弹性纵波在压电-压电半导体周期杆中的传播

Propagation of elastic longitudinal waves in a periodic piezoelectric-piezosemiconductor rod

为研究压电半导体周期结构中的弹性波传播特性,本文采用哈密顿变分原理推导出Love型压电半导体杆的基本方程;再在此基础上,针对由压电介质材料和n型压电半导体材料构成的周期杆,分别构建压电介质杆和压电半导体杆的状态方程;通过界面连续条件给出元胞两侧状态向量(轴向位移、电势、轴向应力和轴向电位移)的传递关系,并利用Bloch理论得到压电-压电半导体周期杆的色散方程。数值研究结果表明:初始电子浓度、元胞内压电半导体相的长度比和杆半径对该周期结构的带隙结构有调控作用;当初始电子浓度、杆长比、杆的半径增加时,第一带隙均会下移。该研究结果为基于压电半导体周期结构的器件设计提供了理论指导。

To investigate the elastic wave propagation properties in the periodic piezoelectric semiconductor(PS)rods,based on Hamilton′s variational principle,the Love-type rod equations for PS rods are derived,and the state equations for piezoelectric and PS rods are obtained,respectively.For a unit cell made of a piezoelectric rod and a PS rod,using the continuity condition of the unit cell′s interface,the transfer matrix for the state vectors,including the axial displacement,electric potential,axial stress,and axial electric displacement at the two surfaces of the unit cell,are established.The dispersion equation is derived using the Bloch theorem.Numerical results show that the band structure modulation can be achieved by changing the initial electron concentration,the length ratio,and the rod radius of the PS phase in a cell.For instance,the first band gap moves down with the increasing initial electron concentration,the length ratio,and the radius of the PS rod.It provides theoretical guidance for designing novel periodic PS structure-based devices.