Stability of the Bulk Phase of Layered ZnO

Recently a novel phase of ZnO has been synthesized which is analogous to $\alpha$-boron nitride, although more three dimensional, and consists of planar hexagonal sheets of ZnO. Examining the dynamic stability of the structure, we find unstable phonon modes over a considerable part of the Brillouin zone. Local-density approximation (LDA) and generalized gradient approximation level calculations have usually been able to predict the structural stability of $s\mathrm{\text{−}}p$ bonded systems. The failure in the present case is a surprise and is traced to the self-interaction error which incorrectly locates the localized Zn $d$ states in the valence band of ZnO. Correcting for this with a Hubbard-like $U$ on the Zn $d$ states, the optimized structure is predicted to be stable. This highlights the fact that the large bond length contraction that one finds in going from $s{p}^3$- to $s{p}^2$-type bonding results in an increased necessity to correct for self-interaction errors.

Figure 1

The (a) Zn $d$ and (b) O $p$ contributions to the density of states (DOS) of ZnO in the experimentally determined $\alpha$-boron nitride structure using LDA potentials. The Zn $s$ contribution is shown in the inset of (a). The zero of energy corresponds to the VBM.

Figure 2

The calculated phonon dispersions for ZnO in the experimentally determined $\alpha$-boron nitride structure along various symmetry directions using LDA potentials.

Figure 3

The displacement of atoms associated with the unstable acoustic mode at (a) the $K$ point and (b) $L$ point. The upper figures show the displacements in $xy$ plane, while the lower figures indicate the displacement in three dimensions. The consequences on the bonding between a representative $d$ orbital and O $p$ orbitals are shown in the insets of (a) and (b) for each set of displacements.

Figure 4

The (a) Zn $d$ and (b) O $p$ contributions to the density of states of ZnO in the theoretically optimized $\alpha$-boron nitride structure with a $U$ of 12 eV on the Zn $d$ states. The Zn $s$ contribution is shown in the inset of (a). The zero of energy corresponds to the VBM.

Figure 5

The calculated phonon dispersions for ZnO in the theoretically optimized $\alpha$-boron nitride structure along various symmetry directions. A $U$ of 12 eV on the Zn $d$ states is used in these calculations.