## 2 Materials and Methods
### Results of Samples ZrN H, ZrN L, ZrN M and ZrN N  
According to the intended objective of this work, the subset of samples ispresented as follows; witness the example of the desired results. In fact, many answers are found to the challenges listed in Section 3 (from point a to f). In Figure 9a, a peak comparison for the three main elemental regions of samples ZrN H, L, N is reported, referring to raw data without any charge correction or manipulation. Sample ZrN M shows many similarities with sample ZrN N and, therefore, it was cut out. Care was taken with the BE range of the X-axis: it was unchanged for each correspondent chemical species to make a reasonable comparison. They were chosen in the following intervals expressed in Binding Energy (BE): [172.0, 192.0] eV for Zr 3d, [390.0, 408.0] for N 1s, and [520.0, 540.0] eV for O 1s. Preliminary and general considerations can be deduced by looking at Figure 9a where the surface behavior of samples H, L and N is reported. Oxygen is revealed on the surface region of all samples, forming native oxides with zirconium, which is ZrO\({}_{2}\) -like and centered at 530.2 eV on the O 1s spectrum, and at about 180 eV on Zr 3d\({}_{5/2}\) line, while the hump of O 1s centered at 531.4 eV and is associated with the ZrON compound. Figure 9: _Cont._The qualitative surface scenario found is common to many transition metal nitrides obtained with different deposition techniques: a thin-layer oxide/hydroxide (eventually oxynitride) is formed after air exposure and the nitrogen signal (N 1s region) cannot be visible (sample H) or distinctly revealed on the surface of samples L and N according to the thickness of the oxide/hydroxide layer. Concordantly, the Zr 3d peak shape changes from sample H to L and N samples, due to the only contributions of oxide/hydroxide in the first row. The situation after in-situ sputtering has been represented in Figure 9b. The oxygen signal goes down to zero for all samples and the Zr 3d peak shape and position can be associated with zirconium nitride. At the same time, the N 1s line stands centered at 397.4 \(\pm\) 0.02 eV with a typical tail from the high-binding-energy side [23]. The absence of oxygen as well as any other kind of contamination for the in-depth samples helped us [24] proceed to a quantitative peak-fit deconvolution in order to extract the synthetic peaks, contributing to the overall experimental peak shapes and the reading of their positions. Finally, XPS quantitative results, for samples L, M and N are reported in Table 4 for the first parts of their complete depth-profiling. The results obtained from each of the two fit functions SLG (30) and LA (a,b,c) are also compared. Figure 9: (**a**): Surface high-resolution spectra of Zr 3d, N 1s and O1s for samples ZrN H, L, N. (**b**): In-depth acquisitions of high-resolution spectra of Zr 3d, N 1s and O1s for samples ZrN H, L, N after two sputter-cycles (labelled as DP region). Calculated stoichiometries (N/Zr ratio, labelled R) for sample ZrN H are reported for completeness for levels n = 2,3,4,5 from the surface (level one) for the fit built-in function LA (a, b, c) as in Table 4: for n = 2 R is 0.92; for n = 3 R is 0.99; for n = 4 R is 1.03; for n = 5 R is 1.19; for n = 6 R is 0.94. A further confirmation of the realization of ZrN stoichiometric coatings comes from the final XPS quantitative results reported in Table 4 for the first four layers of the complete depth-profiling. After some qualitative considerations on N 1s high-resolution XPS spectra parameters (position, FWHM and tail behavior from the high BE side) it can be asserted that samples L, M and N after a gentle sputter-cleaning to remove surface contaminants (i.e., at level 2 of the acquisition) present only one compound, identified as ZrN, presumably with a c-ZrN NaCl-like structure as deduced using x-ray diffraction (XRD) spectra (not reported here) performed on the same samples analyzed using XPS.