Page 346 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

326 SURFACE ACOUSTIC WAVES IN SOLIDS

(10.18)

(10.19)
+ eE k
k
with i, j, k, and / taking the values of 1, 2, or 3.
The strain-mechanical displacement relation is:

(10.20)

The absence of intrinsic charge in the materials is assumed; therefore,

Dj.j=0 (10.21)

The quasi-static approximation is valid because the wavelength of the elastic waves is
much smaller than that of the electromagnetic waves, and the magnetic effects generated
by the electric field can be neglected (Auld 1973a):

= -<f>.k (10.22)
E k
where </> is the electric potential associated with the acoustic wave.
The problem of acoustic wave propagation is fully described in Equations (10.17) to
(10.22). These equations can be reduced through substitution to
u
c
*i — jkl l.jk (10.23)
0 = ejki - efkbjk (10.24)

The geometry for the problem of SAW wave propagation is shown in Figure 10.4. It has
a traction-free surface (x 3 = 0) separating an infinitely deep solid from the free space.
The traction-free boundary conditions are (Viktorov 1967; Varadan and Varadan 1999)

r,- 3 =0 for x 3 = 0 (10.25)

where i takes a value of 1, 2, or 3.
The solutions of the coupled wave Equations (10.23) and (10.24) must satisfy the
mechanical boundary conditions of Equation (10.25). The solutions of interest here are

Figure 10.4 Coordinate system for SAW waves showing the propagation vector