60
A. Shah
J 00 = J
Green
00
= 1.5 × 10
8 mA/cm
2
Assuming, as a coarse approximation: (a) that E g does not vary with T; (b) that
J ph is not modified by temperature; and noting (c) that J 00 = 1.5 × 10
8 mA/cm
2 is a
“true constant”, we can now derive V oc with respect to temperature T, and we obtain:
∂ V oc
∂ T
=
k
q
× ln
J ph
J 00
This can be evaluated numerically, for different values of the bandgap E g , in the
range between 1.1 and 1.8 eV, and we obtain:
∂ V oc
∂ T
≈ −15 × 10
−4 V/
◦ C
(3.16a)
Thereafter, we can divide by the corresponding value of V oc , rendering:
T C =
∂η
∂ T
/η ≈
∂ V oc
∂ T
/V oc ≈ −0.2%/
◦ C × (1 eV/E g ); E g in eV,
(3.16b)
Note that this relationship is only valid for temperatures around 25 °C.
The value of TC in (3.16b) is negative—this means that the solar cell efficiency
η will drop as we increase the operating temperature above 25 °C (STC).
Equation (3.16b) is just a very simple “rule of thumb”, which enables us to roughly
assess the order of magnitude for the temperature coefficient of the efficiency of solar
cells and modules.
Equation (3.16b) means also, that the higher the bandgap of the semiconductor
material is, the lower the magnitude of the relative temperature coefficient T C =
(∂η/∂T )/η will be. From a practical point of view, it is therefore advantageous to use
solar cell absorber materials with high bandgaps, if the actual operating temperature
of the solar cell is going to be high.
Table 3.3 gives the values of TC, based on (3.16b), for the most common solar
cells, listed according to the absorber material they employ.
2. Practical, experimental results
In practice, the values of TC are substantially higher (in magnitude) than those suggested by (3.16b). This will be developed now: Table 3.4 gives values found for
actual, commercial solar cells and modules: In this table, the lowest temperature
dependence is found for amorphous silicon modules (TC ≈ −0.2%/°C), and for
some CdTe modules (TC ≈ −0.25%/°C); and the strongest temperature dependence
for some CIGS
11 modules (TC ≈ −0.39%/°C) and for certain wafer-based crystalline
11 CIGS cells and modules have a large variety in the chemical composition of their absorption layer.
A. Shah
J 00 = J
Green
00
= 1.5 × 10
8 mA/cm
2
Assuming, as a coarse approximation: (a) that E g does not vary with T; (b) that
J ph is not modified by temperature; and noting (c) that J 00 = 1.5 × 10
8 mA/cm
2 is a
“true constant”, we can now derive V oc with respect to temperature T, and we obtain:
∂ V oc
∂ T
=
k
q
× ln
J ph
J 00
This can be evaluated numerically, for different values of the bandgap E g , in the
range between 1.1 and 1.8 eV, and we obtain:
∂ V oc
∂ T
≈ −15 × 10
−4 V/
◦ C
(3.16a)
Thereafter, we can divide by the corresponding value of V oc , rendering:
T C =
∂η
∂ T
/η ≈
∂ V oc
∂ T
/V oc ≈ −0.2%/
◦ C × (1 eV/E g ); E g in eV,
(3.16b)
Note that this relationship is only valid for temperatures around 25 °C.
The value of TC in (3.16b) is negative—this means that the solar cell efficiency
η will drop as we increase the operating temperature above 25 °C (STC).
Equation (3.16b) is just a very simple “rule of thumb”, which enables us to roughly
assess the order of magnitude for the temperature coefficient of the efficiency of solar
cells and modules.
Equation (3.16b) means also, that the higher the bandgap of the semiconductor
material is, the lower the magnitude of the relative temperature coefficient T C =
(∂η/∂T )/η will be. From a practical point of view, it is therefore advantageous to use
solar cell absorber materials with high bandgaps, if the actual operating temperature
of the solar cell is going to be high.
Table 3.3 gives the values of TC, based on (3.16b), for the most common solar
cells, listed according to the absorber material they employ.
2. Practical, experimental results
In practice, the values of TC are substantially higher (in magnitude) than those suggested by (3.16b). This will be developed now: Table 3.4 gives values found for
actual, commercial solar cells and modules: In this table, the lowest temperature
dependence is found for amorphous silicon modules (TC ≈ −0.2%/°C), and for
some CdTe modules (TC ≈ −0.25%/°C); and the strongest temperature dependence
for some CIGS
11 modules (TC ≈ −0.39%/°C) and for certain wafer-based crystalline
11 CIGS cells and modules have a large variety in the chemical composition of their absorption layer.