Recombination groups in database{ …_zb{} } and database{ …_wz{} }¶
There are about 23 identical groups available directly under all zincblende- and wurtzite-related groups. In this section we describe one of them, specifically the group related to recombination models recombination{}.
database{ …{ recombination{} } }¶
This section specifies the coefficients related to recombination processes. These are used when the current equation is solved. In nextnano++, the following recombination processes are included:
Example¶
binary_zb {
name = Si # material name, e.g. Si, GaAs, InP, ...
...
recombination{
# Shockley-Read-Hall recombination
SRH{ tau_n = 1.0e-9 # [s] zero doping scattering time for electrons
nref_n = 1.0e19 # [cm^-3] reference doping concentration for electrons
tau_p = 1.0e-9 # [s] zero doping scattering time for holes
nref_p = 1.0e18 # [cm^-3] reference doping concentration for holes
}
# Auger recombination
Auger{ c_n = 2.8e-31 # [cm^6/s]
c_p = 9.9e-31 # [cm^6/s]
}
# direct recombination
radiative{ c = = 2.0e-10 } # [cm^3/s]
# 2.0e-10 for GaAs, 0 for Si (indirect semiconductor)
}
}
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.
- tau_n
zero doping scattering time for electrons \(\tau_{n0}\)
- type:
double
- unit:
s
- nref_n
reference doping concentration for electrons \(N_{n,ref}\)
- type:
double
- unit:
cm-3
- tau_p
zero doping scattering time for holes \(\tau_{p0}\)
- type:
double
- unit:
s
- nref_p
reference doping concentration for holes and \(N_{p,ref}\)
- type:
double
- unit:
cm-3
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.
- c_n
coefficient \(C_n\)
- type:
double
- unit:
cm6 s-1
- c_p
coefficient \(C_p\)
- type:
double
- unit:
cm6 s-1
More imformation on physics: Auger recombination processes in semiconductor heterostructures.
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.
- c
a coefficient \(C\)
- type:
double
- unit:
cm3 s-1
- example:
2.0e-10 (for GaAs), 0.0 (for Si, indirect semiconductor)
- c_absorption
If
c_absorption > c
, thenc_absorption
will be used instead ofc
as \(C\) to compute absorption coefficients in semiclassical optics. This can be used to enable and control absorption for indirect bandgap materials wherec
practically vanishes. Ideally, for these materials,c_absorption
should be set in the database to values which reproduce the experimentally observed absorption coefficients.
- type:
double
- unit:
cm3 s-1
- default:
1e-11