Solar Simulator Irradiance and Spectral Mismatch
Solar simulators generally attempt to replicate the standard AM1.5G spectrum which has a total integrated irradiance of 1000.4 W/m^{2} over the wavelength range of 280 nm – 4000 nm. Solar simulators will not normally cover the entirety of this wavelength range — especially LED-based solar simulators where wavelengths beyond 1000 nm become increasingly difficult to generate. This causes something of an issue for calibrating the output of solar simulators; should they produce the full 1000.4 W/m^{2} of the solar spectrum, or match the irradiance over the spectral range at which they emit?
For example, the wavelength range of 380 nm – 1000 nm contains approximately 70% of the total AM1.5G irradiance. Does this mean a solar simulator which only outputs light within this wavelength range provide an irradiance of 700 W/m^{2}? Or should it provide 1000 W/m^{2} which would result in a higher visible light irradiance than the standard spectrum?
There are no guidelines on total irradiance given in the standards used to classify solar simulators, and it is not always clear which methodology is being followed. Solar simulator output power is often given in the units of ‘Suns’ where 1 Sun is assumed to be the calibrated output to the AM1.5G spectrum, but it still is not clear whether that is the total irradiance or the irradiance over a truncated wavelength range over which the solar simulator operates.
The situation is complicated further when considering solar cells of different technologies that absorb different wavelength ranges. Cadmium telluride-based cells are only sensitive to light between 400 nm – 800 nm, so compensating for the lack of light above 1000 nm by increasing the amount in the visible would increase the amount of power available to the cells and make them appear more efficient than they are in reality. Silicon solar cells are sensitive to wavelengths beyond 1000 nm, so having no irradiance beyond 1000 nm yet not compensating elsewhere would make them appear less efficient. The efficiency of solar cells is also wavelength dependent (known spectral response), so at which wavelengths you compensate for the missing irradiance effects the apparent efficiency. For this reason, despite strict standards about the classification of solar simulators, efficiency measurements of the same cell on different systems can appear quite different.
This issue essentially comes down to the fact that:
- Not all solar simulators provide the same spectral irradiance.
- Not all solar cells have the same wavelength response.
These conclusions make it difficult to compare efficiency measurements between different PV technologies, or even the same PV technology but measured with different solar simulators.
Spectral Mismatch Factor
A spectral mismatch parameter, M, can be introduced, which can quantify and correct for these differences [1,2]. We need to consider the responses of a ‘reference cell’ under both a ‘reference spectrum’ (e.g., AM1.5G) and our solar simulator spectrum, and the responses of a ‘test cell’ under these same two irradiance conditions.
The short-circuit current, I, produced by a solar cell of area D under irradiance is equal to the integral of spectral irradiance, E(λ) (units of W/m^{2}) multiplied by the spectral response, R(λ) (units of A/W), over the wavelength range (λ_{1} → λ_{2}) that the cell is sensitive to, i.e.
From this, we can assign four different short-circuit currents:
- The short circuit current produced by a reference cell under reference irradiance (we’ll use AM1.5G as an example), .
- The short circuit current produced by a reference cell under a solar simulator, .
- The short circuit current produced by a test cell under reference irradiance, .
- The short circuit current produced by a test cell under a solar simulator, .
The spectral mismatch parameter relates the short-circuit currents measured under the solar simulator to those measured under reference irradiance i.e.
Note that the cell area terms cancel, so there is no requirement for the test and reference cells to be of the same size, so long as the solar simulator can provide uniform illumination of both cells.
Combining (1) and (3), we find
From (4), we see that if E_{sim}(λ) = E_{AM1.5G}(λ), i.e., the spectral irradiance of solar simulator matches the AM1.5G irradiance, M=1. The same is true if R^{test}(λ) = R^{ref}(λ) i.e., the spectral response of the reference and test cells are the same. In either scenario, equation (2) gives
Using the reference cell, the irradiance of the solar simulator can be adjusted so that i.e., the short-circuit current of the reference cell under the solar simulator matches the short-circuit current of the reference cell under AM1.5G illumination. Then, (the measurement of the test cell under the solar simulator is the same as if it would be under AM1.5G irradiance) and an accurate measurement can be taken. This method is useful when the solar simulator exactly matches the AM1.5G spectrum (unlikely) or the test cell is of the same technology and is known to have the same spectral response as the reference cell (quite possible).
It is likely that neither of the above requirements are satisfied and the solar simulator does not exactly match the AM1.5G irradiance and the test cell spectral response is either different to the reference cell or is unknown. Then, equation (4) should be used to calculate M. This requires that the spectral responsivity of both the reference and test cells are known, as well as the spectral irradiance of both sources. While these need to be measured, the form of equation (4) makes measurement a little simpler as relative rather absolute measurements can be used. We can make the substitutions:
- E_{sim}(λ) = ε_{sim}e_{sim}(λ) where e_{sim}(λ) is the relative solar simulator irradiance and ε_{sim} is an unknown proportionality constant.
- E_{5G}(λ) = ε_{AM1.5G} e_{AM1.5G}(λ) where e_{AM1.5G}(λ) is the relative reference irradiance and ε_{AM1.5G} is an unknown proportionality constant.
- R^{test}(λ) = ρ^{test}r^{test}(λ) where r^{test}(λ) is the relative spectral response of the test cell and ρ^{test} is an unknown proportionality constant.
- R^{ref}(λ) = ρ^{ref}r^{ref}(λ) where r^{ref}(λ) is the relative spectral response of the test cell and ρ^{ref} is an unknown proportionality constant.
Substituting these into equation (4) we find:
All of the proportionality constants cancel, leaving
Hence, only relative measurements are required to determine M, negating the need for radiometrically calibrated instrumentation.
The quantity that we want to know is the short-circuit current of the test cell as it would be under AM1.5G illumination. We can rearrange equation (3) to give
If we set the irradiance of the solar simulator using the reference cell such that
where M was calculated using equation (6), we see that
and the measured short-circuit current of the test cell under the solar simulator is equal to what it would be under AM1.5G irradiance. This is valid for all currents, not just the short-circuit current, so any I-V measurements and resulting device metrics are now corrected for the spectral mismatch.
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References
- [1] Errors in short circuit current measurements due to spectral mismatch between sunlight and solar simulators, H.B. Curtis, National Aeronautics and Space Administration, ERDA/NASA-1022/76/3, 1976
- [2] The correction for spectral mismatch effects on the calibration of a cell when using a solar simulator, C.H. Seaman, Jet Propulsion Laboratory, JPL Pub. 81-1, 1981
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