## 5 Conclusions  
Ten ZrN coatings deposited using reactive bipolar pulsed dual magnetron sputtering, at different conditions, were quantitatively characterized by x-ray photoelectron spectroscopy both on the surface region and along their thicknesses, with a high level of accuracy for data elaboration. To the best of the knowledge authors' here, for the first time a comparison of the results for SLG (30) and LA (a,b,c) peak-fitting functions is presented for a TMN binary system. The SLG (30) built-in function systematically over-estimates the N/Zr ratio, because in calculating the synthetic Zr 3d areas SLG (30) it shows a greater discrepancy with experimental curves rather than the LA (a,b,c) function. On N 1s the two functions gave similar results for both built-in functions. The area discrepancies for the Zr 3d spectrum can be related to its complicated peak shape (cfr. Table 4).  
The coatings analyzed were all free from oxygen and any other contamination, except for sample A, presenting a very slight oxygen signal along its thickness. Six of the ten samples analyzed are nearly stoichiometric (1:1 ratio) with an average excursion in the range [0.7, 1] along the depths. This desired result has taken years; also, for the optional facilities present on the deposition apparatus, such as for example the mass spectrometer, this allowed us to acquire the plasma-emission spectra in the proximity of the growing film, thus allowing us to control and avoid oxygen contamination. Twin-deposited samples possess the same chemical features as their brother ones, demonstrating the repeatability of the films under the same experimental conditions.  
A monoatomic Ar+ cluster gun was preferred to the cluster Ar\({}^{+}\)2500 ion gun for depth-profiling acquisitions. The choice was motivated because the cluster ion gun source showed a low yield of nitrogen sputtering inside the sample, probably due to the thermal effects besides mere ballistic phenomena, and also the lower penetration depth respect to the monoatomic source.  
Shake-up satellite peaks of transition metal revealed in XPS core-level spectra have generated confusion and controversies in the literature but their positions and intensities give important information about the system under investigation. In this paper, the authors were faced with shake-up satellites on Zr 3d high-resolution spectra to accurately calculate the stoichiometries of oxygen-free ZrN films, neglecting the satellite contribution from the Zr 3d total area.  
It was observed that shake-up satellite quantitative features changed according to the sample structural order and its chemical composition. In ZrN films (if ZrN or Zr\({}_{3}\)N\({}_{4}\)), a shift was observed in the photopeak position associated to the main line Zr 3d\({}_{5/2}\). It stands at 182.4 \(\pm\) 0.02 for stoichiometric films M, N but changes for over-stoichiometric samples (i.e., B) at 181.79 \(\pm\) 0.02 or where there is little oxygen in-depth, as in sample A (cfr. Figure 1b). A constant peak position of the two satellites was revealed instead along the depth profiling of each film, suggesting homogeneity in the areas analyzed.  
Some of the coatings realized with a new deposition technique and characterized microanalytically using quantitative XPS were shown to be pure, repeatable and with N/Zr ratios of 1:1, suggesting their importance and application in many technological fields [30].  
Conceptualization M.L. and R.A. All the rest M.L. All authors have read and agreed to the published version of the manuscript.  
National Project entitled \"Close to Earth\" acronym CLOSE- Project code ARS01_00141.  
Not applicable.  
Simply contacting [EMAIL_ADDRESS].  
The authors wish to warmly thank [PERSON] for their professional, usefuland always kind support in helping us to understand the multifaceted world of the software CasaXPS, even though a long time has passed since the first show of interest in the software package.  
The authors declare no conflict of interest.