Exact solutions to the electromechanical quantities inside a statically-bent circular ZnO nanowire by taking into account both the piezoelectric property and the semiconducting performance: Part I--Linearized analysis

Abstract

Stress fields in a bent circular ZnO nanowire (ZNW) subjected to a static end force can be decoupled from electric quantities by using the irrotationality of static electric fields, and thus, can be separately solved in advance. Electric fields are proven to be independent of axial-direction (c-axis) except near the end regions, which indicates that carrier redistribution happens only inside the cross-section. Based on the null current condition in static states, a governing equation on carrier concentration is established from the Gauss law. Aiming at small fluctuation of carrier concentration, a linearized analysis is conducted in this paper to obtain the exact solution of all the electromechanical quantities. Piezoelectric potential field in any cross-section of a bent ZNW is numerically analyzed. Effect of initial carrier concentration on both electric fields and output voltage of a ZNW are discussed in detail. It is found that the semiconducting performance results in some reduction in output voltage, which comes from the partial cancellation on the piezoelectric electric fields due to carrier redistribution, i.e., electric leakage. Thus, a smaller initial carrier concentration is more proper for a bent ZNW to energy-harvesting. Specially, the obtained solutions are related to the mobility of electron and the diffusion coefficients of ZNW. Such an analysis technique by coupled electromechanical quantities and carrier concentration as a whole possesses some referential significance to piezotronics.