Quantum high-field corrections to a drift-collision balance model of semiconductor transport

ABSTRACT. We derive a fluid-dynamical model describing electron transport in quantum, high-field regime. In the high-field regime, quantum advection and collisions are comparable and dominant. In this article, high-field regime is modeled starting from Wigner-BGK (Bhatnager-Gross-Krook) equation scaled with an asymptotic parameter epsilon. By applying Chapman-Enskog procedure and then moment methods, we obtain a system of equations with unknown electron position density, fluid velocity, and energy density. Diffusive and quantum terms appear as first order corrections in epsilon. Keywords: Quantum hydrodynamic models, Wigner transport equation, Chapman-Enskog expansion, High-field asymptotics.