## 2 Materials and Methods  
Graphene was grown on commercial 25 \(\upmu\)m thick polycrystalline copper foils (99.5%, Alfa Aesar, Haverhill, MA, USA) in an in-house built chemical vapor deposition (CVD) reactor. The foil was annealed, prior to the graphene deposition, at 1000 \({}^{\circ}\)C in Ar/H\({}_{2}\) (99.999%, Linde Gas, Estonia) flow for 60 min, and then additionally exposed to the mixture of 10% CH\({}_{4}\) (99.999%, Linde Gas, Estonia) in Ar at 1000 \({}^{\circ}\)C for 120 min. Then, the foil was cooled down in an Ar flow. Graphene/Cu foil (20 mm \(\times\) 40 mm) was cut into 5 mm \(\times\) 5 mm pieces and graphene was transferred onto 300 nm thick 10 mm \(\times\) 10 mm Si/SiO\({}_{2}\) substrates by using a wet chemical transferring process described in a publication by [PERSON] et al. [7].  
The Al\({}_{2}\)O\({}_{3}\) thin film was deposited from Al(CH\({}_{3}\))\({}_{3}\) (TMA) and H\({}_{2}\)O in a commercial PicosunTM R-200 (Picosun Oy, Finland) Advanced ALD system. TMA was evaporated at 22 \({}^{\circ}\)C, and 5 cycles with pulse times 0.3-4-0.3-6 s (TMA-N\({}_{2}\)-H\({}_{2}\)O-N\({}_{2}\), respectively) were made at room temperature. For reference the thick Al\({}_{2}\)O\({}_{3}\) film was deposited on graphene with 300 ALD cycles with the same cycle times at 300 \({}^{\circ}\)C. The deposition substrate was Si with 300 nm of amorphous SiO\({}_{2}\) on top of it.  
The surface morphology was characterized by using a scanning electron microscope (SEM) FEI Helios NanoLab 600 (FEI) in a high-resolution mode (10 kV, 86 pA) and composition was performed using an energy-dispersive X-ray (EDX) spectrometer INCA Energy 350 (Oxford Instruments, UK), attached to the SEM Helios NanoLab 600 (FEI)). A diffractometer SmartLabTM (Rigaku, Japan) with a rotating Cu anode (\(\lambda\) = 0.15406 nm) working at 8.1 kW was used for X-ray reflectivity (XRR) measurements for evaluating the thicknesses of the layers. A structural characterization of graphene-based nanostructures was performed by using a micro-Raman spectroscopic system (Renishaw, UK) in Via at an excitation wavelength of 514 nm and the silicon reference was used for calibration. The spectral resolution reached, approximately, 1.5-2 cm\({}^{-1}\).  
The mechanical properties (hardness and Young's modulus) were studied with the nanoindentation method by using the Hysitron Triboindenter TI980 ((Eden Prairie, MN, USA) implementing a Berkovich's diamond tip. The samples were measured in continuous stiffness mode with maximum applied loads of 0.25, 0.5, 2, 5 and 10 mN. Nine nanoindentation measurements were carried out, each with maximum loads with the total of 45 indentation events on each sample, while the distances between single indentation sites were 10 \(\upmu\)m. The calibrated nanoindentation displacement depth was from 5 to 200 nm. The calibration regions for nanoindentation measurements are shown in Figure 1. The occurrence of pile-up, i.e., the vertical redistribution of the material around the tip under load during nanoindentation measurements was investigated by implementing the scanning probe microscopy (SPM) with the same equipment. Gwyddion 2.56 software was used to analyze the SPM images.