3 Solar Cells: Basics
59
Semi-empirical limit (Green)
S-Q limit
Fig. 3.19 Maximum value of the overall (The conversion efficiency for the first step of energy
conversion was given in Sect. 3.2.4, Fig. 3.7.) energy conversion efficiency η of the solar cell as
a function of the band gap E g . Dots show the maximum values obtained for different solar cell
materials in practice [17]. (At Standard Test Conditions, STC, see text)
• The maximum (limit) value of J sc hardly varies with temperature
• The maximum (limit) value of FF varies very little with temperature
• The maximum (limit) value of V oc varies strongly with temperature.
Therefore, we will, in this section, only look at the variation of V oc with temperature, and in a rather rough approximation, assume that the variation of η with
temperature is similar.
We are here interested in the relative temperature coefficient
T C =
∂η
∂ T
/η ≈
∂ V oc
∂ T
/V oc
applicable to the efficiency of solar cells and modules.
1. Fundamental considerations
Fundamental considerations, should, in principle, be based on Thermodynamics,
like the approach of Shockley and Queisser. However, the development of Shockley
and Queisser leads for V oc to mathematical expressions which are cumbersome;
therefore, we will use here for V oc the semi-empirical limit of Martin Green, i.e.
(3.11):
V oc ≈
kT
q
ln
J ph
J 00
+
E g
q
with