Chapter 6
Composite Structures
In acoustoelectric and piezotronic devices, the redistribution or motion of charge
carriers is caused or affected by mechanical loads through the electric field produced
via piezoelectric coupling. This coupling can also happen in composite structures of
piezoelectric dielectrics and nonpiezoelectric semiconductors. In this chapter we
study a few problems of this type.
6.1 Surface Waves
Consider a p-doped nonpiezoelectric semiconductor plate of thickness 2h on a
piezoelectric dielectric half space as shown in Fig. 6.1 along with the coordinate
system. The plate is unelectroded and is without free charges or currents at its
surfaces. We study surface waves propagating in the x 1 direction [1].
Consider the piezoelectric half space first. We limit ourselves to the case of
ceramics poled in the x 3 direction. These materials allow the following anti-plane
motions described by
u 1 ¼ u 2 ¼ 0, u 3 ¼ u 3 x 1 , x 2 , t
ð
Þ, φ ¼ φ x 1 , x 2 , t
ð
Þ,
ð6:1Þ
2S 13
2S 23
&
'
¼ ∇u 3 ,
E 1
E 2
& '
¼ À∇φ,
ð6:2Þ
T 13
T 23
&
'
¼ c 44 ∇u 3 þ e 15 ∇φ,
D 1
D 2
& '
¼ e 15 ∇u 3 À ε 11 ∇φ,
ð6:3Þ
c 44 ∇
2 u 3 þ e 15 ∇
2
φ ¼ ρ€ u 3 ,
e 15 ∇
2 u 3 À ε 11 ∇
2 φ ¼ 0,
ð6:4Þ
© Springer Nature Switzerland AG 2020
J. Yang, Analysis of Piezoelectric Semiconductor Structures,
https://doi.org/10.1007/978-3-030-48206-0_6
141