∇
2 u ¼ À
e
c
∇
2 φ,
ð2:24Þ
∇
2 Δp
ð Þ ¼ À
p 0 μ
p
D
p ∇
2 φ,
∇
2 Δn
ð Þ ¼
n 0 μ
n
D
n ∇
2 φ,
ð2:25Þ
where
k
2
¼
p 0 μ
p
D
p þ
n 0 μ
n
D
n
q
ε
,
ð2:26Þ
Fig. 2.6 Axial strain S 3 (x 3 )
n-doped
x1
x2
p-doped
a
Fig. 2.7 Two piezoelectric
semiconductors and their
circular interface
20
2 Exact Solutions
2 u ¼ À
e
c
∇
2 φ,
ð2:24Þ
∇
2 Δp
ð Þ ¼ À
p 0 μ
p
D
p ∇
2 φ,
∇
2 Δn
ð Þ ¼
n 0 μ
n
D
n ∇
2 φ,
ð2:25Þ
where
k
2
¼
p 0 μ
p
D
p þ
n 0 μ
n
D
n
q
ε
,
ð2:26Þ
Fig. 2.6 Axial strain S 3 (x 3 )
n-doped
x1
x2
p-doped
a
Fig. 2.7 Two piezoelectric
semiconductors and their
circular interface
20
2 Exact Solutions