This chapter describes the physical models employed in **GNU Archimedes**. It is important to fully understand this chapter in order to fully exploit the possibility offered by this code. Obviously, everything here is a brief review of what you can find in papers and books on the Monte Carlo subject. So, if you don't understand some aspects of this chapter, don't esitate to read the papers reported in this chapter. We will, also, describe the simplified MEP (Maximum Entropy Principle) model, which is a simplified version of the MEP model. This model has been developped by A.M.Anile and V.Romano, two professors of the Department of Mathematics and Computer Sciences of the University of Catania. It is a very good model, which is able to give very accurate results, compared to the other hydrodynamical models.

In the present release of **GNU Archimedes** we use a simplified version because it is enough for our purpose, i.e. the coupling of MEP model and Monte Carlo method in order to obtain very accurate simulation results in very short running times.

In the following we report a (i hope) complete list of usefull papers for people interested in the complete MEP model:

"Non parabolic band transport in semiconductors: closure of the moment equations", A.M. Anile, V. Romano, Continuum Mechanics and Thermodynamics, 1999, 11:307-325.

"Non parabolic band transport in semiconductors: closure of the production terms in the moment equations", V. Romano, Cont.Mech.Thermodyn., 1999, 12:31-51.

"Non-parabolic band hydrodynamical model of silicon semiconductors and simulation of electron devices", V.Romano, Mathematical methods in the applied sciences, 2001, 24:439-471.

"2D Simulation of a Silicon MESFET with a Nonpoarabolic Hydrodynamical Model Based on the Maximum Entropy Principle", V.Romano, Journal of Computational Physics, 176, 70-92 (2002)

"Numerical simulation of 2D Silicon MESFET and MOSFET described by the MEP based energy-transport model with a mixed finite elements scheme", A.M. Anile, A. Marrocco, V. Romano, J.M. Sellier, Rapport de recherche, INRIA, N.5095.

"Numerical Simulation of the 2D Non-Parabolic MEP Energy-Transport Model with a Mixed Finite Elements Scheme", A. Marrocco, V. Romano, J.M. Sellier, N.5103.

"Two dimensional MESFET simulation of transients and steady state with kinetic based hydrodynamical models", A.M. Anile, S.F. Liotta, G. Mascali, S. Rinaudo.

"Parabolic hydrodynamical model for bipolar semiconductors devices and low field hole mobility ", G. Mascali, V. Romano, J.M. Sellier, submitted to Continuum Mechanics and Thermodynamics.

"Numerical Simulation of the 2D Non-Parabolic MEP energy-transport model with a mixed finite elements scheme", A.M. Anile, A. Marrocco, V. Romano, J.M. Sellier, submitted to Journal of Computational Electronics.

- The Semiclassical Approach
- The Quantum Effects
- The Particle Dynamics

- Initial Conditions
- Contacts and Boundaries

- The Scattering Process

- The Simplified MEP Model