Trap-Assisted Recombination
This feature is an expanded version of the original Shockley-Read-Hall Recombination feature, with new options to allow for more detailed modeling of traps.
Use the Trap-Assisted Recombination model to set the electron and hole recombination rates in indirect band-gap semiconductors such as silicon under low electric fields. Select this option from the Generation-Recombination submenu.
Recombination and Generation and Theory for Trap-Assisted Recombination: Shockley-Read-Hall Recombination
Trap-Assisted recombination
Select a Domain trapping model:
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 Shockley-Read-Hall model (the default). This option corresponds to the original Shockley-Read-Hall model for steady state recombination via states located at the midgap.
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 Explicit trap distribution. This option allows the specification of a number of discrete traps or a continuous density of trap states at energies within the band-gap. Degrees of freedom are added to the equation system to represent the occupancy of traps at a particular energy.
When Explicit trap distribution is selected as the Domain trapping model, the Discrete Energy Level (Domains) subnode is available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.
Shockley-Read-Hall recombination
This section is available when Shockley-Read-Hall model is selected as the Domain trapping model:
The Shockley-Read-Hall recombination rate is defined as:
with
where γn and γp are the electron and hole degeneracy factors, Nc,0 and Nv,0 are the effective densities of states for the conduction and valence band, Eg is the band gap and ΔEg the band gap narrowing energies (SI unit: V) — scaled by the electron charge, q. Vth=kBT/q, where kB is Boltzmann’s constant and T is the temperature. The parameters τn and τp are carrier lifetimes (SI unit: s) and Et is the trap energy level (SI unit: V) — scaled by the electron charge.
Enter values for the following:
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The Electron lifetime, SRH τn (SI unit: s) is taken From material. For User defined enter a value in the text field. The default is 10 μs.
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The Hole lifetime, SRHτp (SI unit: s) is taken From material. For User defined enter a value in the text field. The default is 10 μs.
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Enter a value for Energy difference between the defect level and the intrinsic level ΔEt (SI unit: V) in the text field. The default is 0 V.
Trapping
This section is available when Explicit trap distribution is selected as the Domain trapping model.
By default, Specify the discrete levels only is selected. Or select Specify continuous and/or discrete levels.
When Explicit trap distribution is selected as the Domain trapping model, and Specify continuous and/or discrete levels is selected above, the Continuous Energy Levels (Domains) subnode is available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.
For either choice:
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The Specify trap species check box is not selected by default. In this case the software does not distinguish between different types of trap and the charge due to the traps is determined by the neutral energy level.
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To set the Neutral energy level, select — Midgap (the default), From valence band edge, From conduction band edge, or Relative. Then enter the applicable information:
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Neutral level for traps (available when From valence band edge or From conduction band edge is selected) E0 (SI unit: V). The default is 0 V.
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Neutral level for traps (between 0 and 1, 0.5 is midgap) (available when Relative is selected) E0 (dimensionless). The default is 0.5.