10.13 Excess-Carrier Profiles
335
(a)
(b)
Fig. 10.36 Excess carrier density profile (10.75) in a linear and b semi-logarithmic plot for S = 0 and S = ∞. Other
parameters are given in panel (a)
− e S 0 = −e D p
∂
∂x
x=0
.
(10.74)
The solution is given as
=
G 0 τ p
1 − α 2 L 2
p
exp (−α x) −
S + α D p
S + D p /L p
exp
−
x
L p
.
(10.75)
For vanishing surface recombination, S = 0, the solution is (Fig. 10.36)
=
G 0 τ p
1 − α 2 L 2
p
exp (−α x) − α L p exp
−
x
L p
.
(10.76)
For αL p 1, (10.65) is recovered. This dependence is the excess-carrier profile if the absorption is
strong, which is a tendency for short wavelengths. The current at the surface, j (x = 0) ∝ ∇ is
zero.
In the case of very strong surface recombination, S → ∞, (10.75) becomes
=
G 0 τ p
1 − α 2 L 2
p
exp (−α x) − exp
−
x
L p
,
(10.77)
with = 0 (Fig. 10.36). The current at the surface is (D p τ p = L
2
p )
j (x = 0) = −e D
∂
∂x
x=0
= −e
G 0 L p
1 + α L p
= −e 0
α L p
1 + α L p
.
(10.78)