Activation Energy For Vacancy Diffusion Research Articles

Activation Energy of Point Defect Diffusion in Low-Temperature Deposited TiN

Low-temperature deposited titanium nitride layers exhibiting increased and distorted lattices are subjected to in situ X-ray diffraction investigations at different temperatures. Annealing at about 450 °C leads to a complete lattice relaxation due to diffusion of point defects in the lattice. The activation energy for this diffusion can be calculated to be 1.23 ± 0.07 eV (while the reported activation energy of vacancy diffusion in TiN films is 2.09 eV). This proves that lattice widening and distortion in titanium nitride films deposited by dc magnetron sputtering at temperatures below 200 °C is mainly due to atoms on interstitial sites, and that the density of vacancies is high enough that most of the interstitial atoms find a vacancy to recombine, which leads to the observed relaxation.

Diffusion mechanisms on Ni surfaces

The embedded atom method (EAM) was previously used to study diffusion of single Ni adatoms on various Ni surfaces; the calculated diffusion rates were in excellent agreement with experiment (C.L. Liu, J.M. Cohen, J.B. Adams and A.F. Voter, Surf. Sci. 253 (1991) 334 [1]). This paper presents calculations of the formation and migration energies of vacancies in Ni surfaces, including (100), (110), (111), (311), and (331). In all cases, the activation energies for vacancy diffusion are higher than those for single adatoms. Formation energies of ledges and kinks on (100), (110), and (111) Ni surfaces were calculated. The interactions of single adatoms with ledges and kinks and diffusion of single adatoms on the stepped Ni surfaces were determined. Finally, MD simulations of surface diffusion of a single adatom on a Ni(111) surface were carried out to confirm the earlier molecular statics calculations and to test a simple Debye model.

Surface morphology of HCI etched silicon wafers: III. the origin of etch pits

Gas phase etching of silicon wafers with HCI at temperatures above 1200 K results in a surface which is either smooth or pitted, depending on temperature and HC1 input concentration. Whereas a smooth surface is the result of a steady flow of steps across the surface, etch pits are the result of a secondary, parallel etching reaction which creates “vacancies” in the surface. It is assumed that these vacancies cluster together to give microscopic holes in the silicon surface, that are large enough to be stable and that allow a vertical etching mechanism giving etch pit formation. It is shown, that the conditions needed for this etch pit formation depend largely on the local undersaturation of the main reaction product SiCl2, the diffusion velocity of vacancies in the silicon surface and the velocity of steps on the surface. Using this concept, a quantitative description for the origin of etch pits and an explanation for the experimentally found transition line between the smooth and pitted regions in the PHC1-T diagram are given, leading to an activation energy for vacancy diffusion in the surface of 70 kcal/mole.

Nuclear Relaxation and Slow Diffusive Motions in CaF2 and NaF

Fluorine relaxation times T1Z , T1D and T2 are measured as functions of temperature in single crystals of CaF2 and NaF. Typical quantities like the activation energy for vacancy diffusion and the formation energy of defect pairs are deduced and reported.

Diffusion-Limited Annealing of Radiation Damage in Germanium

The theory of the previous paper in this journal was used to treat the annealing of radiation damage in $n$-type germanium as studied by Fletcher, Brown, and Wright, and by Augustyniak. The damage was produced by 3-Mev electrons to a density of ${10}^{15}$ defects per cubic centimeter. The damage was assumed to have consisted of vacancy-interstitial pairs which annealed by the diffusion together of interstitials and vacancies. A reasonable fit of the data has been obtained for the initial 50% of the annealing. The data of Augustyniak were fit for all stages of the annealing process. Choice of parameters to fit the data led to the following conclusions: (1) The sum of the diffusion coefficients of interstitials and vacancies is given by ${10}^{11}$ ${{r}_{0}}^{2}\mathrm{exp}(\ensuremath{-}31.6 \mathrm{kcal}/RT)$, where ${r}_{0}$ is the capture radius; (2) the average separation of the interstitial and the vacancy of the pairs produced by 3-Mev electrons is approximately 1.5 ${r}_{0}$, and (3) the first 65% of the annealing occurs by the recombination of each interstitial with the vacancy from which it was originally dislodged. Fair agreement of the activation energy with the previously accepted activation energy for vacancy diffusion suggests vacancy-diffusion annealing. Absence of a more rapid interstitial diffusion indicates that the interstitial does not possess the contracted electron cloud of a positive ion.