Van-Overstraeten Impact Ionization Model for Electrons in Silicon

I think there might be an issue with the Van-Overstraeten impact ionization model implemented in MediumSilicon.cc for electrons in Silicon.

The implementation in Garfield++ uses two distinct regions of E-field (below and above 400kV/cm) with two different sets of parameters (m_eImpactA0 and m_eImpactB0 resp. m_eImpactA1and m_eImpactB1).

When I plot the ElectronAlpha in function of the E-Field (as implemented with this model), I get the orange curve in the attached plot:

ImpactionIonization_Comparison_e.pdf

As one can see, this curve has a pronounced jump at 400kV/cm, where the model switches from one region to another region.

Now: I am unable to find the exact source for having two different set of parameters for electron multiplication in silicon:

• As far as I can tell, Sentaurus SDevice only implements one set of parameters (for electrons).
  • The corresponding curve is shown as a dashed line in the plot, and corresponds to the original 1970 Van-Overstraeten model.
• The Garfield++ source also quotes a paper of Van-Overstraeten and De-Man of 1990.
  • But as far as I can tell, that paper neither advocates for having two different ranges (< and > 400keV).
  • The corresponding curve is shown as a dashed-dotted line in the figure.

So I see two issues:

• The jump in impact ionization parameter at 400kV/cm in my opinion is not physical.
• I can not find a source which motivates the parameters chosen for m_eImpactA0 and m_eImpactB0.

Note:

• The corresponding model for h multiplication in Silicon indeed implements two regions (< and > 400kV/cm)
• This models seems to be implemented correctly in Garfield++ and the corresponding curve does not show any jump (see below)

ImpactionIonization_Comparison_h.pdf

The two plots also show the parameters as extracted from the Uni-Bologna model, as documented in the SDevice Manual, as a reference.