ZnO nanowires (NW) as semiconductor piezoelectric nanostructures have emerged as the focus material for applications in energy harvesting, photonics, sensing, biomedical science, actuators or spintronics. The expression of 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 nanowires, 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 C-AFM together with the piezoelectric vertical coefficient by PFM, and comparing them with the numerical calculations for our model, effective piezoelectric coefficients in the range d33eff ~ 8.6 pm/V - 12.3 pm/V have been extracted for ZnO NWs. We have further demonstrated via simulations the dependence between the effective piezoelectric coefficient d33eff and the geometry and dimensions of the NW (radius to length ratio), revealing that the higher d33eff is obtained for thin and long NW 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.

中文翻译：

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受压电效应影响的单个 ZnO 纳米线的非线性纳米级压电响应

作为半导体压电纳米结构的 ZnO 纳米线 (NW) 已成为能量收集、光子学、传感、生物医学科学、致动器或自旋电子学应用的焦点材料。半导体材料中压电特性的表达被可用载流子的屏蔽效应和压电效应所掩盖，导致复杂的纳米级压电响应信号。在这里，我们开发了一个金属-半导体-金属模型来模拟单个 ZnO 纳米线的压电响应，证明压电系数中的明显非线性是由半导体-金属上的正向和反向偏置肖特基势垒产生的不对称性引起的路口。通过用 C-AFM 直接测量 ZnO 纳米线的实验 IV 特性以及 PFM 的压电垂直系数，并将它们与我们模型的数值计算进行比较，有效压电系数在 d33eff ~ 8.6 pm/V - 12.3 pm/ V 已被提取用于 ZnO 纳米线。我们通过模拟进一步证明了有效压电系数 d33eff 与 NW 的几何形状和尺寸（半径与长度之比）之间的依赖性，揭示了由于电场之间的张量性质比例，对于细长 NW 获得了更高的 d33eff和 NW 几何形状的变形。而且，