While there seems to be plenty of information available about the photoelectric effect and the emission and absorption of photons by conductors (metals) at optical frequencies, I’ve been searching for some time for near layman level descriptions of the details of how low energy photons (i.e. radio frequency) photons are absorbed or emitted by the conduction band electron plasma of a conductor. Does anyone have any good references?

  • $\begingroup$ Your answer lies in the Drude description of a conductor. Search “Drude model”. Any intro solid-state physics text will do. $\endgroup$ – Gilbert Sep 30 at 2:20
  • $\begingroup$ Yes, I had found the Drude theory, but it treats the conduction band elections as a whole, influenced by the electric field of an incident EM wave. I was looking for some description of how incident EM photons with very low energy interact with electrons in the conduction band. $\endgroup$ – techn0mad Sep 30 at 8:00

If a single photon is absorbed in a metal, it promotes an electron from a filled state below the Fermi energy to an empty one above. Photons with infrared or RF frequencies will have too little energy to induce an interband transition, so the transition will be intraband. That is, the photons promote an electron in the conduction band from slightly below the Fermi energy to slightly above in the same band.

Typically, intraband transitions are forbidden for light absorption since they do not conserve energy and momentum. Photons have a large energy and a small momentum, so photon absorption is usually depicted as a “vertical” transition in the material band structure. An intraband transition, on the other hand, is essentially “diagonal”, requiring similar amounts of energy and momentum.

The key here is that in a metal, there are many scattering events (parameterized phenomenologically by the Drude scattering time). This reduces the lifetime of the state and introduces uncertainty in the position of the electron. By the quantum uncertainty principles, the scattering thus relaxes the momentum and energy conservation requirements, allowing “diagonal” transitions.

You can think of this as an indirect transition: That is, when a photon is absorbed, the photon provides the energy, and a scattering partner (e.g. a phonon or impurity) provides the momentum. The likelihood of this occurring is given by the Drude conductivity.

  • $\begingroup$ That’s the sort of detail I was in search of. Can you share any references or citations on this? Thank you! $\endgroup$ – techn0mad Oct 2 at 18:51

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