Analysis of wave-particle drag effect in flexoelectric semiconductor plates via Mindlin method

In this paper, the infinite power series of two-dimensional (2D) differential equations for flexoelectric semiconductor plates are derived by extending the Mindlin method. The zeroth-order and first-order theories are systematically presented and applied to the plate made of cubic crystals of class m3m, identifying explicitly the coupling among wave modes and charge distributions. More specifically, it is observed that the extensional and thickness-stretch waves are coupled with axial motions of free carriers; bending and fundamental shear are coupled with the thickness motions of free carriers, showing the dynamic phenomena of the flexoelectric electronic (flexoelectronic) effect; and the shear-horizontal waves, such as face-shear and thickness-twist, are decoupled. Furthermore, when comparing with the three-dimensional (3D) dispersion relations in the flexoelectric semiconductor plate which are also derived for the first time in this paper, the simple 2D theory is shown to be amazingly accurate. For instance, for an infinite plate of thickness 2h = 0.2 µm, the extension, bending, and shear modes predicted from the present 2D theory agree well with the 3D benchmarks when the actual wavelength is larger than 1.26 µm, i.e., wavelength is at least more than six times of the thickness. To illustrate the flexoelectricity-based wave-particle drag effects, the wave modes and charge distributions are plotted. Due to its simplicity and computational efficiency, the present 2D theory provides us a powerful tool in understanding the physical mechanism of wave-particle drag in flexoelectric semiconductor plates and analyzing acoustoelectric devices when the flexoelectric effect is involved.