What Triggers Electron-Hole Recombination in Semiconductors?

[2ri]

Hello,

This is about a direct band gap semiconductor:
Q1) What induces recombination of an electron in the conduction-band with a hole in the valence-band? Is it the electrostatic attraction between a negatively charged electron and a positively charged hole which induces recombination or something else?

Q2) Suppose we are sending a stream of photon, one photon at a time, towards a semiconductor (direct band-gap). Each photon carries an energy slightly larger than its predecessor photon. In this way ultimately we arrive at a photon which has energy exactly equal to the band-gap energy. The time gap between two consecutive photons is large enough that any excited electron in the semiconductor falls back to the valence band. The question is, when a photon with energy less than the band-gap is incident on a semiconductor, then:
(a) Is it that an electron from valence band absorbs it and lands-up in the middle of energy band-gap, but, since there is no energy-state available for it to occupy, it immediately releases the absorbed energy and falls back to the valence band; and therefore we say that there is no absorption for photons with energy lower than band-gap, or
(b) Is it that an electron never absorbs energy from a photon with energy lower than band-gap; it absorbs energy from a photon only when the photon energy is equal to or greater than the band-gap energy? If this option is true than how does an electron come to know that which photon has energy equal to or greater than band-gap ? it indicates that the electron must be interacting with each of the photons, but does not absorb their energy until the photon energy is equal to or greater than band-gap energy.

I have attached a schematic; my question is that whether the type of transition shown in the schematic allowed ?



Please help me clarify these doubts.

Thank you.

 

[cbetanco]

A1) An electron in the conduction band will spontaneously emit a photon after some characteristic time (called the lifetime), and fall back into the valence band. In the valence band, there will have been an emptz energz state, not occupied by an electron (or occupied by a hole). When the electron in the conduction band emits the photon and hops back into the valence band, it jumps into one of the states not occupied by an electron (or occupied by a hole), and thus "recombines" with this hole. It has nothing to do with electrostatic attraction.

A2) Answer b is correct. The electron cannot absorb a photon with less than the bandgap energy. The electron will interact even with photons with less than the bandgap, but they will not change the energy unless the incident photon has an energy larger than the bandgap, in which case the electron absorbs the photon and makes the transition to an allowed energy state. A photons with less energy than the bandgap will "recoil" or scatter off the electron, changing its momentum, but not its energy.