What is the relation between the short-circuit current and the band gap energy in solar cells?

Question

For the VOC it is:

VOC = E_g - something,

where something is positive and depends on the Urbach energy. Otherwise it should be linear: https://aip.scitation.org/doi/pdf/10.1063/1.49397

For the ISC I didn't find anything. Only one paper on bifacial solar cells, where there Equation (4) gives a formula, but I am not sure if this is helpful for the "general" case (I am writing about CIGS solar cells right now, and a general Theory part, not specifically about CIGS): https://www.researchgate.net/publication/327345077_Thermodynamic_Efficiency_Limit_of_Bifacial_Solar_Cells_for_Various_Spectral_Albedos/figures?lo=1&utm_source=google&utm_medium=organic

Can someone elaborate, please?

Answer 1

Short circuit current depends on the spectrum $S$ and the external quantum efficiency $EQE$ of the solar cell,

$$ I_{ISC} = q \int_{E_1}^{E_2} S(E) EQE(E) dE $$

The number of photons usefully absorbed per second is equal to the short circuit current.

Can you get the Physics of Solar Cells by Jenny Nelson from a library? This is a great book for introducing a physics student to solar cells.