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From my understanding, even if the frequency of a photon is above the threshold frequency, it is not necessary that an electron gets ejected as the photon may have been absorbed by a metal atom multiple layers below the surface, and thus the ejected electron could then get trapped by a metal atom above it.

However, if so then it appears that photoelectric current should have some dependence on the frequency (which it doesn't in my knowledge). This is because the higher KE imparted by the increased frequency would make the probability of electron getting trapped less than before, and thus higher frequency would mean more electrons than before get ejected which implies a greater saturation photocurrent.

So is it just that the fraction of electrons that get trapped instead of just having reduced KE is so low (why?) that it's negligible? Or are one of my assumptions wrong

  1. electrons can get trapped by metal atoms above it

  2. the mechanism by which they get trapped is such that higher KE won't even be a factor, irrespective of KE essentially all that were getting trapped before will still get trapped

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    $\begingroup$ In practice the photoelectric current does depend on the energy of the light somewhat (and not just a little) for the reasons you mentioned. We neglect that for sake of a simple theoretical model, but if you look at practical devices, then you will often find a plot of the quantum efficiency of the device (photomultiplier, photodiode) as a function of frequency. Engineers and experimental physicists can usually not neglect it. $\endgroup$
    – FlatterMann
    Commented Sep 25, 2022 at 4:13
  • $\begingroup$ @FlatterMann thank you, also I forgot to specify but I was talking about saturation photocurrent only, since I already know that when voltage is lower all electrons won't reach anyway due to other factors (?). So to be sure was your answer written with saturation current in mind? $\endgroup$
    – Amadeus
    Commented Sep 25, 2022 at 7:17
  • $\begingroup$ Does this answer your question? Why doesn't photoelectric current increase with frequency of the incident wave? $\endgroup$
    – Farcher
    Commented Sep 25, 2022 at 8:08
  • $\begingroup$ @Farcher no, this is addressing a different confusion only the subject is the same (that too not exactly since I'm specifically talking about saturation current) $\endgroup$
    – Amadeus
    Commented Sep 25, 2022 at 8:40
  • $\begingroup$ @Amadeus The frequency dependence of the quantum efficiency exists in all regimes. It doesn't matter whether a photoelectric device or a photodiode is properly saturated. Photodiodes (which are much easier to come by than photomultipliers) are typically insensitive to blue and UV radiation because the light does not penetrate the semiconductor deep enough. Even technically used photocathodes in PMTs are typically only sensitive over a 2:1 to 5:1 frequency range. $\endgroup$
    – FlatterMann
    Commented Sep 25, 2022 at 9:26

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