# Electron-hole recombination

• 2ri
In summary, the recombination of an electron in the conduction band with a hole in the valence band is not due to electrostatic attraction, but rather the spontaneous emission of a photon and the electron jumping into an unoccupied energy state in the valence band. In a direct band-gap semiconductor, electrons can only absorb photons with energy equal to or greater than the band-gap energy, causing them to transition to an allowed energy state. Photons with less energy than the band-gap will simply scatter off the electron, changing its momentum but not its energy.

#### 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 ?

Thank you.

#### Attachments

• e-h recombination.png
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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.

## 1. What is electron-hole recombination?

Electron-hole recombination is a process in which an electron and a positively charged hole (a vacancy where an electron could be) combine to form a neutral atom or molecule. This process is important in understanding the behavior of semiconductors and other materials.

## 2. How does electron-hole recombination occur?

Electron-hole recombination can occur through three main processes: radiative, non-radiative, and Auger recombination. In radiative recombination, the excess energy is released in the form of light. In non-radiative recombination, the energy is released as heat. Auger recombination involves the transfer of energy to another electron instead of releasing it as light or heat.

## 3. What factors affect the rate of electron-hole recombination?

The rate of electron-hole recombination can be affected by several factors, including the type and concentration of impurities in the material, the temperature, and the presence of defects or traps that can capture the electrons or holes and prevent them from recombining.

## 4. Why is electron-hole recombination important in solar cells?

Solar cells rely on the separation of electrons and holes to generate an electric current. The recombination of these charge carriers reduces the efficiency of the solar cell. Understanding and controlling the rate of electron-hole recombination is crucial in improving the efficiency of solar cells.

## 5. Can electron-hole recombination be reversed?

Yes, electron-hole recombination can be reversed through a process called carrier injection. This involves introducing excess electrons or holes into a material, which can then recombine with the opposite charge carriers. This process is used in devices such as light-emitting diodes (LEDs) and lasers.