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I mean do they always generate photons or is there any recombination where the output is purely phonons or there is no emission at all(In Auger recombination the energy is transferred to another carrier before returning to initial state; so will it produce any photons ??).

Also is it mandatory that the carrier should return to its initial state itself ?

Also is the transition always between lowest band of CB and highest band of VB ?

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  • $\begingroup$ It needs a direct band gap - cannot make light emitting diodes with silicon. $\endgroup$ – Pieter Dec 28 '16 at 8:27
  • $\begingroup$ Radiative emission occurs in both direct and indirect band gap semiconductors. LEDs are made of materials that do radiative emission in the visible spectrum. I have to edit my question title it seems. I made a blunder. $\endgroup$ – Febin Sunny Dec 28 '16 at 8:40
  • $\begingroup$ There are infrared leds, like the ones in the remote control of your tv. $\endgroup$ – Pieter Dec 28 '16 at 8:43
  • $\begingroup$ @Pieter you are correct for a direct recombination. And yes you will not be efficient but it works as phonon assisted optical transition are not that unlikely. Trust me I have seen Silicon glow (with an IR camera) under the correct conditions. $\endgroup$ – user_na Dec 28 '16 at 8:54
  • $\begingroup$ @Pieter Even in indirect band gaps, the recombination result in the release of a phonon and a photon correct ? If no photons are created then where does the remaining energy after adjusting the momentum go ?? $\endgroup$ – Febin Sunny Dec 28 '16 at 8:58
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When you excite a semiconductor you typically generate lots of electrons and holes. When studied in detail they will have a rich dynamic, as there are several recombination paths, as you mention in your question. The question is always how likely is a certain process is to happen, i.e. how big is its transition matrix element.

Optical transitions

The necessary requirement for an optical transition is that you have an electron and a hole in two states, which allow an optical (dipole) transition. For this the typical selection rules must apply, and another important point is the difference in momentum. In Si for example, the highest VB state (at the $\Gamma$ point) and the lowest CB state (close to the $X$ point) have a strong $k$ difference and thus direct optical transitions are not possible. In this case you will need the assistance of phonons to bridge the k difference for the emission of a photon. Another typical process is the build up of exciton states which then later on may perform an optical recombination.

Non radiative transitions As you suggested it is indeed possible to recombine electrons and holes without emitting a photon. The possibly simplest process is the Auger process, where the energy of the electrons and holes transfers to a 3rd particle (electron or hole) which is taking over the energy and becomes excited itself. The problem with a direct phonon emission is that you have to match energy and momentum with the phonon you create. But the properties of phonons are given by their dispersion relation, so the phonon you need might not exist. For perfect semiconductors these direct phonon processes does not play an important role (at least as far as I know - counterexamples are welcome). When defects and impurities come into play this changes. There a several examples of non-raditive relaxations of excited defect states.

For your question if the electron has to return to its initial state again, there is no such thing as "exactly this electron" in QM. Particles are indistinguishable so the answer is no.

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  • $\begingroup$ Thank you. So what will be the output of a non radiative recombination ? $\endgroup$ – Febin Sunny Dec 28 '16 at 9:04
  • $\begingroup$ You will dissipate the energy to the crystal lattice via phonons. $\endgroup$ – user_na Dec 28 '16 at 9:07
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The inter-band recombination with emitting pnonon only is very probable in semiconductors with narrow band gap (when the band gap is comparable to the optical phonon energy). That is actually the main obstacle for making an inversion population for THz and mid-infrared semiconductor lasers. It concerns both interband and intersubband transitions.

Also is the transition always between lowest band of CB and highest band of VB ?

It is most probably, since according to the Fermi-Dirac distribution, most of electrons populate the bottom of the conduction band, while the most of holes populate the top of the valence band.

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