Equation (1.7) makes the right-hand side of Eq. (1.1) 2 homogeneous, while at the
same time makes Eq. (1.2) 3,4 nonhomogeneous. Consider the case of small Δp and
Δn. We linearize Eq. (1.2) 3,4 as
J
p
i ffi qp 0 μ
p
ij E j À qD
p
ij p 0 þ Δp
ð
Þ ,j ,
J
n
i ffi qn 0 μ
n
ij E j þ qD
n
ij n 0 þ Δn
ð
Þ ,j :
ð1:9Þ
When p 0 and n 0 are uniform, Eq. (1.9) becomes homogeneous in E, Δp, and Δn.
With Δp and Δn, Eq. (1.1) 2–4 become
D i,i ¼ q Δp À Δn
ð
Þ ,
q
∂ Δp
ð Þ
∂t
¼ ÀJ
p
i,i ,
q
∂ Δn
ð Þ
∂t
¼ J
n
i,i :
ð1:10Þ
Equation (1.10) 1 also becomes homogeneous. Phenomenological theories involving
electromechanical couplings and mechanical nonlinearities due to large deformations in semiconductors can be found in [7, 8].
1.3 One-Dimensional Problems of Crystals of Class (6mm)
We are mainly interested in ZnO which belongs to the crystal class of (6mm). Under
the compact matrix notation [1–4] with indices p and q ranging from 1 to 6, when the
c-axis of the crystal is along x 3 , the material tensors for ZnO can be represented by
the following matrices:
c pq
 à ¼
c 11 c 12 c 13 0
0
0
c 21 c 11 c 13 0
0
0
c 31 c 31 c 33 0
0
0
0
0
0 c 44 0
0
0
0
0
0 c 44 0
0
0
0
0
0 c 66
0
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
A
,
e ip
 à ¼
0
0
0
0 e 15 0
0
0
0 e 15 0 0
e 31 e 31 e 33 0
0 0
0
B
@
1
C
A,
4
1 Macroscopic Theory
same time makes Eq. (1.2) 3,4 nonhomogeneous. Consider the case of small Δp and
Δn. We linearize Eq. (1.2) 3,4 as
J
p
i ffi qp 0 μ
p
ij E j À qD
p
ij p 0 þ Δp
ð
Þ ,j ,
J
n
i ffi qn 0 μ
n
ij E j þ qD
n
ij n 0 þ Δn
ð
Þ ,j :
ð1:9Þ
When p 0 and n 0 are uniform, Eq. (1.9) becomes homogeneous in E, Δp, and Δn.
With Δp and Δn, Eq. (1.1) 2–4 become
D i,i ¼ q Δp À Δn
ð
Þ ,
q
∂ Δp
ð Þ
∂t
¼ ÀJ
p
i,i ,
q
∂ Δn
ð Þ
∂t
¼ J
n
i,i :
ð1:10Þ
Equation (1.10) 1 also becomes homogeneous. Phenomenological theories involving
electromechanical couplings and mechanical nonlinearities due to large deformations in semiconductors can be found in [7, 8].
1.3 One-Dimensional Problems of Crystals of Class (6mm)
We are mainly interested in ZnO which belongs to the crystal class of (6mm). Under
the compact matrix notation [1–4] with indices p and q ranging from 1 to 6, when the
c-axis of the crystal is along x 3 , the material tensors for ZnO can be represented by
the following matrices:
c pq
 à ¼
c 11 c 12 c 13 0
0
0
c 21 c 11 c 13 0
0
0
c 31 c 31 c 33 0
0
0
0
0
0 c 44 0
0
0
0
0
0 c 44 0
0
0
0
0
0 c 66
0
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
A
,
e ip
 à ¼
0
0
0
0 e 15 0
0
0
0 e 15 0 0
e 31 e 31 e 33 0
0 0
0
B
@
1
C
A,
4
1 Macroscopic Theory