0 ¼ À
∂J
p
∂x
, 0 ¼
∂J
n
∂x
,
ð3:223Þ
T ¼ cS À eE,
D ¼ eS þ εE,
ð3:224Þ
J
p ¼ qpμ
p E À qD
p ∂p
∂x
,
J
n ¼ qnμ
n E þ qD
n ∂n
∂x
,
ð3:225Þ
S ¼
∂u
∂x
, E ¼ À
∂φ
∂x
:
ð3:226Þ
The other is for the small incremental fields:
∂ e
T
∂x
¼ ρ €
e u,
∂ e
D
∂x
¼ q e p À e n
ð
Þ ,
ð3:227Þ
q _
e p ¼ À
∂ e J
p
∂x
, q _
e n ¼
∂ e J
n
∂x
,
ð3:228Þ
e
T ¼ c e S À e e
E,
e
D ¼ e e S þ ε e
E,
ð3:229Þ
e J
p ¼ qpμ
p e
E þ qμ
p E e p À qD
p ∂e p
∂x
,
e J
n ¼ qnμ
n e
E þ qμ
n E e n þ qD
n ∂e n
∂x
,
ð3:230Þ
e S ¼
∂e u
∂x
, e
E ¼ À
∂e φ
∂x
:
ð3:231Þ
Equations (3.227), (3.228), (3.229), (3.230), and (3.231) are linear in the small
incremental fields. Equation (3.230) shows that the initial fields appear as coefficients of the equations for the incremental fields. Since the nonlinearity is due to the
drift current, only E , p , and n affect the incremental fields directly through
Eq. (3.230).
References
1. Z.L. Wang, Piezotronics and Piezo-Phototronics (Science Press, Beijing, 2012, in Chinese)
2. G.Y. Yang, J.K. Du, J. Wang, J.S. Yang, Electromechanical fields in a nonuniform piezoelectric
semiconductor rod. J. Mech. Mater. Struct. 13, 103–120 (2018)
References
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