Ab initiostudy of Cu impurity diffusion in bulk TiN

Abstract

TiN is an important material used as a diffusion barrier in microelectronic devices to prevent copper from contacting silicon. There is, however, little known about the elementary atomistic processes underlying the excellent performance of TiN. In this work, we perform a density functional theory study of the copper impurity diffusion coefficient in bulk TiN. Several diffusion mechanisms are considered. For each mechanism, the temperature effect is taken into account within the quasiharmonic approximation. Moreover, the influence of the TiN stoichiometry on its diffusion properties is taken into account through the change in the concentrations of the intrinsic point defects as a function of composition. These concentrations are obtained via a thermodynamic formalism based on the dilute solution model. We find that in stoichiometric TiN the copper impurity diffusion proceeds via the vacancy mechanism on the Ti sublattice. In the off-stoichiometric ${\mathrm{TiN}}_{0.96}$, the dominant diffusion mechanism switches to the vacancy-mediated diffusion on the N sublattice. The Arrhenius equation for the diffusion coefficient is $D=3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}exp(\ensuremath{-}4.5\phantom{\rule{0.28em}{0ex}}\mathrm{eV}/{k}_{B}T)\phantom{\rule{4pt}{0ex}}{\mathrm{m}}^{2}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for the stoichiometric TiN and $D=6.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}exp(\ensuremath{-}2.7\phantom{\rule{0.28em}{0ex}}\mathrm{eV}/{k}_{B}T)\phantom{\rule{4pt}{0ex}}{\mathrm{m}}^{2}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for the substoichiometric TiN. Our calculations provide the basis for a better interpretation of the experimental measurements.