The propagation of the multi-physical fields coupled Rayleigh wave on the half-space with a gradient piezoelectric semiconductor layer

In this paper, the propagation characteristics of a multi-physical fields coupled Rayleigh surface wave in a semi-infinite piezoelectric medium covering with a functionally gradient piezoelectric semiconductor layer are investigated. First, we can get state transfer equation of piezoelectric semiconductor material from constitutive and governing equations. The transfer and stiffness matrices in the piezoelectric semiconductor material and the piezoelectric material based on the state vector can be got by solving state transfer equation. Furthermore, by combining these matrices of the functionally gradient piezoelectric semiconductor covering layer and the homogeneous piezoelectric half-space, it can be obtained that the total surface stiffness matrix of the Rayleigh wave. Last, it can be obtained that the dispersion curve relation from electrical boundary conditions and mechanical stress freedom. The velocity equations of Rayleigh surface waves propagating along x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}-direction under different electrical boundary conditions and five types of gradient profiles of piezoelectric semiconductor layers are presented. The effects of gradient variation, stable carrier concentration, bias electric fields, and surface boundary conditions on Rayleigh surface waves are investigated. The wave propagation characteristics obtained in this paper have certain theoretical guiding significance for the development of the surface wave devices made of semiconductor materials.