Ab initio study of the stable phases of 1:1 tantalum nitride

Abstract

Integrated circuits will continue to see dimensional shrinking and, as a consequence, the barrier layers needed to stop the diffusion of the metal interconnects into the dielectrics will also need to shrink. One of the key materials used as a barrier layer is tantalum nitride, but it is relatively unexplored from an ab initio perspective. In addition, there seems to be some conflicting data with regard to the most stable crystal structure at ambient conditions for the system. Two crystal structures in the phase diagram (ε-TaN, P6/mmm and δ-TaN, Fm3¯m) and one alternate crystal structure (π-TaN, P6¯2m) are assessed using density functional theory. This study determines the lattice constants, bulk modulus and heat of formation for each of these crystal structures to determine the most stable system. In addition, an assessment of the bonding is done to provide insight into phase stability. The π-TaN is shown to be the most likely crystal structure over ε-TaN or δ-TaN at low temperatures. Vacancy formation energy calculations were done to understand the line compound of TaN at ambient conditions. Vacancy formation on the Ta and N sites were large, suggesting that the π-TaN exists in a very narrow composition range, consistent with the phase diagram. In contrast, Ta vacancies are favorable in the δ-TaN phase, and the shallowness of the Gibbs free energy curve vs. composition is consistent with the δ-TaN phase occurring at 42 to 50at.% on the phase diagram.