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I know from solar cell physics, that in a first approximation, the maximum energy from an exited electron is the energy of the bandgap, no matter how high the electron was excited by a photon in the first place. The rest of the excitation energy is given back from the electron via thermal relaxation.

So for example, if a photon with 3eV excites an electron from the valence band to the conduction band (bandgap 2eV), then the electron will relax thermally by 1eV and only 2eV can be used for generating the voltage.

But why is this?
Why is one not able to get the full excitation energy from an electron?

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  • $\begingroup$ What excites the electron? The question is not so clear. What is the context? You ask which energy is usable in a photovoltaic cell? $\endgroup$
    – lcv
    Commented Mar 15, 2020 at 21:01
  • $\begingroup$ an incoming photon with hf > Eg $\endgroup$
    – Pixel_95
    Commented Mar 15, 2020 at 21:12
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    $\begingroup$ It is a question of time scales. In, say, GaAs, a direct gap semiconductor to speed recombination, the thermal relaxation time of energetic electrons is in the picosecond range, while e-h recombination is nanoseconds. $\endgroup$
    – Jon Custer
    Commented Mar 15, 2020 at 21:44

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This is generally true in most cases, the electron would thermally de-excite to the bottom of the valence band in a time scale and length scale characteristic of the material, and is called the carrier drift regime. However, if the device length is shorter than the mean free path for collisions, the energy recovered is greater than the bandgap energy (Ballistic transport). The same applies if the electrons are extracted out of the system in a time shorter than the average scattering time (Hot Carrier Transport).

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  • $\begingroup$ ok, so basically the length scale from the excited elctron to the extraction point is much longer than the mean free path. hence, the elcetron scatters multiple times before it can be exctracted via the front and back contact. or in short: there are three time scales: $t_{relax}$ -> time it takes an electron to relax to the conduction band edge $t_{ex}$ -> time it takes an electron to be extracted from the device $t_{radRec}$ -> time, it takes an electron to recombine and go to the valence band and now: $t_{relax}$ << $t_{ex}$ << $t_{radRec}$. is that correct? $\endgroup$
    – Pixel_95
    Commented Mar 16, 2020 at 8:48
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    $\begingroup$ Yes, in the carrier drift regime, this would be true. $\endgroup$
    – Hari
    Commented Mar 16, 2020 at 8:52
  • $\begingroup$ ok nice! thank you a lot. and what exactly needs to be fulfilled to be in the crrier drift regime? $\endgroup$
    – Pixel_95
    Commented Mar 16, 2020 at 8:56
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    $\begingroup$ In the carrier drift regime, the excited electrons have enough time and length of material to scatter and relax to the bottom of the band. The scattering mechanisms could be of different types, lattice vibrations(phonons), impurities in the crystal, etc $\endgroup$
    – Hari
    Commented Mar 16, 2020 at 22:48

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