Gao Yifan, Wang Zhong Lin
School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0245, USA.
Nano Lett. 2007 Aug;7(8):2499-505. doi: 10.1021/nl071310j. Epub 2007 Jul 24.
We have applied the perturbation theory for calculating the piezoelectric potential distribution in a nanowire (NW) as pushed by a lateral force at the tip. The analytical solution given under the first-order approximation produces a result that is within 6% from the full numerically calculated result using the finite element method. The calculation shows that the piezoelectric potential in the NW almost does not depend on the z-coordinate along the NW unless very close to the two ends, meaning that the NW can be approximately taken as a "parallel plated capacitor". This is entirely consistent to the model established for nanopiezotronics, in which the potential drop across the nanowire serves as the gate voltage for the piezoelectric field effect transistor. The maximum potential at the surface of the NW is directly proportional to the lateral displacement of the NW and inversely proportional to the cube of its length-to-diameter aspect ratio. The magnitude of piezoelectric potential for a NW of diameter 50 nm and length 600 nm is approximately 0.3 V. This voltage is much larger than the thermal voltage ( approximately 25 mV) and is high enough to drive the metal-semiconductor Schottky diode at the interface between atomic force microscope tip and the ZnO NW, as assumed in our original mechanism for the nanogenerators.
我们已应用微扰理论来计算纳米线（NW）在尖端侧向力作用下的压电势分布。在一阶近似下给出的解析解与使用有限元方法进行的全数值计算结果相差在6%以内。计算表明，纳米线中的压电势几乎不依赖于沿纳米线的z坐标，除非非常靠近两端，这意味着纳米线可近似视为一个“平行板电容器”。这与为纳米压电电子学建立的模型完全一致，在该模型中，纳米线上的电势降用作压电场效应晶体管的栅极电压。纳米线表面的最大电势与纳米线的横向位移成正比，与其长径比的立方成反比。对于直径为50nm、长度为600nm的纳米线，压电势的大小约为0.3V。该电压远大于热电压（约25mV），并且足够高，能够驱动原子力显微镜尖端与ZnO纳米线之间界面处的金属 - 半导体肖特基二极管，正如我们最初的纳米发电机机制中所假设的那样。
