Ab initiostudy of Cu impurity diffusion in bulk TiN

Modeling of Diffusion and Incorporation of Interstitial Oxygen Ions at the TiN/SiO2 Interface

“…The lattice vectors and ion positions were fully optimized to converge the forces with a tolerance of 5 × 10 -3 eV/Å, reproducing the experimental lattice parameters to ≈ 1 % (4.218 Å). The calculated density of states (DoS) shown inFigure 1is in excellent agreement with the previous TiN studies confirming that the region around the Fermi level is composed primarily of Ti d-states 45,46,57. This will act as an important reference for the GB system, the cluster representation of TiN, and the interface with SiO 2 as the DoS around the Fermi level needs to be well described, with an experimental valence band-Fermi level offset with a-SiO 2 of 4.2 eV 58.…”

“…The GB 59 and extend the previous work on Cu diffusion in this GB. 45,46 In common with the bulk TiN, VASP was utilized with the PBEsol functional. 55,56 In this case the 12×6×1…”

“…Finnis43 and Mishin et al44 schemes under the dilute solution approximation, as detailed by Popov et al45,46 …”

Nonequilibrium ab initio molecular dynamics determination of Ti monovacancy migration rates in B1 TiN

“…Ab initio density functional theory (DFT) calculations combined with the nudged elastic band (NEB) [34,35] or the string method [36,37] are typically employed to estimate minimum energy paths and migration energies at 0 K [38][39][40][41][42][43]. Kinetic properties are extrapolated to finite temperatures using transition state theory (TST) [44] by assuming essentially fully harmonic lattice vibrations, or employing quasiharmonic approximations [45,46].…”

Perspectives on the Theory of Defects

“…In this situation, the knowledge of the vacancy concentration as a function of stoichiometry and temperature is of great importance, since it directly enters the diffusion coefficient. Based on DFT calculations, the vacancy concentrations and diffusion coefficient for Cu through bulk TiN for different compositions have been determined (Bochkarev et al, 2016a): At 1,250 K, it is 0.5 × 10 −21 m 2 /s in the stoichiometric case, while for nitrogen deficient TiN 0.96 , it is about 10 −18 m 2 /s, which is more than 3 orders of magnitude larger. Razumovskiy et al (2013) have shown that in ZrC and TiC, vacancy clusters are energetically very favorable: While singlemetal vacancies have large formation energies of ∼ 8 eV, the removal of C atoms close to the metal vacancy reduces the formation energy.…”