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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 present a method for the determination of orientation-dependent mobilities Γ eff(φ) based upon analyses of the detachment-limited coarsening/decay kinetics of equilibrium-shaped two-dimensional islands. An exact analytical expression relating the orientation-dependence of Γ eff(φ) to that of the anisotropic step energies β(φ) is derived. This provides relative values of Γ eff(φ) to within an orientation-independent scale factor that is proportional to the decay rate of the island area. Using in situ high temperature (T =1550–1700 K) low-energy electron microscopy measurements of two-dimensional TiN island coarsening/decay kinetics on TiN(111) terraces for which β(φ) values are known [Phys. Rev. B 67 (2003) 35409], we demonstrate the applicability of our analytic formulation for the determination of absolute Γ eff(φ) values. [Copyright &y& Elsevier]

Laser texturing enables the observation of island decays on the ‘1×1’ high temperature surface of Si(110) by low energy electron microscopy. At temperatures above the phase transition (T=790–980°C), the decay of the island areas exhibits a nonlinear dependence on time indicative of surface diffusion limited mass transport. The aspect ratios of the islands during the decay show a weak temperature dependence despite the fact that surface is anisotropic. We have obtained the activation energy of mass transport, the kink energy, step energy, and step stiffness for Si(110). [Copyright &y& Elsevier]

In situ low-energy electron microscopy was used to study interlayer mass transport kinetics during annealing of three-dimensional (3D) TiN(1 1 1) mounds, consisting of stacked 2D islands, at temperatures T between 1550 and 1700 K. At each T, the islands decay at a constant rate, irrespective of their initial position in the mounds, indicating that mass is not conserved locally. From temperature-dependent island decay rates, we obtain an activation energy of 2.8 ± 0.3 eV. This is consistent with the detachment-limited decay of 2D TiN islands on atomically flat TiN(1 1 1) terraces [Phys. Rev. Lett. 89 (2002) 176102], but significantly smaller than the value, 4.5 ± 0.2 eV, obtained for bulk-diffusion-limited spiral step growth [Nature 429 (2004) 49]. We model the process based upon step flow, while accounting for step–step interactions, step permeability, and bulk mass transport. The results show that TiN(1 1 1) steps are highly permeable and exhibit strong repulsive temperature-dependent step–step interactions that vary between 0.03 and 0.76 eV · Å. The rate-limiting process controlling TiN(1 1 1) mound decay is surface, rather than bulk, diffusion in the detachment-limited regime. [Copyright &y& Elsevier]

We employ in situ high-temperature (1030–1250 K) scanning tunneling microscopy to measure adatom island coarsening/decay kinetics and temporal fluctuations around the equilibrium shapes of two-dimensional TiN vacancy islands on atomically-smooth (0 0 1) and (1 1 1) TiN terraces. Using inverse Legendre transformations of the equilibrium island shapes, we obtain 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 either quantitative island coarsening measurements [in the case of TiN(0 0 1)] or an exact approach for the analysis of shape fluctuations, applicable to highly anisotropic TiN(1 1 1) islands, to determine λ and, hence, absolute orientation-dependent step energies and step stiffnesses. [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]

Abstract: We grow homoepitaxial stoichiometric TiN(001) layers by ultra-high vacuum reactive magnetron sputtering in Ar/N2 mixtures and use scanning tunneling microscopy to study nucleation as a function of the N2 gas fraction and growth temperature T s. The characteristic island size R c necessary to nucleate a new layer decreases continuously with , varying from 18.0 nm at T s =740 °C with f N2 =0.10 to 11.2 nm with . Over the temperature range 600⩽ T s ⩽860 °C, nucleation is diffusion limited with an activation energy E s of 1.1±0.1 eV for TiN(001) growth with and 1.4±0.1 eV in pure N2. We attribute the increase in E s to a higher steady-state N coverage resulting in an increase in the average x-value of the primary surface-diffusing species, TiN x admolecules. [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]