Δp and Δn are antisymmetric about x 3 ¼ 0. We calculate the change of mobile
charges in half of the rod denoted by Q
e as
Q
e
¼
Z 0
ÀL
ρ
e Adx 3 ¼
Z 0
ÀL
q Δp À Δn
ð
Þ Adx 3
¼AT
e 33
c 33
1 À
1
cosh kL
,
Q
e
AT
¼
e 33
c 33
1 À
1
cosh kL
:
ð3:79Þ
Q
e
/(AT) can be used as a measure of the strength of the coupling of interest, i.e., the
effect of f on the redistribution of mobile charges in the rod. When p 0 or n 0 increases,
k increases, coshkL increases, and Q
e increases as expected.
3.7 Electrically Nonlinear Extension by End Forces
Consider the piezoelectric semiconductor rod shown in Fig. 3.9. It is under an axial
force F. F produces an axial stress f ¼ F/A. The difference from the previous section
is that the electrical nonlinearity in the drift current is considered in this section
[5]. f in this section has a different meaning from that in the previous section.
To simplify the notation, we denote
Fig. 3.8 Axial distribution
of electron concentration
48
3 Extension of Rods
charges in half of the rod denoted by Q
e as
Q
e
¼
Z 0
ÀL
ρ
e Adx 3 ¼
Z 0
ÀL
q Δp À Δn
ð
Þ Adx 3
¼AT
e 33
c 33
1 À
1
cosh kL
,
Q
e
AT
¼
e 33
c 33
1 À
1
cosh kL
:
ð3:79Þ
Q
e
/(AT) can be used as a measure of the strength of the coupling of interest, i.e., the
effect of f on the redistribution of mobile charges in the rod. When p 0 or n 0 increases,
k increases, coshkL increases, and Q
e increases as expected.
3.7 Electrically Nonlinear Extension by End Forces
Consider the piezoelectric semiconductor rod shown in Fig. 3.9. It is under an axial
force F. F produces an axial stress f ¼ F/A. The difference from the previous section
is that the electrical nonlinearity in the drift current is considered in this section
[5]. f in this section has a different meaning from that in the previous section.
To simplify the notation, we denote
Fig. 3.8 Axial distribution
of electron concentration
48
3 Extension of Rods