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Subsections
3.7.5 Impact Ionization
The impact ionization (II) models support both the driftdiffusion (DD) and the
hydrodynamic (HD) transport models, therefore, electric field dependent DD II models
and carrier temperature dependent HD II models are used in MINIMOSNT.
3.7.5.1 DriftDiffusion Impact Ionization
In DD simulation the model from [33] is used to calculate the II
generation rates for electrons and holes, respectively. The overall generation
rate is the sum of these two generation rates and can be expressed as a negative
recombination rate.

(3.152) 
The ionization coefficients
and
are expressed by Chynoweth's law



(3.153) 



(3.154) 
The default values are summarized in Table 3.38.
Table 3.38:
Parameter values for DD impact ionization model
Material 
[m] 
[V/m] 

[m] 
[V/m] 

Reference 
Si 
7.03e7 
1.231e8 
1.0 
1.528e8 
2.036e8 
1.0 

Ge 
1.55e9 
1.560e8 
1.0 
1e9 
1.28e8 
1.0 
[33] 
GaAs 
3.5e7 
6.85e7 
2.0 
3.5e7 
6.85e7 
2.0 
[190] 
GaP 
4.0e7 
1.18e8 
2.0 
4.0e7 
1.18e8 
2.0 
[190] 

To account for surface effects, the surface ionization rates
and
can deviate from the
bulk rates. The electron surface ionization rate is calculated in a similar
way (analog for holes)

(3.155) 
is given by (3.120) and depending on the
surface distance describes a smooth transition between the surface and bulk
generation rates. The parameter
denotes a critical
length. The final surface dependent ionization rate
reads

(3.156) 
The effect is considered only for Si and the following values are used:
Table 3.39:
Parameter values for surface DD impact ionization model
Material 
[m] 
[V/m] 
[m] 
[V/m] 
[nm] 
Si 
1.03e7 
1.50e8 
4.0e8 
3.0e8 
10 

In a HD simulation, the carrier temperatures are used as parameters
in the hydrodynamic impact ionization model. The implemented equation for the
electron generation rate depending on the concentration and the bandgap
energy
[191,192] reads (analog for holes)

(3.157) 

(3.158) 
The prefactor depends on the carrier and lattice temperatures and the local
bandgap

(3.159) 
The variables and correspond to 300 K and
,
respectively.
Table 3.40:
Parameter values for HD impact ionization model
Material 
[s] 



Si 
9.531e9 
3.823 
0.346333 
0.0922 

The overall generation rate is the sum of the electron and hole generation
rates, and is equal to a negative recombination rate

(3.160) 
Another simple, but very practical model is available for modeling the impact
ionization rate in all semiconductors. It reads for electrons

(3.161) 
and, respectively, for holes

(3.162) 
The default values recommended for the simple HD II model are summarized in the
following table:
Table 3.41:
Parameter values for HD impact ionization model
Material 
[s] 

Si&Ge 
1e13 
0.92 
IIIVs 
1e13 
1.0 

This model has been already successfully applied in simulation of GaAsbased
and InPbased HEMTs [193,194]. However, it has not been
applied in simulation of IIIV HBTs yet.
Next: 4. Simulation Application
Up: 3.7 Generation and Recombination
Previous: 3.7.4 BandtoBand Tunneling
Vassil Palankovski
20010228