Non-linear nanoscale piezoresponse of single ZnO nanowires affected by piezotronic effect

Zinc oxide (ZnO) nanowires (NWs) as semiconductor piezoelectric nanostructures have emerged as material of interest for applications in energy harvesting, photonics, sensing, biomedical science, actuators or spintronics. The expression for the piezoelectric properties in semiconductor materials is concealed by the screening effect of the available carriers and the piezotronic effect, leading to complex nanoscale piezoresponse signals. Here, we have developed a metal-semiconductor-metal model to simulate the piezoresponse of single ZnO NWs, demonstrating that the apparent non-linearity in the piezoelectric coefficient arises from the asymmetry created by the forward and reversed biased Schottky barriers at the semiconductor-metal junctions. By directly measuring the experimental I-V characteristics of ZnO NWs with conductive atomic force microscope together with the piezoelectric vertical coefficient by piezoresponse force microscopy, and comparing them with the numerical calculations for our model, effective piezoelectric coefficients in the range d _33eff ∼ 8.6 pm V^-1-12.3 pm V^-1 have been extracted for ZnO NWs. We have further demonstrated via simulations the dependence between the effective piezoelectric coefficient d _33eff and the geometry and physical dimensions of the NW (radius to length ratio), revealing that the higher d _33eff is obtained for thin and long NWs due to the tensor nature proportionality between electric fields and deformation in NW geometries. Moreover, the non-linearity of the piezoresponse also leads to multiharmonic electromechanical response observed at the second and higher harmonics that indeed is not restricted to piezoelectric semiconductor materials but can be generalized to any type of asymmetric voltage drops on a piezoelectric structure as well as leaky wide band-gap semiconductor ferroelectrics.