# IGBT Modules - Technologies, Driver and Application (Second Edition) - page 25

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energy. If the energy is sufficient or if further energy is supplied to the new free charge
carriers that have been created (e.g. by an adjacent electrical field), there may be a
multiplicationeffect with the creation ofmore charge carriers.
1.1.5 pn-junction
If an n- and a p-doped region are moved so that they are adjacent, a pn-junction is
created. The sharp concentration gradient of the charge carriers at the barrier region
causes some holes to diffuse from the p-conducting region into the n-conducting region
and conversely, some electrons from the n-conducting region to diffuse into the p-
conducting region. Here they recombine with the relevant charge carriers. Given the
now ionised and stationary doping atoms near the barrier region, the n-region is
positively charged and the p-region becomes negatively charged. A space-charge
region is formed.
Fig. 1.9
pn-junction
The space-charge region creates an electrical fieldwhich leads to a potential difference
or the diffusion voltage U
D
. Finally, the electrical field counteracts the diffusion of the
charge carriers and a state of equilibrium is created. For the currentless pn-junction in
this state the following applies:
0 J J
p n
= =
Eq. 1.35
Or, as pe
if only theholedensity J
p
is considered:
p
p
p
p
diff ,p
drift
,p p
p
dp D
dx)x(E
0
dx
dp D)x(E pq J
J J
µ⋅
−=
=
+ ⋅µ⋅
⋅ = + =
Eq. 1.36
According to theEinstein-Smoluchowski equation
x
x
q
Tk D
µ⋅
=
Eq. 1.37
an be reformulatedas:
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The Einstein-Smoluchowski equation originated in gas theory and is named after the German physicist Albert
Einstein (1879 - 1955) and theAustrian physicist MarianSmoluchowski (1872 - 1917).
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