I am trying to find a formula that defines the general shape of the responsivity vs. wavelength curve for semiconductors such as silicon, Ge, GaAs. (See attached picture for examples of responsivity curves). I would like to find a relationship for responsivity based on existing data for the semiconductor, e.g. band diagram, absorption coefficient, refractive index etc...

I am actually more interested in the generation rate of electron-hole pairs in bulk semiconductors which is a more fundamental concept. After going through multiple well known text books the basics of this process is still unclear. The fundamental questions are:

1. Why is the generation rate of semiconductors which have a sharp increase in absorption coefficient (e.g. direct bandgap semiconductors) show a narrow peak in Generation Rate vs. Wavelength, while those with a slow increase of absorption coefficient (e.g. indirect bandgap) show wider bandwidth in generation rate. Is this due to combined effects of the decreasing photon count vs. wavelength and surface recombination? or is there more to it?

2. Why does the quantum efficiency curve deviate from the generation rate curve. For example for silicon the quantum efficiency is nearly 1 right down to the blue (450nm) but the generation rate (or responsivity) drops rapidly after 600nm.

3. What happens when a photon with eV higher than the bandgap gets absorbed into say a direct bandgap material? Does the electron which is generated simply go to a higher energy level. Surely there is a density of states factor coming into this. Would the electron have a higher probability of being re-emitted than an electron closer to the bandgap? (Any text books that might explain this?)

Even though responsivity is based on measurements of DC current flow which involve factors more than the generation rate i think that generation rate is the dominant mechanism (I could be wrong).

I actually have a method for measuring the generation rate of E-H pairs directly using microwave spectrum analysis which is contact free. However this shows a similar shape to the responsivity curves. The only mechanism that should be limiting this measurement is the carrier generation. The carriers are generated and just remain there while being measured.  So the only limiting factors should be the bulk and surface recombination and of course the decreasing photon count with wavelength. However if that were the case then this still doesn't explain the deviation of the silicon generation rate at 600nm.

Any references to text books that would explain these effects in detail would be most appreciated. All books I have come across seem to avoid explaining these details.