Recombination generally describes the processes by which an electron from the conduction band
makes an energetic transition and neutralizes a hole in the valence band resulting in reduction
of the number of free charge carriers in the semiconductor.
The models for recombination processes relate to the physical mechanisms by which the carriers
make this energetic transition.
Under the recombination tab of the material property editor window, DEVICE provides models
describing various recombination processes including trap-assisted recombination (Also
known as Shockley-Read-Hall or SRH recombination), Auger recombination and radiative recombination.
In addition, it contains models for carrier generation processes including impact ionization,
and band to band tunneling.
The recombination process in the trap-assisted model assumes that there are unoccupied "trap"
states (also referred to deep-level defect states) within the band gap.
Typically, these states result from impurities (either intentional or unintentional), and
the most active ones have energy levels near the middle of the band gap.
Recombination occurs when an electron relaxes (transfers energy to the lattice or emits
a photon) to the trap state from the conduction band, and sequentially, a hole from the valence
band relaxes to the same trap state.
The density of trap states within a material determines the average life time of carriers
(the average time that carriers can survive before getting recombined) and this is taken
as input in the material model.
The higher the density of trap states or recombination rate, the lower the carrier lifetime.
Moreover, DEVICE provides a temperature dependent model for the SRH carrier lifetime, as well
as models that include corrections for doping density and field effects.
The trap energy level can be specified in the model by its offset from the material’s
mid-bandgap energy level.
Auger transitions are three-particle transitions in which two carriers recombine and transfer
energy and/or momentum to a third carrier.
Auger recombinations depend only on carrier density and become significant only at high
The recombination rate is described by a capture coefficient for which a higher value means
a higher recombination rate.
The capture coefficient can be defined to be temperature-dependent.
Moreover, two correction models named White and Basore are available.
The basic model is suitable for devices where Auger recombination is moderate (low injection
The White model can be used as a correction to the basic model, and accounts for the reduction
in the Auger recombination rate observed at high carrier densities.
The Basore model is designed to account for the two regimes related to minority carrier
When using this model, the solver will use the Auger capture rate coefficient defined
in the basic model for low injection conditions, and apply a second coefficient when strong
minority carrier injection dominates.
In a radiative transition, a conduction band electron will relax directly, emitting a photon
whose energy approximately equals that of the band gap, and then recombine with a hole
in the valence band.
The opposite process is called optical generation and occurs when a photon is absorbed by an
electron in the valence band, promoting it to the conduction band and leaving a hole
in its place.
Radiative recombination transitions are typically significant only in materials with a narrow
bandgap, or a bandstructure that permits direct transitions in momentum (e.g. GaAs).
Radiative recombination is typically negligible in bulk silicon.
The recombination rate is determined from the product of a capture rate coefficient
and the carrier density.
The capture rate coefficient can be modeled either as a constant or dependent on temperature.
Impact ionization is a carrier generation process where an electron or hole, accelerated
by a high field, will relax by transferring energy to the lattice.
When energy exceeding the band gap is transferred to the lattice, an electron-hole pair is excited
(and separated by the strong local field), generating additional free carriers.
Above a critical threshold, this process leads to avalanche breakdown.
The impact ionization process is exponentially dependent on the driving field (either the
quasi Fermi level gradient or electric field component in the direction of the current
density) and the local variations in the quasi-Fermi levels (through the current density).
Consequently, it is a highly non-linear process, and its inclusion in the physical model for
the semiconductor can cause divergence in the simulation.
By default, the impact ionization process is not enabled.
When simulating avalanche breakdown, additional settings might be needed to ensure simulation
The band-to-band tunneling is a carrier generation process in which an electron in the valence
band of semiconductor tunnels across the band gap to the conduction band without the assistance
The band gap acts as the potential barrier that the particle tunnels across as a result
of severe band-bending due to high-fields.
Two models for this process are included in DEVICE: the Hurkx and Schenk models.
For more information about these models, see the related links below.
In the next unit, we will explore other material types including conductors and insulators.