# IGBT Modules - Technologies, Driver and Application (Second Edition) - page 21

9
Based on
and
it follows for the total charge carrier density, which
represents a current per surface area:
) p n()x(Eq )x(E pq )x(E nq
J
J J
p
n
p
n
drift
,p
drift
,n
drift
µ⋅ +µ⋅ ⋅
⋅ = ⋅µ⋅ ⋅ + ⋅µ⋅ ⋅ = + =
Eq. 1.15
The expression
) p n(q
p
n
µ⋅ +µ⋅ ⋅
is also described as the specific conductivity of the
semiconductor. Accordingly, the specific resistance
ρ
is defined as:
) p n(q
1
p
n
µ⋅ +µ⋅ ⋅
Eq. 1.16
ρ
:Specific resistance
[
]
cm
⋅Ω
In contrast to the carrier drift, the diffusionmovement originates in the thermal motion of
charge carriers. Thesemove at the average speed v
th
in the time t over the distanced.
Fig. 1.7
Movement in the semiconductor by diffusion
Provided that there is a consistent temperature in a semiconductor, it canmore or less
be assumed that the direction of movement is free and consistent. Taking point 0 in a
semiconductor
, the probability that a charge carrier at point -dwill move to the
right in direction 0 is equal to the probability that it will move to the left, i.e. 50% in each
case. The rate of electrons that flow from the point -d to thepoint 0 can bedescribedas:
n,th
n
v)d(n5.0 )d(R
⋅ − ⋅
= −
Eq. 1.17
R: Carrier flow rate


s cm
1
2
Accordingly, for the rate of holes:
p,th
p
v)d(p5.0 )d(R
⋅ − ⋅
= −
Eq. 1.18
For theexpression n(-d), it canbe approximated, according toTaylor's theore
that:
9
Taylor's theorem postulates that any given function f(x) can be approximated sufficiently accurately using a
Taylor series:
)a( f
!n
)ax(
...
)a(''f
!2
)ax( )a('f
!1
)ax( )a(f )x(f
)n(
0n
n
2
= + ⋅
+ ⋅
+ =
=
1...,11,12,13,14,15,16,17,18,19,20 22,23,24,25,26,27,28,29,30,31,...548