2.8. Generation and recombination rates - semiclassical models
The recombination mechanisms that nextnano++ takes into account for the right-hand-side of (2.7.1.1) are
Shockley-Read-Hall (SRH) recombination
Auger recombination
Radiative recombination
“fixed (applied)”
The equations and parameters used for the three recombination mechanisms on the top are explained here: recombination_model{ }.
The last one “fixed (applied)” is the contribution defined from structure{region{generation{}}} and optics{ photogeneration{ } }. These typically represent generation instead of recombination and used for the simulation of the devices under irradiation such as solar cells or CCDs. (For example, see nextnano++ tutorial GaAs solar cell.)
According to the specification in the section classical{ }, nextnano++ can calculate optoelectronic characteristics of the arbitrary structure by means of the so-called semi-classical model.
In this model, various quantities are calculated from the spontaneous emission rate, which is calculated at each position \(\mathbf{r}\) for the photons with each energy \(E\) based on the energy-resolved carrier densities \(n(\mathbf{r},E)\) and \(p(\mathbf{r},E)\) obtained in the forgoing simulation.
2.8.1. For drift-diffusion
Net radiative recombination
The simplest, and the most important for light emitting devices, process for the generation and recombination of electron-hole pairs is the direct emission or absorption spectra of a photon (radiative recombination) modelled within the formula
where \(C\) is a coefficient.
Shockley-Read-Hall (SRH) recombination
SRH model models the generation/recombination process that is assisted by impurities. The recombination/generation rates depend on the deviation of the carrier concentration from the equilibrium value and the scattering rates depend on the doping concentration. The rate is calculated using the following formulas:
where \(\tau_{n0}\) is zero doping scattering time for electrons, \(N_{n,ref}\) is reference doping concentration for electrons, \(\tau_{p0}\) is zero doping scattering time for holes, and \(N_{p,ref}\) is reference doping concentration for holes.
Auger recombination
More imformation on physics: Auger recombination processes in semiconductor heterostructures.
Auger process is a dominant recombination channel for devices with an extremely high carrier concentrations. It is a three-particle process, therefore, scaling with the third power of the carrier density.
The phonon-assisted Auger recombination rate, which plays an important role especially at high carrier injection, is modeled by the following equation:
where \(C_n\) and \(C_p\) are coefficients.
2.8.2. For semiclassical optical spectra and photogeneration
Spontaneous recombination rate
Where \(C(\mathbf{r})\) [\(\mathrm{cm}^3\mathrm{s}^{-1}\)] is the bimolecular recombination parameter of the material at the position \(\mathbf{r}\), also known as capture coefficient.
It is set in the database as c or c_absorption, see Recombination groups in database{ …_zb{} } and database{ …_wz{} } for further reference.
Then the other optical characteristics like stimulated emission rate, absorption/gain spectrum, and the imaginary part of the dielectric constant are calculated according to this \(R_{\mathrm{spon}}(\mathbf{r}, E)\).
Absorption coefficient
Semiclassical absorption coefficient is calculated based on stimulated recombination per incident photon.
where
The reference equation is eq.(9.2.39) of [ChuangOpto1995].
Generation by the irradiation (fixed(applied))
There is another radiative recombination rate output on recombination.dat called “fixed(applied)”, which should be always negative. This is the contribution of the generation specified from structure{region{generation{}}} and optics{ photogeneration{ } }. When we do not specify either of them, this recombination rate is always 0.
This is mostly used for the analysis of the absorbing devices such as solar cells or CCDs.
Last update: 2025-11-07