A hydrodynamic model for transport in semiconductors without free parameters

Abstract

We derive, using the Entropy Maximum Principle, an expression for the distribution function of carriers as a function of a set of macroscopic quantities (density, velocity, energy, deviatoric stress, energy flux). Given the distribution function, we obtain, for these macroscopic quantities, a hydrodynamic model in which all the constitutive functions (fluxes and collisional productions) are explicitely computed starting from their kinetic expressions. We have applied our model to the simulation of some one-dimensional submicron devices in a temperature range of 77-300 K, obtaining results comparable with Monte Carlo. Computation times are of order of few seconds for a picosecond of simulation.