, the indenter tip penetrated both samples to similar depths, but the graphene layer recovered elastically to a much shallower shape. This would also explain why the graphene layer had a greater impact on Young's modulus than hardness. The relationship between the maximum averaged elastic modulus and loading force is presented in Table 3. The micro-Raman measurements were made on indents and between them to assess the quality of graphene (Figure 7). The change in D-band is clearly visible and we can see the relationship between the loading force and amount of defect rise (Table 3, D-band Area). As we can see, the loading force 10 mN was the increase of the amount of the defects and graphene is broken in the inset place. Despite this, the crystallinity of the graphene remains, i.e., the intensity of the 2D-band was only decreased by 18% compared to the graphene between the indents. [PERSON] et al. [25] found that the grain boundaries (and other defects) in polycrystalline graphene might decrease the mechanical strength of the material. However, it was shown by [PERSON] et al. [26] that the mechanical properties of the grain boundaries of the polycrystalline graphene might be dependent on the production processes and the possibility of grain boundaries possessing similar mechanical strength to pristine graphene. In the present work, at the maximum load of 10 mN, the area influenced by the nanoindentation measurement could have been large enough to reach the grain boundaries where the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Max. Load** & **D-Band Area** & **D-Band Area** & **Max. Ave. Young’s** \\  & **(mN)** & **Measured on Hole** & **between Holes** & **Modulus (Gpa)** \\ \hline \multirow{3}{*}{Si/SiO\({}_{2}\)/G} & 10 & 12,366 & 6578.5 & 96.0 \\  & 5.0 & 5825 & 1767 & 93 \\  & 2.0 & 5653 & 2514 & 88 \\  & 0.5 & 5425 & 3006 & 80 \\ \hline \multirow{3}{*}{Si/SiO\({}_{2}\)/G/Al\({}_{2}\)O\({}_{3}\)} & 10 & 6220 & 3967 & 125 \\  & 5 & 5566 & 3967 & 107 \\ \cline{1-1}  & 2 & 6529 & 1568 & 95 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: This is a table of the relationship between maximum load and amount of defect (area of D band) rose (D-band area fitted by Lorenz). Figure 7: Micro-Raman spectra of graphene-based nanostructures Si/SiO\({}_{2}\)/G, indents made with loading force 10 mN. graphene layer might have been weaker and defective (Figure 7 and Table 3). Wrinkles and bilayers have also been reported to lower the mechanical strength of graphene [25]. All these defects in polycrystalline graphene have been shown to make the graphene more ductile [14; 26], and at the highest load the graphene could start to plastically deform until a fracture at the grain boundaries, leading to deeper indents. For the polycrystalline graphene layer there might exist an optimal deformation size, at which it may possess the ability to recover the deformation during nanoindentation. Pristine graphene or polycrystalline graphene with mechanically stronger grain boundaries could increase [PERSON]'s modulus and hardness further at higher loads. This may at the same time make the material more brittle. In our case it seems that the very thin amorphous Al\({}_{2}\)O\({}_{3}\) layer could possess sufficient mechanical stiffness to cause a steady increase in the modulus with the displacement in Figure 8, acting similarly to the graphene layer.