334
10 Recombination
Fig. 10.35 Charge carrier
density profiles (in a
semi-infinite slab) for
electrons and holes as well
as their difference
p − n = δρ/e, as well as
the associated Dember
potential δφ. The ratio of
electron and hole mobility
in this model calculation
(using silicon material
parameters) was 5.
Adapted from [1048]
10.13.2 Generation in the Bulk
Now, a generation rate following (9.16), realistic for photodiodes and solar cells, is considered,
G(x) = G 0 exp (−α x) ,
(10.69)
i.e. due to light absorption with the (wavelength-dependent) absorption coefficient α. The total generation rate is
G tot =
∞
0
G(x) dx =
G 0
α
.
(10.70)
The total generation rate is equal to the number of photons per second 0 that enter the semiconductor.
The solution of (10.63) is the sum of the homogeneous solution (10.64) and a particular solution
that is given by
= C exp (−α x) .
(10.71)
The constant C is determined to be
C =
G 0 τ p
1 − α 2 L 2
p
.
(10.72)
Therefore, the solution is
= C 1 exp
−
x
L p
+ C 2 exp
x
L p
+
G 0 τ p
1 − α 2 L 2
p
exp (−α x) .
(10.73)
Using again → ∞) = 0 (leading to C 2 = 0) and a recombination velocity S at the front surface,
i.e.