22.4 Solar Cells
627
V oc =
1
β
ln
I L
I s
+ 1
∼ =
1
β
ln
I L
I s
(22.67)
and increases with increasing light power and decreasing dark current. The output power is
P = I V = I s V (exp (βV ) − 1) − I L V .
(22.68)
The condition d P/dV = 0 yields the optimal voltage at which the solar cell has to be operated and is
given by the implicit equation
V m =
1
β
ln
I L /I s + 1
1 + βV m
= V oc −
1
β
ln (1 + βV m ) .
(22.69)
The current at maximum power is
I m = I L
1 −
1 − βV m I s /I L
1 + βV m
∼ = I L
1 −
1
βV m
.
(22.70)
E m is the energy that is delivered per photon at the load resistor at the power maximum. The maximum
power is P m = I L E m /e and E m is given by
E m ∼ = e
V oc −
1
β
ln (1 + βV m ) −
1
β
.
(22.71)
The ideal solar cell has a (power) conversion efficiency η = P m /P in that can be determined from
Fig. 22.57a.
The right curve (1) in Fig. 22.57a shows the integral number n ph of photons in the solar spectrum
(per area and time) with an energy larger than a given one (E g ). For a given value of n ph , the left curve
(a)
2
3
0
1
n (10 cm s )
ph
17
-2 -1
4
3
2
1
0
64
48
32
16
0
j (mA cm )
L
-2
C=1
h >E g
h
0.9eV
(31%)
E m
E g E m
E g =
1.35eV
(1)
(2)
(b)
Fig. 22.57 a Number of photons n ph per area and time in the sun spectrum (AM1.5, C = 1 sun) with an energy larger
than a cutoff energy (curve 1) and graphical method to determine the quantum efficiency (from curve 2). Adapted from
[1877]. b Number of photons in concentrated solar spectrum (AM1.5, C =1000 sun) with an energy larger than a given
energy and graphical method to determine the quantum efficiency of multi-junction solar cells. Adapted from [574]
after [1877]
627
V oc =
1
β
ln
I L
I s
+ 1
∼ =
1
β
ln
I L
I s
(22.67)
and increases with increasing light power and decreasing dark current. The output power is
P = I V = I s V (exp (βV ) − 1) − I L V .
(22.68)
The condition d P/dV = 0 yields the optimal voltage at which the solar cell has to be operated and is
given by the implicit equation
V m =
1
β
ln
I L /I s + 1
1 + βV m
= V oc −
1
β
ln (1 + βV m ) .
(22.69)
The current at maximum power is
I m = I L
1 −
1 − βV m I s /I L
1 + βV m
∼ = I L
1 −
1
βV m
.
(22.70)
E m is the energy that is delivered per photon at the load resistor at the power maximum. The maximum
power is P m = I L E m /e and E m is given by
E m ∼ = e
V oc −
1
β
ln (1 + βV m ) −
1
β
.
(22.71)
The ideal solar cell has a (power) conversion efficiency η = P m /P in that can be determined from
Fig. 22.57a.
The right curve (1) in Fig. 22.57a shows the integral number n ph of photons in the solar spectrum
(per area and time) with an energy larger than a given one (E g ). For a given value of n ph , the left curve
(a)
2
3
0
1
n (10 cm s )
ph
17
-2 -1
4
3
2
1
0
64
48
32
16
0
j (mA cm )
L
-2
C=1
h >E g
h
0.9eV
(31%)
E m
E g E m
E g =
1.35eV
(1)
(2)
(b)
Fig. 22.57 a Number of photons n ph per area and time in the sun spectrum (AM1.5, C = 1 sun) with an energy larger
than a cutoff energy (curve 1) and graphical method to determine the quantum efficiency (from curve 2). Adapted from
[1877]. b Number of photons in concentrated solar spectrum (AM1.5, C =1000 sun) with an energy larger than a given
energy and graphical method to determine the quantum efficiency of multi-junction solar cells. Adapted from [574]
after [1877]