p ¼ À1:1981 Â 10
À5 C=m
2 K
À
Á
,
eλ
c
¼ 0:50808 Â 10
À5 C=m
2 K
À
Á :
ð7:73Þ
Equation (7.73) shows that p and eλ/c have opposite signs, and some cancelation is
present in their combined effect. Therefore it can be expected that when p and e have
the same sign, the temperature effect may be stronger. To verify this, we artificially
change the sign of e in both halves of the junction but not that of p and plot the
corresponding I-V curves in Fig. 7.12. Indeed, the temperature sensitivity is much
stronger than that in Fig. 7.11.
7.4 Extension of Composite Rods
In this section we study the effects of a uniform temperature change on the extensional deformation of the composite rod shown in Fig. 7.13 [4]. It consists of two
piezoelectric dielectric layers and a nonpiezoelectric semiconductor layer. (x,y,z)
correspond to (x 1 ,x 2 ,x 3 ). When the piezoelectric materials are polarized ceramics or
crystals of class (6mm), the poling direction or the c axis is along the z axis.
Equations (7.1), (7.2), (7.3), (7.4), and (7.5) are still valid. They include piezoelectric dielectrics and nonpiezoelectric semiconductors as special cases. We need to
derive a set of one-dimensional equations from Eqs. (7.1), (7.2), (7.3), (7.4), and
(7.5) for the extensional deformation of the composite rod under a uniform temperature change. For a thin composite rod, similar to Eqs. (7.6) and (7.7), we still have,
for the entire rod, approximately
Fig. 7.12 I-V curves of the
heterogeneous junction
when the sign of e is
artificially changed. J
n ¼ I
196
7 Thermal Effects
À5 C=m
2 K
À
Á
,
eλ
c
¼ 0:50808 Â 10
À5 C=m
2 K
À
Á :
ð7:73Þ
Equation (7.73) shows that p and eλ/c have opposite signs, and some cancelation is
present in their combined effect. Therefore it can be expected that when p and e have
the same sign, the temperature effect may be stronger. To verify this, we artificially
change the sign of e in both halves of the junction but not that of p and plot the
corresponding I-V curves in Fig. 7.12. Indeed, the temperature sensitivity is much
stronger than that in Fig. 7.11.
7.4 Extension of Composite Rods
In this section we study the effects of a uniform temperature change on the extensional deformation of the composite rod shown in Fig. 7.13 [4]. It consists of two
piezoelectric dielectric layers and a nonpiezoelectric semiconductor layer. (x,y,z)
correspond to (x 1 ,x 2 ,x 3 ). When the piezoelectric materials are polarized ceramics or
crystals of class (6mm), the poling direction or the c axis is along the z axis.
Equations (7.1), (7.2), (7.3), (7.4), and (7.5) are still valid. They include piezoelectric dielectrics and nonpiezoelectric semiconductors as special cases. We need to
derive a set of one-dimensional equations from Eqs. (7.1), (7.2), (7.3), (7.4), and
(7.5) for the extensional deformation of the composite rod under a uniform temperature change. For a thin composite rod, similar to Eqs. (7.6) and (7.7), we still have,
for the entire rod, approximately
Fig. 7.12 I-V curves of the
heterogeneous junction
when the sign of e is
artificially changed. J
n ¼ I
196
7 Thermal Effects