Custom spectra

Custom spectrum 1			Custom spectrum 2
CSV US/UK (comma delimited) CSV Euro (semicolon delimited)			CSV US/UK (comma delimited) CSV Euro (semicolon delimited)
Wavelength	Spectral intensity		Wavelength	Spectral intensity
Å nm µm mm cm m	W m-2 nm-1		Å nm µm mm cm m	W m-2 nm-1

Custom EQE

Custom EQE
CSV US/UK (comma delimited) CSV Euro (semicolon delimited)
Wavelength	EQE
Å nm µm mm cm m	fraction percentage

Spectral mismatch arises when measuring the current–voltage (IV) curve of a solar cell. Here we describe the origin of spectral mismatch and a procedure to quantify the error it introduces.

IV measurements

The purpose of an IV measurement is to predict how a solar cell would behave if illuminated by a standard solar spectrum—usually the AM1.5g spectrum. This spectrum represents sunlight on a clear day when the sun is high in the sky. By determining a solar cell’s IV behaviour under this standard spectrum, it is possible to its output power when installed in the field.

IV measurements are typically conducted indoors. Being indoors, the measurements aren’t affected by weather conditions or the time of day, and the intensity and spectrum of the illumination can be held constant. The source of the illumination is typically a xenon arc lamp or high-powered LEDs. It is preferable, therefore, for the spectrum emitted by these sources to be identical to the AM1.5g spectrum. In practice, however, light sources cannot exactly match the AM1.5g spectrum and this causes spectral mismatch, as will be described.

Calibrating an IV tester

Before an IV measurement, it is first necessary to ‘calibrate’ the intensity of the illumination. The purpose of this calibration is to set the tester’s illumination intensity such that it approximates the intensity of the AM1.5g spectrum. This is performed by measuring a solar cell with a known current (J_sc) under the AM1.5g spectrum, and by varying the intensity of the lamps until the measured J_sc equals the known J_sc.

At this point, the IV tester is said to be calibrated.

Measuring solar cells with a calibrated IV tester

Following the calibration, the IV tester is used to measure the IV curves of other solar cells under what is, ostensibly at least, a standard test condition.

The accuracy of this measurement will depend on (i) how closely the test spectrum matches the AM1.5g spectrum, and (ii) how closely the external quantum efficiency (EQE) of the calibration cell matches the EQE of the measured cells. (The EQE quantifies how a solar cell’s current depends on the wavelength of the incident light.)

When the IV measurement is inaccurate, the term ‘spectral mismatch’ is used to refer to the error introduced by the test spectrum being different to the standard spectrum.

How to quantify spectral mismatch—an example

1. Set Spectrum A to be the AM1.5g spectrum. This is the standard reference spectrum for measuring non-concentrating terrestrial solar cells and panels.
2. Set Spectrum B to be a xenon-arc lamp. This is the most common type of illumination source used in IV testers.
3. Select an EQE for the calibration cell. E.g., choose a PERL c-Si solar cell, which has a very high and broad EQE for a silicon solar cell.
4. Adjust the scaling factor of Spectrum B until J_scB equals J_scA. At this point, the intensity of the IV test lamp has effectively been calibrated to have an intensity that represents the AM1.5g spectrum for a measurement of the PERL c-Si cell. That is, the calibration cell’s current density under the IV tester is the same as it would be under the AM1.5g spectrum.
5. Now select a different EQE to represent the testing of a different type of cell. This is equivalent to measuring a solar cell on an IV tester that has been calibrated for the PERL cell.
6. Compare J_scB to J_scA. If there is a difference between the two values, it indicates that spectral mismatch would affect the IV measurement.
7. The relative error introduced into the measured short-circuit current density due to spectral mismatch is given by (J_scB – J_scA)/J_scA.

Three cases to consider

1. The test spectrum is almost the same as the AM1.5g spectrum. In this case, J_scB will be similar to J_scA, irrespective of any differences between the EQE of the cell and the reference cell. Thus, there is a significant advantage to using a well-tailored illumination source.
2. The test spectrum is different to the AM1.5g spectrum BUT the EQEs of the calibration cell and the measured cell are almost the same. In this case, there will be very little difference between J_scA and J_scB. Thus, there is a significant advantage to selecting a calibration cell with a similar EQE to the measured cell.
3. The test spectrum is different to the AM1.5g spectrum AND the EQE of the calibration cell is different to the EQE of the measured cell. In this case, the difference between J_scA and J_scB is likely to be significant. If so, the measurement error due to spectral mismatch is significant.

Learn more about spectral mismatch at PVeducation.org.

This calculator determines the short-circuit current density of a solar cell under two separate spectra. It can be used to quantify the 'spectral mismatch' between a solar cell illuminated by sunlight and by an IV tester.

The calculator can also be used to evaluate the spectrum generated by a combination of LEDs, lasers and xenon-arc lamps.

The outputs of the spectral mismatch calculator are determined by the following procedure:

1. The spectral intensity S(λ) of the user-selected spectra are loaded from the spectrum library. The units of spectral intensity are W/m²/nm.
2. The intensity of each spectrum is calculated in two ways:
   1. The total intensity I_total is calculated by integrating the spectral intensity over the entire wavelength range available in the spectrum library.
   2. The bounded intensity I_bounded is calculated by integrating the spectral intensity over the wavelength range defined by the minimum λ_min and maximum λ_max wavelengths set by the user under ‘Options’.
3. Each spectrum is adjusted such that its range is bounded by λ_min and λ_max, and such that the interval between every wavelength is constant and equal to Δλ, where Δλ is set by the user under ‘Options’.
4. Each spectrum is scaled by multiplying its spectral intensity S(λ) by one of the following factors (as selected by the user):
   • Unscaled: 1.
   • Scaling factor: the user-defined scaling factor.
   • Total intensity: the user-defined intensity divided by I_total.
   • Bounded intensity: the user-defined intensity divided by I_bounded.
5. Spectrum A is determined by summing the spectral intensity of its constituent spectra; Spectrum B is determined by summing the spectral intensity of its constituent spectra.
6. The EQE is loaded from the EQE database. The EQE is modified in the same way as the spectra such that it is defined by the user inputs λ_min, λ_max and Δλ.
7. Finally, the outputs for Spectrum A and Spectrum B are calculated by the following equations:
   • Intensity:
   • Photon current density:
   • Short-circuit current density
   where Φ(λ) is the photon flux and equal to S(λ)/E(λ), where E(λ) is the photon energy and equal to h∙c/λ, and where h is Planck’s constant and c is the speed of light.

We thank Aescusoft GmbH for contributing spectral data for LEDs and Xe lamps, and for their feedback in the calculator design.

Neither PV Lighthouse nor any person related to the compilation of this calculator make any warranty, expressed or implied, or assume any legal liability or responsibility for the accuracy, completeness or usefulness of any information disclosed or rendered by this calculator.

Please email corrections, comments or suggestions to support@pvlighthouse.com.au.