3 Solar Cells: Basics
57
where P ideal denotes the limit value for the output power density
9 that the solar cell
can deliver in the “ideal” case, corresponding to Fig. 3.12. We then mathematically
maximize P ideal as a function of V, to find the maximum power point MPP (in this
ideal case) and compute the quantity
F F = P max /(V oc × J sc ) = (V m × J m )/(V oc × J sc ).
This gives us the expression [12]:
F F =
˜
ν oc − ln(˜ ν oc + 0.72V)
˜
ν oc + 1
(3.13)
with:
˜
ν oc =
V oc
nkT /q
Inserting the semi-empirical limit value for V oc , from the preceding paragraph
(3.11), we obtain the two lower curves (n = 1 and n = 2) in Fig. 3.18 representing
the semi-empirical limit for the Fill Factor FF.
10 In the same figure the fundamental
limit for FF is also given, based on the theory of Shockley and Queisser.
Fig. 3.18 Maximum value of Fill Factor FF, as a function of the bandgap E g (see text). The red
curve is the Shockley-Queisser (S-Q) limit. To compute this curve, data from [21] has been used.
The green and the blue curves are semi-empirical limits according to the work of Green [12]. Dots
show the maximum values obtained for different solar cell materials in Research Laboratories [17]
9 Note that in this section we use the symbol P to denote power density, whereas in Sect. 3.5 we
will be using the same symbol P to denote power.
10 The curves for V oc in Fig. 3.17 have been computed for the case n = 1; in fact, curve (2) in
Fig. 3.17 was obtained from (3.11), where one has set n = 1; in order to obtain the corresponding
curves for V oc for the case n = 2, we would need to know more about the recombination within
the depletion region of the solar cell. As such information is not available, we have here simply
combined (3.11) for V oc and n = 1 with (3.13) for n = 2. The result, as presented in Fig. 3.18 under
the heading n = 2, is a very coarse approximation.
57
where P ideal denotes the limit value for the output power density
9 that the solar cell
can deliver in the “ideal” case, corresponding to Fig. 3.12. We then mathematically
maximize P ideal as a function of V, to find the maximum power point MPP (in this
ideal case) and compute the quantity
F F = P max /(V oc × J sc ) = (V m × J m )/(V oc × J sc ).
This gives us the expression [12]:
F F =
˜
ν oc − ln(˜ ν oc + 0.72V)
˜
ν oc + 1
(3.13)
with:
˜
ν oc =
V oc
nkT /q
Inserting the semi-empirical limit value for V oc , from the preceding paragraph
(3.11), we obtain the two lower curves (n = 1 and n = 2) in Fig. 3.18 representing
the semi-empirical limit for the Fill Factor FF.
10 In the same figure the fundamental
limit for FF is also given, based on the theory of Shockley and Queisser.
Fig. 3.18 Maximum value of Fill Factor FF, as a function of the bandgap E g (see text). The red
curve is the Shockley-Queisser (S-Q) limit. To compute this curve, data from [21] has been used.
The green and the blue curves are semi-empirical limits according to the work of Green [12]. Dots
show the maximum values obtained for different solar cell materials in Research Laboratories [17]
9 Note that in this section we use the symbol P to denote power density, whereas in Sect. 3.5 we
will be using the same symbol P to denote power.
10 The curves for V oc in Fig. 3.17 have been computed for the case n = 1; in fact, curve (2) in
Fig. 3.17 was obtained from (3.11), where one has set n = 1; in order to obtain the corresponding
curves for V oc for the case n = 2, we would need to know more about the recombination within
the depletion region of the solar cell. As such information is not available, we have here simply
combined (3.11) for V oc and n = 1 with (3.13) for n = 2. The result, as presented in Fig. 3.18 under
the heading n = 2, is a very coarse approximation.