# Spectral Mismatch Corrections

Measuring solar cell performance consistently

everywhere in the world requires an indoor solar simulator. For most measurements, the solar spectrum

is standardized as air mass 1.5 global, or AM

1.5G, which represents the average solar spectrum in temperate climates. Solar simulators use various lamps to mimic

this AM 1.5G solar spectrum. However,

these lamps generally do not exactly match the AM 1.5G solar spectrum at all

wavelengths which is known as spectral mismatch. Corrections can be made using the spectral

mismatch factor M. This captures the difference in intensity between the AM 1.5G

solar spectrum and the lamp spectrum used for solar simulation. In the graph shown, the wavelength versus

an intensity of two common solar simulator lamps is compared to the AM 1.5G spectrum. It is clear that they are spectral mismatch

shown by varying light intensities at the given wavelengths when compared to AM 1.5G. Spectral mismatch calculations allow us to

standardize solar simulator measurements across labs and on different days. Using a reference cell with the spectral or

spot similar to a test cell will make it easier to account

for the spectral mismatch. Now we can calculate spectral mismatch with

an example. Let us assume that we have a

silicon reference cell for calibration. We are testing a cell with a larger band gap. We can

calculate the spectral mismatch with four terms. First, we measure the external quantum efficiency

(EQE) and spectral response. We

multiply the latter with the AM 1.5G solar spectrum to calculate short circuit current. This goes into the numerator of M. Second, we measure the short circuit current

of the test cell under the lamp spectrum. This factor is multiplied with the first short

circuit current to calculate M. Third, we measure the EQE of the test cell

and multiply the AM 1.5G solar spectrum to calculate its short circuit current. This goes into the denominator of M. Fourth, we measure the short circuit current

of the reference cell under the lamp spectrum. We divide M by this value. The net result is a spectral mismatch term

M that accounts for differences between both the lamp and reference spectra, plus the differences

between test and reference cells. We can thus divide the measured test cell

current by M for more precise comparisons with the literature. You need two cells and four data sets to measure

spectral mismatch M. The cells needed are your reference and test cells. The first data set you’ll need is the air

mass 1.5 global (AM 1.5G) reference spectrum, which is available

on NREL’s website. Second, you’ll need your light source spectrum

which can be measured by you or the manufacturer. Make sure you have the correct units for radians. They much match the

reference spectrum. Finally, you’ll need to know the quantum efficiency

(QE) of the reference cell as well as the QE of your test cell. Now you can get started. We begin by measuring the external quantum

efficiency (EQE) of the reference cell. Using this equation. [Equation on video.] Once you know the spectral response of the

cell multiplied by the AM 1.5G spectrum and a factor proportional to the wavelength to

attain the JSC under one-sun. You can multiply

by the area of the cell to calculate ISC. We will use this value later. Next step is to measure the external quantum

efficiency of your test cell. Then, you can

calculate the SR, JSC, and ISC. We’ll use this value later. Next, measure the short circuit current of

the reference cell with the light source you have. If it doesn’t match with the ISC obtained

in Step 1, adjust the intensity of your source. You can do this by adjusting the distance

between the source and the sample. Now we can measure the short circuit current

of the test cell using the light source you have. Then, we calculate the spectral mismatch factor

M by plugging in the values from the previous step as shown in the equation

here. [Equation on video.] Ideally, M should be as close to unity as

possible. Once you calculate your spectral

mismatch factor M, you can set the one-sun intensity with your reference cell. Then

obtain your JV curve. After you’re done measuring the JV curve of

your test cell, you can apply the spectral mismatch factor by dividing all current values

by M.