IGBT Modules - Technologies, Driver and Application (Second Edition) - page 23

1P
11
+ ⋅µ⋅
⋅ = + =
dx
dn D)x(E nq J
J J
n
n
diff ,n
drift ,n n
Eq. 1.29
+ ⋅µ⋅
⋅ = + =
dx
dp D)x(E pq J
J J
p
p
diff ,p
drift
,p p
Eq. 1.30
p n
J J J
+ =
Eq. 1.31
1.1.4 Charge carrier generation and recombination
In semiconductors there is permanent generation of free charge carriers, which
disappear again after a certain time through recombination with an opposite charged
carrier. Generationmeans that a charge carrier is elevated from the valence band to the
conduction band. Accordingly, recombination means that a charge carrier from the
conduction band falls back into the valence band. As long as the semiconductor
remains thermodynamically balanced, the number of free charge carriers created by
generation and eliminated by recombination is identical. The concentration of the
electrons and holes in the semiconductor in a state of equilibrium is stated as n
0
or p
0
. If
the state of equilibrium is disturbed, for example by the supply of energy from an
external source, theproduct of the charge carrier is increased. Therefore:
0 0
pnpn
> ⋅
Eq. 1.32
The recombination rate for theelectrons and holes can be stated as:
n
0
n
nn r
τ
=
Eq. 1.33
p
0
p
pp r
τ
=
Eq. 1.34
τ
: Carrier lifetime [s]
The carrier lifetime represents the duration an electron (or hole) lasts in the conduction
band (or valence band) before it recombines. During this time, the charge carrier can
travel in average the length L. L is called the diffusion length and is a function of
τ
n
or
τ
p
respectively.
There are threemain types of recombination of charge carriers:
Direct (band-to-band) recombination
with the addition of a photon. The
photon accepts the impulse of the recombining charge carrier. For silicon
power semiconductors, this recombination process has no significance.
Shockley-Read-Hall (SRH) recombination
10
. In SRH recombination, the
charge carrier does not move directly from the conduction band to the valence
band. Instead, it travels via an impurity in the semiconductor, the energy level
of which lies between that of the conduction band and the valence band. The
charge carrier thenmoves into the valence band, releasing its thermal energy.
10
Named besides others after theUnitedStates physicistWilliamBradfordShockley (1910 - 1989).
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