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Wurtzite structure of ZnO with polar  Zn- and O-terminated surfaces. The labeled four atoms indicate the primitive cell. Open and filled symbols represent oxygen and zinc ions, respectively. and denote the lattice constants. The dimensionless parameter is the length of the bond parallel to the axis, in unit of . Here, the initial , , and are , , and 0.3820, respectively.
(Color online) Changes of the polarizations when the axial strains are applied on the  direction of the ZnO structures, related to the direct piezoelectric constant .
(Color online) Calculated surface energies and effective piezoelectric constant of the ZnO nanofilms with different thicknesses. Here the surface energy is defined as the difference between the total energies of the film model and the bulk model with the same number of primitive cells divided by the number of the Zn–O double layers.
(Color online) Calculated orbital-projected DOS of the ZnO nanofilms with 2, 4, 6, 8, 10, and 12 Zn–O double layers, results for the bulk model are drawn as well for comparison. The black (thin), red (dashed), and blue (thick) lines represent the , , and orbitals, respectively. The dashed (black) and solid (green) vertical lines show the centers of the Zn and DOS profiles, respectively. The Fermi levels are located at .
Effective piezoelectric constants (in ) of the 2D ZnO nanofilms.
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