Extended Hydrodynamical Model of Carrier Transport in Semiconductors

A hydrodynamical model based on the theory of extended thermodynamics is presented for carrier transport in semiconductors. Closure relations for fluxes are obtained by employing the maximum entropy principle. The production terms are modeled by fitting the Monte Carlo data for homogeneously doped semiconductors. The mathematical properties of the model are studied. A suitable numerical method, which is a generalization of the Nessyahu–Tadmor scheme to the nonhomogeneous case, is provided. The validity of the constitutive relations has been assessed by comparing the numerical results with detailed Monte Carlo simulations.