Prediction and identification of point defect fingerprints in X-ray photoelectron spectra of TiN$_x$ with 1.18 $\le x \le$ 1.37

We investigate the effect of selected N and Ti point defects in $B$1 TiN on N 1s and Ti\,2p$_{3/2}$ binding energies (BE) by experiments and ab initio calculations. X-ray photoelectron spectroscopy (XPS) measurements of TiN$_x$ films with 1.18 $\le x \le$ 1.37 reveal additional N 1s spectral components at lower binding energies. Ab initio calculations predict that these components are caused by either Ti vacancies, which induce a N 1s BE shift of -0.54 eV in its first N neighbors, and/or N tetrahedral interstitials, which have their N 1s BE shifted by -1.18 eV and shift the BE of their first N neighbors by -0.53 eV. However, based on {\it ab initio} data the tetrahedral N interstitial is estimated to be unstable at room temperature. We, therefore, unambiguously attribute the N 1s spectral components at lower BE in Ti-deficient TiN$_x$ thin films to the presence of Ti vacancies. Furthermore, it is demonstrated that the vacancy concentration in Al-capped Ti-deficient TiN$_x$ can be quantified with the here proposed correlative method based on measured and predicted BE data. Our work highlights the potential of ab initio-guided XPS measurements for detecting and quantifying point defects in $B$1 TiN$_x$.