Continuum model of the potential of charge carriers in a bent piezoelectric ZnO nanowire: analytic and numerical study

Abstract

The piezoelectric potential of a slightly n-doped ZnO nanowire is analytically and numerically solved. We approximated the dopant concentration $(N_d^{+})$ to shift slightly from the intrinsic level toward an n-typed region by increasing the donor concentration. Correspondingly, the electron density is also approximated. The analytic solution of the continuum model indicates that the derived solution is dependent on the lateral force, Bessel function, and Meijer G-function. As per the potential of the nanowire’s cross section, the potential in the tensile side is considered to have screening effects, and the polarity of the potential between the tensile and the compressive is antisymmetric such that the compressive is negative and the tensile is positive. The diameter in the ZnO nanowire used in the model is 200 nm, and the lateral force used is approximately $80 \times 10^{-5}$ N. Although the resulting piezoelectric potential of the NW that is derived from the simplified coefficient form is not accurately estimated, it shows a trend with the scaled values. The difference in the potential between the maximum tensile and compressive value is approximately one order that is consistent with others (Wang and Song, Science 312:242–246, 2006;Gao and Wang, Nano Lett 9:1103–1110, 2009).