Spectral Utilisation I - External Quantum Efficiency

In this post and the next, we consider spectral utilisation.  For a single junction solar cell where the absorber layer has a certain band gap energy (see diagrams below), parts of the solar spectrum below the band gap energy will be ignored.  Here, the blue parts and some of the green parts are absorbed, blue being the most energetic photons.  The red part has energy below the band gap energy, so it is all left out.  In a J-V curve, the J_sc of this cell will be relatively small.

In another solar cell with a lower band gap energy (see diagrams below), the spectrum from blue to some of the red photons are absorbed.  Hence, in a J-V curve, the J_sc will be higher, while the V_oc is reduced.  This is because the separation of the quasi-Fermi levels is smaller.  The outcome of this is that V_oc and J_sc of semiconductor materials are determined by its band gap.

The external quantum efficiency is defined as the number of electrons collected at the contacts/terminals for each incoming photon at a certain wavelength.  This is a measure of the spectral utilisation of a solar cell.

Hence:
EQE(λ) = (J(λ)/q) / Φ(λ)

Due to optical and electrical losses for charge carriers, not every photon reaching the solar cell will lead to electron collection at the contacts/terminals.

The importance of EQE is because there are EQE measurement setups in labs to determine the number of electrons collected and number of photons per wavelength.  Moreover, measuring the J_sc using EQE setup will result in a current density independent of the spectral shape of the light source in use.  The EQE measurement setup using shading masks is also independent of the real contact area of solar cells.

As seen from the equations in the diagram below, the measured EQE and the spectral power density of the AM1.5 solar spectrum, will provide the J_sc of the solar cell.

Finally, it is important to note that for reporting J_sc of solar cells, it is not reliable to do a single J-V measurement.  Measurement using EQE setup is more reliable.

As seen in the diagram below, the EQE is 90% above the band gap, meaning that 10% of photons are lost.  The band gap energy in electron volts (eV) can be found from:

E = hc/λq = 1240/λ

where λ is 1100nm, which is the highest wavelength, in this graph, for photons that are absorbed.  Photons with wavelengths greater than this will not have enough photon energy to cross the band gap.

Reference:
3.3.2 Spectral Utilisation I - External Quantum Efficiency, Delft University of Technology, https://www.youtube.com/watch?v=tbOOuQFVwog