626
22 Light-to-Electricity Conversion
The diffusion current collected at the back contact is obtained from solving (10.73) (now for electrons
in p-type material) with the appropriate boundary conditions (reversely bias depletion layer, n p (w) = 0,
p (∞) = n p (∞) − n p 0 = 0 [1873]):
j D (λ) = e n ph (λ) [1 − R(λ)]
α L n
1 + α L n
exp(−α w) + e n 0
D n
L n
,
(22.63)
Dropping the wavelength dependence and neglecting the dark term, the usual formula is obtained,
j L = e n ph (1 − R)
1 −
exp(−α w)
1 + α L n
,
(22.64)
The last bracket represents the quantum efficiency [1874]. The model can be extended for taking into
account a non-zero surface recombination velocity at the back contact at finite distance [1875].
Here a voltage independent photo-generated current I L is assumed. If the diffusion length is small
compared to the transport path, the carrier collection efficiency η c becomes voltage dependent [1874].
The reduction of the diffusion potential for forward voltage decreases the carrier collection efficiency
[1876], possibly to zero close to the built-in voltage.
The saturation current density is given by (21.132) and (21.133)
j s =
I s
A
= e N C N V
1
N A
D n
τ n
+
1
N D
D p
τ p
exp
−
E g
kT
,
(22.65)
with A being the cell area.
The voltage at I = 0 is termed the open-circuit voltage V oc , the current at V = 0 is termed the
short-circuit current I sc = I L (Fig. 22.56). Only a part of the rectangle I sc × V oc can be used for power
conversion. By choice of the load resistance R L , the work point is set. At I m and V m , the generated
power P m = I m V m is maximal. The filling factor F is defined as the ratio
F =
I m V m
I sc V oc
.
(22.66)
The open-circuit voltage is given by
Fig. 22.56 Schematic I –V
characteristics of a solar
cell under illumination (left
scale) and extracted power
(right scale). The grey area
is the maximum power
rectangle with P m = I m V m
0.0
0.5
-1.0
-0.5
0.0
0.5
1.0
0.0
0.5
I m
I sc
V m V oc
P m
22 Light-to-Electricity Conversion
The diffusion current collected at the back contact is obtained from solving (10.73) (now for electrons
in p-type material) with the appropriate boundary conditions (reversely bias depletion layer, n p (w) = 0,
p (∞) = n p (∞) − n p 0 = 0 [1873]):
j D (λ) = e n ph (λ) [1 − R(λ)]
α L n
1 + α L n
exp(−α w) + e n 0
D n
L n
,
(22.63)
Dropping the wavelength dependence and neglecting the dark term, the usual formula is obtained,
j L = e n ph (1 − R)
1 −
exp(−α w)
1 + α L n
,
(22.64)
The last bracket represents the quantum efficiency [1874]. The model can be extended for taking into
account a non-zero surface recombination velocity at the back contact at finite distance [1875].
Here a voltage independent photo-generated current I L is assumed. If the diffusion length is small
compared to the transport path, the carrier collection efficiency η c becomes voltage dependent [1874].
The reduction of the diffusion potential for forward voltage decreases the carrier collection efficiency
[1876], possibly to zero close to the built-in voltage.
The saturation current density is given by (21.132) and (21.133)
j s =
I s
A
= e N C N V
1
N A
D n
τ n
+
1
N D
D p
τ p
exp
−
E g
kT
,
(22.65)
with A being the cell area.
The voltage at I = 0 is termed the open-circuit voltage V oc , the current at V = 0 is termed the
short-circuit current I sc = I L (Fig. 22.56). Only a part of the rectangle I sc × V oc can be used for power
conversion. By choice of the load resistance R L , the work point is set. At I m and V m , the generated
power P m = I m V m is maximal. The filling factor F is defined as the ratio
F =
I m V m
I sc V oc
.
(22.66)
The open-circuit voltage is given by
Fig. 22.56 Schematic I –V
characteristics of a solar
cell under illumination (left
scale) and extracted power
(right scale). The grey area
is the maximum power
rectangle with P m = I m V m
0.0
0.5
-1.0
-0.5
0.0
0.5
1.0
0.0
0.5
I m
I sc
V m V oc
P m