# IGBT Modules - Technologies, Driver and Application (Second Edition) - page 22

10
dx
dn d )0(n )d(n
⋅ − = −
Eq. 1.19
dx
dp d )0(p )d(p
⋅ − = −
Eq. 1.20
By using
r
it follows:
n,th
n
v
dx
dn d )0(n5.0 )d(R
⋅
⋅ − ⋅
= −
Eq. 1.21
p,th
p
v
dx
dp d )0(p5.0 )d(R
⋅
⋅ − ⋅
= −
Eq. 1.22
The same applies for the rates of the charge carriers that flow left from the point d to the
point 0:
n,th
n
v
dx
dn d )0(n5.0 )d(R
⋅
⋅ + ⋅
=
Eq. 1.23
p,th
p
v
dx
dp d )0(p5.0 )d(R
⋅
⋅ + ⋅
=
Eq. 1.24
By summarising the charge carrier rates that effectively flow through point 0, it follows
that:
dx
dn D
dx
dn d v )d(R)d(R R
n
n,th
n
n n
= ⋅ ⋅
= − −
=
Eq. 1.25
dx
dp D
dx
dp d v )d(R)d(R R
p
p,th
p
p
p
= ⋅ ⋅
= − −
=
Eq. 1.26
D: Diffusion constant
s
cm
2
If the rate of the charge carrier is multiplied by the relevant elementary charge q, the
result is thediffusiondensity:
dx
dn Dq
dx
dn Dq J
n
n
diff ,n
⋅ = ⋅
⋅ =
Eq. 1.27
dx
dp Dq
dx
dp Dq J
p
p
diff ,p
⋅ = ⋅
⋅ =
Eq. 1.28
Finally, for the total charge carrier density fromdrift anddiffusion, it follows that:
The Taylor's theorem and the Taylor series are named after the English mathematician Brook Taylor (1685 -
1731). The approximationusedhere takes a=0 and breaks off after the secondmember of theTaylor series.
1...,12,13,14,15,16,17,18,19,20,21 23,24,25,26,27,28,29,30,31,32,...548