1. Auger recombination (simple explanation)
Auger recombination is a dark (non-radiative) recombination process in semiconductors in which the energy released by an electron–hole pair is transferred to a third carrier rather than emitted as light, becoming important at high carrier densities where it can limit device performance.
To understand how Auger recombination differs from radiative processes, it is useful to first consider free-to-free recombination. As shown on the left-hand side of ??, an electron relaxes into a hole and emits a photon, thereby conserving energy. The recombination rate is typically written as \(R = k np\), since the process requires both an electron and a hole to be present.
However, light does not have to be emitted for energy to be conserved. In Auger recombination, as shown on the right-hand side of ??, an electron again relaxes into a hole, but no photon is produced. Instead, the recombination energy is transferred to a third carrier. In the electron-assisted Auger process, this energy is given to another electron, which is excited higher into the conduction band.
This excited (“hot”) electron does not remain at high energy. At some later time, it relaxes back towards the bottom of the conduction band by emitting phonons. In this two-step process-recombination followed by thermal relaxation-energy is conserved without the emission of light. This is why Auger recombination is referred to as a dark recombination mechanism.
The presence of this third carrier fundamentally changes the carrier-density dependence of the recombination rate. While the initial recombination event still requires an electron and a hole (giving an \(np\) dependence), an additional carrier must be present to absorb the energy. For the electron-assisted process, the rate is therefore proportional to \(n^{2}p\), and for the hole-assisted process it is proportional to \(np^{2}\). Auger recombination is thus a cubic process in carrier density.
The rate of Auger recombination is expressed as
\[R^{AU} = \big(C^{AU}_{n} n + C^{AU}_{p} p\big)\,(np - n_{0}p_{0}) \]
where \(n\) and \(p\) are the electron and hole densities, \(n_{0}\) and \(p_{0}\) are their equilibrium values, and \(C^{AU}_{n}\) and \(C^{AU}_{p}\) are the electron- and hole-assisted Auger coefficients with units of m6s−1. These coefficients describe the probability that the recombination energy of an electron–hole pair is transferred to a third carrier rather than emitted as light.
👉 Explore how Auger recombination works in real simulations in the PN junction tutorial.
Because of its cubic dependence on carrier density, Auger recombination is typically negligible at low injection, but becomes increasingly important at high carrier densities, where it can dominate recombination and act as a significant loss mechanism.
👉 Key point: Auger recombination is dark: no photon is emitted, because the recombination energy is transferred to another carrier rather than to light. The excited carrier then relaxes by emitting phonons, converting the energy into heat.
2. Auger recombination including k-space (momentum explanation)
Above, we introduced recombination using the most common picture found in introductory physics texts, shown in ??. This description focuses on energy, but in all recombination processes both energy and momentum (the k-vector) must be conserved. A more complete representation is therefore given in energy–momentum (E–k) space, shown in ??, where energy is plotted along the vertical axis and momentum (k) along the horizontal axis.
On the left-hand side of ??, free-to-free recombination is shown. An electron relaxes directly into a hole at the same k-vector, so there is no change in momentum. The emitted photon carries negligible crystal momentum, and thus both energy and momentum are conserved in a direct transition.
On the right-hand side, Auger recombination is shown. In this case, an electron recombines with a hole, but the transition does not occur at a single k-vector. Instead, momentum is redistributed between carriers: the recombining electron changes its k-state, while a second electron is excited to a higher energy state and also shifts in k-space. In this way, both energy and momentum are conserved without the emission of a photon.
The excited (“hot”) electron produced in the Auger process subsequently relaxes back towards the bottom of the conduction band by emitting phonons. This delayed relaxation converts the recombination energy into heat, completing the non-radiative Auger process.
FAQs: Auger recombination
What is Auger recombination?
Auger recombination is a non-radiative process in which the energy released by an electron–hole pair is transferred to a third carrier instead of being emitted as a photon.
Why is Auger recombination important?
It becomes significant at high carrier densities and can dominate recombination, reducing efficiency in devices such as LEDs and semiconductor lasers.
When can Auger recombination be ignored?
At low carrier densities, such as in most organic semiconductors or thin-film solar cells under 1-sun illumination, Auger recombination is typically negligible compared to SRH or bimolecular recombination.
Why is Auger recombination called a “dark” process?
Because no photon is emitted; the recombination energy is instead transferred to another carrier and ultimately dissipated as heat via phonons.
3. Where is Auger recombination important in semiconductors?
Auger recombination becomes important in systems where carrier densities are very high. In such conditions, the cubic dependence of the Auger rate on carrier density causes it to rapidly dominate over other recombination pathways. This makes it a critical loss mechanism in III–V semiconductors (e.g. GaAs, InGaN), high-brightness LEDs, and semiconductor lasers, where carrier densities are intentionally driven to high levels during operation. It is also important in silicon solar cells under strong illumination (e.g. concentration) and has been identified as a limiting factor in some inorganic perovskites under high-injection conditions such as pulsed-laser excitation.
By contrast, Auger recombination is typically negligible in systems operating at low carrier density. This includes most organic semiconductors and conventional thin-film solar cells under 1-sun illumination, where carrier densities are too low for cubic processes to become significant. In these regimes, recombination is instead dominated by trap-assisted (SRH) or bimolecular (free-to-free) pathways.
In OghmaNano, the Auger coefficients \(C^{AU}_{n}\) and \(C^{AU}_{p}\) can be set directly in the Electrical parameter editor. This allows Auger recombination to be included when modelling devices in which high carrier densities are expected to impact efficiency and performance.
👉 Next step: Now continue to The need for trap states or apply these concepts in practice in the PN junction tutorial.