# IGBT Modules - Technologies, Driver and Application (Second Edition) - page 27

15
and these are separated from the space-charge field. The range x
SCR
of the space-
charge fieldacross thepn-junction canbe calculatedas follows:
Because of the neutrality, the charge-carrier densities on both sides of the pn-junction
are inequilibrium. Therefore:
n D
p A
xNq xNq
⋅−= ⋅
Eq. 1.42
For the maximum value of the electrical field E
0
on both sides of the pn-junction, the
relationship that applies is:
r 0
n D
r 0
p A
0
xNq xNq
E
ε⋅ε
−=
ε⋅ε
=
Eq. 1.43
ε
0
: Vacuum permittivity
m
F 10
85419 .8
12
ε
r
: Relative permittivit
With the applicationof an external negative voltageU
ext
it follows:
(
)
(
)
n
0
D ext
p
p
0
D ext
n
0
p n
D ext
x
E
U U2
x and x
E
U U2
x
E
2
x x
U U
+
− ⋅
−=
+
− ⋅
= ⇒
= −
Eq. 1.44
By inserting
into
and converting the equation the length x
n
of the
space-charge region in the n-region can be calculated:
(
)
(
)
(
)
(
)
D A D
ext
D A r 0
n
n
A
D
n D
D ext
r 0
n
A
r 0 0
0
D ext
n
N NNq
UUN 2 x
x
N
N
xNq
U U 2 x
Nq
E
E
U U2 x
+ ⋅
− ⋅
⋅ε⋅ε⋅
= ⇒
− ⋅ε⋅ε⋅
−= ⇒
ε⋅ε⋅
+
− ⋅
=
Eq. 1.45
The same applies for the space-charge region in thep-region:
(
)
(
)
(
)
(
)
D A A
ext
D D r 0
p
p
D
A
p A
D ext
r 0
p
D
r 0 0
0
D ext
p
N NNq
UUN 2 x
x
N
N
xNq
U U 2 x
Nq
E
E
U U2 x
+ ⋅
− ⋅
⋅ε⋅ε⋅
= ⇒
− ⋅ε⋅ε⋅
−=
ε⋅ε⋅
− ⋅
−=
Eq. 1.46
13
Permittivity describes howmuch resistance is encounteredwhen formingup anelectric field inside amedium.
14
Relative permittivity is a dimensionless variable and describes amaterial property. For example, silicon has a
relative permittivity of
ε
0
= 11.9.
1...,17,18,19,20,21,22,23,24,25,26 28,29,30,31,32,33,34,35,36,37,...548