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We use molecular dynamics (MD) based on the modified embedded atom method (MEAM) to determine diffusion coefficients and migration pathways for Ti and N adatoms (Ti ad and N ad ) on TiN(111). The reliability of the classical model-potential is verified by comparison with density functional theory (DFT) results at 0 K. MD simulations carried out at temperatures between 600 and 1800 K show that both Ti ad and N ad favor fcc surface sites and migrate among them by passing through metastable hcp positions. We find that N ad species are considerably more mobile than Ti ad on TiN(111); contrary to our previous results on TiN(001). In addition, we show that lattice vibrations at finite temperatures strongly modify the potential energy landscape and result in smaller adatom migration energies, E a = 1.03 for Ti ad and 0.61 eV for N ad , compared to 0 K values E a0K = 1.55 (Ti ad ) and 0.79 eV (N ad ). We also demonstrate that the inclusion of dipole corrections, neglected in previous DFT calculations, is necessary in order to obtain the correct formation energies for polar surfaces such as TiN(111). [ABSTRACT FROM AUTHOR]

Substituting Al for Ti in TiN(001), TiN(011), and N- and Ti-terminated TiN(111) surfaces has significant effects on adatom surface energetics which vary strongly with the adatom species and surface orientation. Here, we investigate Ti, Al, and N adatom surface dynamics using density functional methods. We calculate adatom binding and diffusion energies with both a nudged elastic band and grid-probing techniques. The adatom diffusivities are analyzed within a transition-state theory approximation. We determine the stable and metastable Ti, Al, and N binding sites on all three surfaces as well as the lowest energy migration paths. In general, adatom mobilities are fastest on TiN(001), slower on TiN(111), and slowest on TiN(011). The introduction of Al has two major effects on the surface diffusivity of Ti and Al adatoms. First, Ti adatom diffusivity on TiN(001) is significantly reduced near substituted Al surface atoms; we observe a 200% increase in Ti adatom diffusion barriers out of fourfold hollow sites adjacent to Al surface atoms, while Al adatom diffusivity between bulk sites is largely unaffected. Secondly, on TiN(111), the effect is opposite; Al adatoms are slowed near the substituted Al surface atom, while Ti adatom diffusivity is largely unaffected. In addition, we note the importance of magnetic spin polarization on Ti adatom binding energies and diffusion path. These results are of relevance for the atomistic understanding of Ti 1 − x Al x N alloy and Ti 1 − x Al x N/TiN multilayer thin-film growth processes. [ABSTRACT FROM AUTHOR]

Abstract: 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 ≤600K, 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 (Ds corr) than those estimated from uncorrelated transition probabilities. The temperature-dependent diffusion coefficient is Ds corr (T)=(4.5×10−4 cm2 s−1) exp[−0.55eV/(kBT)]. [Copyright &y& Elsevier]

Ab initio molecular dynamics 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 E des of 1.37eV and an attempt frequency A des =3.4×1013 s−1. E des is essentially equal to the N adatom surface diffusion barrier, Es =1.39eV, while As is only three to four times larger than A des, 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 ~3Å which rapidly increase to ~2eV at a separation of 1.5Å. We obtain good qualitative and quantitative agreement with the above results using the modified embedded atom method potential to perform classical molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

Abstract: 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 1000K, 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 push-out/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. [Copyright &y& Elsevier]

In situ high-temperature (1023–1223 K) scanning tunneling microscopy was used to study the coarsening/decay kinetics of two-dimensional (2D) TiN adatom islands on TiN(0 0 1) terraces and in single-atom-deep vacancy pits. Island coarsening/decay behavior was found to be non-linear with time and to depend on the local environment (i.e., on adatom concentration gradients on the terrace), the signature of surface-diffusion-limited kinetics. Two simple island geometries––a single 2D adatom island on an atomically smooth terrace and a single 2D adatom island within a vacancy island––were used to extract adatom surface transport parameters. We model diffusion-limited island decay kinetics for these configurations based upon steady-state diffusion equations solved by adaptive finite-element methods with a form of the Gibbs–Thomson equation describing anisotropic islands serving as the boundary condition. Calculated decay rates were compared with the experimental results to obtain an activation energy Ea for adatom formation and diffusion on TiN(0 0 1). Ea was found to be 2.6±0.6 and 3.1±0.5 eV for adatom islands in vacancy pits and on terraces, respectively. The difference in the two Ea values corresponds to the step edge Ehrlich barrier, which for TiN(0 0 1) is less than the experimental uncertainties in the measurements. [Copyright &y& Elsevier]

In situ high-temperature (1030–1223 K) scanning tunneling microscopy was used to determine the equilibrium shapes of two-dimensional TiN vacancy islands on atomically smooth terraces of epitaxial TiN(0 0 1) layers. Inverse Legendre transformations of the equilibrium island shapes yield relative step energies as a function of step orientation within an orientation-independent scale factor λ, the equilibrium chemical potential of the island per unit TiN molecular area. We then use quantitative TiN(0 0 1) adatom island coarsening measurements to determine λ and, hence, absolute orientation-dependent step energies β and step stiffnesses β˜. For 〈1 1 0〉 and 〈1 0 0〉 steps on TiN(0 0 1), we obtain: β1 1 0=0.21±0.05 eV/A˚, β1 0 0=0.25±0.05 eV/A˚, β˜1 1 0=0.9±0.2 eV/A˚, and β˜1 0 0=0.07±0.02 eV/A˚. From the β˜ values, we calculate kink formation energies &epsiv;1 1 0=0.40±0.2 eV and &epsiv;1 0 0=0.11±0.1 eV based on the unrestricted terrace-step-kink model. [Copyright &y& Elsevier]

In situ high-temperature scanning tunneling microscopy (STM) was employed to follow the coalescence kinetics of two-dimensional TiN islands on atomically smooth TiN(0 0 1) and TiN(1 1 1) terraces. The results are analyzed using a numerical approach based upon Mullin’s theory for surface relaxation and experimentally determined absolute orientation-dependent step stiffnesses. From the calculated time-dependent island shapes during coalescence, in combination with the STM data, we obtain quantitative values for edge mobilities. [Copyright &y& Elsevier]

We use embedded-atom molecular dynamics simulations to follow the dynamics of adatoms, vacancies, and adatom/vacancy pairs on two-dimensional hexagonal Pt19 clusters on Pt(1 1 1) surfaces at 1000 K. All configurations are found to be quite stable and have essentially the same migration mobilities as compact hexagonal clusters. However, the presence of a single vacancy dramatically decreases the lifetime of an adatom on the cluster by a factor of three. This occurs primarily through an enhancement of the rate of push-out/exchange reactions at the outer cluster edge resulting from vacancy-induced softening of edge atom bonds. Overall, adatoms in the presence of vacancies descend to the terrace via vacancy filling 10% of the time, and through reactions with outer cluster edges the remaining 90%. Direct vacancy filling mechanisms are analogous to, and have similar activation energies with, those at outer cluster edges: adatom hopping over descending steps and push-out/exchange reactions. [Copyright &y& Elsevier]