Computational macroscopic approximations to the one-dimensional relaxation-time kinetic system for semiconductors

We study comparisons of deterministic computational methods for one-dimensional relaxation charged transport in submicron channel devices. Our analysis focuses on the appropriate macroscopic approximations under regimes associated to different devices with similar geometries. We show, when taking standard parameters corresponding to Si devices, that the kinetic one-dimensional relaxation model can be approximated by a multi-fluid domain decomposition technique that incorporates classical drift–diffusion equations with corrections in the current. In addition, when considering physical dimensions corresponding to GaAs devices, the technique requires new hydrodynamics that we propose and compute. Our comparison involves detailed computations of local distribution function solution of the kinetic equation, its first three moments compared with the computed fluid variables, and the presentation of all corresponding current–voltage characteristic curves.