3.2.11.3 Simplified Hydrodynamic Model

In a straight forward approach a simplified model can also be applied for hydrodynamic transport. The generation rates read:

$$G_n(T_n,{\it T}_\mathrm{L},n) = n \cdot A_n \cdot \exp \bigg(\frac{-B_n \cdot {\it E}_\mathrm{g}}{{\it k}_{\mathrm{B}}T_n}\bigg)$$ (3.79)

and:

$$G_p(T_p,{\it T}_\mathrm{L}, p) = p \cdot A_p \cdot \exp \bigg( \frac{-B_p \cdot {\it E}_\mathrm{g}}{{\it k}_{\mathrm{B}}T_p}\bigg)$$ (3.80)

Table 3.32: Impact ionization rates in bulk III-V semiconductors for the simplified impact ionization model.

Material	$A_n=A_p$	$B_n$	$B_p$
	[1/s]	-	-
GaAs	2.7e12	1.36	1.50
Al$_{0.2}$Ga$_{0.8}$As	5e12	1.29	1.37
In$_{0.25}$Ga$_{0.75}$As	6.5e12	1.38	1.56
In$_{0.53}$Ga$_{0.47}$As	9e12	1.38	1.66
In$_{0.52}$Al$_{0.48}$As	4.2e12	1.47	1.87

The parameter $B_i$ is used to obtain a similar threshold energy for the materials as given in the previous section as a function of band gap. This provides a kind of material dependent consistency. The model is numerically less complex than the previous one. Using the parameters $A_\nu$ as an effective fitting constant impact ionization can be included into the simulation: the parameters are derived either from a similar approach as in the previous section, or from the fitting of gate currents. Typical values for the extracted parameters are shown in Table 3.32.