22.4 Solar Cells
629
Fig. 22.59 I –V
characteristics of a solar
cell considering shunt and
series resistances R s and
R sh , respectively. The
efficiency of the real cell
(shaded power rectangle)
is less than 30% of that of
the ideal cell. Adapted
from [1883]
100
50
0
-50
-100
-0.5
0
0.5
1.0
R =0
R =
sh
s
R =5
R =
s
sh
R =5
R =
s
sh 100
R =0
R =
s
sh 100
22.4.3 Real Solar Cells
For a real solar cell, the effect of parallel resistance R sh (shunt resistance due to leakage current, e.g.
by local shorts of the solar cell) and serial resistance R s (due to ohmic loss) must be considered. The
I –V characteristic is then (cf. (21.158))
ln
I + I L
I s
−
V − I R s
I s R sh
+ 1
= β (V − I R s ) .
(22.72)
The serial resistance affects the efficiency more strongly than the shunt resistance (Fig. 22.59). Therefore, it is frequently enough to consider R s only and use (cf. (21.157))
I = I s exp (β(V − I R s )) − I L .
(22.73)
In the example of Fig. 22.59, a serial resistance of 5 reduces the filling factor by a factor of about
four.
At open circuit voltage the photo-generated carriers have nowhere to go; in an ideal solar cell, the
only process is the radiative recombination and the photon escape. Certainly, the internal quantum
efficiency should be high and the non-radiative recombination rate small compared to the radiative
one (cf. Sect. 10.10). The open circuit voltage and thus the energy conversion efficiency depends also
on the light extraction efficiency χ ex which will be discussed in greater detail in the context of LEDs
(Sect. 23.3.3). Based on [1884, 1885], the open circuit voltage V
oc of a real solar cell is reduced
(χ ex ≤ 1) from the ideal value V oc given in (22.67),
V
oc = V oc + β
−1 ln χ ex .
(22.74)
629
Fig. 22.59 I –V
characteristics of a solar
cell considering shunt and
series resistances R s and
R sh , respectively. The
efficiency of the real cell
(shaded power rectangle)
is less than 30% of that of
the ideal cell. Adapted
from [1883]
100
50
0
-50
-100
-0.5
0
0.5
1.0
R =0
R =
sh
s
R =5
R =
s
sh
R =5
R =
s
sh 100
R =0
R =
s
sh 100
22.4.3 Real Solar Cells
For a real solar cell, the effect of parallel resistance R sh (shunt resistance due to leakage current, e.g.
by local shorts of the solar cell) and serial resistance R s (due to ohmic loss) must be considered. The
I –V characteristic is then (cf. (21.158))
ln
I + I L
I s
−
V − I R s
I s R sh
+ 1
= β (V − I R s ) .
(22.72)
The serial resistance affects the efficiency more strongly than the shunt resistance (Fig. 22.59). Therefore, it is frequently enough to consider R s only and use (cf. (21.157))
I = I s exp (β(V − I R s )) − I L .
(22.73)
In the example of Fig. 22.59, a serial resistance of 5 reduces the filling factor by a factor of about
four.
At open circuit voltage the photo-generated carriers have nowhere to go; in an ideal solar cell, the
only process is the radiative recombination and the photon escape. Certainly, the internal quantum
efficiency should be high and the non-radiative recombination rate small compared to the radiative
one (cf. Sect. 10.10). The open circuit voltage and thus the energy conversion efficiency depends also
on the light extraction efficiency χ ex which will be discussed in greater detail in the context of LEDs
(Sect. 23.3.3). Based on [1884, 1885], the open circuit voltage V
oc of a real solar cell is reduced
(χ ex ≤ 1) from the ideal value V oc given in (22.67),
V
oc = V oc + β
−1 ln χ ex .
(22.74)