Stable and metastable structures of the multiphase tantalum nitride system

C. Stampfl and A. J. Freeman

Phys. Rev. B 71, 024111 – Published 20 January 2005

Abstract

Despite its growing technological importance and potential, the tantalum nitride system is suprisingly still relatively unexplored. Using density functional theory and the all-electron total energy full-potential linearized augmented plane-wave method, we investigate the relative stability of a host of structural phases and their associated electronic properties. Through consideration of the effect of the environment via the individual atom chemical potentials, a phase diagram is obtained. Our calculations indicate that there are three stable phases ${Ta}_{5} N_{6}$ , ${Ta}_{2} N$ , and ${Ta}_{3} N_{5}$ —the rest being metastable. The close energies of many structures explains the complexity of this nitride materials system and why the observed structural phases depend very sensitively upon experimental synthesis and growth conditions.

Received 14 May 2004

DOI:https://doi.org/10.1103/PhysRevB.71.024111

Authors & Affiliations

C. Stampfl¹ and A. J. Freeman²

¹School of Physics, The University of Sydney, Sydney 2006 Australia
²Department of Physics and Astronomy, Northwestern University, Evanston, Illinois, 60208, USA

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Vol. 71, Iss. 2 — 1 January 2005

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Images

Figure 1
(Color online) (a) Perspective view of the structure of rocksalt TaN. (b) Corresponding total (upper curve) and partial (Ta and $N$ ) density of states (DOS). Structure of ${Ta}_{4} N_{5}$ : (c) view of the (001) plane and (d) perspective view. The large pale and small dark balls represent Ta and $N$ atoms, respectively. The unit cell is indicated by the lines. (e) Corresponding total DOS (upper curve) and partial (Ta and $N$ ) DOS as indicated; the vertical line at zero energy indicates the Fermi level.Reuse & Permissions
Figure 2
(Color online) Structure of ${Ta}_{3} N_{5}$ : (a) view of the (001) plane where the unit cell is indicated and (b) view of the (100) plane. (c) Total density of states (DOS) and partial (Ta and $N$ ) DOS. Atomic geometry of the ${Ta}_{5} N_{6}$ structure: (d) view of the (0001) plane with the unit cell indicated by the dot-dashed lines, and (e) side view. (f) Corresponding total DOS of ${Ta}_{5} N_{6}$ (upper curve) and partial (Ta and $N$ ) DOS. The large pale and small dark balls represent Ta and $N$ atoms, respectively. The vertical line in the DOS at zero energy marks the Fermi level.Reuse & Permissions
Figure 3
(Color online) Structure of hexagonal $ϵ$ -TaN: (a) view of the (0001) plane and (b) perspective view. The unit cell is indicated by the dot-dashed lines. (c) Total and partial (Ta and $N$ ) DOS. Structure of hexagonal ${Ta}_{2} N$ : (d) view of the (0001) plane and (e) perspective view. The unit cell is indicated by the dot-dashed lines. (f) Total and partial (Ta and $N$ ) DOS of ${Ta}_{2} N$ . The large pale and small dark balls represent Ta and $N$ atoms, respectively. The vertical line in the DOS at zero energy indicates the Fermi level.Reuse & Permissions
Figure 4
The free energy of formation per atom: (a) as a function of $μ_{N}$ for fixed $μ_{Ta} = μ_{Ta}^{0} = E_{Ta - bulk}^{total}$ and (b) as a function of $μ_{Ta}$ for fixed $μ_{N} = μ_{N}^{0} = 1 ∕ 2 E_{N_{2}}^{total}$ . The lines represent the following structures: thick black, ${Ta}_{5} N_{6}$ (labeled); thick black, hex- ${Ta}_{2} N$ (labeled); thick black, ${Ta}_{3} N_{5}$ (labeled); thin black, ${Ta}_{4} N_{5}$ ; thick dot-dashed, rs-TaN; thick dashed, $ϵ$ -TaN; thick dotted, rs- ${Ta}_{4} N_{2}$ (two $N$ vacancies); thick gray rs- ${Ta}_{4} N_{3}$ (one $N$ vacancy); and thick dashed gray rs- ${Ta}_{3} N_{4}$ (one Ta vacancy). The vertical lines guide the eye for the stability region of the stable phases. (c) The phase diagram showing the stable structures as a function of the atom chemical potentials. (d) Resulting phase diagram when omitting the most stable ${Ta}_{5} N_{6}$ structure. For Figs. 4c, 4d, the pressure range corresponding to $μ_{N}$ [cf. Eq. (2)] is shown for two selected temperatures.Reuse & Permissions

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