Recombination (physics)

In plasma physics, recombination is the neutralizing union of electrically positive and negative charge carriers ( ions , electrons ). Recombination is the reverse process to ionization .

Ionization requires the supply of energy , which takes place primarily through high temperatures , light quanta or impact ionization by other particles. So that charged particles that meet each other can recombine, this energy must be released again. This can take place through the emission of photons ( luminescence , for example with lightning , electrometeors or light-emitting diodes ), through energy transfer to other particles, through dissociation into neutral particles or in the form of lattice vibrations (acoustic phonons ).

Recombination in the gas phase

An ionized gas is a plasma . Examples are gas discharges and the ionosphere .

With sufficient pressure and degree of ionization that is triple collision recombination dominant, in which a positive ion with two electrons pushes simultaneously. The ion recombines with the first electron to form a neutral atom . The binding energy that is released is “carried away” by the second electron (similar to the heat radiation in an inelastic collision ). The second electron increases its energy during this process. Alternatively, another atom or molecule can absorb the binding energy. Because of the shorter range of interaction with neutral particles, this process is only competitive with a low degree of ionization. ${\displaystyle X^{(+)}\,}$ ${\displaystyle e^{(-)}\,}$

If the pressure of the neutral gas is also low, a wall or particle surface can act as a catalyst ( wall recombination ). It not only absorbs the binding energy, but also increases the probability of an encounter if electrons or ions linger on the surface ( adsorbate ). Wall recombination is particularly effective with electrically conductive walls.

In the ionosphere the pressure is low and there is no nearby wall. Two types of recombination predominate there:

Dissociative recombination

An electron combines with a molecular ion to form two neutral atoms.

${\displaystyle e^{(-)}+XY^{(+)}\longrightarrow X+Y}$

It can only take place where either molecular ions arise directly or through the ion-atom exchange, which requires neutral molecules.

Ion-atom exchange + separation recombination

First, an ion-atom exchange reaction takes place, the result of which - a molecular ion - separates and recombines.

${\displaystyle X^{(+)}+Y_{2}\longrightarrow XY^{(+)}+Y}$

${\displaystyle e^{(-)}+XY^{(+)}\longrightarrow X+Y}$

Radiation recombination

${\displaystyle e^{(-)}+X^{(+)}\longrightarrow X+h\nu \,}$( is a photon) ${\displaystyle h\nu \,}$

on the other hand is a very slow process and can be ignored for balancing purposes in the ionosphere. More energetic forms can be seen as a transition to secondary radiation . Aurora is not a recombination radiation, it is based on shock excitation, not shock ionization.

dielectric recombination

In dielectric recombination , an electron is captured by a positively charged ion. Another electron of the ion is excited.

Recombination in the semiconductor

In semiconductors , one speaks of recombination when an electron excited into the conduction band relaxes again, that is , when it releases a photon or phonon, it “falls back” into the valence band . One speaks of radiating or radiationless recombination. In light emitting diodes, some of the charge carriers recombine in a radiant manner. In silicon semiconductor components (with an indirect band gap ), on the other hand, almost exclusively radiationless recombination takes place.

The opposite process to recombination is generation , in which an electron and a hole are created through ionization . The ionization energy mostly comes from photons or phonons. The recombination and generation rates are the same in thermodynamic equilibrium .

With recombination, one often takes a simple approach to the rate of recombination, i.e. the number of recombinations per time (and volume).

The following applies to electrons:

${\displaystyle r_{n}={\frac {n-n_{0}}{\tau _{n}}}}$,

The same applies to defect electrons:

${\displaystyle r_{p}={\frac {p-p_{0}}{\tau _{p}}}}$.

${\displaystyle n}$or denote here the concentrations of the charge carriers (electrons or defect electrons), or the equilibrium concentrations and or the effective lifetimes of the charge carriers. The recombination rate clearly increases when the charge carrier concentration is above the equilibrium concentration. ${\displaystyle p}$ ${\displaystyle n_{0}}$ ${\displaystyle p_{0}}$ ${\displaystyle \tau _{n}}$ ${\displaystyle \tau _{p}}$

More specifically, there are many different effects that play a role in the process of recombination.

Photons or phonons, whose energy is greater than the energy gap in the semiconductor, can give up their energy to valence electrons and thus create electron-hole pairs in the semiconductor. These charge carriers (electrons and holes) go through radiation and / or lattice vibrations (phonons) again in the direction of the band edge , since their energy is minimized there. This effect significantly limits the efficiency of solar cells , but it can be reduced by using tandem solar cells . ${\displaystyle (E=h\cdot \nu )}$ ${\displaystyle E_{g}}$

A recombination of these electrons and holes can be either radiating or non-radiating. If they recombine, this effect is called luminescence. It is crucial that a direct semiconductor is necessary for observable radiative recombination , in which there is no difference in momentum between the band minima in the conduction band and band maxima in the valence band.

There are three known types of recombination: radiant, Shockley-Read-Hall, and Auger recombination.

Types of recombination

Radiant recombination

Here an electron recombines radiantly with a hole. The resulting photon has the energy that is at least as large as the energy of the band gap. The charge carrier density with a material-dependent constant recombination factor is usually used as the formula for radiative recombination . With the charge carrier densities and the intrinsic charge carrier density it reads : ${\displaystyle E=h\cdot \nu }$ ${\displaystyle C_{\mathrm {dir} }}$ ${\displaystyle n,p}$ ${\displaystyle n_{i}}$

${\displaystyle R_{\mathrm {dir} }=C_{\mathrm {dir} }\cdot (np-n_{i}^{2})}$

Shockley-Read-Hall recombination

In this recombination mechanism, the electron first jumps to a recombination level that is roughly in the middle of the band gap and then recombines with another jump with a hole. Energy is released in the form of lattice vibrations . The energy levels in the band gap arise from defects in the crystal lattice , such as doping atoms . Since recombination above a band level requires less energy, it is usually more likely than direct recombination. Defect atoms are thus recombination centers or traps (engl. Or traps trap ) for free charge carriers. The SRH recombination is therefore a non-radiative recombination. It can be set with the charge carrier lifetimes and : ${\displaystyle \tau _{n}}$ ${\displaystyle \tau _{p}}$

${\displaystyle R_{\mathrm {SRH} }={\frac {np-n_{i}^{2}}{\tau _{p}\cdot (n+n_{\mathrm {d} })+\tau _{n}\cdot (p+p_{\mathrm {d} })}}}$

The quantities and are defined as follows ( recombination fault energy , intrinsic Fermi level , temperature , Boltzmann constant ): ${\displaystyle n_{d}}$ ${\displaystyle p_{d}}$ ${\displaystyle E_{T}}$ ${\displaystyle E'_{i}}$ ${\displaystyle T}$ ${\displaystyle k_{B}}$

${\displaystyle n_{\mathrm {d} }=n_{i}\cdot \exp \left({\frac {E_{\mathrm {T} }-E_{\mathrm {i} }}{k_{\mathrm {B} }\cdot T}}\right)}$

${\displaystyle p_{\mathrm {d} }=n_{i}\cdot \exp \left({\frac {E_{\mathrm {i} }-E_{\mathrm {T} }}{k_{\mathrm {B} }\cdot T}}\right)}$

Auger recombination

Auger recombination is also a non-radiative recombination. A conduction band electron releases its energy by jumping into a hole in the valence band, but this energy is completely absorbed by another conduction band electron. This electron either relaxes again to the conduction band minimum, i.e. releases its energy again in the form of lattice oscillations in order to minimize its energy, or it leaves the crystal when it is close to the surface (see Auger electron spectroscopy ).

Recombination on the surface

This is a recombination through unbound (also: unsaturated) states on the surface of the semiconductor. On the one hand, these unbound states ( dangling bonds ) cause additional states in the band gap through which electrons and holes can recombine. On the other hand, foreign atoms (dirt, moisture, etc.) can adhere to it. The recombination process via unbound states is usually harmful to components and reduces their service life. In addition, the states on the surface are no longer well-defined, which reduces the predictability of a semiconductor component. However, due to its targeted technical use, this effect is becoming more and more important.

For the calculation can be an approximation of the SRH recombination use, and not here on a discrete affixed spot ( trap is recombined), but through a whole spectrum of recombination centers in the emerging forbidden zone at the surface.

The surface recombination rate is determined as follows:

${\displaystyle R_{0}=\int _{-W_{\text{g}}/2}^{-W_{\text{g}}/2}{\frac {N_{\text{ss}}(W_{\text{t}})\sigma _{\text{r}}v_{\text{th}}(pn-n_{i}^{2})}{n+p+2n_{\text{i}}\cosh \left({\frac {W_{\text{t}}}{kT}}\right)}}\mathrm {d} W_{\text{t}}}$

${\displaystyle \sigma _{\text{r}}}$: Cross section for recombination

${\displaystyle N_{\text{ss}}(0)}$: Surface state density in the middle of the forbidden zone

There are numerous technical processes for passivation , i.e. for saturating unbound surface conditions.

Sources and footnotes

1. ^ The electron concentration profile. In: Ionospheric Physics. University of Leicester, accessed January 8, 2013 .