The points B and E in Fig. 5.5 can be distinguished by taking, for example, the gradient of the carrier temperature into account. To capture both the and region (Fig. 6.4), such a dependence on the gradient of the carrier temperature is introduced:

(6.13)  
(6.14) 

However, the model eqn. (6.12) leads to severe stability problems with the numerical iteration. Furthermore it turned out that the reproduction of the peak is not essential for solving the problem related to SOI simulations since the important point is to allow for a reduced along the channelespecially in the pinchoff region.
In most of the channel region the high energy tail is less populated than that of a MAXWELLian distribution which means that (Fig. 6.6). It is believed that proper modeling of the region is very important for the SOI problem described in Chapter 4, because the smaller amount of carriers in the high energy tail will give reduced hot carrier diffusion into the floating body.

To avoid numerical stability problems a model for as a function of only has been developed
M. Gritsch: Numerical Modeling of SilicononInsulator MOSFETs PDF