Virtual Work Principle for Piezoelectric Semiconductors and Its Application on Extension and Bending of ZnO Nanowires

Abstract

This paper presents the principle of virtual work (PVW) for piezoelectric semiconductors (PSs), which extends the piezoelectric dielectrics to involve the semiconducting effect. As an application of the PVW, a one-dimensional (1D) approximation theory for the extension and bending of PS nanowires is established by directly applying the PVW and Bernoulli–Euler beam theory with the aid of the second-order approximation of electrostatic potential. To illustrate the new model, the mechanical displacement, electrostatic potential, and concentration of electrons for extension and bending deformation of n-type ZnO nanowires are analytically determined. Additionally, numerical results show that, for n-type Zinc Oxide nanowires, the distribution of electrostatic potential is anti-symmetric along the thickness direction for extension deformation. In contrast, the bending deformation causes a symmetric distribution of electrostatic potential characterized by the zeroth-order and the second-order electrostatic potential. Furthermore, these two different deformations result in the redistribution of electrons. The electrostatic potential can be tuned by adjusting the amplitude of the applied mechanical load. Moreover, we find that the increase in doping level will reduce the magnitude of electrostatic potential due to the screening effect. The presented PVW provides a general approach to establishing structural theories and an effective way of implementing numerical methods.

Theoretical Analysis of Piezoelectric Semiconductor Thick Plates with Periodic Boundary Conditions

“…with the initial concentrations set as p 0 = n 0 = 5 × 10 21 m −3 . The Fourier series expansion of the boundary conditions, given in Equation (25), were truncated at appropriate α to ensure the results have sufficient accuracy and that the solution converges. Here, the distribution of the electric displacement component D 3 is chosen as the object of the convergence study.…”

“…For one-dimensional setups, the multi-field coupling problem resulting from using PSCs can be simplified and solved theoretically. There are studies on the extension and bending problems of single-material fibers and nanowires [23][24][25] and on using two materials [26,27] or more [28,29] with PN junctions to form composite fibers. The theoretical analysis of multi-dimensional PSC problems is more difficult due to more complex equilibrium equations, constitutive relations, and multi-field coupling boundary conditions.…”