Propagation of extensional waves in a piezoelectric semiconductor rod

Abstract

We studied the propagation of extensional waves in a thin piezoelectric semiconductor rod of ZnO whose c-axis is along the axis of the rod. The macroscopic theory of piezoelectric semiconductors was used which consists of the coupled equations of piezoelectricity and the conservation of charge. The problem is nonlinear because the drift current is the product of the unknown electric field and the unknown carrier density. A perturbation procedure was used which resulted in two one-way coupled linear problems of piezoelectricity and the conservation of charge, respectively. The acoustic wave and the accompanying electric field were obtained from the equations of piezoelectricity. The motion of carriers was then determined from the conservation of charge using a trigonometric series. It was found that while the acoustic wave was approximated by a sinusoidal wave, the motion of carriers deviates from a sinusoidal wave qualitatively because of the contributions of higher harmonics arising from the originally nonlinear terms. The wave crests become higher and sharper while the troughs are shallower and wider. This deviation is more pronounced for acoustic waves with larger amplitudes. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

Typical transient effects in a piezoelectric semiconductor nanofiber under a suddenly applied axial time-dependent force

“…However, it is noted that the approximate analytical solutions can be obtained by neglecting part of weak interactions as reported in Refs. [29]- [31]. The advantage of these analytical solutions is that they are helpful to reveal the essence of some physical phenomena, although the scope of applications of the introduced assumptions needs to be further verified.…”

“…As an approximation often used in Refs. [12] and [29]- [31], the charge on the right-hand side of Eq. (1b) is neglected to decouple the problem into two one-way coupled problems, i.e., the pure piezoelectric problem and the continuity equation for ∆n.…”

“…[29] and [30] followed by Refs. [12] and [31] to decouple the multi-field coupling equations that would have enabled analytical results to be obtained. It is noted that this assumption resulted in the system being opened, although it is convenient for the purpose of calculation.…”

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