q
∂
∂t
Δp
ð Þ ¼ ÀJ
p
3,3 ,
q
∂
∂t
Δn
ð Þ ¼ J
n
3,3 :
ð6:135Þ
The one-dimensional constitutive relations are from Eqs. (6.80), (6.84), (6.85), and
(6.88):
M ¼ ÀDu 2,33 À 2Ge
1
ð Þ
33 E 3 ,
Q ¼ ÀDu 2,333 À 2Ge
1
ð Þ
33 E ,3 ,
b
D 3 ¼ À2Ge
1
ð Þ
33 u 2,33 þ b εE 3 ,
ð6:136Þ
J
p
3 ffi qp 0 μ
p
33 E 3 À qD
p
33 Δp
ð Þ ,3 ,
J
n
3 ffi qn 0 μ
n
33 E 3 þ qD
n
33 Δn
ð Þ ,3 ,
ð6:137Þ
where, from Eq. (6.74),
E 3 ¼ Àφ ,3 :
ð6:138Þ
The axial electric polarization P 3 and the related effective polarization charge density
ρ
P can be calculated from the following expressions:
Fig. 6.15 (a) A PN junction
in a composite beam. (b)
Doping profile
6.5 Bending of a PN Junction
169
∂
∂t
Δp
ð Þ ¼ ÀJ
p
3,3 ,
q
∂
∂t
Δn
ð Þ ¼ J
n
3,3 :
ð6:135Þ
The one-dimensional constitutive relations are from Eqs. (6.80), (6.84), (6.85), and
(6.88):
M ¼ ÀDu 2,33 À 2Ge
1
ð Þ
33 E 3 ,
Q ¼ ÀDu 2,333 À 2Ge
1
ð Þ
33 E ,3 ,
b
D 3 ¼ À2Ge
1
ð Þ
33 u 2,33 þ b εE 3 ,
ð6:136Þ
J
p
3 ffi qp 0 μ
p
33 E 3 À qD
p
33 Δp
ð Þ ,3 ,
J
n
3 ffi qn 0 μ
n
33 E 3 þ qD
n
33 Δn
ð Þ ,3 ,
ð6:137Þ
where, from Eq. (6.74),
E 3 ¼ Àφ ,3 :
ð6:138Þ
The axial electric polarization P 3 and the related effective polarization charge density
ρ
P can be calculated from the following expressions:
Fig. 6.15 (a) A PN junction
in a composite beam. (b)
Doping profile
6.5 Bending of a PN Junction
169