numerical analysis using COMSOL. The I-V curves of the homogeneous junction
are insensitive to the temperature change. The results for the heterogeneous junction
are shown in Fig. 7.11.
From Sect. 7.1, it is known that the following combination of the effective onedimensional material parameters
p þ
eλ
c
ð7:72Þ
plays a decisive role in the thermal behavior of a ZnO rod. It includes the effects of
the effective one-dimensional pyroelectric, thermoelastic, and piezoelectric constants. With the use of Eq. (7.11), it can be shown that the combination in
Eq. (7.72) is equal to the three-dimensional material constant p 3 . For our ZnO rod,
we have
Table 7.1 Temperature effect on effective polarization charge density at junction interface
Charge (C/m
2
)
P
À
P
+
σ
P
Temperature (K)
θ ¼ 0
Homogeneous
À4.5638 Â 10
À6
À4.5638 Â 10
À6
0
Heterogeneous
À4.5638 Â 10
À6
À4.5638 Â 10
À6
0
Temperature (K)
θ ¼ 0.3
Homogeneous
À6.6335 Â 10
À6
À6.6335 Â 10
À6
0
Heterogeneous
À4.4002 Â 10
À6
À4.7274 Â 10
À6
3.2724 Â 10
À7
Temperature (K)
θ ¼ 0.5
Homogeneous
À8.0134 Â 10
À6
À8.0134 Â 10
À6
0
Heterogeneous
À4.2911 Â 10
À6
À4.8365 Â 10
À6
5.4541 Â 10
À7
Fig. 7.11 I-V curves of the
heterogeneous junction.
J
n ¼ I
7.3 Temperature Effects on PN Junctions
195