As you can see from the precedent papers reported in the introduction of this chapter, the MEP model is a very advanced hydrodynamical model for both electrons and holes in Silicon devices. For our purpose we will need only a simplified version of it. This because, we only need simple initial conditions for the Monte Carlo method. In the following we report a sketch of this model. A paper is under construction and will be refered in the next versions of this manual. The MEP model is based on the closure of the semiclassical Boltzmann equation by means of the maximum entropy principle. Using the relaxation time approximation (for only the moments and not for the energy moment) and using the so-called Liotta-Mascali distribution function which has the following form

(5.26) |

we get the following hydrodynamical model for electrons, which we will call the

(5.27) | |||

(5.28) | |||

(5.29) |

where is a function of the electrons energy, as you can see from the precedent papers. This function is computed numerically and reads:

(5.30) |

Furthermore, we have the following relations:

(5.31) | |||

(5.32) |

For the moment relaxation time we have the following relations which are taken from the Baccarani model:

(5.33) |

where

(5.34) |

with the low field mobility and the lattice temperature. It is very easy to see how to adapt everything to Silicon heavy holes, so we do not report the Simplified MEP model for them.