Solar Cells: Basics
2. Open-circuit voltage V oc
3.5 Solar Cell Efficiency Limits
3.5.2 Variation of Efficiency η in Function of Temperature
In practice, solar cells are rarely operated at a temperatureT =25 °C (STC)—they are in most cases operated at higher temperaturesT > 25 °C. This leads to a drop in their efficiencyη. Therefore, we are going to derive an approximate relationship between solar cell efficiencyηand solar cell operating temperatureT.
Now: η is proportional to the product (Jsc ×Voc × FF), as given in (3.15).
However, one may state:
3 Solar Cells: Basics 59
Semi-empirical limit (Green)
S-Q limit
Fig. 3.19 Maximum value of the overall (The conversion efficiency for thefirststep of energy conversion was given in Sect.3.2.4, Fig.3.7.) energy conversion efficiencyηof the solar cell as a function of the band gapEg. 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 ofJschardly varies with temperature
• The maximum (limit) value ofFFvaries very little with temperature
• The maximum (limit) value ofVocvaries strongly with temperature.
Therefore, we will, in this section, only look at the variation ofVoc with tem-perature, and in a rather rough approximation, assume that the variation ofηwith temperature is similar.
We are here interested in therelativetemperature coefficient T C = ∂η
∂T/η≈∂Voc
∂T /Voc
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 Voc to mathematical expressions which are cumbersome;
therefore, we will use here for Voc the semi-empirical limit of Martin Green, i.e.
(3.11):
Voc≈ kT q ln
Jph
J00
+ Eg
q with
60 A. Shah J00= J00Green=1.5×108mA/cm2
Assuming, as a coarse approximation: (a) thatEg does not vary withT; (b) that Jphis not modified by temperature; and noting (c) thatJ00=1.5×108mA/cm2is a
“true constant”, we can now deriveVocwith respect to temperatureT, and we obtain:
∂Voc
This can be evaluated numerically, for different values of the bandgapEg, in the range between 1.1 and 1.8 eV, and we obtain:
∂Voc
∂T ≈ −15×10−4V/◦C (3.16a) Thereafter, we can divide by the corresponding value ofVoc, rendering:
T C= ∂η
∂T/η≈ ∂Voc
∂T /Voc≈ −0.2%/◦C×(1 eV/Eg); Egin eV, (3.16b) Note that this relationship is only valid for temperatures around 25 °C.
The value ofTC in (3.16b) is negative—this means that the solar cell efficiency ηwill 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 coefficientT C = (∂η/∂T)/ηwill 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.
Table3.3gives the values ofTC, 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 ofTCare substantially higher (in magnitude) than those sug-gested by (3.16b). This will be developed now: Table 3.4gives 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 CIGS11modules (TC≈ −0.39%/°C) and for certain wafer-based crystalline
11CIGS cells and modules have a large variety in the chemical composition of their absorption layer.
3 Solar Cells: Basics 61 Table 3.3 Comparison of the
“theoretical” limit values of the relative temperature coefficientT C=(∂η/∂T)/η for different solar cell types:
CIGS, a-Si, CdTe, and c-Si
BandgapEg [eV] “Theoretical”
value ofTC (3.16b) [%/°C]
CIGS 1.2 ≈ −0.17
Wafer-based crystalline silicon (c-Si)
1.12 ≈ −0.18
Amorphous silicon (a-Si)
1.75 ≈ −0.11
CdTe 1.49 ≈ −0.13
Table 3.4 Comparison of the relative temperature coefficientT C = (∂η/∂T)/η for different solar cell/module types: homojunction c-Si, heterojunction c-Si, a-Si, micromorph, CdTe, and CIGS (based on data and references in [4] for a-Si and micromorph; and on datasheets for all other values)
Type of solar cell/module Range of temperature coefficient T C=(∂η/∂T)/η
Crystalline silicon homojunctions (c-Si) ≈ −0.29%/°C (TOPCON, PERC) to− 0.38%/°C (Al-BSF) (see Chap.5) Crystalline silicon heterojunctions (c-Si/HJT) ≈ −0.3%/°C (see Chap.7) Amorphous silicon (a-Si) ≈ −0.2%/°C (see Chap.6)
Micromorph tandems (µc-Si/a-Si) ≈ −0.3%/°C to−0.35%/°C (see Chap.6)
CdTe ≈ −0.25%/°C to−0.32%/°C (see Chap.8)
CIGS ≈ −0.32%/°C to−0.39%/°C (see Chap.8)
silicon modules (TC ≈ −0.38%/°C); c-Si heterojunction modules [22], as well as some recently developed homojunction c-Si modules are interesting module imple-mentations: they have high efficiencies and relatively low temperature dependence (TC≈ −0.3%/°C).
This situation is illustrated in Fig.3.20.
62 A. Shah
Fig. 3.20 Effect of operating temperatureT on the normalized value of the output powerPmax, at MPP, of typical solar modules, for various cell technologies, based on [23] for CIGS, CdTe and a-Si; and on datasheets for c-Si modules
Thecase of c-Si (wafer-based crystalline silicon)merits, for two reasons, par-ticular attention: (1) these cells account for more than 90% of all cells produced worldwide; (2) they have a large span of practical values ofTC; in datasheets of c-Si cells, we find values running from−0.29 up to−0.38%/°C.
When one looks at the whole picture, which results from studying datasheets and published experimental data, one finds that there is a remarkable relationship between the value ofVocand the magnitude ofTC.
AsVocapproaches its “theoretical” limit value of approximately 800 mV (see Fig.3.17, line 2, green), the magnitude ofTC becomes smaller; thereby,TCtends to approach its “theoretical” limit value of≈ −0.18%/°C.12
Conversely, cells with low values ofVoc, have high magnitudes ofTC, i.e. a strong temperature dependence.
This relationship would fully explain why crystalline silicon heterojunction modules have a remarkably low magnitude ofTC.
Tijmen Slikker of Eternalsun Spire has recently done a series of measurements on different c-Si modules and their temperature behaviour—his results are presented here as Fig.3.21a, b.
3. Concluding remarks
• The relative temperature coefficientTCis a parameter, which is given in the Datasheet of the Module. It varies strongly:
– Between modules using different absorber materials, i.e. the magnitude of TCis much larger for c-Si modules than for CdTe modules.
12We are referring here not to the thermodynamical limit values according to Shockley and Queisser [18], but to the semi-empirical limit values according to Green [12].
3 Solar Cells: Basics 63
Limit value according to Equation (3.16a)
a
b
Fig. 3.21 aRepresentation of the relationship between the value ofVocand the “absolute” temper-ature coefficient∂∂VToc(Courtesy of Eternalsun Spire).bRepresentation of the relationship between the value ofVocand therelativetemperature coefficientTC(Courtesy of Eternalsun Spire)
64 A. Shah – For a given absorber material, e.g. for c-Si, between different module designs and different module implementations. Here, one notices an inter-esting relationship between the value of Voc and the magnitude ofTC:
Modules that have—due to high recombination—low values ofVochave, in general, also a strong temperature dependence, i.e. a high magnitude of TC.13
• The relative temperature coefficientTC is a parameter, which is difficult to determine, both theoretically (many factors not mentioned here play a role) and experimentally (costly equipment is needed for performing laboratory measurements). Therefore, only field tests will reveal the “full truth”.
• The relative temperature coefficientTCis an extremely important parameter for the application of solar modules on rooftops and in tropical countries.
In these cases, the operating temperature of the solar module easily reaches 75 °C, i.e. 50 °C more than under STC conditions. The conversion efficiency of the solar module will thereby be reduced, with respect to the STC value given in the datasheet: for amorphous silicon modules, the efficiency reduc-tion will be around 10%, for CdTe modules it will be between 12 and 15%, for heterojunction c-Si modules and for other recent c-Si modules (such as TOP-CON modules) it will be around 15%, whereas for some other wafer-based crystalline silicon (c-Si) modules, it can be up to approximately 20%.