Simulation of submicron silicon diodes with a non-parabolic hydrodynamical model based on the maximum entropy principle

Abstract

Modeling modern submicron electron devices requires an accurate description of energy transport in order to cope with high-field phenomena such as hot electron propagation, impact ionization and heat generation in the bulk material. Most implemented hydrodynamic models suffer from serious theoretical drawbacks due to the ad hoc treatment of the closure problem (lacking a physically convincing motivation) and the modeling of the production terms (usually assumed to be of the relaxation type and this leads to serious inconsistencies with the Onsager reciprocity relations. In this paper we use a recently introduced moment approach in which the closures for the fluxes and for the production terms are based on the maximum entropy principle in the case of the Kane dispersion relation. Explicit closure relations for higher order fluxes and production terms have been obtained without any free parameters. A preliminary validation of this model has been successfully performed in bulk silicon. We test the model by simulating a one dimensional n/sup +/n-n/sup +/ submicron silicon diode for different values of the channel, applied bias and doping profile. Comparisons with Monte Carlo simulations show that the results are sufficiently accurate for CAD purposes.