Electrostatic Potential in a Bent Piezoelectric Nanowire. The Fundamental Theory of Nanogenerator and Nanopiezotronics

TLDR

The study builds on nanopiezotronics, where the nanowire’s potential drop functions as the gate voltage in a piezoelectric field‑effect transistor. The authors use perturbation theory to compute the piezoelectric potential distribution in a nanowire subjected to a lateral tip force. The perturbation‑theory solution agrees within 6 % of FEM, shows the nanowire behaves like a parallel‑plate capacitor, and predicts a surface potential up to ~0.3 V—sufficient to drive a Schottky diode—scaling with displacement and inversely with the cube of the length‑to‑diameter ratio.

Abstract

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 ∼0.3 V. This voltage is much larger than the thermal voltage (∼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.