Dispersion relations of anti-plane elastic waves in micro-scale one dimensional piezoelectric semiconductor phononic crystals with the consideration of interface effect

Abstract

In this paper, the propagation properties of anti-plane elastic waves in a piezoelectric semiconductor (PS) layered periodic composites are theoretically investigated. The periodic layered composites consist of periodically repeated two micro-scale geometrical thickness PS slabs with different elasticity, piezoelectricity and charge carriers. Following consideration of the coupling mechanical anti-plane displacement, electric potential and perturbation of charge carriers, the influences of interface effects resulted from homo- and hetero-junctions on the dispersion relations of anti-plane elastic waves are systematically discussed. It is found that homo- and hetero-junctions can be approximately treated as rigid imperfect interfaces, which can enhance the width of band-gaps of anti-plane elastic waves, especially for high-frequency short-wavelength anti-plane elastic waves. The establishment of mathematical models and the revelation of physical mechanisms are all fundamental to the analysis and optimization of micro-scale energy harvesters based on the propagation of anti-plane elastic waves.