Ab-initio molecular dynamics (AIMD) simulations based on density functional theory show that N adatoms are chemisorbed in threefold sites close to a N surface atom and between the two diagonally-opposed neighboring Ti surface atoms on TiN(001). The most probable N adatom reaction pathway, even in the presence of nearby N adatoms, is for the N adatom and N surface atom pair to first undergo several exchange reactions and then desorb as a N2 molecule, resulting in a surface anion vacancy, with an activation barrier Edes of 1.37 eV and an attempt frequency Ades = 3.4x10 13 s -1 . Edes is essentially equal to the N adatom surface diffusion barrier, Es = 1.39 eV, whileAs is only three to four times larger than Ades, indicating that isolated N adatoms migrate for only short distances prior to N2 desorption. The probability of N2 desorption via recombination of N adatoms on TiN(001) is much lower due to repulsive adatom/adatom interactions at separations less than ~3 Å which rapidly increase to ~2 eV at a separation of 1.5 Å. We obtain good qualitative and quantitative agreement with the above results using the modified embedded atom method (MEAM) potential to perform classical molecular dynamics (CMD) simulations.
We use classical molecular dynamics and the modified embedded atom method formalism to investigate the dynamics of atomic-scale transport on a low-index model compound surface, TiN(001). Our simulations, totaling 0.25 μs for each case study, follow the pathways and migration kinetics of Ti and N adatoms, as well as TiN x complexes with x = 1-3, which are known to contribute to the growth of TiN thin films by reactive deposition from Ti, N 2 , and N precursors. The simulations are carried out at 1000 K, within the optimal range for TiN(001) epitaxial growth. We find Ti adatoms to be the highest-mobility species on TiN(001), with the primary migration path involving jumps of one nearest-neighbor distance d NN between adjacent fourfold hollow sites along in-plane 100 channels. Long jumps, 2d NN , are also observed, but at much lower frequency. N adatoms, which exhibit significantly lower migration rates than Ti, diffuse along in-plane 110 directions and, when they intersect other N atoms, associatively form N 2 molecules, which desorb at kinetic rates. As expected, TiN and TiN 3 complexes migrate at even lower rates with complex diffusion pathways involving rotations, translations, and rototranslations. TiN 2 trimers, however, are shown to have surprisingly high diffusion rates, above that of N adatoms and almost half that of Ti adatoms. TiN 3 motion is dominated by in-place rotation with negligible diffusion.
Ab initio and classical molecular dynamics (AIMD and CMD) simulations reveal that Ti adatoms on TiN(001) surfaces migrate between neighboring fourfold hollow sites primarily along in-plane <100> channels. <100> and <110> single jumps, as well as <100> double jump rates, obtained directly from MD runs as a function of temperature, are used to determine diffusion activation energies Ea, and attempt frequencies A, for the three preferred Ti adatom migration pathways on TiN(001). From transition rates Aexp[-Ea/(kBT)], we determine adatom surface distribution probabilities as a function of time, which are used to calculate adatom diffusion coefficients Ds(T).AIMD and CMD predictions are consistent and complementary. Using CMD, we investigate the effect on the adatom jump rate of varying the phonon wavelength degrees of freedom by progressively increasing the supercell size. We find that long-wavelength phonons significantly contribute to increasing adatom mobilities at temperatures ≤ 600 K, but not at higher temperatures.Finally, by directly tracking the Ti adatom mean-square displacement during CMD runs, we find that Ti adatom jumps are highly correlated on TiN(001), an effect that yields lower Ds values than those estimated from uncorrelated transition probabilities. The temperature-dependent diffusion coefficient is (T) = (4.5 x 10 -4 cm 2 s -1 ) exp[-0.55 eV/(kBT)].
We use classical molecular dynamics and the modified embedded atom method to determine residence times and descent pathways of Ti and N adatoms on square, single-atom-high, TiN islands on TiN(001). Simulations are carried out at 1000 K, which is within the optimal range for TiN (001) epitaxial growth. Results show that the frequency of descent events, and overall adatom residence times, depend strongly on both the TiN(001) diffusion barrier for each species as well as the adatom island-edge location immediately prior to descent. Ti adatoms, with a low diffusion barrier, rapidly move toward the island periphery, via funneling, where they diffuse along upper island edges. The primary descent mechanism for Ti adatoms is via push-out/exchange with Ti island-edge atoms, a process in which the adatom replaces an island edge atom by moving down while pushing the edge atom out onto the terrace to occupy an epitaxial position along the island edge. Double push-out events are also observed for Ti adatoms descending at N corner positions. N adatoms, with a considerably higher diffusion barrier on TiN(001), require much longer times to reach island edges and, consequently, have significantly longer residence times. N adatoms are found to descend onto the terrace by direct hopping over island edges and corner atoms, as well as by concerted pushout/exchange with N atoms adjacent to Ti corners. For both adspecies, we also observe several complex adatom/island interactions, before and after descent onto the terrace, including two instances of Ti island-atom ascent onto the island surface.
Effects of atomic ordering on the elastic properties of TiN-and VN-based ternary alloys, 2014, Thin Solid Films, (571) elastic constants, compared to ordered structures. We attribute the low C44 values of ordered structures to the formation of fully-bonding states perpendicular to the applied stress. We find that the ductility of these compounds is primarily an effect of the increased valence electron concentration induced upon alloying.
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