thermoelastic and piezoelectric effects. This thermally induced redistribution of
charge carriers suggests the possibility of sensing or transduction between a temperature change and electric currents. In Fig. 7.2, Δn is an order of magnitude
smaller than n 0 for the linearized theory to be valid.
Figure 7.3 shows Δn for different n 0 when θ¼0.1 K, while all other parameters
are kept the same as those for Fig. 7.2. Δn is sensitive to n 0 .
7.2 Effects of a Local Temperature Change
From Sect. 3.8, it is known that local stresses in a piezoelectric semiconductor rod
produce local electric potential barriers and wells and thus forbid the passage of
currents under low voltages. We expect that a local temperature change in a
piezoelectric semiconductor rod does the same and demonstrate it theoretically and
numerically in this section [2]. Consider the ZnO rod as shown in Fig. 7.4. It is doped
into an n-type semiconductor, and hence p is taken to be zero approximately. The rod
is under a local and uniform temperature change within |x 3 | < a. The problem is
static.
The one-dimensional governing equations are taken from the previous section:
T 33,3 ¼ ρ€ u 3 ,
D 3,3 ¼ q Δp À Δn
ð
Þ ,
ð7:29Þ
J
p
3,3 ¼ Àq _
p,
J
n
3,3 ¼ q _
n,
ð7:30Þ
Fig. 7.3 Distribution of
electron concentration
perturbation along the rod
for different n 0 . θ¼0.1 K
182
7 Thermal Effects