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A. Shah
3.5 Solar Cell Efficiency Limits
3.5.1 Limits at STC (Standard Test Conditions)
To calculate the overall energy conversion efficiency η of the solar cell, we must now
divide the electrical output power P out (at MPP) by the input (solar) power P in =
P sun . One has:
P out = V m × J m × A = J sc × V oc × F F × A
(3.14)
Here J sc , V oc and FF have been determined above, and A is the surface area of the
solar cell. On the other hand, P in = P sun is the “power of the sun”, i.e. the total energy
within the solar spectrum per unit of time, for a unit surface. P sun was already used
to calculate the spectral conversion efficiency η S (3.1).
Using this formula for η S we can now write:
η = η S × (J sc × V oc × F F)/
φ E g
(3.15)
The relationship between J sc and E g is given in Fig. 3.16 for AM 1.5 illumination.
Thereby one assumes that the solar cell absorbs all incoming light with wavelengths
shorter than the absorption edge of the semiconductor, and that collection within the
solar cell is ideal.
From (3.11), (3.13) and (3.14) and from Fig. 3.16 one can now compute, numerically, the semi-empirical limit efficiency for single-junction solar cells. The result
is represented in Fig. 3.19, as a function of semiconductor bandgap energy. Furthermore, Fig. 3.19 also gives the fundamental limit, based on the work of Shockley and
Queisser (as tabulated in [21]). The curves in Fig. 3.19, as well as the practically
obtained solar cell values (dots), are valid for so-called Standard Test Conditions,
i.e. for:
• Illumination level corresponding to AM 1.5
• Illumination spectrum corresponding to AM 1.5
• Solar cell temperature 25 °C.
3.5.2 Variation of Efficiency η in Function of Temperature
In practice, solar cells are rarely operated at a temperature T = 25 °C (STC)—they
are in most cases operated at higher temperatures T > 25 °C. This leads to a drop
in their efficiency η. Therefore, we are going to derive an approximate relationship
between solar cell efficiency η and solar cell operating temperature T.
Now: η is proportional to the product (J sc × V oc × FF), as given in (3.15).
However, one may state:
A. Shah
3.5 Solar Cell Efficiency Limits
3.5.1 Limits at STC (Standard Test Conditions)
To calculate the overall energy conversion efficiency η of the solar cell, we must now
divide the electrical output power P out (at MPP) by the input (solar) power P in =
P sun . One has:
P out = V m × J m × A = J sc × V oc × F F × A
(3.14)
Here J sc , V oc and FF have been determined above, and A is the surface area of the
solar cell. On the other hand, P in = P sun is the “power of the sun”, i.e. the total energy
within the solar spectrum per unit of time, for a unit surface. P sun was already used
to calculate the spectral conversion efficiency η S (3.1).
Using this formula for η S we can now write:
η = η S × (J sc × V oc × F F)/
φ E g
(3.15)
The relationship between J sc and E g is given in Fig. 3.16 for AM 1.5 illumination.
Thereby one assumes that the solar cell absorbs all incoming light with wavelengths
shorter than the absorption edge of the semiconductor, and that collection within the
solar cell is ideal.
From (3.11), (3.13) and (3.14) and from Fig. 3.16 one can now compute, numerically, the semi-empirical limit efficiency for single-junction solar cells. The result
is represented in Fig. 3.19, as a function of semiconductor bandgap energy. Furthermore, Fig. 3.19 also gives the fundamental limit, based on the work of Shockley and
Queisser (as tabulated in [21]). The curves in Fig. 3.19, as well as the practically
obtained solar cell values (dots), are valid for so-called Standard Test Conditions,
i.e. for:
• Illumination level corresponding to AM 1.5
• Illumination spectrum corresponding to AM 1.5
• Solar cell temperature 25 °C.
3.5.2 Variation of Efficiency η in Function of Temperature
In practice, solar cells are rarely operated at a temperature T = 25 °C (STC)—they
are in most cases operated at higher temperatures T > 25 °C. This leads to a drop
in their efficiency η. Therefore, we are going to derive an approximate relationship
between solar cell efficiency η and solar cell operating temperature T.
Now: η is proportional to the product (J sc × V oc × FF), as given in (3.15).
However, one may state: