## 2 Materials and Methods
### XPS Characterization
The different ZrN films, deposited using the DPDMS method on conductive substrates, generally did not show any charging shift in spectra, despite sample ZrN D that displayed a 2.1 eV shift to lower binding energies suddenly correcting after spectra acquisition with respect to the lines of a ZrN-standard present in our laboratory database. With respect to the past study [16], the authors changed the fit function from SGL (30) to an \"asymmetric Lorentzian\" LA (a,b,c) included in the built-in functions of the CasaXps v.2.3.24 PR1 software. LA (a,b,c) represents a kind of superset of Voigt function, with three variables and the possibility to include tail asymmetries on both sides in each synthetic peak considered. Nominally the \"a\" variable regulates the shape factor and must be properly chosen in combination with \"b\" and \"c\". From an operative point of view \"a\" regulates the tail behavior on the right side of the synthetic peak (i.e., at high BE), while\" b\" varies in the interval [1, 200] and influences both the tail factor on the left side and the FWHMs values. If properly tuned until an optimized residual standard deviation value is obtained (generally in the range [1, 3]) for numerical residual standard deviation-RSD),\"b\" gives good output results for the peak fits improving the quality of elaborated data and giving a lower margin of errors. Finally, \"c\" is an integer between 0 and 499, relative to the width of the synthetic peak it belongs to, but also influences the tail factor \"a\" and \"b\" variables together. It assumes widely different values during data elaboration. An accurate quantification of XPS data also depends on the ad hoc choice of the range of background subtraction. It absolutely remains a matter of primary importance, otherwise generating unreproducible results. The Shirley method has been chosen and the energy slot for correspondent core regions was assigned and fixed for background subtraction. In Table 2 the start/end points are reported for Zr 3d and N 1s core regions for 3 representative samples of the three groups of films, at surface and after sputtering (level 2). It is worthwhile to point out that the \"start\" and \"end\" points of level 2 remain identical for all the levels of depth profiling under the surface for both N 1s and Zr 3d regions. In Table 2 some experimental values for Shirley subtraction method are reported. also on the specific transmission function of the analyzer. It was activated by ticking the \"intensity correction\" box and filling the empty field with the value \(-0.6\). The theorical constrictions, such as the peak ratio in Zr 3d doublet fixed at 0.67 and the FWHM upper limit fixed at 2 in the satellite doublet, were introduced directly on the synthetic peaks in the \"Narrow quantification window\" of the software. A standard sputter Ar+ ion gun (model EX05) was employed for depth profiles using the bending geometry and shallow-condition angles (60-70\({}^{\circ}\) referred to the perpendicular axis to the surface of the sample). In Table 3 the sputtering parameters are reported for samples of group 1. Similar conditions were applied to samples of groups 2 and 3. Preliminary Preparation Procedures for XPS Experimental Spectra Acquisitions and Definition of Quantitative Parameters of the Research  
Before any activity, a calibration procedure was operated on the VersaProbe II 5000 PHI spectrometer employing a silver reference film, and the spectrometer was also sputter-cleaned to remove the adventitious contamination after air exposure. The mono X-ray source parameters were fixed as suggested by the vendor, to calibrate peak positions, but also to maximize their intensity values and optimize to full width at half maximum (hereon FWHM). After a survey spectrum acquisition check, the Ag 3d doublet was acquired. The Ag 3d\({}_{5/2}\) line position was centered at 368.266 \(\pm\) 0.02 eV of binding energy and the FWHM was 0.8 eV; these values ensure the correct position and the best energy resolution for each peak to be analyzed.