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 onedimensional 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.
Highlights
Modeling of modern semiconductor devices is currently performed by means of two distinct approaches, kinetic models and Fluid Dynamic (FD) models
The most accurate kinetic description is given by Monte Carlo methods, which can take into account explicitely both the band structure and the various scattering phenomena [1, 2]
Other kinetic approaches are based on the choice of particular forms of the non-equilibrium distribution function of carriers
Summary
Dipartimento di Fisica, Universit& di Catania, Corso Italia 57, 1-95129, Catania, Italy," Dipartimento di Matematica, Universitt di Catania, Viale A.Doria 6, 1-95125, Catania, Italy. 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). 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 onedimensional 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
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