Titanium vacancy diffusion in TiN via non-equilibrium ab initio molecular dynamics

Transition metal nitrides (TMNs) refractory ceramic materials are widely employed as wear-resistant protective coatings in industrial machining as well as diffusion barriers inhibiting migration of metal impurities from the interconnects to the semiconducting region of electronic devices. TiN is the prototype of this class of materials and the most studied among TMNs. However, also for this system, a complete picture of the migration processes occurring at the atomic scale is still lacking. In this work I investigate the stability of Ti vacancy configurations and corresponding migration rates in TiN by means of density functional theory (DFT) calculations and ab-initio molecular dynamics simulations (AIMD). DFT calculations show that Ti vacancies tend to stay isolated because of repulsive interaction which decreases as the inverse of the distance between the vacancies.The equilibrium jump rate of single Ti vacancies in TiN is extrapolated temperature as a function of temperature from the results of non-equilibrium AIMD simulations accelerated by a bias force field according to the color diffusion algorithm. For each force field and, the jump occurrence times are fitted with the two parameters Gamma distribution in order to obtain the non equilibrium jump rate with the corresponding uncertainty. Extrapolated equilibrium values show an Arrhenius-like behavior, with activation energy Ea= (3.78 ± 0.28)eV and attempt frequency A = 4.45 (x3.6±1) x 1014 s-1