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.