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_eImpactA1
and 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
andm_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.