Page 339 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

10

Surface Acoustic Waves in Solids

10.1 INTRODUCTION

Acoustics is the study of sound or the time-varying deformations, or vibrations, in a gas,
liquid, or solid.
Some nonconducting crystalline materials become electrically polarised when they are
strained. A basic explanation is that the atoms in the crystal lattice are displaced when it is
placed under an external load. This microscopic displacement produces electrical dipoles
within the crystal and, in some materials, these dipole moments combine to give an average
macroscopic moment or electrical polarisation. This phenomenon is approximately linear
and is known as the direct piezoelectric (PE) effect (Auld 1973a). The direct PE effect
is always accompanied by the inverse PE effect in which the same material will become
strained when it is placed in an external electric field.
A basic understanding of the generation and propagation of acoustic waves (sound) in
PE media is needed to understand the theory of surface acoustic wave (SAW) sensors.
Unfortunately, most textbooks on acoustic wave propagation contain advanced mathe-
matics (Auld 1973a) and that makes it harder to comprehend. Therefore, in this chapter,
we set out the basic underlying principles that describe the general problem of acoustic
wave propagation in solids and derive the basic equations required to describe the prop-
agation of SAWs.
The different ways of representing acoustic wave propagation are outlined in Sec-
tions 10.2 and 10.3. The concepts behind stress and strain over an elastic continuum
are discussed in Section 10.4, along with the general equations and concepts of the
piezoelectric effect. These equations together with the quasi-static approximation of the
electromagnetic field are solved in Section 10.5 in order to derive the generalised expres-
sions for acoustic wave propagation in a PE solid. The boundary conditions that restrict the
propagation of acoustic waves to a semi-infinite solid are included, and the general solu-
tion for a SAW is presented. An overview of the displacement modes in Love, Rayleigh,
and SH-SAW waves are finally presented in Section 10.5. Consequently, this chapter is
only intended to serve as an introduction to the displacement modes of Love, Rayleigh,
and SH waves.
The components of displacements have been shown only for an isotropic elastic solid.
The equations for the complex reciprocity and the assumptions used to derive the pertur-
bation theory are elaborated in Appendix I.
More advanced readers may wish to omit this chapter or refer to specialised text-
books published elsewhere (Love 1934; Ewing et al. 1957; Viktorov 1967; Auld 1973a,b;