Spontaneous bending of piezoelectric nanoribbons: Mechanics, polarization, and space charge coupling

A theory is developed to explain the spontaneous bending of polar ± (0 0 0 1) faceted wurtzite nanoribbons, including the widely studied case of zinc oxide (ZnO) nanoarcs and nanorings. A rigorous thermodynamic treatment shows that bending of these nanoribbons can be primarily attributed to the coupling between piezoelectric effects, electric polarization, and the motion of free charge originating from point defects and/or dopants. The present theory explains the following experimental observations: the magnitude and sign of curvature and how this curvature depends on film thickness and dopant concentration. Good agreement between theory and experiment is obtained with no adjustable parameters. We identify three regimes of bending behavior with distinct thickness dependence for bending radius that depend on free carrier density, film thickness, and elastic, piezoelectric and dielectric constants.