for the very large values of F used, the nonlinear version of the constitutive relations
for currents is chosen, and a numerical analysis using COMSOL is performed. The
results are shown in Fig. 3.32. Again, the homogeneous junction is insensitive to
F and is not shown, but the heterogeneous junction shows a stress sensitivity which
may be used for piezotronic applications.
3.15 Small Fields Superposed on a Finite Bias
Consider the piezoelectric semiconductor rod shown in Fig. 3.33. We study small
dynamic fields superposed on finite static fields called biasing fields in extensional
motions of the rod.
The one-dimensional equations with consideration of electrical nonlinearity are
∂T 3
∂x 3
¼ ρ € u 3 ,
∂D 3
∂x 3
¼ q p À n þ N
þ
D À N
À
A
À
Á
,
ð3:214Þ
q _
p ¼ À
∂J
p
3
∂x 3
, q _
n ¼
∂J
n
3
∂x 3
,
ð3:215Þ
T 3 ¼ c 33 S 3 À e 33 E 3 ,
D 3 ¼ e 33 S 3 þ ε 33 E 3 ,
ð3:216Þ
Fig. 3.32 Effects of F on
the IÀV curves of the
heterogeneous junction
3.15 Small Fields Superposed on a Finite Bias
85