Dispersion relations of in-plane elastic waves in nano-scale one dimensional piezoelectric semiconductor/piezoelectric dielectric phononic crystal with the consideration of interface effect

Abstract

In this paper, the propagation properties of in-plane elastic waves in a nano-scale N-type piezoelectric semiconductor material/piezoelectric dielectric material layered periodic composite are theoretically investigated. Under the background of classical continuum mechanics of solids, the transfer matrix method and the Bloch theorem, the transfer matrices of the N-type piezoelectric semiconductor material, the piezoelectric dielectric material and the interface and the dispersion equation of in-plane Bloch waves are derived mathematically. Basing on the numerical calculation results, we investigate the physical influences of the semiconductor effect, biasing electric fields and the interface effect on the dispersion curves of in-plane elastic waves. It is found that the electron carrier mobility and diffusion will reduce the equivalent rigidity of the N-type piezoelectric semiconductor material, which will be limited by the existence of biasing electric fields. On the basis of the propagation of in-plane elastic waves, both the mathematical model and the physical mechanisms are fundamental to the analysis and optimization of nano-scale energy harvesters.