In this case, it is found that
p
0
¼ n
0
¼ 0:9 Â 10
21 m
À3
¼ a 1 þ a 2
ð
Þ =2 ¼ b 1 þ b 2
ð
Þ =2,
ð3:40Þ
1
k
¼ 1:005 Â 10
À7
ffi 0:1 μm:
ð3:41Þ
We denote the right-hand side of Eq. (3.5) 2 , i.e., the sum of the doping and mobile
charges, by
ρ
e
¼ q p À n þ N
þ
D À N
À
A
À
Á :
ð3:42Þ
Figure 3.3 shows the effects of 2w, i.e., the width of the transition zone, on ρ
e
, the
electric field, and the electric potential. As 2w decreases, the transition zone is
narrower, and all fields change more rapidly there. ρ
e
and the electric field become
stronger. The built-in voltage is not sensitive to w because, as w decreases, the
stronger electric field is over a narrower region, and thus the voltage as the spatial
integration of the electric field does not change much. Far away from the transition
zone, the fields are insensitive to w.
Fig. 3.3 Effects of the width of the transition zone. (a) ρ
e /q. (b) E 3 (x 3 ). (c) φ(x 3 )
3.3 Linearly Graded PN Junction
39