First-principles study of zinc oxide honeycomb structures

We present a first-principles study of the atomic, electronic, and magnetic properties of two-dimensional (2D), single and bilayer ZnO in honeycomb structure and its armchair and zigzag nanoribbons. In order to reveal the dimensionality effects, our study includes also bulk ZnO in wurtzite, zincblende, and hexagonal structures. The stability of 2D ZnO, its nanoribbons and flakes are analyzed by phonon frequency, as well as by finite temperature ab initio molecular-dynamics calculations. 2D ZnO in honeycomb structure and its armchair nanoribbons are nonmagnetic semiconductors but acquire net magnetic moment upon the creation of zinc-vacancy defect. Zigzag ZnO nanoribbons are ferromagnetic metals with spins localized at the oxygen atoms at the edges and have high spin polarization at the Fermi level. However, they change to nonmagnetic metal upon termination of their edges with hydrogen atoms. From the phonon calculations, the fourth acoustical mode specified as twisting mode is also revealed for armchair nanoribbon. Under tensile stress the nanoribbons are deformed elastically maintaining honeycomblike structure but yield at high strains. Beyond yielding point honeycomblike structure undergo a structural change and deform plastically by forming large polygons. The variation in the electronic and magnetic properties of these nanoribbons have been examined under strain. It appears that plastically deformed nanoribbons may offer a new class of materials with diverse properties.

Figure 1

(Color online) Cohesive energies $E_C$ per Zn-O pair, band gaps $E_G$, Zn-O bonds, atomic and energy band structures of 3D (a) wurtzite, (b) zincblende, and (c) hexagonal crystals of bulk ZnO. Red-small and blue-large balls correspond to O and Zn atoms, respectively. The gap between valence and conduction bands are shaded and the zero of energy is set at the Fermi level $E_F$. All structures including lattice constants are fully optimized.

Figure 2

(Color online) Phonon-dispersion curves calculated by force-constant method for 2D monolayer ZnO. Atomic structure and hexagonal lattice vectors are shown by inset.

Figure 3

(Color online) Electronic structure of the 2D monolayer of ZnO. (a) Brillouin zone corresponding to 2D hexagonal lattice and difference charge density, $\Delta \rho$. (b) Energy band structure and density of states projected to the selected orbitals (PDOS) of constituent atoms. The band gap is shaded (painted in yellow) and the zero of energy is set at the Fermi level. Band edges corrected by $G{W}_0$ are indicated by small (light blue) circles. The band gap enlarged after $G{W}_0$ correction is shaded (painted light blue).

Figure 4

(Color online) Vacancy defects in a $\left(7\times 7\right)$ supercell of the monolayer of ZnO. (a) Relaxed atomic structure around the Zn vacancy with isosurfaces of the difference charge density of spin-up and spin-down states, $\Delta \rho =\rho (\uparrow )=\rho (\downarrow )$. Energies $E_i$ of localized states measured from the top of the valance band and the net magnetic moment per supercell in Bohr Magneton ${\mu }_B$. Blue-large and red-small balls indicate Zn and O atoms indicated by arrows. (b) O vacancy. (c) $\text{Zn}+\text{O}$ divacancy. (d) $\text{O}+\text{Zn}$ antisite where neighboring O and Zn atoms are exchanged. The $\left(7\times 7\right)$ supercells each including one type of various vacancy defects are delineated by solid lines.

Figure 5

(Color online) (a) Phonon-dispersion curves of a-ZnO(9) calculated by force-constant method. Right panel presents the magnified view of the low-lying modes. Here the well-known out-of-plane, transverse, and longitudinal acoustical modes are labeled, respectively, as ZA, TA, and LA. The fourth acoustical twisting mode, which is indigenous to quasi-1D nanoribbons, is labeled as TW, because this mode corresponds to the twisting of the nanoribbon along the axis passing through the middle of the ribbon in the infinite direction. (b)DOS calculated for 2D planar ZnO (shown by solid lines); armchair a-ZnO(9) (shown by dashed lines); and a finite-size flake, i.e., a 5 unit cell long a-ZnO(9) (shown by dotted lines). The discrete frequencies due to finite-size structure are Gaussian broaden with $\sigma =8{\text{cm}}^{-1}$ in order to compare with continuous DOS of 2D layer and quasi-1D ribbon. Quasi-1D (nanoribbon) and 0D (flake) honeycomb structures are shown by inset.

Figure 6

(Color online) Atomic and electronic structure of bare and hydrogen-terminated armchair nanoribbons a-ZnO(9). (a) Atomic structure with unit cell comprising $n=9$ Zn-O atom pairs, energy band structure and charge-density isosurfaces of selected states of bare nanoribbons. The charge of the bands of edge states are localized at the edge atoms. (b) Same as (a) but for hydrogen-passivated nanoribbon. Large, medium, and small balls indicate Zn, O, and H atoms, respectively. Unit cells are delineated by dashed lines.

Figure 7

(Color online) Variation in the calculated band gaps of bare and hydrogen-passivated ZnO armchair nanoribbons with their widths $n$. Dashed line indicates the band gap of the infinite 2D ZnO.

Figure 8

(Color online) Bare zigzag nanoribbon $\text{z-ZnO}\left(n\right)$ with $n=9$: (a) honeycomb structure with primitive unit cell delineated and difference charge density $\Delta \rho$ of spin-up and spin-down states. (b) Total density of spin-up and spin-down states (DOS), energy band structure, and isosurface charge density of selected spin states. Large, medium, and small filled balls indicate Zn, O, and H atoms, respectively. (c) and (d) are same as (a) and (b). Yellow-light and blue-dark densities are for spin-up and spin-down states. Similarly red-continuous and blue-dashed curves are spin-up and spin-down spin bands. Black lines are for nonmagnetic (spin-paired) bands.

Figure 9

(Color online) (a) Variation in the strain energy $E_s$ and band gap $E_G$ of the bare $\text{a-ZnO}\left(n\right)$ $\left(n=9\right)$ with the applied uniaxial strain, $ϵ$ are shown by a curve with squares. Calculated tension shown by tin (red) curve is initially linear but deviates from linearity for large $ϵ$. Atomic structure for three different values of strain. The boundaries of the supercells comprising four unit cells and corresponding lattice constants $c$ are indicated by vertical lines. (b) Same as (a) but for bare $\text{a-ZnO}\left(n\right)$ $\left(n=15\right)$. (c) Variation in force constant, $\kappa$ and in-plane stiffness, $C$ of a-ZnO with the width $w$ of the nanoribbons.

Figure 10

(Color online) Variation in the strain energy $E_s$, tension, and magnetic moment $\mu$ per supercell of the bare $\text{z-ZnO}\left(n\right)$ $\left(n=9\right)$ with the applied uniaxial strain. Atomic structures of the bare z-ZnO(9) for three different uniaxial strains. The supercells consist of five unit cells.