# IGBT Modules - Technologies, Driver and Application (Second Edition) - page 26

14
p
dp
q
Tk dx)x(E
−=
Eq. 1.38
By integrating
ia the path of the space-charge region the diffusion voltageU
D
.
canbe calculated:
=
=
−=
0p
0n
p
n
p
p
0n
0p
x
x
D
p
p
ln
q
Tk
p
dp
q
Tk dx)x(E U
Eq. 1.39
U
D
: Diffusion voltage [V]
x
n
: Depth of penetrationof the electrical field into the n-region [cm]
x
p
: Depth of penetrationof the electrical field into the p-region [cm]
p
p0
: Hole density at the edge of the space-charge region in the
p-region [cm
-3
]
p
n0
: Electron density at the edge of the space-charge region in the
p-region [cm
-3
]
The hole density p
p0
at the edge of the p-region represents the density of the acceptors
N
A
in the region.With the aido
p
n0
can be calculated as:
D
2
i
0n
2
i
0n
N
n
n
n p
= =
Eq. 1.40
N
D
: Donor density
n
n0
in this equation is identical to the donor density in the n-region. For the diffusion
voltageU
D
, therefore
anbe reformulated to:
2
i
D A
D
n
NN ln
q
Tk U
=
Eq. 1.41
N
A
: Acceptor density
Example:
The diffusion voltage in silicon, with an acceptor density of
3
17
A
cm 10 N
=
, a donor
density of
3
16
D
cm 10 N
=
and with an intrinsic charge carrier density of
3
10
i
cm 10 45.1 n
=
at room temperature (300K), results in a valueof:
V75.0
)
cm 10 45.1(
cm 10
cm 10 ln
C 10
60218 .1
K300
K
J 10
38065 .1
U
23
10
3
16
3
17
19
23
D
=
=
The equilibrium state can be influenced by the application of an external voltage. If the
positive terminal of a power supply is connected with the n-conducting zone and the
negative terminal with the p-conducting zone, the electrical field that ensues has the
same direction as the space-charge field around the pn-junction and increases its effect.
This gives the result that no significant current can flow through the barrier region.
However, there is a low reverse current within the barrier region, due exclusively to
thermal energy applied from outside, as electron-hole pairs are constantly being formed
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