Propagation of Acoustic Wave in Crystals

Abstract

In this chapter, we will discuss the theory of the acoustic plane wave propagation in solid, which is the basic principle of FBAR. Form the essential strain-displacement equation and equation of motion of particle, Christoffel equation is deduced to describe the propagation of acoustic wave in solid including general medium and piezoelectric material. The propagation of plane wave in isotropic and anisotropic medium are solved from Christoffel equation. The wave propagation in the crystal axis and cubic face are detailed discussed for cubic crystal. One solution describes a pure shear mode wave whose velocity is vertical to the xz-plane. Other two solutions are quasi-shear mode and quasi-longitudinal mode. In the piezoelectric dielectric, the Maxwell equation and Christoffel equation are coupled to form coupled Christoffel equation. A piezoelectric hexagonal crystal is taken as an example to find out the plane-wave solutions of Christoffel equation. There are three kinds of the plane wave propagating in the c axis of the hexagonal crystal, including a longitudinal mode and two shear mode waves. The field quantities of these three kinds of plane wave propagating in c axis are listed.