Δn ¼
ek
2
cq k
2
þ ξ
2
À
ÁB sin ξx,
φ ¼
k B T
q 2 n 0
ek
2
c k
2
þ ξ
2
À
ÁB sin ξx,
u ¼ À
e
2
c 2
k B T
q 2 n 0
k
2
k
2
þ ξ
2
À
ÁB sin ξx þ
B
c
1
ξ
2
sin ξx:
ð3:130Þ
We plot the charges and potential determined by Eq. (3.130) in Fig. 3.16 when
B ¼ 8.5536 Â 10
11 N/m
3 and ξ ¼ 3.4907 Â 10
6 /m. The charge and potential
distributions are also sinusoidal. A series of periodically alternating potential barriers, wells, and charged regions are produced. They are similar to the fields in
Fig. (3.6) due to periodic doping but are produced mechanically here. In this case, for
the effective polarization charge, there is a distributed ρ
P only without concentrated
effective polarization charges at discontinuities because all fields are continuous
everywhere. (a) to (c) show that ρ
P is significantly but not completely screened by
electrons.
Fig. 3.16 Fields for different n 0 . (a) Effective polarization charge density ρ
P
. (b) Electron
concentration perturbation Δn. (c) Screened polarization charge ρ
P À qΔn. (d) Electric potential φ
60
3 Extension of Rods